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cosmopolitan/third_party/mbedtls/test/data/dir-maxpath/18.key
-----BEGIN EC PARAMETERS----- BggqhkjOPQMBBw== -----END EC PARAMETERS----- -----BEGIN EC PRIVATE KEY----- MHcCAQEEIJETLWqIZtnejCGzESDgMnknxqEx5evMGZfzBVPKMwKKoAoGCCqGSM49 AwEHoUQDQgAErHPyZDXGH2zIKTn6y+ZCjhsTiWhkukkCHjTt91HgaU6HtW1NmnDe udsY73BqNHyRLcYNn3Dx0YU5xjAQ9btTdg== -----END EC PRIVATE KEY-----
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cosmopolitan/third_party/mbedtls/test/data/dir-maxpath/09.crt
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cosmopolitan/third_party/mbedtls/test/data/dir-maxpath/c13.pem
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169
jart/cosmopolitan
false
cosmopolitan/third_party/mbedtls/test/data/dir-maxpath/01.crt
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709
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jart/cosmopolitan
false
cosmopolitan/third_party/mbedtls/test/data/dir-maxpath/07.key
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jart/cosmopolitan
false
cosmopolitan/third_party/mbedtls/test/data/dir-maxpath/18.crt
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700
13
jart/cosmopolitan
false
cosmopolitan/third_party/mbedtls/test/data/dir-maxpath/17.key
-----BEGIN EC PARAMETERS----- BggqhkjOPQMBBw== -----END EC PARAMETERS----- -----BEGIN EC PRIVATE KEY----- MHcCAQEEIAiUS1dM3qrcOun8PjKe+rw40L2HG/Y8Dfxl0AfzyIVeoAoGCCqGSM49 AwEHoUQDQgAEayEqtszvZg9vWAixweehXVP0SDbUYX3i7TPruaNx2gJ6KctEvfEc 7hBhC46c6/GSOpJDDGbI/JxWUBfB37hNIA== -----END EC PRIVATE KEY-----
302
9
jart/cosmopolitan
false
cosmopolitan/third_party/mbedtls/test/data/dir-maxpath/c00.pem
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12
jart/cosmopolitan
false
cosmopolitan/third_party/mbedtls/test/data/dir-maxpath/16.crt
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700
13
jart/cosmopolitan
false
cosmopolitan/third_party/mbedtls/test/data/dir-maxpath/c01.pem
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1,340
25
jart/cosmopolitan
false
cosmopolitan/third_party/mbedtls/test/data/dir-maxpath/c11.pem
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-----BEGIN CERTIFICATE----- MIIBpTCCAUugAwIBAgIJAPygloXKk6BwMAoGCCqGSM49BAMCMC8xCzAJBgNVBAYT AlVLMREwDwYDVQQKDAhtYmVkIFRMUzENMAsGA1UEAwwEQ0EwMDAeFw0xNzA2MjIx MTUwMzJaFw0yNzA2MjMxMTUwMzJaMC8xCzAJBgNVBAYTAlVLMREwDwYDVQQKDAht YmVkIFRMUzENMAsGA1UEAwwEQ0EwMDBZMBMGByqGSM49AgEGCCqGSM49AwEHA0IA BFW41/qAwAPpy+Txdc7PKmzZsq9CPiujKU4vpF1ekXnGx2HP420QobwBVVWhkzRm LwdboH2j65dcCKjQ7mv/dxKjUDBOMB0GA1UdDgQWBBQlFYvU5WboI4fcdPoiQs8/ fPHZrTAfBgNVHSMEGDAWgBQlFYvU5WboI4fcdPoiQs8/fPHZrTAMBgNVHRMEBTAD AQH/MAoGCCqGSM49BAMCA0gAMEUCIQC7iRcVzwMyfVK5imirJ7MqJQ04euH4CLOt IZ+SNfaERAIgSU0MWFDosVEIpg8YMqIHeF7Mg4ZyH6+fGazJgVLttUY= -----END CERTIFICATE-----
8,324
145
jart/cosmopolitan
false
cosmopolitan/third_party/mbedtls/test/data/dir-maxpath/17.crt
-----BEGIN CERTIFICATE----- MIIB1zCCAX2gAwIBAgIBATAKBggqhkjOPQQDAjAvMQswCQYDVQQGEwJVSzERMA8G A1UECgwIbWJlZCBUTFMxDTALBgNVBAMMBENBMTYwHhcNMTcwNjIyMTE1MDMzWhcN MjcwNjIzMTE1MDMzWjAvMQswCQYDVQQGEwJVSzERMA8GA1UECgwIbWJlZCBUTFMx DTALBgNVBAMMBENBMTcwWTATBgcqhkjOPQIBBggqhkjOPQMBBwNCAARrISq2zO9m D29YCLHB56FdU/RINtRhfeLtM+u5o3HaAnopy0S98RzuEGELjpzr8ZI6kkMMZsj8 nFZQF8HfuE0go4GJMIGGMB0GA1UdDgQWBBSnjWvpWxZcFnfQ2KGtCg/u6fT/DzBX BgNVHSMEUDBOgBRTw3K0Psy3u/6+3KKSoaQqJnPvPqEzpDEwLzELMAkGA1UEBhMC VUsxETAPBgNVBAoMCG1iZWQgVExTMQ0wCwYDVQQDDARDQTE1ggEBMAwGA1UdEwQF MAMBAf8wCgYIKoZIzj0EAwIDSAAwRQIgDgXjoc6FfMF5W0NziV6vx2BOPNWav01Z ynEP4h9ULnUCIQC1rU4sEId3UdjzTKhpSGTKtaOuPG+b0YdEMPimI4jmVw== -----END CERTIFICATE-----
700
13
jart/cosmopolitan
false
cosmopolitan/third_party/mbedtls/test/data/dir-maxpath/07.crt
-----BEGIN CERTIFICATE----- MIIB2DCCAX2gAwIBAgIBATAKBggqhkjOPQQDAjAvMQswCQYDVQQGEwJVSzERMA8G A1UECgwIbWJlZCBUTFMxDTALBgNVBAMMBENBMDYwHhcNMTcwNjIyMTE1MDMyWhcN MjcwNjIzMTE1MDMyWjAvMQswCQYDVQQGEwJVSzERMA8GA1UECgwIbWJlZCBUTFMx DTALBgNVBAMMBENBMDcwWTATBgcqhkjOPQIBBggqhkjOPQMBBwNCAASNOj4d4MEA 7p/3miijqG4ToE4opKPAm+3BTIGrJTYT14++TSiUICl0ASXj+xeUcLMIaXTN042s LsHxpShzQaL0o4GJMIGGMB0GA1UdDgQWBBREq5J3toJPxZ3O+ssJ5vkkU0RJEzBX BgNVHSMEUDBOgBSjovYaC/m6Li9Tp0V9iZRs9267Q6EzpDEwLzELMAkGA1UEBhMC VUsxETAPBgNVBAoMCG1iZWQgVExTMQ0wCwYDVQQDDARDQTA1ggEBMAwGA1UdEwQF MAMBAf8wCgYIKoZIzj0EAwIDSQAwRgIhAKGcf+c442c/XiwubbaiQvsoZ7EoVxuM oKmia0gPyBNkAiEA83asjJ5FDXQuLyZpczviXrbmqgCPOfYadtvkc0cxMis= -----END CERTIFICATE-----
700
13
jart/cosmopolitan
false
cosmopolitan/third_party/mbedtls/test/data/dir-maxpath/16.key
-----BEGIN EC PARAMETERS----- BggqhkjOPQMBBw== -----END EC PARAMETERS----- -----BEGIN EC PRIVATE KEY----- MHcCAQEEIM0YCnGkEG/TjBxrytP9Ztslm1yoQaWptBxegRzzBRDVoAoGCCqGSM49 AwEHoUQDQgAEO1bKeyZgzZID4f/s5iD5He6NMaLf1jzBZ97gLBrbFN/OTBdH5oXx S4UW2x/YeCY2B4/MtLKVN27lF4X7bwGVWw== -----END EC PRIVATE KEY-----
302
9
jart/cosmopolitan
false
cosmopolitan/third_party/mbedtls/test/data/dir-maxpath/02.key
-----BEGIN EC PARAMETERS----- BggqhkjOPQMBBw== -----END EC PARAMETERS----- -----BEGIN EC PRIVATE KEY----- MHcCAQEEIPW9zE8cjiZ8w17jTAebb4xAmEg6heEEnEaG4lGCd38joAoGCCqGSM49 AwEHoUQDQgAEFh6b9YupX8LzTzj+ZGuktJ+eRL86GmCuqW01z+sjDlv+F2UjyseW aKuBTHtHCsxiCBS9a849VdnM2Afqry4cog== -----END EC PRIVATE KEY-----
302
9
jart/cosmopolitan
false
cosmopolitan/third_party/mbedtls/test/data/dir-maxpath/c04.pem
-----BEGIN CERTIFICATE----- MIIB1jCCAX2gAwIBAgIBATAKBggqhkjOPQQDAjAvMQswCQYDVQQGEwJVSzERMA8G A1UECgwIbWJlZCBUTFMxDTALBgNVBAMMBENBMDMwHhcNMTcwNjIyMTE1MDMyWhcN MjcwNjIzMTE1MDMyWjAvMQswCQYDVQQGEwJVSzERMA8GA1UECgwIbWJlZCBUTFMx DTALBgNVBAMMBENBMDQwWTATBgcqhkjOPQIBBggqhkjOPQMBBwNCAAQUXDgcUVNT 9hovbZE5HL6rjOb7C55wEuWKThV/CcZ4rWrXx7VXHYdD/R3aDA7JSvYpm2sTok4i sblDzhZM/GDNo4GJMIGGMB0GA1UdDgQWBBQox4F1NsZunlsduoGvzIgRSYfB3zBX BgNVHSMEUDBOgBQApzZdtBdD3dLxouQpr/aDiVttd6EzpDEwLzELMAkGA1UEBhMC VUsxETAPBgNVBAoMCG1iZWQgVExTMQ0wCwYDVQQDDARDQTAyggEBMAwGA1UdEwQF MAMBAf8wCgYIKoZIzj0EAwIDRwAwRAIgAkiNhqFAZXSUWEDK91OZvQGdeZOtd6mC +Wv3fGk3t28CIEKOwidkUTUaiPdZ4efmAr+CEeGzdq27ob2S+nqqHqgV -----END CERTIFICATE----- -----BEGIN CERTIFICATE----- MIIB2DCCAX2gAwIBAgIBATAKBggqhkjOPQQDAjAvMQswCQYDVQQGEwJVSzERMA8G A1UECgwIbWJlZCBUTFMxDTALBgNVBAMMBENBMDIwHhcNMTcwNjIyMTE1MDMyWhcN MjcwNjIzMTE1MDMyWjAvMQswCQYDVQQGEwJVSzERMA8GA1UECgwIbWJlZCBUTFMx DTALBgNVBAMMBENBMDMwWTATBgcqhkjOPQIBBggqhkjOPQMBBwNCAAQRDXDNIi1p ereudhqwa2LslXgsxnB63Hu5y5lg+1WPruIYPzD/Ho0APveVdzFLVji19+bE4+tF PYL1SpsN1WfWo4GJMIGGMB0GA1UdDgQWBBQApzZdtBdD3dLxouQpr/aDiVttdzBX BgNVHSMEUDBOgBT5RCgQ0AlZTQbfFB2+6+w0XRvydaEzpDEwLzELMAkGA1UEBhMC VUsxETAPBgNVBAoMCG1iZWQgVExTMQ0wCwYDVQQDDARDQTAxggEBMAwGA1UdEwQF MAMBAf8wCgYIKoZIzj0EAwIDSQAwRgIhAOnd+7bAofkHVa4KFNjv3TCegw1lrhuM 8Of8wgvrTEGoAiEAsS8iKMpSfXH4D0egg4gLamE6akde965rDtySU+ve9lg= -----END CERTIFICATE----- -----BEGIN CERTIFICATE----- MIIB1zCCAX2gAwIBAgIBATAKBggqhkjOPQQDAjAvMQswCQYDVQQGEwJVSzERMA8G A1UECgwIbWJlZCBUTFMxDTALBgNVBAMMBENBMDEwHhcNMTcwNjIyMTE1MDMyWhcN MjcwNjIzMTE1MDMyWjAvMQswCQYDVQQGEwJVSzERMA8GA1UECgwIbWJlZCBUTFMx DTALBgNVBAMMBENBMDIwWTATBgcqhkjOPQIBBggqhkjOPQMBBwNCAAQWHpv1i6lf wvNPOP5ka6S0n55EvzoaYK6pbTXP6yMOW/4XZSPKx5Zoq4FMe0cKzGIIFL1rzj1V 2czYB+qvLhyio4GJMIGGMB0GA1UdDgQWBBT5RCgQ0AlZTQbfFB2+6+w0XRvydTBX BgNVHSMEUDBOgBSh3uHkX5nj86yFEFwjscSWM40P+qEzpDEwLzELMAkGA1UEBhMC VUsxETAPBgNVBAoMCG1iZWQgVExTMQ0wCwYDVQQDDARDQTAwggEBMAwGA1UdEwQF MAMBAf8wCgYIKoZIzj0EAwIDSAAwRQIhAI7unGW/gr9tOc3i+dF5N815srgh+FrX oj9Et74EcSpTAiBubv+vOH0DE0gmYI11HeAIgutWqqMIC72dZlwTF/Vi3g== -----END CERTIFICATE----- -----BEGIN CERTIFICATE----- MIIB3jCCAYWgAwIBAgIBATAKBggqhkjOPQQDAjAvMQswCQYDVQQGEwJVSzERMA8G A1UECgwIbWJlZCBUTFMxDTALBgNVBAMMBENBMDAwHhcNMTcwNjIyMTE1MDMyWhcN MjcwNjIzMTE1MDMyWjAvMQswCQYDVQQGEwJVSzERMA8GA1UECgwIbWJlZCBUTFMx DTALBgNVBAMMBENBMDEwWTATBgcqhkjOPQIBBggqhkjOPQMBBwNCAAQznn9zHHwL GO8VR4W9V7vMlxCdoojzEOiX5Y6JtPtFOz866ueHY6zoN0/mJ6DnqnSXilJIUUeW 6eGfqmka7nxko4GRMIGOMB0GA1UdDgQWBBSh3uHkX5nj86yFEFwjscSWM40P+jBf BgNVHSMEWDBWgBQlFYvU5WboI4fcdPoiQs8/fPHZraEzpDEwLzELMAkGA1UEBhMC VUsxETAPBgNVBAoMCG1iZWQgVExTMQ0wCwYDVQQDDARDQTAwggkA/KCWhcqToHAw DAYDVR0TBAUwAwEB/zAKBggqhkjOPQQDAgNHADBEAiBasbuinP+pJTU4oDCVD8zQ 1rJBDSOKIEyWu84/D6Hj6wIgVMPUoO01bPhzllAa/gW8Xk/daey09SBgN3AT9pWU TDA= -----END CERTIFICATE----- -----BEGIN CERTIFICATE----- MIIBpTCCAUugAwIBAgIJAPygloXKk6BwMAoGCCqGSM49BAMCMC8xCzAJBgNVBAYT AlVLMREwDwYDVQQKDAhtYmVkIFRMUzENMAsGA1UEAwwEQ0EwMDAeFw0xNzA2MjIx MTUwMzJaFw0yNzA2MjMxMTUwMzJaMC8xCzAJBgNVBAYTAlVLMREwDwYDVQQKDAht YmVkIFRMUzENMAsGA1UEAwwEQ0EwMDBZMBMGByqGSM49AgEGCCqGSM49AwEHA0IA BFW41/qAwAPpy+Txdc7PKmzZsq9CPiujKU4vpF1ekXnGx2HP420QobwBVVWhkzRm LwdboH2j65dcCKjQ7mv/dxKjUDBOMB0GA1UdDgQWBBQlFYvU5WboI4fcdPoiQs8/ fPHZrTAfBgNVHSMEGDAWgBQlFYvU5WboI4fcdPoiQs8/fPHZrTAMBgNVHRMEBTAD AQH/MAoGCCqGSM49BAMCA0gAMEUCIQC7iRcVzwMyfVK5imirJ7MqJQ04euH4CLOt IZ+SNfaERAIgSU0MWFDosVEIpg8YMqIHeF7Mg4ZyH6+fGazJgVLttUY= -----END CERTIFICATE-----
3,436
61
jart/cosmopolitan
false
cosmopolitan/third_party/mbedtls/test/data/dir-maxpath/10.key
-----BEGIN EC PARAMETERS----- BggqhkjOPQMBBw== -----END EC PARAMETERS----- -----BEGIN EC PRIVATE KEY----- MHcCAQEEIPuPPMxo5e2doI7YfDp60qmEn4YwYs2sb5QlOpFQ3BIJoAoGCCqGSM49 AwEHoUQDQgAEeo5RimyXeYYg8Te/PYJDnMKchyPcEcAqwAwDsDpDHjwT0ZcBnZu5 sO2fxAJrtus0Zv4XMq7ODKpNi2mw4zyPVw== -----END EC PRIVATE KEY-----
302
9
jart/cosmopolitan
false
cosmopolitan/third_party/mbedtls/test/data/dir1/test-ca.crt
Certificate: Data: Version: 3 (0x2) Serial Number: 0 (0x0) Signature Algorithm: sha1WithRSAEncryption Issuer: C=NL, O=PolarSSL, CN=PolarSSL Test CA Validity Not Before: Feb 12 14:44:00 2011 GMT Not After : Feb 12 14:44:00 2021 GMT Subject: C=NL, O=PolarSSL, CN=PolarSSL Test CA Subject Public Key Info: Public Key Algorithm: rsaEncryption RSA Public Key: (2048 bit) Modulus (2048 bit): 00:c0:df:37:fc:17:bb:e0:96:9d:3f:86:de:96:32: 7d:44:a5:16:a0:cd:21:f1:99:d4:ec:ea:cb:7c:18: 58:08:94:a5:ec:9b:c5:8b:df:1a:1e:99:38:99:87: 1e:7b:c0:8d:39:df:38:5d:70:78:07:d3:9e:d9:93: e8:b9:72:51:c5:ce:a3:30:52:a9:f2:e7:40:70:14: cb:44:a2:72:0b:c2:e5:40:f9:3e:e5:a6:0e:b3:f9: ec:4a:63:c0:b8:29:00:74:9c:57:3b:a8:a5:04:90: 71:f1:bd:83:d9:3f:d6:a5:e2:3c:2a:8f:ef:27:60: c3:c6:9f:cb:ba:ec:60:7d:b7:e6:84:32:be:4f:fb: 58:26:22:03:5b:d4:b4:d5:fb:f5:e3:96:2e:70:c0: e4:2e:bd:fc:2e:ee:e2:41:55:c0:34:2e:7d:24:72: 69:cb:47:b1:14:40:83:7d:67:f4:86:f6:31:ab:f1: 79:a4:b2:b5:2e:12:f9:84:17:f0:62:6f:27:3e:13: 58:b1:54:0d:21:9a:73:37:a1:30:cf:6f:92:dc:f6: e9:fc:ac:db:2e:28:d1:7e:02:4b:23:a0:15:f2:38: 65:64:09:ea:0c:6e:8e:1b:17:a0:71:c8:b3:9b:c9: ab:e9:c3:f2:cf:87:96:8f:80:02:32:9e:99:58:6f: a2:d5 Exponent: 65537 (0x10001) X509v3 extensions: X509v3 Basic Constraints: CA:TRUE X509v3 Subject Key Identifier: B4:5A:E4:A5:B3:DE:D2:52:F6:B9:D5:A6:95:0F:EB:3E:BC:C7:FD:FF X509v3 Authority Key Identifier: keyid:B4:5A:E4:A5:B3:DE:D2:52:F6:B9:D5:A6:95:0F:EB:3E:BC:C7:FD:FF DirName:/C=NL/O=PolarSSL/CN=PolarSSL Test CA serial:00 Signature Algorithm: sha1WithRSAEncryption b8:fd:54:d8:00:54:90:8b:25:b0:27:dd:95:cd:a2:f7:84:07: 1d:87:89:4a:c4:78:11:d8:07:b5:d7:22:50:8e:48:eb:62:7a: 32:89:be:63:47:53:ff:b6:be:f1:2e:8c:54:c0:99:3f:a0:b9: 37:23:72:5f:0d:46:59:8f:d8:47:cd:97:4c:9f:07:0c:12:62: 09:3a:24:e4:36:d9:e9:2c:da:38:d0:73:75:61:d7:c1:6c:26: 8b:9b:e0:d5:dc:67:ed:8c:6b:33:d7:74:22:3c:4c:db:b5:8d: 2a:ce:2c:0d:08:59:05:09:05:a6:39:9f:b3:67:1b:e2:83:e5: e1:8f:53:f6:67:93:c7:f9:6f:76:44:58:12:e8:3a:d4:97:e7: e9:c0:3e:a8:7a:72:3d:87:53:1f:e5:2c:84:84:e7:9a:9e:7f: 66:d9:1f:9b:f5:13:48:b0:4d:14:d1:de:b2:24:d9:78:7d:f5: 35:cc:58:19:d1:d2:99:ef:4d:73:f8:1f:89:d4:5a:d0:52:ce: 09:f5:b1:46:51:6a:00:8e:3b:cc:6f:63:01:00:99:ed:9d:a6: 08:60:cd:32:18:d0:73:e0:58:71:d9:e5:d2:53:d7:8d:d0:ca: e9:5d:2a:0a:0d:5d:55:ec:21:50:17:16:e6:06:4a:cd:5e:de: f7:e0:e9:54 -----BEGIN CERTIFICATE----- MIIDhzCCAm+gAwIBAgIBADANBgkqhkiG9w0BAQUFADA7MQswCQYDVQQGEwJOTDER MA8GA1UEChMIUG9sYXJTU0wxGTAXBgNVBAMTEFBvbGFyU1NMIFRlc3QgQ0EwHhcN MTEwMjEyMTQ0NDAwWhcNMjEwMjEyMTQ0NDAwWjA7MQswCQYDVQQGEwJOTDERMA8G A1UEChMIUG9sYXJTU0wxGTAXBgNVBAMTEFBvbGFyU1NMIFRlc3QgQ0EwggEiMA0G CSqGSIb3DQEBAQUAA4IBDwAwggEKAoIBAQDA3zf8F7vglp0/ht6WMn1EpRagzSHx mdTs6st8GFgIlKXsm8WL3xoemTiZhx57wI053zhdcHgH057Zk+i5clHFzqMwUqny 50BwFMtEonILwuVA+T7lpg6z+exKY8C4KQB0nFc7qKUEkHHxvYPZP9al4jwqj+8n YMPGn8u67GB9t+aEMr5P+1gmIgNb1LTV+/Xjli5wwOQuvfwu7uJBVcA0Ln0kcmnL R7EUQIN9Z/SG9jGr8XmksrUuEvmEF/Bibyc+E1ixVA0hmnM3oTDPb5Lc9un8rNsu KNF+AksjoBXyOGVkCeoMbo4bF6BxyLObyavpw/LPh5aPgAIynplYb6LVAgMBAAGj gZUwgZIwDAYDVR0TBAUwAwEB/zAdBgNVHQ4EFgQUtFrkpbPe0lL2udWmlQ/rPrzH /f8wYwYDVR0jBFwwWoAUtFrkpbPe0lL2udWmlQ/rPrzH/f+hP6Q9MDsxCzAJBgNV BAYTAk5MMREwDwYDVQQKEwhQb2xhclNTTDEZMBcGA1UEAxMQUG9sYXJTU0wgVGVz dCBDQYIBADANBgkqhkiG9w0BAQUFAAOCAQEAuP1U2ABUkIslsCfdlc2i94QHHYeJ SsR4EdgHtdciUI5I62J6Mom+Y0dT/7a+8S6MVMCZP6C5NyNyXw1GWY/YR82XTJ8H DBJiCTok5DbZ6SzaONBzdWHXwWwmi5vg1dxn7YxrM9d0IjxM27WNKs4sDQhZBQkF pjmfs2cb4oPl4Y9T9meTx/lvdkRYEug61Jfn6cA+qHpyPYdTH+UshITnmp5/Ztkf m/UTSLBNFNHesiTZeH31NcxYGdHSme9Nc/gfidRa0FLOCfWxRlFqAI47zG9jAQCZ 7Z2mCGDNMhjQc+BYcdnl0lPXjdDK6V0qCg1dVewhUBcW5gZKzV7e9+DpVA== -----END CERTIFICATE-----
4,357
81
jart/cosmopolitan
false
cosmopolitan/third_party/mbedtls/test/data/dir2/test-ca.crt
Certificate: Data: Version: 3 (0x2) Serial Number: 0 (0x0) Signature Algorithm: sha1WithRSAEncryption Issuer: C=NL, O=PolarSSL, CN=PolarSSL Test CA Validity Not Before: Feb 12 14:44:00 2011 GMT Not After : Feb 12 14:44:00 2021 GMT Subject: C=NL, O=PolarSSL, CN=PolarSSL Test CA Subject Public Key Info: Public Key Algorithm: rsaEncryption RSA Public Key: (2048 bit) Modulus (2048 bit): 00:c0:df:37:fc:17:bb:e0:96:9d:3f:86:de:96:32: 7d:44:a5:16:a0:cd:21:f1:99:d4:ec:ea:cb:7c:18: 58:08:94:a5:ec:9b:c5:8b:df:1a:1e:99:38:99:87: 1e:7b:c0:8d:39:df:38:5d:70:78:07:d3:9e:d9:93: e8:b9:72:51:c5:ce:a3:30:52:a9:f2:e7:40:70:14: cb:44:a2:72:0b:c2:e5:40:f9:3e:e5:a6:0e:b3:f9: ec:4a:63:c0:b8:29:00:74:9c:57:3b:a8:a5:04:90: 71:f1:bd:83:d9:3f:d6:a5:e2:3c:2a:8f:ef:27:60: c3:c6:9f:cb:ba:ec:60:7d:b7:e6:84:32:be:4f:fb: 58:26:22:03:5b:d4:b4:d5:fb:f5:e3:96:2e:70:c0: e4:2e:bd:fc:2e:ee:e2:41:55:c0:34:2e:7d:24:72: 69:cb:47:b1:14:40:83:7d:67:f4:86:f6:31:ab:f1: 79:a4:b2:b5:2e:12:f9:84:17:f0:62:6f:27:3e:13: 58:b1:54:0d:21:9a:73:37:a1:30:cf:6f:92:dc:f6: e9:fc:ac:db:2e:28:d1:7e:02:4b:23:a0:15:f2:38: 65:64:09:ea:0c:6e:8e:1b:17:a0:71:c8:b3:9b:c9: ab:e9:c3:f2:cf:87:96:8f:80:02:32:9e:99:58:6f: a2:d5 Exponent: 65537 (0x10001) X509v3 extensions: X509v3 Basic Constraints: CA:TRUE X509v3 Subject Key Identifier: B4:5A:E4:A5:B3:DE:D2:52:F6:B9:D5:A6:95:0F:EB:3E:BC:C7:FD:FF X509v3 Authority Key Identifier: keyid:B4:5A:E4:A5:B3:DE:D2:52:F6:B9:D5:A6:95:0F:EB:3E:BC:C7:FD:FF DirName:/C=NL/O=PolarSSL/CN=PolarSSL Test CA serial:00 Signature Algorithm: sha1WithRSAEncryption b8:fd:54:d8:00:54:90:8b:25:b0:27:dd:95:cd:a2:f7:84:07: 1d:87:89:4a:c4:78:11:d8:07:b5:d7:22:50:8e:48:eb:62:7a: 32:89:be:63:47:53:ff:b6:be:f1:2e:8c:54:c0:99:3f:a0:b9: 37:23:72:5f:0d:46:59:8f:d8:47:cd:97:4c:9f:07:0c:12:62: 09:3a:24:e4:36:d9:e9:2c:da:38:d0:73:75:61:d7:c1:6c:26: 8b:9b:e0:d5:dc:67:ed:8c:6b:33:d7:74:22:3c:4c:db:b5:8d: 2a:ce:2c:0d:08:59:05:09:05:a6:39:9f:b3:67:1b:e2:83:e5: e1:8f:53:f6:67:93:c7:f9:6f:76:44:58:12:e8:3a:d4:97:e7: e9:c0:3e:a8:7a:72:3d:87:53:1f:e5:2c:84:84:e7:9a:9e:7f: 66:d9:1f:9b:f5:13:48:b0:4d:14:d1:de:b2:24:d9:78:7d:f5: 35:cc:58:19:d1:d2:99:ef:4d:73:f8:1f:89:d4:5a:d0:52:ce: 09:f5:b1:46:51:6a:00:8e:3b:cc:6f:63:01:00:99:ed:9d:a6: 08:60:cd:32:18:d0:73:e0:58:71:d9:e5:d2:53:d7:8d:d0:ca: e9:5d:2a:0a:0d:5d:55:ec:21:50:17:16:e6:06:4a:cd:5e:de: f7:e0:e9:54 -----BEGIN CERTIFICATE----- MIIDhzCCAm+gAwIBAgIBADANBgkqhkiG9w0BAQUFADA7MQswCQYDVQQGEwJOTDER MA8GA1UEChMIUG9sYXJTU0wxGTAXBgNVBAMTEFBvbGFyU1NMIFRlc3QgQ0EwHhcN MTEwMjEyMTQ0NDAwWhcNMjEwMjEyMTQ0NDAwWjA7MQswCQYDVQQGEwJOTDERMA8G A1UEChMIUG9sYXJTU0wxGTAXBgNVBAMTEFBvbGFyU1NMIFRlc3QgQ0EwggEiMA0G CSqGSIb3DQEBAQUAA4IBDwAwggEKAoIBAQDA3zf8F7vglp0/ht6WMn1EpRagzSHx mdTs6st8GFgIlKXsm8WL3xoemTiZhx57wI053zhdcHgH057Zk+i5clHFzqMwUqny 50BwFMtEonILwuVA+T7lpg6z+exKY8C4KQB0nFc7qKUEkHHxvYPZP9al4jwqj+8n YMPGn8u67GB9t+aEMr5P+1gmIgNb1LTV+/Xjli5wwOQuvfwu7uJBVcA0Ln0kcmnL R7EUQIN9Z/SG9jGr8XmksrUuEvmEF/Bibyc+E1ixVA0hmnM3oTDPb5Lc9un8rNsu KNF+AksjoBXyOGVkCeoMbo4bF6BxyLObyavpw/LPh5aPgAIynplYb6LVAgMBAAGj gZUwgZIwDAYDVR0TBAUwAwEB/zAdBgNVHQ4EFgQUtFrkpbPe0lL2udWmlQ/rPrzH /f8wYwYDVR0jBFwwWoAUtFrkpbPe0lL2udWmlQ/rPrzH/f+hP6Q9MDsxCzAJBgNV BAYTAk5MMREwDwYDVQQKEwhQb2xhclNTTDEZMBcGA1UEAxMQUG9sYXJTU0wgVGVz dCBDQYIBADANBgkqhkiG9w0BAQUFAAOCAQEAuP1U2ABUkIslsCfdlc2i94QHHYeJ SsR4EdgHtdciUI5I62J6Mom+Y0dT/7a+8S6MVMCZP6C5NyNyXw1GWY/YR82XTJ8H DBJiCTok5DbZ6SzaONBzdWHXwWwmi5vg1dxn7YxrM9d0IjxM27WNKs4sDQhZBQkF pjmfs2cb4oPl4Y9T9meTx/lvdkRYEug61Jfn6cA+qHpyPYdTH+UshITnmp5/Ztkf m/UTSLBNFNHesiTZeH31NcxYGdHSme9Nc/gfidRa0FLOCfWxRlFqAI47zG9jAQCZ 7Z2mCGDNMhjQc+BYcdnl0lPXjdDK6V0qCg1dVewhUBcW5gZKzV7e9+DpVA== -----END CERTIFICATE-----
4,357
81
jart/cosmopolitan
false
cosmopolitan/third_party/mbedtls/test/data/dir2/test-ca2.crt
-----BEGIN CERTIFICATE----- MIICUjCCAdegAwIBAgIJAMFD4n5iQ8zoMAoGCCqGSM49BAMCMD4xCzAJBgNVBAYT Ak5MMREwDwYDVQQKEwhQb2xhclNTTDEcMBoGA1UEAxMTUG9sYXJzc2wgVGVzdCBF QyBDQTAeFw0xMzA5MjQxNTQ5NDhaFw0yMzA5MjIxNTQ5NDhaMD4xCzAJBgNVBAYT Ak5MMREwDwYDVQQKEwhQb2xhclNTTDEcMBoGA1UEAxMTUG9sYXJzc2wgVGVzdCBF QyBDQTB2MBAGByqGSM49AgEGBSuBBAAiA2IABMPaKzRBN1gvh1b+/Im6KUNLTuBu ww5XUzM5WNRStJGVOQsj318XJGJI/BqVKc4sLYfCiFKAr9ZqqyHduNMcbli4yuiy aY7zQa0pw7RfdadHb9UZKVVpmlM7ILRmFmAzHqOBoDCBnTAdBgNVHQ4EFgQUnW0g JEkBPyvLeLUZvH4kydv7NnwwbgYDVR0jBGcwZYAUnW0gJEkBPyvLeLUZvH4kydv7 NnyhQqRAMD4xCzAJBgNVBAYTAk5MMREwDwYDVQQKEwhQb2xhclNTTDEcMBoGA1UE AxMTUG9sYXJzc2wgVGVzdCBFQyBDQYIJAMFD4n5iQ8zoMAwGA1UdEwQFMAMBAf8w CgYIKoZIzj0EAwIDaQAwZgIxAMO0YnNWKJUAfXgSJtJxexn4ipg+kv4znuR50v56 t4d0PCu412mUC6Nnd7izvtE2MgIxAP1nnJQjZ8BWukszFQDG48wxCCyci9qpdSMv uCjn8pwUOkABXK8Mss90fzCfCEOtIA== -----END CERTIFICATE-----
867
16
jart/cosmopolitan
false
cosmopolitan/third_party/mbedtls/test/data/dir3/test-ca.crt
Certificate: Data: Version: 3 (0x2) Serial Number: 0 (0x0) Signature Algorithm: sha1WithRSAEncryption Issuer: C=NL, O=PolarSSL, CN=PolarSSL Test CA Validity Not Before: Feb 12 14:44:00 2011 GMT Not After : Feb 12 14:44:00 2021 GMT Subject: C=NL, O=PolarSSL, CN=PolarSSL Test CA Subject Public Key Info: Public Key Algorithm: rsaEncryption RSA Public Key: (2048 bit) Modulus (2048 bit): 00:c0:df:37:fc:17:bb:e0:96:9d:3f:86:de:96:32: 7d:44:a5:16:a0:cd:21:f1:99:d4:ec:ea:cb:7c:18: 58:08:94:a5:ec:9b:c5:8b:df:1a:1e:99:38:99:87: 1e:7b:c0:8d:39:df:38:5d:70:78:07:d3:9e:d9:93: e8:b9:72:51:c5:ce:a3:30:52:a9:f2:e7:40:70:14: cb:44:a2:72:0b:c2:e5:40:f9:3e:e5:a6:0e:b3:f9: ec:4a:63:c0:b8:29:00:74:9c:57:3b:a8:a5:04:90: 71:f1:bd:83:d9:3f:d6:a5:e2:3c:2a:8f:ef:27:60: c3:c6:9f:cb:ba:ec:60:7d:b7:e6:84:32:be:4f:fb: 58:26:22:03:5b:d4:b4:d5:fb:f5:e3:96:2e:70:c0: e4:2e:bd:fc:2e:ee:e2:41:55:c0:34:2e:7d:24:72: 69:cb:47:b1:14:40:83:7d:67:f4:86:f6:31:ab:f1: 79:a4:b2:b5:2e:12:f9:84:17:f0:62:6f:27:3e:13: 58:b1:54:0d:21:9a:73:37:a1:30:cf:6f:92:dc:f6: e9:fc:ac:db:2e:28:d1:7e:02:4b:23:a0:15:f2:38: 65:64:09:ea:0c:6e:8e:1b:17:a0:71:c8:b3:9b:c9: ab:e9:c3:f2:cf:87:96:8f:80:02:32:9e:99:58:6f: a2:d5 Exponent: 65537 (0x10001) X509v3 extensions: X509v3 Basic Constraints: CA:TRUE X509v3 Subject Key Identifier: B4:5A:E4:A5:B3:DE:D2:52:F6:B9:D5:A6:95:0F:EB:3E:BC:C7:FD:FF X509v3 Authority Key Identifier: keyid:B4:5A:E4:A5:B3:DE:D2:52:F6:B9:D5:A6:95:0F:EB:3E:BC:C7:FD:FF DirName:/C=NL/O=PolarSSL/CN=PolarSSL Test CA serial:00 Signature Algorithm: sha1WithRSAEncryption b8:fd:54:d8:00:54:90:8b:25:b0:27:dd:95:cd:a2:f7:84:07: 1d:87:89:4a:c4:78:11:d8:07:b5:d7:22:50:8e:48:eb:62:7a: 32:89:be:63:47:53:ff:b6:be:f1:2e:8c:54:c0:99:3f:a0:b9: 37:23:72:5f:0d:46:59:8f:d8:47:cd:97:4c:9f:07:0c:12:62: 09:3a:24:e4:36:d9:e9:2c:da:38:d0:73:75:61:d7:c1:6c:26: 8b:9b:e0:d5:dc:67:ed:8c:6b:33:d7:74:22:3c:4c:db:b5:8d: 2a:ce:2c:0d:08:59:05:09:05:a6:39:9f:b3:67:1b:e2:83:e5: e1:8f:53:f6:67:93:c7:f9:6f:76:44:58:12:e8:3a:d4:97:e7: e9:c0:3e:a8:7a:72:3d:87:53:1f:e5:2c:84:84:e7:9a:9e:7f: 66:d9:1f:9b:f5:13:48:b0:4d:14:d1:de:b2:24:d9:78:7d:f5: 35:cc:58:19:d1:d2:99:ef:4d:73:f8:1f:89:d4:5a:d0:52:ce: 09:f5:b1:46:51:6a:00:8e:3b:cc:6f:63:01:00:99:ed:9d:a6: 08:60:cd:32:18:d0:73:e0:58:71:d9:e5:d2:53:d7:8d:d0:ca: e9:5d:2a:0a:0d:5d:55:ec:21:50:17:16:e6:06:4a:cd:5e:de: f7:e0:e9:54 -----BEGIN CERTIFICATE----- MIIDhzCCAm+gAwIBAgIBADANBgkqhkiG9w0BAQUFADA7MQswCQYDVQQGEwJOTDER MA8GA1UEChMIUG9sYXJTU0wxGTAXBgNVBAMTEFBvbGFyU1NMIFRlc3QgQ0EwHhcN MTEwMjEyMTQ0NDAwWhcNMjEwMjEyMTQ0NDAwWjA7MQswCQYDVQQGEwJOTDERMA8G A1UEChMIUG9sYXJTU0wxGTAXBgNVBAMTEFBvbGFyU1NMIFRlc3QgQ0EwggEiMA0G CSqGSIb3DQEBAQUAA4IBDwAwggEKAoIBAQDA3zf8F7vglp0/ht6WMn1EpRagzSHx mdTs6st8GFgIlKXsm8WL3xoemTiZhx57wI053zhdcHgH057Zk+i5clHFzqMwUqny 50BwFMtEonILwuVA+T7lpg6z+exKY8C4KQB0nFc7qKUEkHHxvYPZP9al4jwqj+8n YMPGn8u67GB9t+aEMr5P+1gmIgNb1LTV+/Xjli5wwOQuvfwu7uJBVcA0Ln0kcmnL R7EUQIN9Z/SG9jGr8XmksrUuEvmEF/Bibyc+E1ixVA0hmnM3oTDPb5Lc9un8rNsu KNF+AksjoBXyOGVkCeoMbo4bF6BxyLObyavpw/LPh5aPgAIynplYb6LVAgMBAAGj gZUwgZIwDAYDVR0TBAUwAwEB/zAdBgNVHQ4EFgQUtFrkpbPe0lL2udWmlQ/rPrzH /f8wYwYDVR0jBFwwWoAUtFrkpbPe0lL2udWmlQ/rPrzH/f+hP6Q9MDsxCzAJBgNV BAYTAk5MMREwDwYDVQQKEwhQb2xhclNTTDEZMBcGA1UEAxMQUG9sYXJTU0wgVGVz dCBDQYIBADANBgkqhkiG9w0BAQUFAAOCAQEAuP1U2ABUkIslsCfdlc2i94QHHYeJ SsR4EdgHtdciUI5I62J6Mom+Y0dT/7a+8S6MVMCZP6C5NyNyXw1GWY/YR82XTJ8H DBJiCTok5DbZ6SzaONBzdWHXwWwmi5vg1dxn7YxrM9d0IjxM27WNKs4sDQhZBQkF pjmfs2cb4oPl4Y9T9meTx/lvdkRYEug61Jfn6cA+qHpyPYdTH+UshITnmp5/Ztkf m/UTSLBNFNHesiTZeH31NcxYGdHSme9Nc/gfidRa0FLOCfWxRlFqAI47zG9jAQCZ 7Z2mCGDNMhjQc+BYcdnl0lPXjdDK6V0qCg1dVewhUBcW5gZKzV7e9+DpVA== -----END CERTIFICATE-----
4,357
81
jart/cosmopolitan
false
cosmopolitan/third_party/mbedtls/test/data/dir3/Readme
This is just to make sure files that don't parse as certs are ignored.
71
2
jart/cosmopolitan
false
cosmopolitan/third_party/mbedtls/test/data/dir3/test-ca2.crt
-----BEGIN CERTIFICATE----- MIICUjCCAdegAwIBAgIJAMFD4n5iQ8zoMAoGCCqGSM49BAMCMD4xCzAJBgNVBAYT Ak5MMREwDwYDVQQKEwhQb2xhclNTTDEcMBoGA1UEAxMTUG9sYXJzc2wgVGVzdCBF QyBDQTAeFw0xMzA5MjQxNTQ5NDhaFw0yMzA5MjIxNTQ5NDhaMD4xCzAJBgNVBAYT Ak5MMREwDwYDVQQKEwhQb2xhclNTTDEcMBoGA1UEAxMTUG9sYXJzc2wgVGVzdCBF QyBDQTB2MBAGByqGSM49AgEGBSuBBAAiA2IABMPaKzRBN1gvh1b+/Im6KUNLTuBu ww5XUzM5WNRStJGVOQsj318XJGJI/BqVKc4sLYfCiFKAr9ZqqyHduNMcbli4yuiy aY7zQa0pw7RfdadHb9UZKVVpmlM7ILRmFmAzHqOBoDCBnTAdBgNVHQ4EFgQUnW0g JEkBPyvLeLUZvH4kydv7NnwwbgYDVR0jBGcwZYAUnW0gJEkBPyvLeLUZvH4kydv7 NnyhQqRAMD4xCzAJBgNVBAYTAk5MMREwDwYDVQQKEwhQb2xhclNTTDEcMBoGA1UE AxMTUG9sYXJzc2wgVGVzdCBFQyBDQYIJAMFD4n5iQ8zoMAwGA1UdEwQFMAMBAf8w CgYIKoZIzj0EAwIDaQAwZgIxAMO0YnNWKJUAfXgSJtJxexn4ipg+kv4znuR50v56 t4d0PCu412mUC6Nnd7izvtE2MgIxAP1nnJQjZ8BWukszFQDG48wxCCyci9qpdSMv uCjn8pwUOkABXK8Mss90fzCfCEOtIA== -----END CERTIFICATE-----
867
16
jart/cosmopolitan
false
cosmopolitan/third_party/mbedtls/test/data/base64/cli_cid.txt
// Client, CID 0xBEEF 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
1,623
3
jart/cosmopolitan
false
cosmopolitan/third_party/mbedtls/test/data/base64/def_b64_ff.bin
// Ensure that the b64 parser continues after encountering a 0xFF // character. Note that this byte is invalid UTF-8, making this // entire file invalid UTF-8. Use care when editing. // -> ÿ <- AhUAAH8AAA4AAABtAAAAAF6HQx3MqAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAACG2QbHbUj8eGpdx5KVIebiwk0jvRj9/3m6BOSzpA7qBXeEunhqr3D11NE7ciGjeHMAAACAAAAAAAAAAAAAAAAAAV6HQx248L77RH0Z973tSYNQ8zBsz861CZG5/T09TJz3XodDHe/iJ+cgXb5An3zTdnTBtw3EWAb68T+gCE33GN8AAAAAAAAAAAAAAAEAAAAAAAAAAwAAAQAAAAAAAgAAAA==
489
6
jart/cosmopolitan
false
cosmopolitan/third_party/mbedtls/test/data/base64/srv_min_cfg.txt
// Minimal configuration AhUAAAMAAAAAAABjAAAAAF6LZlLMqAAgUGktPmpSPbzRPipeCpYJtp5SNIIjTr3R121WF9AeWN4tmKbRhhv+yPMjY0yWPrHLy7lLLhwNFBwCD6eQ0ULZZ15Fi2Rhae/4ZkAR0BN2iCMAAACAAAAAXotmUkMC6aU6s7O5InjmEEeg4ySLZkNDf0Ut/s06/cBei2ZS+kkKS3sJso2u418jlrlKiesyUOW+xXwOD8bYZQAAAQAAAAAAAgAA
274
3
jart/cosmopolitan
false
cosmopolitan/third_party/mbedtls/test/data/base64/def_b64_too_big_2.txt
// Context with added '1234' in the middle of code to simulate too much data 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
1,674
3
jart/cosmopolitan
false
cosmopolitan/third_party/mbedtls/test/data/base64/srv_no_keep_cert.txt
// Without MBEDTLS_SSL_KEEP_PEER_CERTIFICATE AhUAAAMAAAAAAABiAAAAAF6MKhTMqAAgSKCqXrcrmjqOBpxsGO3itQB09YgsSJwXmZB12QlB+wwhiof0mzAN0hupkLxu4Yyc9SgyFoEDPKJk8TiRo8bO2rkEfPItB5lUFkJwzdeuGVMAAACAAABejCoUbOvW/qbIhlAKPDit31OByjhzXYt+rZNtvknHLV6MKhRMr8xnL27SNFX1iypTpQ7/ksAtPGXQjWvkQWfwAAABAAAAAAACAAA=
294
3
jart/cosmopolitan
false
cosmopolitan/third_party/mbedtls/test/data/base64/cli_no_packing.txt
// Without DTLS packing AhUAAH8AAA4AAAQ8AAAAAF6LCM/MqAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAACfl0tXNmshIQEqiEflQGnVUKkIFl1on/Mu0pjWes3XwQgdwmy9xMzpVyYU5gBOsOEAAAAAAAM7MIIDNzCCAh+gAwIBAgIBAjANBgkqhkiG9w0BAQsFADA7MQswCQYDVQQGEwJOTDERMA8GA1UECgwIUG9sYXJTU0wxGTAXBgNVBAMMEFBvbGFyU1NMIFRlc3QgQ0EwHhcNMTkwMjEwMTQ0NDA2WhcNMjkwMjEwMTQ0NDA2WjA0MQswCQYDVQQGEwJOTDERMA8GA1UECgwIUG9sYXJTU0wxEjAQBgNVBAMMCWxvY2FsaG9zdDCCASIwDQYJKoZIhvcNAQEBBQADggEPADCCAQoCggEBAMFNo93nzR3RBNdJcriZrA545Do8Ss86ExbQWuTNowCIp+4ea5anUrSQ7y1yej4kmvy2NKwk9XfgJmSMnLAofaHa6ozmyRyWvP7BBFKzNtSj+uGxdtiQwWG0ZlI2oiZTqqt0Xgd9GYLbKtgfoNkNHC1JZvdbJXNG6AuKT2kMtQCQ4dqCEGZ9rlQri2V5kaHiYcPNQEkI7mgM8YuG0ka/0LiqEQMef1aoGh5EGA8PhYvai0Re4hjGYi/HZo36Xdh98yeJKQHFkA4/J/EwyEoO79bex8cna8cFPXrEAjyaHT4P6DSYW8tzS1KW2BGiLICIaTla0w+w3lkvEcf36hIBMJcCAwEAAaNNMEswCQYDVR0TBAIwADAdBgNVHQ4EFgQUpQXoZLjc32APUBJNYKhkr02LQ5MwHwYDVR0jBBgwFoAUtFrkpbPe0lL2udWmlQ/rPrzH/f8wDQYJKoZIhvcNAQELBQADggEBAC465FJhPqel7zJngHIHJrqj/wVAxGAFOTF396XKATGAp+HRCqJ81Ry60CNK1jDzk8dv6M6UHoS7RIFiM/9rXQCbJfiPD5xMTejZp5n5UYHAmxsxDaazfA5FuBhkfokKK6jD4Eq91C94xGKb6X4/VkaPF7cqoBBw/bHxawXc0UEPjqayiBpCYU/rJoVZgLqFVP7Px3sva1nOrNx8rPPI1hJ+ZOg8maiPTxHZnBVLakSSLQy/sWeWyazO1RnrbxjrbgQtYKz0e3nwGpu1w13vfckFmUSBhHXH7AAS/HpKC4IH7G2GAk3+n8iSSN71sZzpxonQwVbopMZqLmbBm/7WPLcAAJRTvlE7NmNNLDESUBoGC+K2AHIKA+/lhdRVF4YcMvvqCBYFB5tj0oyCikftfjNbvjl9YPGqcRXk664YieWv/pz8U1FOENipbjXF9lFhgedG2Xanh/2FwHX5txYiHIJxJeLEKCXp5Sjt9XBvQsrryxLyX9l+zkLKm7bCAcrfk4h/YoqxecAI63isG9vnrS7o07iD/3mOAAFRgAAAAF6LCM+1uRpyaoyfzuNGBJK9DgBWIWtrPpu7KM8qsC/FXosIz/YIPhveZ8Z4IR0g/McAMQwzQoK5tScSE0DD3BwAAAAAAAAAAAAAAAEAAAAAAAAAAwEAAQAAAAAAAgAAAA==
1,617
3
jart/cosmopolitan
false
cosmopolitan/third_party/mbedtls/test/data/base64/v2.19.1.txt
// Context creaded by MbedTLS v.2.19.1 AhMBAH8AAA8AAAGjAAAAAF5iHYLArgAgkQE4V2NJsjbOuO52ws/u75f6Cg126zWeI7a+kaxTqKLbdWWZmW3PP+SflLxBA7Trpb0qZ5MP8+m0leylnLcDt2TtIWR49MOuiJuvVuMJmtwAAAAAAAE2MIIBMjCB2qADAgECAgYBcK9AtOYwCgYIKoZIzj0EAwIwDTELMAkGA1UEAwwCY2EwIBcNMjAwMzA2MDk1MDE4WhgPMjA1NjAyMjYwOTUwMThaMDMxDzANBgNVBAcTBjE2MDAwMTENMAsGA1UECxMEYWNjMTERMA8GA1UEAxMIZGV2aWNlMDEwWTATBgcqhkjOPQIBBggqhkjOPQMBBwNCAARn0TtinN6/runzIuF2f2uTH1f0mQOFXu3uRPtQji2ObccSsw6Cn9z7XWK9fRgeoOKA0WZC+O9L9IEWieS13ajFMAoGCCqGSM49BAMCA0cAMEQCIFoavpekQjIqubJ09jkMR+iiUpkGdFRla1R7onnc5iEOAiBAvYr8j9QqjpM2jColTS1cI0z29PBbuasq4HI6YCj0wgAAAAAAAAAAAAFeYh2Ct3LnESwmdWzU+xs7vV2Q0T5HJ8y4ckhpO7wOoF5iHYJ38gKFI3Qdc3BR48GV7nuBUKZeI1YJExQchj1WCAY6dEyghLpHAAAAAAAAAAAAAAAAAQAAAAAAAAADAAABAAAAAAACAAAA
756
3
jart/cosmopolitan
false
cosmopolitan/third_party/mbedtls/test/data/base64/def_b64_too_big_1.txt
// Context with added '1234' at the begining to simulate too much data in the base64 code 1234AhUAAH8AAA4AAAQ8AAAAAF6HQx3MqAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAACG2QbHbUj8eGpdx5KVIebiwk0jvRj9/3m6BOSzpA7qBXeEunhqr3D11NE7ciGjeHMAAAAAAAM7MIIDNzCCAh+gAwIBAgIBAjANBgkqhkiG9w0BAQsFADA7MQswCQYDVQQGEwJOTDERMA8GA1UECgwIUG9sYXJTU0wxGTAXBgNVBAMMEFBvbGFyU1NMIFRlc3QgQ0EwHhcNMTkwMjEwMTQ0NDA2WhcNMjkwMjEwMTQ0NDA2WjA0MQswCQYDVQQGEwJOTDERMA8GA1UECgwIUG9sYXJTU0wxEjAQBgNVBAMMCWxvY2FsaG9zdDCCASIwDQYJKoZIhvcNAQEBBQADggEPADCCAQoCggEBAMFNo93nzR3RBNdJcriZrA545Do8Ss86ExbQWuTNowCIp+4ea5anUrSQ7y1yej4kmvy2NKwk9XfgJmSMnLAofaHa6ozmyRyWvP7BBFKzNtSj+uGxdtiQwWG0ZlI2oiZTqqt0Xgd9GYLbKtgfoNkNHC1JZvdbJXNG6AuKT2kMtQCQ4dqCEGZ9rlQri2V5kaHiYcPNQEkI7mgM8YuG0ka/0LiqEQMef1aoGh5EGA8PhYvai0Re4hjGYi/HZo36Xdh98yeJKQHFkA4/J/EwyEoO79bex8cna8cFPXrEAjyaHT4P6DSYW8tzS1KW2BGiLICIaTla0w+w3lkvEcf36hIBMJcCAwEAAaNNMEswCQYDVR0TBAIwADAdBgNVHQ4EFgQUpQXoZLjc32APUBJNYKhkr02LQ5MwHwYDVR0jBBgwFoAUtFrkpbPe0lL2udWmlQ/rPrzH/f8wDQYJKoZIhvcNAQELBQADggEBAC465FJhPqel7zJngHIHJrqj/wVAxGAFOTF396XKATGAp+HRCqJ81Ry60CNK1jDzk8dv6M6UHoS7RIFiM/9rXQCbJfiPD5xMTejZp5n5UYHAmxsxDaazfA5FuBhkfokKK6jD4Eq91C94xGKb6X4/VkaPF7cqoBBw/bHxawXc0UEPjqayiBpCYU/rJoVZgLqFVP7Px3sva1nOrNx8rPPI1hJ+ZOg8maiPTxHZnBVLakSSLQy/sWeWyazO1RnrbxjrbgQtYKz0e3nwGpu1w13vfckFmUSBhHXH7AAS/HpKC4IH7G2GAk3+n8iSSN71sZzpxonQwVbopMZqLmbBm/7WPLcAAJTfQC2Ek91INP5ihHNzImPOAHJCk+YTO/pQuEnNWwXbdmKAi+IRp671iAwtpkjSxCBXVzKX925F1A66caCOQptlw+9zFukDQgblM2JyAJLG0j6B4RtBTDWJ8ZTMUPHUoLJoEpm8APZgRi//DMRyCKP9pbBLGlDzgUvl0w11LzBAlJHkWau5NoqQBlG7w4HFrKweovskAAFRgAAAAF6HQx248L77RH0Z973tSYNQ8zBsz861CZG5/T09TJz3XodDHe/iJ+cgXb5An3zTdnTBtw3EWAb68T+gCE33GN8AAAAAAAAAAAAAAAEAAAAAAAAAAwAAAQAAAAAAAgAAAA==
1,687
3
jart/cosmopolitan
false
cosmopolitan/third_party/mbedtls/test/data/base64/cli_no_keep_cert.txt
// Without MBEDTLS_SSL_KEEP_PEER_CERTIFICATE AhUAAAMAAAAAAACCAAAAAF6MKhTMqAAgSKCqXrcrmjqOBpxsGO3itQB09YgsSJwXmZB12QlB+wwhiof0mzAN0hupkLxu4Yyc9SgyFoEDPKJk8TiRo8bO2rkEfPItB5lUFkJwzdeuGVMAAAAABiCAy8MWqlj4vnIv0mswJvB35hyCOYWZ+fcZ6t5LzZgXPl6MKhRs69b+psiGUAo8OK3fU4HKOHNdi36tk22+ScctXowqFEyvzGcvbtI0VfWLKlOlDv+SwC08ZdCNa+RBZ/AAAAEAAAAAAAIAAA==
338
3
jart/cosmopolitan
false
cosmopolitan/third_party/mbedtls/test/data/base64/mtu_10000.txt
// MTU=10000 AhUAAH8AAA4AAABtAAAAAF6LDkzMqAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABx06kxYooMLGPyUMoB46EF2zTJzmZEM4le5aKihcHpFEfgrX/eWQZFWa7cak79ihwAAACAAAAAAAAAAAAAAAAAAV6LDkz9bigMk9q0WiDmgYhX8ppbfgbtMCfruvVQNiFWXosOTJ3R2+J+TaSChmjtS8sD+y1Zruhe/SJE7y9D+5YAAAAAAAAAAAAAAAEAAAAAAAAAAwAAAQAAAAAAAicQAA==
306
3
jart/cosmopolitan
false
cosmopolitan/third_party/mbedtls/test/data/base64/empty.txt
0
1
jart/cosmopolitan
false
cosmopolitan/third_party/mbedtls/test/data/base64/srv_def.txt
// Server context with default MbedTLS configuration AhUAAH8AAA4AAABtAAAAAF6HQx3MqAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAACG2QbHbUj8eGpdx5KVIebiwk0jvRj9/3m6BOSzpA7qBXeEunhqr3D11NE7ciGjeHMAAACAAAAAAAAAAAAAAAAAAV6HQx248L77RH0Z973tSYNQ8zBsz861CZG5/T09TJz3XodDHe/iJ+cgXb5An3zTdnTBtw3EWAb68T+gCE33GN8AAAAAAAAAAAAAAAEAAAAAAAAAAwAAAQAAAAAAAgAAAA==
346
3
jart/cosmopolitan
false
cosmopolitan/third_party/mbedtls/test/data/base64/srv_no_mfl.txt
// Without MBEDTLS_SSL_MAX_FRAGMENT_LENGTH AhUAAHcAAA4AAABsAAAAAF6LDLPMqAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA0fzGzO1ysljMgZr4gduigvRXr2AK5X8j8c6vHTOpc2ncFS3UN2ojwD2tOaM3+/XIAAACAAAAAAAAAAAAAAAABXosMs1xs+Mj8BIL6v01qtHWV7w+psxGwLctaGSSL0aZeiwyzskPeDCL0isOzh+JoPgzS/mVtMc0GykGpZaFBugAAAAAAAAAAAAAAAQAAAAAAAAADAAABAAAAAAACAAAA
332
3
jart/cosmopolitan
false
cosmopolitan/third_party/mbedtls/test/data/base64/mfl_1024.txt
// MFL=1024 AhUAAH8AAA4AAABtAAAAAF6K+GLMqAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAACHeeQKPVt9RpB8nLTB6C2AhxRzB0r/OBbXbMPm6jb1rkR+qrXZAUFRvGfGxlqqGWwAAACAAAAAAAAAAAAAAAIAAV6K+GJIXNnpKTr9HZQW6WEH7YSYhhRRqOO6xvf8QL6/Xor4YhOxOJYk23w3AwDvVAofeWnVAfJnExe5ipdSxnAAAAAAAAAAAAAAAAEAAAAAAAAAAwAAAQAAAAAAAgAAAA===
306
3
jart/cosmopolitan
false
cosmopolitan/third_party/mbedtls/test/data/base64/srv_no_packing.txt
// Without DTLS packing AhUAAH8AAA4AAABtAAAAAF6LCM/MqAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAACfl0tXNmshIQEqiEflQGnVUKkIFl1on/Mu0pjWes3XwQgdwmy9xMzpVyYU5gBOsOEAAACAAAAAAAAAAAAAAAAAAV6LCM+1uRpyaoyfzuNGBJK9DgBWIWtrPpu7KM8qsC/FXosIz/YIPhveZ8Z4IR0g/McAMQwzQoK5tScSE0DD3BwAAAAAAAAAAAAAAAEAAAAAAAAAAwEAAQAAAAAAAgAAAA==
317
3
jart/cosmopolitan
false
cosmopolitan/third_party/mbedtls/test/data/base64/cli_ciphersuite.txt
// TLS-RSA-WITH-AES-256-CCM-8 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
1,623
3
jart/cosmopolitan
false
cosmopolitan/third_party/mbedtls/test/data/base64/srv_cid.txt
// Server, CID 0xDEAD AhUAAH8AAA8AAABtAAAAAF6MZUPMqAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABh7h8/aprLN1fS0KwLkZzKcsa5LNtDW7sYu7d1z7fNetuRjLJpX/A1mTSqeBY7li8AAACAAAAAAAAAAAAAAAAAAV6MZUNak74BhbcgvZ2M8WhZKjQyCix7GJzRs4SqnD7iXoxlQ7YXjsVI0K/xyMOJPkT9ZcPEi/2jHGIte1ZduW4C3q0Cvu8AAAAAAAAAAAAAAAIAAAAAAAAABwAAAQAAAAAAAwAAAA==
323
3
jart/cosmopolitan
false
cosmopolitan/third_party/mbedtls/test/data/base64/cli_no_mfl.txt
// Without MBEDTLS_SSL_MAX_FRAGMENT_LENGTH 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
1,632
3
jart/cosmopolitan
false
cosmopolitan/third_party/mbedtls/test/data/base64/cli_def.txt
// Client context with default MbedTLS configuration 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
1,646
3
jart/cosmopolitan
false
cosmopolitan/third_party/mbedtls/test/data/base64/def_bad_b64.txt
// Context with added extra 'A' before '==' add the end to simulate bad length of base64 code 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
1,688
3
jart/cosmopolitan
false
cosmopolitan/third_party/mbedtls/test/data/base64/cli_no_alpn.txt
// Without MBEDTLS_SSL_ALPN 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
1,618
4
jart/cosmopolitan
false
cosmopolitan/third_party/mbedtls/test/data/base64/srv_no_alpn.txt
// Without MBEDTLS_SSL_ALPN AhUAAH8AAAYAAABtAAAAAF6LDSzMqAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAB1lCUO8B/805UzCOLZzWDAEA8anfLpbuWTrnFSR2puZktvEiR8nXdATN0yKS94oSAAAACAAAAAAAAAAAAAAAAAAV6LDSwWt0QWgmNg4Zv2yYhf4Pdexpi/QTIqWyD2AQVjXosNLLK1vz/upFHrJlizjH5uSBUJCpQZJczrBgxBmGoAAAAAAAAAAAAAAAEAAAAAAAAAAwAAAQAAAAAAAgAA
317
3
jart/cosmopolitan
false
cosmopolitan/third_party/mbedtls/test/data/base64/def_b64_too_big_3.txt
// Context with added '1234' before '==' add the end to simulate too much data in the base64 code AhUAAH8AAA4AAAQ8AAAAAF6HQx3MqAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAACG2QbHbUj8eGpdx5KVIebiwk0jvRj9/3m6BOSzpA7qBXeEunhqr3D11NE7ciGjeHMAAAAAAAM7MIIDNzCCAh+gAwIBAgIBAjANBgkqhkiG9w0BAQsFADA7MQswCQYDVQQGEwJOTDERMA8GA1UECgwIUG9sYXJTU0wxGTAXBgNVBAMMEFBvbGFyU1NMIFRlc3QgQ0EwHhcNMTkwMjEwMTQ0NDA2WhcNMjkwMjEwMTQ0NDA2WjA0MQswCQYDVQQGEwJOTDERMA8GA1UECgwIUG9sYXJTU0wxEjAQBgNVBAMMCWxvY2FsaG9zdDCCASIwDQYJKoZIhvcNAQEBBQADggEPADCCAQoCggEBAMFNo93nzR3RBNdJcriZrA545Do8Ss86ExbQWuTNowCIp+4ea5anUrSQ7y1yej4kmvy2NKwk9XfgJmSMnLAofaHa6ozmyRyWvP7BBFKzNtSj+uGxdtiQwWG0ZlI2oiZTqqt0Xgd9GYLbKtgfoNkNHC1JZvdbJXNG6AuKT2kMtQCQ4dqCEGZ9rlQri2V5kaHiYcPNQEkI7mgM8YuG0ka/0LiqEQMef1aoGh5EGA8PhYvai0Re4hjGYi/HZo36Xdh98yeJKQHFkA4/J/EwyEoO79bex8cna8cFPXrEAjyaHT4P6DSYW8tzS1KW2BGiLICIaTla0w+w3lkvEcf36hIBMJcCAwEAAaNNMEswCQYDVR0TBAIwADAdBgNVHQ4EFgQUpQXoZLjc32APUBJNYKhkr02LQ5MwHwYDVR0jBBgwFoAUtFrkpbPe0lL2udWmlQ/rPrzH/f8wDQYJKoZIhvcNAQELBQADggEBAC465FJhPqel7zJngHIHJrqj/wVAxGAFOTF396XKATGAp+HRCqJ81Ry60CNK1jDzk8dv6M6UHoS7RIFiM/9rXQCbJfiPD5xMTejZp5n5UYHAmxsxDaazfA5FuBhkfokKK6jD4Eq91C94xGKb6X4/VkaPF7cqoBBw/bHxawXc0UEPjqayiBpCYU/rJoVZgLqFVP7Px3sva1nOrNx8rPPI1hJ+ZOg8maiPTxHZnBVLakSSLQy/sWeWyazO1RnrbxjrbgQtYKz0e3nwGpu1w13vfckFmUSBhHXH7AAS/HpKC4IH7G2GAk3+n8iSSN71sZzpxonQwVbopMZqLmbBm/7WPLcAAJTfQC2Ek91INP5ihHNzImPOAHJCk+YTO/pQuEnNWwXbdmKAi+IRp671iAwtpkjSxCBXVzKX925F1A66caCOQptlw+9zFukDQgblM2JyAJLG0j6B4RtBTDWJ8ZTMUPHUoLJoEpm8APZgRi//DMRyCKP9pbBLGlDzgUvl0w11LzBAlJHkWau5NoqQBlG7w4HFrKweovskAAFRgAAAAF6HQx248L77RH0Z973tSYNQ8zBsz861CZG5/T09TJz3XodDHe/iJ+cgXb5An3zTdnTBtw3EWAb68T+gCE33GN8AAAAAAAAAAAAAAAEAAAAAAAAAAwAAAQAAAAAAAgAAAA1234==
1,695
3
jart/cosmopolitan
false
cosmopolitan/third_party/mbedtls/test/data/base64/cli_min_cfg.txt
// Minimal configuration 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
1,378
3
jart/cosmopolitan
false
cosmopolitan/third_party/mbedtls/test/data/base64/srv_ciphersuite.txt
// TLS-RSA-WITH-AES-256-CCM-8 AhUAAH8AAA4AAABtAAAAAF6K4ynAoQAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAADLBIQUrrPh7jxYz9e55cJvfpOkuBf2ZiVovlYa1Dkwbimp5q/CoWIn48C0x3Yj6N0AAACAAAAAAAAAAAAAAAAAAV6K4yksMvMV19qRq+eNokGn0j9Q5tjE88EK8jfM7gksXorjKR6zhXhttFGIFkNNAmmKuuDQGVmX1yCoHiJFonUAAAAAAAAAAAAAAAEAAAAAAAAAAwAAAQAAAAAAAgAAAA==
323
3
jart/cosmopolitan
false
cosmopolitan/third_party/bzip2/bzgrep
#!/bin/sh # Bzgrep wrapped for bzip2, # adapted from zgrep by Philippe Troin <[email protected]> for Debian GNU/Linux. ## zgrep notice: ## zgrep -- a wrapper around a grep program that decompresses files as needed ## Adapted from a version sent by Charles Levert <[email protected]> PATH="/usr/bin:$PATH"; export PATH prog=`echo $0 | sed 's|.*/||'` case "$prog" in *egrep) grep=${EGREP-egrep} ;; *fgrep) grep=${FGREP-fgrep} ;; *) grep=${GREP-grep} ;; esac pat="" while test $# -ne 0; do case "$1" in -e | -f) opt="$opt $1"; shift; pat="$1" if test "$grep" = grep; then # grep is buggy with -e on SVR4 grep=egrep fi;; -A | -B) opt="$opt $1 $2"; shift;; -*) opt="$opt $1";; *) if test -z "$pat"; then pat="$1" else break; fi;; esac shift done if test -z "$pat"; then echo "grep through bzip2 files" echo "usage: $prog [grep_options] pattern [files]" exit 1 fi list=0 silent=0 op=`echo "$opt" | sed -e 's/ //g' -e 's/-//g'` case "$op" in *l*) list=1 esac case "$op" in *h*) silent=1 esac if test $# -eq 0; then bzip2 -cdfq | $grep $opt "$pat" exit $? fi res=0 for i do if test -f "$i"; then :; else if test -f "$i.bz2"; then i="$i.bz2"; fi; fi if test $list -eq 1; then bzip2 -cdfq "$i" | $grep $opt "$pat" 2>&1 > /dev/null && echo $i r=$? elif test $# -eq 1 -o $silent -eq 1; then bzip2 -cdfq "$i" | $grep $opt "$pat" r=$? else j=$(echo "$i" | sed 's/\\/&&/g;s/|/\\&/g;s/&/\\&/g') j=`printf "%s" "$j" | tr '\n' ' '` # A trick adapted from # https://groups.google.com/forum/#!original/comp.unix.shell/x1345iu10eg/Nn1n-1r1uU0J # that has the same effect as the following bash code: # bzip2 -cdfq "$i" | $grep $opt "$pat" | sed "s|^|${j}:|" # r=${PIPESTATUS[1]} exec 3>&1 eval ` exec 4>&1 >&3 3>&- { bzip2 -cdfq "$i" 4>&- } | { $grep $opt "$pat" 4>&-; echo "r=$?;" >&4 } | sed "s|^|${j}:|" ` fi test "$r" -ne 0 && res="$r" done exit $res
2,054
86
jart/cosmopolitan
false
cosmopolitan/third_party/bzip2/bzip2.c
#include "libc/calls/calls.h" #include "libc/calls/struct/sigaction.h" #include "libc/calls/struct/stat.h" #include "libc/calls/struct/stat.macros.h" #include "libc/errno.h" #include "libc/log/log.h" #include "libc/mem/gc.internal.h" #include "libc/mem/mem.h" #include "libc/runtime/runtime.h" #include "libc/stdio/stdio.h" #include "libc/str/str.h" #include "libc/sysv/consts/o.h" #include "libc/sysv/consts/s.h" #include "libc/sysv/consts/sig.h" #include "libc/time/struct/utimbuf.h" #include "libc/time/time.h" #include "third_party/bzip2/bzlib.h" /* clang-format off */ /*-----------------------------------------------------------*/ /*--- A block-sorting, lossless compressor bzip2.c ---*/ /*-----------------------------------------------------------*/ /* ------------------------------------------------------------------ This file is part of bzip2/libbzip2, a program and library for lossless, block-sorting data compression. bzip2/libbzip2 version 1.0.8 of 13 July 2019 Copyright (C) 1996-2019 Julian Seward <[email protected]> Please read the WARNING, DISCLAIMER and PATENTS sections in the README file. This program is released under the terms of the license contained in the file LICENSE. ------------------------------------------------------------------ */ #define BZ_UNIX 1 /*---------------------------------------------*/ /*-- Some stuff for all platforms. --*/ #define ERROR_IF_EOF(i) { if ((i) == EOF) ioError(); } #define ERROR_IF_NOT_ZERO(i) { if ((i) != 0) ioError(); } #define ERROR_IF_MINUS_ONE(i) { if ((i) == (-1)) ioError(); } /*---------------------------------------------*/ /*-- Platform-specific stuff. --*/ #if BZ_UNIX #define PATH_SEP '/' #define MY_LSTAT lstat #define MY_STAT stat #define MY_S_ISREG S_ISREG #define MY_S_ISDIR S_ISDIR #define APPEND_FILESPEC(root, name) \ root=snocString((root), (name)) #define APPEND_FLAG(root, name) \ root=snocString((root), (name)) #define SET_BINARY_MODE(fd) /**/ #endif /* BZ_UNIX */ /*---------------------------------------------*/ /*-- Some more stuff for all platforms :-) --*/ typedef char Char; typedef unsigned char Bool; typedef unsigned char UChar; typedef int Int32; typedef unsigned int UInt32; typedef short Int16; typedef unsigned short UInt16; #define True ((Bool)1) #define False ((Bool)0) /*-- IntNative is your platform's `native' int size. Only here to avoid probs with 64-bit platforms. --*/ typedef int IntNative; /*---------------------------------------------------*/ /*--- Misc (file handling) data decls ---*/ /*---------------------------------------------------*/ Int32 verbosity; Bool keepInputFiles, smallMode, deleteOutputOnInterrupt; Bool forceOverwrite, testFailsExist, unzFailsExist, noisy; Int32 numFileNames, numFilesProcessed, blockSize100k; Int32 exitValue; /*-- source modes; F==file, I==stdin, O==stdout --*/ #define SM_I2O 1 #define SM_F2O 2 #define SM_F2F 3 /*-- operation modes --*/ #define OM_Z 1 #define OM_UNZ 2 #define OM_TEST 3 Int32 opMode; Int32 srcMode; #define FILE_NAME_LEN 1034 Int32 longestFileName; Char inName [FILE_NAME_LEN]; Char outName[FILE_NAME_LEN]; Char tmpName[FILE_NAME_LEN]; Char *progName; Char progNameReally[FILE_NAME_LEN]; FILE *outputHandleJustInCase; Int32 workFactor; static void panic ( const Char* ) wontreturn; static void ioError ( void ) wontreturn; static void outOfMemory ( void ) wontreturn; static void configError ( void ) wontreturn; static void crcError ( void ) wontreturn; static void cleanUpAndFail ( Int32 ) wontreturn; static void compressedStreamEOF ( void ) wontreturn; static void copyFileName ( Char*, Char* ); static void* myMalloc ( Int32 ); static void applySavedFileAttrToOutputFile ( IntNative fd ); /*---------------------------------------------------*/ /*--- An implementation of 64-bit ints. Sigh. ---*/ /*--- Roll on widespread deployment of ANSI C9X ! ---*/ /*---------------------------------------------------*/ typedef struct { UChar b[8]; } UInt64; static void uInt64_from_UInt32s ( UInt64* n, UInt32 lo32, UInt32 hi32 ) { n->b[7] = (UChar)((hi32 >> 24) & 0xFF); n->b[6] = (UChar)((hi32 >> 16) & 0xFF); n->b[5] = (UChar)((hi32 >> 8) & 0xFF); n->b[4] = (UChar) (hi32 & 0xFF); n->b[3] = (UChar)((lo32 >> 24) & 0xFF); n->b[2] = (UChar)((lo32 >> 16) & 0xFF); n->b[1] = (UChar)((lo32 >> 8) & 0xFF); n->b[0] = (UChar) (lo32 & 0xFF); } static double uInt64_to_double ( UInt64* n ) { Int32 i; double base = 1.0; double sum = 0.0; for (i = 0; i < 8; i++) { sum += base * (double)(n->b[i]); base *= 256.0; } return sum; } static Bool uInt64_isZero ( UInt64* n ) { Int32 i; for (i = 0; i < 8; i++) if (n->b[i] != 0) return 0; return 1; } /* Divide *n by 10, and return the remainder. */ static Int32 uInt64_qrm10 ( UInt64* n ) { UInt32 rem, tmp; Int32 i; rem = 0; for (i = 7; i >= 0; i--) { tmp = rem * 256 + n->b[i]; n->b[i] = tmp / 10; rem = tmp % 10; } return rem; } /* ... and the Whole Entire Point of all this UInt64 stuff is so that we can supply the following function. */ static void uInt64_toAscii ( char* outbuf, UInt64* n ) { Int32 i, q; UChar buf[32]; Int32 nBuf = 0; UInt64 n_copy = *n; do { q = uInt64_qrm10 ( &n_copy ); buf[nBuf] = q + '0'; nBuf++; } while (!uInt64_isZero(&n_copy)); outbuf[nBuf] = 0; for (i = 0; i < nBuf; i++) outbuf[i] = buf[nBuf-i-1]; } /*---------------------------------------------------*/ /*--- Processing of complete files and streams ---*/ /*---------------------------------------------------*/ /*---------------------------------------------*/ static Bool myfeof ( FILE* f ) { Int32 c = fgetc ( f ); if (c == EOF) return True; ungetc ( c, f ); return False; } /*---------------------------------------------*/ static void compressStream ( FILE *stream, FILE *zStream ) { BZFILE* bzf = NULL; UChar *ibuf = gc(malloc(5000)); Int32 nIbuf; UInt32 nbytes_in_lo32, nbytes_in_hi32; UInt32 nbytes_out_lo32, nbytes_out_hi32; Int32 bzerr, bzerr_dummy, ret; SET_BINARY_MODE(stream); SET_BINARY_MODE(zStream); if (ferror(stream)) goto errhandler_io; if (ferror(zStream)) goto errhandler_io; bzf = BZ2_bzWriteOpen ( &bzerr, zStream, blockSize100k, verbosity, workFactor ); if (bzerr != BZ_OK) goto errhandler; if (verbosity >= 2) (fprintf) ( stderr, "\n" ); while (True) { if (myfeof(stream)) break; nIbuf = fread ( ibuf, sizeof(UChar), 5000, stream ); if (ferror(stream)) goto errhandler_io; if (nIbuf > 0) BZ2_bzWrite ( &bzerr, bzf, (void*)ibuf, nIbuf ); if (bzerr != BZ_OK) goto errhandler; } BZ2_bzWriteClose64 ( &bzerr, bzf, 0, &nbytes_in_lo32, &nbytes_in_hi32, &nbytes_out_lo32, &nbytes_out_hi32 ); if (bzerr != BZ_OK) goto errhandler; if (ferror(zStream)) goto errhandler_io; ret = fflush ( zStream ); if (ret == EOF) goto errhandler_io; if (zStream != stdout) { Int32 fd = fileno ( zStream ); if (fd < 0) goto errhandler_io; applySavedFileAttrToOutputFile ( fd ); ret = fclose ( zStream ); outputHandleJustInCase = NULL; if (ret == EOF) goto errhandler_io; } outputHandleJustInCase = NULL; if (ferror(stream)) goto errhandler_io; ret = fclose ( stream ); if (ret == EOF) goto errhandler_io; if (verbosity >= 1) { if (nbytes_in_lo32 == 0 && nbytes_in_hi32 == 0) { (fprintf) ( stderr, " no data compressed.\n"); } else { Char buf_nin[32], buf_nout[32]; UInt64 nbytes_in, nbytes_out; double nbytes_in_d, nbytes_out_d; uInt64_from_UInt32s ( &nbytes_in, nbytes_in_lo32, nbytes_in_hi32 ); uInt64_from_UInt32s ( &nbytes_out, nbytes_out_lo32, nbytes_out_hi32 ); nbytes_in_d = uInt64_to_double ( &nbytes_in ); nbytes_out_d = uInt64_to_double ( &nbytes_out ); uInt64_toAscii ( buf_nin, &nbytes_in ); uInt64_toAscii ( buf_nout, &nbytes_out ); (fprintf) ( stderr, "%6.3f:1, %6.3f bits/byte, " "%5.2f%% saved, %s in, %s out.\n", nbytes_in_d / nbytes_out_d, (8.0 * nbytes_out_d) / nbytes_in_d, 100.0 * (1.0 - nbytes_out_d / nbytes_in_d), buf_nin, buf_nout ); } } return; errhandler: BZ2_bzWriteClose64 ( &bzerr_dummy, bzf, 1, &nbytes_in_lo32, &nbytes_in_hi32, &nbytes_out_lo32, &nbytes_out_hi32 ); switch (bzerr) { case BZ_CONFIG_ERROR: configError(); break; case BZ_MEM_ERROR: outOfMemory (); break; case BZ_IO_ERROR: errhandler_io: ioError(); break; default: panic ( "compress:unexpected error" ); } panic ( "compress:end" ); /*notreached*/ } /*---------------------------------------------*/ static Bool uncompressStream ( FILE *zStream, FILE *stream ) { BZFILE* bzf = NULL; Int32 bzerr, bzerr_dummy, ret, nread, streamNo, i; UChar *obuf = gc(malloc(5000)); UChar *unused = gc(malloc(BZ_MAX_UNUSED)); Int32 nUnused; void* unusedTmpV; UChar* unusedTmp; nUnused = 0; streamNo = 0; SET_BINARY_MODE(stream); SET_BINARY_MODE(zStream); if (ferror(stream)) goto errhandler_io; if (ferror(zStream)) goto errhandler_io; while (True) { bzf = BZ2_bzReadOpen ( &bzerr, zStream, verbosity, (int)smallMode, unused, nUnused ); if (bzf == NULL || bzerr != BZ_OK) goto errhandler; streamNo++; while (bzerr == BZ_OK) { nread = BZ2_bzRead ( &bzerr, bzf, obuf, 5000 ); if (bzerr == BZ_DATA_ERROR_MAGIC) goto trycat; if ((bzerr == BZ_OK || bzerr == BZ_STREAM_END) && nread > 0) fwrite ( obuf, sizeof(UChar), nread, stream ); if (ferror(stream)) goto errhandler_io; } if (bzerr != BZ_STREAM_END) goto errhandler; BZ2_bzReadGetUnused ( &bzerr, bzf, &unusedTmpV, &nUnused ); if (bzerr != BZ_OK) panic ( "decompress:bzReadGetUnused" ); unusedTmp = (UChar*)unusedTmpV; for (i = 0; i < nUnused; i++) unused[i] = unusedTmp[i]; BZ2_bzReadClose ( &bzerr, bzf ); if (bzerr != BZ_OK) panic ( "decompress:bzReadGetUnused" ); if (nUnused == 0 && myfeof(zStream)) break; } closeok: if (ferror(zStream)) goto errhandler_io; if (stream != stdout) { Int32 fd = fileno ( stream ); if (fd < 0) goto errhandler_io; applySavedFileAttrToOutputFile ( fd ); } ret = fclose ( zStream ); if (ret == EOF) goto errhandler_io; if (ferror(stream)) goto errhandler_io; ret = fflush ( stream ); if (ret != 0) goto errhandler_io; if (stream != stdout) { ret = fclose ( stream ); outputHandleJustInCase = NULL; if (ret == EOF) goto errhandler_io; } outputHandleJustInCase = NULL; if (verbosity >= 2) (fprintf) ( stderr, "\n " ); return True; trycat: if (forceOverwrite) { rewind(zStream); while (True) { if (myfeof(zStream)) break; nread = fread ( obuf, sizeof(UChar), 5000, zStream ); if (ferror(zStream)) goto errhandler_io; if (nread > 0) fwrite ( obuf, sizeof(UChar), nread, stream ); if (ferror(stream)) goto errhandler_io; } goto closeok; } errhandler: BZ2_bzReadClose ( &bzerr_dummy, bzf ); switch (bzerr) { case BZ_CONFIG_ERROR: configError(); break; case BZ_IO_ERROR: errhandler_io: ioError(); break; case BZ_DATA_ERROR: crcError(); case BZ_MEM_ERROR: outOfMemory(); case BZ_UNEXPECTED_EOF: compressedStreamEOF(); case BZ_DATA_ERROR_MAGIC: if (zStream != stdin) fclose(zStream); if (stream != stdout) fclose(stream); if (streamNo == 1) { return False; } else { if (noisy) (fprintf) ( stderr, "\n%s: %s: trailing garbage after EOF ignored\n", progName, inName ); return True; } default: panic ( "decompress:unexpected error" ); } panic ( "decompress:end" ); return True; /*notreached*/ } /*---------------------------------------------*/ static Bool testStream ( FILE *zStream ) { BZFILE* bzf = NULL; Int32 bzerr, bzerr_dummy, ret, streamNo, i; UChar *obuf = gc(malloc(5000)); UChar *unused = gc(malloc(BZ_MAX_UNUSED)); Int32 nUnused; void* unusedTmpV; UChar* unusedTmp; nUnused = 0; streamNo = 0; SET_BINARY_MODE(zStream); if (ferror(zStream)) goto errhandler_io; while (True) { bzf = BZ2_bzReadOpen ( &bzerr, zStream, verbosity, (int)smallMode, unused, nUnused ); if (bzf == NULL || bzerr != BZ_OK) goto errhandler; streamNo++; while (bzerr == BZ_OK) { BZ2_bzRead ( &bzerr, bzf, obuf, 5000 ); if (bzerr == BZ_DATA_ERROR_MAGIC) goto errhandler; } if (bzerr != BZ_STREAM_END) goto errhandler; BZ2_bzReadGetUnused ( &bzerr, bzf, &unusedTmpV, &nUnused ); if (bzerr != BZ_OK) panic ( "test:bzReadGetUnused" ); unusedTmp = (UChar*)unusedTmpV; for (i = 0; i < nUnused; i++) unused[i] = unusedTmp[i]; BZ2_bzReadClose ( &bzerr, bzf ); if (bzerr != BZ_OK) panic ( "test:bzReadGetUnused" ); if (nUnused == 0 && myfeof(zStream)) break; } if (ferror(zStream)) goto errhandler_io; ret = fclose ( zStream ); if (ret == EOF) goto errhandler_io; if (verbosity >= 2) (fprintf) ( stderr, "\n " ); return True; errhandler: BZ2_bzReadClose ( &bzerr_dummy, bzf ); if (verbosity == 0) (fprintf) ( stderr, "%s: %s: ", progName, inName ); switch (bzerr) { case BZ_CONFIG_ERROR: configError(); break; case BZ_IO_ERROR: errhandler_io: ioError(); break; case BZ_DATA_ERROR: (fprintf) ( stderr, "data integrity (CRC) error in data\n" ); return False; case BZ_MEM_ERROR: outOfMemory(); case BZ_UNEXPECTED_EOF: (fprintf) ( stderr, "file ends unexpectedly\n" ); return False; case BZ_DATA_ERROR_MAGIC: if (zStream != stdin) fclose(zStream); if (streamNo == 1) { (fprintf) ( stderr, "bad magic number (file not created by bzip2)\n" ); return False; } else { if (noisy) (fprintf) ( stderr, "trailing garbage after EOF ignored\n" ); return True; } default: panic ( "test:unexpected error" ); } panic ( "test:end" ); return True; /*notreached*/ } /*---------------------------------------------------*/ /*--- Error [non-] handling grunge ---*/ /*---------------------------------------------------*/ /*---------------------------------------------*/ static void setExit ( Int32 v ) { if (v > exitValue) exitValue = v; } /*---------------------------------------------*/ static void cadvise ( void ) { if (noisy) (fprintf) ( stderr, "\nIt is possible that the compressed file(s) have become corrupted.\n" "You can use the -tvv option to test integrity of such files.\n\n" "You can use the `bzip2recover' program to attempt to recover\n" "data from undamaged sections of corrupted files.\n\n" ); } /*---------------------------------------------*/ static void showFileNames ( void ) { if (noisy) (fprintf) ( stderr, "\tInput file = %s, output file = %s\n", inName, outName ); } /*---------------------------------------------*/ static void cleanUpAndFail ( Int32 ec ) { IntNative retVal; struct MY_STAT statBuf; if ( srcMode == SM_F2F && opMode != OM_TEST && deleteOutputOnInterrupt ) { /* Check whether input file still exists. Delete output file only if input exists to avoid loss of data. Joerg Prante, 5 January 2002. (JRS 06-Jan-2002: other changes in 1.0.2 mean this is less likely to happen. But to be ultra-paranoid, we do the check anyway.) */ retVal = MY_STAT ( inName, &statBuf ); if (retVal == 0) { if (noisy) (fprintf) ( stderr, "%s: Deleting output file %s, if it exists.\n", progName, outName ); if (outputHandleJustInCase != NULL) fclose ( outputHandleJustInCase ); retVal = remove ( outName ); if (retVal != 0) (fprintf) ( stderr, "%s: WARNING: deletion of output file " "(apparently) failed.\n", progName ); } else { (fprintf) ( stderr, "%s: WARNING: deletion of output file suppressed\n", progName ); (fprintf) ( stderr, "%s: since input file no longer exists. Output file\n", progName ); (fprintf) ( stderr, "%s: `%s' may be incomplete.\n", progName, outName ); (fprintf) ( stderr, "%s: I suggest doing an integrity test (bzip2 -tv)" " of it.\n", progName ); } } if (noisy && numFileNames > 0 && numFilesProcessed < numFileNames) { (fprintf) ( stderr, "%s: WARNING: some files have not been processed:\n" "%s: %d specified on command line, %d not processed yet.\n\n", progName, progName, numFileNames, numFileNames - numFilesProcessed ); } setExit(ec); exit(exitValue); } /*---------------------------------------------*/ static void panic ( const Char* s ) { (fprintf) ( stderr, "\n%s: PANIC -- internal consistency error:\n" "\t%s\n" "\tThis is a BUG. Please report it to:\n" "\[email protected]\n", progName, s ); showFileNames(); cleanUpAndFail( 3 ); } /*---------------------------------------------*/ static void crcError ( void ) { (fprintf) ( stderr, "\n%s: Data integrity error when decompressing.\n", progName ); showFileNames(); cadvise(); cleanUpAndFail( 2 ); } /*---------------------------------------------*/ static void compressedStreamEOF ( void ) { if (noisy) { (fprintf) ( stderr, "\n%s: Compressed file ends unexpectedly;\n\t" "perhaps it is corrupted? *Possible* reason follows.\n", progName ); perror ( progName ); showFileNames(); cadvise(); } cleanUpAndFail( 2 ); } /*---------------------------------------------*/ static void ioError ( void ) { (fprintf) ( stderr, "\n%s: I/O or other error, bailing out. " "Possible reason follows.\n", progName ); perror ( progName ); showFileNames(); cleanUpAndFail( 1 ); } /*---------------------------------------------*/ static void mySignalCatcher ( IntNative n ) { (fprintf) ( stderr, "\n%s: Control-C or similar caught, quitting.\n", progName ); cleanUpAndFail(1); } /*---------------------------------------------*/ static void mySIGSEGVorSIGBUScatcher ( IntNative n ) { if (opMode == OM_Z) (fprintf) ( stderr, "\n%s: Caught a SIGSEGV or SIGBUS whilst compressing.\n" "\n" " Possible causes are (most likely first):\n" " (1) This computer has unreliable memory or cache hardware\n" " (a surprisingly common problem; try a different machine.)\n" " (2) A bug in the compiler used to create this executable\n" " (unlikely, if you didn't compile bzip2 yourself.)\n" " (3) A real bug in bzip2 -- I hope this should never be the case.\n" " The user's manual, Section 4.3, has more info on (1) and (2).\n" " \n" " If you suspect this is a bug in bzip2, or are unsure about (1)\n" " or (2), feel free to report it to: [email protected].\n" " Section 4.3 of the user's manual describes the info a useful\n" " bug report should have. If the manual is available on your\n" " system, please try and read it before mailing me. If you don't\n" " have the manual or can't be bothered to read it, mail me anyway.\n" "\n", progName ); else (fprintf) ( stderr, "\n%s: Caught a SIGSEGV or SIGBUS whilst decompressing.\n" "\n" " Possible causes are (most likely first):\n" " (1) The compressed data is corrupted, and bzip2's usual checks\n" " failed to detect this. Try bzip2 -tvv my_file.bz2.\n" " (2) This computer has unreliable memory or cache hardware\n" " (a surprisingly common problem; try a different machine.)\n" " (3) A bug in the compiler used to create this executable\n" " (unlikely, if you didn't compile bzip2 yourself.)\n" " (4) A real bug in bzip2 -- I hope this should never be the case.\n" " The user's manual, Section 4.3, has more info on (2) and (3).\n" " \n" " If you suspect this is a bug in bzip2, or are unsure about (2)\n" " or (3), feel free to report it to: [email protected].\n" " Section 4.3 of the user's manual describes the info a useful\n" " bug report should have. If the manual is available on your\n" " system, please try and read it before mailing me. If you don't\n" " have the manual or can't be bothered to read it, mail me anyway.\n" "\n", progName ); showFileNames(); if (opMode == OM_Z) cleanUpAndFail( 3 ); else { cadvise(); cleanUpAndFail( 2 ); } } /*---------------------------------------------*/ static void outOfMemory ( void ) { (fprintf) ( stderr, "\n%s: couldn't allocate enough memory\n", progName ); showFileNames(); cleanUpAndFail(1); } /*---------------------------------------------*/ static void configError ( void ) { (fprintf) ( stderr, "bzip2: I'm not configured correctly for this platform!\n" "\tI require Int32, Int16 and Char to have sizes\n" "\tof 4, 2 and 1 bytes to run properly, and they don't.\n" "\tProbably you can fix this by defining them correctly,\n" "\tand recompiling. Bye!\n" ); setExit(3); exit(exitValue); } /*---------------------------------------------------*/ /*--- The main driver machinery ---*/ /*---------------------------------------------------*/ /* All rather crufty. The main problem is that input files are stat()d multiple times before use. This should be cleaned up. */ /*---------------------------------------------*/ static void pad ( Char *s ) { Int32 i; if ( (Int32)strlen(s) >= longestFileName ) return; for (i = 1; i <= longestFileName - (Int32)strlen(s); i++) (fprintf) ( stderr, " " ); } /*---------------------------------------------*/ static void copyFileName ( Char* to, Char* from ) { if ( strlen(from) > FILE_NAME_LEN-10 ) { (fprintf) ( stderr, "bzip2: file name\n`%s'\n" "is suspiciously (more than %d chars) long.\n" "Try using a reasonable file name instead. Sorry! :-)\n", from, FILE_NAME_LEN-10 ); setExit(1); exit(exitValue); } strncpy(to,from,FILE_NAME_LEN-10); to[FILE_NAME_LEN-10]='\0'; } /*---------------------------------------------*/ static Bool fileExists ( Char* name ) { FILE *tmp = fopen ( name, "rb" ); Bool exists = (tmp != NULL); if (tmp != NULL) fclose ( tmp ); return exists; } /*---------------------------------------------*/ /* Open an output file safely with O_EXCL and good permissions. This avoids a race condition in versions < 1.0.2, in which the file was first opened and then had its interim permissions set safely. We instead use open() to create the file with the interim permissions required. (--- --- rw-). For non-Unix platforms, if we are not worrying about security issues, simple this simply behaves like fopen. */ static FILE* fopen_output_safely ( Char* name, const char* mode ) { # if BZ_UNIX FILE* fp; IntNative fh; fh = open(name, O_WRONLY|O_CREAT|O_EXCL, S_IWUSR|S_IRUSR); if (fh == -1) return NULL; fp = fdopen(fh, mode); if (fp == NULL) close(fh); return fp; # else return fopen(name, mode); # endif } /*---------------------------------------------*/ /*-- if in doubt, return True --*/ static Bool notAStandardFile ( Char* name ) { IntNative i; struct MY_STAT statBuf; i = MY_LSTAT ( name, &statBuf ); if (i != 0) return True; if (MY_S_ISREG(statBuf.st_mode)) return False; return True; } /*---------------------------------------------*/ /*-- rac 11/21/98 see if file has hard links to it --*/ static Int32 countHardLinks ( Char* name ) { IntNative i; struct MY_STAT statBuf; i = MY_LSTAT ( name, &statBuf ); if (i != 0) return 0; return (statBuf.st_nlink - 1); } /*---------------------------------------------*/ /* Copy modification date, access date, permissions and owner from the source to destination file. We have to copy this meta-info off into fileMetaInfo before starting to compress / decompress it, because doing it afterwards means we get the wrong access time. To complicate matters, in compress() and decompress() below, the sequence of tests preceding the call to saveInputFileMetaInfo() involves calling fileExists(), which in turn establishes its result by attempting to fopen() the file, and if successful, immediately fclose()ing it again. So we have to assume that the fopen() call does not cause the access time field to be updated. Reading of the man page for stat() (man 2 stat) on RedHat 7.2 seems to imply that merely doing open() will not affect the access time. Therefore we merely need to hope that the C library only does open() as a result of fopen(), and not any kind of read()-ahead cleverness. It sounds pretty fragile to me. Whether this carries across robustly to arbitrary Unix-like platforms (or even works robustly on this one, RedHat 7.2) is unknown to me. Nevertheless ... */ #if BZ_UNIX static struct MY_STAT fileMetaInfo; #endif static void saveInputFileMetaInfo ( Char *srcName ) { # if BZ_UNIX IntNative retVal; /* Note use of stat here, not lstat. */ retVal = MY_STAT( srcName, &fileMetaInfo ); ERROR_IF_NOT_ZERO ( retVal ); # endif } static void applySavedTimeInfoToOutputFile ( Char *dstName ) { # if BZ_UNIX IntNative retVal; struct utimbuf uTimBuf; uTimBuf.actime = fileMetaInfo.st_atime; uTimBuf.modtime = fileMetaInfo.st_mtime; retVal = utime ( dstName, &uTimBuf ); ERROR_IF_NOT_ZERO ( retVal ); # endif } static void applySavedFileAttrToOutputFile ( IntNative fd ) { # if BZ_UNIX IntNative retVal; retVal = fchmod ( fd, fileMetaInfo.st_mode ); ERROR_IF_NOT_ZERO ( retVal ); (void) fchown ( fd, fileMetaInfo.st_uid, fileMetaInfo.st_gid ); /* chown() will in many cases return with EPERM, which can be safely ignored. */ # endif } /*---------------------------------------------*/ static Bool containsDubiousChars ( Char* name ) { # if BZ_UNIX /* On unix, files can contain any characters and the file expansion * is performed by the shell. */ return False; # else /* ! BZ_UNIX */ /* On non-unix (Win* platforms), wildcard characters are not allowed in * filenames. */ for (; *name != '\0'; name++) if (*name == '?' || *name == '*') return True; return False; # endif /* BZ_UNIX */ } /*---------------------------------------------*/ #define BZ_N_SUFFIX_PAIRS 4 const Char* zSuffix[BZ_N_SUFFIX_PAIRS] = { ".bz2", ".bz", ".tbz2", ".tbz" }; const Char* unzSuffix[BZ_N_SUFFIX_PAIRS] = { "", "", ".tar", ".tar" }; static Bool hasSuffix ( Char* s, const Char* suffix ) { Int32 ns = strlen(s); Int32 nx = strlen(suffix); if (ns < nx) return False; if (strcmp(s + ns - nx, suffix) == 0) return True; return False; } static Bool mapSuffix ( Char* name, const Char* oldSuffix, const Char* newSuffix ) { if (!hasSuffix(name,oldSuffix)) return False; name[strlen(name)-strlen(oldSuffix)] = 0; strcat ( name, newSuffix ); return True; } /*---------------------------------------------*/ static void compress ( Char *name ) { FILE *inStr; FILE *outStr; Int32 n, i; struct MY_STAT statBuf; deleteOutputOnInterrupt = False; if (name == NULL && srcMode != SM_I2O) panic ( "compress: bad modes\n" ); switch (srcMode) { case SM_I2O: copyFileName ( inName, (Char*)"(stdin)" ); copyFileName ( outName, (Char*)"(stdout)" ); break; case SM_F2F: copyFileName ( inName, name ); copyFileName ( outName, name ); strcat ( outName, ".bz2" ); break; case SM_F2O: copyFileName ( inName, name ); copyFileName ( outName, (Char*)"(stdout)" ); break; } if ( srcMode != SM_I2O && containsDubiousChars ( inName ) ) { if (noisy) (fprintf) ( stderr, "%s: There are no files matching `%s'.\n", progName, inName ); setExit(1); return; } if ( srcMode != SM_I2O && !fileExists ( inName ) ) { (fprintf) ( stderr, "%s: Can't open input file %s: %s.\n", progName, inName, strerror(errno) ); setExit(1); return; } for (i = 0; i < BZ_N_SUFFIX_PAIRS; i++) { if (hasSuffix(inName, zSuffix[i])) { if (noisy) (fprintf) ( stderr, "%s: Input file %s already has %s suffix.\n", progName, inName, zSuffix[i] ); setExit(1); return; } } if ( srcMode == SM_F2F || srcMode == SM_F2O ) { MY_STAT(inName, &statBuf); if ( MY_S_ISDIR(statBuf.st_mode) ) { (fprintf)( stderr, "%s: Input file %s is a directory.\n", progName,inName); setExit(1); return; } } if ( srcMode == SM_F2F && !forceOverwrite && notAStandardFile ( inName )) { if (noisy) (fprintf) ( stderr, "%s: Input file %s is not a normal file.\n", progName, inName ); setExit(1); return; } if ( srcMode == SM_F2F && fileExists ( outName ) ) { if (forceOverwrite) { remove(outName); } else { (fprintf) ( stderr, "%s: Output file %s already exists.\n", progName, outName ); setExit(1); return; } } if ( srcMode == SM_F2F && !forceOverwrite && (n=countHardLinks ( inName )) > 0) { (fprintf) ( stderr, "%s: Input file %s has %d other link%s.\n", progName, inName, n, n > 1 ? "s" : "" ); setExit(1); return; } if ( srcMode == SM_F2F ) { /* Save the file's meta-info before we open it. Doing it later means we mess up the access times. */ saveInputFileMetaInfo ( inName ); } switch ( srcMode ) { case SM_I2O: inStr = stdin; outStr = stdout; if ( isatty ( fileno ( stdout ) ) ) { (fprintf) ( stderr, "%s: I won't write compressed data to a terminal.\n", progName ); (fprintf) ( stderr, "%s: For help, type: `%s --help'.\n", progName, progName ); setExit(1); return; }; break; case SM_F2O: inStr = fopen ( inName, "rb" ); outStr = stdout; if ( isatty ( fileno ( stdout ) ) ) { (fprintf) ( stderr, "%s: I won't write compressed data to a terminal.\n", progName ); (fprintf) ( stderr, "%s: For help, type: `%s --help'.\n", progName, progName ); if ( inStr != NULL ) fclose ( inStr ); setExit(1); return; }; if ( inStr == NULL ) { (fprintf) ( stderr, "%s: Can't open input file %s: %s.\n", progName, inName, strerror(errno) ); setExit(1); return; }; break; case SM_F2F: inStr = fopen ( inName, "rb" ); outStr = fopen_output_safely ( outName, "wb" ); if ( outStr == NULL) { (fprintf) ( stderr, "%s: Can't create output file %s: %s.\n", progName, outName, strerror(errno) ); if ( inStr != NULL ) fclose ( inStr ); setExit(1); return; } if ( inStr == NULL ) { (fprintf) ( stderr, "%s: Can't open input file %s: %s.\n", progName, inName, strerror(errno) ); if ( outStr != NULL ) fclose ( outStr ); setExit(1); return; }; break; default: panic ( "compress: bad srcMode" ); break; } if (verbosity >= 1) { (fprintf) ( stderr, " %s: ", inName ); pad ( inName ); fflush ( stderr ); } /*--- Now the input and output handles are sane. Do the Biz. ---*/ outputHandleJustInCase = outStr; deleteOutputOnInterrupt = True; compressStream ( inStr, outStr ); outputHandleJustInCase = NULL; /*--- If there was an I/O error, we won't get here. ---*/ if ( srcMode == SM_F2F ) { applySavedTimeInfoToOutputFile ( outName ); deleteOutputOnInterrupt = False; if ( !keepInputFiles ) { IntNative retVal = remove ( inName ); ERROR_IF_NOT_ZERO ( retVal ); } } deleteOutputOnInterrupt = False; } /*---------------------------------------------*/ static void uncompress ( Char *name ) { FILE *inStr; FILE *outStr; Int32 n, i; Bool magicNumberOK; Bool cantGuess; struct MY_STAT statBuf; deleteOutputOnInterrupt = False; if (name == NULL && srcMode != SM_I2O) panic ( "uncompress: bad modes\n" ); cantGuess = False; switch (srcMode) { case SM_I2O: copyFileName ( inName, (Char*)"(stdin)" ); copyFileName ( outName, (Char*)"(stdout)" ); break; case SM_F2F: copyFileName ( inName, name ); copyFileName ( outName, name ); for (i = 0; i < BZ_N_SUFFIX_PAIRS; i++) if (mapSuffix(outName,zSuffix[i],unzSuffix[i])) goto zzz; cantGuess = True; strcat ( outName, ".out" ); break; case SM_F2O: copyFileName ( inName, name ); copyFileName ( outName, (Char*)"(stdout)" ); break; } zzz: if ( srcMode != SM_I2O && containsDubiousChars ( inName ) ) { if (noisy) (fprintf) ( stderr, "%s: There are no files matching `%s'.\n", progName, inName ); setExit(1); return; } if ( srcMode != SM_I2O && !fileExists ( inName ) ) { (fprintf) ( stderr, "%s: Can't open input file %s: %s.\n", progName, inName, strerror(errno) ); setExit(1); return; } if ( srcMode == SM_F2F || srcMode == SM_F2O ) { MY_STAT(inName, &statBuf); if ( MY_S_ISDIR(statBuf.st_mode) ) { (fprintf)( stderr, "%s: Input file %s is a directory.\n", progName,inName); setExit(1); return; } } if ( srcMode == SM_F2F && !forceOverwrite && notAStandardFile ( inName )) { if (noisy) (fprintf) ( stderr, "%s: Input file %s is not a normal file.\n", progName, inName ); setExit(1); return; } if ( /* srcMode == SM_F2F implied && */ cantGuess ) { if (noisy) (fprintf) ( stderr, "%s: Can't guess original name for %s -- using %s\n", progName, inName, outName ); /* just a warning, no return */ } if ( srcMode == SM_F2F && fileExists ( outName ) ) { if (forceOverwrite) { remove(outName); } else { (fprintf) ( stderr, "%s: Output file %s already exists.\n", progName, outName ); setExit(1); return; } } if ( srcMode == SM_F2F && !forceOverwrite && (n=countHardLinks ( inName ) ) > 0) { (fprintf) ( stderr, "%s: Input file %s has %d other link%s.\n", progName, inName, n, n > 1 ? "s" : "" ); setExit(1); return; } if ( srcMode == SM_F2F ) { /* Save the file's meta-info before we open it. Doing it later means we mess up the access times. */ saveInputFileMetaInfo ( inName ); } switch ( srcMode ) { case SM_I2O: inStr = stdin; outStr = stdout; if ( isatty ( fileno ( stdin ) ) ) { (fprintf) ( stderr, "%s: I won't read compressed data from a terminal.\n", progName ); (fprintf) ( stderr, "%s: For help, type: `%s --help'.\n", progName, progName ); setExit(1); return; }; break; case SM_F2O: inStr = fopen ( inName, "rb" ); outStr = stdout; if ( inStr == NULL ) { (fprintf) ( stderr, "%s: Can't open input file %s:%s.\n", progName, inName, strerror(errno) ); if ( inStr != NULL ) fclose ( inStr ); setExit(1); return; }; break; case SM_F2F: inStr = fopen ( inName, "rb" ); outStr = fopen_output_safely ( outName, "wb" ); if ( outStr == NULL) { (fprintf) ( stderr, "%s: Can't create output file %s: %s.\n", progName, outName, strerror(errno) ); if ( inStr != NULL ) fclose ( inStr ); setExit(1); return; } if ( inStr == NULL ) { (fprintf) ( stderr, "%s: Can't open input file %s: %s.\n", progName, inName, strerror(errno) ); if ( outStr != NULL ) fclose ( outStr ); setExit(1); return; }; break; default: panic ( "uncompress: bad srcMode" ); break; } if (verbosity >= 1) { (fprintf) ( stderr, " %s: ", inName ); pad ( inName ); fflush ( stderr ); } /*--- Now the input and output handles are sane. Do the Biz. ---*/ outputHandleJustInCase = outStr; deleteOutputOnInterrupt = True; magicNumberOK = uncompressStream ( inStr, outStr ); outputHandleJustInCase = NULL; /*--- If there was an I/O error, we won't get here. ---*/ if ( magicNumberOK ) { if ( srcMode == SM_F2F ) { applySavedTimeInfoToOutputFile ( outName ); deleteOutputOnInterrupt = False; if ( !keepInputFiles ) { IntNative retVal = remove ( inName ); ERROR_IF_NOT_ZERO ( retVal ); } } } else { unzFailsExist = True; deleteOutputOnInterrupt = False; if ( srcMode == SM_F2F ) { IntNative retVal = remove ( outName ); ERROR_IF_NOT_ZERO ( retVal ); } } deleteOutputOnInterrupt = False; if ( magicNumberOK ) { if (verbosity >= 1) (fprintf) ( stderr, "done\n" ); } else { setExit(2); if (verbosity >= 1) (fprintf) ( stderr, "not a bzip2 file.\n" ); else (fprintf) ( stderr, "%s: %s is not a bzip2 file.\n", progName, inName ); } } /*---------------------------------------------*/ static void testf ( Char *name ) { FILE *inStr; Bool allOK; struct MY_STAT statBuf; deleteOutputOnInterrupt = False; if (name == NULL && srcMode != SM_I2O) panic ( "testf: bad modes\n" ); copyFileName ( outName, (Char*)"(none)" ); switch (srcMode) { case SM_I2O: copyFileName ( inName, (Char*)"(stdin)" ); break; case SM_F2F: copyFileName ( inName, name ); break; case SM_F2O: copyFileName ( inName, name ); break; } if ( srcMode != SM_I2O && containsDubiousChars ( inName ) ) { if (noisy) (fprintf) ( stderr, "%s: There are no files matching `%s'.\n", progName, inName ); setExit(1); return; } if ( srcMode != SM_I2O && !fileExists ( inName ) ) { (fprintf) ( stderr, "%s: Can't open input %s: %s.\n", progName, inName, strerror(errno) ); setExit(1); return; } if ( srcMode != SM_I2O ) { MY_STAT(inName, &statBuf); if ( MY_S_ISDIR(statBuf.st_mode) ) { (fprintf)( stderr, "%s: Input file %s is a directory.\n", progName,inName); setExit(1); return; } } switch ( srcMode ) { case SM_I2O: if ( isatty ( fileno ( stdin ) ) ) { (fprintf) ( stderr, "%s: I won't read compressed data from a terminal.\n", progName ); (fprintf) ( stderr, "%s: For help, type: `%s --help'.\n", progName, progName ); setExit(1); return; }; inStr = stdin; break; case SM_F2O: case SM_F2F: inStr = fopen ( inName, "rb" ); if ( inStr == NULL ) { (fprintf) ( stderr, "%s: Can't open input file %s:%s.\n", progName, inName, strerror(errno) ); setExit(1); return; }; break; default: panic ( "testf: bad srcMode" ); break; } if (verbosity >= 1) { (fprintf) ( stderr, " %s: ", inName ); pad ( inName ); fflush ( stderr ); } /*--- Now the input handle is sane. Do the Biz. ---*/ outputHandleJustInCase = NULL; allOK = testStream ( inStr ); if (allOK && verbosity >= 1) (fprintf) ( stderr, "ok\n" ); if (!allOK) testFailsExist = True; } /*---------------------------------------------*/ static void license ( void ) { (fprintf) ( stderr, "bzip2, a block-sorting file compressor. " "Version %s.\n" " \n" " Copyright (C) 1996-2019 by Julian Seward.\n" " \n" " This program is free software; you can redistribute it and/or modify\n" " it under the terms set out in the LICENSE file, which is included\n" " in the bzip2 source distribution.\n" " \n" " This program is distributed in the hope that it will be useful,\n" " but WITHOUT ANY WARRANTY; without even the implied warranty of\n" " MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the\n" " LICENSE file for more details.\n" " \n", BZ2_bzlibVersion() ); } /*---------------------------------------------*/ static void usage ( Char *fullProgName ) { (fprintf) ( stderr, "bzip2, a block-sorting file compressor. " "Version %s.\n" "\n usage: %s [flags and input files in any order]\n" "\n" " -h --help print this message\n" " -d --decompress force decompression\n" " -z --compress force compression\n" " -k --keep keep (don't delete) input files\n" " -f --force overwrite existing output files\n" " -t --test test compressed file integrity\n" " -c --stdout output to standard out\n" " -q --quiet suppress noncritical error messages\n" " -v --verbose be verbose (a 2nd -v gives more)\n" " -L --license display software version & license\n" " -V --version display software version & license\n" " -s --small use less memory (at most 2500k)\n" " -1 .. -9 set block size to 100k .. 900k\n" " --fast alias for -1\n" " --best alias for -9\n" "\n" " If invoked as `bzip2', default action is to compress.\n" " as `bunzip2', default action is to decompress.\n" " as `bzcat', default action is to decompress to stdout.\n" "\n" " If no file names are given, bzip2 compresses or decompresses\n" " from standard input to standard output. You can combine\n" " short flags, so `-v -4' means the same as -v4 or -4v, &c.\n" # if BZ_UNIX "\n" # endif , BZ2_bzlibVersion(), fullProgName ); } /*---------------------------------------------*/ static void redundant ( Char* flag ) { (fprintf) ( stderr, "%s: %s is redundant in versions 0.9.5 and above\n", progName, flag ); } /*---------------------------------------------*/ /*-- All the garbage from here to main() is purely to implement a linked list of command-line arguments, into which main() copies argv[1 .. argc-1]. The purpose of this exercise is to facilitate the expansion of wildcard characters * and ? in filenames for OSs which don't know how to do it themselves, like MSDOS, Windows 95 and NT. The actual Dirty Work is done by the platform- specific macro APPEND_FILESPEC. --*/ typedef struct zzzz { Char *name; struct zzzz *link; } Cell; /*---------------------------------------------*/ static void *myMalloc ( Int32 n ) { void* p; p = malloc ( (size_t)n ); if (p == NULL) outOfMemory (); return p; } /*---------------------------------------------*/ static Cell *mkCell ( void ) { Cell *c; c = (Cell*) myMalloc ( sizeof ( Cell ) ); c->name = NULL; c->link = NULL; return c; } /*---------------------------------------------*/ static Cell *snocString ( Cell *root, Char *name ) { if (root == NULL) { Cell *tmp = mkCell(); tmp->name = (Char*) myMalloc ( 5 + strlen(name) ); strcpy ( tmp->name, name ); return tmp; } else { Cell *tmp = root; while (tmp->link != NULL) tmp = tmp->link; tmp->link = snocString ( tmp->link, name ); return root; } } /*---------------------------------------------*/ static void addFlagsFromEnvVar ( Cell** argList, Char* varName ) { Int32 i, j, k; Char *envbase, *p; envbase = getenv(varName); if (envbase != NULL) { p = envbase; i = 0; while (True) { if (p[i] == 0) break; p += i; i = 0; while (isspace((Int32)(p[0]))) p++; while (p[i] != 0 && !isspace((Int32)(p[i]))) i++; if (i > 0) { k = i; if (k > FILE_NAME_LEN-10) k = FILE_NAME_LEN-10; for (j = 0; j < k; j++) tmpName[j] = p[j]; tmpName[k] = 0; APPEND_FLAG(*argList, tmpName); } } } } /*---------------------------------------------*/ #define ISFLAG(s) (strcmp(aa->name, (s))==0) IntNative main ( IntNative argc, Char *argv[] ) { Int32 i, j; Char *tmp; Cell *argList; Cell *aa; Bool decode; /*-- Be really really really paranoid :-) --*/ if (sizeof(Int32) != 4 || sizeof(UInt32) != 4 || sizeof(Int16) != 2 || sizeof(UInt16) != 2 || sizeof(Char) != 1 || sizeof(UChar) != 1) configError(); /*-- Initialise --*/ outputHandleJustInCase = NULL; smallMode = False; keepInputFiles = False; forceOverwrite = False; noisy = True; verbosity = 0; blockSize100k = 9; testFailsExist = False; unzFailsExist = False; numFileNames = 0; numFilesProcessed = 0; workFactor = 30; deleteOutputOnInterrupt = False; exitValue = 0; i = j = 0; /* avoid bogus warning from egcs-1.1.X */ /*-- Set up signal handlers for mem access errors --*/ signal (SIGSEGV, mySIGSEGVorSIGBUScatcher); # if BZ_UNIX # ifndef __DJGPP__ signal (SIGBUS, mySIGSEGVorSIGBUScatcher); # endif # endif copyFileName ( inName, (Char*)"(none)" ); copyFileName ( outName, (Char*)"(none)" ); copyFileName ( progNameReally, argv[0] ); progName = &progNameReally[0]; for (tmp = &progNameReally[0]; *tmp != '\0'; tmp++) if (*tmp == PATH_SEP) progName = tmp + 1; /*-- Copy flags from env var BZIP2, and expand filename wildcards in arg list. --*/ argList = NULL; addFlagsFromEnvVar ( &argList, (Char*)"BZIP2" ); addFlagsFromEnvVar ( &argList, (Char*)"BZIP" ); for (i = 1; i <= argc-1; i++) APPEND_FILESPEC(argList, argv[i]); /*-- Find the length of the longest filename --*/ longestFileName = 7; numFileNames = 0; decode = True; for (aa = argList; aa != NULL; aa = aa->link) { if (ISFLAG("--")) { decode = False; continue; } if (aa->name[0] == '-' && decode) continue; numFileNames++; if (longestFileName < (Int32)strlen(aa->name) ) longestFileName = (Int32)strlen(aa->name); } /*-- Determine source modes; flag handling may change this too. --*/ if (numFileNames == 0) srcMode = SM_I2O; else srcMode = SM_F2F; /*-- Determine what to do (compress/uncompress/test/cat). --*/ /*-- Note that subsequent flag handling may change this. --*/ opMode = OM_Z; if ( (strstr ( progName, "unzip" ) != 0) || (strstr ( progName, "UNZIP" ) != 0) ) opMode = OM_UNZ; if ( (strstr ( progName, "z2cat" ) != 0) || (strstr ( progName, "Z2CAT" ) != 0) || (strstr ( progName, "zcat" ) != 0) || (strstr ( progName, "ZCAT" ) != 0) ) { opMode = OM_UNZ; srcMode = (numFileNames == 0) ? SM_I2O : SM_F2O; } /*-- Look at the flags. --*/ for (aa = argList; aa != NULL; aa = aa->link) { if (ISFLAG("--")) break; if (aa->name[0] == '-' && aa->name[1] != '-') { for (j = 1; aa->name[j] != '\0'; j++) { switch (aa->name[j]) { case 'c': srcMode = SM_F2O; break; case 'd': opMode = OM_UNZ; break; case 'z': opMode = OM_Z; break; case 'f': forceOverwrite = True; break; case 't': opMode = OM_TEST; break; case 'k': keepInputFiles = True; break; case 's': smallMode = True; break; case 'q': noisy = False; break; case '1': blockSize100k = 1; break; case '2': blockSize100k = 2; break; case '3': blockSize100k = 3; break; case '4': blockSize100k = 4; break; case '5': blockSize100k = 5; break; case '6': blockSize100k = 6; break; case '7': blockSize100k = 7; break; case '8': blockSize100k = 8; break; case '9': blockSize100k = 9; break; case 'V': case 'L': license(); break; case 'v': verbosity++; break; case 'h': usage ( progName ); exit ( 0 ); break; default: (fprintf) ( stderr, "%s: Bad flag `%s'\n", progName, aa->name ); usage ( progName ); exit ( 1 ); break; } } } } /*-- And again ... --*/ for (aa = argList; aa != NULL; aa = aa->link) { if (ISFLAG("--")) break; if (ISFLAG("--stdout")) srcMode = SM_F2O; else if (ISFLAG("--decompress")) opMode = OM_UNZ; else if (ISFLAG("--compress")) opMode = OM_Z; else if (ISFLAG("--force")) forceOverwrite = True; else if (ISFLAG("--test")) opMode = OM_TEST; else if (ISFLAG("--keep")) keepInputFiles = True; else if (ISFLAG("--small")) smallMode = True; else if (ISFLAG("--quiet")) noisy = False; else if (ISFLAG("--version")) license(); else if (ISFLAG("--license")) license(); else if (ISFLAG("--exponential")) workFactor = 1; else if (ISFLAG("--repetitive-best")) redundant(aa->name); else if (ISFLAG("--repetitive-fast")) redundant(aa->name); else if (ISFLAG("--fast")) blockSize100k = 1; else if (ISFLAG("--best")) blockSize100k = 9; else if (ISFLAG("--verbose")) verbosity++; else if (ISFLAG("--help")) { usage ( progName ); exit ( 0 ); } else if (strncmp ( aa->name, "--", 2) == 0) { (fprintf) ( stderr, "%s: Bad flag `%s'\n", progName, aa->name ); usage ( progName ); exit ( 1 ); } } if (verbosity > 4) verbosity = 4; if (opMode == OM_Z && smallMode && blockSize100k > 2) blockSize100k = 2; if (opMode == OM_TEST && srcMode == SM_F2O) { (fprintf) ( stderr, "%s: -c and -t cannot be used together.\n", progName ); exit ( 1 ); } if (srcMode == SM_F2O && numFileNames == 0) srcMode = SM_I2O; if (opMode != OM_Z) blockSize100k = 0; if (srcMode == SM_F2F) { signal (SIGINT, mySignalCatcher); signal (SIGTERM, mySignalCatcher); # if BZ_UNIX signal (SIGHUP, mySignalCatcher); # endif } if (opMode == OM_Z) { if (srcMode == SM_I2O) { compress ( NULL ); } else { decode = True; for (aa = argList; aa != NULL; aa = aa->link) { if (ISFLAG("--")) { decode = False; continue; } if (aa->name[0] == '-' && decode) continue; numFilesProcessed++; compress ( aa->name ); } } } else if (opMode == OM_UNZ) { unzFailsExist = False; if (srcMode == SM_I2O) { uncompress ( NULL ); } else { decode = True; for (aa = argList; aa != NULL; aa = aa->link) { if (ISFLAG("--")) { decode = False; continue; } if (aa->name[0] == '-' && decode) continue; numFilesProcessed++; uncompress ( aa->name ); } } if (unzFailsExist) { setExit(2); exit(exitValue); } } else { testFailsExist = False; if (srcMode == SM_I2O) { testf ( NULL ); } else { decode = True; for (aa = argList; aa != NULL; aa = aa->link) { if (ISFLAG("--")) { decode = False; continue; } if (aa->name[0] == '-' && decode) continue; numFilesProcessed++; testf ( aa->name ); } } if (testFailsExist) { if (noisy) { (fprintf) ( stderr, "\n" "You can use the `bzip2recover' program to attempt to recover\n" "data from undamaged sections of corrupted files.\n\n" ); } setExit(2); exit(exitValue); } } /* Free the argument list memory to mollify leak detectors (eg) Purify, Checker. Serves no other useful purpose. */ aa = argList; while (aa != NULL) { Cell* aa2 = aa->link; if (aa->name != NULL) free(aa->name); free(aa); aa = aa2; } return exitValue; } /*-----------------------------------------------------------*/ /*--- end bzip2.c ---*/ /*-----------------------------------------------------------*/
56,661
1,949
jart/cosmopolitan
false
cosmopolitan/third_party/bzip2/LICENSE
-------------------------------------------------------------------------- This program, "bzip2", the associated library "libbzip2", and all documentation, are copyright (C) 1996-2019 Julian R Seward. All rights reserved. Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met: 1. Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer. 2. The origin of this software must not be misrepresented; you must not claim that you wrote the original software. If you use this software in a product, an acknowledgment in the product documentation would be appreciated but is not required. 3. Altered source versions must be plainly marked as such, and must not be misrepresented as being the original software. 4. The name of the author may not be used to endorse or promote products derived from this software without specific prior written permission. THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. Julian Seward, [email protected] bzip2/libbzip2 version 1.0.8 of 13 July 2019 --------------------------------------------------------------------------
1,896
43
jart/cosmopolitan
false
cosmopolitan/third_party/bzip2/words1
Doing 6 tests (3 compress, 3 uncompress) ... If there's a problem, things might stop at this point.
103
5
jart/cosmopolitan
false
cosmopolitan/third_party/bzip2/words2
Checking test results. If any of the four "cmp"s which follow report any differences, something is wrong. If you can't easily figure out what, please let me know ([email protected]).
185
6
jart/cosmopolitan
false
cosmopolitan/third_party/bzip2/blocksort.c
/* clang-format off */ /*-------------------------------------------------------------*/ /*--- Block sorting machinery ---*/ /*--- blocksort.c ---*/ /*-------------------------------------------------------------*/ /* ------------------------------------------------------------------ This file is part of bzip2/libbzip2, a program and library for lossless, block-sorting data compression. bzip2/libbzip2 version 1.0.8 of 13 July 2019 Copyright (C) 1996-2019 Julian Seward <[email protected]> Please read the WARNING, DISCLAIMER and PATENTS sections in the README file. This program is released under the terms of the license contained in the file LICENSE. ------------------------------------------------------------------ */ #include "libc/mem/gc.internal.h" #include "libc/mem/mem.h" #include "third_party/bzip2/bzlib_private.inc" /*---------------------------------------------*/ /*--- Fallback O(N log(N)^2) sorting ---*/ /*--- algorithm, for repetitive blocks ---*/ /*---------------------------------------------*/ /*---------------------------------------------*/ static __inline__ void fallbackSimpleSort ( UInt32* fmap, UInt32* eclass, Int32 lo, Int32 hi ) { Int32 i, j, tmp; UInt32 ec_tmp; if (lo == hi) return; if (hi - lo > 3) { for ( i = hi-4; i >= lo; i-- ) { tmp = fmap[i]; ec_tmp = eclass[tmp]; for ( j = i+4; j <= hi && ec_tmp > eclass[fmap[j]]; j += 4 ) fmap[j-4] = fmap[j]; fmap[j-4] = tmp; } } for ( i = hi-1; i >= lo; i-- ) { tmp = fmap[i]; ec_tmp = eclass[tmp]; for ( j = i+1; j <= hi && ec_tmp > eclass[fmap[j]]; j++ ) fmap[j-1] = fmap[j]; fmap[j-1] = tmp; } } /*---------------------------------------------*/ #define fswap(zz1, zz2) \ { Int32 zztmp = zz1; zz1 = zz2; zz2 = zztmp; } #define fvswap(zzp1, zzp2, zzn) \ { \ Int32 yyp1 = (zzp1); \ Int32 yyp2 = (zzp2); \ Int32 yyn = (zzn); \ while (yyn > 0) { \ fswap(fmap[yyp1], fmap[yyp2]); \ yyp1++; yyp2++; yyn--; \ } \ } #define fmin(a,b) ((a) < (b)) ? (a) : (b) #define fpush(lz,hz) { stackLo[sp] = lz; \ stackHi[sp] = hz; \ sp++; } #define fpop(lz,hz) { sp--; \ lz = stackLo[sp]; \ hz = stackHi[sp]; } #define FALLBACK_QSORT_SMALL_THRESH 10 #define FALLBACK_QSORT_STACK_SIZE 100 static void fallbackQSort3 ( UInt32* fmap, UInt32* eclass, Int32 loSt, Int32 hiSt ) { Int32 unLo, unHi, ltLo, gtHi, n, m; Int32 sp, lo, hi; UInt32 med, r, r3; Int32 stackLo[FALLBACK_QSORT_STACK_SIZE]; Int32 stackHi[FALLBACK_QSORT_STACK_SIZE]; r = 0; sp = 0; fpush ( loSt, hiSt ); while (sp > 0) { AssertH ( sp < FALLBACK_QSORT_STACK_SIZE - 1, 1004 ); fpop ( lo, hi ); if (hi - lo < FALLBACK_QSORT_SMALL_THRESH) { fallbackSimpleSort ( fmap, eclass, lo, hi ); continue; } /* Random partitioning. Median of 3 sometimes fails to avoid bad cases. Median of 9 seems to help but looks rather expensive. This too seems to work but is cheaper. Guidance for the magic constants 7621 and 32768 is taken from Sedgewick's algorithms book, chapter 35. */ r = ((r * 7621) + 1) % 32768; r3 = r % 3; if (r3 == 0) med = eclass[fmap[lo]]; else if (r3 == 1) med = eclass[fmap[(lo+hi)>>1]]; else med = eclass[fmap[hi]]; unLo = ltLo = lo; unHi = gtHi = hi; while (1) { while (1) { if (unLo > unHi) break; n = (Int32)eclass[fmap[unLo]] - (Int32)med; if (n == 0) { fswap(fmap[unLo], fmap[ltLo]); ltLo++; unLo++; continue; }; if (n > 0) break; unLo++; } while (1) { if (unLo > unHi) break; n = (Int32)eclass[fmap[unHi]] - (Int32)med; if (n == 0) { fswap(fmap[unHi], fmap[gtHi]); gtHi--; unHi--; continue; }; if (n < 0) break; unHi--; } if (unLo > unHi) break; fswap(fmap[unLo], fmap[unHi]); unLo++; unHi--; } AssertD ( unHi == unLo-1, "fallbackQSort3(2)" ); if (gtHi < ltLo) continue; n = fmin(ltLo-lo, unLo-ltLo); fvswap(lo, unLo-n, n); m = fmin(hi-gtHi, gtHi-unHi); fvswap(unLo, hi-m+1, m); n = lo + unLo - ltLo - 1; m = hi - (gtHi - unHi) + 1; if (n - lo > hi - m) { fpush ( lo, n ); fpush ( m, hi ); } else { fpush ( m, hi ); fpush ( lo, n ); } } } #undef fmin #undef fpush #undef fpop #undef fswap #undef fvswap #undef FALLBACK_QSORT_SMALL_THRESH #undef FALLBACK_QSORT_STACK_SIZE /*---------------------------------------------*/ /* Pre: nblock > 0 eclass exists for [0 .. nblock-1] ((UChar*)eclass) [0 .. nblock-1] holds block ptr exists for [0 .. nblock-1] Post: ((UChar*)eclass) [0 .. nblock-1] holds block All other areas of eclass destroyed fmap [0 .. nblock-1] holds sorted order bhtab [ 0 .. 2+(nblock/32) ] destroyed */ #define SET_BH(zz) bhtab[(zz) >> 5] |= ((UInt32)1 << ((zz) & 31)) #define CLEAR_BH(zz) bhtab[(zz) >> 5] &= ~((UInt32)1 << ((zz) & 31)) #define ISSET_BH(zz) (bhtab[(zz) >> 5] & ((UInt32)1 << ((zz) & 31))) #define WORD_BH(zz) bhtab[(zz) >> 5] #define UNALIGNED_BH(zz) ((zz) & 0x01f) static void fallbackSort ( UInt32* fmap, UInt32* eclass, UInt32* bhtab, Int32 nblock, Int32 verb ) { Int32 ftab[257]; Int32 ftabCopy[256]; Int32 H, i, j, k, l, r, cc, cc1; Int32 nNotDone; Int32 nBhtab; UChar* eclass8 = (UChar*)eclass; /*-- Initial 1-char radix sort to generate initial fmap and initial BH bits. --*/ if (verb >= 4) VPrintf0 ( " bucket sorting ...\n" ); for (i = 0; i < 257; i++) ftab[i] = 0; for (i = 0; i < nblock; i++) ftab[eclass8[i]]++; for (i = 0; i < 256; i++) ftabCopy[i] = ftab[i]; for (i = 1; i < 257; i++) ftab[i] += ftab[i-1]; for (i = 0; i < nblock; i++) { j = eclass8[i]; k = ftab[j] - 1; ftab[j] = k; fmap[k] = i; } nBhtab = 2 + (nblock / 32); for (i = 0; i < nBhtab; i++) bhtab[i] = 0; for (i = 0; i < 256; i++) SET_BH(ftab[i]); /*-- Inductively refine the buckets. Kind-of an "exponential radix sort" (!), inspired by the Manber-Myers suffix array construction algorithm. --*/ /*-- set sentinel bits for block-end detection --*/ for (i = 0; i < 32; i++) { SET_BH(nblock + 2*i); CLEAR_BH(nblock + 2*i + 1); } /*-- the log(N) loop --*/ H = 1; while (1) { if (verb >= 4) VPrintf1 ( " depth %6d has ", H ); j = 0; for (i = 0; i < nblock; i++) { if (ISSET_BH(i)) j = i; k = fmap[i] - H; if (k < 0) k += nblock; eclass[k] = j; } nNotDone = 0; r = -1; while (1) { /*-- find the next non-singleton bucket --*/ k = r + 1; while (ISSET_BH(k) && UNALIGNED_BH(k)) k++; if (ISSET_BH(k)) { while (WORD_BH(k) == 0xffffffff) k += 32; while (ISSET_BH(k)) k++; } l = k - 1; if (l >= nblock) break; while (!ISSET_BH(k) && UNALIGNED_BH(k)) k++; if (!ISSET_BH(k)) { while (WORD_BH(k) == 0x00000000) k += 32; while (!ISSET_BH(k)) k++; } r = k - 1; if (r >= nblock) break; /*-- now [l, r] bracket current bucket --*/ if (r > l) { nNotDone += (r - l + 1); fallbackQSort3 ( fmap, eclass, l, r ); /*-- scan bucket and generate header bits-- */ cc = -1; for (i = l; i <= r; i++) { cc1 = eclass[fmap[i]]; if (cc != cc1) { SET_BH(i); cc = cc1; }; } } } if (verb >= 4) VPrintf1 ( "%6d unresolved strings\n", nNotDone ); H *= 2; if (H > nblock || nNotDone == 0) break; } /*-- Reconstruct the original block in eclass8 [0 .. nblock-1], since the previous phase destroyed it. --*/ if (verb >= 4) VPrintf0 ( " reconstructing block ...\n" ); j = 0; for (i = 0; i < nblock; i++) { while (ftabCopy[j] == 0) j++; ftabCopy[j]--; eclass8[fmap[i]] = (UChar)j; } AssertH ( j < 256, 1005 ); } #undef SET_BH #undef CLEAR_BH #undef ISSET_BH #undef WORD_BH #undef UNALIGNED_BH /*---------------------------------------------*/ /*--- The main, O(N^2 log(N)) sorting ---*/ /*--- algorithm. Faster for "normal" ---*/ /*--- non-repetitive blocks. ---*/ /*---------------------------------------------*/ /*---------------------------------------------*/ static __inline__ Bool mainGtU ( UInt32 i1, UInt32 i2, UChar* block, UInt16* quadrant, UInt32 nblock, Int32* budget ) { Int32 k; UChar c1, c2; UInt16 s1, s2; AssertD ( i1 != i2, "mainGtU" ); /* 1 */ c1 = block[i1]; c2 = block[i2]; if (c1 != c2) return (c1 > c2); i1++; i2++; /* 2 */ c1 = block[i1]; c2 = block[i2]; if (c1 != c2) return (c1 > c2); i1++; i2++; /* 3 */ c1 = block[i1]; c2 = block[i2]; if (c1 != c2) return (c1 > c2); i1++; i2++; /* 4 */ c1 = block[i1]; c2 = block[i2]; if (c1 != c2) return (c1 > c2); i1++; i2++; /* 5 */ c1 = block[i1]; c2 = block[i2]; if (c1 != c2) return (c1 > c2); i1++; i2++; /* 6 */ c1 = block[i1]; c2 = block[i2]; if (c1 != c2) return (c1 > c2); i1++; i2++; /* 7 */ c1 = block[i1]; c2 = block[i2]; if (c1 != c2) return (c1 > c2); i1++; i2++; /* 8 */ c1 = block[i1]; c2 = block[i2]; if (c1 != c2) return (c1 > c2); i1++; i2++; /* 9 */ c1 = block[i1]; c2 = block[i2]; if (c1 != c2) return (c1 > c2); i1++; i2++; /* 10 */ c1 = block[i1]; c2 = block[i2]; if (c1 != c2) return (c1 > c2); i1++; i2++; /* 11 */ c1 = block[i1]; c2 = block[i2]; if (c1 != c2) return (c1 > c2); i1++; i2++; /* 12 */ c1 = block[i1]; c2 = block[i2]; if (c1 != c2) return (c1 > c2); i1++; i2++; k = nblock + 8; do { /* 1 */ c1 = block[i1]; c2 = block[i2]; if (c1 != c2) return (c1 > c2); s1 = quadrant[i1]; s2 = quadrant[i2]; if (s1 != s2) return (s1 > s2); i1++; i2++; /* 2 */ c1 = block[i1]; c2 = block[i2]; if (c1 != c2) return (c1 > c2); s1 = quadrant[i1]; s2 = quadrant[i2]; if (s1 != s2) return (s1 > s2); i1++; i2++; /* 3 */ c1 = block[i1]; c2 = block[i2]; if (c1 != c2) return (c1 > c2); s1 = quadrant[i1]; s2 = quadrant[i2]; if (s1 != s2) return (s1 > s2); i1++; i2++; /* 4 */ c1 = block[i1]; c2 = block[i2]; if (c1 != c2) return (c1 > c2); s1 = quadrant[i1]; s2 = quadrant[i2]; if (s1 != s2) return (s1 > s2); i1++; i2++; /* 5 */ c1 = block[i1]; c2 = block[i2]; if (c1 != c2) return (c1 > c2); s1 = quadrant[i1]; s2 = quadrant[i2]; if (s1 != s2) return (s1 > s2); i1++; i2++; /* 6 */ c1 = block[i1]; c2 = block[i2]; if (c1 != c2) return (c1 > c2); s1 = quadrant[i1]; s2 = quadrant[i2]; if (s1 != s2) return (s1 > s2); i1++; i2++; /* 7 */ c1 = block[i1]; c2 = block[i2]; if (c1 != c2) return (c1 > c2); s1 = quadrant[i1]; s2 = quadrant[i2]; if (s1 != s2) return (s1 > s2); i1++; i2++; /* 8 */ c1 = block[i1]; c2 = block[i2]; if (c1 != c2) return (c1 > c2); s1 = quadrant[i1]; s2 = quadrant[i2]; if (s1 != s2) return (s1 > s2); i1++; i2++; if (i1 >= nblock) i1 -= nblock; if (i2 >= nblock) i2 -= nblock; k -= 8; (*budget)--; } while (k >= 0); return False; } /*---------------------------------------------*/ /*-- Knuth's increments seem to work better than Incerpi-Sedgewick here. Possibly because the number of elems to sort is usually small, typically <= 20. --*/ static Int32 incs[14] = { 1, 4, 13, 40, 121, 364, 1093, 3280, 9841, 29524, 88573, 265720, 797161, 2391484 }; static void mainSimpleSort ( UInt32* ptr, UChar* block, UInt16* quadrant, Int32 nblock, Int32 lo, Int32 hi, Int32 d, Int32* budget ) { Int32 i, j, h, bigN, hp; UInt32 v; bigN = hi - lo + 1; if (bigN < 2) return; hp = 0; while (incs[hp] < bigN) hp++; hp--; for (; hp >= 0; hp--) { h = incs[hp]; i = lo + h; while (True) { /*-- copy 1 --*/ if (i > hi) break; v = ptr[i]; j = i; while ( mainGtU ( ptr[j-h]+d, v+d, block, quadrant, nblock, budget ) ) { ptr[j] = ptr[j-h]; j = j - h; if (j <= (lo + h - 1)) break; } ptr[j] = v; i++; /*-- copy 2 --*/ if (i > hi) break; v = ptr[i]; j = i; while ( mainGtU ( ptr[j-h]+d, v+d, block, quadrant, nblock, budget ) ) { ptr[j] = ptr[j-h]; j = j - h; if (j <= (lo + h - 1)) break; } ptr[j] = v; i++; /*-- copy 3 --*/ if (i > hi) break; v = ptr[i]; j = i; while ( mainGtU ( ptr[j-h]+d, v+d, block, quadrant, nblock, budget ) ) { ptr[j] = ptr[j-h]; j = j - h; if (j <= (lo + h - 1)) break; } ptr[j] = v; i++; if (*budget < 0) return; } } } /*---------------------------------------------*/ /*-- The following is an implementation of an elegant 3-way quicksort for strings, described in a paper "Fast Algorithms for Sorting and Searching Strings", by Robert Sedgewick and Jon L. Bentley. --*/ #define mswap(zz1, zz2) \ { Int32 zztmp = zz1; zz1 = zz2; zz2 = zztmp; } #define mvswap(zzp1, zzp2, zzn) \ { \ Int32 yyp1 = (zzp1); \ Int32 yyp2 = (zzp2); \ Int32 yyn = (zzn); \ while (yyn > 0) { \ mswap(ptr[yyp1], ptr[yyp2]); \ yyp1++; yyp2++; yyn--; \ } \ } static __inline__ UChar mmed3 ( UChar a, UChar b, UChar c ) { UChar t; if (a > b) { t = a; a = b; b = t; }; if (b > c) { b = c; if (a > b) b = a; } return b; } #define mmin(a,b) ((a) < (b)) ? (a) : (b) #define mpush(lz,hz,dz) { stackLo[sp] = lz; \ stackHi[sp] = hz; \ stackD [sp] = dz; \ sp++; } #define mpop(lz,hz,dz) { sp--; \ lz = stackLo[sp]; \ hz = stackHi[sp]; \ dz = stackD [sp]; } #define mnextsize(az) (nextHi[az]-nextLo[az]) #define mnextswap(az,bz) \ { Int32 tz; \ tz = nextLo[az]; nextLo[az] = nextLo[bz]; nextLo[bz] = tz; \ tz = nextHi[az]; nextHi[az] = nextHi[bz]; nextHi[bz] = tz; \ tz = nextD [az]; nextD [az] = nextD [bz]; nextD [bz] = tz; } #define MAIN_QSORT_SMALL_THRESH 20 #define MAIN_QSORT_DEPTH_THRESH (BZ_N_RADIX + BZ_N_QSORT) #define MAIN_QSORT_STACK_SIZE 100 static void mainQSort3 ( UInt32* ptr, UChar* block, UInt16* quadrant, Int32 nblock, Int32 loSt, Int32 hiSt, Int32 dSt, Int32* budget ) { Int32 unLo, unHi, ltLo, gtHi, n, m, med; Int32 sp, lo, hi, d; Int32 stackLo[MAIN_QSORT_STACK_SIZE]; Int32 stackHi[MAIN_QSORT_STACK_SIZE]; Int32 stackD [MAIN_QSORT_STACK_SIZE]; Int32 nextLo[3]; Int32 nextHi[3]; Int32 nextD [3]; sp = 0; mpush ( loSt, hiSt, dSt ); while (sp > 0) { AssertH ( sp < MAIN_QSORT_STACK_SIZE - 2, 1001 ); mpop ( lo, hi, d ); if (hi - lo < MAIN_QSORT_SMALL_THRESH || d > MAIN_QSORT_DEPTH_THRESH) { mainSimpleSort ( ptr, block, quadrant, nblock, lo, hi, d, budget ); if (*budget < 0) return; continue; } med = (Int32) mmed3 ( block[ptr[ lo ]+d], block[ptr[ hi ]+d], block[ptr[ (lo+hi)>>1 ]+d] ); unLo = ltLo = lo; unHi = gtHi = hi; while (True) { while (True) { if (unLo > unHi) break; n = ((Int32)block[ptr[unLo]+d]) - med; if (n == 0) { mswap(ptr[unLo], ptr[ltLo]); ltLo++; unLo++; continue; }; if (n > 0) break; unLo++; } while (True) { if (unLo > unHi) break; n = ((Int32)block[ptr[unHi]+d]) - med; if (n == 0) { mswap(ptr[unHi], ptr[gtHi]); gtHi--; unHi--; continue; }; if (n < 0) break; unHi--; } if (unLo > unHi) break; mswap(ptr[unLo], ptr[unHi]); unLo++; unHi--; } AssertD ( unHi == unLo-1, "mainQSort3(2)" ); if (gtHi < ltLo) { mpush(lo, hi, d+1 ); continue; } n = mmin(ltLo-lo, unLo-ltLo); mvswap(lo, unLo-n, n); m = mmin(hi-gtHi, gtHi-unHi); mvswap(unLo, hi-m+1, m); n = lo + unLo - ltLo - 1; m = hi - (gtHi - unHi) + 1; nextLo[0] = lo; nextHi[0] = n; nextD[0] = d; nextLo[1] = m; nextHi[1] = hi; nextD[1] = d; nextLo[2] = n+1; nextHi[2] = m-1; nextD[2] = d+1; if (mnextsize(0) < mnextsize(1)) mnextswap(0,1); if (mnextsize(1) < mnextsize(2)) mnextswap(1,2); if (mnextsize(0) < mnextsize(1)) mnextswap(0,1); AssertD (mnextsize(0) >= mnextsize(1), "mainQSort3(8)" ); AssertD (mnextsize(1) >= mnextsize(2), "mainQSort3(9)" ); mpush (nextLo[0], nextHi[0], nextD[0]); mpush (nextLo[1], nextHi[1], nextD[1]); mpush (nextLo[2], nextHi[2], nextD[2]); } } #undef mswap #undef mvswap #undef mpush #undef mpop #undef mmin #undef mnextsize #undef mnextswap #undef MAIN_QSORT_SMALL_THRESH #undef MAIN_QSORT_DEPTH_THRESH #undef MAIN_QSORT_STACK_SIZE /*---------------------------------------------*/ /* Pre: nblock > N_OVERSHOOT block32 exists for [0 .. nblock-1 +N_OVERSHOOT] ((UChar*)block32) [0 .. nblock-1] holds block ptr exists for [0 .. nblock-1] Post: ((UChar*)block32) [0 .. nblock-1] holds block All other areas of block32 destroyed ftab [0 .. 65536 ] destroyed ptr [0 .. nblock-1] holds sorted order if (*budget < 0), sorting was abandoned */ #define BIGFREQ(b) (ftab[((b)+1) << 8] - ftab[(b) << 8]) #define SETMASK (1 << 21) #define CLEARMASK (~(SETMASK)) static void mainSort ( UInt32* ptr, UChar* block, UInt16* quadrant, UInt32* ftab, Int32 nblock, Int32 verb, Int32* budget ) { Int32 i, j, k, ss, sb; Bool bigDone[256]; Int32 *runningOrder = gc(calloc(256,4)); Int32 *copyStart = gc(calloc(256,4)); Int32 *copyEnd = gc(calloc(256,4)); UChar c1; Int32 numQSorted; UInt16 s; if (verb >= 4) VPrintf0 ( " main sort initialise ...\n" ); /*-- set up the 2-byte frequency table --*/ for (i = 65536; i >= 0; i--) ftab[i] = 0; j = block[0] << 8; i = nblock-1; for (; i >= 3; i -= 4) { quadrant[i] = 0; j = (j >> 8) | ( ((UInt16)block[i]) << 8); ftab[j]++; quadrant[i-1] = 0; j = (j >> 8) | ( ((UInt16)block[i-1]) << 8); ftab[j]++; quadrant[i-2] = 0; j = (j >> 8) | ( ((UInt16)block[i-2]) << 8); ftab[j]++; quadrant[i-3] = 0; j = (j >> 8) | ( ((UInt16)block[i-3]) << 8); ftab[j]++; } for (; i >= 0; i--) { quadrant[i] = 0; j = (j >> 8) | ( ((UInt16)block[i]) << 8); ftab[j]++; } /*-- (emphasises close relationship of block & quadrant) --*/ for (i = 0; i < BZ_N_OVERSHOOT; i++) { block [nblock+i] = block[i]; quadrant[nblock+i] = 0; } if (verb >= 4) VPrintf0 ( " bucket sorting ...\n" ); /*-- Complete the initial radix sort --*/ for (i = 1; i <= 65536; i++) ftab[i] += ftab[i-1]; s = block[0] << 8; i = nblock-1; for (; i >= 3; i -= 4) { s = (s >> 8) | (block[i] << 8); j = ftab[s] -1; ftab[s] = j; ptr[j] = i; s = (s >> 8) | (block[i-1] << 8); j = ftab[s] -1; ftab[s] = j; ptr[j] = i-1; s = (s >> 8) | (block[i-2] << 8); j = ftab[s] -1; ftab[s] = j; ptr[j] = i-2; s = (s >> 8) | (block[i-3] << 8); j = ftab[s] -1; ftab[s] = j; ptr[j] = i-3; } for (; i >= 0; i--) { s = (s >> 8) | (block[i] << 8); j = ftab[s] -1; ftab[s] = j; ptr[j] = i; } /*-- Now ftab contains the first loc of every small bucket. Calculate the running order, from smallest to largest big bucket. --*/ for (i = 0; i <= 255; i++) { bigDone [i] = False; runningOrder[i] = i; } { Int32 vv; Int32 h = 1; do h = 3 * h + 1; while (h <= 256); do { h = h / 3; for (i = h; i <= 255; i++) { vv = runningOrder[i]; j = i; while ( BIGFREQ(runningOrder[j-h]) > BIGFREQ(vv) ) { runningOrder[j] = runningOrder[j-h]; j = j - h; if (j <= (h - 1)) goto zero; } zero: runningOrder[j] = vv; } } while (h != 1); } /*-- The main sorting loop. --*/ numQSorted = 0; for (i = 0; i <= 255; i++) { /*-- Process big buckets, starting with the least full. Basically this is a 3-step process in which we call mainQSort3 to sort the small buckets [ss, j], but also make a big effort to avoid the calls if we can. --*/ ss = runningOrder[i]; /*-- Step 1: Complete the big bucket [ss] by quicksorting any unsorted small buckets [ss, j], for j != ss. Hopefully previous pointer-scanning phases have already completed many of the small buckets [ss, j], so we don't have to sort them at all. --*/ for (j = 0; j <= 255; j++) { if (j != ss) { sb = (ss << 8) + j; if ( ! (ftab[sb] & SETMASK) ) { Int32 lo = ftab[sb] & CLEARMASK; Int32 hi = (ftab[sb+1] & CLEARMASK) - 1; if (hi > lo) { if (verb >= 4) VPrintf4 ( " qsort [0x%x, 0x%x] " "done %d this %d\n", ss, j, numQSorted, hi - lo + 1 ); mainQSort3 ( ptr, block, quadrant, nblock, lo, hi, BZ_N_RADIX, budget ); numQSorted += (hi - lo + 1); if (*budget < 0) return; } } ftab[sb] |= SETMASK; } } AssertH ( !bigDone[ss], 1006 ); /*-- Step 2: Now scan this big bucket [ss] so as to synthesise the sorted order for small buckets [t, ss] for all t, including, magically, the bucket [ss,ss] too. This will avoid doing Real Work in subsequent Step 1's. --*/ { for (j = 0; j <= 255; j++) { copyStart[j] = ftab[(j << 8) + ss] & CLEARMASK; copyEnd [j] = (ftab[(j << 8) + ss + 1] & CLEARMASK) - 1; } for (j = ftab[ss << 8] & CLEARMASK; j < copyStart[ss]; j++) { k = ptr[j]-1; if (k < 0) k += nblock; c1 = block[k]; if (!bigDone[c1]) ptr[ copyStart[c1]++ ] = k; } for (j = (ftab[(ss+1) << 8] & CLEARMASK) - 1; j > copyEnd[ss]; j--) { k = ptr[j]-1; if (k < 0) k += nblock; c1 = block[k]; if (!bigDone[c1]) ptr[ copyEnd[c1]-- ] = k; } } AssertH ( (copyStart[ss]-1 == copyEnd[ss]) || /* Extremely rare case missing in bzip2-1.0.0 and 1.0.1. Necessity for this case is demonstrated by compressing a sequence of approximately 48.5 million of character 251; 1.0.0/1.0.1 will then die here. */ (copyStart[ss] == 0 && copyEnd[ss] == nblock-1), 1007 ) for (j = 0; j <= 255; j++) ftab[(j << 8) + ss] |= SETMASK; /*-- Step 3: The [ss] big bucket is now done. Record this fact, and update the quadrant descriptors. Remember to update quadrants in the overshoot area too, if necessary. The "if (i < 255)" test merely skips this updating for the last bucket processed, since updating for the last bucket is pointless. The quadrant array provides a way to incrementally cache sort orderings, as they appear, so as to make subsequent comparisons in fullGtU() complete faster. For repetitive blocks this makes a big difference (but not big enough to be able to avoid the fallback sorting mechanism, exponential radix sort). The precise meaning is: at all times: for 0 <= i < nblock and 0 <= j <= nblock if block[i] != block[j], then the relative values of quadrant[i] and quadrant[j] are meaningless. else { if quadrant[i] < quadrant[j] then the string starting at i lexicographically precedes the string starting at j else if quadrant[i] > quadrant[j] then the string starting at j lexicographically precedes the string starting at i else the relative ordering of the strings starting at i and j has not yet been determined. } --*/ bigDone[ss] = True; if (i < 255) { Int32 bbStart = ftab[ss << 8] & CLEARMASK; Int32 bbSize = (ftab[(ss+1) << 8] & CLEARMASK) - bbStart; Int32 shifts = 0; while ((bbSize >> shifts) > 65534) shifts++; for (j = bbSize-1; j >= 0; j--) { Int32 a2update = ptr[bbStart + j]; UInt16 qVal = (UInt16)(j >> shifts); quadrant[a2update] = qVal; if (a2update < BZ_N_OVERSHOOT) quadrant[a2update + nblock] = qVal; } AssertH ( ((bbSize-1) >> shifts) <= 65535, 1002 ); } } if (verb >= 4) VPrintf3 ( " %d pointers, %d sorted, %d scanned\n", nblock, numQSorted, nblock - numQSorted ); } #undef BIGFREQ #undef SETMASK #undef CLEARMASK /*---------------------------------------------*/ /* Pre: nblock > 0 arr2 exists for [0 .. nblock-1 +N_OVERSHOOT] ((UChar*)arr2) [0 .. nblock-1] holds block arr1 exists for [0 .. nblock-1] Post: ((UChar*)arr2) [0 .. nblock-1] holds block All other areas of block destroyed ftab [ 0 .. 65536 ] destroyed arr1 [0 .. nblock-1] holds sorted order */ void BZ2_blockSort ( EState* s ) { UInt32* ptr = s->ptr; UChar* block = s->block; UInt32* ftab = s->ftab; Int32 nblock = s->nblock; Int32 verb = s->verbosity; Int32 wfact = s->workFactor; UInt16* quadrant; Int32 budget; Int32 budgetInit; Int32 i; if (nblock < 10000) { fallbackSort ( s->arr1, s->arr2, ftab, nblock, verb ); } else { /* Calculate the location for quadrant, remembering to get the alignment right. Assumes that &(block[0]) is at least 2-byte aligned -- this should be ok since block is really the first section of arr2. */ i = nblock+BZ_N_OVERSHOOT; if (i & 1) i++; quadrant = (UInt16*)(&(block[i])); /* (wfact-1) / 3 puts the default-factor-30 transition point at very roughly the same place as with v0.1 and v0.9.0. Not that it particularly matters any more, since the resulting compressed stream is now the same regardless of whether or not we use the main sort or fallback sort. */ if (wfact < 1 ) wfact = 1; if (wfact > 100) wfact = 100; budgetInit = nblock * ((wfact-1) / 3); budget = budgetInit; mainSort ( ptr, block, quadrant, ftab, nblock, verb, &budget ); if (verb >= 3) VPrintf3 ( " %d work, %d block, ratio %5.2f\n", budgetInit - budget, nblock, (float)(budgetInit - budget) / (float)(nblock==0 ? 1 : nblock) ); if (budget < 0) { if (verb >= 2) VPrintf0 ( " too repetitive; using fallback" " sorting algorithm\n" ); fallbackSort ( s->arr1, s->arr2, ftab, nblock, verb ); } } s->origPtr = -1; for (i = 0; i < s->nblock; i++) if (ptr[i] == 0) { s->origPtr = i; break; }; AssertH( s->origPtr != -1, 1003 ); } /*-------------------------------------------------------------*/ /*--- end blocksort.c ---*/ /*-------------------------------------------------------------*/
30,862
1,098
jart/cosmopolitan
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cosmopolitan/third_party/bzip2/sample1.bz2
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false
cosmopolitan/third_party/bzip2/CHANGES
------------------------------------------------------------------ This file is part of bzip2/libbzip2, a program and library for lossless, block-sorting data compression. bzip2/libbzip2 version 1.0.8 of 13 July 2019 Copyright (C) 1996-2019 Julian Seward <[email protected]> Please read the WARNING, DISCLAIMER and PATENTS sections in the README file. This program is released under the terms of the license contained in the file LICENSE. ------------------------------------------------------------------ 0.9.0 ~~~~~ First version. 0.9.0a ~~~~~~ Removed 'ranlib' from Makefile, since most modern Unix-es don't need it, or even know about it. 0.9.0b ~~~~~~ Fixed a problem with error reporting in bzip2.c. This does not effect the library in any way. Problem is: versions 0.9.0 and 0.9.0a (of the program proper) compress and decompress correctly, but give misleading error messages (internal panics) when an I/O error occurs, instead of reporting the problem correctly. This shouldn't give any data loss (as far as I can see), but is confusing. Made the inline declarations disappear for non-GCC compilers. 0.9.0c ~~~~~~ Fixed some problems in the library pertaining to some boundary cases. This makes the library behave more correctly in those situations. The fixes apply only to features (calls and parameters) not used by bzip2.c, so the non-fixedness of them in previous versions has no effect on reliability of bzip2.c. In bzlib.c: * made zero-length BZ_FLUSH work correctly in bzCompress(). * fixed bzWrite/bzRead to ignore zero-length requests. * fixed bzread to correctly handle read requests after EOF. * wrong parameter order in call to bzDecompressInit in bzBuffToBuffDecompress. Fixed. In compress.c: * changed setting of nGroups in sendMTFValues() so as to do a bit better on small files. This _does_ effect bzip2.c. 0.9.5a ~~~~~~ Major change: add a fallback sorting algorithm (blocksort.c) to give reasonable behaviour even for very repetitive inputs. Nuked --repetitive-best and --repetitive-fast since they are no longer useful. Minor changes: mostly a whole bunch of small changes/ bugfixes in the driver (bzip2.c). Changes pertaining to the user interface are: allow decompression of symlink'd files to stdout decompress/test files even without .bz2 extension give more accurate error messages for I/O errors when compressing/decompressing to stdout, don't catch control-C read flags from BZIP2 and BZIP environment variables decline to break hard links to a file unless forced with -f allow -c flag even with no filenames preserve file ownerships as far as possible make -s -1 give the expected block size (100k) add a flag -q --quiet to suppress nonessential warnings stop decoding flags after --, so files beginning in - can be handled resolved inconsistent naming: bzcat or bz2cat ? bzip2 --help now returns 0 Programming-level changes are: fixed syntax error in GET_LL4 for Borland C++ 5.02 let bzBuffToBuffDecompress return BZ_DATA_ERROR{_MAGIC} fix overshoot of mode-string end in bzopen_or_bzdopen wrapped bzlib.h in #ifdef __cplusplus ... extern "C" { ... } close file handles under all error conditions added minor mods so it compiles with DJGPP out of the box fixed Makefile so it doesn't give problems with BSD make fix uninitialised memory reads in dlltest.c 0.9.5b ~~~~~~ Open stdin/stdout in binary mode for DJGPP. 0.9.5c ~~~~~~ Changed BZ_N_OVERSHOOT to be ... + 2 instead of ... + 1. The + 1 version could cause the sorted order to be wrong in some extremely obscure cases. Also changed setting of quadrant in blocksort.c. 0.9.5d ~~~~~~ The only functional change is to make bzlibVersion() in the library return the correct string. This has no effect whatsoever on the functioning of the bzip2 program or library. Added a couple of casts so the library compiles without warnings at level 3 in MS Visual Studio 6.0. Included a Y2K statement in the file Y2K_INFO. All other changes are minor documentation changes. 1.0 ~~~ Several minor bugfixes and enhancements: * Large file support. The library uses 64-bit counters to count the volume of data passing through it. bzip2.c is now compiled with -D_FILE_OFFSET_BITS=64 to get large file support from the C library. -v correctly prints out file sizes greater than 4 gigabytes. All these changes have been made without assuming a 64-bit platform or a C compiler which supports 64-bit ints, so, except for the C library aspect, they are fully portable. * Decompression robustness. The library/program should be robust to any corruption of compressed data, detecting and handling _all_ corruption, instead of merely relying on the CRCs. What this means is that the program should never crash, given corrupted data, and the library should always return BZ_DATA_ERROR. * Fixed an obscure race-condition bug only ever observed on Solaris, in which, if you were very unlucky and issued control-C at exactly the wrong time, both input and output files would be deleted. * Don't run out of file handles on test/decompression when large numbers of files have invalid magic numbers. * Avoid library namespace pollution. Prefix all exported symbols with BZ2_. * Minor sorting enhancements from my DCC2000 paper. * Advance the version number to 1.0, so as to counteract the (false-in-this-case) impression some people have that programs with version numbers less than 1.0 are in some way, experimental, pre-release versions. * Create an initial Makefile-libbz2_so to build a shared library. Yes, I know I should really use libtool et al ... * Make the program exit with 2 instead of 0 when decompression fails due to a bad magic number (ie, an invalid bzip2 header). Also exit with 1 (as the manual claims :-) whenever a diagnostic message would have been printed AND the corresponding operation is aborted, for example bzip2: Output file xx already exists. When a diagnostic message is printed but the operation is not aborted, for example bzip2: Can't guess original name for wurble -- using wurble.out then the exit value 0 is returned, unless some other problem is also detected. I think it corresponds more closely to what the manual claims now. 1.0.1 ~~~~~ * Modified dlltest.c so it uses the new BZ2_ naming scheme. * Modified makefile-msc to fix minor build probs on Win2k. * Updated README.COMPILATION.PROBLEMS. There are no functionality changes or bug fixes relative to version 1.0.0. This is just a documentation update + a fix for minor Win32 build problems. For almost everyone, upgrading from 1.0.0 to 1.0.1 is utterly pointless. Don't bother. 1.0.2 ~~~~~ A bug fix release, addressing various minor issues which have appeared in the 18 or so months since 1.0.1 was released. Most of the fixes are to do with file-handling or documentation bugs. To the best of my knowledge, there have been no data-loss-causing bugs reported in the compression/decompression engine of 1.0.0 or 1.0.1. Note that this release does not improve the rather crude build system for Unix platforms. The general plan here is to autoconfiscate/ libtoolise 1.0.2 soon after release, and release the result as 1.1.0 or perhaps 1.2.0. That, however, is still just a plan at this point. Here are the changes in 1.0.2. Bug-reporters and/or patch-senders in parentheses. * Fix an infinite segfault loop in 1.0.1 when a directory is encountered in -f (force) mode. (Trond Eivind Glomsrod, Nicholas Nethercote, Volker Schmidt) * Avoid double fclose() of output file on certain I/O error paths. (Solar Designer) * Don't fail with internal error 1007 when fed a long stream (> 48MB) of byte 251. Also print useful message suggesting that 1007s may be caused by bad memory. (noticed by Juan Pedro Vallejo, fixed by me) * Fix uninitialised variable silly bug in demo prog dlltest.c. (Jorj Bauer) * Remove 512-MB limitation on recovered file size for bzip2recover on selected platforms which support 64-bit ints. At the moment all GCC supported platforms, and Win32. (me, Alson van der Meulen) * Hard-code header byte values, to give correct operation on platforms using EBCDIC as their native character set (IBM's OS/390). (Leland Lucius) * Copy file access times correctly. (Marty Leisner) * Add distclean and check targets to Makefile. (Michael Carmack) * Parameterise use of ar and ranlib in Makefile. Also add $(LDFLAGS). (Rich Ireland, Bo Thorsen) * Pass -p (create parent dirs as needed) to mkdir during make install. (Jeremy Fusco) * Dereference symlinks when copying file permissions in -f mode. (Volker Schmidt) * Majorly simplify implementation of uInt64_qrm10. (Bo Lindbergh) * Check the input file still exists before deleting the output one, when aborting in cleanUpAndFail(). (Joerg Prante, Robert Linden, Matthias Krings) Also a bunch of patches courtesy of Philippe Troin, the Debian maintainer of bzip2: * Wrapper scripts (with manpages): bzdiff, bzgrep, bzmore. * Spelling changes and minor enhancements in bzip2.1. * Avoid race condition between creating the output file and setting its interim permissions safely, by using fopen_output_safely(). No changes to bzip2recover since there is no issue with file permissions there. * do not print senseless report with -v when compressing an empty file. * bzcat -f works on non-bzip2 files. * do not try to escape shell meta-characters on unix (the shell takes care of these). * added --fast and --best aliases for -1 -9 for gzip compatibility. 1.0.3 (15 Feb 05) ~~~~~~~~~~~~~~~~~ Fixes some minor bugs since the last version, 1.0.2. * Further robustification against corrupted compressed data. There are currently no known bitstreams which can cause the decompressor to crash, loop or access memory which does not belong to it. If you are using bzip2 or the library to decompress bitstreams from untrusted sources, an upgrade to 1.0.3 is recommended. This fixes CAN-2005-1260. * The documentation has been converted to XML, from which html and pdf can be derived. * Various minor bugs in the documentation have been fixed. * Fixes for various compilation warnings with newer versions of gcc, and on 64-bit platforms. * The BZ_NO_STDIO cpp symbol was not properly observed in 1.0.2. This has been fixed. 1.0.4 (20 Dec 06) ~~~~~~~~~~~~~~~~~ Fixes some minor bugs since the last version, 1.0.3. * Fix file permissions race problem (CAN-2005-0953). * Avoid possible segfault in BZ2_bzclose. From Coverity's NetBSD scan. * 'const'/prototype cleanups in the C code. * Change default install location to /usr/local, and handle multiple 'make install's without error. * Sanitise file names more carefully in bzgrep. Fixes CAN-2005-0758 to the extent that applies to bzgrep. * Use 'mktemp' rather than 'tempfile' in bzdiff. * Tighten up a couple of assertions in blocksort.c following automated analysis. * Fix minor doc/comment bugs. 1.0.5 (10 Dec 07) ~~~~~~~~~~~~~~~~~ Security fix only. Fixes CERT-FI 20469 as it applies to bzip2. 1.0.6 (6 Sept 10) ~~~~~~~~~~~~~~~~~ * Security fix for CVE-2010-0405. This was reported by Mikolaj Izdebski. * Make the documentation build on Ubuntu 10.04 1.0.7 (27 Jun 19) ~~~~~~~~~~~~~~~~~ * Fix undefined behavior in the macros SET_BH, CLEAR_BH, & ISSET_BH * bzip2: Fix return value when combining --test,-t and -q. * bzip2recover: Fix buffer overflow for large argv[0] * bzip2recover: Fix use after free issue with outFile (CVE-2016-3189) * Make sure nSelectors is not out of range (CVE-2019-12900) 1.0.8 (13 Jul 19) ~~~~~~~~~~~~~~~~~ * Accept as many selectors as the file format allows. This relaxes the fix for CVE-2019-12900 from 1.0.7 so that bzip2 allows decompression of bz2 files that use (too) many selectors again. * Fix handling of large (> 4GB) files on Windows. * Cleanup of bzdiff and bzgrep scripts so they don't use any bash extensions and handle multiple archives correctly. * There is now a bz2-files testsuite at https://sourceware.org/git/bzip2-tests.git
12,256
357
jart/cosmopolitan
false
cosmopolitan/third_party/bzip2/bzip2recover.c
#include "libc/calls/calls.h" #include "libc/errno.h" #include "libc/fmt/fmt.h" #include "libc/log/log.h" #include "libc/mem/mem.h" #include "libc/runtime/runtime.h" #include "libc/stdio/stdio.h" #include "libc/str/str.h" /* clang-format off */ /*-----------------------------------------------------------*/ /*--- Block recoverer program for bzip2 ---*/ /*--- bzip2recover.c ---*/ /*-----------------------------------------------------------*/ /* ------------------------------------------------------------------ This file is part of bzip2/libbzip2, a program and library for lossless, block-sorting data compression. bzip2/libbzip2 version 1.0.8 of 13 July 2019 Copyright (C) 1996-2019 Julian Seward <[email protected]> Please read the WARNING, DISCLAIMER and PATENTS sections in the README file. This program is released under the terms of the license contained in the file LICENSE. ------------------------------------------------------------------ */ /* This program is a complete hack and should be rewritten properly. It isn't very complicated. */ /* This program records bit locations in the file to be recovered. That means that if 64-bit ints are not supported, we will not be able to recover .bz2 files over 512MB (2^32 bits) long. On GNU supported platforms, we take advantage of the 64-bit int support to circumvent this problem. Ditto MSVC. This change occurred in version 1.0.2; all prior versions have the 512MB limitation. */ #ifdef __GNUC__ typedef unsigned long long int MaybeUInt64; # define MaybeUInt64_FMT "%Lu" #else #ifdef _MSC_VER typedef unsigned __int64 MaybeUInt64; # define MaybeUInt64_FMT "%I64u" #else typedef unsigned int MaybeUInt64; # define MaybeUInt64_FMT "%u" #endif #endif typedef unsigned int UInt32; typedef int Int32; typedef unsigned char UChar; typedef char Char; typedef unsigned char Bool; #define True ((Bool)1) #define False ((Bool)0) #define BZ_MAX_FILENAME 2000 Char inFileName[BZ_MAX_FILENAME]; Char outFileName[BZ_MAX_FILENAME]; Char progName[BZ_MAX_FILENAME]; MaybeUInt64 bytesOut = 0; MaybeUInt64 bytesIn = 0; /*---------------------------------------------------*/ /*--- Header bytes ---*/ /*---------------------------------------------------*/ #define BZ_HDR_B 0x42 /* 'B' */ #define BZ_HDR_Z 0x5a /* 'Z' */ #define BZ_HDR_h 0x68 /* 'h' */ #define BZ_HDR_0 0x30 /* '0' */ /*---------------------------------------------------*/ /*--- I/O errors ---*/ /*---------------------------------------------------*/ /*---------------------------------------------*/ static void readError ( void ) { (fprintf) ( stderr, "%s: I/O error reading `%s', possible reason follows.\n", progName, inFileName ); perror ( progName ); (fprintf) ( stderr, "%s: warning: output file(s) may be incomplete.\n", progName ); exit ( 1 ); } /*---------------------------------------------*/ static void writeError ( void ) { (fprintf) ( stderr, "%s: I/O error reading `%s', possible reason follows.\n", progName, inFileName ); perror ( progName ); (fprintf) ( stderr, "%s: warning: output file(s) may be incomplete.\n", progName ); exit ( 1 ); } /*---------------------------------------------*/ static void mallocFail ( Int32 n ) { (fprintf) ( stderr, "%s: malloc failed on request for %d bytes.\n", progName, n ); (fprintf) ( stderr, "%s: warning: output file(s) may be incomplete.\n", progName ); exit ( 1 ); } /*---------------------------------------------*/ static void tooManyBlocks ( Int32 max_handled_blocks ) { (fprintf) ( stderr, "%s: `%s' appears to contain more than %d blocks\n", progName, inFileName, max_handled_blocks ); (fprintf) ( stderr, "%s: and cannot be handled. To fix, increase\n", progName ); (fprintf) ( stderr, "%s: BZ_MAX_HANDLED_BLOCKS in bzip2recover.c, and recompile.\n", progName ); exit ( 1 ); } /*---------------------------------------------------*/ /*--- Bit stream I/O ---*/ /*---------------------------------------------------*/ typedef struct { FILE* handle; Int32 buffer; Int32 buffLive; Char mode; } BitStream; /*---------------------------------------------*/ static BitStream* bsOpenReadStream ( FILE* stream ) { BitStream *bs = malloc ( sizeof(BitStream) ); if (bs == NULL) mallocFail ( sizeof(BitStream) ); bs->handle = stream; bs->buffer = 0; bs->buffLive = 0; bs->mode = 'r'; return bs; } /*---------------------------------------------*/ static BitStream* bsOpenWriteStream ( FILE* stream ) { BitStream *bs = malloc ( sizeof(BitStream) ); if (bs == NULL) mallocFail ( sizeof(BitStream) ); bs->handle = stream; bs->buffer = 0; bs->buffLive = 0; bs->mode = 'w'; return bs; } /*---------------------------------------------*/ static void bsPutBit ( BitStream* bs, Int32 bit ) { if (bs->buffLive == 8) { Int32 retVal = putc ( (UChar) bs->buffer, bs->handle ); if (retVal == EOF) writeError(); bytesOut++; bs->buffLive = 1; bs->buffer = bit & 0x1; } else { bs->buffer = ( (bs->buffer << 1) | (bit & 0x1) ); bs->buffLive++; }; } /*---------------------------------------------*/ /*-- Returns 0 or 1, or 2 to indicate EOF. --*/ static Int32 bsGetBit ( BitStream* bs ) { if (bs->buffLive > 0) { bs->buffLive --; return ( ((bs->buffer) >> (bs->buffLive)) & 0x1 ); } else { Int32 retVal = getc ( bs->handle ); if ( retVal == EOF ) { if (errno != 0) readError(); return 2; } bs->buffLive = 7; bs->buffer = retVal; return ( ((bs->buffer) >> 7) & 0x1 ); } } /*---------------------------------------------*/ static void bsClose ( BitStream* bs ) { Int32 retVal; if ( bs->mode == 'w' ) { while ( bs->buffLive < 8 ) { bs->buffLive++; bs->buffer <<= 1; }; retVal = putc ( (UChar) (bs->buffer), bs->handle ); if (retVal == EOF) writeError(); bytesOut++; retVal = fflush ( bs->handle ); if (retVal == EOF) writeError(); } retVal = fclose ( bs->handle ); if (retVal == EOF) { if (bs->mode == 'w') writeError(); else readError(); } free ( bs ); } /*---------------------------------------------*/ static void bsPutUChar ( BitStream* bs, UChar c ) { Int32 i; for (i = 7; i >= 0; i--) bsPutBit ( bs, (((UInt32) c) >> i) & 0x1 ); } /*---------------------------------------------*/ static void bsPutUInt32 ( BitStream* bs, UInt32 c ) { Int32 i; for (i = 31; i >= 0; i--) bsPutBit ( bs, (c >> i) & 0x1 ); } /*---------------------------------------------*/ static Bool endsInBz2 ( Char* name ) { Int32 n = strlen ( name ); if (n <= 4) return False; return (name[n-4] == '.' && name[n-3] == 'b' && name[n-2] == 'z' && name[n-1] == '2'); } /*---------------------------------------------------*/ /*--- ---*/ /*---------------------------------------------------*/ /* This logic isn't really right when it comes to Cygwin. */ #ifdef _WIN32 # define BZ_SPLIT_SYM '\\' /* path splitter on Windows platform */ #else # define BZ_SPLIT_SYM '/' /* path splitter on Unix platform */ #endif #define BLOCK_HEADER_HI 0x00003141UL #define BLOCK_HEADER_LO 0x59265359UL #define BLOCK_ENDMARK_HI 0x00001772UL #define BLOCK_ENDMARK_LO 0x45385090UL /* Increase if necessary. However, a .bz2 file with > 50000 blocks would have an uncompressed size of at least 40GB, so the chances are low you'll need to up this. */ #define BZ_MAX_HANDLED_BLOCKS 50000 MaybeUInt64 bStart [BZ_MAX_HANDLED_BLOCKS]; MaybeUInt64 bEnd [BZ_MAX_HANDLED_BLOCKS]; MaybeUInt64 rbStart[BZ_MAX_HANDLED_BLOCKS]; MaybeUInt64 rbEnd [BZ_MAX_HANDLED_BLOCKS]; Int32 main ( Int32 argc, Char** argv ) { FILE* inFile; FILE* outFile; BitStream* bsIn, *bsWr; Int32 b, wrBlock, currBlock, rbCtr; MaybeUInt64 bitsRead; UInt32 buffHi, buffLo, blockCRC; Char* p; strncpy ( progName, argv[0], BZ_MAX_FILENAME-1); progName[BZ_MAX_FILENAME-1]='\0'; inFileName[0] = outFileName[0] = 0; (fprintf) ( stderr, "bzip2recover 1.0.8: extracts blocks from damaged .bz2 files.\n" ); if (argc != 2) { (fprintf) ( stderr, "%s: usage is `%s damaged_file_name'.\n", progName, progName ); switch (sizeof(MaybeUInt64)) { case 8: (fprintf)(stderr, "\trestrictions on size of recovered file: None\n"); break; case 4: (fprintf)(stderr, "\trestrictions on size of recovered file: 512 MB\n"); (fprintf)(stderr, "\tto circumvent, recompile with MaybeUInt64 as an\n" "\tunsigned 64-bit int.\n"); break; default: (fprintf)(stderr, "\tsizeof(MaybeUInt64) is not 4 or 8 -- " "configuration error.\n"); break; } exit(1); } if (strlen(argv[1]) >= BZ_MAX_FILENAME-20) { (fprintf) ( stderr, "%s: supplied filename is suspiciously (>= %d chars) long. Bye!\n", progName, (int)strlen(argv[1]) ); exit(1); } strcpy ( inFileName, argv[1] ); inFile = fopen ( inFileName, "rb" ); if (inFile == NULL) { (fprintf) ( stderr, "%s: can't read `%s'\n", progName, inFileName ); exit(1); } bsIn = bsOpenReadStream ( inFile ); (fprintf) ( stderr, "%s: searching for block boundaries ...\n", progName ); bitsRead = 0; buffHi = buffLo = 0; currBlock = 0; bStart[currBlock] = 0; rbCtr = 0; while (True) { b = bsGetBit ( bsIn ); bitsRead++; if (b == 2) { if (bitsRead >= bStart[currBlock] && (bitsRead - bStart[currBlock]) >= 40) { bEnd[currBlock] = bitsRead-1; if (currBlock > 0) (fprintf) ( stderr, " block %d runs from " MaybeUInt64_FMT " to " MaybeUInt64_FMT " (incomplete)\n", currBlock, bStart[currBlock], bEnd[currBlock] ); } else currBlock--; break; } buffHi = (buffHi << 1) | (buffLo >> 31); buffLo = (buffLo << 1) | (b & 1); if ( ( (buffHi & 0x0000ffff) == BLOCK_HEADER_HI && buffLo == BLOCK_HEADER_LO) || ( (buffHi & 0x0000ffff) == BLOCK_ENDMARK_HI && buffLo == BLOCK_ENDMARK_LO) ) { if (bitsRead > 49) { bEnd[currBlock] = bitsRead-49; } else { bEnd[currBlock] = 0; } if (currBlock > 0 && (bEnd[currBlock] - bStart[currBlock]) >= 130) { (fprintf) ( stderr, " block %d runs from " MaybeUInt64_FMT " to " MaybeUInt64_FMT "\n", rbCtr+1, bStart[currBlock], bEnd[currBlock] ); rbStart[rbCtr] = bStart[currBlock]; rbEnd[rbCtr] = bEnd[currBlock]; rbCtr++; } if (currBlock >= BZ_MAX_HANDLED_BLOCKS) tooManyBlocks(BZ_MAX_HANDLED_BLOCKS); currBlock++; bStart[currBlock] = bitsRead; } } bsClose ( bsIn ); /*-- identified blocks run from 1 to rbCtr inclusive. --*/ if (rbCtr < 1) { (fprintf) ( stderr, "%s: sorry, I couldn't find any block boundaries.\n", progName ); exit(1); }; (fprintf) ( stderr, "%s: splitting into blocks\n", progName ); inFile = fopen ( inFileName, "rb" ); if (inFile == NULL) { (fprintf) ( stderr, "%s: can't open `%s'\n", progName, inFileName ); exit(1); } bsIn = bsOpenReadStream ( inFile ); /*-- placate gcc's dataflow analyser --*/ blockCRC = 0; bsWr = 0; bitsRead = 0; outFile = NULL; wrBlock = 0; while (True) { b = bsGetBit(bsIn); if (b == 2) break; buffHi = (buffHi << 1) | (buffLo >> 31); buffLo = (buffLo << 1) | (b & 1); if (bitsRead == 47+rbStart[wrBlock]) blockCRC = (buffHi << 16) | (buffLo >> 16); if (outFile != NULL && bitsRead >= rbStart[wrBlock] && bitsRead <= rbEnd[wrBlock]) { bsPutBit ( bsWr, b ); } bitsRead++; if (bitsRead == rbEnd[wrBlock]+1) { if (outFile != NULL) { bsPutUChar ( bsWr, 0x17 ); bsPutUChar ( bsWr, 0x72 ); bsPutUChar ( bsWr, 0x45 ); bsPutUChar ( bsWr, 0x38 ); bsPutUChar ( bsWr, 0x50 ); bsPutUChar ( bsWr, 0x90 ); bsPutUInt32 ( bsWr, blockCRC ); bsClose ( bsWr ); outFile = NULL; } if (wrBlock >= rbCtr) break; wrBlock++; } else if (bitsRead == rbStart[wrBlock]) { /* Create the output file name, correctly handling leading paths. (31.10.2001 by Sergey E. Kusikov) */ Char* split; Int32 ofs, k; for (k = 0; k < BZ_MAX_FILENAME; k++) outFileName[k] = 0; strcpy (outFileName, inFileName); split = strrchr (outFileName, BZ_SPLIT_SYM); if (split == NULL) { split = outFileName; } else { ++split; } /* Now split points to the start of the basename. */ ofs = split - outFileName; (sprintf) (split, "rec%5d", wrBlock+1); for (p = split; *p != 0; p++) if (*p == ' ') *p = '0'; strcat (outFileName, inFileName + ofs); if ( !endsInBz2(outFileName)) strcat ( outFileName, ".bz2" ); (fprintf) ( stderr, " writing block %d to `%s' ...\n", wrBlock+1, outFileName ); outFile = fopen ( outFileName, "wb" ); if (outFile == NULL) { (fprintf) ( stderr, "%s: can't write `%s'\n", progName, outFileName ); exit(1); } bsWr = bsOpenWriteStream ( outFile ); bsPutUChar ( bsWr, BZ_HDR_B ); bsPutUChar ( bsWr, BZ_HDR_Z ); bsPutUChar ( bsWr, BZ_HDR_h ); bsPutUChar ( bsWr, BZ_HDR_0 + 9 ); bsPutUChar ( bsWr, 0x31 ); bsPutUChar ( bsWr, 0x41 ); bsPutUChar ( bsWr, 0x59 ); bsPutUChar ( bsWr, 0x26 ); bsPutUChar ( bsWr, 0x53 ); bsPutUChar ( bsWr, 0x59 ); } } (fprintf) ( stderr, "%s: finished\n", progName ); return 0; } /*-----------------------------------------------------------*/ /*--- end bzip2recover.c ---*/ /*-----------------------------------------------------------*/
15,223
521
jart/cosmopolitan
false
cosmopolitan/third_party/bzip2/compress.c
/* clang-format off */ /*-------------------------------------------------------------*/ /*--- Compression machinery (not incl block sorting) ---*/ /*--- compress.c ---*/ /*-------------------------------------------------------------*/ /* ------------------------------------------------------------------ This file is part of bzip2/libbzip2, a program and library for lossless, block-sorting data compression. bzip2/libbzip2 version 1.0.8 of 13 July 2019 Copyright (C) 1996-2019 Julian Seward <[email protected]> Please read the WARNING, DISCLAIMER and PATENTS sections in the README file. This program is released under the terms of the license contained in the file LICENSE. ------------------------------------------------------------------ */ /* CHANGES 0.9.0 -- original version. 0.9.0a/b -- no changes in this file. 0.9.0c -- changed setting of nGroups in sendMTFValues() so as to do a bit better on small files */ #include "third_party/bzip2/bzlib_private.inc" /*---------------------------------------------------*/ /*--- Bit stream I/O ---*/ /*---------------------------------------------------*/ /*---------------------------------------------------*/ void BZ2_bsInitWrite ( EState* s ) { s->bsLive = 0; s->bsBuff = 0; } /*---------------------------------------------------*/ static void bsFinishWrite ( EState* s ) { while (s->bsLive > 0) { s->zbits[s->numZ] = (UChar)(s->bsBuff >> 24); s->numZ++; s->bsBuff <<= 8; s->bsLive -= 8; } } /*---------------------------------------------------*/ #define bsNEEDW(nz) \ { \ while (s->bsLive >= 8) { \ s->zbits[s->numZ] \ = (UChar)(s->bsBuff >> 24); \ s->numZ++; \ s->bsBuff <<= 8; \ s->bsLive -= 8; \ } \ } /*---------------------------------------------------*/ static __inline__ void bsW ( EState* s, Int32 n, UInt32 v ) { bsNEEDW ( n ); s->bsBuff |= (v << (32 - s->bsLive - n)); s->bsLive += n; } /*---------------------------------------------------*/ static void bsPutUInt32 ( EState* s, UInt32 u ) { bsW ( s, 8, (u >> 24) & 0xffL ); bsW ( s, 8, (u >> 16) & 0xffL ); bsW ( s, 8, (u >> 8) & 0xffL ); bsW ( s, 8, u & 0xffL ); } /*---------------------------------------------------*/ static void bsPutUChar ( EState* s, UChar c ) { bsW( s, 8, (UInt32)c ); } /*---------------------------------------------------*/ /*--- The back end proper ---*/ /*---------------------------------------------------*/ /*---------------------------------------------------*/ static void makeMaps_e ( EState* s ) { Int32 i; s->nInUse = 0; for (i = 0; i < 256; i++) if (s->inUse[i]) { s->unseqToSeq[i] = s->nInUse; s->nInUse++; } } /*---------------------------------------------------*/ static void generateMTFValues ( EState* s ) { UChar yy[256]; Int32 i, j; Int32 zPend; Int32 wr; Int32 EOB; /* After sorting (eg, here), s->arr1 [ 0 .. s->nblock-1 ] holds sorted order, and ((UChar*)s->arr2) [ 0 .. s->nblock-1 ] holds the original block data. The first thing to do is generate the MTF values, and put them in ((UInt16*)s->arr1) [ 0 .. s->nblock-1 ]. Because there are strictly fewer or equal MTF values than block values, ptr values in this area are overwritten with MTF values only when they are no longer needed. The final compressed bitstream is generated into the area starting at (UChar*) (&((UChar*)s->arr2)[s->nblock]) These storage aliases are set up in bzCompressInit(), except for the last one, which is arranged in compressBlock(). */ UInt32* ptr = s->ptr; UChar* block = s->block; UInt16* mtfv = s->mtfv; makeMaps_e ( s ); EOB = s->nInUse+1; for (i = 0; i <= EOB; i++) s->mtfFreq[i] = 0; wr = 0; zPend = 0; for (i = 0; i < s->nInUse; i++) yy[i] = (UChar) i; for (i = 0; i < s->nblock; i++) { UChar ll_i; AssertD ( wr <= i, "generateMTFValues(1)" ); j = ptr[i]-1; if (j < 0) j += s->nblock; ll_i = s->unseqToSeq[block[j]]; AssertD ( ll_i < s->nInUse, "generateMTFValues(2a)" ); if (yy[0] == ll_i) { zPend++; } else { if (zPend > 0) { zPend--; while (True) { if (zPend & 1) { mtfv[wr] = BZ_RUNB; wr++; s->mtfFreq[BZ_RUNB]++; } else { mtfv[wr] = BZ_RUNA; wr++; s->mtfFreq[BZ_RUNA]++; } if (zPend < 2) break; zPend = (zPend - 2) / 2; }; zPend = 0; } { register UChar rtmp; register UChar* ryy_j; register UChar rll_i; rtmp = yy[1]; yy[1] = yy[0]; ryy_j = &(yy[1]); rll_i = ll_i; while ( rll_i != rtmp ) { register UChar rtmp2; ryy_j++; rtmp2 = rtmp; rtmp = *ryy_j; *ryy_j = rtmp2; }; yy[0] = rtmp; j = ryy_j - &(yy[0]); mtfv[wr] = j+1; wr++; s->mtfFreq[j+1]++; } } } if (zPend > 0) { zPend--; while (True) { if (zPend & 1) { mtfv[wr] = BZ_RUNB; wr++; s->mtfFreq[BZ_RUNB]++; } else { mtfv[wr] = BZ_RUNA; wr++; s->mtfFreq[BZ_RUNA]++; } if (zPend < 2) break; zPend = (zPend - 2) / 2; }; zPend = 0; } mtfv[wr] = EOB; wr++; s->mtfFreq[EOB]++; s->nMTF = wr; } /*---------------------------------------------------*/ #define BZ_LESSER_ICOST 0 #define BZ_GREATER_ICOST 15 static void sendMTFValues ( EState* s ) { Int32 v, t, i, j, gs, ge, totc, bt, bc, iter; Int32 nSelectors=0, alphaSize, minLen, maxLen, selCtr; Int32 nGroups, nBytes; /*-- UChar len [BZ_N_GROUPS][BZ_MAX_ALPHA_SIZE]; is a global since the decoder also needs it. Int32 code[BZ_N_GROUPS][BZ_MAX_ALPHA_SIZE]; Int32 rfreq[BZ_N_GROUPS][BZ_MAX_ALPHA_SIZE]; are also globals only used in this proc. Made global to keep stack frame size small. --*/ UInt16 cost[BZ_N_GROUPS]; Int32 fave[BZ_N_GROUPS]; UInt16* mtfv = s->mtfv; if (s->verbosity >= 3) VPrintf3( " %d in block, %d after MTF & 1-2 coding, " "%d+2 syms in use\n", s->nblock, s->nMTF, s->nInUse ); alphaSize = s->nInUse+2; for (t = 0; t < BZ_N_GROUPS; t++) for (v = 0; v < alphaSize; v++) s->len[t][v] = BZ_GREATER_ICOST; /*--- Decide how many coding tables to use ---*/ AssertH ( s->nMTF > 0, 3001 ); if (s->nMTF < 200) nGroups = 2; else if (s->nMTF < 600) nGroups = 3; else if (s->nMTF < 1200) nGroups = 4; else if (s->nMTF < 2400) nGroups = 5; else nGroups = 6; /*--- Generate an initial set of coding tables ---*/ { Int32 nPart, remF, tFreq, aFreq; nPart = nGroups; remF = s->nMTF; gs = 0; while (nPart > 0) { tFreq = remF / nPart; ge = gs-1; aFreq = 0; while (aFreq < tFreq && ge < alphaSize-1) { ge++; aFreq += s->mtfFreq[ge]; } if (ge > gs && nPart != nGroups && nPart != 1 && ((nGroups-nPart) % 2 == 1)) { aFreq -= s->mtfFreq[ge]; ge--; } if (s->verbosity >= 3) VPrintf5( " initial group %d, [%d .. %d], " "has %d syms (%4.1f%%)\n", nPart, gs, ge, aFreq, (100.0 * (float)aFreq) / (float)(s->nMTF) ); for (v = 0; v < alphaSize; v++) if (v >= gs && v <= ge) s->len[nPart-1][v] = BZ_LESSER_ICOST; else s->len[nPart-1][v] = BZ_GREATER_ICOST; nPart--; gs = ge+1; remF -= aFreq; } } /*--- Iterate up to BZ_N_ITERS times to improve the tables. ---*/ for (iter = 0; iter < BZ_N_ITERS; iter++) { for (t = 0; t < nGroups; t++) fave[t] = 0; for (t = 0; t < nGroups; t++) for (v = 0; v < alphaSize; v++) s->rfreq[t][v] = 0; /*--- Set up an auxiliary length table which is used to fast-track the common case (nGroups == 6). ---*/ if (nGroups == 6) { for (v = 0; v < alphaSize; v++) { s->len_pack[v][0] = (s->len[1][v] << 16) | s->len[0][v]; s->len_pack[v][1] = (s->len[3][v] << 16) | s->len[2][v]; s->len_pack[v][2] = (s->len[5][v] << 16) | s->len[4][v]; } } nSelectors = 0; totc = 0; gs = 0; while (True) { /*--- Set group start & end marks. --*/ if (gs >= s->nMTF) break; ge = gs + BZ_G_SIZE - 1; if (ge >= s->nMTF) ge = s->nMTF-1; /*-- Calculate the cost of this group as coded by each of the coding tables. --*/ for (t = 0; t < nGroups; t++) cost[t] = 0; if (nGroups == 6 && 50 == ge-gs+1) { /*--- fast track the common case ---*/ register UInt32 cost01, cost23, cost45; register UInt16 icv; cost01 = cost23 = cost45 = 0; # define BZ_ITER(nn) \ icv = mtfv[gs+(nn)]; \ cost01 += s->len_pack[icv][0]; \ cost23 += s->len_pack[icv][1]; \ cost45 += s->len_pack[icv][2]; \ BZ_ITER(0); BZ_ITER(1); BZ_ITER(2); BZ_ITER(3); BZ_ITER(4); BZ_ITER(5); BZ_ITER(6); BZ_ITER(7); BZ_ITER(8); BZ_ITER(9); BZ_ITER(10); BZ_ITER(11); BZ_ITER(12); BZ_ITER(13); BZ_ITER(14); BZ_ITER(15); BZ_ITER(16); BZ_ITER(17); BZ_ITER(18); BZ_ITER(19); BZ_ITER(20); BZ_ITER(21); BZ_ITER(22); BZ_ITER(23); BZ_ITER(24); BZ_ITER(25); BZ_ITER(26); BZ_ITER(27); BZ_ITER(28); BZ_ITER(29); BZ_ITER(30); BZ_ITER(31); BZ_ITER(32); BZ_ITER(33); BZ_ITER(34); BZ_ITER(35); BZ_ITER(36); BZ_ITER(37); BZ_ITER(38); BZ_ITER(39); BZ_ITER(40); BZ_ITER(41); BZ_ITER(42); BZ_ITER(43); BZ_ITER(44); BZ_ITER(45); BZ_ITER(46); BZ_ITER(47); BZ_ITER(48); BZ_ITER(49); # undef BZ_ITER cost[0] = cost01 & 0xffff; cost[1] = cost01 >> 16; cost[2] = cost23 & 0xffff; cost[3] = cost23 >> 16; cost[4] = cost45 & 0xffff; cost[5] = cost45 >> 16; } else { /*--- slow version which correctly handles all situations ---*/ for (i = gs; i <= ge; i++) { UInt16 icv = mtfv[i]; for (t = 0; t < nGroups; t++) cost[t] += s->len[t][icv]; } } /*-- Find the coding table which is best for this group, and record its identity in the selector table. --*/ bc = 999999999; bt = -1; for (t = 0; t < nGroups; t++) if (cost[t] < bc) { bc = cost[t]; bt = t; }; totc += bc; fave[bt]++; s->selector[nSelectors] = bt; nSelectors++; /*-- Increment the symbol frequencies for the selected table. --*/ if (nGroups == 6 && 50 == ge-gs+1) { /*--- fast track the common case ---*/ # define BZ_ITUR(nn) s->rfreq[bt][ mtfv[gs+(nn)] ]++ BZ_ITUR(0); BZ_ITUR(1); BZ_ITUR(2); BZ_ITUR(3); BZ_ITUR(4); BZ_ITUR(5); BZ_ITUR(6); BZ_ITUR(7); BZ_ITUR(8); BZ_ITUR(9); BZ_ITUR(10); BZ_ITUR(11); BZ_ITUR(12); BZ_ITUR(13); BZ_ITUR(14); BZ_ITUR(15); BZ_ITUR(16); BZ_ITUR(17); BZ_ITUR(18); BZ_ITUR(19); BZ_ITUR(20); BZ_ITUR(21); BZ_ITUR(22); BZ_ITUR(23); BZ_ITUR(24); BZ_ITUR(25); BZ_ITUR(26); BZ_ITUR(27); BZ_ITUR(28); BZ_ITUR(29); BZ_ITUR(30); BZ_ITUR(31); BZ_ITUR(32); BZ_ITUR(33); BZ_ITUR(34); BZ_ITUR(35); BZ_ITUR(36); BZ_ITUR(37); BZ_ITUR(38); BZ_ITUR(39); BZ_ITUR(40); BZ_ITUR(41); BZ_ITUR(42); BZ_ITUR(43); BZ_ITUR(44); BZ_ITUR(45); BZ_ITUR(46); BZ_ITUR(47); BZ_ITUR(48); BZ_ITUR(49); # undef BZ_ITUR } else { /*--- slow version which correctly handles all situations ---*/ for (i = gs; i <= ge; i++) s->rfreq[bt][ mtfv[i] ]++; } gs = ge+1; } if (s->verbosity >= 3) { VPrintf2 ( " pass %d: size is %d, grp uses are ", iter+1, totc/8 ); for (t = 0; t < nGroups; t++) VPrintf1 ( "%d ", fave[t] ); VPrintf0 ( "\n" ); } /*-- Recompute the tables based on the accumulated frequencies. --*/ /* maxLen was changed from 20 to 17 in bzip2-1.0.3. See comment in huffman.c for details. */ for (t = 0; t < nGroups; t++) BZ2_hbMakeCodeLengths ( &(s->len[t][0]), &(s->rfreq[t][0]), alphaSize, 17 /*20*/ ); } AssertH( nGroups < 8, 3002 ); AssertH( nSelectors < 32768 && nSelectors <= BZ_MAX_SELECTORS, 3003 ); /*--- Compute MTF values for the selectors. ---*/ { UChar pos[BZ_N_GROUPS], ll_i, tmp2, tmp; for (i = 0; i < nGroups; i++) pos[i] = i; for (i = 0; i < nSelectors; i++) { ll_i = s->selector[i]; j = 0; tmp = pos[j]; while ( ll_i != tmp ) { j++; tmp2 = tmp; tmp = pos[j]; pos[j] = tmp2; }; pos[0] = tmp; s->selectorMtf[i] = j; } }; /*--- Assign actual codes for the tables. --*/ for (t = 0; t < nGroups; t++) { minLen = 32; maxLen = 0; for (i = 0; i < alphaSize; i++) { if (s->len[t][i] > maxLen) maxLen = s->len[t][i]; if (s->len[t][i] < minLen) minLen = s->len[t][i]; } AssertH ( !(maxLen > 17 /*20*/ ), 3004 ); AssertH ( !(minLen < 1), 3005 ); BZ2_hbAssignCodes ( &(s->code[t][0]), &(s->len[t][0]), minLen, maxLen, alphaSize ); } /*--- Transmit the mapping table. ---*/ { Bool inUse16[16]; for (i = 0; i < 16; i++) { inUse16[i] = False; for (j = 0; j < 16; j++) if (s->inUse[i * 16 + j]) inUse16[i] = True; } nBytes = s->numZ; for (i = 0; i < 16; i++) if (inUse16[i]) bsW(s,1,1); else bsW(s,1,0); for (i = 0; i < 16; i++) if (inUse16[i]) for (j = 0; j < 16; j++) { if (s->inUse[i * 16 + j]) bsW(s,1,1); else bsW(s,1,0); } if (s->verbosity >= 3) VPrintf1( " bytes: mapping %d, ", s->numZ-nBytes ); } /*--- Now the selectors. ---*/ nBytes = s->numZ; bsW ( s, 3, nGroups ); bsW ( s, 15, nSelectors ); for (i = 0; i < nSelectors; i++) { for (j = 0; j < s->selectorMtf[i]; j++) bsW(s,1,1); bsW(s,1,0); } if (s->verbosity >= 3) VPrintf1( "selectors %d, ", s->numZ-nBytes ); /*--- Now the coding tables. ---*/ nBytes = s->numZ; for (t = 0; t < nGroups; t++) { Int32 curr = s->len[t][0]; bsW ( s, 5, curr ); for (i = 0; i < alphaSize; i++) { while (curr < s->len[t][i]) { bsW(s,2,2); curr++; /* 10 */ }; while (curr > s->len[t][i]) { bsW(s,2,3); curr--; /* 11 */ }; bsW ( s, 1, 0 ); } } if (s->verbosity >= 3) VPrintf1 ( "code lengths %d, ", s->numZ-nBytes ); /*--- And finally, the block data proper ---*/ nBytes = s->numZ; selCtr = 0; gs = 0; while (True) { if (gs >= s->nMTF) break; ge = gs + BZ_G_SIZE - 1; if (ge >= s->nMTF) ge = s->nMTF-1; AssertH ( s->selector[selCtr] < nGroups, 3006 ); if (nGroups == 6 && 50 == ge-gs+1) { /*--- fast track the common case ---*/ UInt16 mtfv_i; UChar* s_len_sel_selCtr = &(s->len[s->selector[selCtr]][0]); Int32* s_code_sel_selCtr = &(s->code[s->selector[selCtr]][0]); # define BZ_ITAH(nn) \ mtfv_i = mtfv[gs+(nn)]; \ bsW ( s, \ s_len_sel_selCtr[mtfv_i], \ s_code_sel_selCtr[mtfv_i] ) BZ_ITAH(0); BZ_ITAH(1); BZ_ITAH(2); BZ_ITAH(3); BZ_ITAH(4); BZ_ITAH(5); BZ_ITAH(6); BZ_ITAH(7); BZ_ITAH(8); BZ_ITAH(9); BZ_ITAH(10); BZ_ITAH(11); BZ_ITAH(12); BZ_ITAH(13); BZ_ITAH(14); BZ_ITAH(15); BZ_ITAH(16); BZ_ITAH(17); BZ_ITAH(18); BZ_ITAH(19); BZ_ITAH(20); BZ_ITAH(21); BZ_ITAH(22); BZ_ITAH(23); BZ_ITAH(24); BZ_ITAH(25); BZ_ITAH(26); BZ_ITAH(27); BZ_ITAH(28); BZ_ITAH(29); BZ_ITAH(30); BZ_ITAH(31); BZ_ITAH(32); BZ_ITAH(33); BZ_ITAH(34); BZ_ITAH(35); BZ_ITAH(36); BZ_ITAH(37); BZ_ITAH(38); BZ_ITAH(39); BZ_ITAH(40); BZ_ITAH(41); BZ_ITAH(42); BZ_ITAH(43); BZ_ITAH(44); BZ_ITAH(45); BZ_ITAH(46); BZ_ITAH(47); BZ_ITAH(48); BZ_ITAH(49); # undef BZ_ITAH } else { /*--- slow version which correctly handles all situations ---*/ for (i = gs; i <= ge; i++) { bsW ( s, s->len [s->selector[selCtr]] [mtfv[i]], s->code [s->selector[selCtr]] [mtfv[i]] ); } } gs = ge+1; selCtr++; } AssertH( selCtr == nSelectors, 3007 ); if (s->verbosity >= 3) VPrintf1( "codes %d\n", s->numZ-nBytes ); } /*---------------------------------------------------*/ void BZ2_compressBlock ( EState* s, Bool is_last_block ) { if (s->nblock > 0) { BZ_FINALISE_CRC ( s->blockCRC ); s->combinedCRC = (s->combinedCRC << 1) | (s->combinedCRC >> 31); s->combinedCRC ^= s->blockCRC; if (s->blockNo > 1) s->numZ = 0; if (s->verbosity >= 2) VPrintf4( " block %d: crc = 0x%08x, " "combined CRC = 0x%08x, size = %d\n", s->blockNo, s->blockCRC, s->combinedCRC, s->nblock ); BZ2_blockSort ( s ); } s->zbits = (UChar*) (&((UChar*)s->arr2)[s->nblock]); /*-- If this is the first block, create the stream header. --*/ if (s->blockNo == 1) { BZ2_bsInitWrite ( s ); bsPutUChar ( s, BZ_HDR_B ); bsPutUChar ( s, BZ_HDR_Z ); bsPutUChar ( s, BZ_HDR_h ); bsPutUChar ( s, (UChar)(BZ_HDR_0 + s->blockSize100k) ); } if (s->nblock > 0) { bsPutUChar ( s, 0x31 ); bsPutUChar ( s, 0x41 ); bsPutUChar ( s, 0x59 ); bsPutUChar ( s, 0x26 ); bsPutUChar ( s, 0x53 ); bsPutUChar ( s, 0x59 ); /*-- Now the block's CRC, so it is in a known place. --*/ bsPutUInt32 ( s, s->blockCRC ); /*-- Now a single bit indicating (non-)randomisation. As of version 0.9.5, we use a better sorting algorithm which makes randomisation unnecessary. So always set the randomised bit to 'no'. Of course, the decoder still needs to be able to handle randomised blocks so as to maintain backwards compatibility with older versions of bzip2. --*/ bsW(s,1,0); bsW ( s, 24, s->origPtr ); generateMTFValues ( s ); sendMTFValues ( s ); } /*-- If this is the last block, add the stream trailer. --*/ if (is_last_block) { bsPutUChar ( s, 0x17 ); bsPutUChar ( s, 0x72 ); bsPutUChar ( s, 0x45 ); bsPutUChar ( s, 0x38 ); bsPutUChar ( s, 0x50 ); bsPutUChar ( s, 0x90 ); bsPutUInt32 ( s, s->combinedCRC ); if (s->verbosity >= 2) VPrintf1( " final combined CRC = 0x%08x\n ", s->combinedCRC ); bsFinishWrite ( s ); } } /*-------------------------------------------------------------*/ /*--- end compress.c ---*/ /*-------------------------------------------------------------*/
20,591
674
jart/cosmopolitan
false
cosmopolitan/third_party/bzip2/sample1.ref
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«re˜areŽ¡‘,t•¸ãw“o›ˆÚas-y“et˜uÜrnrešGsoãŽlv“e˜d–ˆÚi#sqsue˜s.“Fir•s“t•Uly‘ÿ*ª,–ˆÚas“di#sõTcusqs1Çe˜d“b#eloš¸ãw,“w˜e“h˜a˜v˜e“a“dšÕTeep“d˜eGs#ireŽ¡‘,tÜro›ÞQa•¸ãv“oid˜monomorphiñÆc˜anÃŽalys1ÇeGs˜of˜an“y˜kin“d.˜CDSs˜as˜pre•Gs1Çen±ÇtµUe“d˜so˜f#ar˜are˜purelyŽ¡‘,monomorphiñÆc.–;¯BecaŸÿus1Çe“of“t•Uhš¸ãe“n˜eešGd“tÜro“cloqs1Çely“exp˜oqs1Çe“d•ÕTep#en¸ãd“encie˜s›;¯b#et•¸ãw“een˜su•Ub-Ž¡‘,partàs–©¿of“t•Uhš¸ãe“inpuÜrt“an˜d“suš•Ub-partàs“of“t˜hš¸ãe“ou•ÜrtÊªpu“t,–©¿it“i#s“not“cleqar“hÃŽo˜w“t•Uh˜ey“mÃŽay“b#eŽ¡‘,us1ÇešGd–ý,in“a“p˜oãŽlymorphiñÆc“w¸ãay›ÿ*ª.“F˜or“ r•s“t-ordÕTe «r‘ý,MFš¸ãG-s“t˜yle–ý, xpGoin±Çt˜inÜrg,“pGoãŽlymorph-Ž¡‘,i•#sm›Q¹i“s˜not˜a˜probãŽlem:˜K•¸ãu•Ubiak‘[KHL91Ž‘‡"]˜h“as˜impãŽlem“en±ÇtµUe•Gd˜a˜p“oãŽlymorphiñÆc˜pro‘Ž8ject¸ãionŽ¡‘,anÃŽalys1Çe «r–UUwit•Uh“MFš¸ãG“ xpGoin±Çt˜inÜrg“in“t•Uh˜e“Glasgo˜w“Hask˜ell“compile «r.Ž¡‘;A‘—Èmore–—øimm¸ãešGdiaÀtµUe“probãŽlem“wit•Uh“lazy“ xp˜oin±Çtš¸ãinÜrg“i#s“hÃŽo˜w“tÜro“dÕTeqal“wit•Uh“mo•Gd˜ule“s.Ž¡‘,A‘dScrudÕTe›dWsõTc•¸ãh“em“e˜i#s˜tÜro˜expGort˜wh“aÀtµUev“e «r˜partàs˜of˜t•Uh“e˜a“bqstract˜fuÜrnct“ion˜graph˜h“a“v“eŽ¡‘,b#een–{SaggregaÀtµUeGd“whilst“compilinšÜrg“t•Uh¸ãe“dÕTe nin˜g“moGd¸ãule.“If,“compilin˜g“somš¸ãe“ot•Uh˜e «rŽ¡‘,moGd•¸ãule,›êt•Uh“e˜compile «r˜n“eeGds˜tÜro˜kno“w˜t•Uh“e˜ xpGoin±Çt˜aÀt˜som“e˜pGoin±Çt˜for˜whiñÆc“h˜noŽ¡‘,informÃŽaÀtš¸ãion–Òi#s“a˜v‘ÿqÇaila˜bãŽle,“it“i#s“som˜et˜im˜ešGs“p˜o•qs“s#ibãŽle–ÒtÜro“mÃŽak¸ãe“a“safe“e˜st¸ãimÃŽaÀtµUe“us#inÜrgŽ¡‘,monotÜroniñÆcit•¸ãy›UUan“d˜t•Uh“e˜informÃŽaÀt“ion˜whiñÆc“h˜Äis˜²a“v‘ÿqÇaila“bãŽle.Ž¡‘;F‘ÿ*ªor–ò!exampãŽle,“h•¸ãa“vinÜrg›ò!exp•GortµUe“d˜µG–Ìj²=“¸f²(µxŸÿ±1Ž–|sµ;›ª¨f‘ßùxŸÿ±1Ž“²)µ;˜²(µxŸÿ±2Ž“µ;˜f‘ßùxŸÿ±2Ž“²)¸g–ò!²w¸ãe“mÃŽay“wi#sh“tÜroŽ¡‘,knoš¸ãw–˜`(µf‘õ xŸÿ±3Ž‘|s²)“in“t•Uh˜e“cas1Çe“wh˜e «re“µxŸÿ±3Ž‘ ]ð¸v‘á}µxŸÿ±1Ž‘ Ó²an˜d“µxŸÿ±3Ž‘ ]ð¸v‘á}µxŸÿ±2Ž‘|s².“Since“µf‘«ï²i#s“monotÜroniñÆcŽ¡‘,it–GGfoãŽlloš¸ãws“t•Uh˜aÀt“µf–mâxŸÿ±3ޑ֯¸v‘ZSµf“xŸÿ±1Ž‘ú²an˜d›GGµf“xŸÿ±3ޑ֯¸v‘ZSµf“xŸÿ±2Ž‘|s²,˜an¸ãd˜so˜µf“xŸÿ±3ޑ֯¸v‘ZS²(µf“xŸÿ±1Ž‘Vž¸u‘Ú+µf“xŸÿ±2Ž‘|s²).Ž¡‘,Pro•¸ãvidÕTeGd›/õw“e˜are˜w“oràkinÜrg˜in˜a˜f*«ram“ew“oràk˜wh“e «re˜o“v“e «reGst“imÃŽaÀt“ion˜i•#s˜safe,˜t•Uhi“s˜giv¸ãeGsŽ¡‘,an›UUap•¸ãpro“ximÃŽaÀtµUe˜v‘ÿqÇalue˜for˜µf‘Ú§xŸÿ±3Ž‘|s².ŽŽŽŒ‹V gÌ\ ý¯3¤ 2Ì\ ýäܚ‘a²Cleqarly‘ÿ*ª,–üítš•Uh¸ãe“bigge «r“t˜h¸ãe“exp•GortµUe“d–üíµG²,“t˜h¸ãe“b#etŸÿtµUe «r“t˜hš¸ãe“e•Gst˜imÃŽaÀtµUe“s–üít•Uh˜aÀt“can“b#e“mÃŽadÕTeޤ ‘Rf*«rom–ÔTit.“BuÜrt“t•Uhš¸ãe“whÃŽoãŽle“purpGoqs1Çe“of“MF˜Gs“i#s“tÜro“k˜eep“µG“²as“smÃŽall“as“pGo•qs“s#ibãŽle,Ž¡‘Rcon±Çt•¸ãaininÜrg›ûp#e «rh“apqs˜a˜h“an“dful˜of˜pGoin±Çtàs˜ouÜrt˜of˜t•UhÃŽousan“ds˜of˜can“didÜraÀtµUeGs.˜Thi#sŽ¡‘Rmilit¸ãaÀtµUešGs–3Oagainst“mÃŽakinÜrg“go˜o˜d“ap•¸ãpro“ximÃŽaÀt“ions.–3OW‘ÿ*ªors1Çe,“not“all“t•Uh¸ãe“p˜oin±Çtàs“in“µGŽ¡‘R²mšÃŽay–•b#e“us1ÇeGd“in“m˜akinÜrg“t•Uhš¸ãe“ap˜pro˜ximÃŽaÀt˜ion:“in“t•Uh˜e“exampãŽle“a˜bGo˜v˜e,“w˜e“are“limitµUeGdŽ¡‘Rt•Üro›UUus#in“g˜pGoin±Çtàs˜¸f²(µy•[Ù;‘ª¨f‘Ú§y“²)–Ǹ2“µG–Ž0¸j“µxŸÿ±3Ž‘C‹¸v‘ǵy[Ù¸g².Ž¡‘aA‘>ås1Çeconš¸ãd,–?!equally“u•Ürn˜eGdifyin“g‘?!soãŽlu“t˜ion–?!i#s“tšÜro“expGort“not“only“µG²,“bu˜t“t•Uh¸ãe“re-Ž¡‘Rcurs#ivš¸ãe–ïGdomÃŽain“equaÀt˜ion“f*«rom“wh˜ence“it“cam˜e“{“or“ev˜en“t•Uh˜e“source“tµUext“whiñÆc˜hŽ¡‘Rb#egašÀt–dt•Uh¸ãe“equa˜tš¸ãion.“Th˜en,“wh˜en“µG“²cannot“answ˜eš «r“a“que˜ry‘ÿ*ª,“it“i#s“extµUenš¸ãdÕTeGd,“in“t•Uh˜eŽ¡‘RmÃŽann¸ãe «r›:ùdÕTe•GsõTcr*«ib#e“d˜aš¸ãb“o˜v˜e,–:ùas“requireGd.“If“t•Uh˜e“a˜bqstract“in±ÇtµUe «rpret˜aÀt˜ions“get“large,Ž¡‘Rdš¸ãu•Ürmpin“g–®/t•Uh˜em“inš±ÇtÜro“in˜tµUe «rfš#ace“ leGs“mÃŽay“not“b˜e“pract¸ãiñÆcal.“Thi˜s“sõTc•¸ãh“em“e–®/also“h¸ãas“aŽ¡‘Rmore›‘xsu••Ubt“le˜w•¸ãešqakn“eGs˜s.›‘xA‘‘hcru“cial˜ins#igh“t˜i#s˜t•Uh“aÀt˜ n“dinÜrg˜t•Uh“e˜ xpGoin±Çt˜of˜a˜domÃŽainŽ¡‘RequaÀt•¸ãion›¬ÐmÃŽak“eGs˜it˜st“an“d˜on˜itàs˜o“wn:˜it˜no˜lonÜrge• «r˜refe“renceGs˜an•¸ãy˜ot•Uh“e «r˜equaÀt“ion.Ž¡‘RCons#idÕTe «r–͗t•Uhš¸ãe“foãŽllo˜winÜrg“t•Uhree“mo•Gd˜ule“s–͗dÕTe ninÜrg“recurs#iv˜e“fuÜrnct˜ions“Áf²,“Ág“²an˜d“Áh“²wit•UhŽ¡‘Rcorre•Gsp“on•¸ãdinÜrg›UUequaÀt“ions˜Áf#²,˜Ág#˜²an“d˜Áh#²:Ž©¤m‘a¿÷Ámodule–?ýF(f)“where“{‘D?Ùf“=“...“f“...‘$¿ë}Ž¡‘a¿÷module–?ýG(g)“where“{“import“F;‘¿÷g“=“...“g“...“f“...“}Ž¡‘a¿÷module–?ýH(h)“where“{“import“G;‘¿÷h“=“...“h“...“g“...“}ަ‘R²Du•Ürmpin“g–UUt•Uhš¸ãe“uÜrnsoãŽlv˜eGd“domÃŽain“equaÀt˜ions“inš±ÇtÜro“in˜tµUe «rf#ace“(Á.hi²)“ lešGs“giv¸ãe˜s:ަ‘a¿÷ÁF.hi:‘¿÷f#–?ý=“...“f#“...Ž¡‘a¿÷G.hi:‘¿÷g#–?ý=“...“g#“...“f#“...Ž¡‘a¿÷H.hi:‘¿÷h#–?ý=“...“h#“...“g#“...ަ‘R²Wh•¸ãen›óªmoGd“ule˜ÁH‘ó²i•#s˜compileGd˜it˜mÃŽay˜b“e˜n•¸ãeceGsqsary˜tÜro˜extµUen“d˜t•Uh“e˜fuÜrnct“ion˜graphŽ¡‘Rfor–NôÁg#².“Th¸ãe“trouš•UbãŽle“i#s“t˜hi#s“m¸ãešqans“re˜adinÜrg“in±ÇtµUe «rf#ace“ÁF.hi“²ev¸ãen“tš•UhÃŽough“t˜h¸ãe“tµUext“ofŽ¡‘Rmo•Gd¸ãule›¹úÁH‘¹Ó²do#e“s˜not˜direct•Uly˜refe• «r˜tÜro˜ÁF²:˜in˜gen¸ãe“ral,˜it˜migh•¸ãt˜b#e˜n“eceGs•qsary˜tÜro˜re“ad˜allŽ¡‘Rin±ÇtµUe «rf#aceGs–؍in“t•Uhš¸ãe“do˜wn˜w˜ard“cloqsure“of“ÁH².“An˜y“sõTc˜h˜em˜e“whiñÆc˜h“expGortàs“inš±ÇtÜro“in˜tµUe «rf#aceŽ¡‘R le•Gs›՜refe «rence“s˜t•Üro˜fu“nct•¸ãions˜in˜ot•Uh“e «r˜mošGd“ule˜s–՜su e «rs“t•Uhš¸ãe“sam˜e“probãŽlem.“MÜre «relyŽ¡‘RinlininšÜrg–?]refe «renceGs“t˜o“ot•Uhš¸ãe «r“equaÀt˜ions“do#eGs“not“h˜elp,“as“t•Uhi#s“mÃŽak˜eGs“t•Uh˜e“in±ÇtµUe «rf#aceGsŽ¡‘Rcon±Çt•¸ãain›UUev“e «ryt•UhinÜrg˜b#elo“w˜t•Uh“em˜in˜t•Uh“e˜hie «rarc“h“y‘ÿ*ª,˜an“d˜h“ence˜v“e «ry˜large:ަ‘a¿÷ÁF.hi:‘¿÷f#–?ý=“...“f#“...Ž¡¡‘a¿÷G.hi:‘¿÷g#–?ý=“letrec“f#“=“...“f#“...‘/?åin“...“g#“...“f#“...Ž¡¡‘a¿÷H.hi:‘¿÷h#–?ý=“letrec“f#“=“...“f#“...‘/?åinŽ¡’¥ÿÐletrec–?ýg#“=“...“g#“...“f#“...‘ úin“...“g#“...“h#“...ަ‘R²BecaŸÿusš1Çe–ÃÊof“t•Uh¸ãeGs˜e“diculÜrt¸ãiešGs,“lazy“ xp˜oin±Çt¸ãinÜrg“do#e˜s“not“s1Çeem“tÜro“ t“w¸ãell“in“anŽ¡‘Ren•¸ãvironm“en±Çt›UUwh“e «re˜s1Çepara•ÀtµUe˜compila“t•¸ãion˜i#s˜t•Uh“e˜norm.ŽŸ¤m‘R»2.3‘ üP®9oßJlymorphišï¥c–ÕTor“Monomorphi˜c?ަ‘R²P•¸ãaram“etr*«iñÆc–~VpGoãŽlymorphiš#sm“i˜s“an“impGortš¸ãan±Çt“elem˜en±Çt“of“t•Uh˜e“t˜ypš#e“systµUems“of“moGdÕTe «r˜nŽ¡‘Rfu•Ürnct¸ãionÃŽal›UUlan“guageGs.˜Giv•¸ãen˜a˜param“etr*«i•ñÆcally˜pGoãŽlymorphi“c˜fuÜrnct•¸ãion,˜w“e˜could:ŽŽŽŒ‹kJ gÌ\ ý¯3¤ 2Ì\ ýäܚ‘2@»{ŽŽŽ‘=²ReGdo–ÂÝt•Uhš¸ãe“anÃŽalys•#i“s–ÂÝfor“eqac˜h“di e «ren±Çt“inst˜an±Çt˜iaÀt˜ion“of“t•Uh˜e“fuÜrnct˜ion.“Thiš#s“i˜sޤ ‘=equiv‘ÿqÇalen±Çt–ߗtšÜro“expan¸ãdin˜g“ou˜t“t•Uh¸ãe“program“in±Çt˜o“a“coãŽllect¸ãion“of“monomorphiñÆcŽ¡‘=inst¸ãanceGs–UUbš#efore“anÃŽalys˜i˜s.Ž© Åٍ‘2@»{ŽŽŽ‘=²AnÃŽalys1Çe–&´t•Uhš¸ãe“fuÜrnct˜ion“once,“an˜d“us1Çe“pGoãŽlymorphiñÆc“in˜v‘ÿqÇar*«iance“reGsulšÜrtàs“t˜o“dÕTeqalŽ¡‘=wit••Uh›UUdi e «ren±Çt“ly˜inst•¸ãan±Çt“iaÀtµUe•Gd˜us1Çe“s˜laÀtµUe «r˜on.ŽŸQ‹‘,An–™æoft-quotµUeGd“di#sadv‘ÿqÇan±Çtš¸ãage“of“t•Uh˜e“form˜e «r“ap˜proac˜h“i#s“t•Uh˜aÀt“pGoãŽlymorphiñÆc“fuÜrnct˜ionsŽ¡‘,mšÃŽay–ãDb#e“an˜alys1ÇeGd“m˜anš¸ãy“t˜im˜eGs,“whiñÆc˜h“i#s“w˜astµUeful.“In“t•Uh˜e“w˜or•s“t–ãDcas1Çe,“t•Uh˜e“n•UuÜrm‘ÿ|qb#e «r“ofŽ¡‘,inst¸ãancešGs–àcan“b#e“exp˜on•¸ãen±Çt“ial–àin“tš•Uh¸ãe“lenÜrgt˜h“of“t˜hš¸ãe“program.“Nev˜e «rt•Uh˜eleGsqs,“su˜c˜h“b#e-Ž¡‘,h•¸ãa“viour–tfdoš#eGs“not“ap¸ãp˜eqar“tšÜro“oGccur.“M˜eqasuremš¸ãen±Çtàs“b˜y“Maràk“Jon˜eGs“of“s#ix“su•Ubqst˜an±Çt˜ialŽ¡‘,programs–6{in“t•Uhš¸ãe“Ánofib“²suitµUe‘[P˜ar92Ž‘qË]“suggeGst“a“t˜w˜ofoãŽld“increqas1Çe“in“t•Uh˜e“n•UuÜrm‘ÿ|qb#e «r“ofŽ¡‘,binš¸ãdinÜrg–¯groupqs‘[Jon93Ž‘±Ì].“F‘ÿ*ªurt•Uh˜e «r,“only“sš#impãŽle“li˜st-h•¸ãan“dlin•Ürg›¯fu“nct•¸ãions˜lik“e˜Ámap˜²an“dŽ¡‘,Áfoldr›S¨²h•¸ãa“v“e˜a˜large˜n•UuÜrm‘ÿ|qb#e «r˜of˜inst“anceGs,˜an“d˜su“c“h˜fuÜrnct“ions˜are˜oftµUen˜inlin“eGd˜b“yŽ¡‘,o•¸ãpt“imi•#s“inÜrg–°ícompile «rs“an•¸ãyw“ay‘ÿ*ª.–°íSo“monomorphiñÆc“anšÃŽalys•#i“s–°ím˜ay“not“actš¸ãually“in˜v˜oãŽlv˜eŽ¡‘,m•Uu•¸ãc“h›%d“upãŽliñÆcaÀt“ion˜of˜w“oràk.˜Obqs1Çe «rv“e˜also˜t•Uh“aÀt˜s#ince˜t•Uh“e˜a“bqstract˜in±ÇtµUe 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«ren±Çt“mo•Gdš¸ãule“s.–È[W‘ÿ*ªoràk“b˜y“Baraki,“Hugh˜eGsŽ¡‘,an•¸ãd›mLaŸÿuÜrnc“h“bury‘[Bar93Ž‘,˜HL92bŽ‘!»X]˜(tÜro˜m“en±Çt“ion˜buÜrt˜a˜few)˜h“as˜ešGst“a“bãŽli#sh“e˜d‘mtµUec“h-Ž¡‘,niquešGs–0#for“b˜ot•Uh“forwš¸ãard“an˜d“bac˜kw˜ard“pGoãŽlymorphišñÆc“str*«i˜ctn¸ãešGsqs“anÃŽalys1Çe˜s.“Bac¸ãk-Ž¡‘,wš¸ãard–¯%anÃŽalys1ÇeGs“len˜d“t•Uh˜ems1Çelv˜eGs“part˜iñÆcularly“w˜ell“tÜro“su˜c˜h“an“ap˜proac˜h:“Sect˜ion“5Ž¡‘,of‘[Sew94Ž‘8ç]›ËdÕTe•GsõTcr*«ib#e“s˜su•¸ãc“h˜an˜anÃŽalys•#i“s˜in˜cons“id•ÕTe «ra¸ãbãŽle˜d“et•¸ãail.˜Baraki's˜w“oràk˜in“diñÆc-Ž¡‘,aÀtµUeGs–ÕþhÃŽoš¸ãw“som˜e“forw˜ard“anšÃŽalys1ÇeGs“m˜ay“b#e“m˜adÕTe“pGoãŽlymorphiñÆc:‘[Sew94Ž‘8ç],“Sect¸ãion“3Ž¡‘,dÕTe•GsõTcr*«ib#e“s–UUan“impãŽlem•¸ãen±Çt“aÀt“ion.ަ‘;F‘ÿ*ªor›œd r•s“t˜ordÕTe «r˜fuÜrnct•¸ãions,˜pGoãŽlymorphiñÆc˜tµUec“hniqueGs˜giv“e˜t•Uh“e˜sam“e˜reGsulÜrtàs˜asŽ¡‘,monomorphiñÆc›82anÃŽalys•#i“s:˜t••Uh¸ãey˜are˜exact.˜BuÜrt˜in˜t“h•¸ãe˜high“e• «r˜ordÕTe“r˜cas1Çe,˜accuracyŽ¡‘,mšÃŽay–äÍb#e“loqst.“F‘ÿ*ªor“bac•¸ãkw“ard–äÍan˜alys1ÇeGs,“whiñÆcš¸ãh“are“inh˜eš «ren±Çt•Uly“ r•s“t-ordÕTe˜r,–äÍt•Uhi#s“mÃŽayŽ¡‘,b#e›Çaccept•¸ãa“bãŽle.˜F‘ÿ*ªor˜ot•Uh“e «r˜anÃŽalys1ÇeGs,˜t•Uh“e˜mÃŽagnit“udÕTe˜of˜t•Uhi#s˜probãŽlem˜h“as˜y“et˜tÜro˜b#eŽ¡‘,quan±Çt¸ãi eGd.ŽŸ!Ý<‘,»2.4‘ üHigh®9eš Dr–ÕTor“ r•-s“t‘ÕTordÎîe˜r?ŽŸÝ<‘,²High¸ãe• «r›½ ordÕTe“r˜ xpGoin±Çt¸ãin•Ürg˜i#s˜dicul“t˜b#eca•Ÿÿus1Çe˜t•Uh¸ãe˜laÀt“t•¸ãiñÆce˜s#izeGs˜for˜fuÜrnct“ion˜spaceGsŽ¡‘,gro¸ãw–8ãso“rapidly›ÿ*ª.“F˜or“exampãŽle,“in“str*«iñÆctnš¸ãeGsqs“anÃŽalys•#i“s,–8ãan“itµUem“of“t˜yp#e“Á[Int]–?ý->“[Int]Ž¡‘,²migh•¸ãt›†±a“bqstract˜tÜro˜domÃŽain˜[»4–\¸!“»4²],˜whiñÆc•¸ãh˜h“as˜35˜pGoin±Çtàs.˜AddinÜrg˜a˜s1Çecon“d˜para-Ž¡‘,mš¸ãetµUe «r–o«of“t•Uh˜e“sam˜e“t˜yp#e“giv˜ešGs“domÃŽain“[»4–Ǹ!“»4“¸!“»4²],–o«wit•Uh“24,696“p˜oin±Çtàs,“an“increqas1ÇeŽ¡‘,of›¾Úo•¸ãv“e «r˜700˜t“im“eGs.˜Th“e˜n•UuÜrm‘ÿ|qb#e «r˜of˜pGoin±Çtàs˜in˜[»4–võ¸!“»4“¸!“»4“¸!“»4²]˜i#s˜ce «rt•¸ãainly˜v“e «ryŽŽŽŒ‹|  gÌ\ ý¯3¤ 2Ì\ ýäܚ‘R²large.–ÂoManš¸ãy“fuÜrnct˜ionÃŽal“param˜etµUe «rs“h˜a˜v˜e“t˜yp#ešGs“more“compãŽliñÆcaÀtµUe˜d“tš•Uh¸ãan“t˜hi#s,“an¸ãdޤ ‘RcalculaÀtš¸ãinÜrg–UUcompãŽletµUe“ xpGoin±Çtàs“in“t•Uh˜ešGir“pre˜s1Çence“i#s“impract¸ãiñÆcal.Ž¡‘aFixpGoin±Çt•¸ãinÜrg›øÖb“y˜tµUe «rm˜rewr*«it“inÜrg˜som“et“im“eGs˜f#ails˜in˜t•Uh“e˜preGs1Çence˜of˜fuÜrnct“ionÃŽalŽ¡‘Rparamš¸ãetµUe «rs.–¥ In“t•Uh˜e“gen˜e «ral“cas1Çe,“high˜eš «r“ordÕTe˜r“equaÀtš¸ãions“cannot“b#e“soãŽlv˜eGd,“b#ecaŸÿus1ÇeŽ¡‘Rt•Uh¸ãe•Gir›æ xp“oin±Çtàs˜dÕTep#en•¸ãd˜on˜t•Uh“e˜ xpGoin±Çtàs˜of˜t•Uh“e˜fuÜrnct“ionÃŽal˜param“etµUe «rs.˜Th“e˜usualŽ¡‘Rmš¸ãet•UhÃŽoGd–՛of“rewr*«it˜inÜrg“adjacen±Çt“ap˜pro˜ximÃŽaÀt˜ions“tšÜro“normÃŽal“form“f#ails“t˜o“dÕTetµUect“anŽ¡‘Ro•¸ãv“e «rall–` 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«raÀt•µUe‘c&b#etŸÿt“e˜r–c&cošGdÕTe‘[PJ93Ž‘ñË,“Hal93Ž‘ªG]“all“e˜it•Uh¸ãe «r“sugge˜st“or“impãŽly“t•Uhš¸ãaÀt“bac˜kw˜ardsŽ¡‘RinformÃŽaÀtš¸ãion–F.i#s“wh˜aÀt“i#s“act˜ually“us1Çeful.“T‘ÿ*ªak˜en“tÜroget•Uh˜e «r,“t•Uh˜e“cas1Çe“for“buildinÜrg“aŽ¡‘Rbac•¸ãkw“ards›UUa“bqstract˜in±ÇtµUe «rpret“aÀt“ion˜s1Çeems˜o“v“e «rwh“elminÜrg.ަ‘aSpace›äblimit•¸ãaÀt“ions˜precludÕTe˜m•Uu“c“h˜di•#sõTcusqs“ion˜of˜t•Uh•¸ãe˜a“bqstract˜in±ÇtµUe «rpret“aÀt“ion.Ž¡‘RSuce–¾±it“tÜro“say“t•Uh¸ãaÀt“it“iš#s“f˜airly“con•¸ãv“en±Çt“ionÃŽal:›¾±t•Uh“e˜o“v“e «rall˜stru“ct“ure˜i•#s˜s“imilar˜tÜroŽ¡‘Rt•Uh¸ãaÀt›—pre•Gs1Çen±ÇtµUe“d˜b•¸ãy˜John˜Hugh“eGs˜in‘[Hug90Ž‘>],˜alÜrt••UhÃŽough˜t“h•¸ãe˜m“ec“h“ani#sm˜for˜dÕTeqalinÜrgŽ¡‘Rwit•Uh–¸ØdÜraÀtš¸ãa“stru˜ct˜ureGs,“cons•tru˜ctÜror“s–¸Øan˜d“cas1Çe“tµUeš «rms“i#s“di e˜ren±Çt.“As“wit•Uh“an¸ãy“purelyŽ¡‘Rbac•¸ãkw“ard›¬ anÃŽalys•#i“s,˜high¸ãe• «r-ordÕTe“r˜anÃŽalys•#i“s˜i“s˜impGo•qs“s#ibãŽle,˜so˜w•¸ãe˜nÃŽaiv“ely˜asqsuÜrm“e˜t•Uh“aÀtŽ¡‘Rall–UUušÜrnkno¸ãwn“fu˜nctš¸ãions“do“not“dÕTemÃŽan˜d“t•Uh˜eGir“arguÜrm˜en±Çtàs“aÀt“all.ަ‘aMan•¸ãy›pbac“kw“ard˜a“bqstract˜in±ÇtµUe «rpret“aÀt“ions˜go˜tÜro˜a˜gre•qaÀt˜dÕTe“al˜of˜trou•UbãŽle˜tÜro˜moGdÕTelŽ¡‘RdÜraÀt•¸ãa›’ƒstru“ct“ureGs˜w“ell,˜t•Uh“e «reÕTb“y˜in“d“u“cinÜrg˜cons#idÕTe «ra“b•ãŽle˜comp“liñÆcaÀt•¸ãion˜in˜t•Uh“e˜mÃŽac“hin“e «ryŽ¡‘RwhiñÆcš¸ãh–×dÕTeqals“wit•Uh“dÜraÀt˜a“stru˜ct˜ureGs“{“constru˜ctšÜror“fu˜nctš¸ãions“an˜d“Ácase²s.“F–ÿ*ªort˜uÜrnÃŽaÀtµUely“,Ž¡‘Rt•Uh•¸ãe›YpreGs1Çen±Çt“aÀt“ion˜can˜b•#e˜s“impãŽli eGd˜b•¸ãy˜t•Uh“e˜obqs1Çe «rv‘ÿqÇaÀt“ion˜t•Uh“aÀt,˜pro“vidÕTeGd˜t•Uh“e˜a“bqstrac-Ž¡‘Rtš¸ãion–»nof“Ácase²s“an˜d“constru˜ctšÜror“fu˜nctš¸ãions“ob#eys“ce «rt˜ain“constrain±Çtàs,“it“do#eGsn't“mÃŽaÀt-Ž¡‘RtµUe «r– <ašÀt“all“wh¸ãa˜t“tš•Uh¸ãey“are.“So“t˜hš¸ãe“bac˜kw˜ards“a˜bqstract˜ion“can“bš#e“sp˜eci eGd“wit•UhÃŽouÜrtŽ¡‘Rsayin•Ürg›iDan¸ãyt•Uhin“g˜m•Uu•¸ãc“h˜a“bGou•Ürt˜d“aÀt•¸ãa˜stru“ct“ureGs.˜Su•Ubqs1Çequen±Çt˜param“etµUe «r*«i#saÀt“ions˜ofŽ¡‘Rit›?ïproGd•¸ãu“ce˜compãŽletµUe,˜w“oràkñÆa“bãŽle˜a“bqstract˜in±ÇtµUe «rpret“aÀt“ions,˜an“d˜di e «ren±Çt˜param“et-Ž¡‘Re «r*«i#saÀtš¸ãions–„7can“proGd˜u˜ce“in±ÇtµUe «rpret˜aÀt˜ions“givinÜrg“v˜eš «ry“di e˜ren±Çt“levš¸ãels“of“dÕTet˜ail“forŽ¡‘RdÜraÀt•¸ãa›ºstru“ct“ure•Gs.˜Thi#s˜mo“d•¸ãular˜ap“proac“h˜an“d˜som“e˜param“etµUe «r*«i#saÀt“ions˜of˜it˜areŽ¡‘RdÕTev•¸ãelo“p#eGd–UUin‘[Sew94Ž‘8ç],“Sectš¸ãion“5;“w˜e“ouÜrt•Ulin˜e“on˜e“su˜c˜h“param˜etµUe «r*«i#saÀt˜ion“shÃŽort•Uly‘ÿ*ª.ަ‘aAn–Ÿ'impGortš¸ãan±Çt“feqaÀt˜ure“of“t•Uh˜e“a˜bqstract˜ion“i#s“t•Uh˜aÀt“suit˜a˜bãŽle“param˜etµUe «r*«i#saÀt˜ionsŽ¡‘RprošGd•¸ãu“ce–çœp˜oãŽlymorphiñÆcally“in¸ãv‘ÿqÇar*«ianš±Çt“in˜tµUe «rpret•¸ãaÀt“ions.›çœP“oãŽlymorphiñÆc˜in“v‘ÿqÇar*«iance˜f#acil-Ž¡‘Rit¸ãa•ÀtšµUeGs‘˜Ùs1Çepara“t˜e›˜Ùcompila“t•¸ãion,˜as˜di#sõTcusqs1ÇeGd˜in˜Sect“ion‘2.3,˜an“d˜it˜also˜m“eqans˜t•Uh“e˜s#izeŽ¡‘Rof–Š tµUeš «rms“gen¸ãe˜raÀtµUeGd“bš¸ãy“(h˜ence,“t•Uh˜e“coqst“of‘Ç)“a˜bqstract“in±ÇtµUe «rpret˜aÀt˜ion“i#s“not“relaÀtµUeGdŽ¡‘RtÜro–Ã6t•Uhš¸ãe“inst˜an±Çt˜iaÀt˜ion.“Thiš#s“i˜s“in“mšÃŽaràk¸ãeGd“con±Çtrast“tÜro,“for“exampãŽle,“W‘ÿ*ªadle «r's“or*«igin˜alŽ¡‘Rnon- a•Àt‘¢*in±ÇtµUe «rpretš¸ãa“t˜ion‘[W‘ÿ*ªad87Ž‘],–¢*in“whiñÆc˜h“a˜bqstract˜ion“of“Ácase“²expreGsqs#ions“couldŽ¡‘Rgen¸ãeš «raÀt•µUe‘†kt“e˜rms–†kwhÃŽoqs1Çe“s#izešGs“gro¸ãw“exp˜on•¸ãen±Çt“ially–†kwitš•Uh“t˜h¸ãe“s#ize“of“t˜hš¸ãe“inst˜an±Çt˜iaÀt˜inÜrgŽ¡‘Rt¸ãyp#eGs.ަ‘aBac•¸ãkw“ards›{str*«iñÆctn“e•Gsqs˜anÃŽalys1Çe“s˜w¸ãoràk,˜in˜a˜s•1Çens“e,˜b•¸ãy˜dÕTetµUect“inÜrg˜f•*«ree˜v‘ÿqÇar“ia¸ãbãŽleGs˜inŽŽŽŒ‹ ¹ø gÌ\ ý¯3¤ 2Ì\ ýäܚ‘,²expreGsšqs#ions.–õœBecaŸÿus1Çe“mo˜st“v‘ÿqÇar*«iaš¸ãbãŽleGs“do“not“ap˜p#ešqar“f*«ree“in“mo˜st“expreGs˜s#ions,“aޤ ‘,n•ÃŽaiv¸ãe›Ýâan“alys•#i“s˜will˜tµUen•¸ãd˜tÜro˜gen“e «raÀtµUe˜mÃŽan“y˜h•Uuge˜tµUe «rms˜whiñÆc“h˜tr*«ivially˜reGd“u“ce˜tÜroŽ¡‘,¸?²,–h®t•Uhš¸ãe“pGoin±Çt“dÕTenot˜inÜrg“ze «ro“dÕTemÃŽan˜d.“St˜ill,“gen˜e «raÀt˜inÜrg“t•Uh˜eGs1Çe“tš•UhinÜrgs,“t˜hš¸ãen“reGd˜u˜cinÜrgŽ¡‘,t•Uh•¸ãem,›Õt“ak“eGs˜e ort,˜an“d˜it˜pro“v“eGs˜v‘ÿqÇalua“b•ãŽle˜tÜro˜p“lan±Çt˜ce «rt•¸ãain˜k“ey˜rewr*«itµUe˜ruleGs˜ins#idÕTeŽ¡‘,t•Uh•¸ãe›aša“bqstract˜in±Çt•µUeš «rpret“e˜r–ašitàs1Çelf“tÜro“s#idÕTešGstµUep“t•Uh¸ãe“pro˜ce˜sqs“{“a“tr*«ivial“mo˜di caÀtš¸ãion“tÜro“t•Uh˜eŽ¡‘,co•GdÕTe.›î†Incorp“oraÀt•¸ãinÜrg˜four˜of˜t•Uh“e˜moqst˜pGo“pular˜s#impãŽle˜rewr*«itµUe˜ruleGs˜dramÃŽaÀt“iñÆcallyŽ¡‘,cuÜrtàs–Ât•Uhš¸ãe“s#ize“of“gen˜e «raÀtšµUeGd“t˜e «rms“anš¸ãd“so“expan˜ds“t•Uh˜e“ranšÜrge“of“source“fu˜nct¸ãions“forŽ¡‘,whiñÆc•¸ãh›UUa“bqstract˜in±ÇtµUe «rpret“aÀt“ion˜can˜b#e˜don“e˜in˜reqasonÃŽa“bãŽle˜t“im“e.ŽŸp‘,»Thš®9e–ÖWHe µad-Str1iï¥ct“P˜aram˜etª"e Dr1i(äsa¶ft˜ion‘LÛ²Our›nimpãŽlem•¸ãen±Çt“aÀt“ion˜us1Çe•Gs˜a˜p“o•¸ãw“e «rfulŽ¡‘,param•¸ãetµUe «r*«iš#saÀt“ion‘½ dÕTeGs˜ign“eGd–½ tÜro“givš¸ãe“dÕTet˜ailešGd“re˜sulÜrtàs“for“t•Uhš¸ãe“v‘ÿqÇast“mÃŽa‘Ž8jor*«it˜y“of“dÜraÀt˜aŽ¡‘,dÕTeclaraÀtš¸ãions–òËa“Hask˜ell“programm˜e «r“could“reqasonÃŽa˜bãŽly“us1Çe.“Thiš#s“i˜s“in“con±ÇtrastŽ¡‘,tšÜro–ÎÒt•Uh¸ãe“oft•µUen-limit“eGd–ÎÒran˜ge“of“tš¸ãyp#eGs“whiñÆc˜h“ot•Uh˜e «r“impãŽlem˜en±Çt˜aÀt˜ions“can“dÕTeqal“wit•Uh,Ž¡‘,som•¸ãet“im“eGs–Díjusšt“li#s˜tàs‘[HH91Ž‘],“som•¸ãet“im“eGs–Día“fulle «r“ranšÜrge“of“d˜ašÀt¸ãa“dÕTeclara˜tš¸ãions“wh˜e «reŽ¡‘,construš¸ãct•Üror‘Ìêargu“m˜en±Çtàs–ÌêmÃŽay“b#e“on˜e“of“t•Uh˜e“t˜yp#e“v‘ÿqÇar*«ia˜bãŽleGs,“or“a“recurs#iv˜e“call“tÜro“t•Uh˜eŽ¡‘,t¸ãyp#e,–\ bušÜrt“not•Uhin˜g“els1Çe‘([Sew91Ž‘8ç],“Sectš¸ãion“6).“Th˜e“param˜etµUe «r*«i#saÀt˜ion“iš#s“dÕTe•Gs˜ign¸ãe“d‘\ tÜroŽ¡‘,dÕTetµUect–¶.hš¸ãeqad“str*«iñÆctn˜eGsqs.“W‘ÿ*ªe“w˜an±ÇtµUeGd“tÜro“mo˜v˜e“aw˜ay“f*«rom“t•Uh˜e“protÜrot˜yp#e“st˜age“an˜dŽ¡‘,creqaÀtµUe–äÍan“anÃŽalys•#i“s–äÍwhiñÆcš¸ãh“(1)“giv˜eGs“us1Çeful“informÃŽaÀt˜ion“for,“e ect˜iv˜ely‘ÿ*ª,“an˜y“(non-Ž¡‘,fuÜrnct•¸ãionÃŽally-t“yp#e•Gd)›{—co“dÕTe˜f*«ragm•¸ãen±Çt,˜an“d˜(2)˜gen“e «ra•ÀtµUeGs˜informÃŽa“t•¸ãion˜tÜro˜sup“pGort˜allŽ¡‘,kno•¸ãwn›[ str*«iñÆctn“e•Gsqs-relaÀtµUe“d˜transformÃŽaÀt•¸ãions˜{˜h“ence˜t•Uh“e˜n“eeGd˜for˜h“ešqad-str*«iñÆctn“eGs˜s.Ž¡‘,Thš¸ãe–UreGsulÜrt“i#s“t•Uh˜aÀt“t•Uh˜e“param˜etµUe «r*«i#saÀt˜ion“i#s“raÀt•Uh˜e «r“compãŽliñÆcaÀtµUeGd,“so“w˜e“will“try“an˜dŽ¡‘,con•¸ãv“ey›UUt•Uh“e˜eGsqs1Çen±Çt“ial˜idÕTeqas˜wit•Uh˜an˜exampãŽle.ŽŸ j‘;Th•¸ãe›e¶param“etµUe «r*«i#saÀt“ion˜dÕTe «r*«iv“eGs˜f*«rom˜Bur#n's˜idÕTeqa˜of˜ev‘ÿqÇaluaÀt“ion˜transform“e «rs.Ž¡‘,[Sew91Ž‘8ç]–Ipgen¸ãe «rališ#s1ÇeGd“t•Uhi˜s“tšÜro“w¸ãoràk“for“a“widÕTe «r“ran˜ge“of“d˜aÀtš¸ãa“t˜yp#eGs,“an˜d‘[Sew94Ž‘8ç]Ž¡‘,furt•Uh•¸ãe «r›¯extµUen“d•ÕTeGd˜it˜tÜro˜d“etµUect˜h•¸ãešqad-str*«iñÆctn“eGs˜s.–¯Let“us“consš#idÕTe «r“li˜stàs.“Li˜sštàs“a¸ãbqs˜tractŽ¡‘,tÜro––Æt•Uhree“coãŽllect¸ãions“of“pšGoin±Çtàs:“b˜otŸÿtšÜrom“(ÁB²),“dÕTenot¸ãin˜g“no“ev‘ÿqÇaluaÀtš¸ãion,“t•Uh˜e“s1Çet“ÁW[a]²,Ž¡‘,dÕTenot•¸ãinÜrg›ð7ev‘ÿqÇaluaÀt“ion˜tÜro˜w“eqak˜h“eqad˜normÃŽal˜form,˜an“d˜t•Uh“en,˜if˜a˜cons˜cell˜i#s˜pro-Ž¡‘,d•¸ãu“ceGd,›Î|ev‘ÿqÇaluaÀt“ion˜of˜t•Uh“e˜ r•s“t˜elem•¸ãen±Çt˜wit•Uh˜Áa²,˜an“d˜t•Uh“e˜s1Çet˜ÁS[a][b]²,˜dÕTenot“inÜrgŽ¡‘,ev‘ÿqÇaluaÀtš¸ãion–4²of“t•Uh˜e“compãŽletµUe“stru˜ct˜ure“of“t•Uh˜e“li#st,“ev‘ÿqÇaluaÀt˜ion“of“t•Uh˜e“ r•s“t‘4²elem˜en±ÇtŽ¡‘,witš•Uh–Áa“²an¸ãd“all“t˜h¸ãe“reGst“wit˜h“Áb².“If“w¸ãe“moGdÕTel“in±ÇtµUege «rs“wit˜h“t˜hš¸ãe“t˜w˜o“ev‘ÿqÇaluaÀtÜrors“Á0Ž¡‘,²(no-ev›ÿqÇal)–UUan¸ãd“Á1“²(ev˜al),“t•Uhš¸ãe“laÀtŸÿt˜iñÆce“for“Á[Int]“²b#ecom˜eGs:ŽŸY©’Ù?ÁS[1][1]Ž¡’Óÿ /‘$¿ë\Ž¡’¹¿¯S[1][0]‘?ñS[0][1]Ž¡’¾ÿ¬/‘ÿô\‘î/Ž¡’©ÿ¸W[1]‘?ñS[0][0]Ž¡’¾ÿ¬\‘ÿô/Ž¡’Ä?©W[0]Ž¡’ο£|Ž¡’ο£BŽŸC?‘;²F‘ÿ*ªor–ÛexampãŽle,“ÁW[1]“²i#s“a“h¸ãeqad-str*«iñÆct“ev›ÿqÇaluaÀtÜror,“ev˜aluaÀt¸ãinšÜrg“t˜o“wš¸ãeqak“h˜eqad“normÃŽalŽ¡‘,form,– ]anš¸ãd“t•Uh˜e“h˜eqad“ÁInt“²tÜrošGo,“if“p˜o•qs“s#ibãŽle.– ]ÁS[0][1]“²mš¸ãeqan“ev‘ÿqÇaluaÀtµUe“t•Uh˜e“en±Çt˜ire“li#stŽ¡‘,stru•¸ãct“ure,›u¤an“d˜all˜ÁInt²s˜except˜t•Uh“e˜ 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«r“tÜro“reqac¸ãh“normÃŽal“form.ŽŽŽŒ‹ ç gÌ\ ý¯3¤ 2Ì\ ýäܚ‘,»Makin×g–“t…Thš®9e“rewr1itª"e Dr“w˜orÛ2k“w˜ell‘fʲOnce–«a“normÃŽal“form“hš¸ãas“b#een“d•ÕTecid“eGd–«on“an˜dޤ ‘,suit•¸ãa“bãŽle–.çrewr*«itšµUe“ruleGs“gen¸ãe «raÀt˜eGd,“t•Uhš¸ãe «re“i#s“st˜ill“t•Uh˜e“i#sqsue“of“hÃŽo˜w“t•Uh˜e“ruleGs“are“tÜro“b#eŽ¡‘,ap¸ãpãŽliešGd.–žÂThi#s“b˜oils“doš¸ãwn“tÜro“a“proba˜b•ãŽly-irreconcila˜b“le–žÂcon iñÆct“b#et˜w˜een“inn˜e «rmoqst-Ž¡‘, r•s“t–Çcanš¸ãd“ouÜrtµUe «rmoqs•t- r“s“t–Çcrewr*«it˜inÜrg.“Bot•Uh“straÀtµUegieGs“w˜oràk“w˜ell“m•Uu˜c˜h“of“t•Uh˜e“t˜im˜e,Ž¡‘,buÜrt–¥þbGotš•Uh“also“su e «r“f*«rom“paÀt˜hÃŽoãŽlogiñÆcal“in±ÇtµUe «ractš¸ãions“b#et˜w˜een“tšµUe «rms“emitŸÿt˜eGd“b¸ãyŽ¡‘,t•Uh•¸ãe›°a“bqstract˜in±Çt•µUeš «rpret“e˜r–°anš¸ãd“som˜e“of“t•Uh˜e“rewr*«itµUe“ruleGs.“In“t•Uh˜eGsš1Çe“cas˜eGs,“rewr*«it¸ãinÜrgŽ¡‘,can›pØt•¸ãak“e˜a˜smÃŽall˜tµUe «rm˜an“d˜expan“d˜it˜expGon“en±Çt“ially˜tÜro˜a˜gigan±Çt“iñÆc˜in±ÇtšµUe «rm“eGdiaÀt˜eŽ¡‘,tµUe «rm–Ånb#efore“empãŽloš¸ãyinÜrg“som˜e“ot•Uh˜e «r“rule“tšÜro“shr*«ink“it“t˜o“anot•Uh¸ãeš «r“smÃŽall“tµUe˜rm.“Th¸ãeŽ¡‘,e ect–ªñon“pš#e «rformÃŽance“i˜s“di˜sastrous.“GetŸÿt¸ãinšÜrg“rou˜nš¸ãd“t•Uhi#s“probãŽlem“requireGs“a“h˜ybr*«idŽ¡‘,rešGd•¸ãu“ct“ion–YÐstraÀtµUegy“whiñÆc¸ãh“tr*«ie˜s“tÜro“a•¸ãv“oid›YÐkno“wn˜paÀt•UhÃŽoãŽlogiñÆcal˜cas1ÇeGs.˜Thi#s˜w“oràks˜w“ell,Ž¡‘,al•Ürt•UhÃŽough›'©dÕTecidin“g˜on˜t•Uh¸ãe˜spãŽlit˜requireGs˜a˜gre•qaÀt˜dÕTe“al˜of˜dÕTet•¸ãaileGd˜in“v“eGst“igaÀt“ion˜in±ÇtÜroŽ¡‘,tš•Uh¸ãe–UUpreci#s1Çe“dynÃŽamiñÆcs“of“t˜hš¸ãe“reGd˜u˜ct˜ion“systµUem“as“ap˜pãŽlieGd“tÜro“reqali#st˜iñÆc“w˜oràkloads.Ž© Âó‘;W‘ÿ*ªaÀt•¸ãc“hinÜrg›wÅt•Uh“e˜rewr*«itµUe «r˜aÀt˜w“oràk˜rev“eqaleGd˜anot•Uh“e• «r˜in±ÇtµUe“reGst¸ãin•Ürg,˜bu“t,˜in˜retroqsp#ect,Ž¡‘,ušÜrnsurpr*«i•#s“in˜g›Ƈf“act:˜t•Uh•¸ãe˜a“bqstract˜in±Çt•µUeš «rpret“e˜r's›Ƈ\v•¸ãoGca“bulary"˜of˜tµUe «rm-com‘ÿ|qbinÃŽaÀt“ionsŽ¡‘,emitŸÿtšµUeGd–˜…i#s“part¸ãiñÆcularly“limit˜eGd.“Thš¸ãe“sam˜e“smÃŽall“coãŽllect˜ion“of“idioms“oGccurs“o˜v˜e «rŽ¡‘,an•¸ãd›˜“o“v“e «r˜again.˜Som“e˜of˜t•Uh“eGs1Çe˜idioms˜are˜extrem“ely˜common,˜buÜrt˜t•Uh“ey˜are˜alsoŽ¡‘,quitšµUe–õbig.“Big“t˜eš «rms“are“a“p#e˜rformÃŽance“lia•¸ãbilit“y;›õcons•#i“st•µUen±Çt•Uly˜smÃŽall˜t“e «rms˜t“en¸ãd˜tÜroŽ¡‘,giv•¸ãe›¬m•Uu“c“h˜b•#etŸÿtµUe «r˜p“e «rform•ÃŽance.˜Th¸ãaÀt˜m“ak•¸ãeGs˜it˜aÀtŸÿtract“iv“e˜tÜro˜capt“ure˜su“c“h˜idiomsŽ¡‘,in–Ôÿsp#ecial,“nš¸ãew“tµUe «rms,“an˜d“adjust“t•Uh˜e“rewr*«itµUe“ruleGs“accordinÜrgly‘ÿ*ª.“Thiš#s“shÃŽould“b˜eŽ¡‘,donš¸ãe–Õïspar*«inÜrgly‘ÿ*ª,“s#ince“t•Uh˜e“tšµUe «rm“rewr*«it˜e «r“b#ecom¸ãeGs“compãŽliñÆcaÀt˜eGd“bš¸ãy“h˜a˜vinšÜrg“t˜o“dÕTeqalŽ¡‘,wit••Uh›Óm“ulÜrt•¸ãipãŽle˜repreGs1Çen±Çt“aÀt“ions˜of˜t•Uh“e˜sam“e˜tµUe «rm.˜St“ill,˜capt“ur*«inÜrg˜just˜t“w“o˜commonŽ¡‘,idioms–ƒ„likš¸ãe“t•Uhi#s“h˜as“giv˜en“p#e «rformÃŽance“gains“v˜e «ry“roughly“on“t•Uh˜e“ordÕTe «r“of“25Ž¡‘,t•¸ãim“eGs–UUfor“som¸ãe“inpuÜrtàs.ަ‘;Ev¸ãen–?witš•Uh“t˜hi#s“tr*«iñÆc•¸ãk“e «ry‘ÿ*ª,‘?t˜h“e›?a“bqstract˜in±Çt•µUeš «rpret“e˜r–?can“som•¸ãet“im“eGs–?emit“tµUe˜rms“soŽ¡‘,large–®ªt•Uhš¸ãey“sw˜amp“t•Uh˜e“rewr*«itµUe «r.“In“t•Uhiš#s“s˜it•¸ãuaÀt“ion–®ªit“i˜s“h¸ãelpful“tÜro“dÕTevi˜s1Çe“a“w¸ãay“tÜroŽ¡‘,pruÜrnš¸ãe–™çtµUe «rms“so“t•Uh˜e“moqst“impGort˜an±Çt“informÃŽaÀt˜ion“i#s“ret˜ain˜eGd,“whilst“dramÃŽaÀt˜iñÆcallyŽ¡‘,shr*«inkinšÜrg–ªðt•Uh¸ãe“tµUe «rm.“Of“cours1Çe,“dÕTe nin˜g“wh¸ãašÀt“informÃŽa˜tš¸ãion“i#s“impGort˜an±Çt“an˜d“hÃŽo˜wŽ¡‘,safetš¸ãy–.€i#s“pre•Gs1Çe «rv˜e“d–.€dÕTep#en˜ds“en±Çt˜irely“on“t•Uh˜e“a˜bqstract“in±ÇtµUe «rpret˜aÀt˜ion.“F‘ÿ*ªor“t•Uhi#s“kin˜dŽ¡‘,of–KÒstr*«iñÆctnš¸ãeGsqs“anÃŽalys•#i“s,–KÒit“i#s“safe“tÜro“repãŽlace“an˜y“tµUe «rm“b˜y“¸?²,“s#ince“¸?“²c˜h˜aractµUe «r*«i#s1ÇeGs“\noŽ¡‘,dÕTemÃŽan•¸ãd".›ÊòTh“e˜sõTc“h“em“e˜empãŽlo“y“eGd˜pruÜrn“eGs˜t•µUe «rms˜aft“e «r˜a˜sp#eci e•Gd˜dÕTept•Uh˜of˜n¸ãe“stµUe“dŽ¡‘,ÁW–Ú8²or›Ú[ÁS“²constru•¸ãct“ions˜h“as˜b•#een˜s1Çeen.˜Thi“s˜dÕTept•Uh-bas1ÇeGd˜pru•Ürnin“g,˜whilst˜crudÕTe,˜i#sŽ¡‘,f*«requen±Çt•Uly›ä²e ect•¸ãiv“e,˜buÜrt˜do#eGs˜not˜w“oràk˜w“ell˜for˜v“e «ry˜widÕTe,˜sh“allo“w˜tµUe «rms.˜F‘ÿ*ªurt•Uh“e «rŽ¡‘,in•¸ãv“eGst“igaÀt“ion–¤in±ÇtšÜro“clev¸ãe• «re“r–¤pru˜nin˜g“straÀtµUegieGs,“anš¸ãd“t•Uh˜eGir“relaÀt˜ionship“tšÜro“widÕTenin˜g,Ž¡‘,could–UUb#e“w•¸ãort•Uh“while.ŽŸ!ÎÀ‘,»3.4‘ üIn¦ tª"e Drf(äacin×g–ÕTt…Thš®9e“a˜b µs-tract“in¦ t•ª"eš Drpret“e˜r–ÕTan®9d“ xpQÇoin¦ 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«rformÃŽanceŽ¡‘,re•GsulÜrtàs›uHrep“ortµUe“d˜b#elo•¸ãw˜could˜n“ev“e «r˜h“a“v“e˜b#een˜ac“hiev“eGd,˜nor˜ev“en˜ap“proac“h“eGd,ŽŽŽŒ‹ý¢ gÌ\ ý¯3¤ 2Ì\ ýäܚ‘R²h•¸ãad›k7t•Uh“e˜in±Çt•µUeš «rpret“e˜r–k7b#een“wrš*«itŸÿtµUen“in“a“str˜iñÆct“lanšÜrguage,“SML,“for“exampãŽle.“F‘ÿ*ªu˜t•Uh¸ãe «rޤ ‘RdÕTetš¸ãails–UUare“a˜v‘ÿqÇaila˜bãŽle“in‘[Sew94Ž‘8ç],“Sect˜ion“4.Ž© ÷‘aTh•¸ãe›Ø comm“en±Çtàs˜t•Uhree˜paragraphs˜bac“k˜regardinÜrg˜idioms˜an“d˜t•Uh“e˜t•µUe «rm˜rewr*«it“e «rŽ¡‘Rb#elie–üÀa“more“fu•Ürnš¸ãd“am˜en±Çt˜al–üÀdÕTeGs#ign“ aw“whiñÆc˜h“limitàs“p#eš «rformÃŽance:“s1Çe˜r*«ious“an¸ãdŽ¡‘RextµUens#iv•¸ãe›Q¹sh“ar*«inÜrg˜lo•qs“s1Çe•Gs.˜Th¸ãe˜idiom-sp“otŸÿt•¸ãinÜrg˜tr*«iñÆc“k˜giv“eGs˜big˜p•#e «rformÃŽance˜sp“eeGd¸ãupqsŽ¡‘Rpr•*«imÃŽar“ily–¸„b#ecaŸÿus1Çe“it“a•¸ãv“oids›¸„d“upãŽliñÆcaÀt“ion˜of˜arbitrar*«ily˜large˜su•UbtµUe «rms.˜Man“y˜of˜t•Uh“eŽ¡‘Rcas1ÇeGs–=Ñof“t•Uhš¸ãe“a˜bqstract“in±Çt•µUeš «rpret“e˜r›=Ñd¸ãupãŽliñÆcaÀt“e˜t“e «rms˜in¸ãdi#sõTcr*«iminÃŽaÀt“ely‘ÿ*ª.˜All˜t•Uhi#s˜pGoin±ÇtàsŽ¡‘RtÜro–ÚÈa“nš¸ãeeGd“for“expãŽliñÆcit“sh˜ar*«inÜrg“in“tµUe «rms:“non-recurs#iv˜e“a˜bqstract“Álet²s.“MoGdifyinÜrgŽ¡‘Rt•Uh¸ãe–ÃËtšµUe «rm“rewr*«it˜e «r“tšÜro“w¸ãoràk“wit•Uh“Álet²s“sou˜nš¸ãds“leGsqs“t•Uh˜an“straigh˜tforw˜ard,“so“it“migh˜tŽ¡‘Rb#e–zuhš¸ãelpful“tÜro“bGorro˜w“k˜ey“idÕTeqas“f*«rom“t•Uh˜e“call-b˜y-n˜eešGd“lam‘ÿ|qb˜dÜra“calculus“dÕTe˜sõTcr*«ib#e˜dŽ¡‘Rin‘[AFMŸü^ÿ±+Ž‘£²95Ž‘'Õ]].ަ‘aGo•Go“d–>+p#eš «rformÃŽance“hinÜrgeGs“on“gen•¸ãe˜raÀt“inÜrg–>+smÃŽall“tµUe˜rms“anš¸ãd“k˜eepinÜrg“t•Uh˜em“smÃŽallŽ¡‘Rt••UhroughÃŽouÜrt›/<t“h¸ãeGir˜v‘ÿqÇar*«ious˜mÃŽan•Ürglin“gs.˜IdÕTeqally‘ÿ*ª,˜t••Uh¸ãe˜s#ize˜of˜t“h•¸ãe˜a“bqstract˜in±Çt•µUeš «rpret“e˜r'sŽ¡‘Rou•ÜrtÊªpu“t–F†shšÃŽould“b#e“pro•¸ãpGort“ion˜al–F†only“tÜro“tš•Uh¸ãe“s#ize“of“t˜h¸ãe“source“program.“Thiš#s“i˜sŽ¡‘Rproba•¸ãbãŽly›˜ÑuÜrnreqali#st“iñÆc.˜Nev“e «rt•Uh“ele•Gsqs,˜dÕTe“s#ign•¸ãe «rs˜of˜a“bqstract˜in±ÇtµUe «rpret“aÀt“ions˜w“ouldŽ¡‘Rbš#e–>w¸ãell“advi˜s1ÇeGd“tšÜro“str*«iv¸ãe“t˜o•¸ãw“ards–>t•Uhi#s“goal.“As“an“exampãŽle,“Phil“W‘ÿ*ªadle «r's“or*«i-Ž¡‘RginšÃŽal–a"non- aÀt“str*«iñÆctn¸ãeGsqs“an˜alys•#i“s›a"sõTc•¸ãh“em“e‘[W‘ÿ*ªad87Ž‘]˜ga“v“e˜an˜in±ÇtµUe «rpret“aÀt“ion˜of˜ÁcaseŽ¡‘R²expreGsqs#ions–eHwhiñÆcš¸ãh“expan˜ds“expGon˜en±Çt˜ially“witš•Uh“t˜hš¸ãe“s#ize“of“inst˜an±Çt˜iaÀt˜inÜrg“t˜ypš#eGs.“Thi˜sŽ¡‘Rrenš¸ãdÕTe «rs–ݕit“impract˜iñÆcal“for“all“buÜrt“t•Uh˜e“t˜inieGst“programs“([Sew94Ž‘8ç],“Sect˜ion“5.8).“OurŽ¡‘Rbac•¸ãkw“ards›åf*«ram“ew“oràk˜i#s˜pGoãŽlymorphiñÆcally˜in“v‘ÿqÇar*«ian±Çt,˜so˜it˜a“v“oids˜t•Uh“aÀt˜part“iñÆcularŽ¡‘RhÃŽorror,–×õbuÜrt“it“stš¸ãill“h˜as“pãŽlen±Çt˜y“of“pGotµUen±Çt˜ial“for“o˜pt˜imi#saÀt˜ion“us#inÜrg“a˜bqstract“Álet²s.Ž¡‘RTh¸ãe–vÒpGoin±Çt“of“t•Uhiš#s“exampãŽle“i˜s“tš•Uh¸ãaÀt,“wit˜h“a“litŸÿt˜le“care,“m˜u•¸ãc“h–vÒof“t˜hš¸ãe“\exp•Gon˜en±Çt˜ialn˜e“sqs"Ž¡‘Rcan–UUb#e“enÜrginš¸ãee «reGd“aw˜ay‘ÿ*ª,“givinÜrg“su•Ubqst˜an±Çt˜ial“pš#e «rformÃŽance“b˜en¸ãe tàs.ŽŸ è7‘RÓ4‘ €Re`sulÐtÔËsŽŸÑ‘R»4.1‘ üIn–ÕTt…Th®9e“smº}allŽŸÑ‘R²Th•¸ãe›6wtµUec“hnoãŽlogy˜dÕTe•GsõTcr*«ib#e“d˜aš¸ãb“o˜v˜e–6ww˜as“constru˜ctµUešGd“ins#idÕTe“a“purp˜oqs1Çe-builÜrt“dÕTev¸ãel-Ž¡‘Ro•¸ãpm“en±Çt›-`f*«ram“ew“oràk.˜Th“e˜f*«ram“ew“oràk˜i#s˜a˜quiñÆc“k-an“d-dirt“y˜impãŽlem“en±Çt“aÀt“ion˜of˜t•Uh“eŽ¡‘Rf*«ron±Çt–&Åpart“of“a“compileš «r“for“an“o•¸ãv“e˜rloadinÜrg-f*«ree–&Åsu•Ubqs1Çet“of“Haskš¸ãell,“dÕTe•Gs#ign˜e“d‘&ÅtÜroŽ¡‘Rf•#acilitš¸ãaÀtµUe‘Ÿúexp“e• «r*«im˜en±Çt˜aÀt˜ion.‘ŸúA‘Ÿ¤high˜e“r-ordÕTe“r–Ÿúremo˜v‘ÿqÇal“transformÃŽaÀt˜ion“in“t•Uh˜e“st˜yleŽ¡‘Rof–³LNelan‘[Nel91Ž‘¸ç]“allo¸ãws“ r•s“t-ordÕTe «r–³LanšÃŽalys1ÇeGs“of“programs“m˜akinÜrg“su•Ubqst•¸ãan±Çt“ial‘³Lus1ÇeŽ¡‘Rof›Áhigh¸ãe• «r-ordÕTe“r˜fuÜrnct•¸ãions.˜All˜anÃŽalys1ÇeGs˜w“e «re˜don“e˜monomorphiñÆcally‘ÿ*ª,˜tÜro˜mÃŽak“eŽ¡‘Rcompar*«i#son–¶Ûwit•Uh“a“forwš¸ãard“in±ÇtµUe «rpret˜aÀt˜ion“f#aire «r.“F‘ÿ*ªor“t•Uh˜e“bac˜kw˜ards“anÃŽalys1ÇeGs,Ž¡‘Rof–Lþcours1Çe,“t•Uh¸ãe 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‘Z˶ÐProgram‘H‡ŸLτ ff‘™š„ ffŽ’\–Tim¾9e‘H‡ŸLτ ffŽ’¸gÌReAÇs äid‘H‡ŸLτ ff‘™š„ ffŽ’ܤøTim¾9e‘H‡ŸLτ ffŽ’ý¹ReAÇs äid‘H‡ŸLτ ff‘™š„ ffŽ’!EåTim¾9e‘H‡ŸLτ ffŽ’A©¦ReAÇs äidŽŽ‘YePŸ³5‰ffUŸ³1‘keÜavlTreeŽ‘(ÌŸLτ ff‘™š„ ffŽ‘;V`Ð9.58‘H‡ŸLτ ffŽ‘c,É1514‘H‡ŸLτ ff‘™š„ ffŽ’‡žÂ0.23‘H‡ŸLτ ffŽ’¬"öó3¼j‘¹ cmti9Þ197‘H‡ŸLτ ff‘™š„ ffŽ’Ì?¯Ð0.27‘H‡ŸLτ ffŽ’ðÃãÞ200ŽŽ¡‘ ÆÜlifeŽ‘(ÌŸLτ ff‘™š„ ffŽ‘2dÐ359.20‘H‡ŸLτ ffŽ‘^ŒË11203‘H‡ŸLτ ff‘™š„ ffŽ’‡žÂ2.01‘H‡ŸLτ ffŽ’¬m´628‘H‡ŸLτ ff‘™š„ ffŽ’Ì?¯2.97‘H‡ŸLτ ffŽ’ðÃãÞ615ŽŽ¡‘ ޑÜfftŽ‘(ÌŸLτ ff‘™š„ ffŽ‘6¶bÐ28.76‘H‡ŸLτ ffŽ‘bÉ!Þ1473‘H‡ŸLτ ff‘™š„ ffŽ’‡žÂÐ6.38‘H‡ŸLτ ffŽ’§jÞ1473‘H‡ŸLτ ff‘™š„ ffŽ’Ì?¯Ð8.38‘H‡ŸLτ ffŽ’ì ûÞ1524ŽŽ¡‘ ޑÜidaŽ‘(ÌŸLτ ff‘™š„ ffŽ‘6¶bÐ920+‘H‡ŸLτ ffŽ‘W[54000+‘H‡ŸLτ ff‘™š„ ffŽ’‡žÂ9.32‘H‡ŸLτ ffŽ’§jÞ1725‘H‡ŸLτ ff‘™š„ ffŽ’Ì?¯Ð7.70‘H‡ŸLτ ffŽ’ì ûÞ1734ŽŽŽŽŽŸ:³3‘,ÑT‘ÿÌa´Cbá´le‘†1.–¬ßÐPš¾9e ÞrformÈance“of“a˜bNs”tract“in·¤t•ºîeš Þrpret“e˜r”s›¬ß(t•¾9im“e˜in˜s. econ“ds,˜re•AÇs äidØ‡encie“s˜in˜Kb¾9ytºîe“s).ޤ 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Þr“ScienceAÇs,Ž¡‘Xa²Ch•¾9alm“eš Þr”s‘TUniv“e˜r”s äit“y–Tof“T–ÿ:«ec¾9hnoå±logy“.Ž¡‘,[Hal93]ŽŽ‘Xa²CordØ‡elia‘V.––ZHall.‘šKUsš äinßg“s”tr'xiò×ctn¾9eAÇsNs“anÈalys˜i˜s“in“practš¾9iò×ce“for“dßaÄÍt˜a“s”tru˜ct˜ureAÇs.Ž¡‘Xa²In–{John‘T.“O'Donnš¾9ell“an˜d“K˜evin“Hammon˜d,“eAÇditßor”s,“ÞGlasgow‘–þWorkshopŽ¡‘Xa²on–¡F‘ÿJªunctional“Pr•‡o“gr“ammingÐ,–ÔwW‘ÿ:«orâfkshÈoš¾9pNs“in“Compu•ßt˜in“g,–ÔwAyr,“ScotTlan˜d,“JulyŽ¡‘Xa²1993.‘TSpr'xinßge• Þr-V‘ÿ:«e“rlag.Ž¡‘,[HH91]ŽŽ‘Xa²SeØ‡bas”tš¾9ian–ºHußn·¤t“an˜d“Chr'xi äs“Hankin.‘€™FixešAÇd“p˜oinš·¤tâfs“an¾9d“f'xron˜tš¾9ie Þr”s:“a“n˜ew“p äe Þr-Ž¡‘Xa²sp äect•¾9iv“e.‘ ÃÞJournal–0Sof“F‘ÿJªunctional“Pr•‡o“gr“ammingÐ,–ôÇ1(1):91“{“120,“JanTuary“1991.Ž¡‘,[HL92a]ŽŽ‘Xa²Piet•ºîe Þr‘H.›çøHart“el˜an•¾9d˜Ko äen‘G.˜Lanšßgen“do äen.‘ Benc“hmÈarâfkin˜g‘çøimpå±lem“en·¤t“aÄÍt“ionsŽ¡‘Xa²of–(flazy“fušßnct¾9ionÈal“lan˜guagešAÇs.‘M„T‘ÿ:«ec¾9hniò×cal“rep˜ort,“Depart•¾9m“en·¤t–(fof“Compußtºîe ÞrŽ¡‘Xa²Sys”tºîems,–ê¾F‘ÿ:«aculßtš¾9y“of“Ma•ÄÍtTh˜emÈa“t˜iò×cs–ê¾an˜d“Compußtºîe Þr“Science,“Univ˜e Þr”s äit˜y“of“Am-Ž¡‘Xa²s”tºîe• Þrdßam,›TDecem†Pb äe“r˜1992.Ž¡‘,[HL92b]ŽŽ‘Xa²John–æ Hughš¾9eAÇs“an˜d“John“La§3ußnc˜h˜bury‘ÿ:«.‘ ‚çPro‘ƒŽject˜ions“for“pAÇoå±lymorphiò×c“ r•”s“t-Ž¡‘Xa²ordØ‡e Þr–þòs”tr'xiò×ctn¾9eAÇsNs“anÈalys• äi“s.‘†In‘þòÞMathematic•‡al›9ªStructur“es˜in˜Computer˜Scienc“eÐ,Ž¡‘Xa²v•¾9oå±lußm“e‘2,–TpageAÇs“301{326,“1992.Ž¡‘,[HM94]ŽŽ‘Xa²C.›L.–B9Hankin“an¾9d“D.˜Le“M¾ª‘û¡Xet•¾9ay“e• Þr.‘Ÿ—De“r•'xivinßg›B9algor“itThms˜f“rom˜t¾9yp äe˜infe ÞrenceŽ¡‘Xa²sys”tºîems:›–(A‘ÿ|rp•¾9på±liò×caÄÍt“ion˜tßo˜s”tr'xiò×ctn“eAÇsNs˜anÈalys• äi“s.‘”—In˜ÞPr•‡o“c“e“e“dings–¯Þof“POPL'94Ð,Ž¡‘Xa²1994.Ž¡‘,[Hug90]ŽŽ‘Xa²John›˜œHugh•¾9eAÇs.‘¡Compile-t“im“e˜anÈalys• äi“s˜of˜fußnct•¾9ionÈal˜programs.‘¡In˜Da“vid‘A.Ž¡‘Xa²T‘ÿ:«ur än¾9e Þr,–ó eAÇditßor,“ÞR•‡ese“ar“ch–ðxT›ÿJªopics“in“F˜unctional“Pr•‡o“gr“ammingÐ.‘ó Addi äson-Ž¡‘Xa²W›ÿ:«eAÇsley–¨DPuTbå±li äshinßg“Compan¾9y˜,“1990.‘Ï®F˜rom“tTh¾9e“1987“Y˜eNar“of“Programminßg,Ž¡‘Xa²Univ•¾9e Þrš”s äit“y–Tof“T‘ÿ:«exas,“A‘ÿ|rus˜t¾9in,“T‘ÿ:«exas.Ž¡‘,[Hußn91]ŽŽ‘Xa²SeØ‡bas”t¾9ian‘ŸHußn·¤t.‘¯2ÞAÃŽbstr•‡act›¸Interpr“etation˜of˜F‘ÿJªunctional˜L“anguages:˜F‘ÿJªr“omŽ¡‘Xa²Theš‡ory–?fto“Pr˜actic˜eÐ.‘'ÞPhD‘€tTh¾9eAÇs• äi“s,›ÄImp“e• Þr'xial˜Coå±llege,˜Univš¾9e“r”s äit˜y–Äof“Lon˜don,Ž¡‘Xa²1991.ŽŽŽŒ‹W+ gÌ\ ý¯3¤ 2Ì\ ýäܚ‘RÐ[JM86]ŽŽ‘~a²Ne•AÇil‘D.› Jon¾9e“s˜an•¾9d˜Alan˜Mycroft.‘îpDaÄÍt“a˜ o“w˜anÈalys• äi“s˜of˜ap•¾9på±liò×caÄÍt“iv“e˜programsޤ ‘~a²us äinšßg–¬·minimÈal“fu˜nctš¾9ion“graphs:“A‘ÿ|rbr'xidgeAÇd“v˜e Þr”s äion.‘óIn“ÞThirte‡enth‘îAÃŽCM‘îSym-Ž¡‘~a²pš‡osium–Ó/on“Principles“of“Pr˜o˜gr˜amming“L˜anguages,“St.“Petersbur˜g,“FloridaÐ,Ž¡‘~a²pageAÇs–T296{306,“1986.Ž¡‘R[Jon93]ŽŽ‘~a²Marâfk‘P‘ÿ:«.›«LJon•¾9eAÇs.‘ò”P“art“ial˜ev‘ÿ|raluaÄÍt“ion˜for˜diò×ct“ionÈary-f'xree˜o“v“e 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äi“s,˜Ar'xizonÈa˜St•¾9aÄÍtºîe˜Univ“e Þr”s äit“y‘ÿ:«,˜1991.Ž¡‘R[NN92]ŽŽ‘~a²F.‘Nielson–Danš¾9d“H.R.“Nielson.‘ Finitºîen˜eAÇsNs“con˜dit˜ions“for“ xešAÇd“p˜oin·¤t“itºîe Þra-Ž¡‘~a²t•¾9ion.‘|¦T‘ÿ:«ec“hniò×cal–ŒgrepAÇort,“Compußtºîeš Þr“Science“Depart•¾9m“en·¤t,–ŒgAarhTus“Univ•¾9e˜r”s äit“y‘ÿ:«,Ž¡‘~a²DenmÈarâfk,–TF‘ÿ:«eØ‡bruary“1992.Ž¡‘R[NoAÇc93]ŽŽ‘~a²Erš'xiò×c‘֓NoAÇc•¾9k“e Þr.‘—Str˜iò×ctn“eAÇsNs›֓anÈalys• äi“s˜us“inßg˜a•¾9bNs”tract˜reAÇd“u“ct“ion.‘—In˜ÞPr•‡o“c“e“e“dings‘‘ofŽ¡‘~a²FPCA93,–N<Cop‡enhagen,“DenmarkÐ,–TJußn¾9e“1993.Ž¡‘R[P¾9ar92]ŽŽ‘~a²Will›/¥P•¾9art“ain.‘cTh“e˜Ünofib˜Ðb äenc“hmÈarâfk˜suitºîe˜of˜h“ask“ell˜programs.‘cIn˜ÞFifthŽ¡‘~a²AÃŽnnual–N<Glasgow“Workshop“on“F‘ÿJªunctional“Pr•‡o“gr“amming,‘N<AyrÐ,‘T1992.Ž¡‘R[PC87]ŽŽ‘~a²Simon–‘ÁPš¾9eytßon“Jon˜eAÇs“an˜d“Chr'xi äs“Clac˜k.‘Œ˜Fin˜dinßg“ xpAÇoin·¤tâfs“in“a˜bNs”tract“in·¤tºîe Þr-Ž¡‘~a²pret•¾9aÄÍt“ion.‘Ó.In–VkS.‘A‘ÿ|rbramsky“an¾9d“C.L.“Hankin,“eAÇditßor”s,“ÞAÃŽbstr•‡act‘žÍInterpr“etationŽ¡‘~a²of›R`De•‡clar“ative˜L“anguagesÐ,–0kCompußtºîe Þr”s“anš¾9d“Th˜eAÇir“A‘ÿ|rp˜på±liò×caÄÍt˜ions,“c˜h˜aptºîe Þr‘11,Ž¡‘~a²pagešAÇs–T246{265.“Elli äs“Horw¾9o˜o˜d,“1987.Ž¡‘R[PJ93]ŽŽ‘~a²Will›nP•¾9art“ain˜an“d˜Simon˜L.‘P“eytßon˜Jon“eAÇs.‘"EM•ßeNasur'xin“g˜tTh•¾9e˜e ect“iv“en“eAÇsNs˜of˜aŽ¡‘~a²s äimpå±le–áas”tr'xiò×ctnš¾9eAÇsNs“anÈalys. e Þr.‘–In“John‘T.“O'Donn˜ell“an˜d“K˜evin“Hammon˜d,“eAÇd-Ž¡‘~a²itßor”s,›@&ÞGlasgow–u•Workshop“on“F‘ÿJªunctional“Pr•‡o“gr“ammingÐ,˜W‘ÿ:«orâfkshÈo¾9pNs˜in˜Com-Ž¡‘~a²pu•ßtš¾9in“g,–TAyr,“ScotTlan˜d,“July“1993.“Spr'xinßge• Þr-V‘ÿ:«e“rlag.Ž¡‘R[RoNs93]ŽŽ‘~a²Mads‘ÆúRoNs. enš¾9d•ßa“hl.‘+2High˜e• Þr-ordØ‡e“r–Æúc˜h˜aot˜iò×c“itºîe ÞraÄÍt˜ion“s. equenceAÇs.‘+2In“ÞPLILP'93Ð,Ž¡‘~a²pageAÇs–T332{345,“T‘ÿ:«allinn,“Es”tšßonia,“1993.“Spr'xin˜ge• 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cosmopolitan/third_party/bzip2/crctable.c
/*-*- mode:c;indent-tabs-mode:nil;c-basic-offset:2;tab-width:8;coding:utf-8 -*-│ │vi: set net ft=c ts=2 sts=2 sw=2 fenc=utf-8 :vi│ ╞══════════════════════════════════════════════════════════════════════════════╡ │ Copyright 2021 Justine Alexandra Roberts Tunney │ │ │ │ Permission to use, copy, modify, and/or distribute this software for │ │ any purpose with or without fee is hereby granted, provided that the │ │ above copyright notice and this permission notice appear in all copies. │ │ │ │ THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL │ │ WARRANTIES WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED │ │ WARRANTIES OF MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE │ │ AUTHOR BE LIABLE FOR ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL │ │ DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR │ │ PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER │ │ TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR │ │ PERFORMANCE OF THIS SOFTWARE. │ ╚─────────────────────────────────────────────────────────────────────────────*/ #ifdef TINY uint32_t BZ2_crc32Table[256]; static textstartup void BZ2_crc32Table_init() { unsigned i, j, u; for (i = 0; i < 256; ++i) { u = i << 24; for (j = 8; j; --j) { if ((int32_t)u < 0) { u = (u << 1) ^ 0x04c11db7; } else { u <<= 1; } } BZ2_crc32Table[i] = u; } if (BZ2_crc32Table[0] || BZ2_crc32Table[255] != 0xb1f740b4) { __builtin_trap(); } } const void *const BZ2_crc32Table_ctor[] initarray = { BZ2_crc32Table_init, }; #else const uint32_t BZ2_crc32Table[256] = { 0x00000000, 0x04c11db7, 0x09823b6e, 0x0d4326d9, 0x130476dc, 0x17c56b6b, 0x1a864db2, 0x1e475005, 0x2608edb8, 0x22c9f00f, 0x2f8ad6d6, 0x2b4bcb61, 0x350c9b64, 0x31cd86d3, 0x3c8ea00a, 0x384fbdbd, 0x4c11db70, 0x48d0c6c7, 0x4593e01e, 0x4152fda9, 0x5f15adac, 0x5bd4b01b, 0x569796c2, 0x52568b75, 0x6a1936c8, 0x6ed82b7f, 0x639b0da6, 0x675a1011, 0x791d4014, 0x7ddc5da3, 0x709f7b7a, 0x745e66cd, 0x9823b6e0, 0x9ce2ab57, 0x91a18d8e, 0x95609039, 0x8b27c03c, 0x8fe6dd8b, 0x82a5fb52, 0x8664e6e5, 0xbe2b5b58, 0xbaea46ef, 0xb7a96036, 0xb3687d81, 0xad2f2d84, 0xa9ee3033, 0xa4ad16ea, 0xa06c0b5d, 0xd4326d90, 0xd0f37027, 0xddb056fe, 0xd9714b49, 0xc7361b4c, 0xc3f706fb, 0xceb42022, 0xca753d95, 0xf23a8028, 0xf6fb9d9f, 0xfbb8bb46, 0xff79a6f1, 0xe13ef6f4, 0xe5ffeb43, 0xe8bccd9a, 0xec7dd02d, 0x34867077, 0x30476dc0, 0x3d044b19, 0x39c556ae, 0x278206ab, 0x23431b1c, 0x2e003dc5, 0x2ac12072, 0x128e9dcf, 0x164f8078, 0x1b0ca6a1, 0x1fcdbb16, 0x018aeb13, 0x054bf6a4, 0x0808d07d, 0x0cc9cdca, 0x7897ab07, 0x7c56b6b0, 0x71159069, 0x75d48dde, 0x6b93dddb, 0x6f52c06c, 0x6211e6b5, 0x66d0fb02, 0x5e9f46bf, 0x5a5e5b08, 0x571d7dd1, 0x53dc6066, 0x4d9b3063, 0x495a2dd4, 0x44190b0d, 0x40d816ba, 0xaca5c697, 0xa864db20, 0xa527fdf9, 0xa1e6e04e, 0xbfa1b04b, 0xbb60adfc, 0xb6238b25, 0xb2e29692, 0x8aad2b2f, 0x8e6c3698, 0x832f1041, 0x87ee0df6, 0x99a95df3, 0x9d684044, 0x902b669d, 0x94ea7b2a, 0xe0b41de7, 0xe4750050, 0xe9362689, 0xedf73b3e, 0xf3b06b3b, 0xf771768c, 0xfa325055, 0xfef34de2, 0xc6bcf05f, 0xc27dede8, 0xcf3ecb31, 0xcbffd686, 0xd5b88683, 0xd1799b34, 0xdc3abded, 0xd8fba05a, 0x690ce0ee, 0x6dcdfd59, 0x608edb80, 0x644fc637, 0x7a089632, 0x7ec98b85, 0x738aad5c, 0x774bb0eb, 0x4f040d56, 0x4bc510e1, 0x46863638, 0x42472b8f, 0x5c007b8a, 0x58c1663d, 0x558240e4, 0x51435d53, 0x251d3b9e, 0x21dc2629, 0x2c9f00f0, 0x285e1d47, 0x36194d42, 0x32d850f5, 0x3f9b762c, 0x3b5a6b9b, 0x0315d626, 0x07d4cb91, 0x0a97ed48, 0x0e56f0ff, 0x1011a0fa, 0x14d0bd4d, 0x19939b94, 0x1d528623, 0xf12f560e, 0xf5ee4bb9, 0xf8ad6d60, 0xfc6c70d7, 0xe22b20d2, 0xe6ea3d65, 0xeba91bbc, 0xef68060b, 0xd727bbb6, 0xd3e6a601, 0xdea580d8, 0xda649d6f, 0xc423cd6a, 0xc0e2d0dd, 0xcda1f604, 0xc960ebb3, 0xbd3e8d7e, 0xb9ff90c9, 0xb4bcb610, 0xb07daba7, 0xae3afba2, 0xaafbe615, 0xa7b8c0cc, 0xa379dd7b, 0x9b3660c6, 0x9ff77d71, 0x92b45ba8, 0x9675461f, 0x8832161a, 0x8cf30bad, 0x81b02d74, 0x857130c3, 0x5d8a9099, 0x594b8d2e, 0x5408abf7, 0x50c9b640, 0x4e8ee645, 0x4a4ffbf2, 0x470cdd2b, 0x43cdc09c, 0x7b827d21, 0x7f436096, 0x7200464f, 0x76c15bf8, 0x68860bfd, 0x6c47164a, 0x61043093, 0x65c52d24, 0x119b4be9, 0x155a565e, 0x18197087, 0x1cd86d30, 0x029f3d35, 0x065e2082, 0x0b1d065b, 0x0fdc1bec, 0x3793a651, 0x3352bbe6, 0x3e119d3f, 0x3ad08088, 0x2497d08d, 0x2056cd3a, 0x2d15ebe3, 0x29d4f654, 0xc5a92679, 0xc1683bce, 0xcc2b1d17, 0xc8ea00a0, 0xd6ad50a5, 0xd26c4d12, 0xdf2f6bcb, 0xdbee767c, 0xe3a1cbc1, 0xe760d676, 0xea23f0af, 0xeee2ed18, 0xf0a5bd1d, 0xf464a0aa, 0xf9278673, 0xfde69bc4, 0x89b8fd09, 0x8d79e0be, 0x803ac667, 0x84fbdbd0, 0x9abc8bd5, 0x9e7d9662, 0x933eb0bb, 0x97ffad0c, 0xafb010b1, 0xab710d06, 0xa6322bdf, 0xa2f33668, 0xbcb4666d, 0xb8757bda, 0xb5365d03, 0xb1f740b4, }; #endif
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jart/cosmopolitan
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cosmopolitan/third_party/bzip2/README.cosmo
DESCRIPTION bzip2 is a lossless compression algorithm that's slower than deflate but achieves better compression ratios w/ Burrows–Wheeler transform. ORIGIN commit 6a8690fc8d26c815e798c588f796eabe9d684cf0 (HEAD, tag: bzip2-1.0.8) Author: Mark Wielaard <[email protected]> Date: Sat Jul 13 17:17:58 2019 +0200 Prepare for 1.0.8 release.
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jart/cosmopolitan
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cosmopolitan/third_party/bzip2/README
This is the README for bzip2/libzip2. This version is fully compatible with the previous public releases. ------------------------------------------------------------------ This file is part of bzip2/libbzip2, a program and library for lossless, block-sorting data compression. bzip2/libbzip2 version 1.0.8 of 13 July 2019 Copyright (C) 1996-2019 Julian Seward <[email protected]> Please read the WARNING, DISCLAIMER and PATENTS sections in this file. This program is released under the terms of the license contained in the file LICENSE. ------------------------------------------------------------------ Complete documentation is available in Postscript form (manual.ps), PDF (manual.pdf) or html (manual.html). A plain-text version of the manual page is available as bzip2.txt. HOW TO BUILD -- UNIX Type 'make'. This builds the library libbz2.a and then the programs bzip2 and bzip2recover. Six self-tests are run. If the self-tests complete ok, carry on to installation: To install in /usr/local/bin, /usr/local/lib, /usr/local/man and /usr/local/include, type make install To install somewhere else, eg, /xxx/yyy/{bin,lib,man,include}, type make install PREFIX=/xxx/yyy If you are (justifiably) paranoid and want to see what 'make install' is going to do, you can first do make -n install or make -n install PREFIX=/xxx/yyy respectively. The -n instructs make to show the commands it would execute, but not actually execute them. HOW TO BUILD -- UNIX, shared library libbz2.so. Do 'make -f Makefile-libbz2_so'. This Makefile seems to work for Linux-ELF (RedHat 7.2 on an x86 box), with gcc. I make no claims that it works for any other platform, though I suspect it probably will work for most platforms employing both ELF and gcc. bzip2-shared, a client of the shared library, is also built, but not self-tested. So I suggest you also build using the normal Makefile, since that conducts a self-test. A second reason to prefer the version statically linked to the library is that, on x86 platforms, building shared objects makes a valuable register (%ebx) unavailable to gcc, resulting in a slowdown of 10%-20%, at least for bzip2. Important note for people upgrading .so's from 0.9.0/0.9.5 to version 1.0.X. All the functions in the library have been renamed, from (eg) bzCompress to BZ2_bzCompress, to avoid namespace pollution. Unfortunately this means that the libbz2.so created by Makefile-libbz2_so will not work with any program which used an older version of the library. I do encourage library clients to make the effort to upgrade to use version 1.0, since it is both faster and more robust than previous versions. HOW TO BUILD -- Windows 95, NT, DOS, Mac, etc. It's difficult for me to support compilation on all these platforms. My approach is to collect binaries for these platforms, and put them on the master web site (https://sourceware.org/bzip2/). Look there. However (FWIW), bzip2-1.0.X is very standard ANSI C and should compile unmodified with MS Visual C. If you have difficulties building, you might want to read README.COMPILATION.PROBLEMS. At least using MS Visual C++ 6, you can build from the unmodified sources by issuing, in a command shell: nmake -f makefile.msc (you may need to first run the MSVC-provided script VCVARS32.BAT so as to set up paths to the MSVC tools correctly). VALIDATION Correct operation, in the sense that a compressed file can always be decompressed to reproduce the original, is obviously of paramount importance. To validate bzip2, I used a modified version of Mark Nelson's churn program. Churn is an automated test driver which recursively traverses a directory structure, using bzip2 to compress and then decompress each file it encounters, and checking that the decompressed data is the same as the original. Please read and be aware of the following: WARNING: This program and library (attempts to) compress data by performing several non-trivial transformations on it. Unless you are 100% familiar with *all* the algorithms contained herein, and with the consequences of modifying them, you should NOT meddle with the compression or decompression machinery. Incorrect changes can and very likely *will* lead to disastrous loss of data. DISCLAIMER: I TAKE NO RESPONSIBILITY FOR ANY LOSS OF DATA ARISING FROM THE USE OF THIS PROGRAM/LIBRARY, HOWSOEVER CAUSED. Every compression of a file implies an assumption that the compressed file can be decompressed to reproduce the original. Great efforts in design, coding and testing have been made to ensure that this program works correctly. However, the complexity of the algorithms, and, in particular, the presence of various special cases in the code which occur with very low but non-zero probability make it impossible to rule out the possibility of bugs remaining in the program. DO NOT COMPRESS ANY DATA WITH THIS PROGRAM UNLESS YOU ARE PREPARED TO ACCEPT THE POSSIBILITY, HOWEVER SMALL, THAT THE DATA WILL NOT BE RECOVERABLE. That is not to say this program is inherently unreliable. Indeed, I very much hope the opposite is true. bzip2/libbzip2 has been carefully constructed and extensively tested. PATENTS: To the best of my knowledge, bzip2/libbzip2 does not use any patented algorithms. However, I do not have the resources to carry out a patent search. Therefore I cannot give any guarantee of the above statement. WHAT'S NEW IN 0.9.0 (as compared to 0.1pl2) ? * Approx 10% faster compression, 30% faster decompression * -t (test mode) is a lot quicker * Can decompress concatenated compressed files * Programming interface, so programs can directly read/write .bz2 files * Less restrictive (BSD-style) licensing * Flag handling more compatible with GNU gzip * Much more documentation, i.e., a proper user manual * Hopefully, improved portability (at least of the library) WHAT'S NEW IN 0.9.5 ? * Compression speed is much less sensitive to the input data than in previous versions. Specifically, the very slow performance caused by repetitive data is fixed. * Many small improvements in file and flag handling. * A Y2K statement. WHAT'S NEW IN 1.0.x ? See the CHANGES file. I hope you find bzip2 useful. Feel free to contact the developers at [email protected] if you have any suggestions or queries. Many people mailed me with comments, suggestions and patches after the releases of bzip-0.15, bzip-0.21, and bzip2 versions 0.1pl2, 0.9.0, 0.9.5, 1.0.0, 1.0.1, 1.0.2 and 1.0.3, and the changes in bzip2 are largely a result of this feedback. I thank you for your comments. bzip2's "home" is https://sourceware.org/bzip2/ Julian Seward [email protected] Cambridge, UK. 18 July 1996 (version 0.15) 25 August 1996 (version 0.21) 7 August 1997 (bzip2, version 0.1) 29 August 1997 (bzip2, version 0.1pl2) 23 August 1998 (bzip2, version 0.9.0) 8 June 1999 (bzip2, version 0.9.5) 4 Sept 1999 (bzip2, version 0.9.5d) 5 May 2000 (bzip2, version 1.0pre8) 30 December 2001 (bzip2, version 1.0.2pre1) 15 February 2005 (bzip2, version 1.0.3) 20 December 2006 (bzip2, version 1.0.4) 10 December 2007 (bzip2, version 1.0.5) 6 Sept 2010 (bzip2, version 1.0.6) 27 June 2019 (bzip2, version 1.0.7) 13 July 2019 (bzip2, version 1.0.8)
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cosmopolitan/third_party/bzip2/makefile.msc
# Makefile for Microsoft Visual C++ 6.0 # usage: nmake -f makefile.msc # K.M. Syring ([email protected]) # Fixed up by JRS for bzip2-0.9.5d release. CC=cl CFLAGS= -DWIN32 -MD -Ox -D_FILE_OFFSET_BITS=64 -nologo OBJS= blocksort.obj \ huffman.obj \ crctable.obj \ randtable.obj \ compress.obj \ decompress.obj \ bzlib.obj all: lib bzip2 test bzip2: lib $(CC) $(CFLAGS) -o bzip2 bzip2.c libbz2.lib setargv.obj $(CC) $(CFLAGS) -o bzip2recover bzip2recover.c lib: $(OBJS) lib /out:libbz2.lib $(OBJS) test: bzip2 type words1 .\\bzip2 -1 < sample1.ref > sample1.rb2 .\\bzip2 -2 < sample2.ref > sample2.rb2 .\\bzip2 -3 < sample3.ref > sample3.rb2 .\\bzip2 -d < sample1.bz2 > sample1.tst .\\bzip2 -d < sample2.bz2 > sample2.tst .\\bzip2 -ds < sample3.bz2 > sample3.tst @echo All six of the fc's should find no differences. @echo If fc finds an error on sample3.bz2, this could be @echo because WinZip's 'TAR file smart CR/LF conversion' @echo is too clever for its own good. Disable this option. @echo The correct size for sample3.ref is 120,244. If it @echo is 150,251, WinZip has messed it up. fc sample1.bz2 sample1.rb2 fc sample2.bz2 sample2.rb2 fc sample3.bz2 sample3.rb2 fc sample1.tst sample1.ref fc sample2.tst sample2.ref fc sample3.tst sample3.ref clean: del *.obj del libbz2.lib del bzip2.exe del bzip2recover.exe del sample1.rb2 del sample2.rb2 del sample3.rb2 del sample1.tst del sample2.tst del sample3.tst .c.obj: $(CC) $(CFLAGS) -c $*.c -o $*.obj
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jart/cosmopolitan
false
cosmopolitan/third_party/bzip2/bzdiff
#!/bin/sh # sh is buggy on RS/6000 AIX 3.2. Replace above line with #!/bin/ksh # Bzcmp/diff wrapped for bzip2, # adapted from zdiff by Philippe Troin <[email protected]> for Debian GNU/Linux. # Bzcmp and bzdiff are used to invoke the cmp or the diff pro- # gram on compressed files. All options specified are passed # directly to cmp or diff. If only 1 file is specified, then # the files compared are file1 and an uncompressed file1.gz. # If two files are specified, then they are uncompressed (if # necessary) and fed to cmp or diff. The exit status from cmp # or diff is preserved. PATH="/usr/bin:/bin:$PATH"; export PATH prog=`echo $0 | sed 's|.*/||'` case "$prog" in *cmp) comp=${CMP-cmp} ;; *) comp=${DIFF-diff} ;; esac OPTIONS= FILES= for ARG do case "$ARG" in -*) OPTIONS="$OPTIONS $ARG";; *) if test -f "$ARG"; then FILES="$FILES $ARG" else echo "${prog}: $ARG not found or not a regular file" exit 1 fi ;; esac done if test -z "$FILES"; then echo "Usage: $prog [${comp}_options] file [file]" exit 1 fi set $FILES if test $# -eq 1; then FILE=`echo "$1" | sed 's/.bz2$//'` bzip2 -cd "$FILE.bz2" | $comp $OPTIONS - "$FILE" STAT="$?" elif test $# -eq 2; then case "$1" in *.bz2) case "$2" in *.bz2) F=`echo "$2" | sed 's|.*/||;s|.bz2$||'` tmp=`mktemp "${TMPDIR:-/tmp}"/bzdiff.XXXXXXXXXX` || { echo 'cannot create a temporary file' >&2 exit 1 } bzip2 -cdfq "$2" > "$tmp" bzip2 -cdfq "$1" | $comp $OPTIONS - "$tmp" STAT="$?" /bin/rm -f "$tmp";; *) bzip2 -cdfq "$1" | $comp $OPTIONS - "$2" STAT="$?";; esac;; *) case "$2" in *.bz2) bzip2 -cdfq "$2" | $comp $OPTIONS "$1" - STAT="$?";; *) $comp $OPTIONS "$1" "$2" STAT="$?";; esac;; esac else echo "Usage: $prog [${comp}_options] file [file]" exit 1 fi exit "$STAT"
2,140
77
jart/cosmopolitan
false
cosmopolitan/third_party/bzip2/bzgrep.1
\"Shamelessly copied from zmore.1 by Philippe Troin <[email protected]> \"for Debian GNU/Linux .TH BZGREP 1 .SH NAME bzgrep, bzfgrep, bzegrep \- search possibly bzip2 compressed files for a regular expression .SH SYNOPSIS .B bzgrep [ grep_options ] .BI [\ -e\ ] " pattern" .IR filename ".\|.\|." .br .B bzegrep [ egrep_options ] .BI [\ -e\ ] " pattern" .IR filename ".\|.\|." .br .B bzfgrep [ fgrep_options ] .BI [\ -e\ ] " pattern" .IR filename ".\|.\|." .SH DESCRIPTION .IR Bzgrep is used to invoke the .I grep on bzip2-compressed files. All options specified are passed directly to .I grep. If no file is specified, then the standard input is decompressed if necessary and fed to grep. Otherwise the given files are uncompressed if necessary and fed to .I grep. .PP If .I bzgrep is invoked as .I bzegrep or .I bzfgrep then .I egrep or .I fgrep is used instead of .I grep. If the GREP environment variable is set, .I bzgrep uses it as the .I grep program to be invoked. For example: for sh: GREP=fgrep bzgrep string files for csh: (setenv GREP fgrep; bzgrep string files) .SH AUTHOR Charles Levert ([email protected]). Adapted to bzip2 by Philippe Troin <[email protected]> for Debian GNU/Linux. .SH "SEE ALSO" grep(1), egrep(1), fgrep(1), bzdiff(1), bzmore(1), bzless(1), bzip2(1)
1,297
57
jart/cosmopolitan
false
cosmopolitan/third_party/bzip2/bz_internal_error.c
/*-*- mode:c;indent-tabs-mode:nil;c-basic-offset:2;tab-width:8;coding:utf-8 -*-│ │vi: set net ft=c ts=2 sts=2 sw=2 fenc=utf-8 :vi│ ╞══════════════════════════════════════════════════════════════════════════════╡ │ Copyright 2021 Justine Alexandra Roberts Tunney │ │ │ │ Permission to use, copy, modify, and/or distribute this software for │ │ any purpose with or without fee is hereby granted, provided that the │ │ above copyright notice and this permission notice appear in all copies. │ │ │ │ THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL │ │ WARRANTIES WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED │ │ WARRANTIES OF MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE │ │ AUTHOR BE LIABLE FOR ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL │ │ DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR │ │ PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER │ │ TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR │ │ PERFORMANCE OF THIS SOFTWARE. │ ╚─────────────────────────────────────────────────────────────────────────────*/ void bz_internal_error(int err) { __builtin_trap(); }
1,893
23
jart/cosmopolitan
false
cosmopolitan/third_party/bzip2/bzmore
#!/bin/sh # Bzmore wrapped for bzip2, # adapted from zmore by Philippe Troin <[email protected]> for Debian GNU/Linux. PATH="/usr/bin:$PATH"; export PATH prog=`echo $0 | sed 's|.*/||'` case "$prog" in *less) more=less ;; *) more=more ;; esac if test "`echo -n a`" = "-n a"; then # looks like a SysV system: n1=''; n2='\c' else n1='-n'; n2='' fi oldtty=`stty -g 2>/dev/null` if stty -cbreak 2>/dev/null; then cb='cbreak'; ncb='-cbreak' else # 'stty min 1' resets eof to ^a on both SunOS and SysV! cb='min 1 -icanon'; ncb='icanon eof ^d' fi if test $? -eq 0 -a -n "$oldtty"; then trap 'stty $oldtty 2>/dev/null; exit' 0 2 3 5 10 13 15 else trap 'stty $ncb echo 2>/dev/null; exit' 0 2 3 5 10 13 15 fi if test $# = 0; then if test -t 0; then echo usage: $prog files... else bzip2 -cdfq | eval $more fi else FIRST=1 for FILE do if test $FIRST -eq 0; then echo $n1 "--More--(Next file: $FILE)$n2" stty $cb -echo 2>/dev/null ANS=`dd bs=1 count=1 2>/dev/null` stty $ncb echo 2>/dev/null echo " " if test "$ANS" = 'e' -o "$ANS" = 'q'; then exit fi fi if test "$ANS" != 's'; then echo "------> $FILE <------" bzip2 -cdfq "$FILE" | eval $more fi if test -t; then FIRST=0 fi done fi
1,259
62
jart/cosmopolitan
false
cosmopolitan/third_party/bzip2/bzlib.h
#ifndef _BZLIB_H #define _BZLIB_H #include "libc/stdio/stdio.h" #define BZ_RUN 0 #define BZ_FLUSH 1 #define BZ_FINISH 2 #define BZ_OK 0 #define BZ_RUN_OK 1 #define BZ_FLUSH_OK 2 #define BZ_FINISH_OK 3 #define BZ_STREAM_END 4 #define BZ_SEQUENCE_ERROR (-1) #define BZ_PARAM_ERROR (-2) #define BZ_MEM_ERROR (-3) #define BZ_DATA_ERROR (-4) #define BZ_DATA_ERROR_MAGIC (-5) #define BZ_IO_ERROR (-6) #define BZ_UNEXPECTED_EOF (-7) #define BZ_OUTBUFF_FULL (-8) #define BZ_CONFIG_ERROR (-9) #define BZ_MAX_UNUSED 5000 #if !(__ASSEMBLER__ + __LINKER__ + 0) COSMOPOLITAN_C_START_ typedef struct { char *next_in; unsigned int avail_in; unsigned int total_in_lo32; unsigned int total_in_hi32; char *next_out; unsigned int avail_out; unsigned int total_out_lo32; unsigned int total_out_hi32; void *state; void *(*bzalloc)(void *, int, int); void (*bzfree)(void *, void *); void *opaque; } bz_stream; /*-- Core (low-level) library functions --*/ int BZ2_bzCompressInit(bz_stream *, int, int, int); int BZ2_bzCompress(bz_stream *, int); int BZ2_bzCompressEnd(bz_stream *); int BZ2_bzDecompressInit(bz_stream *, int, int); int BZ2_bzDecompress(bz_stream *); int BZ2_bzDecompressEnd(bz_stream *); /*-- High(er) level library functions --*/ typedef void BZFILE; BZFILE *BZ2_bzReadOpen(int *, FILE *, int, int, void *, int); void BZ2_bzReadClose(int *, BZFILE *); void BZ2_bzReadGetUnused(int *, BZFILE *, void **, int *); int BZ2_bzRead(int *, BZFILE *, void *, int); BZFILE *BZ2_bzWriteOpen(int *, FILE *, int, int, int); void BZ2_bzWrite(int *, BZFILE *, void *, int); void BZ2_bzWriteClose(int *, BZFILE *, int, unsigned int *, unsigned int *); void BZ2_bzWriteClose64(int *, BZFILE *, int, unsigned int *, unsigned int *, unsigned int *, unsigned int *); int BZ2_bzBuffToBuffCompress(char *, unsigned int *, char *, unsigned int, int, int, int); int BZ2_bzBuffToBuffDecompress(char *, unsigned int *, char *, unsigned int, int, int); /*-- Code contributed by Yoshioka Tsuneo ([email protected]) to support better zlib compatibility. This code is not _officially_ part of libbzip2 (yet); I haven't tested it, documented it, or considered the threading-safeness of it. If this code breaks, please contact both Yoshioka and me. --*/ const char *BZ2_bzlibVersion(void); BZFILE *BZ2_bzopen(const char *, const char *); BZFILE *BZ2_bzdopen(int, const char *); int BZ2_bzread(BZFILE *, void *, int); int BZ2_bzwrite(BZFILE *, void *, int); int BZ2_bzflush(BZFILE *); void BZ2_bzclose(BZFILE *); const char *BZ2_bzerror(BZFILE *, int *); COSMOPOLITAN_C_END_ #endif /* !(__ASSEMBLER__ + __LINKER__ + 0) */ #endif /* _BZLIB_H */
2,836
92
jart/cosmopolitan
false
cosmopolitan/third_party/bzip2/bzlib.c
/* clang-format off */ /*-------------------------------------------------------------*/ /*--- Library top-level functions. ---*/ /*--- bzlib.c ---*/ /*-------------------------------------------------------------*/ /* ------------------------------------------------------------------ This file is part of bzip2/libbzip2, a program and library for lossless, block-sorting data compression. bzip2/libbzip2 version 1.0.8 of 13 July 2019 Copyright (C) 1996-2019 Julian Seward <[email protected]> Please read the WARNING, DISCLAIMER and PATENTS sections in the README file. This program is released under the terms of the license contained in the file LICENSE. ------------------------------------------------------------------ */ /* CHANGES 0.9.0 -- original version. 0.9.0a/b -- no changes in this file. 0.9.0c -- made zero-length BZ_FLUSH work correctly in bzCompress(). fixed bzWrite/bzRead to ignore zero-length requests. fixed bzread to correctly handle read requests after EOF. wrong parameter order in call to bzDecompressInit in bzBuffToBuffDecompress. Fixed. */ #include "libc/calls/calls.h" #include "libc/mem/mem.h" #include "third_party/bzip2/bzlib_private.inc" /*---------------------------------------------------*/ /*--- Compression stuff ---*/ /*---------------------------------------------------*/ /*---------------------------------------------------*/ #ifndef BZ_NO_STDIO void BZ2_bz__AssertH__fail ( int errcode ) { fprintf(stderr, "\n\nbzip2/libbzip2: internal error number %d.\n" "This is a bug in bzip2/libbzip2, %s.\n" "Please report it to: [email protected]. If this happened\n" "when you were using some program which uses libbzip2 as a\n" "component, you should also report this bug to the author(s)\n" "of that program. Please make an effort to report this bug;\n" "timely and accurate bug reports eventually lead to higher\n" "quality software. Thanks.\n\n", errcode, BZ2_bzlibVersion() ); if (errcode == 1007) { fprintf(stderr, "\n*** A special note about internal error number 1007 ***\n" "\n" "Experience suggests that a common cause of i.e. 1007\n" "is unreliable memory or other hardware. The 1007 assertion\n" "just happens to cross-check the results of huge numbers of\n" "memory reads/writes, and so acts (unintendedly) as a stress\n" "test of your memory system.\n" "\n" "I suggest the following: try compressing the file again,\n" "possibly monitoring progress in detail with the -vv flag.\n" "\n" "* If the error cannot be reproduced, and/or happens at different\n" " points in compression, you may have a flaky memory system.\n" " Try a memory-test program. I have used Memtest86\n" " (www.memtest86.com). At the time of writing it is free (GPLd).\n" " Memtest86 tests memory much more thorougly than your BIOSs\n" " power-on test, and may find failures that the BIOS doesn't.\n" "\n" "* If the error can be repeatably reproduced, this is a bug in\n" " bzip2, and I would very much like to hear about it. Please\n" " let me know, and, ideally, save a copy of the file causing the\n" " problem -- without which I will be unable to investigate it.\n" "\n" ); } exit(3); } #endif /*---------------------------------------------------*/ static int bz_config_ok ( void ) { if (sizeof(int) != 4) return 0; if (sizeof(short) != 2) return 0; if (sizeof(char) != 1) return 0; return 1; } /*---------------------------------------------------*/ static void* default_bzalloc ( void* opaque, Int32 items, Int32 size ) { void* v = malloc ( items * size ); return v; } static void default_bzfree ( void* opaque, void* addr ) { if (addr != NULL) free ( addr ); } /*---------------------------------------------------*/ static void prepare_new_block ( EState* s ) { Int32 i; s->nblock = 0; s->numZ = 0; s->state_out_pos = 0; BZ_INITIALISE_CRC ( s->blockCRC ); for (i = 0; i < 256; i++) s->inUse[i] = False; s->blockNo++; } /*---------------------------------------------------*/ static void init_RL ( EState* s ) { s->state_in_ch = 256; s->state_in_len = 0; } static Bool isempty_RL ( EState* s ) { if (s->state_in_ch < 256 && s->state_in_len > 0) return False; else return True; } /*---------------------------------------------------*/ int BZ2_bzCompressInit ( bz_stream* strm, int blockSize100k, int verbosity, int workFactor ) { Int32 n; EState* s; if (!bz_config_ok()) return BZ_CONFIG_ERROR; if (strm == NULL || blockSize100k < 1 || blockSize100k > 9 || workFactor < 0 || workFactor > 250) return BZ_PARAM_ERROR; if (workFactor == 0) workFactor = 30; if (strm->bzalloc == NULL) strm->bzalloc = default_bzalloc; if (strm->bzfree == NULL) strm->bzfree = default_bzfree; s = BZALLOC( sizeof(EState) ); if (s == NULL) return BZ_MEM_ERROR; s->strm = strm; s->arr1 = NULL; s->arr2 = NULL; s->ftab = NULL; n = 100000 * blockSize100k; s->arr1 = BZALLOC( n * sizeof(UInt32) ); s->arr2 = BZALLOC( (n+BZ_N_OVERSHOOT) * sizeof(UInt32) ); s->ftab = BZALLOC( 65537 * sizeof(UInt32) ); if (s->arr1 == NULL || s->arr2 == NULL || s->ftab == NULL) { if (s->arr1 != NULL) BZFREE(s->arr1); if (s->arr2 != NULL) BZFREE(s->arr2); if (s->ftab != NULL) BZFREE(s->ftab); if (s != NULL) BZFREE(s); return BZ_MEM_ERROR; } s->blockNo = 0; s->state = BZ_S_INPUT; s->mode = BZ_M_RUNNING; s->combinedCRC = 0; s->blockSize100k = blockSize100k; s->nblockMAX = 100000 * blockSize100k - 19; s->verbosity = verbosity; s->workFactor = workFactor; s->block = (UChar*)s->arr2; s->mtfv = (UInt16*)s->arr1; s->zbits = NULL; s->ptr = (UInt32*)s->arr1; strm->state = s; strm->total_in_lo32 = 0; strm->total_in_hi32 = 0; strm->total_out_lo32 = 0; strm->total_out_hi32 = 0; init_RL ( s ); prepare_new_block ( s ); return BZ_OK; } /*---------------------------------------------------*/ static void add_pair_to_block ( EState* s ) { Int32 i; UChar ch = (UChar)(s->state_in_ch); for (i = 0; i < s->state_in_len; i++) { BZ_UPDATE_CRC( s->blockCRC, ch ); } s->inUse[s->state_in_ch] = True; switch (s->state_in_len) { case 1: s->block[s->nblock] = (UChar)ch; s->nblock++; break; case 2: s->block[s->nblock] = (UChar)ch; s->nblock++; s->block[s->nblock] = (UChar)ch; s->nblock++; break; case 3: s->block[s->nblock] = (UChar)ch; s->nblock++; s->block[s->nblock] = (UChar)ch; s->nblock++; s->block[s->nblock] = (UChar)ch; s->nblock++; break; default: s->inUse[s->state_in_len-4] = True; s->block[s->nblock] = (UChar)ch; s->nblock++; s->block[s->nblock] = (UChar)ch; s->nblock++; s->block[s->nblock] = (UChar)ch; s->nblock++; s->block[s->nblock] = (UChar)ch; s->nblock++; s->block[s->nblock] = ((UChar)(s->state_in_len-4)); s->nblock++; break; } } /*---------------------------------------------------*/ static void flush_RL ( EState* s ) { if (s->state_in_ch < 256) add_pair_to_block ( s ); init_RL ( s ); } /*---------------------------------------------------*/ #define ADD_CHAR_TO_BLOCK(zs,zchh0) \ { \ UInt32 zchh = (UInt32)(zchh0); \ /*-- fast track the common case --*/ \ if (zchh != zs->state_in_ch && \ zs->state_in_len == 1) { \ UChar ch = (UChar)(zs->state_in_ch); \ BZ_UPDATE_CRC( zs->blockCRC, ch ); \ zs->inUse[zs->state_in_ch] = True; \ zs->block[zs->nblock] = (UChar)ch; \ zs->nblock++; \ zs->state_in_ch = zchh; \ } \ else \ /*-- general, uncommon cases --*/ \ if (zchh != zs->state_in_ch || \ zs->state_in_len == 255) { \ if (zs->state_in_ch < 256) \ add_pair_to_block ( zs ); \ zs->state_in_ch = zchh; \ zs->state_in_len = 1; \ } else { \ zs->state_in_len++; \ } \ } /*---------------------------------------------------*/ static Bool copy_input_until_stop ( EState* s ) { Bool progress_in = False; if (s->mode == BZ_M_RUNNING) { /*-- fast track the common case --*/ while (True) { /*-- block full? --*/ if (s->nblock >= s->nblockMAX) break; /*-- no input? --*/ if (s->strm->avail_in == 0) break; progress_in = True; ADD_CHAR_TO_BLOCK ( s, (UInt32)(*((UChar*)(s->strm->next_in))) ); s->strm->next_in++; s->strm->avail_in--; s->strm->total_in_lo32++; if (s->strm->total_in_lo32 == 0) s->strm->total_in_hi32++; } } else { /*-- general, uncommon case --*/ while (True) { /*-- block full? --*/ if (s->nblock >= s->nblockMAX) break; /*-- no input? --*/ if (s->strm->avail_in == 0) break; /*-- flush/finish end? --*/ if (s->avail_in_expect == 0) break; progress_in = True; ADD_CHAR_TO_BLOCK ( s, (UInt32)(*((UChar*)(s->strm->next_in))) ); s->strm->next_in++; s->strm->avail_in--; s->strm->total_in_lo32++; if (s->strm->total_in_lo32 == 0) s->strm->total_in_hi32++; s->avail_in_expect--; } } return progress_in; } /*---------------------------------------------------*/ static Bool copy_output_until_stop ( EState* s ) { Bool progress_out = False; while (True) { /*-- no output space? --*/ if (s->strm->avail_out == 0) break; /*-- block done? --*/ if (s->state_out_pos >= s->numZ) break; progress_out = True; *(s->strm->next_out) = s->zbits[s->state_out_pos]; s->state_out_pos++; s->strm->avail_out--; s->strm->next_out++; s->strm->total_out_lo32++; if (s->strm->total_out_lo32 == 0) s->strm->total_out_hi32++; } return progress_out; } /*---------------------------------------------------*/ static Bool handle_compress ( bz_stream* strm ) { Bool progress_in = False; Bool progress_out = False; EState* s = strm->state; while (True) { if (s->state == BZ_S_OUTPUT) { progress_out |= copy_output_until_stop ( s ); if (s->state_out_pos < s->numZ) break; if (s->mode == BZ_M_FINISHING && s->avail_in_expect == 0 && isempty_RL(s)) break; prepare_new_block ( s ); s->state = BZ_S_INPUT; if (s->mode == BZ_M_FLUSHING && s->avail_in_expect == 0 && isempty_RL(s)) break; } if (s->state == BZ_S_INPUT) { progress_in |= copy_input_until_stop ( s ); if (s->mode != BZ_M_RUNNING && s->avail_in_expect == 0) { flush_RL ( s ); BZ2_compressBlock ( s, (Bool)(s->mode == BZ_M_FINISHING) ); s->state = BZ_S_OUTPUT; } else if (s->nblock >= s->nblockMAX) { BZ2_compressBlock ( s, False ); s->state = BZ_S_OUTPUT; } else if (s->strm->avail_in == 0) { break; } } } return progress_in || progress_out; } /*---------------------------------------------------*/ int BZ2_bzCompress ( bz_stream *strm, int action ) { Bool progress; EState* s; if (strm == NULL) return BZ_PARAM_ERROR; s = strm->state; if (s == NULL) return BZ_PARAM_ERROR; if (s->strm != strm) return BZ_PARAM_ERROR; preswitch: switch (s->mode) { case BZ_M_IDLE: return BZ_SEQUENCE_ERROR; case BZ_M_RUNNING: if (action == BZ_RUN) { progress = handle_compress ( strm ); return progress ? BZ_RUN_OK : BZ_PARAM_ERROR; } else if (action == BZ_FLUSH) { s->avail_in_expect = strm->avail_in; s->mode = BZ_M_FLUSHING; goto preswitch; } else if (action == BZ_FINISH) { s->avail_in_expect = strm->avail_in; s->mode = BZ_M_FINISHING; goto preswitch; } else return BZ_PARAM_ERROR; case BZ_M_FLUSHING: if (action != BZ_FLUSH) return BZ_SEQUENCE_ERROR; if (s->avail_in_expect != s->strm->avail_in) return BZ_SEQUENCE_ERROR; progress = handle_compress ( strm ); if (s->avail_in_expect > 0 || !isempty_RL(s) || s->state_out_pos < s->numZ) return BZ_FLUSH_OK; s->mode = BZ_M_RUNNING; return BZ_RUN_OK; case BZ_M_FINISHING: if (action != BZ_FINISH) return BZ_SEQUENCE_ERROR; if (s->avail_in_expect != s->strm->avail_in) return BZ_SEQUENCE_ERROR; progress = handle_compress ( strm ); if (!progress) return BZ_SEQUENCE_ERROR; if (s->avail_in_expect > 0 || !isempty_RL(s) || s->state_out_pos < s->numZ) return BZ_FINISH_OK; s->mode = BZ_M_IDLE; return BZ_STREAM_END; } return BZ_OK; /*--not reached--*/ } /*---------------------------------------------------*/ int BZ2_bzCompressEnd ( bz_stream *strm ) { EState* s; if (strm == NULL) return BZ_PARAM_ERROR; s = strm->state; if (s == NULL) return BZ_PARAM_ERROR; if (s->strm != strm) return BZ_PARAM_ERROR; if (s->arr1 != NULL) BZFREE(s->arr1); if (s->arr2 != NULL) BZFREE(s->arr2); if (s->ftab != NULL) BZFREE(s->ftab); BZFREE(strm->state); strm->state = NULL; return BZ_OK; } /*---------------------------------------------------*/ /*--- Decompression stuff ---*/ /*---------------------------------------------------*/ /*---------------------------------------------------*/ int BZ2_bzDecompressInit ( bz_stream* strm, int verbosity, int small ) { DState* s; if (!bz_config_ok()) return BZ_CONFIG_ERROR; if (strm == NULL) return BZ_PARAM_ERROR; if (small != 0 && small != 1) return BZ_PARAM_ERROR; if (verbosity < 0 || verbosity > 4) return BZ_PARAM_ERROR; if (strm->bzalloc == NULL) strm->bzalloc = default_bzalloc; if (strm->bzfree == NULL) strm->bzfree = default_bzfree; s = BZALLOC( sizeof(DState) ); if (s == NULL) return BZ_MEM_ERROR; s->strm = strm; strm->state = s; s->state = BZ_X_MAGIC_1; s->bsLive = 0; s->bsBuff = 0; s->calculatedCombinedCRC = 0; strm->total_in_lo32 = 0; strm->total_in_hi32 = 0; strm->total_out_lo32 = 0; strm->total_out_hi32 = 0; s->smallDecompress = (Bool)small; s->ll4 = NULL; s->ll16 = NULL; s->tt = NULL; s->currBlockNo = 0; s->verbosity = verbosity; return BZ_OK; } /*---------------------------------------------------*/ /* Return True iff data corruption is discovered. Returns False if there is no problem. */ static Bool unRLE_obuf_to_output_FAST ( DState* s ) { UChar k1; if (s->blockRandomised) { while (True) { /* try to finish existing run */ while (True) { if (s->strm->avail_out == 0) return False; if (s->state_out_len == 0) break; *( (UChar*)(s->strm->next_out) ) = s->state_out_ch; BZ_UPDATE_CRC ( s->calculatedBlockCRC, s->state_out_ch ); s->state_out_len--; s->strm->next_out++; s->strm->avail_out--; s->strm->total_out_lo32++; if (s->strm->total_out_lo32 == 0) s->strm->total_out_hi32++; } /* can a new run be started? */ if (s->nblock_used == s->save_nblock+1) return False; /* Only caused by corrupt data stream? */ if (s->nblock_used > s->save_nblock+1) return True; s->state_out_len = 1; s->state_out_ch = s->k0; BZ_GET_FAST(k1); BZ_RAND_UPD_MASK; k1 ^= BZ_RAND_MASK; s->nblock_used++; if (s->nblock_used == s->save_nblock+1) continue; if (k1 != s->k0) { s->k0 = k1; continue; }; s->state_out_len = 2; BZ_GET_FAST(k1); BZ_RAND_UPD_MASK; k1 ^= BZ_RAND_MASK; s->nblock_used++; if (s->nblock_used == s->save_nblock+1) continue; if (k1 != s->k0) { s->k0 = k1; continue; }; s->state_out_len = 3; BZ_GET_FAST(k1); BZ_RAND_UPD_MASK; k1 ^= BZ_RAND_MASK; s->nblock_used++; if (s->nblock_used == s->save_nblock+1) continue; if (k1 != s->k0) { s->k0 = k1; continue; }; BZ_GET_FAST(k1); BZ_RAND_UPD_MASK; k1 ^= BZ_RAND_MASK; s->nblock_used++; s->state_out_len = ((Int32)k1) + 4; BZ_GET_FAST(s->k0); BZ_RAND_UPD_MASK; s->k0 ^= BZ_RAND_MASK; s->nblock_used++; } } else { /* restore */ UInt32 c_calculatedBlockCRC = s->calculatedBlockCRC; UChar c_state_out_ch = s->state_out_ch; Int32 c_state_out_len = s->state_out_len; Int32 c_nblock_used = s->nblock_used; Int32 c_k0 = s->k0; UInt32* c_tt = s->tt; UInt32 c_tPos = s->tPos; char* cs_next_out = s->strm->next_out; unsigned int cs_avail_out = s->strm->avail_out; Int32 ro_blockSize100k = s->blockSize100k; /* end restore */ UInt32 avail_out_INIT = cs_avail_out; Int32 s_save_nblockPP = s->save_nblock+1; unsigned int total_out_lo32_old; while (True) { /* try to finish existing run */ if (c_state_out_len > 0) { while (True) { if (cs_avail_out == 0) goto return_notr; if (c_state_out_len == 1) break; *( (UChar*)(cs_next_out) ) = c_state_out_ch; BZ_UPDATE_CRC ( c_calculatedBlockCRC, c_state_out_ch ); c_state_out_len--; cs_next_out++; cs_avail_out--; } s_state_out_len_eq_one: { if (cs_avail_out == 0) { c_state_out_len = 1; goto return_notr; }; *( (UChar*)(cs_next_out) ) = c_state_out_ch; BZ_UPDATE_CRC ( c_calculatedBlockCRC, c_state_out_ch ); cs_next_out++; cs_avail_out--; } } /* Only caused by corrupt data stream? */ if (c_nblock_used > s_save_nblockPP) return True; /* can a new run be started? */ if (c_nblock_used == s_save_nblockPP) { c_state_out_len = 0; goto return_notr; }; c_state_out_ch = c_k0; BZ_GET_FAST_C(k1); c_nblock_used++; if (k1 != c_k0) { c_k0 = k1; goto s_state_out_len_eq_one; }; if (c_nblock_used == s_save_nblockPP) goto s_state_out_len_eq_one; c_state_out_len = 2; BZ_GET_FAST_C(k1); c_nblock_used++; if (c_nblock_used == s_save_nblockPP) continue; if (k1 != c_k0) { c_k0 = k1; continue; }; c_state_out_len = 3; BZ_GET_FAST_C(k1); c_nblock_used++; if (c_nblock_used == s_save_nblockPP) continue; if (k1 != c_k0) { c_k0 = k1; continue; }; BZ_GET_FAST_C(k1); c_nblock_used++; c_state_out_len = ((Int32)k1) + 4; BZ_GET_FAST_C(c_k0); c_nblock_used++; } return_notr: total_out_lo32_old = s->strm->total_out_lo32; s->strm->total_out_lo32 += (avail_out_INIT - cs_avail_out); if (s->strm->total_out_lo32 < total_out_lo32_old) s->strm->total_out_hi32++; /* save */ s->calculatedBlockCRC = c_calculatedBlockCRC; s->state_out_ch = c_state_out_ch; s->state_out_len = c_state_out_len; s->nblock_used = c_nblock_used; s->k0 = c_k0; s->tt = c_tt; s->tPos = c_tPos; s->strm->next_out = cs_next_out; s->strm->avail_out = cs_avail_out; /* end save */ } return False; } /*---------------------------------------------------*/ __inline__ Int32 BZ2_indexIntoF ( Int32 indx, Int32 *cftab ) { Int32 nb, na, mid; nb = 0; na = 256; do { mid = (nb + na) >> 1; if (indx >= cftab[mid]) nb = mid; else na = mid; } while (na - nb != 1); return nb; } /*---------------------------------------------------*/ /* Return True iff data corruption is discovered. Returns False if there is no problem. */ static Bool unRLE_obuf_to_output_SMALL ( DState* s ) { UChar k1; if (s->blockRandomised) { while (True) { /* try to finish existing run */ while (True) { if (s->strm->avail_out == 0) return False; if (s->state_out_len == 0) break; *( (UChar*)(s->strm->next_out) ) = s->state_out_ch; BZ_UPDATE_CRC ( s->calculatedBlockCRC, s->state_out_ch ); s->state_out_len--; s->strm->next_out++; s->strm->avail_out--; s->strm->total_out_lo32++; if (s->strm->total_out_lo32 == 0) s->strm->total_out_hi32++; } /* can a new run be started? */ if (s->nblock_used == s->save_nblock+1) return False; /* Only caused by corrupt data stream? */ if (s->nblock_used > s->save_nblock+1) return True; s->state_out_len = 1; s->state_out_ch = s->k0; BZ_GET_SMALL(k1); BZ_RAND_UPD_MASK; k1 ^= BZ_RAND_MASK; s->nblock_used++; if (s->nblock_used == s->save_nblock+1) continue; if (k1 != s->k0) { s->k0 = k1; continue; }; s->state_out_len = 2; BZ_GET_SMALL(k1); BZ_RAND_UPD_MASK; k1 ^= BZ_RAND_MASK; s->nblock_used++; if (s->nblock_used == s->save_nblock+1) continue; if (k1 != s->k0) { s->k0 = k1; continue; }; s->state_out_len = 3; BZ_GET_SMALL(k1); BZ_RAND_UPD_MASK; k1 ^= BZ_RAND_MASK; s->nblock_used++; if (s->nblock_used == s->save_nblock+1) continue; if (k1 != s->k0) { s->k0 = k1; continue; }; BZ_GET_SMALL(k1); BZ_RAND_UPD_MASK; k1 ^= BZ_RAND_MASK; s->nblock_used++; s->state_out_len = ((Int32)k1) + 4; BZ_GET_SMALL(s->k0); BZ_RAND_UPD_MASK; s->k0 ^= BZ_RAND_MASK; s->nblock_used++; } } else { while (True) { /* try to finish existing run */ while (True) { if (s->strm->avail_out == 0) return False; if (s->state_out_len == 0) break; *( (UChar*)(s->strm->next_out) ) = s->state_out_ch; BZ_UPDATE_CRC ( s->calculatedBlockCRC, s->state_out_ch ); s->state_out_len--; s->strm->next_out++; s->strm->avail_out--; s->strm->total_out_lo32++; if (s->strm->total_out_lo32 == 0) s->strm->total_out_hi32++; } /* can a new run be started? */ if (s->nblock_used == s->save_nblock+1) return False; /* Only caused by corrupt data stream? */ if (s->nblock_used > s->save_nblock+1) return True; s->state_out_len = 1; s->state_out_ch = s->k0; BZ_GET_SMALL(k1); s->nblock_used++; if (s->nblock_used == s->save_nblock+1) continue; if (k1 != s->k0) { s->k0 = k1; continue; }; s->state_out_len = 2; BZ_GET_SMALL(k1); s->nblock_used++; if (s->nblock_used == s->save_nblock+1) continue; if (k1 != s->k0) { s->k0 = k1; continue; }; s->state_out_len = 3; BZ_GET_SMALL(k1); s->nblock_used++; if (s->nblock_used == s->save_nblock+1) continue; if (k1 != s->k0) { s->k0 = k1; continue; }; BZ_GET_SMALL(k1); s->nblock_used++; s->state_out_len = ((Int32)k1) + 4; BZ_GET_SMALL(s->k0); s->nblock_used++; } } } /*---------------------------------------------------*/ int BZ2_bzDecompress ( bz_stream *strm ) { Bool corrupt; DState* s; if (strm == NULL) return BZ_PARAM_ERROR; s = strm->state; if (s == NULL) return BZ_PARAM_ERROR; if (s->strm != strm) return BZ_PARAM_ERROR; while (True) { if (s->state == BZ_X_IDLE) return BZ_SEQUENCE_ERROR; if (s->state == BZ_X_OUTPUT) { if (s->smallDecompress) corrupt = unRLE_obuf_to_output_SMALL ( s ); else corrupt = unRLE_obuf_to_output_FAST ( s ); if (corrupt) return BZ_DATA_ERROR; if (s->nblock_used == s->save_nblock+1 && s->state_out_len == 0) { BZ_FINALISE_CRC ( s->calculatedBlockCRC ); if (s->verbosity >= 3) VPrintf2 ( " {0x%08x, 0x%08x}", s->storedBlockCRC, s->calculatedBlockCRC ); if (s->verbosity >= 2) VPrintf0 ( "]" ); if (s->calculatedBlockCRC != s->storedBlockCRC) return BZ_DATA_ERROR; s->calculatedCombinedCRC = (s->calculatedCombinedCRC << 1) | (s->calculatedCombinedCRC >> 31); s->calculatedCombinedCRC ^= s->calculatedBlockCRC; s->state = BZ_X_BLKHDR_1; } else { return BZ_OK; } } if (s->state >= BZ_X_MAGIC_1) { Int32 r = BZ2_decompress ( s ); if (r == BZ_STREAM_END) { if (s->verbosity >= 3) VPrintf2 ( "\n combined CRCs: stored = 0x%08x, computed = 0x%08x", s->storedCombinedCRC, s->calculatedCombinedCRC ); if (s->calculatedCombinedCRC != s->storedCombinedCRC) return BZ_DATA_ERROR; return r; } if (s->state != BZ_X_OUTPUT) return r; } } AssertH ( 0, 6001 ); return 0; /*NOTREACHED*/ } /*---------------------------------------------------*/ int BZ2_bzDecompressEnd ( bz_stream *strm ) { DState* s; if (strm == NULL) return BZ_PARAM_ERROR; s = strm->state; if (s == NULL) return BZ_PARAM_ERROR; if (s->strm != strm) return BZ_PARAM_ERROR; if (s->tt != NULL) BZFREE(s->tt); if (s->ll16 != NULL) BZFREE(s->ll16); if (s->ll4 != NULL) BZFREE(s->ll4); BZFREE(strm->state); strm->state = NULL; return BZ_OK; } /*---------------------------------------------------*/ /*--- File I/O stuff ---*/ /*---------------------------------------------------*/ #define BZ_SETERR(eee) \ { \ if (bzerror != NULL) *bzerror = eee; \ if (bzf != NULL) bzf->lastErr = eee; \ } typedef struct { FILE* handle; Char buf[BZ_MAX_UNUSED]; Int32 bufN; Bool writing; bz_stream strm; Int32 lastErr; Bool initialisedOk; } bzFile; /*---------------------------------------------*/ static Bool myfeof ( FILE* f ) { Int32 c = fgetc ( f ); if (c == EOF) return True; ungetc ( c, f ); return False; } /*---------------------------------------------------*/ BZFILE* BZ2_bzWriteOpen ( int* bzerror, FILE* f, int blockSize100k, int verbosity, int workFactor ) { Int32 ret; bzFile* bzf = NULL; BZ_SETERR(BZ_OK); if (f == NULL || (blockSize100k < 1 || blockSize100k > 9) || (workFactor < 0 || workFactor > 250) || (verbosity < 0 || verbosity > 4)) { BZ_SETERR(BZ_PARAM_ERROR); return NULL; }; if (ferror(f)) { BZ_SETERR(BZ_IO_ERROR); return NULL; }; bzf = malloc ( sizeof(bzFile) ); if (bzf == NULL) { BZ_SETERR(BZ_MEM_ERROR); return NULL; }; BZ_SETERR(BZ_OK); bzf->initialisedOk = False; bzf->bufN = 0; bzf->handle = f; bzf->writing = True; bzf->strm.bzalloc = NULL; bzf->strm.bzfree = NULL; bzf->strm.opaque = NULL; if (workFactor == 0) workFactor = 30; ret = BZ2_bzCompressInit ( &(bzf->strm), blockSize100k, verbosity, workFactor ); if (ret != BZ_OK) { BZ_SETERR(ret); free(bzf); return NULL; }; bzf->strm.avail_in = 0; bzf->initialisedOk = True; return bzf; } /*---------------------------------------------------*/ void BZ2_bzWrite ( int* bzerror, BZFILE* b, void* buf, int len ) { Int32 n, n2, ret; bzFile* bzf = (bzFile*)b; BZ_SETERR(BZ_OK); if (bzf == NULL || buf == NULL || len < 0) { BZ_SETERR(BZ_PARAM_ERROR); return; }; if (!(bzf->writing)) { BZ_SETERR(BZ_SEQUENCE_ERROR); return; }; if (ferror(bzf->handle)) { BZ_SETERR(BZ_IO_ERROR); return; }; if (len == 0) { BZ_SETERR(BZ_OK); return; }; bzf->strm.avail_in = len; bzf->strm.next_in = buf; while (True) { bzf->strm.avail_out = BZ_MAX_UNUSED; bzf->strm.next_out = bzf->buf; ret = BZ2_bzCompress ( &(bzf->strm), BZ_RUN ); if (ret != BZ_RUN_OK) { BZ_SETERR(ret); return; }; if (bzf->strm.avail_out < BZ_MAX_UNUSED) { n = BZ_MAX_UNUSED - bzf->strm.avail_out; n2 = fwrite ( (void*)(bzf->buf), sizeof(UChar), n, bzf->handle ); if (n != n2 || ferror(bzf->handle)) { BZ_SETERR(BZ_IO_ERROR); return; }; } if (bzf->strm.avail_in == 0) { BZ_SETERR(BZ_OK); return; }; } } /*---------------------------------------------------*/ void BZ2_bzWriteClose ( int* bzerror, BZFILE* b, int abandon, unsigned int* nbytes_in, unsigned int* nbytes_out ) { BZ2_bzWriteClose64 ( bzerror, b, abandon, nbytes_in, NULL, nbytes_out, NULL ); } void BZ2_bzWriteClose64 ( int* bzerror, BZFILE* b, int abandon, unsigned int* nbytes_in_lo32, unsigned int* nbytes_in_hi32, unsigned int* nbytes_out_lo32, unsigned int* nbytes_out_hi32 ) { Int32 n, n2, ret; bzFile* bzf = (bzFile*)b; if (bzf == NULL) { BZ_SETERR(BZ_OK); return; }; if (!(bzf->writing)) { BZ_SETERR(BZ_SEQUENCE_ERROR); return; }; if (ferror(bzf->handle)) { BZ_SETERR(BZ_IO_ERROR); return; }; if (nbytes_in_lo32 != NULL) *nbytes_in_lo32 = 0; if (nbytes_in_hi32 != NULL) *nbytes_in_hi32 = 0; if (nbytes_out_lo32 != NULL) *nbytes_out_lo32 = 0; if (nbytes_out_hi32 != NULL) *nbytes_out_hi32 = 0; if ((!abandon) && bzf->lastErr == BZ_OK) { while (True) { bzf->strm.avail_out = BZ_MAX_UNUSED; bzf->strm.next_out = bzf->buf; ret = BZ2_bzCompress ( &(bzf->strm), BZ_FINISH ); if (ret != BZ_FINISH_OK && ret != BZ_STREAM_END) { BZ_SETERR(ret); return; }; if (bzf->strm.avail_out < BZ_MAX_UNUSED) { n = BZ_MAX_UNUSED - bzf->strm.avail_out; n2 = fwrite ( (void*)(bzf->buf), sizeof(UChar), n, bzf->handle ); if (n != n2 || ferror(bzf->handle)) { BZ_SETERR(BZ_IO_ERROR); return; }; } if (ret == BZ_STREAM_END) break; } } if ( !abandon && !ferror ( bzf->handle ) ) { fflush ( bzf->handle ); if (ferror(bzf->handle)) { BZ_SETERR(BZ_IO_ERROR); return; }; } if (nbytes_in_lo32 != NULL) *nbytes_in_lo32 = bzf->strm.total_in_lo32; if (nbytes_in_hi32 != NULL) *nbytes_in_hi32 = bzf->strm.total_in_hi32; if (nbytes_out_lo32 != NULL) *nbytes_out_lo32 = bzf->strm.total_out_lo32; if (nbytes_out_hi32 != NULL) *nbytes_out_hi32 = bzf->strm.total_out_hi32; BZ_SETERR(BZ_OK); BZ2_bzCompressEnd ( &(bzf->strm) ); free ( bzf ); } /*---------------------------------------------------*/ BZFILE* BZ2_bzReadOpen ( int* bzerror, FILE* f, int verbosity, int small, void* unused, int nUnused ) { bzFile* bzf = NULL; int ret; BZ_SETERR(BZ_OK); if (f == NULL || (small != 0 && small != 1) || (verbosity < 0 || verbosity > 4) || (unused == NULL && nUnused != 0) || (unused != NULL && (nUnused < 0 || nUnused > BZ_MAX_UNUSED))) { BZ_SETERR(BZ_PARAM_ERROR); return NULL; }; if (ferror(f)) { BZ_SETERR(BZ_IO_ERROR); return NULL; }; bzf = malloc ( sizeof(bzFile) ); if (bzf == NULL) { BZ_SETERR(BZ_MEM_ERROR); return NULL; }; BZ_SETERR(BZ_OK); bzf->initialisedOk = False; bzf->handle = f; bzf->bufN = 0; bzf->writing = False; bzf->strm.bzalloc = NULL; bzf->strm.bzfree = NULL; bzf->strm.opaque = NULL; while (nUnused > 0) { bzf->buf[bzf->bufN] = *((UChar*)(unused)); bzf->bufN++; unused = ((void*)( 1 + ((UChar*)(unused)) )); nUnused--; } ret = BZ2_bzDecompressInit ( &(bzf->strm), verbosity, small ); if (ret != BZ_OK) { BZ_SETERR(ret); free(bzf); return NULL; }; bzf->strm.avail_in = bzf->bufN; bzf->strm.next_in = bzf->buf; bzf->initialisedOk = True; return bzf; } /*---------------------------------------------------*/ void BZ2_bzReadClose ( int *bzerror, BZFILE *b ) { bzFile* bzf = (bzFile*)b; BZ_SETERR(BZ_OK); if (bzf == NULL) { BZ_SETERR(BZ_OK); return; }; if (bzf->writing) { BZ_SETERR(BZ_SEQUENCE_ERROR); return; }; if (bzf->initialisedOk) (void)BZ2_bzDecompressEnd ( &(bzf->strm) ); free ( bzf ); } /*---------------------------------------------------*/ int BZ2_bzRead ( int* bzerror, BZFILE* b, void* buf, int len ) { Int32 n, ret; bzFile* bzf = (bzFile*)b; BZ_SETERR(BZ_OK); if (bzf == NULL || buf == NULL || len < 0) { BZ_SETERR(BZ_PARAM_ERROR); return 0; }; if (bzf->writing) { BZ_SETERR(BZ_SEQUENCE_ERROR); return 0; }; if (len == 0) { BZ_SETERR(BZ_OK); return 0; }; bzf->strm.avail_out = len; bzf->strm.next_out = buf; while (True) { if (ferror(bzf->handle)) { BZ_SETERR(BZ_IO_ERROR); return 0; }; if (bzf->strm.avail_in == 0 && !myfeof(bzf->handle)) { n = fread ( bzf->buf, sizeof(UChar), BZ_MAX_UNUSED, bzf->handle ); if (ferror(bzf->handle)) { BZ_SETERR(BZ_IO_ERROR); return 0; }; bzf->bufN = n; bzf->strm.avail_in = bzf->bufN; bzf->strm.next_in = bzf->buf; } ret = BZ2_bzDecompress ( &(bzf->strm) ); if (ret != BZ_OK && ret != BZ_STREAM_END) { BZ_SETERR(ret); return 0; }; if (ret == BZ_OK && myfeof(bzf->handle) && bzf->strm.avail_in == 0 && bzf->strm.avail_out > 0) { BZ_SETERR(BZ_UNEXPECTED_EOF); return 0; }; if (ret == BZ_STREAM_END) { BZ_SETERR(BZ_STREAM_END); return len - bzf->strm.avail_out; }; if (bzf->strm.avail_out == 0) { BZ_SETERR(BZ_OK); return len; }; } return 0; /*not reached*/ } /*---------------------------------------------------*/ void BZ2_bzReadGetUnused ( int* bzerror, BZFILE* b, void** unused, int* nUnused ) { bzFile* bzf = (bzFile*)b; if (bzf == NULL) { BZ_SETERR(BZ_PARAM_ERROR); return; }; if (bzf->lastErr != BZ_STREAM_END) { BZ_SETERR(BZ_SEQUENCE_ERROR); return; }; if (unused == NULL || nUnused == NULL) { BZ_SETERR(BZ_PARAM_ERROR); return; }; BZ_SETERR(BZ_OK); *nUnused = bzf->strm.avail_in; *unused = bzf->strm.next_in; } /*---------------------------------------------------*/ /*--- Misc convenience stuff ---*/ /*---------------------------------------------------*/ /*---------------------------------------------------*/ int BZ2_bzBuffToBuffCompress ( char* dest, unsigned int* destLen, char* source, unsigned int sourceLen, int blockSize100k, int verbosity, int workFactor ) { bz_stream strm; int ret; if (dest == NULL || destLen == NULL || source == NULL || blockSize100k < 1 || blockSize100k > 9 || verbosity < 0 || verbosity > 4 || workFactor < 0 || workFactor > 250) return BZ_PARAM_ERROR; if (workFactor == 0) workFactor = 30; strm.bzalloc = NULL; strm.bzfree = NULL; strm.opaque = NULL; ret = BZ2_bzCompressInit ( &strm, blockSize100k, verbosity, workFactor ); if (ret != BZ_OK) return ret; strm.next_in = source; strm.next_out = dest; strm.avail_in = sourceLen; strm.avail_out = *destLen; ret = BZ2_bzCompress ( &strm, BZ_FINISH ); if (ret == BZ_FINISH_OK) goto output_overflow; if (ret != BZ_STREAM_END) goto errhandler; /* normal termination */ *destLen -= strm.avail_out; BZ2_bzCompressEnd ( &strm ); return BZ_OK; output_overflow: BZ2_bzCompressEnd ( &strm ); return BZ_OUTBUFF_FULL; errhandler: BZ2_bzCompressEnd ( &strm ); return ret; } /*---------------------------------------------------*/ int BZ2_bzBuffToBuffDecompress ( char* dest, unsigned int* destLen, char* source, unsigned int sourceLen, int small, int verbosity ) { bz_stream strm; int ret; if (dest == NULL || destLen == NULL || source == NULL || (small != 0 && small != 1) || verbosity < 0 || verbosity > 4) return BZ_PARAM_ERROR; strm.bzalloc = NULL; strm.bzfree = NULL; strm.opaque = NULL; ret = BZ2_bzDecompressInit ( &strm, verbosity, small ); if (ret != BZ_OK) return ret; strm.next_in = source; strm.next_out = dest; strm.avail_in = sourceLen; strm.avail_out = *destLen; ret = BZ2_bzDecompress ( &strm ); if (ret == BZ_OK) goto output_overflow_or_eof; if (ret != BZ_STREAM_END) goto errhandler; /* normal termination */ *destLen -= strm.avail_out; BZ2_bzDecompressEnd ( &strm ); return BZ_OK; output_overflow_or_eof: if (strm.avail_out > 0) { BZ2_bzDecompressEnd ( &strm ); return BZ_UNEXPECTED_EOF; } else { BZ2_bzDecompressEnd ( &strm ); return BZ_OUTBUFF_FULL; }; errhandler: BZ2_bzDecompressEnd ( &strm ); return ret; } /*---------------------------------------------------*/ /*-- Code contributed by Yoshioka Tsuneo ([email protected]) to support better zlib compatibility. This code is not _officially_ part of libbzip2 (yet); I haven't tested it, documented it, or considered the threading-safeness of it. If this code breaks, please contact both Yoshioka and me. --*/ /*---------------------------------------------------*/ /*---------------------------------------------------*/ /*-- return version like "0.9.5d, 4-Sept-1999". --*/ const char * BZ2_bzlibVersion(void) { return BZ_VERSION; } #ifndef BZ_NO_STDIO /*---------------------------------------------------*/ #if defined(_WIN32) || defined(OS2) || defined(MSDOS) # include <fcntl.h> # include <io.h> # define SET_BINARY_MODE(file) setmode(fileno(file),O_BINARY) #else # define SET_BINARY_MODE(file) #endif static BZFILE * bzopen_or_bzdopen ( const char *path, /* no use when bzdopen */ int fd, /* no use when bzdopen */ const char *mode, int open_mode) /* bzopen: 0, bzdopen:1 */ { int bzerr; char unused[BZ_MAX_UNUSED]; int blockSize100k = 9; int writing = 0; char mode2[10] = ""; FILE *fp = NULL; BZFILE *bzfp = NULL; int verbosity = 0; int workFactor = 30; int smallMode = 0; int nUnused = 0; if (mode == NULL) return NULL; while (*mode) { switch (*mode) { case 'r': writing = 0; break; case 'w': writing = 1; break; case 's': smallMode = 1; break; default: if (isdigit((int)(*mode))) { blockSize100k = *mode-BZ_HDR_0; } } mode++; } strcat(mode2, writing ? "w" : "r" ); strcat(mode2,"b"); /* binary mode */ if (open_mode==0) { if (path==NULL || strcmp(path,"")==0) { fp = (writing ? stdout : stdin); SET_BINARY_MODE(fp); } else { fp = fopen(path,mode2); } } else { #ifdef BZ_STRICT_ANSI fp = NULL; #else fp = fdopen(fd,mode2); #endif } if (fp == NULL) return NULL; if (writing) { /* Guard against total chaos and anarchy -- JRS */ if (blockSize100k < 1) blockSize100k = 1; if (blockSize100k > 9) blockSize100k = 9; bzfp = BZ2_bzWriteOpen(&bzerr,fp,blockSize100k, verbosity,workFactor); } else { bzfp = BZ2_bzReadOpen(&bzerr,fp,verbosity,smallMode, unused,nUnused); } if (bzfp == NULL) { if (fp != stdin && fp != stdout) fclose(fp); return NULL; } return bzfp; } /*---------------------------------------------------*/ /*-- open file for read or write. ex) bzopen("file","w9") case path="" or NULL => use stdin or stdout. --*/ BZFILE * BZ2_bzopen ( const char *path, const char *mode ) { return bzopen_or_bzdopen(path,-1,mode,/*bzopen*/0); } /*---------------------------------------------------*/ BZFILE * BZ2_bzdopen ( int fd, const char *mode ) { return bzopen_or_bzdopen(NULL,fd,mode,/*bzdopen*/1); } /*---------------------------------------------------*/ int BZ2_bzread (BZFILE* b, void* buf, int len ) { int bzerr, nread; if (((bzFile*)b)->lastErr == BZ_STREAM_END) return 0; nread = BZ2_bzRead(&bzerr,b,buf,len); if (bzerr == BZ_OK || bzerr == BZ_STREAM_END) { return nread; } else { return -1; } } /*---------------------------------------------------*/ int BZ2_bzwrite (BZFILE* b, void* buf, int len ) { int bzerr; BZ2_bzWrite(&bzerr,b,buf,len); if(bzerr == BZ_OK){ return len; }else{ return -1; } } /*---------------------------------------------------*/ int BZ2_bzflush (BZFILE *b) { /* do nothing now... */ return 0; } /*---------------------------------------------------*/ void BZ2_bzclose (BZFILE* b) { int bzerr; FILE *fp; if (b==NULL) {return;} fp = ((bzFile *)b)->handle; if(((bzFile*)b)->writing){ BZ2_bzWriteClose(&bzerr,b,0,NULL,NULL); if(bzerr != BZ_OK){ BZ2_bzWriteClose(NULL,b,1,NULL,NULL); } }else{ BZ2_bzReadClose(&bzerr,b); } if(fp!=stdin && fp!=stdout){ fclose(fp); } } /*---------------------------------------------------*/ /*-- return last error code --*/ static const char *bzerrorstrings[] = { "OK" ,"SEQUENCE_ERROR" ,"PARAM_ERROR" ,"MEM_ERROR" ,"DATA_ERROR" ,"DATA_ERROR_MAGIC" ,"IO_ERROR" ,"UNEXPECTED_EOF" ,"OUTBUFF_FULL" ,"CONFIG_ERROR" ,"???" /* for future */ ,"???" /* for future */ ,"???" /* for future */ ,"???" /* for future */ ,"???" /* for future */ ,"???" /* for future */ }; const char * BZ2_bzerror (BZFILE *b, int *errnum) { int err = ((bzFile *)b)->lastErr; if(err>0) err = 0; *errnum = err; return bzerrorstrings[err*-1]; } #endif /*-------------------------------------------------------------*/ /*--- end bzlib.c ---*/ /*-------------------------------------------------------------*/
45,840
1,574
jart/cosmopolitan
false
cosmopolitan/third_party/bzip2/bzip2.txt
NAME bzip2, bunzip2 - a block-sorting file compressor, v1.0.8 bzcat - decompresses files to stdout bzip2recover - recovers data from damaged bzip2 files SYNOPSIS bzip2 [ -cdfkqstvzVL123456789 ] [ filenames ... ] bunzip2 [ -fkvsVL ] [ filenames ... ] bzcat [ -s ] [ filenames ... ] bzip2recover filename DESCRIPTION bzip2 compresses files using the Burrows-Wheeler block sorting text compression algorithm, and Huffman coding. Compression is generally considerably better than that achieved by more conventional LZ77/LZ78-based compressors, and approaches the performance of the PPM family of sta- tistical compressors. The command-line options are deliberately very similar to those of GNU gzip, but they are not identical. bzip2 expects a list of file names to accompany the com- mand-line flags. Each file is replaced by a compressed version of itself, with the name "original_name.bz2". Each compressed file has the same modification date, per- missions, and, when possible, ownership as the correspond- ing original, so that these properties can be correctly restored at decompression time. File name handling is naive in the sense that there is no mechanism for preserv- ing original file names, permissions, ownerships or dates in filesystems which lack these concepts, or have serious file name length restrictions, such as MS-DOS. bzip2 and bunzip2 will by default not overwrite existing files. If you want this to happen, specify the -f flag. If no file names are specified, bzip2 compresses from standard input to standard output. In this case, bzip2 will decline to write compressed output to a terminal, as this would be entirely incomprehensible and therefore pointless. bunzip2 (or bzip2 -d) decompresses all specified files. Files which were not created by bzip2 will be detected and ignored, and a warning issued. bzip2 attempts to guess the filename for the decompressed file from that of the compressed file as follows: filename.bz2 becomes filename filename.bz becomes filename filename.tbz2 becomes filename.tar filename.tbz becomes filename.tar anyothername becomes anyothername.out If the file does not end in one of the recognised endings, .bz2, .bz, .tbz2 or .tbz, bzip2 complains that it cannot guess the name of the original file, and uses the original name with .out appended. As with compression, supplying no filenames causes decom- pression from standard input to standard output. bunzip2 will correctly decompress a file which is the con- catenation of two or more compressed files. The result is the concatenation of the corresponding uncompressed files. Integrity testing (-t) of concatenated compressed files is also supported. You can also compress or decompress files to the standard output by giving the -c flag. Multiple files may be com- pressed and decompressed like this. The resulting outputs are fed sequentially to stdout. Compression of multiple files in this manner generates a stream containing multi- ple compressed file representations. Such a stream can be decompressed correctly only by bzip2 version 0.9.0 or later. Earlier versions of bzip2 will stop after decom- pressing the first file in the stream. bzcat (or bzip2 -dc) decompresses all specified files to the standard output. bzip2 will read arguments from the environment variables BZIP2 and BZIP, in that order, and will process them before any arguments read from the command line. This gives a convenient way to supply default arguments. Compression is always performed, even if the compressed file is slightly larger than the original. Files of less than about one hundred bytes tend to get larger, since the compression mechanism has a constant overhead in the region of 50 bytes. Random data (including the output of most file compressors) is coded at about 8.05 bits per byte, giving an expansion of around 0.5%. As a self-check for your protection, bzip2 uses 32-bit CRCs to make sure that the decompressed version of a file is identical to the original. This guards against corrup- tion of the compressed data, and against undetected bugs in bzip2 (hopefully very unlikely). The chances of data corruption going undetected is microscopic, about one chance in four billion for each file processed. Be aware, though, that the check occurs upon decompression, so it can only tell you that something is wrong. It can't help you recover the original uncompressed data. You can use bzip2recover to try to recover data from damaged files. Return values: 0 for a normal exit, 1 for environmental problems (file not found, invalid flags, I/O errors, &c), 2 to indicate a corrupt compressed file, 3 for an internal consistency error (eg, bug) which caused bzip2 to panic. OPTIONS -c --stdout Compress or decompress to standard output. -d --decompress Force decompression. bzip2, bunzip2 and bzcat are really the same program, and the decision about what actions to take is done on the basis of which name is used. This flag overrides that mechanism, and forces bzip2 to decompress. -z --compress The complement to -d: forces compression, regardless of the invocation name. -t --test Check integrity of the specified file(s), but don't decompress them. This really performs a trial decompression and throws away the result. -f --force Force overwrite of output files. Normally, bzip2 will not overwrite existing output files. Also forces bzip2 to break hard links to files, which it otherwise wouldn't do. bzip2 normally declines to decompress files which don't have the correct magic header bytes. If forced (-f), however, it will pass such files through unmodified. This is how GNU gzip behaves. -k --keep Keep (don't delete) input files during compression or decompression. -s --small Reduce memory usage, for compression, decompression and testing. Files are decompressed and tested using a modified algorithm which only requires 2.5 bytes per block byte. This means any file can be decompressed in 2300k of memory, albeit at about half the normal speed. During compression, -s selects a block size of 200k, which limits memory use to around the same figure, at the expense of your compression ratio. In short, if your machine is low on memory (8 megabytes or less), use -s for everything. See MEMORY MANAGEMENT below. -q --quiet Suppress non-essential warning messages. Messages pertaining to I/O errors and other critical events will not be suppressed. -v --verbose Verbose mode -- show the compression ratio for each file processed. Further -v's increase the ver- bosity level, spewing out lots of information which is primarily of interest for diagnostic purposes. -L --license -V --version Display the software version, license terms and conditions. -1 (or --fast) to -9 (or --best) Set the block size to 100 k, 200 k .. 900 k when compressing. Has no effect when decompressing. See MEMORY MANAGEMENT below. The --fast and --best aliases are primarily for GNU gzip compatibility. In particular, --fast doesn't make things signifi- cantly faster. And --best merely selects the default behaviour. -- Treats all subsequent arguments as file names, even if they start with a dash. This is so you can han- dle files with names beginning with a dash, for example: bzip2 -- -myfilename. --repetitive-fast --repetitive-best These flags are redundant in versions 0.9.5 and above. They provided some coarse control over the behaviour of the sorting algorithm in earlier ver- sions, which was sometimes useful. 0.9.5 and above have an improved algorithm which renders these flags irrelevant. MEMORY MANAGEMENT bzip2 compresses large files in blocks. The block size affects both the compression ratio achieved, and the amount of memory needed for compression and decompression. The flags -1 through -9 specify the block size to be 100,000 bytes through 900,000 bytes (the default) respec- tively. At decompression time, the block size used for compression is read from the header of the compressed file, and bunzip2 then allocates itself just enough memory to decompress the file. Since block sizes are stored in compressed files, it follows that the flags -1 to -9 are irrelevant to and so ignored during decompression. Compression and decompression requirements, in bytes, can be estimated as: Compression: 400k + ( 8 x block size ) Decompression: 100k + ( 4 x block size ), or 100k + ( 2.5 x block size ) Larger block sizes give rapidly diminishing marginal returns. Most of the compression comes from the first two or three hundred k of block size, a fact worth bearing in mind when using bzip2 on small machines. It is also important to appreciate that the decompression memory requirement is set at compression time by the choice of block size. For files compressed with the default 900k block size, bunzip2 will require about 3700 kbytes to decompress. To support decompression of any file on a 4 megabyte machine, bunzip2 has an option to decompress using approximately half this amount of memory, about 2300 kbytes. Decompres- sion speed is also halved, so you should use this option only where necessary. The relevant flag is -s. In general, try and use the largest block size memory con- straints allow, since that maximises the compression achieved. Compression and decompression speed are virtu- ally unaffected by block size. Another significant point applies to files which fit in a single block -- that means most files you'd encounter using a large block size. The amount of real memory touched is proportional to the size of the file, since the file is smaller than a block. For example, compressing a file 20,000 bytes long with the flag -9 will cause the compressor to allocate around 7600k of memory, but only touch 400k + 20000 * 8 = 560 kbytes of it. Similarly, the decompressor will allocate 3700k but only touch 100k + 20000 * 4 = 180 kbytes. Here is a table which summarises the maximum memory usage for different block sizes. Also recorded is the total compressed size for 14 files of the Calgary Text Compres- sion Corpus totalling 3,141,622 bytes. This column gives some feel for how compression varies with block size. These figures tend to understate the advantage of larger block sizes for larger files, since the Corpus is domi- nated by smaller files. Compress Decompress Decompress Corpus Flag usage usage -s usage Size -1 1200k 500k 350k 914704 -2 2000k 900k 600k 877703 -3 2800k 1300k 850k 860338 -4 3600k 1700k 1100k 846899 -5 4400k 2100k 1350k 845160 -6 5200k 2500k 1600k 838626 -7 6100k 2900k 1850k 834096 -8 6800k 3300k 2100k 828642 -9 7600k 3700k 2350k 828642 RECOVERING DATA FROM DAMAGED FILES bzip2 compresses files in blocks, usually 900kbytes long. Each block is handled independently. If a media or trans- mission error causes a multi-block .bz2 file to become damaged, it may be possible to recover data from the undamaged blocks in the file. The compressed representation of each block is delimited by a 48-bit pattern, which makes it possible to find the block boundaries with reasonable certainty. Each block also carries its own 32-bit CRC, so damaged blocks can be distinguished from undamaged ones. bzip2recover is a simple program whose purpose is to search for blocks in .bz2 files, and write each block out into its own .bz2 file. You can then use bzip2 -t to test the integrity of the resulting files, and decompress those which are undamaged. bzip2recover takes a single argument, the name of the dam- aged file, and writes a number of files "rec00001file.bz2", "rec00002file.bz2", etc, containing the extracted blocks. The output filenames are designed so that the use of wildcards in subsequent pro- cessing -- for example, "bzip2 -dc rec*file.bz2 > recov- ered_data" -- processes the files in the correct order. bzip2recover should be of most use dealing with large .bz2 files, as these will contain many blocks. It is clearly futile to use it on damaged single-block files, since a damaged block cannot be recovered. If you wish to min- imise any potential data loss through media or transmis- sion errors, you might consider compressing with a smaller block size. PERFORMANCE NOTES The sorting phase of compression gathers together similar strings in the file. Because of this, files containing very long runs of repeated symbols, like "aabaabaabaab ..." (repeated several hundred times) may compress more slowly than normal. Versions 0.9.5 and above fare much better than previous versions in this respect. The ratio between worst-case and average-case compression time is in the region of 10:1. For previous versions, this figure was more like 100:1. You can use the -vvvv option to mon- itor progress in great detail, if you want. Decompression speed is unaffected by these phenomena. bzip2 usually allocates several megabytes of memory to operate in, and then charges all over it in a fairly ran- dom fashion. This means that performance, both for com- pressing and decompressing, is largely determined by the speed at which your machine can service cache misses. Because of this, small changes to the code to reduce the miss rate have been observed to give disproportionately large performance improvements. I imagine bzip2 will per- form best on machines with very large caches. CAVEATS I/O error messages are not as helpful as they could be. bzip2 tries hard to detect I/O errors and exit cleanly, but the details of what the problem is sometimes seem rather misleading. This manual page pertains to version 1.0.8 of bzip2. Com- pressed data created by this version is entirely forwards and backwards compatible with the previous public releases, versions 0.1pl2, 0.9.0, 0.9.5, 1.0.0, 1.0.1, 1.0.2 and above, but with the following exception: 0.9.0 and above can correctly decompress multiple concatenated compressed files. 0.1pl2 cannot do this; it will stop after decompressing just the first file in the stream. bzip2recover versions prior to 1.0.2 used 32-bit integers to represent bit positions in compressed files, so they could not handle compressed files more than 512 megabytes long. Versions 1.0.2 and above use 64-bit ints on some platforms which support them (GNU supported targets, and Windows). To establish whether or not bzip2recover was built with such a limitation, run it without arguments. In any event you can build yourself an unlimited version if you can recompile it with MaybeUInt64 set to be an unsigned 64-bit integer. AUTHOR Julian Seward, [email protected] https://sourceware.org/bzip2/ The ideas embodied in bzip2 are due to (at least) the fol- lowing people: Michael Burrows and David Wheeler (for the block sorting transformation), David Wheeler (again, for the Huffman coder), Peter Fenwick (for the structured cod- ing model in the original bzip, and many refinements), and Alistair Moffat, Radford Neal and Ian Witten (for the arithmetic coder in the original bzip). I am much indebted for their help, support and advice. See the man- ual in the source distribution for pointers to sources of documentation. Christian von Roques encouraged me to look for faster sorting algorithms, so as to speed up compres- sion. Bela Lubkin encouraged me to improve the worst-case compression performance. Donna Robinson XMLised the docu- mentation. The bz* scripts are derived from those of GNU gzip. Many people sent patches, helped with portability problems, lent machines, gave advice and were generally helpful.
18,997
392
jart/cosmopolitan
false
cosmopolitan/third_party/bzip2/dlltest.dsp
# Microsoft Developer Studio Project File - Name="dlltest" - Package Owner=<4> # Microsoft Developer Studio Generated Build File, Format Version 5.00 # ** •ҏW‚µ‚È‚¢‚Å‚­‚¾‚³‚¢ ** # TARGTYPE "Win32 (x86) Console Application" 0x0103 CFG=dlltest - Win32 Debug !MESSAGE ‚±‚ê‚Í—LŒø‚ÈÒ²¸Ì§²Ù‚ł͂ ‚è‚Ü‚¹‚ñB ‚±‚ÌÌßÛ¼Þª¸Ä‚ðËÞÙÄނ·‚邽‚ß‚É‚Í NMAKE ‚ðŽg—p‚µ‚Ä‚­‚¾‚³‚¢B !MESSAGE [Ò²¸Ì§²Ù‚Ì´¸½Îß°Ä] ºÏÝÄނðŽg—p‚µ‚ÄŽÀs‚µ‚Ä‚­‚¾‚³‚¢ !MESSAGE !MESSAGE NMAKE /f "dlltest.mak". !MESSAGE !MESSAGE NMAKE ‚ÌŽÀsŽž‚ɍ\¬‚ðŽw’è‚Å‚«‚Ü‚· !MESSAGE ºÏÝÄÞ ×²Ýã‚Åϸۂ̐ݒè‚ð’è‹`‚µ‚Ü‚·B—á: !MESSAGE !MESSAGE NMAKE /f "dlltest.mak" CFG="dlltest - Win32 Debug" !MESSAGE !MESSAGE ‘I‘ð‰Â”\‚ÈËÞÙÄÞ Ó°ÄÞ: !MESSAGE !MESSAGE "dlltest - Win32 Release" ("Win32 (x86) Console Application" —p) !MESSAGE "dlltest - Win32 Debug" ("Win32 (x86) Console Application" —p) !MESSAGE # Begin Project # PROP Scc_ProjName "" # PROP Scc_LocalPath "" CPP=cl.exe RSC=rc.exe !IF "$(CFG)" == "dlltest - Win32 Release" # PROP BASE Use_MFC 0 # PROP BASE Use_Debug_Libraries 0 # PROP BASE Output_Dir "Release" # PROP BASE Intermediate_Dir "Release" # PROP BASE Target_Dir "" # PROP Use_MFC 0 # PROP Use_Debug_Libraries 0 # PROP Output_Dir "Release" # PROP Intermediate_Dir "Release" # PROP Ignore_Export_Lib 0 # PROP Target_Dir "" # ADD BASE CPP /nologo /W3 /GX /O2 /D "WIN32" /D "NDEBUG" /D "_CONSOLE" /D "_MBCS" /YX /FD /c # ADD CPP /nologo /W3 /GX /O2 /D "WIN32" /D "NDEBUG" /D "_CONSOLE" /D "_MBCS" /YX /FD /c # ADD BASE RSC /l 0x411 /d "NDEBUG" # ADD RSC /l 0x411 /d "NDEBUG" BSC32=bscmake.exe # ADD BASE BSC32 /nologo # ADD BSC32 /nologo LINK32=link.exe # ADD BASE LINK32 kernel32.lib user32.lib gdi32.lib winspool.lib comdlg32.lib advapi32.lib shell32.lib ole32.lib oleaut32.lib uuid.lib odbc32.lib odbccp32.lib /nologo /subsystem:console /machine:I386 # ADD LINK32 kernel32.lib user32.lib gdi32.lib winspool.lib comdlg32.lib advapi32.lib shell32.lib ole32.lib oleaut32.lib uuid.lib odbc32.lib odbccp32.lib /nologo /subsystem:console /machine:I386 /out:"minibz2.exe" !ELSEIF "$(CFG)" == "dlltest - Win32 Debug" # PROP BASE Use_MFC 0 # PROP BASE Use_Debug_Libraries 1 # PROP BASE Output_Dir "dlltest_" # PROP BASE Intermediate_Dir "dlltest_" # PROP BASE Target_Dir "" # PROP Use_MFC 0 # PROP Use_Debug_Libraries 1 # PROP Output_Dir "dlltest_" # PROP Intermediate_Dir "dlltest_" # PROP Ignore_Export_Lib 0 # PROP Target_Dir "" # ADD BASE CPP /nologo /W3 /Gm /GX /Zi /Od /D "WIN32" /D "_DEBUG" /D "_CONSOLE" /D "_MBCS" /YX /FD /c # ADD CPP /nologo /W3 /Gm /GX /Zi /Od /D "WIN32" /D "_DEBUG" /D "_CONSOLE" /D "_MBCS" /YX /FD /c # ADD BASE RSC /l 0x411 /d "_DEBUG" # ADD RSC /l 0x411 /d "_DEBUG" BSC32=bscmake.exe # ADD BASE BSC32 /nologo # ADD BSC32 /nologo LINK32=link.exe # ADD BASE LINK32 kernel32.lib user32.lib gdi32.lib winspool.lib comdlg32.lib advapi32.lib shell32.lib ole32.lib oleaut32.lib uuid.lib odbc32.lib odbccp32.lib /nologo /subsystem:console /debug /machine:I386 /pdbtype:sept # ADD LINK32 kernel32.lib user32.lib gdi32.lib winspool.lib comdlg32.lib advapi32.lib shell32.lib ole32.lib oleaut32.lib uuid.lib odbc32.lib odbccp32.lib /nologo /subsystem:console /debug /machine:I386 /out:"minibz2.exe" /pdbtype:sept !ENDIF # Begin Target # Name "dlltest - Win32 Release" # Name "dlltest - Win32 Debug" # Begin Source File SOURCE=.\bzlib.h # End Source File # Begin Source File SOURCE=.\dlltest.c # End Source File # End Target # End Project
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jart/cosmopolitan
false
cosmopolitan/third_party/bzip2/release-update.sh
#!/bin/bash # Script to run after a release has been tagged, signed and pushed # to git. Will do a fresh checkout, verify the git tag, do fresh # build/dist, sign the dist with gpg, create a backup copy in HOME, # upload the tar.gz and sig to sourceware, checkout bzip2-htdocs, # copy over the new changes, manual, etc. and git push that to update # https://sourceware.org/bzip2/ # Any error is fatal set -e # We take one argument, the version (e.g. 1.0.7) if [ $# -ne 1 ]; then echo "$0 <version> (e.g. 1.0.7)" exit 1 fi VERSION="$1" echo echo " === NOTE === " echo echo "Requires a sourceware account in the bzip2 group." echo echo "Make sure the git repo was tagged, signed and pushed" echo "If not, please double check the source tree is release ready first" echo "You probably want to run ./prepare-release.sh $VERSION first." echo "Then do:" echo echo " git tag -s -m \"bzip2 $VERSION release\" bzip2-$VERSION" echo " git push --tags" echo read -p "Do you want to continue creating/uploading the release (yes/no)? " if [ "x$REPLY" != "xyes" ]; then echo "OK, till next time." exit fi echo "OK, creating and updating the release." # Create a temporary directoy and make sure it is cleaned up. tempdir=$(mktemp -d) || exit trap "rm -rf -- ${tempdir}" EXIT pushd "${tempdir}" # Checkout git clone git://sourceware.org/git/bzip2.git cd bzip2 git tag --verify "bzip2-${VERSION}" git checkout -b "$VERSION" "bzip2-${VERSION}" # Create dist (creates bzip2-${VERSION}.tar.gz) make dist # Sign (creates bzip2-${VERSION}.tar.gz.sig) gpg -b bzip2-${VERSION}.tar.gz # Create backup copy echo "Putting a backup copy in $HOME/bzip2-$VERSION" mkdir $HOME/bzip2-$VERSION cp bzip2-${VERSION}.tar.gz bzip2-${VERSION}.tar.gz.sig $HOME/bzip2-$VERSION/ # Upload scp bzip2-${VERSION}.tar.gz bzip2-${VERSION}.tar.gz.sig \ sourceware.org:/sourceware/ftp/pub/bzip2/ ssh sourceware.org "(cd /sourceware/ftp/pub/bzip2 \ && ln -sf bzip2-$VERSION.tar.gz bzip2-latest.tar.gz \ && ln -sf bzip2-$VERSION.tar.gz.sig bzip2-latest.tar.gz.sig \ && ls -lah bzip2-latest*)" # Update homepage, manual, etc. cd "${tempdir}" git clone ssh://sourceware.org/git/bzip2-htdocs.git cp bzip2/CHANGES bzip2/bzip.css bzip2-htdocs/ cp bzip2/bzip.css bzip2/bzip2.txt bzip2/manual.{html,pdf} bzip2-htdocs/manual/ cd bzip2-htdocs # Update version in html pages. sed -i -e "s/The current stable version is bzip2 [0-9]\.[0-9]\.[0-9]\+/The current stable version is bzip2 ${VERSION}/" *.html */*.html git commit -a -m "Update for bzip2 $VERSION release" git show git push # Cleanup popd trap - EXIT exit
2,598
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jart/cosmopolitan
false
cosmopolitan/third_party/bzip2/sample2.ref
÷ƒ’À;è TeX output 1995.10.19:1430‹ÿÿÿÿ •ºâ ý? £ þŸŒ÷‘dßdóÂÖN ff cmbx12¼Strictness–ffAnalysis‘I™‘ø4a“Grande“Vitesse:ޤ‘¼¦Rewriting–ffthe“rules“of“the“Ev‘ÿ™aluation“T‘þ¦fransformers“gameŽ¡‘5†ÈóX«Q ff cmr12»Second–³/draft:›D>OctobdCer“19,“1995.˜Commenš›¼ts“are“w˜elcomed.ŸúÆ=ó !",š cmsy10¸ŽŽŽŸy”’È@ó(Kñ`y ó3 cmr10ÓJulian‘¦fSew²!ardŽŽ¤ ™™‘5)JDepartmenš²!t–¦fof“Computer“Science,“Univ˜ersit˜y“of“Manc˜hester,“M13“9PL,“UKŽŽ¡’°>?ó7ßê<x ó3 cmtt10â[email protected]ŽŽŽŽŽŽŽ ú þ"‘íºâóñkAH cmssbx10¹AbstractŽ©†´‘íºâóo´‹Ç cmr9ºThis–l¾papAÇer“presen¾9ts“the“design“of“a“strictness“analyser“pri-ޤ ‘íºâmarily–u‰inš¾9tended“to“assist“in“the“parallelisation“of“Hask˜ellŽ¡‘íºâprograms.‘åôThe–qàanalyser“generates“detailed“ev‘ÿ|raluation“trans-Ž¡‘íºâformer–â'information“suitable“for“use“in“a“parallel“graph“re-Ž¡‘íºâduction–ssmac¾9hine.‘6ÍBy“tuning“the“design“to“handle“commonŽ¡‘íºâcases–H'rapidly‘ÿ:«,‘TÛwš¾9e“ac˜hiev˜e“go•AÇo“d›H'p“erformance˜o•¾9v“er˜a˜range˜ofŽ¡‘íºârealistic–ö~test“inputs,‘.Èof“sizes“up“to“a“thousand“lines.‘¿îP¾9er-Ž¡‘íºâformance–ó/ gures“are“presen¾9ted.‘¶F‘ÿ:«rom“measuring“the“timeŽ¡‘íºâit–!Stakš¾9es“Glasgo˜w“Hask˜ell“0.10“to“compile“those“same“pro-Ž¡‘íºâgrams,‘ªit–w3is“apparenš¾9t“that“the“analyser“is“sucien˜tly“quic˜kŽ¡‘íºâto–ߥbšAÇe“approac¾9hing“the“p˜oin¾9t“where“incorp˜orating“it“in¾9to“aŽ¡‘íºâHask¾9ell–Tcompiler“is“a“viable“propAÇosition.ŽŸ ‘íºâOur–ƒ€strictness“analyser“conš¾9tains“three“ma‘ƒŽjor“inno˜v‘ÿ|rations.Ž¡‘íºâFirstly‘ÿ:«,‘î“w•¾9e›à emplo“y˜a˜mixed˜forw“ard˜and˜bac“kw“ards˜analy-Ž¡‘íºâsis,‘l whic•¾9h›'‚allo“ws˜us˜to˜do˜pro‘ƒŽjection˜analysis˜ev“en˜in˜theŽ¡‘íºâpresence–¼Fof“higher“order“functions.‘ESecondly‘ÿ:«,‘æwš¾9e“solv˜e“theŽ¡‘íºâresulting–Õ¹recursiv¾9e“domain“equations“using“a“sophisticatedŽ¡‘íºâterm–±rewriting“system,–Nlwhicš¾9h,“as–±far“as“w˜e“kno˜w,‘Nlhas“abilitiesŽ¡‘íºâfar–9~bAÇeyš¾9ond“previous“rewrite“based“solv˜ers“in“abstract“in˜ter-Ž¡‘íºâpretation–Èsystems.‘ªFinally‘ÿ:«,‘×xwš¾9e“a˜v˜oid“man˜y“of“the“dicultiesŽ¡‘íºâof–|ôhigher“order“analysis“b¾9y“automatically“transforming“outŽ¡‘íºâmost–Thigher“order“functions“bšAÇefore“analysis“b˜egins.ŽŸ-‘íºâ¹1Ž‘ü”IntroFfductionަ‘íºâºHigher-order,‘Zûnon- at–,dstrictness“analysis“tecš¾9hniques“ha˜v˜e“ac-Ž¡‘íºâquired–¡a“reputation“for“bšAÇeing“to˜o“exp˜ensiv¾9e“for“use“in“pro-Ž¡‘íºâduction–Âscompilers.‘ÐThis“is“a“pitš¾9y‘ÿ:«,‘Ósince“man˜y“suc˜h“functionsŽ¡‘íºâbAÇeha•¾9v“e–ãin“relativš¾9ely“simple“w˜a˜ys,‘~whic˜h“suggests“their“ab-Ž¡‘íºâstract–TbšAÇeha¾9viour“could“b˜e“divined“without“m•¾9uc“h‘Tdicult“y‘ÿ:«.ŽŸ ‘íºâOne–ãof“the“main“themes“whicš¾9h“c˜haracterised“the“pastŽ¡‘íºâdecade's–Ÿadv‘ÿ|rances“in“hardwš¾9are“and“soft˜w˜are“pAÇerformanceŽ¡‘íºâis–5£that“of“measuremenš¾9t-lead“design.‘}\This“sc˜hoAÇol“of“though˜tŽ¡‘íºâbases–Ødesign“on“measuring“what“programs“do“most“often,Ž¡‘íºâand–WQmaking“these“common“activities“as“fast“as“pAÇossible,‘}Rev¾9enŽ¡‘íºâat––ïthe“expAÇense“of“sloš¾9wing“do˜wn“less“common“opAÇerations.Ž¡‘íºâThese–,Ôideas,‘r´elabAÇorated“in“Hennessy“&“P¾9atterson“[HP90Ž‘zú],Ž‘íºâŸÀ‰ff_ÿ Ÿ34‘ +bŸüûró °Ü0ncmsy5¶ŽŽ‘Yóٓ Rcmr7±My–}^apš7ologies“for“the“dog-rough“tÈãyp˜esetting.‘|ÂThis“will“b˜e“ 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rstŽ¡’õºâimplemen¾9tation,‘jthere–Þÿis“ample“scopšAÇe“for“p˜erformance“im-Ž¡’õºâpro•¾9v“emen“t.ަ’õºâThis–XpapAÇer“argues“in“fa•¾9v“our–Xof“a“measuremenš¾9t-lead“approac˜hŽ¡’õºâfor–¢qthe“implemenš¾9tation“of“seman˜tic“analysis“tec˜hniques“forŽ¡’õºâfunctional–ßlanguages.‘ UA‘Þôma‘ƒŽjor“emphasis“is“to“feed“the“anal-Ž¡’õºâyser–LÈthe“kinds“of“programs“pAÇeople“really“write,‘Z¥rather“thanŽ¡’õºâbasing–Øïdesign“decisions“on“the“usual“Mic•¾9k“ey–ØïMouse“exam-Ž¡’õºâples–ý¬ošAÇccurring“so“frequen¾9tly“in“pap˜ers“on“the“sub‘ƒŽject.‘ÕxT‘ÿ:«oŽ¡’õºâthis–Ëend,‘¿ètest“inputs“ha•¾9v“e–ËbšAÇeen“tak¾9en“from“the“b˜enc¾9hmarkŽ¡’õºâsuites–Tof“Hartel“[HL92Ž‘÷l]“and“Pš¾9artain“[P˜ar92Ž‘‡Ç].ަ’õºâSucš¾9h–?®an“approac˜h“rev˜eals“some“in˜teresting“facts.‘›~F‘ÿ:«or“ex-Ž¡’õºâample,‘Õçw•¾9e›¯cdisco“v“ered˜the˜main˜limitation˜on˜analyser˜pAÇer-Ž¡’õºâformance–#¼wš¾9as“not“the“necessit˜y“to“iterate“to“and“detect“ x-Ž¡’õºâpšAÇoin¾9ts,‘¨as–ŒÐhad“b˜een“assumed“bš¾9y“so“man˜y“theoretics.‘îïRather,Ž¡’õºâit–aàw¾9as“the“sheer“size“of“the“terms“generated“during“the“ab-Ž¡’õºâstract–cBinš¾9terpretation“phase.‘;By“in˜troAÇducing“a“little“moreŽ¡’õºâin•¾9telligence›þGin“to˜that˜phase,‘8ƒterm˜size˜is˜cut˜dramatically‘ÿ:«,Ž¡’õºâgiving–Ta“correspšAÇonding“p˜erformance“increase.ަ’õºâSimilarly‘ÿ:«,‘h­pAÇolymorphism–Xis“dealt“with“bš¾9y“the“crude“mec˜ha-Ž¡’õºânism–Áof“a“monomorphisation“pass“bAÇefore“analysis.‘/·PreviousŽ¡’õºâw•¾9ork“ers,›™pincluding‘m“yself,˜assumed–this“w¾9as“a“\bad“thing"Ž¡’õºâ(see–¿Š[HH91Ž‘>]“and“[Sew93Ž‘/]),‘гand“put“m•¾9uc“h–¿Še ort“in¾9to“devisingŽ¡’õºâpšAÇolymorphic–¢analysis“metho˜ds“[Bar91Ž‘ U].‘5Y‘ÿ:«et“the“feared“co˜deŽ¡’õºâexplosion,–қit›Áíseems,“simply˜do•AÇes˜not˜happ“en.‘£Measuremen¾9tsŽ¡’õºâbš¾9y–›<Mark“Jones“on“a“13000“line“Hask˜ell“program“{“the“sourceŽ¡’õºâcoAÇde–TDof“this“analyser“{“revš¾9eal“that“only“a“v˜ery“few“pAÇoly-Ž¡’õºâmorphic–G‡functions,›Tfor“example“óMߤN cmtt9ëMmap“ºand“ëMfoldrº,˜are“used“atŽ¡’õºâa–†large“n•¾9um“bAÇer–†of“instances.‘µCertainly‘ÿ:«,‘¿’monomorphisationŽ¡’õºâdošAÇes–wÎnot“cause“an¾9y“noticeable“p˜erformance“problems“for“thisŽ¡’õºâanalyser.‘#¸A‘mm•¾9uc“h–mbAÇetter“reason“for“disliking“monomorphicŽ¡’õºâanalyses–‹#is“that“they“signi can¾9tly“complicate“life“when“moAÇd-Ž¡’õºâules–TappAÇear“on“the“scene.ŽŽŽŽŽŽŽŒ‹* •ºâ ý? £ ý€‘íºâ¹1.1Ž‘G·Overview–LÎof“papFferŽŸm‘íºâºThe–†Iremainder“of“the“inš¾9troAÇduction“is“dev˜oted“to“an“o˜v˜erviewޤ ‘íºâof–Tthe“analyser,“henceforth“referred“to“as“óNt ‰: cmbx9ëNAnnaº.Ž© ‘íºâSection–“”2“deals“with“tec¾9hnical“preliminaries.‘—/In“particular,Ž¡‘íºâwš¾9e– nexamine“ho˜w“t˜ypšAÇes“in“the“source“program“are“mapp˜ed“toŽ¡‘íºâabstract– Èdomains“suitable“for“the“con¾9trol“of“parallel“ev‘ÿ|ralua-Ž¡‘íºâtion.ަ‘íºâThe–Ï~abstract“in¾9terpretation“used“forms“the“sub‘ƒŽject“of“sec-Ž¡‘íºâtion–e<3.‘ 'A‘dåv‘ÿ|rarian¾9t“of“the“pro‘ƒŽjection“analysis“describAÇed“inŽ¡‘íºâsection–,ê6“of“[Hug87Ž‘ó'],‘rÐthe“tecš¾9hnique“is“a“mixed“bac˜kw˜ardsŽ¡‘íºâand–œàforwš¾9ards“analysis,‘þÂwith“the“aim“of“pAÇerforming“bac˜k-Ž¡‘íºâwš¾9ards– 4analysis.‘By“supplying“just“enough“\forw˜ards"“infor-Ž¡‘íºâmation–lîto“turn“functions“in¾9to“ rst“class“citizens,‘Žthe“analysisŽ¡‘íºâdeals–Çsensibly“with“higher-order“functions,‘ókpartial“applica-Ž¡‘íºâtions–Tand“functions“inside“data“structures.ަ‘íºâSection–öÇ4“presen¾9ts,›/$in“detail,˜the“elabAÇorate“term“rewritingŽ¡‘íºâsystem–lused“to“detect“ xed“pAÇoinš¾9ts“in“the“recursiv˜e“domainŽ¡‘íºâequations–Tgenerated“bš¾9y“the“abstract“in˜terpreter.ަ‘íºâF‘ÿ:«unctional–f¢programmers“ha•¾9v“e–f¢long“observ¾9ed“that“large“partsŽ¡‘íºâof–zŠthe“programs“they“write“can“bAÇe“mec¾9hanically“transformedŽ¡‘íºâto›eçha•¾9v“e˜no˜higher-order˜functions.‘(Anna˜exploits˜this˜toŽ¡‘íºâgo•AÇo“d–„e ect,‘Ÿ³transforming“a•¾9w“a“y–„as“man¾9y“higher-order“func-Ž¡‘íºâtions–ias“pšAÇossible“b˜efore“analysis.‘Ç"Common“higher“order“func-Ž¡‘íºâtions–c|whicš¾9h“encapsulate“particular“forms“of“recursion,‘wsuc˜hŽ¡‘íºâas–gëMfoldrº,‘{are“trivially“remo•¾9v“ed.‘ÌEv“en–gmore“dicult“forms,Ž¡‘íºâlikš¾9e–P$the“monads“so“bAÇelo˜v˜ed“in“certain“quarters“[W‘ÿ:«ad92Ž‘¿˜]“areŽ¡‘íºâtransformable.›)ªNev¾9ertheless,‘…some–odiculties“remain.˜Sec-Ž¡‘íºâtion–Âo5“discusses“all“this“in“detail.‘ÎW‘ÿ:«e“also“loAÇok“brie y“at“theŽ¡‘íºâmonomorphiser.ަ‘íºâFinally‘ÿ:«,›/²in–÷9section“6,˜all“these“go•AÇo“dies–÷9are“dra¾9wn“togetherŽ¡‘íºâwith–@’a“discussion“of“the“system's“pAÇerformance,‘kand“of“relatedŽ¡‘íºâand–Tfurther“w¾9ork.ŽŸÚ‘íºâ¹1.2Ž‘G·Overview–LÎof“the“analyser's“front“endŽŸm‘íºâºAnna–pis“a“large“Hask¾9ell“program,‘B·consisting“of“more“thanŽ¡‘íºâ13000–7lines.›¿OpAÇeration“is“simple.˜Anna“reads“a“source“pro-Ž¡‘íºâgram–Cyon“the“standard“input,‘Oand“pAÇerforms“extensiv¾9e“trans-Ž¡‘íºâformations–»ñon“the“program,‘ÍÒprinš¾9ting“it“out“at“v‘ÿ|rarious“pAÇoin˜tsŽ¡‘íºâon–1Ðthe“w•¾9a“y–ÿ:«.‘qåFinally“,‘8ïthe–1Ðstrictness“information“is“generatedŽ¡‘íºâand‘Tprin¾9ted.ަ‘íºâThe–y¦language“accepted“is“a“subset“of“Hask¾9ell.‘IfMissing“fea-Ž¡‘íºâtures–are“anš¾9ything“to“do“with“o˜v˜erloading,‘CmoAÇdules“or“arra˜ys.Ž¡‘íºâBecause–Òàof“these,‘à+o ering“up“arbitrary“Hask¾9ell“programs“forŽ¡‘íºâanalysis–«is“a“dicult“task:‘çGall“o•¾9v“erloading–«has“to“bAÇe“resolv¾9edŽ¡‘íºâbš¾9y–óhand,‘*‚a“tedious“business.‘µ«The“lac˜k“of“mošAÇdule“supp˜ortŽ¡‘íºâdoAÇes–rœnot“pro•¾9v“e›rœm“uc“h˜of˜a˜problem,‘“(since˜m“ultimoAÇdule˜inputsŽ¡‘íºâare–nsimply“concatenated“inš¾9to“one“massiv˜e“program,‘moAÇduloŽ¡‘íºâsolving–|Íthe“oAÇdd“renaming“problem“along“the“w•¾9a“y‘ÿ:«.‘RÚAnnaŽ¡‘íºâknoš¾9ws–`Ynothing“abAÇout“the“Hask˜ell“prelude,‘sand“the“relev‘ÿ|ran˜tŽ¡‘íºâparts–Õof“this“tošAÇo“need“to“b˜e“inserted“inš¾9to“the“inputs.‘A‘Õv˜eryŽ¡‘íºâfew–(opAÇerations“are“takš¾9en“as“primitiv˜e:‘AÏëM(+)º,–l¯ëM(-)º,“ëM(*)‘(ºandŽ¡‘íºâëM(/)º,›š~all–{Çof“t¾9ypAÇe“ëMInt–¹–->“Int“->“Intº,˜comparisons‘{ÇëM(<)º,˜ëM(<=)º,Ž¡‘íºâëM(==)º,–n¾ëM(/=)º,“ëM(>)–Eºand“ëM(>=)º,›n¾of“t¾9ypAÇe“ëMInt–¹–->“Int“->“Boolº,˜andŽ¡‘íºâcon•¾9v“ersion–=ífunctions“ëMchr“ºand“ëMord“ºof“t¾9ypAÇe“ëMInt–¹–->“Char‘=íºandŽ¡‘íºâëMChar–¹–->“Int–¦ÍºrespAÇectivš¾9ely‘ÿ:«.‘ÐÚA‘¦§v‘ÿ|ralid“program“m˜ust“supply“aŽ¡‘íºâbinding–»for“ëMmainº,‘Íbut“unlikš¾9e“a“Hask˜ell“program,‘Íthis“ma˜y“bAÇeŽ¡‘íºâof–Tanš¾9y“t˜ypAÇe.ަ‘íºâDespite–iÉthis“meagre“collection“of“primitivš¾9es,‘¾æAnna“kno˜wsŽ¡‘íºâabAÇout–fmost“of“the“built-in“Haskš¾9ell“t˜ypšAÇes,‘‰including“b˜o˜oleans,Ž¡‘íºâc¾9haracters,–T„strings,“lists–Gáand“tuples.‘´Although“some“impAÇor-ŽŽŽ ý€’õºâtanš¾9t–Ü»features“of“Hask˜ell“are“missing,‘è the“subset“allo˜ws“Annaޤ ’õºâto–:CbAÇe“fed“real-wš¾9orld“programs“of“considerable“complexit˜y‘ÿ:«,Ž¡’õºâalbAÇeit–Tafter“some“considerable“massaging.Ž© ’õºâProbably–g)the“bAÇest“w•¾9a“y–g)to“think“of“Anna“is“as“a“framew¾9orkŽ¡’õºâfor–¡Itrying“out“new“analysis“tec¾9hniques.‘ÀNHence,‘ÄFthe“systemŽ¡’õºâlogically–%Ýconsists“of“t•¾9w“o–%Ýparts:‘=‚the“analysis“propAÇer,‘)ÿand“theŽ¡’õºâsuppAÇorting–uÏframewš¾9ork.‘=àThe“in˜terface“bAÇet˜w˜een“the“t˜w˜o“isŽ¡’õºâreasonably–ÃVclean,‘Ó¼so“c¾9hanging“the“nature“of“the“analysis“canŽ¡’õºâbAÇe–Íudone“without“m•¾9uc“h›Íuuphea“v‘ÿ|ral.‘DÓThis˜section˜foAÇcusses˜onŽ¡’õºâthe–TsuppAÇorting“framew¾9ork.ަ’õºâBecause–×'wš¾9e“w˜an˜t“to“exercise“the“analyses“on“functional“pro-Ž¡’õºâgrams–T'of“realistic“size,‘zÊthe“suppAÇorting“framew¾9ork“is“necessar-Ž¡’õºâily–¼Ûlarge“and“complex.‘þòIndeed,‘΍the“analysis“part“is“curren¾9tlyŽ¡’õºâthe–è¶smaller“of“the“t•¾9w“o.‘–•The›è¶framew“ork˜con“tains˜a˜go•AÇo“dlyŽ¡’õºâpart–Áof“what“one“migh¾9t“expAÇect“to“ nd“in“a“full-scale“com-Ž¡’õºâpiler–Tfor“the“same“language:ŽŸÐO’äóP©±Ê cmsy9ëPŽŽŽ’ :âºF‘ÿ:«ollo¾9wing–= the“parsing“stage,‘†÷desugaring“and“patternŽ¡’ :âmatc¾9hing–0ãtransformations“are“carried“out.‘oThese“pro-Ž¡’ :âduce–ÝyëNCoreº,‘O‚a“minimal“functional“language“used“asŽ¡’ :âan– -inš¾9termediate“form“in“the“Glasgo˜w“Hask˜ell“com-Ž¡’ :âpiler–îž[PHHP93Ž‘#µø],‘ö\and“tš¾9ypical“of“the“in˜termediate“formsŽ¡’ :âof–|Ïv‘ÿ|rarious“other“compilers,‘–®for“example“the“ChalmersŽ¡’ :âHask¾9ell-B‘¶}Compiler–¶§[Aug87Ž‘ó'].‘hAll“further“transforma-Ž¡’ :âtions–òprior“to“strictness“analysis“propAÇer“are“Core-to-Ž¡’ :âCore‘Ttransformations.Ž©34’äëPŽŽŽ’ :âºA‘MÌdepAÇendancy–Nanalysis“phase“splits“the“program“upŽ¡’ :âinš¾9to–µyminimal“m˜utually“recursiv˜e“groups,‘and“marksŽ¡’ :ânon-recursivš¾9e–M>bindings“as“suc˜h.‘Ä.All“subsequen˜t“trans-Ž¡’ :âformations–Bare“required“to“main¾9tain“depAÇendancy“order.ަ’äëPŽŽŽ’ :âºA‘Ízcrude–͌but“e ectivš¾9e“Core“simpli cation“pass“remo˜v˜esŽ¡’ :âunš¾9used– ºbindings,‘ Øand“substitutes“in“constan˜t“bindingsŽ¡’ :âonly–:used“once.‘ÆThis“helps“to“clean“up“the“rather“messyŽ¡’ :âoutput–`-of“the“desugarer.‘üûThe“former“feature“is“usefulŽ¡’ :âfor–;ždebugging“the“analyser.‘ÓÞBecause“a“binding“for“ëMmainŽ¡’ :âºmš¾9ust–“ìbAÇe“supplied,‘­Îthe“simpli er“will“ev˜en˜tually“remo˜v˜eŽ¡’ :âall–´bindings“not“reac¾9hable“from“ëMmainº.‘êIf“the“analyser“isŽ¡’ :âseen–‘¹to“malfunction,‘¬ arbitrary“subsections“of“the“inputŽ¡’ :âprogram–can“bAÇe“discarded“simply“bš¾9y“c˜hanging“the“b•AÇo“dyŽ¡’ :âof–¥ëMmainº,‘Éunš¾9til“what“remains“is“small“enough“to“mak˜eŽ¡’ :âdebugging‘Tviable.ަ’äëPŽŽŽ’ :âºRemoš¾9ving–.“nested“en˜vironmen˜ts“mak˜es“subsequen˜tŽ¡’ :âtransformations–i®and“analyses“simpler.‘ã9T‘ÿ:«o“this“end,‘ŒtheŽ¡’ :âprogram–Vis“ attened“out“bš¾9y“a“moAÇdi ed“Johnsson-st˜yleŽ¡’ :âlam•¾9bAÇda-lifter›‰[Joh85Ž‘Ä9],‘¥!follo“w“ed˜b“y˜another˜depAÇendancyŽ¡’ :âanalysis‘Tpass.ަ’äëPŽŽŽ’ :âºThe– Ûprogram“is“noš¾9w“t˜ypAÇec˜hec˜k˜ed,‘¼using“a“standardŽ¡’ :âMilner-Hindley–ƒinferencer“deriv¾9ed“from“Chapter“9“ofŽ¡’ :âPš¾9eyton–…uJones'“b•AÇo“ok–…u[P˜ey87Ž‘Hª].‘lÒEv˜ery“noAÇde“in“the“CoreŽ¡’ :âtree–;has“a“tš¾9ypAÇe“expression“attac˜hed.‘hAlthough“a“com-Ž¡’ :âplete–mannotation“is“rather“expAÇensivš¾9e,‘ ³it“is“essen˜tial“forŽ¡’ :âsubsequen¾9t‘Tpasses.ަ’äëPŽŽŽ’ :âºThe–þNsingle“most“complicated“transformation,‘8Œhigher-Ž¡’ :âorder–ôfunction“remoš¾9v‘ÿ|ral“(also“kno˜wn“as“spAÇecialisationŽ¡’ :âor–z rsti cation)“noš¾9w“follo˜ws.‘(âThe“presen˜t“naiv˜e“im-Ž¡’ :âplemen¾9tation,›|xdescribAÇed–g×in“Section“5,˜is“slo¾9w“but“cor-Ž¡’ :ârect.‘™cMost–é¥if“not“all“of“the“higher-orderness“of“t¾9ypi-Ž¡’ :âcal–Q™programs“can“bAÇe“remo•¾9v“ed.‘Ñ>This–Q™transformation“isŽ¡’ :âcomplicated–¹ybš¾9y“the“need“to“main˜tain“t˜ypAÇe“annotationsŽ¡’ :âcorrectly‘ÿ:«.ŽŽŽŽŽŸ’çjã2ŽŽŒ‹ •ºâ ý? £ ý€‘ûäëPŽŽŽ‘:âºFinally‘ÿ:«,‘ŸSthe–ƒºprogram“is“monomorphised.‘g¡This“pass“isޤ 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it–«is“easy“to“see“ho¾9w“the“output“of“the“strictnessŽ¡‘íºâanalyser–ççpropšAÇer“p˜ertains“to“the“desugared“program.‘”)OnlyŽ¡‘íºât•¾9w“o–Ttransformations“givš¾9e“m˜uc˜h“trouble:ŽŸ؍‘ûäëPŽŽŽ‘:âºLamš¾9bAÇda-lifting–psimply“mo˜v˜es“bindings“from“inner“lev-Ž¡‘:âels–Véto“the“top“lev¾9el,‘|ÿand“adds“extra“parameters.‘Ü÷With“aŽ¡‘:âlittle›¢bb•AÇo“okk¾9eeping,‘¹_it˜is˜p“ossible˜to˜k•¾9eep˜trac“k˜of˜whereŽ¡‘:ânested–pŸbindings“ended“up,‘‡rso“that“strictness“informa-Ž¡‘:âtion–Tcan“bAÇe“related“bac¾9k“to“them.ŽŸ×x‘ûäëPŽŽŽ‘:âºHigher-order–1tfunction“remoš¾9v‘ÿ|ral“will“only“ev˜er“remo˜v˜eŽ¡‘:âhigher-order–NTfunctions“whicš¾9h“ha˜v˜e“bAÇecome“irrelev‘ÿ|ran˜tŽ¡‘:âbšAÇecause–Gˆof“sp˜ecialisation.‘³ All“ rst-order“functions“areŽ¡‘:âpreservš¾9ed.‘ gwW‘ÿ:«e–.Vare“really“only“in˜terested“in“deriv-Ž¡‘:âing–†Xev‘ÿ|raluation“transformers“for“the“ 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v‘ÿ|ralianš¾9tly“suppAÇorted“those“bra˜v˜e“enough“to“tak˜eŽ¡‘íºâthem–¡´up“[PHHP93Ž‘#µø].‘ÁIn“retrospAÇect,‘ÄÌthere“are“three“reasonsŽ¡‘íºâwhš¾9y–TAnna“w˜as“not“built“in˜to“Glasgo˜w“Hask˜ell:ŽŸ؍‘ø‰1.ŽŽŽ‘:âAš¾9t–Ïçthe“time“w˜ork“on“Anna“bAÇegun,‘þ‹in“the“summer“ofŽ¡‘:â1991,‘ÖGlasgoš¾9w's–¼compiler“(v˜ersion“0.02)“w˜as“in“still“inŽ¡‘:âthe–TproAÇcess“of“dev•¾9elopmen“t.Ž©×x‘ø‰2.ŽŽŽ‘:âUn•¾9til›gFrecen“tly‘ÿ:«,‘»Ãthe˜analyser˜w“as˜relativ“ely˜feeble,‘»ÃsoŽ¡‘:âthe–ú¹need“to“feed“it“realistic“Hask¾9ell“programs“has“onlyŽ¡‘:ârecen¾9tly‘Tarisen.ަ‘ø‰3.ŽŽŽ‘:âThe–…Ïmost“impAÇortan¾9t“reason,–¢ƒthough,“is–…Ïthis:‘Ô­Anna“hadŽ¡‘:âb•AÇeen›êdev¾9elop“ed˜using˜Mark˜Jones'˜marv•¾9ellous˜in“terac-Ž¡‘:âtiv•¾9e›¯?en“vironmen“t,‘êGofer.‘úiMerging˜Anna˜in“to˜the˜Glas-Ž¡‘:âgo•¾9w›À Hask“ell˜w“orld˜w“ould˜ha“v“e˜mean“t˜compiling˜withŽ¡‘:âa–yêHaskš¾9ell“compiler“and“this“w˜ould“easily“ha˜v˜e“put“anŽ¡‘:âorder–m£of“magnitude“on“the“edit-compile-run“cycle“time.ŽŸٍ‘íºâAs–ŀAnna“bšAÇecomes“more“and“more“p˜o•¾9w“erful,‘Õwthe›ŀincen“tiv“e˜toŽ¡‘íºâbuild–'it“inš¾9to“a“real“compiler“gro˜ws.‘êThis“is“de nitely“a“longŽ¡‘íºâterm‘Tob‘ƒŽjectiv¾9e.ŽŸ ‘íºâ¹2Ž‘ü”T‘ÿ,Ìechnical‘LÎp•¹™relimina“riesŽŸ†´‘íºâ2.1Ž‘G·Some‘LÎterminologyŽŸm‘íºâºThe–ÿanalyser's“fron¾9t“end“proAÇduces“a“ëNCore––Åsyn´Ctax“treeº,‘ *inŽ¡‘íºâwhic•¾9h›Rev“ery˜noAÇde˜is˜decorated˜with˜its˜t“ypAÇe.‘Ò¥This˜is˜fed˜toŽ¡‘íºâthe–oëNabstract‘¢bin´Cterpreter“ºpropAÇer,‘Bµwhic¾9h“translates“to“anŽ¡‘íºâabstract›9=form:‘dBëNrecursiv´Ce–Üádomain“equationsº.‘ˆ,The˜ëN x-Ž¡‘íºâpK¼oin´Cter–›€ºsolvš¾9es“these“equations“b˜y“iterating“to“their“greatestŽŽŽ ý€’õºâ xed–népAÇoinš¾9ts,‘…Ndetecting“equalit˜y“of“adjacen˜t“appro˜ximationsޤ ’õºâb¾9y–š³reducing“them“to“ëNnormal›ÿšform“ºusing“the“ëNterm˜rewrit-Ž¡’õºâing‘ŒÊsystemº,–Tand“comparing“those“normal“forms.ŽŸ ’õºâThere–Tare“t•¾9w“o–Tkinds“of“abstract“en•¾9tit“y‘ÿ:«.Ž©ÐO’äëPŽŽŽ’ :âëNCon´Ctexts–eºdenote“an“amoun¾9t“of“ev‘ÿ|raluation“that“shouldŽ¡’ :âbAÇe–àUapplied“to“a“data“structure“or“function.‘ }sTheseŽ¡’ :âare– Dsometimes“referred“to“as“ëNdemands“ºor“ëNbac•´Ckw“ardsŽ¡’ :âv‘ÿh‰aluesº,‘á¦but–…–wš¾9e“will“stic˜k“with“ëNcon´Ctext“ºwhere“pAÇos-Ž¡’ :âsible.‘ÑÊW‘ÿ:«e–ürlater“inš¾9troAÇduce“a“Hask˜ell“t˜ypAÇe“ëMContext“ºtoŽ¡’ :âmoAÇdel‘Tcon¾9texts.ŽŸ34’äëPŽŽŽ’ :âëNAbstract‘CFv‘ÿh‰alues–Õzºamounš¾9t“to“some“tric˜k˜ery“w˜e“will“in-Ž¡’ :âtroAÇduce–øÙto“deal“with“higher“order“functions.‘òAn“alter-Ž¡’ :ânativ•¾9e›ýname,‘['whic“h˜is˜again˜a“v“oided˜where˜pAÇossible,Ž¡’ :âis–"’ëNforw´Card‘œ v‘ÿh‰alueº.‘D*The“correspAÇonding“Haskš¾9ell“t˜ypAÇe“isŽ¡’ :âëMAbsValº.ަ’õºâThis–?¿papAÇer“is“primarily“concerned“with“disco•¾9v“ering‘?¿ho“wŽ¡’õºâsource–Ý(language“functions“bAÇeha•¾9v“e–Ý(viz-a-viz“con¾9texts.‘síNev-Ž¡’õºâertheless,‘ßgthe–¶ýoutput“of“the“abstract“in¾9terpreter“is“one“ab-Ž¡’õºâstract–EÙv›ÿ|ralue“pAÇer“Core“function.‘×GCon¾9texts“and“abstract“v˜aluesŽ¡’õºâin•¾9tert“wine,‘Öfso–¯Éthe“ëMContext“ºand“ëMAbsVal“ºtš¾9ypAÇes“are“m˜utuallyŽ¡’õºârecursivš¾9e.‘ÄThe–÷Üabstract“in˜terpreter“itself“is“de ned“as“theŽ¡’õºâfunction–TëMZ“ºin“section“3.6.1.Ž© ’õºâCon¾9texts–ˆand“abstract“v‘ÿ|ralues“are,›¤Zin“a“sense,˜strongly“t¾9ypAÇed.Ž¡’õºâEac•¾9h›£Bcon“text˜is˜a˜mem“bAÇer˜of˜a˜particular˜ëNcon´Ctext‘ udomainº,Ž¡’õºâand–nSmost“opAÇerations“on“con¾9texts“are“only“meaningful“if“theirŽ¡’õºâopAÇerands–ÿ8are“dra¾9wn“from“particular“domains.‘Abstract“v‘ÿ|ral-Ž¡’õºâues–zÌare“also“strongly“t¾9ypAÇed.‘L×Although“the“domains“for“ab-Ž¡’õºâstract–uv‘ÿ|ralues“are,›[¼strictly“spAÇeaking,˜di erenš¾9t“from“con˜textŽ¡’õºâdomains,›£Âw¾9e–‡]will“ignore“abstract“v‘ÿ|ralue“domains.‘íInstead,˜w¾9eŽ¡’õºâonly–“ýconsider“con¾9text“domains,‘³§henceforth“referred“to“sim-Ž¡’õºâply–Tas“ëNdomainsº,‘Tand“pretend“that“for“eac¾9h“domain“there“isŽ¡’õºâa–Tfamily“of“con¾9texts,“and“a“family“of“abstract“v‘ÿ|ralues.ަ’õºâF‘ÿ:«or–Z}eacš¾9h“Milner-Hindley“t˜ypšAÇe,‘kÇthere“is“a“corresp˜onding“do-Ž¡’õºâmain.‘}+In–5’general,‘=¢there“maš¾9y“bAÇe“man˜y“di eren˜t“t˜ypAÇes“whic˜hŽ¡’õºâmap–´Üto“the“same“domain.‘ûThe“next“section“de nes,‘ܾinfor-Ž¡’õºâmally–ÿ:«,‘đthis›°`mapping.‘úÉW“e˜then˜re ne˜the˜mapping˜sligh¾9tly˜inŽ¡’õºâsection–T2.2.4,“and“formalise“it“in“section“2.2.5.Ž©5’õºâ¹2.2Ž’ G·Domains–LÎfoš¹™r“p˜rojection“analysisŽŸm’õºâºA‘@primary–@*aim“of“these“analyses“is“to“generate“informationŽ¡’õºâuseful–Õúfor“exploiting“a“parallel“macš¾9hine.‘RT‘ÿ:«o“this“end,‘â¦w˜e“useŽ¡’õºâdomains–9³whicš¾9h“are“bAÇest“view˜ed“as“a“generalisation“of“theŽ¡’õºâev‘ÿ|raluation–âétransformers“inš¾9troAÇduced“b˜y“Burn“[Bur87Ž‘Žã].‘ ¢TheseŽ¡’õºâare–Tinš¾9troAÇduced“b˜y“example.ަ’õºâ¹2.2.1Ž’úíBase‘LÎt¹™ypFfesŽŸm’õºâºBase–¥ˆt¾9ypšAÇes“ëMInt“ºand“ëMChar“ºare“mapp˜ed“to“a“t•¾9w“o‘¥ˆp˜oin“t‘¥ˆdomainŽ¡’õºâëM2–¹–=“{0,“1}º,‘Ú8with–²ØëM0“ºmeaning“\do“not“ev‘ÿ|raluate“this"“and“ëM1Ž¡’õºâºmeaning–n·\ev›ÿ|raluate“fully".‘äæIn“this“case“only‘ÿ:«,‘ full“ev˜aluation“isŽ¡’õºâthe–§Usame“as“ev‘ÿ|raluation“to“w¾9eak“head“normal“form“(WHNF).ަ’õºâ¹2.2.2Ž’úíNon-recursive–LÎstructured“t¹™ypFfesŽŸm’õºâºConsider–DÕthe“inš¾9terpretation“of“a“familiar“non-recursiv˜e“struc-Ž¡’õºâtured–mBt¾9ypšAÇe:‘ÌMëM(Int,‘¹–Int)º.‘$;W‘ÿ:«e“need“to“mo˜del“the“ev‘ÿ|raluatorsŽ¡’õºâfor–¤the“compAÇonenš¾9ts“of“the“pair“separately‘ÿ:«,‘øso“there“m˜ust“bAÇeŽ¡’õºâa–ÃprošAÇduct“in•¾9v“olv“ed:‘wÿëM(2–¹–x“2)º.‘%ÆAn–Ãev‘ÿ|raluator“corresp˜ondingŽŽŽŽŽŸ’çjã3ŽŽŒ‹<à•ºâ ý? £ ý€‘íºâºto–AØanš¾9y“suc˜h“pAÇoin˜t“w˜ould“ rst“ha˜v˜e“to“ev‘ÿ|raluate“the“pair“clo-ޤ ‘íºâsure–~ëto“WHNF,“so“it“could“get“its“hands“on“the“individualŽ¡‘íºâcompAÇonen•¾9ts.‘ ÕSo›à„w“e˜really˜need˜a˜ fth˜pAÇoin“t˜represen“ting˜anŽ¡‘íºâev‘ÿ|raluator–õˆwhicš¾9h“doAÇes“nothing“at“all.‘×The“o˜v˜erall“in˜terpreta-Ž¡‘íºâtion–Tis“ëMLift–¹–(2“x“2)º.ŽŸ ‘íºâAš¾9t–Fóthis“pAÇoin˜t“it“is“con˜v˜enien˜t“to“in˜troAÇduce“a“notation“forŽ¡‘íºâpšAÇoin¾9ts–çåto“b˜e“used“throughout“this“pap˜er.‘ KThe“b˜ottom“p˜oin¾9tŽ¡‘íºâof–¶the“abAÇo•¾9v“e–¶domain“is“written“as“an“underscore,‘UÎëM_º.‘•TheŽ¡‘íºâother–¼·four“are“written“in“the“form“ëMU[x,‘¹–y]“ºwhere“the“ëMUŽ¡‘íºâºstands–\Vfor“\go“up“the“ëMLiftº",‘Vand“the“ëMx“ºand“ëMy“ºare“the“relev‘ÿ|ran¾9tŽ¡‘íºâpro•AÇduct›»comp“onen•¾9ts.‘5¥The˜o“v“erall˜collection˜of˜ev‘ÿ|raluators˜isŽ¡‘íºâth¾9us–ZVwritten“ëM{_,–¹–U[0,0],“U[0,1],“U[1,0],“U[1,1]}‘ZVºwithŽ¡‘íºâthe–Tfollo¾9wing“ordering:Ž©ÐO‘_ òëMU[1,1]Ž¡‘Zg\/‘Y„\Ž¡‘> ØU[0,1]‘%̰U[1,0]Ž¡‘Zg\\‘Y„/Ž¡‘_ òU[0,0]Ž¡‘mM´|Ž¡‘mM´_ަ‘íºâºHoš¾9w– \doAÇes“this“generalise“to“arbitrary“non-recursiv˜e“struc-Ž¡‘íºâtured›%t•¾9ypAÇes?‘K¢W‘ÿ:«ell,‘(þv“ery˜simply‘ÿ:«.‘K¢A‘% non-recursiv“e˜structuredŽ¡‘íºât¾9ypšAÇe–ŽÆis“mo˜delled“b¾9y“the“single“lifting“of“the“pro˜duct“of“what-Ž¡‘íºâevš¾9er–=Fits“t˜ypšAÇe“v‘ÿ|rariables“are“b˜ound“to.‘”GF‘ÿ:«urther“details“are“ir-Ž¡‘íºârelev‘ÿ|ranš¾9t.‘3That's–ǎbAÇecause“w˜e“observ˜e“the“guiding“rule“thatŽ¡‘íºâall–ãÂob‘ƒŽjects“correspšAÇonding“to“a“particular“t¾9yp˜e“v‘ÿ|rariable“areŽ¡‘íºâtreated–6ïas“a“single“en•¾9tit“y‘ÿ:«.‘AThis–6ïrule“is“impAÇosed“for“the“pur-Ž¡‘íºâpAÇose–…of“kš¾9eeping“things“reasonably“straigh˜tforw˜ard.‘k°F‘ÿ:«or“ex-Ž¡‘íºâample,‘Tgiv¾9en:ަ‘ûç¤ëMdata–¹–Foo“a“b“=“MkFoo“a“bŽ¡‘9TB|–¹–MkA“aŽ¡‘9TB|–¹–MkB“bŽ¡¡‘ûç¤data–¹–Grok“a“b“c“=“MkGrok“a“b“cŽ¡‘G|–¹–GrokodileDundee“a“a“a“b“b“cަ‘íºâºa–±~v‘ÿ|ralue“of“ëM(Foo–¹–Int“Int)–±~ºis“mappAÇed“to“ëMLift–¹–(2“x“2)º,Ž¡‘íºâand›S­ëM(Grok–¹–Int“Int“Int)˜ºto˜ëMLift“(2“x“2“x“2)º.‘ ×|MoreŽ¡‘íºâcomplicated–{parameterisations“giv¾9e“rise“to“more“com-Ž¡‘íºâplicated–щdomains.‘ QThe“t¾9ypAÇe“ëM(Grok–¹–Int“(Foo“Int“Int)Ž¡‘íºâ(Grok–¹–Int“Int“Int))–i®ºhas“a“91“pAÇoin¾9t“domainŽ¡‘íºâëMLift–¹–(2“x“Lift“(2“x“2)“x“Lift“(2“x“2“x“2))º.ŽŸ ‘íºâIt–úKis“wš¾9orth“understanding“that“the“n˜um˜bšAÇer“of“pro˜duct“com-Ž¡‘íºâpAÇonenš¾9ts–ãýis“equal“to“the“n˜um˜bAÇer“of“t˜ypAÇe“v‘ÿ|rariables,‘§and“en-Ž¡‘íºâtirely–®unrelated“to“the“n•¾9um“bAÇer–®of“parameters“of“an¾9y“partic-Ž¡‘íºâular–g[constructor.‘…A‘gFcon¾9text“ëMU[1,0,0]“ºapplied“to“an“ob‘ƒŽjectŽ¡‘íºâof–µt¾9ypAÇe“ëM(Grok–¹–Int“Int“Int)–µºmeans:‘)1ev‘ÿ|raluate“the“ob‘ƒŽject“toŽ¡‘íºâthe–·| rst“constructor.‘çThen,›àif“it“is“a“ëMMkGrokº,˜ev‘ÿ|raluate“theŽ¡‘íºâ rst–{5argumenš¾9t.‘NOtherwise,‘”­it“m˜ust“bAÇe“a“ëMGrokodileDundeeº,Ž¡‘íºâso–&Eev‘ÿ|raluate“the“ rst“three“parameters.‘ODW‘ÿ:«e“treat“the“ rstŽ¡‘íºâargumen¾9t–΍to“ëMMkGrok“ºand“the“ rst“three“of“ëMGrokodileDundeeŽ¡‘íºâºas–¸da“single“en•¾9tit“y–¸dbšAÇecause“they“all“corresp˜ond“to“the“sameŽ¡‘íºât¾9ypAÇe–Tv‘ÿ|rariable,“ëMaº,“in“the“declaration.ŽŸ5‘íºâ¹2.2.3Ž‘ úíRecursive–LÎstructured“t¹™ypFfesŽŸm‘íºâºSo–QQfar,‘`Qthings“are“reasonably“straigh•¾9tforw“ard.‘ÐhBut‘QQde ningŽ¡‘íºâev‘ÿ|raluators–1œfor“recursivš¾9e“t˜ypšAÇes“is“a“mine eld,‘8®partly“b˜ecauseŽ¡‘íºâthere–exare“so“manš¾9y“alternativ˜e“form˜ulations“[W‘ÿ:«ad87Ž‘¿˜]“[WH87Ž‘±].Ž¡‘íºâAs–v¸it“happAÇens,‘Ïthe“form¾9ulation“used“in“Anna“is“a“trivialŽŽŽ ý€’õºâv‘ÿ|rariation–JÕof“the“rule“for“non-recursivš¾9e“t˜ypAÇes,‘sUbut“justi cationޤ ’õºâis–Tnot“so“easy‘ÿ:«.ŽŸ ’õºâThe–#§rule“is“idenš¾9tical“to“the“non-recursiv˜e“case,‘g;except“forŽ¡’õºâthe–ïÖfollo¾9wing“mošAÇdi cation:‘ ±the“single“lifting“of“the“pro˜duct,Ž¡’õºâwritten–¥+ëMLiftº,›É is“replaced“b¾9y“a“double“lifting,˜ëMLift2º.‘ËõNo¾9w,Ž¡’õºâgiv¾9en–Tthe“pseudo-declarationŽ©ÐO’ç¤ëMdata–¹–[a]“=“[]Ž¡’.mê|–¹–a“:“[a]ަ’õºâºit–Tis“easy“to“see“that“the“domain“for“ëM[Int]“ºis“ëMLift2‘¹–(2)º,‘c¶aŽ¡’õºâfour–‰@pšAÇoin¾9t“domain“corresp˜onding“precisely“to“the“in¾9terpreta-Ž¡’õºâtion–for“that“tš¾9ypAÇe“made“b˜y“W›ÿ:«adler“[W˜ad87Ž‘¿˜]“and“later“justi-Ž¡’õºâ ed–!b¾9y“Burn“[Bur87Ž‘Žã].‘ËExtending“the“notation“of“the“previousŽ¡’õºâsection,‘Dqwš¾9e–7write“the“pAÇoin˜ts“in“this“domain“as“ëM{_,–¹–U_,“UU[0]Ž¡’õºâºand–Ý®ëMUU[1]}º,‘Äunderstanding“them“to“denote“the“ev‘ÿ|raluatorsŽ¡’õºâwhic¾9h–TBurn“called“ëM{E0,–¹–E1,“E2–Tºand“ëME3}º:ަ’äëPŽŽŽ’ :âëM_º:‘pDo–Tnot“ev‘ÿ|raluate“at“all“(ëME0º).Ž©34’äëPŽŽŽ’ :âëMU_º:‘¹Ev‘ÿ|raluate–æas“far“as“the“ rst“constructor,›üthat“is,˜toŽ¡’ :âw¾9eak–Thead“normal“form“(ëME1º).ަ’äëPŽŽŽ’ :âëMUU[0]º:‘pEv‘ÿ|raluate–Tthe“en¾9tire“structure“of“the“list“(ëME2º).ަ’äëPŽŽŽ’ :âëMUU[1]º:‘˺Ev‘ÿ|raluate–ìùthe“en¾9tire“structure“of“the“list,‘"âandŽ¡’ :âall–Tthe“elemen¾9ts“(ëME3º).ŽŸÐO’õºâIn–T“general,‘{!a“recursivš¾9e“t˜ypAÇe“of“ëMn“ºparameters“has“ev‘ÿ|raluators“ofŽ¡’õºâthe–þ form“ëM{_,›¹–U_“ºand“ëMUU[x1˜...˜xn]}º.‘­The“ëMUU[x1˜...˜xn]Ž¡’õºâºpAÇoinš¾9ts–O›denote“ev‘ÿ|raluating“the“en˜tire“structure,‘^,and“then“ap-Ž¡’õºâplying–«Hev‘ÿ|raluator“ëMx1“ºto“eac¾9h“ob‘ƒŽject“correspAÇonding“to“the“ rstŽ¡’õºâparameter,‘WëMx2–¬ºto“ob‘ƒŽjects“correspAÇonding“to“the“second“pa-Ž¡’õºârameter,›³Cand–`zso“on.‘ýâW‘ÿ:«e“will“see,˜in“Section“4,˜that“thisŽ¡’õºâconceptual–¸partitioning“of“all“recursivš¾9e“domain“pAÇoin˜ts“in˜toŽ¡’õºâthree–ž#sections“is“crucial“to“the“w¾9orking“of“the“term“rewritingŽ¡’õºâsystem–œbused“to“detect“ xpAÇoinš¾9ts.‘ôSimilarly‘ÿ:«,‘´“the“non-recursiv˜eŽ¡’õºâpAÇoin•¾9ts›¼ãma“y˜bAÇe˜partitioned˜in“to˜t“w“o:‘ð7ëM{_˜ºand˜ëMU[x1–¹–...“xn]}º.Ž© ’õºâThe–ºguiding“principle,›#>originally“stated“b¾9y“W‘ÿ:«adler,˜is“toŽ¡’õºâmoAÇdel–“tthe“recursivš¾9e“t˜ypAÇes“b˜y“letting“the“sub-ev‘ÿ|raluatorsŽ¡’õºâin–')ëMUU[...]“ºv‘ÿ|ralues“bAÇe“represen•¾9tativ“e–')of“the“least“de nedŽ¡’õºâelemenš¾9t–óèof“that“t˜ypAÇe“in“the“structure.‘¸,Imagine“w˜eŽ¡’õºâha•¾9v“e–©Õa“list“of“tš¾9ypAÇe“ëM[(Int,‘¹–Int)]º,‘Žôwhic˜h“induces“do-Ž¡’õºâmain›ªvëMLift2–¹–(Lift“(2“x“2))º,‘Ͼand˜w•¾9e˜kno“w˜that˜ev‘ÿ|raluatorŽ¡’õºâëMUU[U[0,1]]–°Ÿºis“the“strongest“that“can“safely“bAÇe“applied“(thatŽ¡’õºâis,‘mwithout–³danger“of“non-termination)“to“the“list.‘õzNo¾9wŽ¡’õºâsuppAÇose–Âwš¾9e“obtain“another“list“for“whic˜h“ëMUU[U[1,0]]“ºis“theŽ¡’õºâstrongest–ßsafe“ev‘ÿ|raluator,‘MÄand“appAÇend“it“to“the“original.‘ÉIWhatŽ¡’õºâis–ôHthe“bšAÇest“ev‘ÿ|raluator“that“can“b˜e“applied“to“the“new“list?Ž¡’õºâIt–O}cannot“bAÇe“either“of“the“originals,‘žsince“that“risks“non-Ž¡’õºâtermination.‘'HThe–nGmost“wš¾9e“can“ev‘ÿ|raluate“an˜y“particular“ele-Ž¡’õºâmen¾9t–luwhilst“remaining“safe“is“ëMU[0,0]º,‘‚=so“the“bAÇest“that“canŽ¡’õºâbAÇe–applied“to“the“list“as“a“whole“is“ëMUU[U[0,0]]“º{“the“great-Ž¡’õºâest›fÉlo•¾9w“er˜bAÇound˜of˜the˜v‘ÿ|ralues˜for˜the˜original˜lists.‘ÏW‘ÿ:«adlerŽ¡’õºâsummarised–”Sthis“bš¾9y“stating“that“a“list“is“c˜haracterised“\b˜yŽ¡’õºâits–¦Ùleast“de ned“elemenš¾9t"“but“w˜e“need“to“bAÇe“more“precise:Ž¡’õºâa–— list“is“cš¾9haracterised“b˜y“the“greatest“ev‘ÿ|raluator“that“canŽ¡’õºâsafely–D•bAÇe“applied“to“anš¾9y“elemen˜t,‘Peev˜en“if“a“stronger“ev‘ÿ|ralua-Ž¡’õºâtor–Icould“bšAÇe“applied“to“sp˜eci c“elemen¾9ts.‘Ø~The“same“principleŽ¡’õºâgeneralises–SÔto“structured“tš¾9ypAÇes“of“an˜y“n˜um˜bAÇer“of“parameters,Ž¡’õºâwith–^the“greatest-lo•¾9w“er-bAÇound›^c“haracterisation˜oAÇccurring˜in-Ž¡’õºâdepAÇendenš¾9tly–Tfor“eac˜h“parameter.ަ’õºâThis–(abstraction,›FËwhilst“simple,˜assumes“that“programs“treatŽ¡’õºâall–ð elemenš¾9ts“of“the“same“t˜ypAÇe“inside“a“structure“in“the“sameŽŽŽŽŽŸ’çjã4ŽŽŒ‹[” •ºâ ý? £ ý€‘íºâºw•¾9a“y–ÿ:«.‘ F“or–åÜexample,‘ï[it“assumes“list“proAÇcessing“functions“treatޤ ‘íºâall–èÍelemenš¾9ts“in“the“list“the“same“w˜a˜y–ÿ:«.‘ ˜F“unctions–èÍnot“pla˜yingŽ¡‘íºâalong–Áwith“this“ma¾9y“induce“bad,›Ñ÷but“safe,˜results.‘^Consider:ޤÐO‘ûç¤ëMtail–¹–(x:xs)“=“xsŽ¡‘íºâºIf–¿^wš¾9e“apply“a“ëMUU[1]“ºev‘ÿ|raluator“to“ëM(tail‘¹–zs)º,‘éàwhat“can“w˜eޤ ‘íºâev‘ÿ|raluate–Œ%ëMzs“ºwith?‘€ãUnfortunately‘ÿ:«,›©Ùnot“ëMUU[1]º,˜since“the“ele-Ž¡‘íºâmenš¾9t–"that“ëMtail“ºthro˜ws“a˜w˜a˜y“migh˜t“just“ha˜v˜e“bAÇeen“the“one-Ž¡‘íºâand-only–¥þnon-terminating“ëMInt“ºin“the“list.‘ÎmErring“on“theŽ¡‘íºâside–ààof“safetš¾9y“th˜us“restricts“the“ev‘ÿ|raluator“for“ëMzs“ºto“ëMUU[0]º,Ž¡‘íºâand–%îloses“all“the“pAÇoten¾9tial“parallelism“in“ev‘ÿ|raluating“the“ele-Ž¡‘íºâmen¾9ts–+in“the“rest“of“the“list.‘3ôOne“upshot“of“this,‘ also“notedŽ¡‘íºâbš¾9y–/RW‘ÿ:«adler,‘uÒis“that“de ning“functions“directly“b˜y“pattern-Ž¡‘íºâmatcš¾9hing– ×is“essen˜tial“to“get“go•AÇo“d– ×results.‘ùúIn“the“exampleŽ¡‘íºâbAÇeloš¾9w,‘Âthe–­1analyser“giv˜es“a“m˜uc˜h“bAÇetter“result“for“ëMsum1“ºthanŽ¡‘íºâëMsum2º,–Tdespite“them“haš¾9ving“iden˜tical“strictness“propAÇerties.Ž©ÐO‘ûç¤ëMsum1–¹–[]‘Y„=“0Ž¡‘ûç¤sum1–¹–(x:xs)‘ s,=“x“+“sum1“xsŽ¡¡‘ûç¤sum2–¹–xs‘Y„=“if‘æXnull“xsŽ¡‘BÇnthen‘ s,0Ž¡‘BÇnelse‘ s,head–¹–xs“+“sum2“(tail“xs)ަ‘íºâºA‘áórelated–âdefect“is“the“inabilit¾9y“of“these“domains“to“captureŽ¡‘íºâthe–K@notion“of“head“strictness.‘¾3A‘K2head“strict“function“is“oneŽ¡‘íºâwhicš¾9h–Æ>ev‘ÿ|raluates“the“ rst“item“in“a“list“whenev˜er“it“ev‘ÿ|raluatesŽ¡‘íºâthe– 'list“as“far“as“the“ rst“constructor,‘IÛand“disco•¾9v“ers– 'it“toŽ¡‘íºâbAÇe–‹non-nil.‘}ªHead“strictness“is“useful“in“a“sequen¾9tial“imple-Ž¡‘íºâmen¾9tation,‘so–îan“extension“of“the“domains“to“capture“theseŽ¡‘íºâpropšAÇerties–Tw¾9ould“increase“the“useful“scop˜e“of“this“analyser.Ž©5‘íºâ¹2.2.4Ž‘ úíMoFfdifying–LÎthe“notationŽŸm‘íºâºThe›,ÀabAÇo•¾9v“e˜mapping˜assigns˜domain˜ëMLift‘¹–()˜ºto˜allŽ¡‘íºâen•¾9umeration› ¹At“ypAÇes,‘ b:for˜example˜the˜familiar˜t“ypAÇeŽ¡‘íºâëMdata–¹–Bool“=“False“|“Trueº.‘<<Observ¾9e–ʘthat“ëMLift‘¹–()“ºis“iso-Ž¡‘íºâmorphic–ôto“the“t•¾9w“o-pšAÇoin“t–ôdomain“used“for“base“t¾9yp˜es,‘®œandŽ¡‘íºârighš¾9tly–Tso.‘pAfter“all,“w˜e“could,“conceptually‘ÿ:«,“de neޤÐO‘íºâëMdata–¹–Int“=“...“-3“|“-2“|“-1“|“0“|“1“|“2“|“3“...Ž¡‘íºâºand–Twš¾9e'd“certainly“expAÇect“a“t˜w˜o-pAÇoin˜t“domain“for“it!ŽŸ ‘íºâThis–ãisomorphism“can“bAÇe“used“to“simplify“the“domain“struc-ޤ ‘íºâture,‘¶~and–žÈth¾9us“the“strictness“analysis“itself.‘ôìW‘ÿ:«e“forget“abAÇoutŽ¡‘íºâdomain–žÁëM2º,‘and“instead“map“base“t¾9ypAÇes“ëMInt“ºand“ëMChar“ºtoŽ¡‘íºâëMLift›¹–()º,‘Ówith–8ípAÇoin¾9ts“ëM{_,˜U[]}“ºreplacing“ëM{0,˜1}º.‘‡;Hence-Ž¡‘íºâforth–Tthe“new“notation“is“used.ަ‘íºâ¹2.2.5Ž‘ úíSumma¹™ryŽŸm‘íºâºLet–ö‹ëMD(t)“ºdenote“the“domain“for“some“t¾9ypAÇe“ëMtº.‘-Let“ëMtypeNameŽ¡‘íºâºbšAÇe–V5the“name“of“some“structured“t¾9yp˜e,‘fmand“ëMte1–¹–...“ten‘V5ºb˜eŽ¡‘íºâsome–Tarbitrary“t¾9ypAÇe“expressions.‘pëMD“ºis“de ned“as:ŽŸÐO‘ûç¤ëMD(Int)‘,Â=–¹–Lift“()Ž¡‘ûç¤D(Char)‘ s,=–¹–Lift“()Ž¡¡‘ûç¤D(typeName–¹–te1“...“ten)Ž¡‘ f=–¹–Lift‘ s,(D(te1)“x“...“x“D(ten))Ž¡‘‡’if–¹–typeName“denotes“a“non-recursive“typeŽŽŽ ý€¤ ’f=–¹–Lift2“(D(te1)“x“...“x“D(ten))Ž¡’‡’if–¹–typeName“denotes“a“recursive“typeŽŸR³’õºâºThe–mconcept“of“a“function-v‘ÿ|ralued“con¾9text“seems“rather“mean-Ž¡’õºâingless,–Tand“is“left“unde ned“un¾9til“section“3.2.ŽŸ! ’õºâ¹2.2.6Ž’úíRestrictions–LÎon“structured“t¹™ypFfesŽŸm’õºâºThe–šÂastute“reader“maš¾9y“ha˜v˜e“noticed“the“examples“abAÇo˜v˜eŽ¡’õºâha•¾9v“e–ž6bAÇeen“rather“restricted.‘ô»In“particular,‘¶ none“of“them“hadŽ¡’õºâconstan•¾9t›Ø~t“ypAÇes˜as˜an˜argumen“t˜to˜an“y˜constructor.‘)But˜thisŽ¡’õºâsituation–Â7is“commonplace,‘Ò×for“example“as“the“ëMInt“ºcon•¾9v“eyingŽ¡’õºâbalancing–Tinformation“in“the“follo¾9wing“tree“declaration:Ž©kҍ’ç¤ëMdata–¹–AVLTree“a“bŽ¡’f=‘¹–ALeafŽ¡’f|–¹–ANode“Int“(AVLTree“a“b)“a“b“(AVLTree“a“b)ަ’õºâºInstead–ðiof“extending“the“domain-generating“rules“to“co•¾9v“erŽ¡’õºâsuc¾9h–˜¦cases,‘¹zit“is“simpler“to“factorise“out“the“o ending“ëMIntº,Ž¡’õºâgenerating–Ta“second“t¾9ypAÇe“ëMAVLTree2º:ަ’ç¤ëMdata–¹–AVLTree2“i“a“bŽ¡’f=‘¹–ALeaf2Ž¡’f|–¹–ANode2“i“(AVLTree2“i“a“b)“a“b“(AVLTree2“i“a“b)ަ’õºâ(AVLTree2–¹–Int“a“b)–½(ºis“an“isomorphicŽ¡’õºâtš¾9ypAÇe–“]to“ëM(AVLTree–¹–a“b)º,‘²ßat–“]the“same“t˜ypšAÇe“b˜eing“a“t¾9yp˜e“forŽ¡’õºâwhic•¾9h›tŒw“e˜kno“w˜ho“w˜to˜generate˜an˜abstract˜domain.‘æØCon“v“e-Ž¡’õºânien•¾9tly‘ÿ:«,‘Þ±Milner-Hindley›¶lt“ypAÇec“hec“k“ers˜are˜amenable˜to˜suc“hŽ¡’õºâsubstitutions.ŽŸ ’õºâFinally‘ÿ:«,‘yNobservš¾9e–eOthat“there“are“certain“t˜ypAÇes“for“whic˜h“it“isŽ¡’õºâhard–Tto“devise“a“sensible“set“of“ev‘ÿ|raluators,“for“example:ަ’ç¤ëMdata–¹–Foo“a“bŽ¡’f=–¹–MkFoo“a“b“(Foo“(Foo“a“b)“(Foo“a“b))ަ’õºâºThe–D€solution“adopted“in“Anna“is“simply“to“deem“these“ille-Ž¡’õºâgal.‘ÍW‘ÿ:«e–¸require“that,›àÐin“a“t¾9ypAÇe“declaration,˜argumen¾9ts“onŽ¡’õºâconstructors–e"are“either“simple“v‘ÿ|rariables“(here,›yëMa“ºor“ëMbº),˜or“aŽ¡’õºâsimple–Áìrecursiv¾9e“instance“of“the“structure“(here,‘íëMFoo–¹–a“bº).Ž¡’õºâThese–þwrestrictions“seem“inconsequen¾9tial“for“real“programs,Ž¡’õºâand›Tha•¾9v“e˜b•AÇeen˜rep“orted˜quite˜indep“endan¾9tly˜in˜[KHL91Ž‘(Ô].ŽŸ! ’õºâ¹2.3Ž’ G·The–LÎCoš¹™re“datat˜ypFfeŽŸm’õºâºThe–5extensivš¾9ely“mangled“source“program“ev˜en˜tually“passedŽ¡’õºâto–œ‰the“abstract“inš¾9terpreter“is“a“t˜ypAÇe-annotated“tree,‘¾Vrepre-Ž¡’õºâsenš¾9ting–íÃa“simple“functional“language.‘@Eac˜h“noAÇde“in“the“treeŽ¡’õºâcarries– Fwith“it“an“annotation.‘½GThe“Haskš¾9ell“data“t˜ypAÇe“usedŽ¡’õºâis–áìparameterised“o•¾9v“er–áìbšAÇoth“the“t¾9yp˜e“of“the“annotations,‘ì4andŽ¡’õºâthe–Ttš¾9ypAÇe“of“the“iden˜ti er“names:ަ’ç¤ëMtype–¹–AnnExpr“a“bŽ¡’f=–¹–(b,“AnnExpr'“a“b)Ž¡¡’ç¤data–¹–AnnExpr'“a“bŽ¡’f=‘¹–AVar‘ŸîaŽ¡’f|‘¹–AConstr‘ s,aŽ¡’f|‘¹–ALit‘ŸîIntŽ¡’f|–¹–AAp‘Y„(AnnExpr“a“b)“(AnnExpr“a“b)Ž¡’f|–¹–ALet‘ŸîBool“[AnnBind“a“b]“(AnnExpr“a“b)ŽŽŽŽŽŸ’çjãº5ŽŽŒ‹zõ •ºâ ý? £ ý€‘ fëM|–¹–ACase‘æX(AnnExpr“a“b)“[AnnAlt“a“b]ޤ ‘ f|–¹–ALam‘Ÿî[a]“(AnnExpr“a“b)Ž¡¡‘ûç¤type–¹–AnnBind“a“bŽ¡‘ f=–¹–(a,“AnnExpr“a“b)Ž¡¡‘ûç¤type–¹–AnnAlt“a“bŽ¡‘ f=–¹–(a,“([a],“AnnExpr“a“b))ŽŸ⍑íºâºThe–È rst“and“second“parameters“on“an“ëMAnnExpr“ºt¾9ypAÇe“are“forŽ¡‘íºâthe–Gidenš¾9ti er“and“annotation“t˜ypšAÇes“resp˜ectiv¾9ely–ÿ:«.‘±ËF“or‘Gexam-Ž¡‘íºâple,‘Fif–<Uthe“tš¾9ypAÇe“of“iden˜ti ers“is“ëMIdº,‘Fand“that“of“t˜ypAÇe“expres-Ž¡‘íºâsions–J·ëMTExprº,‘Xthe“t¾9ypšAÇe“of“the“corresp˜onding“Core“expressionŽ¡‘íºâis‘TëM(AnnExpr–¹–Id“TExpr)º.Ž© ‘íºâMost–³Šcases“are“straigh•¾9tforw“ard.‘÷The–³ŠëMAVar“ºterm“represen¾9tsŽ¡‘íºâan–Ûidenš¾9tifer,‘!=whilst“ëMAConstr“ºrepresen˜ts“a“constructor“name.Ž¡‘íºâLiteral–=v‘ÿ|ralues“are“represenš¾9ted“b˜y“ëMALitº,‘G and“applications“b˜yŽ¡‘íºâëMAApº.‘ÛÕLamš¾9bAÇda–S‚terms“are“represen˜ted“b˜y“ëMALamº,‘zFwhic˜h“can“bindŽ¡‘íºâan–Tarbitrary“n•¾9um“bAÇer–Tof“formal“parameters.ަ‘íºâThat›€llea•¾9v“es˜the˜t“w“o˜tric“ky˜ones.‘]·A‘€let/rec˜expression˜isŽ¡‘íºârepresen•¾9ted›c1b“y˜ëMALetº,‘¶¨whic“h˜has˜a˜b•AÇo“olean˜ ag˜indicatingŽ¡‘íºâwhether–û this“is“a“recursiv¾9e“binding,›Ka“list“of“bindings,˜and“aŽ¡‘íºâmain–Ðexpression“in“whicš¾9h“those“bindings“can“bAÇe“used.‘DEac˜hŽ¡‘íºâbinding–Säis“an“iden¾9ti er“paired“with“the“v‘ÿ|ralue“it“is“bAÇoundŽ¡‘íºâto.‘À_Case–ö¤expressions,›.÷denoted“b¾9y“ëMACaseº,˜conš¾9tain“a“switc˜hŽ¡‘íºâexpression,‘“Rand–za“list“of“alternativ•¾9es.‘JÑEac“h›zalternativ“e˜is˜aŽ¡‘íºâtriple–œ±of“constructor“name,‘¾ˆconstructor“argumen¾9ts“and“theŽ¡‘íºâappropriate–›vrigh¾9t-hand“side.‘óÑThe“use“of“nested“pairs“is“moreŽ¡‘íºâcon•¾9v“enien“t–Tfor“cošAÇding“purp˜oses.ަ‘íºâAll–š7phases“doš¾9wnstream“of“the“lam˜bAÇda-lifter“exploit“certainŽ¡‘íºâassumptions–-abAÇout“the“form“of“the“program.‘cÆThe“most“im-Ž¡‘íºâpAÇortan¾9t–,§are“that“there“are“no“nested“ëMALetsº,‘[0that“the“programŽ¡‘íºâis–‰fin“depAÇendancy“order,‘¦kand“that“no“iden¾9ti er“is“unde nedŽ¡‘íºâor–Tm¾9ultiply“de ned“in“the“same“scopAÇe.ŽŸyx‘íºâ¹2.4Ž‘G·Compiling–LÎpa¹™rallel“coFfdeŽŸm‘íºâºEv‘ÿ|raluation–ÓÅtransformers“are“suppAÇosedly“exploited“b¾9y“com-Ž¡‘íºâpiling–³ÿmš¾9ultiple“copies“of“eac˜h“function,‘Ûªup“to“one“cop˜y“forŽ¡‘íºâeac•¾9h›·kcon“text˜in˜whic“h˜the˜result˜migh“t˜bAÇe˜demanded.‘µF‘ÿ:«orŽ¡‘íºâeac•¾9h›Ÿcop“y‘ÿ:«,‘qcompile-time˜analysis˜indicates˜ho“w˜m“uc“h˜de-Ž¡‘íºâmand–ŽÙpropagates“to“the“parameters“of“the“function,‘í:andŽ¡‘íºâth•¾9us› sho“w˜m“uc“h˜the˜argumen“ts˜to˜the˜call˜ma“y˜bAÇe˜ev‘ÿ|raluatedŽ¡‘íºâbAÇefore–æéthe“call.‘ ÷In“this“manner,‘ð2demand“propagation“is“pre-Ž¡‘íºâservš¾9ed–T­as“far“as“this“st˜yle“of“static“analysis“mak˜es“pAÇossible.Ž¡‘íºâOf–žcourse,‘Ú0all“this“is“done“in“pursuit“of“the“o•¾9v“erall‘žgoal:Ž¡‘íºâmaximising–a~aš¾9v‘ÿ|railable“parallelism.‘íAn“equally“impAÇortan˜t“is-Ž¡‘íºâsue,›2«not–,Ídiscussed“here,˜is“hoš¾9w“to“a˜v˜oid“excessiv˜e“ ne-grainŽ¡‘íºâparallelism.ަ‘íºâAll–q.wš¾9ell“and“go•AÇo“d,‘H#but–q.the“pAÇoten˜tial“for“coAÇde“explo-Ž¡‘íºâsion–x¥renders“a“naivš¾9e“implemen˜tation“impractical.‘ FbCon-Ž¡‘íºâsider–šsa“function“delivš¾9ering“a“result“of“the“con˜triv˜ed“t˜ypAÇeŽ¡‘íºâëM(Grok–¹–Int›2Œ(Foo“Int“Int)“(Grok“Int“Int“Int))˜ºdiscussedŽ¡‘íºâin–­îsection“2.2.2.‘æ>Since“the“domain“has“91“pAÇoinš¾9ts,‘Ôit“w˜ouldŽ¡‘íºâappšAÇear–rnecessary“to“compile“90“v¾9ersions“of“the“co˜de,‘™ùomit-Ž¡‘íºâting–çêthe“v¾9ersion“for“no“demand“at“all“on“the“output.‘ MBurn'sŽ¡‘íºâearly–‡wš¾9ork“simply“ignored“the“problem“b˜y“restricting“itselfŽ¡‘íºâto–ó¶lists“of“ëMIntº,‘+Nfor“whic¾9h“at“most“3“copies“of“coAÇde“are“re-Ž¡‘íºâquired.‘7aQuite–Èúwhat“to“do“abšAÇout“complex“t•¾9yp˜es,‘õãwhic“h‘Èúin-Ž¡‘íºâduce–.ÃproAÇduct“domains,‘5or“non-trivial“instan¾9tiations“of“lists,Ž¡‘íºâis–Tnot“clear.ަ‘íºâThis–½unsatisfactory“state“of“a airs“can“to“some“exten¾9t“bAÇeŽ¡‘íºâalleviated–·bš¾9y“restricting“ourselv˜es“to“compiling“just“a“subsetŽŽŽ ý€’õºâof–"Üall“the“pAÇossible“vš¾9ersions“of“eac˜h“function.‘EThen,‘f=whenޤ ’õºâthe–Ëîoutput“of“a“function“is“demanded“in“a“conš¾9text“for“whic˜hŽ¡’õºâno–ë½vš¾9ersion“has“bAÇeen“compiled,‘ôthe“v˜ersion“used“is“that“com-Ž¡’õºâpiled–kafor“the“greatest“demand“less“than“the“demand“w¾9e“re-Ž¡’õºâquired.‘­«Observš¾9e–E½that“the“c˜hoice“of“alternativ˜e“is“not“neces-Ž¡’õºâsarily›3unique,–`Qbut,“pro•¾9vided˜w“e˜compiled˜in˜a˜fully˜sequen“tialŽ¡’õºâ(that–4Õis,›<¶WHNF‘4Ídemand)“v¾9ersion,˜an“alternativ¾9e“is“at“leastŽ¡’õºâguaranš¾9teed–±9to“exist.‘ðOf“course,‘Ø2some“pAÇoten˜tial“parallelismŽ¡’õºâma•¾9y›˜w“ell˜bAÇe˜lost:‘!Ïsuc“h˜is˜the˜price˜for˜restricting˜the˜coAÇdeŽ¡’õºâexplosion–Tto“a“tolerable“magnitude.Ž© ’õºâThe–FØcenš¾9tral“question,–p%then,“is–FØwhic˜h“v˜ersions“to“compile“coAÇdeŽ¡’õºâfor.‘NoOne–{TpAÇerson“who“has“v•¾9en“tured›{Tin“to˜this˜quagmire˜isŽ¡’õºâMin•¾9tc“hev.‘£F‘ÿ:«or–Çìhis“MSc“dissertation“[Min92Ž‘o™],‘×gMin•¾9tc“hev‘ÇìbuiltŽ¡’õºâa–á@simš¾9ulation“of“a“parallel“graph“reduction“mac˜hine,‘;whic˜hŽ¡’õºâunderstands–áthree“levš¾9els“of“demand:‘6none“at“all,‘ Åw˜eak“headŽ¡’õºânormal–gÊform“demand,‘|gand“full“demand.‘ÑAn“immediate“ad-Ž¡’õºâv‘ÿ|ranš¾9tage–Ùlis“that“these“pAÇoin˜ts“apply“to“all“structured“t˜ypAÇes,Ž¡’õºâincluding–!Ôtuples“and“complex“instanš¾9tiations“of“t˜ypAÇes,‘Rˆand“areŽ¡’õºâthš¾9us–¨¢more“widely“applicable“than“Burn's“sc˜heme.‘Ö[Encour-Ž¡’õºâagingly‘ÿ:«,›ï$ev¾9en–Ôwith“so“few“ev‘ÿ|raluators,˜Min•¾9tc“hev–Ôfound“thatŽ¡’õºâsubstan•¾9tial›¿–amoun“ts˜of˜parallel˜activit“y˜w“ere˜generated,‘мv‘ÿ|ral-Ž¡’õºâidating–·&his“approac•¾9h.‘åRecen“tly–·&it“has“bAÇeen“suggested“thatŽ¡’õºâa–#Ófourth“ev›ÿ|raluator“migh¾9t“bAÇe“pro tably“included:‘9nev˜aluationŽ¡’õºâof–ýKthe“enš¾9tire“structure“of“a“recursiv˜e“t˜ypAÇe,‘7Ibut“no“ev‘ÿ|ralua-Ž¡’õºâtion–M of“the“compAÇonenš¾9ts.‘ÅSThis“mak˜es“no“sense,›[³of“course,˜inŽ¡’õºâa–YTnon-recursivš¾9e“t˜ypAÇe,–jTor,“alternativ˜ely‘ÿ:«,“one–YTcan“regard“it“asŽ¡’õºâequiv›ÿ|ralen¾9t–Tto“the“WHNF“ev˜aluator,“in“this“case.ަ’õºâA‘.öfurther–/Äcomplication“is“what“to“do“abšAÇout“p˜olymor-Ž¡’õºâphic–‡­functions.‘ s|W‘ÿ:«e“maš¾9y“compile“three“v˜ersions“of“theŽ¡’õºâëMreverse–ª ºfunction,‘Ï:w¾9orking“from“the“ev‘ÿ|raluators“of“the“sim-Ž¡’õºâplest–…Ÿinstance,‘¡±but“then“what“do“wš¾9e“do“giv˜en“an“ev‘ÿ|raluatorŽ¡’õºâëMUU[U[1,0]]–G*ºapplied“to“a“use“of“ëMreverse“ºat“non-base“instanceŽ¡’õºâëM[(Int,–¹–Int)]“->“[(Int,“Int)]º?‘aêSuce–,}it“to“sa¾9y“that“aŽ¡’õºâpšAÇossible–solution“is“only“to“compile“v¾9ersions“of“p˜olymorphicŽ¡’õºâfunctions–ð½based“on“their“ev‘ÿ|raluators“for“simplest“instances,Ž¡’õºâand–Âause“safe“approš¾9ximation“tec˜hniques“based“on“Conc“mapsŽ¡’õºâto–ä`handle“the“non-base“instances.‘ See“[HH91Ž‘>],›î*section“5,˜forŽ¡’õºâan–@–in¾9troAÇduction“to“Conc“maps.‘ՆMy“MSc“dissertation“[Sew91Ž‘/]Ž¡’õºâindicates–#­ho¾9w“Conc“maps“are“useful“in“matters“of“pAÇolymor-Ž¡’õºâphism,–Ta“theme“explored“further“in“[Sew93Ž‘/].ަ’õºâNoš¾9w,‘ê¹if–àthe“compiler“is“only“going“to“mak˜e“coAÇde“for“a“few“ofŽ¡’õºâall– äthe“pAÇossible“ev‘ÿ|raluators“for“a“function“returning“an“ob‘ƒŽjectŽ¡’õºâof–)bcomplex“t¾9ypšAÇe,‘.fwhat“is“the“p˜oin¾9t“of“doing“strictness“anal-Ž¡’õºâysis–UÛwith“the“full“complemen¾9t“of“ev‘ÿ|raluators?‘ÞAfter“all,‘eüthisŽ¡’õºâamounš¾9ts–×ato“doing“a“detailed“analysis,‘åthen“thro˜wing“a˜w˜a˜yŽ¡’õºâmost–çof“the“detail“in“the“ nal“answš¾9er.‘÷)It“w˜ould“certainlyŽ¡’õºâbAÇe›JØm•¾9uc“h˜quic“k“er˜just˜to˜w“ork˜with˜those˜few˜ev‘ÿ|raluators˜w“eŽ¡’õºâare–—\really“inš¾9terested“in.‘òsNev˜ertheless,‘°Ždoing“that“risks“losingŽ¡’õºâin¾9termediate‘ˆ°detail,–¥‡and,“ultimately‘ÿ:«,“parallelism,“comparedŽ¡’õºâwith––/the“expAÇensivš¾9e“approac˜h.‘òBuilding“an“abstract“in˜terpre-Ž¡’õºâtation–gXfor“the“el“cš¾9heapAÇo“approac˜h“migh˜t“also“bAÇe“rather“dif-Ž¡’õºâ cult,‘;and–sthe“inš¾9terpreter“w˜ould“ha˜v˜e“to“bAÇe“rewritten“ev˜eryŽ¡’õºâtime–™®the“particular“subset“of“inš¾9teresting“ev‘ÿ|raluators“c˜hanged.ަ’õºâA‘‘x nal–‘™inš¾9teresting“ca˜v˜eat“pAÇertains“to“higher-order“functions.Ž¡’õºâAs–6Üexplained“to•¾9w“ards–6Üthe“end“of“section“1.2,‘=it“loAÇoks“dif-Ž¡’õºâ cult–Ä4to“exploit“parallelism“in“higher-order“functions“if“w¾9eŽ¡’õºâdo–é†not“w•¾9an“t–é†to“engage“in“complicated“manipulation“of“ev‘ÿ|ral-Ž¡’õºâuation–˜¬transformers“at“run-time.‘¦xOne“can“therefore“rea-Ž¡’õºâsonably–ÈÞargue“that“the“higher-order“remo¾9v‘ÿ|ral“transformationŽ¡’õºâ( rsti cation)–ždescribAÇed“in“section“5“enhances“parallelism.Ž¡’õºâWhat–& rsti cation“doAÇes“is“to“disco•¾9v“er–&statically“some“of“theŽ¡’õºâfunctional–Èparameters“passed“to“higher-order“functions,‘ÓäandŽ¡’õºâspAÇecialise–;them“accordingly‘ÿ:«,‘Ltgenerating“ rst-order“replace-ŽŽŽŽŽŸ’çjã6ŽŽŒ‹“§ •ºâ ý? £ ý€‘íºâºmenš¾9ts.‘KøThese–Ï×can“then“bAÇe“parallelised“in“the“normal“w˜a˜y‘ÿ:«,ޤ ‘íºâwithout–8Vhaš¾9ving“to“resort“to“complicated“run-time“mac˜hinery‘ÿ:«.Ž¡‘íºâMa¾9ybšAÇe,–Ô¦then,“this–Äztransformation“should“b˜e“incorp˜orated“asŽ¡‘íºâa–Tmatter“of“course“in¾9to“go•AÇo“d–Tparallelising“compilers.ŽŸ-‘íºâ¹3Ž‘ü”The–LÎabstract“interp¹™retationŽŸ†´‘íºâ3.1Ž‘G·Prelimina¹™riesޤm‘íºâ3.1.1Ž‘ úíThe–LÎnotion“of“fo•¹™rw“a“rds–LÎand“backw•¹™a“rdsŽ¡‘íºâºSemanš¾9tic–`êanalyses“of“functional“languages“seem“to“fall“in˜toޤ ‘íºât•¾9w“o›Ôvcamps:‘š³forw“ards˜and˜bac“kw“ards.‘YÕT‘ÿ:«o˜see˜the˜in“tuitiv“eŽ¡‘íºâmeaning–Tof“this,“consider“a“function“application:ޤÐO‘ûç¤ëM(f–¹–x“y“z)Ž¡‘íºâºA‘èforwš¾9ard–è‡analysis“generates“information“abAÇout“ëMf“ºwhic˜hޤ ‘íºâtells–MÑus“propAÇerties“of“the“application“ëM(f–¹–x“y“z)–MѺif“wš¾9e“kno˜wŽ¡‘íºâthe–¤epropAÇerties“of“the“individual“argumen¾9ts,–È)ëMxº,“ëMy–¤eºand“ëMzº.‘ɤInŽ¡‘íºâother–ٚw¾9ords,‘ ¬the“analysis“propagates“information“óR¼j‘¹ cmti9ëRforwar‡dsŽ¡‘íºâºthrough–ªµfunctions.‘ܓF‘ÿ:«orw¾9ard“analyses“tend“to“bšAÇe“exp˜ensiv¾9eŽ¡‘íºâbšAÇecause–зthey“ha•¾9v“e–зto“consider“all“p˜ossible“in¾9teractions“b˜e-Ž¡‘íºât•¾9w“een›²¢argumen“ts.‘ô[On˜the˜other˜hand,‘Ùöone˜gets˜a˜v“ery˜de-Ž¡‘íºâtailed–Tpicture“of“what“is“going“on.Ž© ‘íºâA‘ù§bac•¾9kw“ard›ú$analysis,‘sXb“y˜con“trast,‘sXgenerates˜informationŽ¡‘íºâabšAÇout–ÑúëMf“ºwhic¾9h“tells“us“the“prop˜erties“of“the“individual“argu-Ž¡‘íºâmenš¾9ts–HŒëMxº,‘qëMy“ºand“ëMz“ºif“w˜e“kno˜w“some“propAÇert˜y“of“the“applicationŽ¡‘íºâëM(f–¹–x“y“z)º.‘ñThat– ×is,‘Va“bac•¾9kw“ards– ×analysis“propagates“prop-Ž¡‘íºâerties›®4ëRb•‡ackwar“ds˜ºthrough˜functions.‘úBac•¾9kw“ard˜analyses˜ma“yŽ¡‘íºâb•AÇe›2Ÿc¾9heap“er˜to˜do,‘_÷but˜they˜ma•¾9y˜also˜giv“e˜less˜detailed˜results.ަ‘íºâNoš¾9w,‘åfor–ٌreasons“whic˜h“will“shortly“bAÇecome“apparen˜t,‘åAnnaŽ¡‘íºâdoAÇes–Åua“comš¾9bined“forw˜ard“and“bac˜kw˜ard“analysis.‘ÐThe“prop-Ž¡‘íºâerties–\>whicš¾9h“Anna“propagates“forw˜ards“through“functionsŽ¡‘íºâare–{the“abstract“v‘ÿ|ralues,‘”‡whilst“those“whicš¾9h“ o˜w“bac˜kw˜ardsŽ¡‘íºâare–h conš¾9texts.‘â®T‘ÿ:«o“set“the“stage,‘жobserv˜e“critically“that“ëRAÃŽnna'sŽ¡‘íºâmain–¥±purpš‡ose“is“to“determine“the“b˜ackwar˜ds“b˜ehaviour“ofŽ¡‘íºâthe›sour•‡c“e˜language˜functionsº.‘ÒThe–Èzpresence“of“forw¾9ard“(ab-Ž¡‘íºâstract)–÷ v‘ÿ|ralues“is“a“necessary“evil“whic¾9h“enables“us“to“dealŽ¡‘íºâcleanly–Ú[with“higher-order“functions.‘k†The“discussion“whic¾9hŽ¡‘íºâno•¾9w›sæfollo“ws˜mak“es˜more˜sense˜if˜y“ou˜k“eep˜a˜clear˜notion˜thatŽ¡‘íºâabstract–=xv‘ÿ|ralues“correspAÇond“to“a“forwš¾9ards“ o˜w“of“information,Ž¡‘íºâwhilst–Tconš¾9texts“correspAÇond“to“a“bac˜kw˜ards“ o˜w.ŽŸ5‘íºâ¹3.1.2Ž‘ úíA–LÎfundamental“pš¹™roblem“with“backw˜a˜rds“analysisŽŸm‘íºâºBac•¾9kw“ards–Ø.strictness“analysis“wš¾9ould“bAÇe“straigh˜tforw˜ard,Ž¡‘íºâw¾9ere–_˜it“not“for“the“higher-order“nature“of“the“language“underŽ¡‘íºâanalysis.‘pT‘ÿ:«o–Tsee“the“problem,“consider“ëMapplyº:ޤÐO‘ûç¤ëMapply–¹–f“x“=“f“xŽ¡‘íºâºGiv¾9en–hôsome“demand“on“a“use“of“apply‘ÿ:«,›}ÜëM(apply–¹–g“y)º,˜whatޤ ‘íºâdemand– [maš¾9y“bAÇe“propagated“to“ëMyº?‘…Without“kno˜wing“ho˜wŽ¡‘íºâëMg–8ºpropagates“demand“to“its“argumenš¾9t,‘1the“only“safe“answ˜erŽ¡‘íºâis›E\none".‘«‡Ho•¾9w“ev“er,‘òkno“wing˜what˜ëMg˜ºis˜implies˜ha“ving˜aŽ¡‘íºâforw•¾9ard›áµ o“w˜of˜information,‘ìas˜w“ell˜as˜the˜bac“kw“ard˜ o“w˜ofŽ¡‘íºâdemand–Tw¾9e“started“with.ަ‘íºâThings–º«loAÇok“grimmer“when“w¾9e“put“functions“inside“dataŽ¡‘íºâstructures,–Tthen“ sh“them“out“and“apply“them:ŽŸÐO‘ûç¤ëM1–¹–+“(head“xs“(y+1))ŽŽŽ ý€’õºâºwhere›½åëMxs–¹–::“[Int“->“Int]º.‘$There˜is˜no˜w•¾9a“y˜to˜tell˜whatޤ ’õºâdemand–Tcould“bAÇe“propagated“to“ëMyº.Ž© ’õºâThe–ísolution“really“lies“in“building“a“comš¾9bined“bac˜kw˜ardsŽ¡’õºâand–¯×forwš¾9ards“analysis.‘ëøW‘ÿ:«ra˜y“[W‘ÿ:«ra85Ž‘:C]“made“a“start“on“theŽ¡’õºâproblem,‘Yÿbut–LDit“toAÇok“the“w¾9ork“of“Hughes“[Hug87Ž‘ó']“to“gener-Ž¡’õºâalise–O‰W‘ÿ:«raš¾9y's“results“to“the“pAÇoin˜t“of“general“applicabilit˜y‘ÿ:«.‘ڂTheŽ¡’õºâresulting–÷˜analysis“is“rather“hard“to“understand,–0)so,“ratherŽ¡’õºâthan–ˆ×attempting“a“head-on“assault,‘¥¸w¾9e“loAÇok“ rst“at“under-Ž¡’õºâlying–Tissues,“starting“o “with“some“new“concepts.ŽŸºç’õºâ¹3.2Ž’ G·F¹™unction‘LÎcontextsŽŸm’õºâºDealing–-øwith“functions“propAÇerly“means“turning“them“in¾9toŽ¡’õºâ rst-class–Âlcitizens“for“the“purpAÇoses“of“the“abstract“in¾9ter-Ž¡’õºâpreter.‘‰Section–ž2.2“discussed“the“notion“of“demand“(or“con-Ž¡’õºâtext)–Q/on“a“data“structure.‘ÐW‘ÿ:«e“no¾9w“extend“the“notion“ofŽ¡’õºâcon¾9text–Tto“functions.ަ’õºâSince– Êa“con¾9text“really“denotes“a“demand“for“ev‘ÿ|raluation,‘ ætheŽ¡’õºâidea–¶ of“a“function“conš¾9text“seems“prett˜y“meaningless:‘]ßafterŽ¡’õºâall,‘¹§hoš¾9w–˜Écan“a“function“bAÇe“ev‘ÿ|raluated?‘¦ÐBut“imagine“w˜e“de-Ž¡’õºâ ned–¼#a“function“conš¾9text“as“a“pair,‘å×con˜taining“the“abstractŽ¡’õºâv‘ÿ|ralue–RÚof“the“argumenš¾9t,‘b<and“the“con˜text“for“the“result“of“anŽ¡’õºâapplication–Áof“the“function.‘ ·By“making“the“analysis“fullyŽ¡’õºâcurried–v3from“noš¾9w“on,‘Žkw˜e“can“consider“all“functions“as“ha˜v-Ž¡’õºâing–æ;just“one“argumen¾9t.‘ ½Then,›ï§for“example,˜the“con¾9text“on“aŽ¡’õºâfunction–Tof“t•¾9w“o›Targumen“ts,˜suc“h˜as˜ëMapplyº,˜loAÇoks˜lik“e:Ž©Y ’ç¤ëM(abstract–¹–value“of“first“argument,Ž¡’f(abstract–¹–value“of“second“argument,Ž¡’Íücontext–¹–on“result)Ž¡’ç¤)ަ’õºâºSucš¾9h–Qªa“sc˜heme“w˜ould“solv˜e“the“problem“outlined“abAÇo˜v˜e,‘`¿b˜yŽ¡’õºâsupplying–ÌDthe“v‘ÿ|ralue“of“the“ rst“parameter,‘Úáallo¾9wing“demandŽ¡’õºâto–úêbAÇe“propagated“on¾9to“the“second“parameter.‘¢This“abstractŽ¡’õºâv›ÿ|ralue–‹aof“the“ rst“parameter“is“just“the“relev˜anš¾9t“con˜text“func-Ž¡’õºâtion,›ߞbut–ƒöwhat“of“the“abstract“v‘ÿ|ralue“of“the“second,˜non-Ž¡’õºâfunctional–Ͷparameter?‘‘W‘ÿ:«ell,‘Ü wš¾9e“are“simply“not“in˜terested“inŽ¡’õºâit,–Tso“wš¾9e“map“it“to“the“1-pAÇoin˜t“domain.ŽŸ ’õºâThe–ÌÝwš¾9orld“no˜w“bšAÇecomes“p˜opulated“bš¾9y“t˜w˜o“spAÇecies“of“v‘ÿ|ralues:ަ’äëPŽŽŽ’ :âëNCon´Ctexts–‘±º(also“called“bac•¾9kw“ards›‘±v–ÿ|ralues,‘¬ev“aluators˜orŽ¡’ 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:âare–›¬the“second“kind“of“abstract“en•¾9tit“y–›¬describAÇed“in“sec-Ž¡’ :âtion–ê2.1.‘÷They“are“designed“purely“to“con•¾9v“ey‘êcon“textsŽ¡’ :âto–=^anš¾9y“place“in˜v˜olving“a“call“to“an“unkno˜wn“function,Ž¡’ :âsucš¾9h–‰ôas“in“the“t˜w˜o“problematic“examples“abAÇo˜v˜e.‘zOTheŽ¡’ :âabstract–+v‘ÿ|ralues“of“non-function“ob‘ƒŽjects“are“alw•¾9a“ys‘+irrel-Ž¡’ :âev‘ÿ|ran¾9t–¤ãand“are“mappšAÇed“to“a“1-p˜oin¾9t“domain,‘»`whose“sin-Ž¡’ :âgle–G°pšAÇoin¾9t“is“denoted“ëM#º,‘pÒfor“the“time“b˜eing.‘×äThe“abstractŽŽŽŽŽŸ’çjã7ŽŽŒ‹·7 •ºâ ý? £ ýõ¦dŸÂl΍‘íºâŸ¾S4‰fföÌ̤ÿþ•Ì͟wٚ„~٘ffŸ·32‘8ŸÚŒÍ‰ff†C,¡“¤„ ff‘fg„ ff‘33ŸüÿþºDe ning‘Tequation‘"V¡„ ffŽ‘p·Disassem¾9bles–Ta“...‘"½¤Ÿ„ ffŽ’ß• proAÇducing–Tthe“...‘a˜Ÿ„ ff‘fg„ ffŽŽ©fh‰ff†C,¡“Ÿ„ ff‘fg„ ff‘hæ„ ffŽ’ÙûtŸ„ ffŽ’„C,Ÿ„ ff‘fg„ ffŽŽ¤ “¤„ ff‘fg„ ff‘33ŸüÿþëMFncA› s,(Fnc–¹–a“c)˜=“a‘33¡„ ffŽ‘p·ºfunctional‘Tcon¾9text‘ @OŸ„ ffŽ’ß• abstract–Tv‘ÿ|ralue“of“the“argumen¾9t‘'õ¡Ÿ„ ff‘fg„ ffŽŽ¡“¤„ ff‘fg„ ff‘33ŸüÿþëMFncC› s,(Fnc–¹–a“c)˜=“c‘33¡„ ffŽ‘p·ºfunctional‘Tcon¾9text‘ @OŸ„ ffŽ’ß• con¾9text–Ton“the“result‘PRŸ„ ff‘fg„ ffŽŽ¡“¤„ ff‘fg„ ff›33ŸüÿþëMFvalA–¹–(Fval“c“a)“=“a˜¡„ ffŽ‘p·ºfunctional–Tabstract“v‘ÿ|ralue‘33Ÿ„ ffŽ’ß• abstract–Tv‘ÿ|ralue“map:‘pargumen¾9t“to“result‘33Ÿ„ ff‘fg„ ffŽŽ¡“¤„ ff‘fg„ ff›33ŸüÿþëMFvalC–¹–(Fval“c“a)“=“c˜¡„ ffŽ‘p·ºfunctional–Tabstract“v‘ÿ|ralue‘33Ÿ„ ffŽ’ß• conš¾9text–Tmap:‘presult“to“argumen˜t‘ @OŸ„ ff‘fg„ ffŽŽ¡“Ÿ„ ff‘fg„ ff‘hæ„ ffŽ’ÙûtŸ„ ffŽ’„C,Ÿ„ ff‘fg„ ffŽŽ¦‰ff†C,ŽŽŽŸ;Ì̍’˜TT‘ÿ:«able–T1:‘pSelector“functions“for“functional“en¾9titiesŽŽŸ Ž’öff„~٘ffŽŽŸx@‰fföÌ̎ŽŽŽ  Yœ þ¦d‘:âv›ÿ|ralue–2&of“a“function-v˜alued“ob‘ƒŽject“is“also“a“pair“(butޤ ‘:âquite–7îunrelated“to“ëMFnc“ºpairs),‘À”written“ëM(Fval–¹–c“a)º,Ž¡‘:âwith–J¡ëMFval“ºreminding“us“this“is“a“ëNF‘ÿÌunctional‘£jabstractŽ¡‘:âV‘þÑALueº.‘ë=The›ît•¾9w“o˜compAÇonen“ts˜are˜bAÇoth˜maps.‘ë=TheŽ¡‘:â 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ne“four“selectors“ëMFncAº,Ž¡‘íºâëMFncCº,–؄ëMFvalA›Øtºand“ëMFvalC˜ºto“disassem¾9ble“ëMFncºs“and“ëMFvalºs,‘ä­withŽ¡‘íºâthe–¯œbAÇehaš¾9viour“sho˜wn“in“T›ÿ:«able“1.‘úˆHopAÇefully˜,‘Ãôtheir“names“willŽ¡‘íºâserv¾9e–Tas“a“reminder“of“their“meaning.Ž© ‘íºâLet's– ©‰start“with“the“simplest“function“imaginable:Ž¡‘íºâëMid–¹–::“Int“->“Intº.‘ðThe– Óonly“remotely“inš¾9teresting“thing“w˜eŽ¡‘íºâcan–“îsaš¾9y“abAÇout“ëMid“ºis“that“it“simply“propagates“the“con˜text“onŽ¡‘íºâits–4£result“to“the“conš¾9text“on“its“argumen˜t.‘z]So,‘<wsuppAÇosing“w˜eŽ¡‘íºânoš¾9w–Xwrite“do˜wn“a“mapping“from“the“con˜text“on“the“resultŽ¡‘íºâto–Tthe“conš¾9text“on“the“argumen˜t,“w˜e“get:ޤy®‘ûç¤ëM(\c–¹–->“c)Ž¡‘íºâºLet's–]ÃbAÇe“clear“what“this“is.‘õ½It's“ëRnot“ºa“con¾9text,‘oßand“it's“alsoޤ ‘íºâëRnot–Ë{ºan“abstract“v‘ÿ|ralue.‘ÒIt's“a“map“from“conš¾9texts“to“con˜texts.ަ‘íºâBut–×that's“not“go•AÇo“d–×enough.‘aúW‘ÿ:«e“said“earlier“that“AnnaŽ¡‘íºâprošAÇduces–êone“abstract“v‘ÿ|ralue“p˜er“Core“function.‘32So“what“doŽ¡‘íºâw¾9e–«(proAÇduce“for“ëMidº?‘ÝíF‘ÿ:«or“a“start,›Нsince“ëMid“ºis“a“function,˜w¾9eŽ¡‘íºâmš¾9ust–²Wget“a“functional“abstract“v‘ÿ|ralue:‘êñan“ëMFval“ºterm.‘ûqIt“m˜ustŽ¡‘íºâloAÇok‘Tlik¾9e:Ž©‹‘ûç¤ëMid–¹–=“Fval“context_mapŽ¡‘+'€abstract_value_mapަ‘íºâºNo•¾9w,‘Éthe›¶con“text˜map,‘Éas˜w“e˜just˜men“tioned,‘Émaps˜the˜con-Ž¡‘íºâtext–]ªon“ëMid“ºto“the“conš¾9text“on“ëMidº's“argumen˜t.‘ß7And“the“con˜textŽ¡‘íºâon–÷±ëMidº,›ýžsince“ëMid“ºis“a“function,˜mš¾9ust“bAÇe“a“function“con˜text,‘ýžofŽ¡‘íºâthe–øÜform“ëM(Fnc–¹–a“c)º,‘1¾where–øÜëMc“ºis“the“bit“w¾9e're“really“after.Ž¡‘íºâThis–&givš¾9es“a“con˜text“map“of“ëM(\c–¹–->“FncC“c)º,‘Úso–&w˜e'v˜e“no˜wŽ¡‘íºâgot:ަ‘ûç¤ëMid–¹–=“Fval“(\c“->“FncC“c)Ž¡‘+'€abstract_value_mapŽŽŽ þ¦d’õºâºWhat–¸ñof“the“abstract“v‘ÿ|ralue“map?‘HIt“tells“us“what“the“ab-ޤ 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’õºâMoš¾9ving–Ton“to“ëM(+)–¹–::“Int“->“Int“->“Int‘Tºgiv˜es:ަ’ç¤ëM(+)–¹–=“Fval“(\c1“->“FncC“(FncC“c1))Ž¡’7á(\a1–¹–->“Fval“(\c2“->“FncC“c2)Ž¡’uM´(\a2–¹–->“#))ަ’õºâºThis–Õ¨time“currying“comes“inš¾9to“pla˜y‘ÿ:«.‘]kThat's“wh˜y“the“termŽ¡’õºâwhicš¾9h–Qƒmaps“the“abstract“v‘ÿ|ralue“of“the“ rst“argumen˜t“to“theŽ¡’õºâabstract–èv‘ÿ|ralue“of“the“result“returns“a“ëMFval“ºterm:‘Ââthe“\re-Ž¡’õºâsult"–oØhere“has“t¾9ypAÇe“ëMInt–¹–->“Intº.‘+ûClearly‘ÿ:«,‘†yëM(+)–oغsimply“prop-Ž¡’õºâagates–5conš¾9text“on“the“o˜v˜erall“result“to“bAÇoth“argumen˜ts,Ž¡’õºâwhicš¾9h–‹§is“wh˜y“the“con˜text“maps“for“the“t˜w˜o“argumen˜tsŽ¡’õºâare›%+ëM(\c1–¹–->“FncC“(FncC“c1))˜ºand˜ëM(\c2“->“FncC“c2)º.‘KõIfŽ¡’õºâthis–seems“a“little“m¾9ysterious,‘*íbšAÇear“in“mind“that“b˜othŽ¡’õºâëM(FncC–¹–(FncC“c1))–Xºand“ëM(FncC‘¹–c2)“ºrefer“to“the“con¾9text“onŽ¡’õºâthe–Of nal“result.‘ ʧThat's“bAÇecause“ëMc1“ºbinds“to“a“con¾9textŽ¡’õºâin›M¬ëMInt–¹–->“Int“->“Intº,‘ÛÁwhic¾9h˜is˜necessarily˜of˜the˜formŽ¡’õºâëM(Fnc–¹–#“(Fnc“#“cc))–ܺwhere“ëMcc“ºis“the“con¾9text“on“the“ nalŽ¡’õºâresult.‘òeSimilarly‘ÿ:«,‘°nëMc2–—4ºis“a“conš¾9text“of“t˜ypAÇe“ëMInt–¹–->“Intº,‘°nha˜vingŽ¡’õºâthe–~;form“ëM(Fnc–¹–#“cc)–~;ºwhere“ëMcc“ºis“again“the“con¾9text“on“theŽ¡’õºâ nal‘Tresult.ŽŸ ’õºâNoš¾9w–Û?for“something“altogether“more“adv˜en˜turous:‘ÿfthe“famil-Ž¡’õºâiar–ªxëMapply“ºfunction,‘ÏÁat“t¾9ypAÇe“ëM(Int–¹–->“Int)“->“Int“->“Intº.Ž¡’õºâThis–ÔÈexample“is“easier“to“follo¾9w“if“one“bAÇears“in“mind“thatŽ¡’õºâëM(apply–¹–f“x)–íºreduces“immediately“to“ëM(f‘¹–x)º,‘“so“anš¾9y“con˜textŽ¡’õºâapplied–öÖto“the“former“expression“also“applies“directly“to“theŽ¡’õºâlatter.‘ZWhat–á¢the“rather“formidable“term“bšAÇelo¾9w“do˜es“is“toŽ¡’õºâroute–[†the“con¾9text“from“the“result“of“calling“ëMapply“ºto“theŽ¡’õºâresult–Tof“calling“the“higher-order“parameter.ŽŽŽŽŽŽŸ’çjã8ŽŽŒ‹ Ör •ºâ ý? £ ý€‘ûç¤ëMapply–¹–=“Fval“(\c1“->“Fnc“(FncA“(FncC“c1))ޤ ‘rJ(FncC–¹–(FncC“c1)))Ž¡‘9TB(\a1–¹–->“Fval“(\c2“->“(FvalC“a1)Ž¡’œ(Fnc–¹–(FncA“c2)Ž¡’´-~(FncC‘¹–c2))Ž¡‘vÀà(\a2–¹–->“(FvalA“a1)“a2))ŽŸj‘íºâºFirst–Hfof“all,‘Õ*consider“what“the“function“con¾9text“ëMc1“ºwillŽ¡‘íºâget–3bšAÇound“to“m¾9ust“lo˜ok“lik¾9e:‘-ëM(Fnc›¹–a_ho“(Fnc˜#˜c_final))Ž¡‘íºâºwhere–‚¹ëMa_ho“ºus“the“abstract“(or“forw¾9ard)“v‘ÿ|ralue“of“the“func-Ž¡‘íºâtional–º˜parameter“and“ëMc_final“ºis“the“con¾9text“on“the“resultŽ¡‘íºâof–Èapplying“this“functional“parameter“to“something.‘4ÏNo¾9w,Ž¡‘íºâterm‘NëM(\c1–¹–->“Fnc“(FncA“(FncC“c1))“(FncC“(FncC“c1)))Ž¡‘íºâºmaps–ì;conš¾9text“on“ëMapply“ºto“con˜text“on“the“ rst“parameter.Ž¡‘íºâAs–˜ythis“is“a“functional“parameter,‘¹Bit“mak¾9es“sense“that“thisŽ¡‘íºâexpression–4 is“built“from“a“ëMFncº.‘ÑXSo“just“what“con¾9text“is“propa-Ž¡‘íºâgated–Ðnto“the“functional“parameter?‘yW‘ÿ:«ell,‘Þ6the“abstract“v‘ÿ|ralueŽ¡‘íºâm¾9ust–åîbAÇe“the“same“as“the“abstract“v‘ÿ|ralue“of“the“second“pa-Ž¡‘íºârameter–¬½to“ëMapplyº,‘җand“this“v‘ÿ|ralue“(whicš¾9h“m˜ust“bAÇe“ëM#º)“is“ex-Ž¡‘íºâtracted–´qb¾9y“the“term“ëM(FncA–¹–(FncC“c1))–´qºSimilarly‘ÿ:«,‘Ü8the“con-Ž¡‘íºâtext–sson“the“result“of“the“functional“parameter“m¾9ust“bAÇe“theŽ¡‘íºâsame–øsas“the“conš¾9text“on“the“o˜v˜erall“result“of“ëMapplyº,‘þ9giv˜en“b˜yŽ¡‘íºâëM(FncC–¹–(FncC“c1))º.Ž© ‘íºâEvš¾9erything–”else“is“easier“to“follo˜w.‘DžV‘ÿ:«ariable“ëMa1“ºwill“get“bAÇoundŽ¡‘íºâto– cthe“abstract“v‘ÿ|ralue“of“the“functional“parameter,‘'whic¾9hŽ¡‘íºâm¾9ust–"bAÇe“a“ëMFval“ºterm.‘ So“ëM(FvalC‘¹–a1)“ºreturns“the“map“usedŽ¡‘íºâbš¾9y–Çdthe“functional“parameter“to“translate“con˜text“on“itself“toŽ¡‘íºâconš¾9text–½on“its“ rst“argumen˜t.‘¬The“map“is“applied“to“theŽ¡‘íºâsame–ÜYfunction“conš¾9text“as“w˜as“built“in“the“preceding“para-Ž¡‘íºâgraph,‘;„except–3áthat“references“to“ëM(FncC‘¹–c1)“ºare“replaced“b¾9yŽ¡‘íºâëMc2º,–Twhic¾9h“is“the“same“thing.ަ‘íºâFinally‘ÿ:«,‘ëÆthe–Àâabstract“v‘ÿ|ralue“of“the“result“is“givš¾9en“b˜y“apply-Ž¡‘íºâing–æJthe“abstract“v‘ÿ|ralue“map“of“the“functional“parameter,Ž¡‘íºâëM(FvalA‘¹–a1)º,‘–to–¦the“abstract“v‘ÿ|ralue“of“the“second“parameter,Ž¡‘íºâëMa2º.ަ‘íºâTw•¾9o›Aimpro“v“emen“ts˜are˜pAÇossible.‘ŸÎFirstly‘ÿ:«,‘Lthe˜abstract˜v‘ÿ|ralueŽ¡‘íºâof–+the“result“mš¾9ust“simply“bAÇe“ëM#º,‘0~since“the“result“t˜ypAÇe“is“ëMIntº.Ž¡‘íºâSecondly‘ÿ:«,‘examination–C~of“the“de nition“of“ëMFncA‘C0ºand“ëMFncCŽ¡‘íºâºshoš¾9ws–u'that“ëM(Fnc–¹–(FncA“c)“(FncC“c))–u'ºis“equiv‘ÿ|ralen˜t“simplyŽ¡‘íºâto–TëMcº.‘pThe“impro•¾9v“ed›Tv“ersion˜is:Ž©j‘ûç¤ëMapply–¹–=“Fval“(\c1“->“FncC“c1)Ž¡‘9TB(\a1–¹–->“Fval“(\c2“->“(FvalC“a1)“c2)Ž¡‘vÀà(\a2–¹–->“#))ަ‘íºâºThe–ƒmec¾9hanism“for“dealing“with“functions“and“applicationsŽ¡‘íºâis–jLthe“hardest“part“of“the“abstract“in¾9terpreter“to“understand.Ž¡‘íºâA‘1õlittle–2/time“spAÇen¾9t“making“sense“of“this“last“example“is“a“wiseŽ¡‘íºâin•¾9v“estmen“t.ŽŸ ‘íºâWhš¾9y–Gšis“it“necessary“to“propagate“demand“in˜to“functionalŽ¡‘íºâparameters?‘pW‘ÿ:«ell,‘Tconsider:ަ‘ûç¤ëMadd1–¹–x“=“apply“(+“x)“1ަ‘íºâºIf–ë5demand“isn't“propagated“in¾9to“ëMapplyº's“functional“parame-Ž¡‘íºâter,‘$there– Xwill“bAÇe“no“demand“on“term“ëM(+‘¹–x)“ºand“none“on“ëMxº,Ž¡‘íºâgiving–[the“impression“that“ëMadd1“ºis“not“strict,‘ when“really“itŽ¡‘íºâis.ŽŸ e‘íºâ¹3.3Ž‘G·Mo¹™re–LÎabFfout“abstract“valuesŽŸm‘íºâºAll–:onon-function“expressions“yield“an“abstract“v‘ÿ|ralue“in“a“unitŽ¡‘íºâdomain.‘Ï3Ho•¾9w“ev“er,–Ê{v‘ÿ|ralue›¦@ëM#º,“used˜in˜the˜examples˜abAÇo•¾9v“e,‘Ê{isŽŽŽ ý€’õºâtoAÇo–Ë indiscriminating.‘=—The“Hask¾9ell“declaration“for“abstractޤ ’õºâv‘ÿ|ralues–TloAÇoks“(almost)“lik¾9e“this:Ž©ÐO’ç¤ëMdata‘¹–AbsValŽ¡’f=‘¹–ANonRec‘ s,[AbsVal]Ž¡’f|‘¹–ARec‘Ÿî[AbsVal]Ž¡’f|–¹–Fval‘ŸîContext“AbsValŽ¡¡’f|‘¹–AbsVar‘,ÂIdŽ¡’f|–¹–AbsLam‘,ÂId“AbsValŽ¡’f|–¹–AbsAp‘æXAbsVal“AbsValŽ¡¡’f|‘¹–FncA‘ŸîContextŽ¡’f|‘¹–FvalA‘æXAbsValŽ¡’f|–¹–SelA‘ŸîInt“AbsValŽ¡’f|‘¹–AMeet‘æX[AbsVal]ަ’õºâºThe–¢ëMARec“ºand“ëMANonRec“ºterms“de ne“abstract“v‘ÿ|raluesŽ¡’õºâfor–ø3recursivš¾9e“and“non-recursiv˜e“t˜yp•AÇes,‘°êresp“ectiv˜ely‘ÿ:«.‘ Å InŽ¡’õºâbšAÇoth–¬cases,‘¾the“asso˜ciated“list“of“ëMAbsValºs“are“the“ab-Ž¡’õºâstract–v‘ÿ|ralues“of“the“parameters“of“the“t¾9ypAÇe.‘ èF‘ÿ:«or“ex-Ž¡’õºâample,‘|þa–Üterm“of“t¾9ypAÇe“ëM[(Int,‘¹–Int)]“ºhas“abstract“v‘ÿ|ralueŽ¡’õºâëM(Rec–¹–[NonRec“[NonRec“[],“NonRec“[]]])º,‘†½giv¾9en–pthat“ëMIntŽ¡’õºâºis–NFtreated“as“an“enš¾9umeration“and“th˜us“maps“to“ëM(NonRec‘¹–[])º.Ž¡’õºâIt– Ôis“impAÇortanš¾9t“to“realise“that“this“v‘ÿ|ralue“is“still“unitary‘ÿ:«,‘Tlik˜eŽ¡’õºâëM#º,‘”Êbut–Hhas“the“added“adv‘ÿ|ran¾9tage“that“it“can“bAÇe“disassem-Ž¡’õºâbled–“~to“revš¾9eal“its“unitary“sub•AÇcomp“onen˜ts,‘­vas–“~necessitated“b˜yŽ¡’õºâthe–µƒabstract“inš¾9terpretation“of“ëMcase“ºstatemen˜ts.‘ü€ConstructorŽ¡’õºâëMSelA–Tºis“used“for“this,“with“meaning:Ž©ÐO’ç¤ëMSelA–¹–n“(ARec‘æX[a1“...“an“...“ak])‘ s,=“anŽ¡’ç¤SelA–¹–n“(ANonRec“[a1“...“an“...“ak])‘ s,=“anަ’õºâFvalº,‘pµëMFncA–^[ºand›^nëMFvalA“ºw•¾9ere˜in“troAÇduced˜in˜the˜previous˜sec-Ž¡’õºâtion.‘ÎÒëMAbsVarº,‘[ ëMAbsLam–,{ºand“ëMAbsAp“ºallo¾9w“references“to“abstract-Ž¡’õºâv–ÿ|ralued›°qv“ariables,‘8and˜for˜the˜creation˜and˜application˜ofŽ¡’õºâabstract-v‘ÿ|ralued–g9mappings.‘ Observš¾9e“that“w˜e“often“omitŽ¡’õºâëMAbsVar–îRºand“ëMAbsApº,›$’when“the“meaning“is“ob¾9vious,˜and“ab-Ž¡’õºâbreviate›TëM(AbsLam–¹–a“e)˜ºto˜ëM(\a“->“e)º.ŽŸ ’õºâConsider‘TagainޤÐO’ç¤ëM1–¹–+“(head“xs“(y+1))Ž¡’õºâºwhere›tÕëMxs–¹–::“[Int“->“Int]º.‘:ôW‘ÿ:«e˜expAÇect˜ëMxs˜ºto˜ha•¾9v“e˜bAÇeenޤ ’õºâbAÇound–Ô*to“an“abstract“v‘ÿ|ralue“whic¾9h“can“supply“a“sensibleŽ¡’õºâconš¾9text-mapping–:$function.‘ŠàOnce“again,‘CXw˜e“c˜haracterise“theŽ¡’õºâlist–F0bš¾9y“the“least“elemen˜t,‘ožthis“time“the“least“con˜text“function,Ž¡’õºâin–Tit.‘pSo,“suppAÇosingޤÐO’ç¤ëMxs–¹–=“[id,“id]“where“id“x“=“xŽ¡’õºâºthe–Tabstract“v‘ÿ|ralue“of“ëMxs“ºwill“bAÇe:Ž¡’ç¤ëMARec–¹–[‘ s,Fval“(\c1“->“FncC“c1)Ž© ’ATB(\a1–¹–->“ANonRec“[])‘ s,]Ž¡’õºâºThe–ìÅe ect“of“the“ëMhead“ºfunction“is“to“wrap“ëMSelA‘¹–1“ºaroundަ’õºâthis–ƒöterm,‘ŸŸmaking“the“abstract“v›ÿ|ralue“of“ëMid“ºa¾9v˜ailable“whereަ’õºâit–Tis“needed.‘pBut,“noš¾9w,“if“ëMxs“ºw˜ere“de ned“asŽ¡’ç¤ëMxs–¹–=“[id,“const]“where“id“x‘Ÿî=“xަ’p”const–¹–x‘ s,=“42ŽŽŽŽŽŸ’çjãº9ŽŽŒ‹ óÆ •ºâ ý? £ ý€‘íºâºwš¾9e–²need“to“bAÇe“more“cautious.‘òµSince“the“abstract“in˜terpre-ޤ ‘íºâtation–ybcannot“distinguish“items“in“lists,‘Òewš¾9e“m˜ust“arrangeŽ¡‘íºâthat–´öthe“function“whicš¾9h“emerges“from“the“list“represen˜ts“theŽ¡‘íºâw•¾9eak“er–b˜ev‘ÿ|raluator:‘¶ùëMconstº.‘=That“requires“the“list“as“a“wholeŽ¡‘íºâto›Tha•¾9v“e˜v‘ÿ|ralue:Ž©Zû‘ûç¤ëMARec–¹–[‘ s,Fval“(\c1“->“_)Ž¡‘9TB(\a1–¹–->“ANonRec“[])‘ s,]ަ‘íºâºThe–2upshot“of“all“this“is“that“the“abstract“v‘ÿ|ralue“of“a“listŽ¡‘íºâconš¾9taining–©functions“is“c˜haracterised“b˜y“the“least“functionŽ¡‘íºâin–ʾthe“list,‘øwith“the“principle“extending“analogously“to“allŽ¡‘íºâother–„8structures.‘iIn“order“to“carry“that“out,‘ßða“greatest-Ž¡‘íºâlo•¾9w“er-b•AÇound›¯‘op“eration˜is˜needed˜for˜abstract˜v‘ÿ|ralues.‘ú„This˜isŽ¡‘íºâwhat–Tthe“ëMAMeet“ºterm“is“for.ŽŸì͍‘íºâ¹3.4Ž‘G·Mo¹™re–LÎabFfout“contextsŽŸm‘íºâºThis–æ.is“a“go•AÇo“d›æ.p“oin•¾9t˜at˜whic“h˜to˜wheel˜in˜the˜Hask“ell˜decla-Ž¡‘íºâration–0&for“conš¾9texts.‘læUnfortunately‘ÿ:«,‘6Ûit“is“ev˜en“more“cum˜bAÇer-Ž¡‘íºâsome–Tthan“the“ëMAbsVal“ºdeclaration.‘pNev¾9ertheless:ަ‘ûç¤ëMdata‘¹–ContextŽ¡‘ f=‘¹–Stop1Ž¡‘ f|‘¹–Up1‘Y„[Context]Ž¡‘ f|‘¹–Stop2Ž¡‘ f|‘¹–Up2Ž¡‘ f|‘¹–UpUp2‘æX[Context]Ž¡‘ f|–¹–Fnc‘Y„AbsVal“ContextŽ¡¡‘ f|‘¹–FncC‘ŸîContextŽ¡‘ f|‘¹–FvalC‘æXAbsValŽ¡¡‘ f|‘¹–CJoin‘æX[Context]Ž¡‘ f|‘¹–CMeet‘æX[Context]Ž¡¡‘ f|‘¹–CtxVar‘,ÂIdŽ¡‘ f|–¹–CtxLam‘,ÂId“ContextŽ¡‘ f|–¹–CtxAp‘æXContext“ContextŽ¡¡‘ f|–¹–SelU‘ŸîInt“ContextŽ¡‘ f|–¹–SelUU‘æXInt“ContextŽ¡‘ f|–¹–CaseU‘æXContext“Context“ContextŽ¡‘ f|–¹–CaseUU‘,ÂContext“Context“Context“ContextŽ¡¡‘ f|‘¹–DefU‘ŸîContextŽ¡‘ f|‘¹–DefUU‘æXContextަ‘íºâºThe–S rst“six“are“for“building“literal“con¾9texts.‘Õ«ëMStop1“ºandŽ¡‘íºâëMUp1–yOºpšAÇertain“to“p˜oin¾9ts“in“ëMLift–¹–(D1“x“...“x“Dn)º,‘˜„with‘yOëMStop1Ž¡‘íºâºrepresen¾9ting–§the“bšAÇottom“p˜oin¾9t“ëM_º,‘Y|and“ëM(Up1–¹–[x1“...“xn])Ž¡‘íºâºrepresenš¾9ting–the“pAÇoin˜t“ëMU[x1–¹–...“xn]º.‘Similarly‘ÿ:«,–TëMStop2º,“ëMUp2Ž¡‘íºâºand›$uëM(UpUp2–¹–[x1“...“xn])˜ºrepresen•¾9t˜the˜pAÇoin“ts˜ëM_º,‘h=ëMU_˜ºandŽ¡‘íºâëMUU[x1–¹–...“xn]–&ºin“the“domain“ëMLift2–¹–(D1“x“...“x“Dn)º.‘ɶëMFncŽ¡‘íºâºis–Šeused“for“building“function-v‘ÿ|ralued“con¾9texts,‘¦/as“discussed“inŽ¡‘íºâsection–Hj3.2.‘µ³Finally‘ÿ:«,‘U0ëMDefU›H]ºand“ëMDefUU˜ºexist“to“help“the“termŽ¡‘íºârewriting–Tsystem,“as“describAÇed“in“section“4.4.Ž© ‘íºâëMFncC–(åºand›)!ëMFvalC“ºw¾9ere˜also˜discussed˜in˜section˜3.2.‘Í´ëMCJoin˜ºandŽ¡‘íºâëMCMeet–]=ºunsurprisingly“denote“the“least“uppAÇer“and“greatestŽ¡‘íºâlo•¾9w“er–TbšAÇounds“of“their“resp˜ectivš¾9e“argumen˜t“lists.ަ‘íºâëMCtxVarº,‘ÙæëMCtxLam–L0ºand“ëMCtxAp“ºare“exact“equiv‘ÿ|ralen¾9ts“to“theŽ¡‘íºâëMAbsVarº,‘"åëMAbsLam–ìûºand“ëMAbsAp“ºdiscussed“in“section“3.3.‘£fTheyŽ¡‘íºâproš¾9vide–ÿ¤a“w˜a˜y“to“reference“con˜text-v›ÿ|ralued“v˜ariables,‘úand“al-Ž¡‘íºâloš¾9w–8the“creation“and“application“of“con˜text-v‘ÿ|ralued“maps.ŽŽŽ ý€’õºâOnce–¡šagain,‘«note“that“w¾9e“often“omit“ëMCtxVar“ºand“ëMCtxApº,ޤ ’õºâwhen–³the“meaning“is“ob¾9vious,‘ƺand“abbreviate“ëM(CtxLam–¹–c“e)Ž¡’õºâºto‘TëM(\c–¹–->“e)º.ŽŸ ’õºâF‘ÿ:«ar–ù%and“a•¾9w“a“y–ù%the“most“in¾9teresting“constructs“are“the“lastŽ¡’õºâfour.‘¢yëMCaseU–Aöºand›BëMCaseUU“ºallo•¾9w˜partial˜disassem“bly˜of˜v‘ÿ|raluesŽ¡’õºâin›6mëMLift–¹–(D1“x“...“x“Dn)˜ºand˜ëMLift2“(D1“x“...“x“Dn)˜ºre-Ž¡’õºâspAÇectiv¾9ely‘ÿ:«,‘…fin–;Éthe“manner“discussed“in“section“2.2.3.‘ÎTheŽ¡’õºâexact–Tseman¾9tics“are:Ž©´º’ç¤ëMCaseU–¹–Stop1‘,Âx“y‘ s,=“xŽ¡’ç¤CaseU–¹–(Up1“_)“x“y‘ s,=“yŽ¡¡’ç¤CaseUU–¹–Stop2‘Ÿîx“y“z‘ s,=“xŽ¡’ç¤CaseUU–¹–Up2‘!x“y“z‘ s,=“yŽ¡’ç¤CaseUU–¹–(UpUp2“_)“x“y“z‘ s,=“zަ’õºâºNote–üdthat“the“switc¾9h“v‘ÿ|ralues“are“restricted“to“bAÇeing“in“do-Ž¡’õºâmains›½ëMLift–¹–(D1“x“...“x“Dn)˜ºand˜ëMLift2“(D1“x“...“x“Dn)Ž¡’õºâºrespAÇectiv•¾9ely‘ÿ:«.‘Switc“h–¾…v‘ÿ|ralues“from“an¾9y“other“domain“consti-Ž¡’õºâtute–$´an“ill-formed“con¾9text.‘J‘ëMCaseU›$°ºand“ëMCaseUU˜ºterms“denoteŽ¡’õºâa–îmapping“from“their“switc¾9h“expressions“to“one“of“the“al-Ž¡’õºâternativ•¾9es.‘ò(As›<suc“h,‘C¶a˜w“ell-formed˜ëMCaseU–ýºor˜ëMCaseUU“ºm¾9ustŽ¡’õºâdenote–7aa“monotonic“mapping,‘åso“wš¾9e“impAÇose“the“seman˜ticŽ¡’õºâconstrain¾9t–Tthat“ëMxŽ‘ `°ëPv‘‘ÆëMyŽ‘ Ý"ëPv‘‘ÆëMzŽ‘K\º.ŽŸ ’õºâAs–~,yš¾9ou“migh˜t“suspAÇect,‘˜aëMSelU›~ºand“ëMSelUU˜ºare“selectors“in“theŽ¡’õºâspirit–Tof“ëMSelAº,“discussed“in“section“3.3.‘pSeman¾9tics“are:ަ’ç¤ëMSelU‘ s,n–¹–(Up1‘,Â[x1“...“xn“...“xk])“=“xnŽ¡’ç¤SelUU–¹–n“(UpUp2“[x1“...“xn“...“xk])“=“xnަ’õºâºBut–åthere“is“a“vš¾9ery“strong“seman˜tic“constrain˜t“here:‘+“it“isŽ¡’õºâillegal–Â'to“apply“ëMSelU›Âºor“ëMSelUU˜ºto“a“v›ÿ|ralue“unless“that“v˜alue“isŽ¡’õºâproš¾9v–ÿ|rably‘Eequiv“alen˜t–Eto“an“ëMUp1›¹–[...]“ºor“ëMUpUp2˜[...]“ºv‘ÿ|ralueŽ¡’õºârespAÇectivš¾9ely‘ÿ:«.‘¦ùThis–C‚means,‘O for“some“arbitrary“con˜text“ëMcº,‘O theŽ¡’õºâfolloš¾9wing–Texpressions“are“lik˜ely“to“bAÇe“ill-formed:ަ’ç¤ëMSelU‘ s,n‘¹–cŽ¡’ç¤SelUU–¹–n“cަ’õºâºThe–×>one“and“only“w•¾9a“y–×>to“makš¾9e“them“w˜ell-formed“is“to“wrapŽ¡’õºâthe–rappropriate“spAÇecies“of“ëMCase“ºterm“around“them,‘‰Élea¾9vingŽ¡’õºâthe–TëMSel“ºin“the“greatest-v‘ÿ|ralue“arm:ަ’ç¤ëMCaseU‘ s,c–¹–(...whatever...)“(SelU“n“c)Ž¡¡’ç¤CaseUU–¹–c“(...whatever...)“(...whatever...)Ž¡’~Àà(SelUU–¹–n“c)ަ’õºâºIn–ŽìbšAÇoth“cases,‘­Rthe“term“ëM(Sel–¹–n“c)–Žìºma¾9y“not“app˜ear“in“an¾9yŽ¡’õºâplace–Ôømark¾9ed“\ëM...whatever...º".‘[]Note“that“the“ëMSel“ºtermŽ¡’õºâmaš¾9y–2—appAÇear“an˜ywhere“within“the“greatest-v‘ÿ|ralue“arm,‘yçandŽ¡’õºâis–“|not“restricted“to“the“top“lev¾9el,‘³as“this“example“seems“toŽ¡’õºâsuggest.ŽŸþ'’õºâ¹3.5Ž’ G·Constructo¹™r–LÎfunctions“and“case“statementsŽŸm’õºâºThe–˜source-language“trappings“of“structured“tš¾9ypAÇes“giv˜e“riseŽ¡’õºâto–Nôsome“of“the“more“inš¾9teresting“parts“of“the“abstract“in˜ter-Ž¡’õºâpreter,‘NOand›Bêw•¾9arran“t˜a˜section˜to˜themselv“es.‘¥1First,‘NOthough,Ž¡’õºâsome–Tterminology‘ÿ:«.‘pA“structured“tš¾9ypAÇe“is“de ned“lik˜e“this:ަ’ç¤ëMdata–¹–typeName“v1“...“vk“=“C1“t11“...“t1mŽ¡’uM´|‘Ÿî...Ž¡’uM´|–¹–Cn“t1n“...“tnmŽŽŽŽŽŸ’åäº10ŽŽŒ‹  › •ºâ ý? £ ý€‘íºâºThis–˜de nes“a“tš¾9ypAÇe“called“ëMtypeNameº,‘¿©param˜terised“b˜y“t˜ypAÇeޤ ‘íºâv‘ÿ|rariables–Î@ëMv1“ºto“ëMvkº,‘Üxwith“constructors“ëMC1“ºto“ëMCnº.‘¿The“t¾9ypAÇe“ex-Ž¡‘íºâpressions–÷ýëMt11“ºto“ëMtnmº,‘ýÛwhicš¾9h“form“the“argumen˜ts“to“the“con-Ž¡‘íºâstructors,‘ñ are–Åhea¾9vily“constrained“in“the“manner“discussedŽ¡‘íºâin– 1section“2.2.6:‘*they“maš¾9y“only“bAÇe“either“one“of“the“t˜ypAÇeŽ¡‘íºâv‘ÿ|rariables,›i ëMv1–¹–...“vkº,˜or–XLa“direct“recursivš¾9e“call“to“the“t˜ypAÇe:Ž¡‘íºâëM(typeName–¹–v1“...“vk)º.ŽŸ ‘íºâBecause–€ of“this“constrain•¾9t,‘š¹eac“h–€ constructor“argumen¾9t“in“aŽ¡‘íºâv‘ÿ|ralid–&ìde nition“can“bAÇe“classi ed“either“as“a“recursiv¾9e“call“ëMRecº,Ž¡‘íºâor–Yas“one“of“the“tš¾9ypAÇe“v‘ÿ|rariables,‘jžëMVar‘¹–n“ºwhere“ëMn“ºis“a“n˜um˜bAÇerŽ¡‘íºâdenoting–Twhic¾9h“v‘ÿ|rariable.‘pF‘ÿ:«or“example,“the“de nitionŽ©ÐO‘ûç¤ëMdata–¹–AVLTree“i“a“bŽ¡‘ f=‘¹–ALeafŽ¡‘ f|–¹–ANode“i“(AVLTree“i“a“b)“a“b“(AVLTree“i“a“b)ަ‘íºâºcan,–Tin“principle,“bAÇe“rewritten“asަ‘ûç¤ëMdata–¹–AVLTree“(of“3“type“variables)Ž¡‘ f=‘¹–ALeafŽ¡‘ f|–¹–ANode“(Var“1)“Rec“(Var“2)“(Var“3)“Recަ‘íºâºW‘ÿ:«e–) noš¾9w“de ne“t˜w˜o“strange“functions,‘-øëMargkind“ºand“ëMupdateº,Ž¡‘íºâto–ӎassist“in“the“discussion“bAÇeloš¾9w.‘ WNeither“are“mean˜t“toŽ¡‘íºâbAÇe–¿ implemenš¾9table.‘”Rather,‘éxthey“serv˜e“as“con˜v˜enien˜t“nota-Ž¡‘íºâtional–êRdevices,‘‘and“are“bAÇest“illustrated“b¾9y“example.‘›jTheyŽ¡‘íºâare–§ÍbAÇoth“meaningless“unless“the“particular“constructor“ap-Ž¡‘íºâplication–Tthey“are“assoAÇciated“with“is“stated.ŽŸ ‘íºâëMargkind–…ºtells“us“what“part“of“a“data“tš¾9ypAÇe“a“giv˜en“construc-Ž¡‘íºâtor–×ìargumenš¾9t“correspAÇonds“to:‘ý¼either“a“certain“t˜ypAÇe“v‘ÿ|rariable,Ž¡‘íºâor–ý3a“recursivš¾9e“instance“of“the“t˜ypšAÇe.‘eF‘ÿ:«or“example,‘b˜earing“inŽ¡‘íºâmind–~the“declaration“abAÇo•¾9v“e,‘˜Pgiv“en–~the“constructor“applica-Ž¡‘íºâtion‘TëM(ANode–¹–i“l“a“b“r)º:ަ‘ûç¤ëMargkind–¹–i“=“Var“1Ž¡‘ûç¤argkind–¹–l“=“RecŽ¡‘ûç¤argkind–¹–a“=“Var“2Ž¡‘ûç¤argkind–¹–b“=“Var“3Ž¡‘ûç¤argkind–¹–r“=“Recަ‘íºâupdate–G ºreplaces“a“particular“v‘ÿ|ralue“in“a“supplied“list“withŽ¡‘íºâanother–Œ†v‘ÿ|ralue.‘‚It“ nds“out“whic¾9h“lošAÇcation“to“up˜date“b¾9yŽ¡‘íºâusing– wëMargkindº,‘J@expAÇecting“an“answ¾9er“of“the“form“ëM(Var‘¹–i)º,Ž¡‘íºâwhereupšAÇon–B‡ëMi“ºis“used“as“the“lo˜cation.‘¤ It“is“in¾9v‘ÿ|ralid“to“useŽ¡‘íºâëMupdate–ëºin“a“w•¾9a“y›ëwhic“h˜w“ould˜cause˜the˜call˜to˜argkindŽ¡‘íºâto–Ö_return“ëMRecº.‘ _’Again,‘F¡using“the“constructor“applicationŽ¡‘íºâëM(ANode–¹–i“l“a“b“r)º:ަ‘ûç¤ëMupdate–¹–i“"my"‘,Â["the",“"cat",“"sat"]Ž¡‘ f=–¹–["my",‘ s,"cat",“"sat"]Ž¡¡‘ûç¤update–¹–a“"dog"‘ s,["the",“"cat",“"sat"]Ž¡‘ f=–¹–["the",“"dog",“"sat"]Ž¡¡‘ûç¤update–¹–b“"ran"‘ s,["the",“"cat",“"sat"]Ž¡‘ZÐ=–¹–["the",“"cat",“"ran"]ަ‘íºâºButަ‘ûç¤ëMupdate–¹–l“x“xsŽ¡‘ûç¤update–¹–r“x“xsަ‘íºâºare–TbAÇoth“illegal“since“ëMargkind›¹–l“º=“ëMargkind˜r“º=“ëMRecº.ŽŽŽ ý€’õºâThe–$Êexample“used“ëMupdate“ºto“replace“w¾9ords“in“a“list“thereof“toޤ ’õºâemphasise–C6ëMupdateº's“pAÇolymorphic“nature.‘¦Note“that“ëMupdateŽ¡’õºâºis›Ïalw•¾9a“ys˜used˜with˜a˜constructor˜wrappAÇed˜round˜the˜ nalŽ¡’õºâlist–ö¸argumenš¾9t.‘<This“constructor“is“re-attac˜hed“to“the“result:Ž©¹’ç¤ëMupdate–¹–i“"my"Ž¡’‡’(SomeConstructor–¹–["the",“"cat",“"sat"])Ž¡’f=–¹–(SomeConstructor“["my",‘ s,"cat",“"sat"])ަ’õºâºF‘ÿ:«or–` the“sakš¾9e“of“clarit˜y‘ÿ:«,‘r¸this“inconsequen˜tial“detail“is“hence-Ž¡’õºâforth‘Tignored.ŽŸ ’õºâRecall–wªfrom“section“2.2.5“that“function“ëMD‘wOºreturns“the“do-Ž¡’õºâmain–Ì.assošAÇciated“with“a“particular“t¾9yp˜e.‘@ýF‘ÿ:«our“more“handyŽ¡’õºâfunctions–wcof“similar“ilk“are“ëMtopº,–çëMbotº,“ëMtopfv–wcºand“ëMwhnfº.‘BTheŽ¡’õºâ rst›‚´t•¾9w“o˜simply˜generate˜the˜greatest˜and˜least˜con“texts˜in˜aŽ¡’õºâparticular–5©domain.‘ÑâëMtopfv(D)‘5pºgenerates“the“greatest“abstractŽ¡’õºâv‘ÿ|ralue–Tin“domain“ëMDº.ަ’ç¤ëMtop–¹–(Lift‘ s,(D1“x“...“x“Dn))Ž¡’f=–¹–Up1‘,Â[top(D1)“...“top(Dn)]Ž¡’ç¤top–¹–(Lift2“(D1“x“...“x“Dn))Ž¡’f=–¹–UpUp2“[top(D1)“...“top(Dn)]Ž¡’ç¤top–¹–(Ds“->“Dt)Ž¡’f=–¹–(\c“->“top(Ds))Ž¡¡’ç¤bot–¹–(Lift‘ s,(D1“x“...“x“Dn))Ž¡’f=‘¹–Stop1Ž¡’ç¤bot–¹–(Lift2“(D1“x“...“x“Dn))Ž¡’f=‘¹–Stop2Ž¡’ç¤bot–¹–(Ds“->“Dt)Ž¡’f=–¹–(\c“->“bot(Ds))Ž¡¡’ç¤topfv–¹–(Lift‘ s,(D1“x“...“x“Dn))Ž¡’f=–¹–ANonRec“[topfv(D1)“...“topfv(Dn)]Ž¡’ç¤topfv–¹–(Lift2“(D1“x“...“x“Dn))Ž¡’f=–¹–ARec‘æX[topfv(D1)“...“topfv(Dn)]Ž¡’ç¤topfv–¹–(Ds“->“Dt)Ž¡’f=–¹–Fval“(\c“->“top(Ds))Ž¡’3'€(\a–¹–->“topfv(Dt))ަ’õºâwhnf(D)‘ž…ºis–ž£the“w¾9eak“head“normal“form“ev‘ÿ|raluator“for“domainŽ¡’õºâëMDº.–TThis“only“mak¾9es“sense“for“certain“v‘ÿ|ralues“of“ëMDº:ަ’ç¤ëMwhnf–¹–(Lift‘ s,(D1“x“...“x“Dn))Ž¡’f=‘,ÂUp1–¹–[bot(D1)“...“bot(Dn)]Ž¡’ç¤whnf–¹–(Lift2“(D1“x“...“x“Dn))Ž¡’f=–¹–UpUp2“[bot(D1)“...“bot(Dn)]ަ’õºâºFinally‘ÿ:«,–Tfor“the“record,“a“Core“ëMcase“ºexpression“loAÇoks“lik¾9eަ’ç¤ëMcase–¹–switchExpression“ofŽ¡’fC1–¹–p11“...“p1m“->“rhs1Ž¡’3'€...Ž¡’fCn–¹–p1n“...“pnm“->“rhsnަ’õºâºwhere–X%it“is“assumed“that“all“constructors“are“presen¾9t.‘ääThisŽ¡’õºâis–Tassured“bš¾9y“the“pattern-matc˜hing“phase“of“the“desugarer.ŽŸ ’õºâThe–ífour“folloš¾9wing“sections“doAÇcumen˜t“the“ o˜w“of“abstractŽ¡’õºâv‘ÿ|ralues–^and“con¾9texts“through“constructor“applications“andŽ¡’õºâëMcase–¤'ºexpressions.‘ö¶In“some“w•¾9a“ys,‘ºÊthe›¤'t“w“o˜are˜oppAÇosites:‘ãÚcon-Ž¡’õºâstructor–kapplications“build“structures,‘O1whilst“ëMcase“ºexpres-Ž¡’õºâsions–‹Mdisassemš¾9ble“them.‘~ZAn“in˜teresting“dualit˜y“arises“fromŽ¡’õºâthis.‘ÌThe– o¾9w“of“abstract“v‘ÿ|ralues“though“case“expressionsŽ¡’õºâis– uncannily“similar“to“the“ oš¾9w“of“con˜texts“v‘ÿ|ralues“throughŽ¡’õºâconstructors,–Tand“vice“v¾9ersa.ŽŽŽŽŽŸ’åä11ŽŽŒ‹ & •ºâ ý? £ ý€‘íºâ¹3.5.1Ž‘ úíConstructoš¹™r–LÎfunctions:‘fhabstract“value“p˜ropagationŽŸm‘íºâºHoš¾9w–1do“abstract“v‘ÿ|ralues“ o˜w“through“a“constructor?‘4Theޤ ‘íºâdiscussion–§Éof“section“3.3“implied“that“the“the“ëM(:)“ºfunctionŽ¡‘íºâm•¾9ust›TbAÇeha“v“e˜something˜lik“e:ޤeh‘ûç¤ëM(:)–¹–=“\x“xs“->“AMeet“[xs,“ARec“[x]]Ž¡‘íºâºObservš¾9e–‹¦that“the“apparen˜tly“pAÇolymorphic“nature“of“this“def-ޤ ‘íºâinition–©is“incidenš¾9tal.‘ï7In“general,‘¨Ìgiv˜en“an“arit˜y-n“constructorŽ¡‘íºâëMC‘öºand–ùargumen¾9ts“ëMa1–¹–...“an–ùºwhere“ëM(C–¹–a1“...“an)“::“tauº,Ž¡‘íºâthe–Tforwš¾9ard“bAÇeha˜viour“of“C“is:Ž©eh‘ûç¤ëM\a1–¹–...“an“->“AMeet“[e1“...“en]Ž¡¡‘ûç¤ei–¹–=“aiŽ¡‘‡’if–¹–argkind“ai“=“RecŽ¡¡‘ f=–¹–ARec“(update“ai“ai“topfv(D(tau)))Ž¡‘‡’if‘,Âargkind–¹–ai“==“Var“xŽ¡‘‡’and‘ s,C–¹–is“from“a“recursive“typeŽ¡¡‘ f=–¹–ANonRec“(update“ai“ai“topfv(D(tau)))Ž¡‘‡’if‘,Âargkind–¹–ai“==“Var“xŽ¡‘‡’and‘ s,C–¹–is“from“a“non-recursive“typeަ‘íºâºNullary–„fconstructors“simply“acquire“the“top“abstract“v‘ÿ|ralueŽ¡‘íºâof–¸‡the“relev‘ÿ|ran¾9t“domain“(bAÇear“in“mind“that,‘Ëfor“a“domain“notŽ¡‘íºâcon¾9taining–“ófunction“spaces,‘³›this“is“the“same“as“the“bAÇottomŽ¡‘íºâpAÇoin¾9t).‘pThe–TëM[]“ºcase“for“ëM[Int]º,“for“example,“is:ަ‘ûç¤ëM[]–¹–=“topfv(D(“[Int]“))Ž¡‘ f=–¹–topfv(“Lift2“(Lift“())“)Ž¡‘ f=–¹–ARec“[ANonRec“[]]ަ‘íºâºThe–Ã3motiv¾9e“in“all“this“is“to“ensure“that“the“abstract“v‘ÿ|ralue“ofŽ¡‘íºâa–Žconstructor“application“is“cš¾9haracterised,‘µfor“eac˜h“parame-Ž¡‘íºâterising–Ttš¾9ypAÇe,“b˜y“the“least“v‘ÿ|ralue“of“that“t˜ypAÇe.ŽŸ ‘íºâAs–K[an“example,‘×consider“an“ob‘ƒŽjectŽ¡‘íºâof–‹þtš¾9ypAÇe“ëM(AVLTree–¹–Int“Int“Int)º.‘€oCon˜texts–‹þfor“that“t˜ypAÇeŽ¡‘íºâare–®ædra¾9wn“from“the“domain“ëMLift2–¹–(Lift“()“x“Lift“()“xŽ¡‘íºâLift‘¹–())º.‘ #ÀW‘ÿ:«e–ÄexpAÇect“the“abstract“v‘ÿ|ralue“returned“b¾9yŽ¡‘íºâbšAÇoth–þ¾the“ëMALeaf“ºand“ëMANode“ºconstructors“to“b˜e“of“the“formŽ¡‘íºâëMARec–¹–[ii,“aa,“bb]–Íºwhere“ëMii“ºrepresen¾9ts“the“least“abstractŽ¡‘íºâv‘ÿ|ralue–Qof“anš¾9y“ob‘ƒŽject“correspAÇonding“to“t˜ypAÇe“v‘ÿ|rariable“ëMi“ºin“theŽ¡‘íºât¾9ypAÇe–TAde nition,›cüand“similarly“for“ëMaa“ºand“ëMbbº.‘Ù7So,˜at“this“in-Ž¡‘íºâstanš¾9tiation,‘ Wthe–ƒabstract“v‘ÿ|ralue“bAÇeha˜viour“of“the“constructorsŽ¡‘íºâis:Ž©J®‘ûç¤ëMALeaf–¹–=“ARec“[ANonRec“[],“ANonRec“[],“ANonRec“[]]Ž¡¡‘ûç¤ANodeŽ¡‘ûç¤=–¹–\i“l“a“b“r“->Ž¡‘ZÐAMeetŽ¡‘ZÐ[–¹–ARec“[i,‘/?ÜANonRec“[],“ANonRec“[]],Ž¡‘Íül,Ž¡‘ÍüARec–¹–[ANonRec“[],“a,‘/?ÜANonRec“[]],Ž¡‘ÍüARec–¹–[ANonRec“[],“ANonRec“[],“b‘*†F],Ž¡‘ÍürŽ¡‘ZÐ]ަ‘íºâºNon-recursiv•¾9e›`~t“ypAÇes˜are˜dealt˜with˜in˜an˜exactly˜analogousŽ¡‘íºâmanner.‘ÒJF‘ÿ:«or–6âexample,‘c`the“bAÇeha¾9viour“of“the“pairing“construc-Ž¡‘íºâtor–Tat“t¾9ypAÇe“ëMInt–¹–->“Int“->“(Int,“Int)‘TºisŽŽŽ ý€’ç¤ëM(,)ޤ ’ç¤=–¹–\x“y“->Ž¡’ ZÐAMeetŽ¡’ ZÐ[–¹–ANonRec“[x,‘/?ÜANonRec“[]],Ž¡’ÍüANonRec–¹–[ANonRec“[],“y‘*†F]Ž¡’ ZÐ]Ž©q’õºâºIf–_¨yš¾9our“instincts“tell“y˜ou“this“is“m˜uc˜h“ado“abAÇout“nothing,‘ƒþy˜ouŽ¡’õºâare–;!correct.‘ØSince“all“these“examples“build“structures“with-Ž¡’õºâout–¦ïem¾9bAÇedded“function“spaces,‘½the“result“v‘ÿ|ralues“are“unitary‘ÿ:«,Ž¡’õºâand–Tma¾9y“bAÇe“written:ަ’ç¤ëM[]‘ s,=‘/?ÜARec–¹–[ANonRec“[]]Ž¡’ç¤(:)–¹–=“\x“xs“->“ARec“[ANonRec“[]]Ž¡¡’ç¤(,)–¹–=“\x“y“->“ANonRec“[ANonRec“[],“ANonRec“[]]Ž¡¡’ç¤ALeaf–¹–=“ARec“[ANonRec“[],“ANonRec“[],“ANonRec“[]]Ž¡’ç¤ANode–¹–=“\i“l“a“b“r“->Ž¡’)´TARec–¹–[ANonRec“[],“ANonRec“[],“ANonRec“[]]ŽŸ?’õºâ¹3.5.2Ž’úíConstructoš¹™r–LÎfunctions:‘fhcontext“p˜ropagationŽŸm’õºâºThe–Qname“of“the“game“here“is“to“saš¾9y“what“con˜text“propagatesŽ¡’õºâfrom–ƒMa“non-nš¾9ullary“constructor“to“its“argumen˜ts.‘fZIn˜tuitingŽ¡’õºâ rst–Ton“ëM[Int]º,“ëM(:)“ºexhibits“the“folloš¾9wing“bAÇeha˜viour:ަ’õºâëMDemand–¹–on“(x:xs)›Y„Demand“on“x˜Demand“on“xsŽ¡’õºâ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~Ž¡’ÿ.UU[U[]]‘FßÊU[]‘B&4UU[U[]]Ž¡’ÿ.UU[_]‘PRö_‘K™`UU[_]Ž¡’ÿ.U_‘^¸_‘K™`_Ž¡’ÿ._‘c9N_‘K™`_ަ’õºâºA‘÷½ëMUU[U[]]–÷źconš¾9text“causes“ev‘ÿ|raluation“of“the“en˜tire“structureŽ¡’õºâof–,pthe“list,‘27and“all“the“ëMIntºs“in“it“toAÇo.‘aÅSo“wš¾9e“ma˜y“propagateŽ¡’õºâëMU[]–˜!ºto“ëMx“ºand“ëMUU[U[]]“ºto“the“tail“of“the“list.‘¤ÖThe“sameŽ¡’õºâreasoning–9œexplains“the“propagation“of“a“ëMUU[_]“ºcon•¾9text.‘Ó3No“w,Ž¡’õºâwhat–`iof“ëMU_º?‘à"This“ev›ÿ|raluator“simply“ev˜aluates“to“WHNF,“thatŽ¡’õºâis,–‹the,“ rst›ýØconstructor,“and˜giv•¾9es˜up.‘œSo˜zero˜con“text˜ma“yŽ¡’õºâbAÇe–Èýpropagated“to“either“head“or“tail.‘þSimilarly‘ÿ:«,‘ØBzero“con¾9textŽ¡’õºâpropagates–Tfrom“zero“con¾9text“on“ëM(x:xs)º.ŽŸ ’õºâIs–;Žthere“a“pattern“here?‘The“con¾9text“on“ëMxs“ºis“that“same“asŽ¡’õºâthe–ÜMconš¾9text“on“ëM(x:xs)“ºexcept“at“the“WHNF‘ÜpAÇoin˜t,‘ whilstŽ¡’õºâthe–#'con¾9text“on“ëMx“ºis“\ëMyº"“in“the“ëMUU[y]“ºcases,‘&œand“none“other-Ž¡’õºâwise.‘áÊThis–¬rlatter“opšAÇeration“could“b˜e“regarded“as“droppingŽ¡’õºâthe–rdouble-lifting,‘É*and“selecting“the“ rst“prošAÇduct“comp˜o-Ž¡’õºânenš¾9t.‘”W‘ÿ:«riting–ÍÁthe“con˜text“on“ëM(x:xs)“ºas“ëMalphaº,‘Ücon˜text“on“ëMxŽ¡’õºâºand–TëMxs“ºrespšAÇectiv¾9ely“could“b˜e“written“as:ަ’ç¤ëMDropUU–¹–1“alphaŽ¡’ç¤ZapWHNF‘¹–alphaަ’õºâºImplemen¾9ting–ºZëMDropUU›¹íºand“ëMZapWHNF˜ºdirectly“causes“ma‘ƒŽjorŽ¡’õºâproblems–Ÿ³in“the“term-rewriting“system.‘»F–ÿ:«ortunately“,‘JtheŽ¡’õºâëMCaseUU–Tºand“ëMSelUU“ºprimitiv¾9es“can“bAÇe“used“instead:ަ’útxëMDropUU–¹–n“alpha“=“CaseUU“alpha“_“_“(SelUU“n“alpha)Ž¡’útxZapWHNF–¹–alpha‘ s,=“CaseUU“alpha“_“_“alphaަ’õºâºAnalogising–Š•the“informal“argumen¾9t“leads“to“a“general“rule.Ž¡’õºâGivš¾9en–@an“arit˜y-ëMn“ºconstructor“ëMC‘?´ºand“argumen˜ts“ëMa1–¹–...“anŽ¡’õºâºwhere›S$ëM(C–¹–a1“...“an)“::“tauº,‘¢˜con¾9text˜ëMalpha˜ºon˜the˜con-Ž¡’õºâstructor–Tapplication“proAÇduces“conš¾9text“on“ëMai“ºas“follo˜ws:ŽŽŽŽŽŸ’åä12ŽŽŒ‹ =ý •ºâ ý? £ ý€‘ûç¤ëMai‘ s,=–¹–ZapWHNF“alphaޤ ‘A(if‘,Âargkind–¹–ai“==“RecŽ¡¡‘Íü=–¹–DropUU“x“alphaŽ¡‘A(if‘,Âargkind–¹–ai“==“Var“xŽ¡‘A(and‘ s,C–¹–is“from“a“recursive“typeŽ¡¡‘Íü=–¹–DropU“x“alphaŽ¡‘A(if‘,Âargkind–¹–ai“==“Var“xŽ¡‘A(and‘ s,C–¹–is“from“a“non-recursive“typeŽŸ¹'‘íºâºThe–}iëMAVLTree“ºexample“at“instance“ëM(AVLTree–¹–Int“Int“Int)Ž¡‘íºâºbAÇeha•¾9v“es–Lqas“folloš¾9ws“for“a“con˜text“ëMalpha“ºapplied“toŽ¡‘íºâëM(ANode–¹–i“l“a“b“r)º:Ž©s]‘ûç¤ëMVariable‘!DemandŽ¡‘ûç¤~~~~~~~~~~~~~~~~~~~~~~~~~~~~~Ž¡‘ûç¤i‘B&4DropUU–¹–1“alphaŽ¡‘ûç¤l‘B&4ZapWHNF‘ s,alphaŽ¡‘ûç¤a‘B&4DropUU–¹–2“alphaŽ¡‘ûç¤b‘B&4DropUU–¹–3“alphaŽ¡‘ûç¤r‘B&4ZapWHNF‘ s,alphaަ‘íºâºConš¾9text–9%propagation“for“non-recursiv˜e“t˜ypšAÇes“b˜eha•¾9v“es–9%in“aŽ¡‘íºâsimilar–N¬manner,‘]except“that“it“is“no“longer“pAÇossible“to“gen-Ž¡‘íºâerate–)]ëMZapWHNFº,“and“the“drop-select“opAÇerator“only“drops“oneŽ¡‘íºâpAÇoinš¾9t,‘ö%instead–îYof“t˜w˜o.‘rThis“opAÇerator,‘ö%called“ëMDropUº,“is“imple-Ž¡‘íºâmen¾9ted‘Tasޤ¹'‘ûç¤ëMDropU–¹–n“alpha‘ s,=“CaseU“alpha“_“(SelU“n“alpha)Ž¡‘íºâºF‘ÿ:«or–ÿ7a“con¾9text“ëMalpha“ºapplied“to“ëM(x,–¹–y)“::“(Int,“Int)º,‘£theޤ ‘íºâcon¾9texts–ÒËpropagated“to“ëMx“ºand“ëMy“ºare“ëM(DropU–¹–1“alpha)‘Ò˺andŽ¡‘íºâëM(DropU–¹–2“alpha)‘TºrespAÇectiv¾9ely‘ÿ:«.ŽŸ ‘íºâT‘ÿ:«ranslation–gvof“ëMDropUº,“ëMDropUU›gJºand“ëMZapWHNF˜ºin¾9to“the“ëMCase“ºandŽ¡‘íºâëMSel– ݺprimitiv¾9es“requires“some“passing“around“of“domains,‘[soŽ¡‘íºâthat–¥the“appropriate“kind“of“bšAÇottom“v‘ÿ|ralues“can“b˜e“man¾9ufac-Ž¡‘íºâtured.ŽŸÿ‘íºâ¹3.5.3Ž‘ úíCase–LÎexpš¹™ressions:‘fhabstract“value“p˜ropagationŽŸm‘íºâºThe–æQtask“here“is“to“ gure“out“what“abstract“v‘ÿ|ralues“to“at-Ž¡‘íºâtacš¾9h–ôÚto“constructor“v‘ÿ|rariables“in“a“case“expression,‘ûYgiv˜en“theŽ¡‘íºâabstract–TUv‘ÿ|ralue“of“the“switc¾9h“expression.‘ÙrThe“solution“is“re-Ž¡‘íºâmark‘ÿ|rably–`äsimilar“to“propagation“of“con¾9texts“to“constructorŽ¡‘íºâargumen•¾9ts,‘^3and›O follo“ws˜a˜theme˜whic“h˜should˜b•AÇe˜b“ecomingŽ¡‘íºâfamiliar.‘pGiv¾9en–Ta“case“expressionŽ©¹'‘ûç¤ëMcase–¹–sw“ofŽ¡‘ f...Ž¡‘ fC–¹–a1“...“an“->“rhsŽ¡‘ f...ަ‘íºâºand–L¹an“abstract“v‘ÿ|ralue“assoAÇciated“with“ëMsw“ºof“ëMfswº,‘tØthe“abstractŽ¡‘íºâv‘ÿ|ralue–TassoAÇciated“with“ëMai“ºisަ‘ûç¤ëMai‘ s,=‘¹–fswŽ¡‘A(if‘,Âargkind–¹–ai“==“RecŽ¡¡‘Íü=–¹–SelA“x“fswŽ¡‘A(if‘,Âargkind–¹–ai“==“Var“xަ‘íºâºLet–wØthe“abstract“v‘ÿ|ralue“of“the“switc¾9h“expression“bAÇe“denotedŽ¡‘íºâëMfswº.‘pF‘ÿ:«or–TëM[Int]“ºwš¾9e“ha˜v˜e:ŽŽŽ ý€’ç¤ëMcase–¹–sw“ofޤ ’f[]‘Ÿî->‘ s,rhs1Ž¡’f(x:xs)‘¹–->‘ s,rhs2ޤƒ’õºâºgiving–Tbindings“ofŽ¡’ç¤ëMx– s,--->“SelA–¹–1“fswŽ© ’ç¤xs‘¹–--->‘ s,fswŽ¡’õºâ(AVLTree–¹–Int“Int“Int)‘Tºgiv¾9es:Ž¡’ç¤ëMcase–¹–sw“ofަ’fALeaf‘8³->‘¹–rhs1ަ’fANode–¹–i“l“a“b“r‘ s,->“rhs2ަ¦’ç¤i– s,--->“SelA–¹–1“fswަ’ç¤l– s,--->“fswަ’ç¤a– s,--->“SelA–¹–2“fswަ’ç¤b– s,--->“SelA–¹–3“fswަ’ç¤r– s,--->“fswŽ¡’õºâºFinally‘ÿ:«,–TëM(Int,‘¹–Int)“ºgiv¾9es:Ž¡’ç¤ëMcase–¹–sw“ofަ’f(x,–¹–y)‘ s,->“rhs1ަ¦’ç¤x– s,--->“SelA–¹–1“fswަ’ç¤y– s,--->“SelA–¹–2“fswޤô’õºâ¹3.5.4Ž’úíCase–LÎexpš¹™ressions:‘fhcontext“p˜ropagationŽŸm’õºâºThis–Ñösection“establishes“hoš¾9w“con˜text“on“a“ëMcase“ºexpressionަ’õºâpropagates–kto“conš¾9text“on“the“switc˜h“expression.‘¦First,‘Àaަ’õºâsubsidiary‘Tresult.Ž¡’õºâ¹F•¹™o“rw“a“rds›LÎp“ropagation˜of˜contexts˜though˜constructo“rsŽŸm’õºâºGiv¾9en–5%a“constructor“application“ëM(C–¹–a1“...“an)“::“tauº,‘aütheަ’õºâmethoAÇd–G˜of“section“3.5.2“can“tell“us“hoš¾9w“con˜text“on“this“ap-ަ’õºâplication–C¸maps“to“conš¾9text“on“ëMa1–¹–...“anº.‘§›Ho˜w˜ev˜er,‘OQw˜e‘C¸no˜wަ’õºâneed–Hgto“run“the“proAÇcess“in“rev•¾9erse.‘µªGiv“en–Hgsome“con¾9textsަ’õºâëMc1–¹–...“cn–Lºon“ëMa1–¹–...“anº,‘´w•¾9e›Lw“an“t˜to˜ nd˜the˜greatest˜con-ަ’õºâtext–õÈëMalpha“ºthat“ma¾9y“bAÇe“put“on“the“application,‘üconstrainedަ’õºâso–that“the“conš¾9texts“that“section“3.5.2“indicates“w˜ould“thenަ’õºâpropagate–ºto“ëMa1–¹–...“an–ººare“less“than“or“equal“ëMc1–¹–...“cnަ’õºâºrespAÇectiv¾9ely‘ÿ:«.ŽŸ ’õºâThe–ñ§folloš¾9wing“sc˜heme“is“o ered,‘øÉagain“without“justi cation.ަ’õºâIf–TëMC“ºis“from“a“recursivš¾9e“t˜ypAÇe:ޤƒ’ç¤ëMalpha–¹–=“CJoin“[Up2,“CMeet“[e1“...“en]]ަ¦’ç¤ei–¹–=“aiަ’‡’if‘,Âargkind–¹–ai“==“Recަ¦’f=–¹–update“ai“ai“top(D(tau))ަ’‡’if‘,Âargkind–¹–ai“==“Var“xŽ¡’õºâºIf–pëMC‘Pºis“from“a“non-recursivš¾9e“t˜ypšAÇe,‘¯6ëM(argkind‘¹–ai)“ºcannot“b˜eަ’õºâëMRecº,–Tso“this“simpli es“to:Ž¡’ç¤ëMalpha–¹–=“CMeet“[e1“...“en]ަ¦’ç¤ei–¹–=“update“ai“ai“top(D(tau))ަ’‡’if‘,Âargkind–¹–ai“==“Var“xŽŽŽŽŽŸ’åäº13ŽŽŒ‹U  •ºâ ý? £ ý€‘íºâºFinally‘ÿ:«,–Tfor“nš¾9ullary“constructors,“lik˜e“ëM[]º:ޤk‘ûç¤ëMalpha–¹–=“ctop(D(tau))Ž¡‘íºâºExamples:‘pgiv¾9en›TëM(a1,–¹–a2)“::“(Int,“Int)º,˜w¾9e˜getŽ¡‘ûç¤ëMalpha–¹–=“CMeet“[“Up1“[c1,‘æXU[]“],Ž© ‘GUp1–¹–[U[],‘,Âc2]“]Ž¡‘íºâ(a1:a2)–¹–::“[Int]‘Tºgiv¾9esŽ¡‘ûç¤ëMalpha–¹–=“CJoin“[“Up2,ަ‘GCMeet–¹–[“UpUp2“[c1],ަ‘mM´c2‘¹–]ަ‘> Ø]Ž¡‘íºâ[]–¹–::“[Int]‘Tºgiv¾9esŽ¡‘ûç¤ëMalpha–¹–=“UpUp2“[Up1“[]]Ž¡‘íºâ(ANode–¹–a1“a2“a3“a4“a5)“::“(ATree“Int“Int“Int)‘Tºgiv¾9esŽ¡‘ûç¤ëMalpha–¹–=“CJoinަ‘!´T[‘¹–Up2,ަ‘+'€CMeet–¹–[“UpUp2“[c1,‘æXU[],‘,ÂU[]“],ަ‘Pô0c2,ަ‘Pô0UpUp2–¹–[U[],‘,Âc3,‘æXU[]“],ަ‘Pô0UpUp2‘¹–[U[],–,ÂU[],“c4‘ s,],ަ‘Pô0c5‘¹–]ަ‘!´T]ŽŸ덑íºâ¹Using–LÎthe“lemmaŽŸm‘íºâºAnd–»inoš¾9w“to“return“to“the“main“theme.‘¯A˜t“this“pAÇoin˜t,‘äîit'sަ‘íºânecessary–{¸to“inš¾9troAÇduce“a“function“w˜e“will“see“a“lot“more“ofަ‘íºâlater.‘ßThe–¾yfunction“ëMC‘¾Mºtells“us“hoš¾9w“m˜uc˜h“con˜text“is“propa-ަ‘íºâgated–s]to“a“v‘ÿ|rariable“ëMx“ºwhen“con¾9text“ëMalpha“ºis“propagated“toަ‘íºâsome–>Óarbitrary“expression“ëMeº.‘˜îOf“course,‘I3if“ëMx“ºdošAÇes“not“o˜ccurަ‘íºâfree–Tin“ëMeº,“the“answ¾9er“is“none.‘pW‘ÿ:«e“write“this“asŽ¡‘ûç¤ëMC–¹–x“[e]“rho“alphaŽ¡‘íºâºwith–¿Žthe“ëMe“ºin“square“brac•¾9k“ets–¿Žto“emphasise“that“ëMC‘¿bºregardsަ‘íºâit–m¦as“a“synš¾9tactic“ob‘ƒŽject.‘%fAs“bAÇecomes“apparen˜t“later,‘ƒ»ëMC‘mºalsoަ‘íºârequires–„an“en•¾9vironmen“t–„ëMrho“ºwhic¾9h“supplies“abstract“v‘ÿ|raluesަ‘íºâfor–Tall“free“v‘ÿ|rariables“in“ëMeº.ŽŸ ‘íºâRecall–Tthat“a“ëMcase“ºexpression“loAÇoks“lik¾9e“this:Ž¡‘ûç¤ëMcase–¹–sw“ofަ‘ fC1–¹–p11“...“p1m“->“rhs1ަ‘ f...ަ‘ fCn–¹–p1n“...“pnm“->“rhsnŽ¡‘íºâºNo•¾9w,‘S•giv“en›ïcon“text˜ëMalpha˜ºo“v“erall,‘S•what˜is˜the˜con“text˜onަ‘íºâëMswº?‘`aThe–Ö¤ rst“step“is“to“ nd“the“con¾9text“on“ëMp11–¹–...“pnmº.ަ‘íºâThese–Tconš¾9text“are“giv˜en“b˜y:Ž¡‘ûç¤ëM(C–¹–p11“[rhs1]“rho1“alpha)‘,Â...ަ‘ûç¤(C–¹–p1m“[rhs1]“rho1“alpha)ަ¦‘ûç¤...ަ¦‘ûç¤(C–¹–p1n“[rhsn]“rhon“alpha)‘,Â...ަ‘ûç¤(C–¹–pnm“[rhsn]“rhon“alpha)ŽŽŽ ý€’õºâºF‘ÿ:«or–D=eacš¾9h“particular“constructor,‘Oöthe“original“en˜viron-ޤ ’õºâmenš¾9t–ÑõëMrho“ºis“augmen˜ted“with“abstract“v‘ÿ|ralue“bindings“forŽ¡’õºâthe–0v‘ÿ|rariables“assoAÇciated“with“that“constructor,‘vÌgeneratingŽ¡’õºâëMrho1–¹–...“rhonº.‘ˆThese–ëœv‘ÿ|ralues“are“deriv¾9ed“from“the“abstractŽ¡’õºâv‘ÿ|ralue–å„of“the“switc¾9h“expression,‘ïas“describAÇed“in“section“3.5.3.Ž© ’õºâThe–ôHnext“step“is“to“ gure“out“what“con¾9text“can“bAÇe“safelyŽ¡’õºâapplied–wËto“eacš¾9h“constructor,‘hkno˜wing“the“con˜texts“on“theirŽ¡’õºâindividual–.4argumen¾9ts.‘gThe“methošAÇd“describ˜ed“in“the“lemmaŽ¡’õºâis–}Ùapplied,›×úonce“for“eac¾9h“constructor,˜to“the“con¾9texts“forŽ¡’õºâëMp11–¹–...“pnm–®ºjust“computed,‘TJgiving“ëMalpha1–¹–...“alphanº.Ž¡’õºâThese–<mv‘ÿ|ralues“are“comš¾9bined“to“giv˜e“the“o˜v˜erall“con˜text“onŽ¡’õºâëMsw‘Tºas:ޤÐO’ç¤ëMCMeet–¹–[alpha1“...“alphan]Ž¡’õºâºUsing–6uëMCMeet“ºto“merge“these“v‘ÿ|ralues“re ects“the“fact“that“w¾9eޤ ’õºâcannot–Øknoš¾9w“whic˜h“alternativ˜e“will“bAÇe“selected“at“compileŽ¡’õºâtime.‘ÿThe–½bšAÇest“safe“v‘ÿ|ralue“whic¾9h“can“b˜e“obtained“is“the“leastŽ¡’õºâof–Tanš¾9y“of“alternativ˜es.ަ’õºâUnfortunately‘ÿ:«,‘*¹there–ó?is“one“spAÇecial“case“where“this“form¾9u-Ž¡’õºâlation–¤"is“wrong.‘ÈÙWhen“the“switc¾9h“expression“is“of“a“re-Ž¡’õºâcursiv•¾9e›‹èt“ypAÇe,‘éŒlik“e˜ëM[Int]º,‘éŒone˜ nds˜that˜propagating˜zeroŽ¡’õºâcon•¾9text›¼®on“to˜the˜ëMcase˜ºexpression˜proAÇduces˜non-zero˜con“textŽ¡’õºâon–x!the“switc¾9h“expression.‘D×This“unsafe“result“can“bAÇe“tracedŽ¡’õºâto–á7the“case“for“recursivš¾9e“t˜ypšAÇes“b˜eing“of“the“form“ëMalpha“º=Ž¡’õºâëMCJoin–¹–[Up2,“...]º,‘swhicš¾9h– ûimpAÇoses“a“minim˜um“v‘ÿ|ralue“of“ëMUp2Ž¡’õºâºon–²ºthe“conš¾9text“con˜tributed“b˜y“eac˜h“constructor.‘ô¡SimplyŽ¡’õºâthro•¾9wing›o½a“w“a“y˜the˜ëMUp2˜ºclamping˜bit˜causes˜more˜problemsŽ¡’õºâthan–@¨it“solv¾9es.‘žkA‘@bšAÇetter“solution“is“to“explicitly“imp˜ose“theŽ¡’õºârequired–æ¯condition“that“zero“o•¾9v“erall›æ¯con“text˜proAÇduces˜zeroŽ¡’õºâconš¾9text–ì7on“the“switc˜h“expression.‘¡Recalling“that“ëMalpha“ºisŽ¡’õºâthe›To•¾9v“erall˜con“text,˜this˜is˜done˜b“y˜writingޤÐO’ç¤ëMCaseU–¹–alpha“_“(CMeet“[alpha1“...“alphan])Ž¡’õºâºorŽ¡’ç¤ëMCaseUU–¹–alpha“_“(CMeet“[alpha1“...“alphan])Ž© ’JÇn(CMeet–¹–[alpha1“...“alphan])Ž¡’õºâºdepšAÇending–CÝon“the“domain“of“ëMalphaº.‘֞The“p˜ossible“duplicationަ’õºâof–the“ëM(CMeet–¹–[alpha1“...“alphan])–ºterm“is“regrettable,ަ’õºâand–@Ecould“pšAÇoten¾9tially“cause“ma‘ƒŽjor“p˜erformance“problems.ަ’õºâSection–T6.1“shoš¾9ws“ho˜w“these“ma˜y“bAÇe“a˜v˜oided.ŽŸ ’õºâThe–®øcomplications“in“this“business“seem“endless.‘é\W‘ÿ:«e“ha•¾9v“eަ’õºâjust–Tcreated“y¾9et“another“problem.‘pConsider:Ž¡’ç¤ëMlet‘ s,id–¹–y“=“y“inަ’‡’case–¹–e“ofަ’)´T[]‘Y„->‘¹–idަ’)´T(x:xs)‘ s,->‘¹–idŽ¡’õºâºThis–míëMcase“ºexpression“returns“a“function,‘„whic¾9h“is“pAÇerfectlyަ’õºâlegitimate.‘ý:But–µ—the“o•¾9v“erall›µ—con“text˜on˜it,–ݨëMalphaº,“will˜bAÇe˜aަ’õºâfunction– Êcon¾9text,‘Igand“it“is“quite“meaningless“to“scrutiniseަ’õºâsuc¾9h–a“v‘ÿ|ralue“with“ëMCaseU›ºor“ëMCaseUUº.“A˜little“thoughš¾9t“rev˜ealsަ’õºâa–yDsimple“solution.‘H?The“ëMcase“ºexpression“returns“a“function,ަ’õºâwhic•¾9h‘^Cwill,›‚áev“en“tually‘ÿ:«,˜bAÇe–^Capplied“to“something.‘ßjWhat“reallyަ’õºâmatters–“Jis“the“con¾9text“on“the“ nal“result“of“that“application:ަ’õºâif–ínon-zero,‘MÏit“means“the“ëMcase“ºexpression“will“ev•¾9en“tually‘íha“v“eަ’õºâto–ú5bAÇe“enš¾9tered,‘ÿ¢in“order“to“generate“a“function“whic˜h“in“turnަ’õºâgenerates–‘ýsome“result“to“satisfy“the“demand.‘ð¨So,‘¬Ball“w¾9e“needަ’õºâdo,›Ùªif–²fëMalpha“ºis“a“function“con¾9text,˜is“test“the“ nal“con¾9textŽŽŽŽŽŸ’åä14ŽŽŒ‹hp •ºâ ý? £ ý€‘íºâºencapsulated–„Yin“ëMalphaº,‘¡Yrather“than“ëMalpha“ºitself.‘ìGetting“theޤ ‘íºâ nal–x\conš¾9text“out“of“an“ëMnº-arit˜y“function“con˜text“is“easily“doneŽ¡‘íºâbš¾9y–̅wrapping“ëMn“FncC‘ÌVºselectors“round“it.‘BSo“con˜text“on“theŽ¡‘íºâswitcš¾9h–Texpression,“in“terms“of“ëMalphaº,“no˜w“loAÇoks“lik˜e:Ž©«“‘ûç¤ëMCaseUU–¹–(FncC“(FncC“.....“(FncC“alpha)“.....))Ž¡‘ú¾_Ž¡‘ú¾(CMeet–¹–[alpha1“...“alphan])Ž¡‘ú¾(CMeet–¹–[alpha1“...“alphan])ަ‘íºâºThe›Á²n•¾9um“bAÇer˜of˜ëMFncCºs˜is˜equal˜to˜the˜arit“y˜of˜ëMalphaº,‘Òlif˜ëMalphaŽ¡‘íºâºhappšAÇens–+to“b˜e“a“function“con¾9text.‘_!ëMcase“ºexpressions“return-Ž¡‘íºâing–=åfunctions“seem“to“bšAÇe“rarities,‘hüso“usually“there“will“b˜e“zeroŽ¡‘íºâëMFncCºs.‘üThe–´ZcorrespšAÇonding“mo˜di cation“of“the“ëMCaseU‘´Aºv¾9ersionŽ¡‘íºâis–•Lobš¾9vious,‘®èand“it“only“remains“to“sa˜y“that“c˜hošAÇosing“b˜et•¾9w“eenŽ¡‘íºâthe›Ð.t•¾9w“o˜no“w˜depAÇends˜on˜the˜ nal˜con“text˜encapsulated˜inŽ¡‘íºâëMalpha–Tºwhen“ëMalpha“ºis“a“function“con¾9text.ŽŸ ‘íºâAs–élour“long“journey“through“the“forest“of“suppAÇorting“ma-Ž¡‘íºâcš¾9hinery–ò¢comes“to“a“close,‘ù’so“the“ nal“destination“dra˜ws“in˜toŽ¡‘íºâsighš¾9t:‘ˆíthe–K“de nition“of“the“abstract“in˜terpreter“propAÇer.‘¿,W‘ÿ:«eŽ¡‘íºâpause–ÀGbut“brie y“to“takš¾9e“respite“in“the“follo˜wing“example,Ž¡‘íºâthen–Temš¾9bark“upAÇon“the“ nal“straigh˜t:‘psection“3.6.ަ‘ûç¤ëMcase–¹–vs“ofŽ¡‘ f[]‘Y„->‘¹–0Ž¡‘ f(x:xs)‘ s,->‘¹–xަ‘íºâºClearly‘ÿ:«,‘ÿkëMvs–¹–::“[Int]–ùðºand“the“o•¾9v“erall›ùðt“ypAÇe˜is˜ëMIntº.‘OSo˜a˜con-Ž¡‘íºâtext–« ëMalpha“ºplaced“on“the“result“m¾9ust“bAÇe“in“domain“ëMLift‘¹–()º,Ž¡‘íºâwith–Dthe“resulting“con¾9text“on“ëMvs“ºin“ëMLift2–¹–(Lift“())º.‘¨ÁSec-Ž¡‘íºâtion–Ýï3.5.4“indicates“that“the“ëM[]“ºcase“conš¾9tributes“con˜textŽ¡‘íºâëMUpUp2–¹–[Up1“[]]º.‘ØNo¾9w,‘þNpropagating–øŒëMalpha“ºto“the“ëM(:)“ºalter-Ž¡‘íºânativš¾9e–¯Üputs“con˜text“ëMalpha“ºon“ëMx“ºand“ëMStop2“º(that“is,‘Ä'none)“onŽ¡‘íºâëMxsº.‘˜ÙComš¾9bining–”"these“t˜w˜o,›³Õagain“using“section“3.5.4,˜sho¾9wsŽ¡‘íºâthat–Tthe“conš¾9text“propagated“b˜y“this“alternativ˜e“is:ަ‘ZÐëMCJoin–¹–[Up2,“CMeet“[alpha,“Stop2]]Ž¡‘ûç¤=–¹–CJoin“[Up2,“Stop2]Ž¡‘ûç¤=‘¹–Up2ަ‘íºâºThis–Tgivš¾9es“o˜v˜erall“con˜text“on“ëMvs“ºas:ަ‘ZÐëMCaseU–¹–alpha“Stop2Ž¡‘> Ø(CMeet–¹–[UpUp2“[Up1“[]],“Up2])Ž¡¡‘ûç¤=–¹–CaseU“alpha“Stop2“Up2ަ‘íºâºThat's›þin•¾9tuitiv“ely˜correct:‘Ñwith˜no˜demand˜on˜the˜resultingŽ¡‘íºâëMIntº,‘RÐthere's–F„no“(ëMStop2º)“demand“on“the“incoming“list.‘¯ÿOth-Ž¡‘íºâerwise,‘Ûw•¾9e›è&ma“y˜ev‘ÿ|raluate˜the˜list˜to˜WHNF‘çð(ëMUp2º),‘Ûthat˜is,Ž¡‘íºâto–údthe“ rst“constructor.‘uIt“is“a“pit¾9y“these“domains“can't“tellŽ¡‘íºâus–w?abAÇout“the“head-strictness“here:‘àGgiv¾9en“non-zero“demand,Ž¡‘íºâit's–~Ýobš¾9vious“w˜e“can“not“only“ev‘ÿ|raluate“to“the“ rst“construc-Ž¡‘íºâtor,‘Êbut–û§can“also“ev‘ÿ|raluate“the“ rst“elemen¾9t“of“the“list“if“it“isŽ¡‘íºânon-empt¾9y‘ÿ:«.ŽŸ™.‘íºâ¹3.6Ž‘G·De ning–LÎthe“abstract“interp¹™reterŽŸm‘íºâºSection–J3.5.4“inš¾9troAÇduced“the“con˜text- nding“function“ëMCº.“W‘ÿ:«eŽ¡‘íºâno•¾9w›‚Ÿaugmen“t˜this˜with˜ëMZº,˜the˜abstract˜in“terpreter˜itself.‘dPëMCŽ¡‘íºâºtak•¾9es›cJan“y˜Core˜expression,‘†æa˜con“text˜on˜that˜expression,‘†æandŽ¡‘íºâa–ˆ‚v›ÿ|rariable,‘¤­and“returns“the“resulting“con¾9text“on“the“v˜ariable.Ž¡‘íºâëMZ‘ø¯ºtak•¾9es›ø·an“y˜Core˜expression,‘þpand˜returns˜the˜abstract˜v‘ÿ|ralueŽ¡‘íºâof–Ç that“expression.‘XSince“the“forwš¾9ard“and“bac˜kw˜ard“ o˜ws“ofŽ¡‘íºâinformation–ÛÔare“heaš¾9vily“in˜tert˜wined,‘ tëMC›Û¡ºand“ëMZ˜ºare“m¾9utuallyŽ¡‘íºârecursiv¾9e.‘pIn–Ta“call“to“ëMC“ºorëMZŽŽŽ ý€’ç¤C–¹–x“[e]“rho“alphaޤ ’ç¤Z‘,Â[e]‘¹–rhoŽ©¦à’õºâx–³Uºis“a“v‘ÿ|rariable,›ÚÔëMe“ºis“a“Core“expression,˜ëMalpha“ºis“a“con¾9text,Ž¡’õºâand–ëMrho“ºis“an“en•¾9vironmen“t–binding“all“free“v‘ÿ|rariables“in“ëMe“ºtoŽ¡’õºâabstract–Æâv‘ÿ|ralues.‘1As“implemen¾9ted,‘óEbAÇoth“functions“carry“anŽ¡’õºâextra–.ßparameter“used“to“help“generate“new“v‘ÿ|rariable“names.Ž¡’õºâëMC‘Rºalso–Tcarries“the“domain“of“ëMx“ºso“it“can“generate“the“appro-Ž¡’õºâpriate–‡€bAÇottom“v‘ÿ|ralue“when“needed.‘rôRecall“also“that“a“CoreŽ¡’õºâexpression–·is“a“pair,‘Ééthe“ rst“part“of“whicš¾9h“is“the“t˜ypAÇe“of“theŽ¡’õºâexpression,–Tand“the“second“the“expression“propAÇer.ŽŸ-’õºâ¹3.6.1Ž’úíDe nition–LÎof“ëMZŽŸm’õºâºThe–:»abstract“v›ÿ|ralue“of“a“literal“is“a“v˜alue“in“the“appropriateŽ¡’õºâone-pAÇoin¾9t‘Tdomain.ަ’ç¤ëMZ–¹–(tau,“ALit“n)“rho‘ s,=“ANonRec“[]ަ’õºâºV‘ÿ:«ariables›Tha•¾9v“e˜their˜v‘ÿ|ralues˜loAÇok“ed˜up.ަ’ç¤ëMZ–¹–(tau,“AVar“v)“rho‘ s,=“rho“vަ’õºâºApplications–÷are“a“little“more“tric¾9ky‘ÿ:«.‘\YFirst,‘ڟthe“abstractŽ¡’õºâv‘ÿ|ralue–æôof“the“function“is“created.‘‘PF‘ÿ:«rom“that,‘\the“abstract-Ž¡’õºâv‘ÿ|ralue-map–ô0is“extracted“using“ëMFvalAº,,‘úÑand“applied“to“the“ab-Ž¡’õºâstract–êv‘ÿ|ralue“of“the“argumenš¾9t“to“giv˜e“the“abstract“v‘ÿ|ralue“ofŽ¡’õºâthe‘Tresult.ަ’ç¤ëMZ–¹–(tau,“AAp“f“e)“rhoŽ¡’f=–¹–AbsAp“(FvalA“(Z“f“rho))“(Z“e“rho)ަ’õºâºLamš¾9bAÇda–üyterms“are“a“lot“more“tric˜ky‘ÿ:«.‘ÑÞLet“ëMa“ºand“ëMc“ºdenoteŽ¡’õºânew‘Tv‘ÿ|rariables.ަ’ç¤ëMZ–¹–(tau,“ALam“[x]“e)“rhoŽ¡’f=–¹–Fval“(CtxLam“c“(C“x“e“rho_c“(FncC“(CtxVar“c))))Ž¡’3'€(AbsLam–¹–a“(Z“e“rho_a))Ž¡’‡’whereŽ¡’)´Trho_c–¹–=“rho“{x“->“FncA“(CtxVar“c)}Ž¡’)´Trho_a–¹–=“rho“{x“->“AbsVar“a}ަ’õºâºAn–ëMFval“ºis“returned.‘!ŒIts“ rst“compAÇonen¾9t“is“a“map“from“theŽ¡’õºâfunction–™ªconš¾9text“ëMc“ºon“ëM(\x.e)“ºto“the“con˜text“on“parameterŽ¡’õºâëMx.–i>ºBear“in“mind“that“ëMc“ºwill“get“bAÇound“to“a“term“of“theŽ¡’õºâform›eÉëM(Fnc–¹–aa“cc)º,‘yçwhere˜ëMaa˜ºis˜the˜abstract˜v‘ÿ|ralue˜suppliedŽ¡’õºâfor– ëMx,“ºand“ëMcc“ºis“the“conš¾9text“on“ëMe.“ºSo“the“con˜text“on“ëMxŽ¡’õºâºis–š¦found“bš¾9y“ nding“ëMC‘šAºof“ëMx“ºin“ëMeº,‘ûúwith“ëMrho“ºaugmen˜ted“b˜yŽ¡’õºâbinding–ïTëMx“ºto“ëMaa,“ºthat“is,›öîto“ëMFncA–¹–(CtxVar“c)º,˜and–ïTwith“theŽ¡’õºâcon¾9text– zon“the“b•AÇo“dy– zof“the“function,– ëMeº,“equal– zto“ëMccº,‘ that“is,Ž¡’õºâëMFncC–¹–(CtxVar“c)º.Ž© ’õºâThe–ôJsecond“ëMFval“ºcompAÇonen¾9t“maps“the“abstract“v‘ÿ|ralue“ëMa“ºof“ëMxŽ¡’õºâºto–½µthe“abstract“v‘ÿ|ralue“of“ëMe.“ºThis“is“easily“done“b¾9y“computingŽ¡’õºâëMZ–Tºof“ëMeº,“with“ëMrho“ºmoAÇdi ed“to“bind“ëMx“ºto“ëMAbsVar‘¹–aº.ަ’õºâThe–TëMACase“ºcase“is“quite“easy:Ž©¦à’ç¤ëMZ–¹–(tau,“ACase“sw“[(cname1,“(pars1,“rhs1))“...Ž¡’Xô0(cnamen,–¹–(parsn,“rhsn))])Ž¡’frhoŽ¡’f=–¹–AMeet“[Z“rhs1“rho1“...“Z“rhsn“rhon]ަ’õºâºThe–xaugmenš¾9ted“en˜vironmen˜ts“ëMrhoi“(1–¹–<=“i“<=“n)–xºare“ob-Ž¡’õºâtained– Rbš¾9y“extending“ëMrho“ºto“pro˜vide“bindings“for“ëMparsi“ºinŽŽŽŽŽŸ’åä15ŽŽŒ‹ò •ºâ ý? £ ý€‘íºâºview–Œ‡of“the“v‘ÿ|ralue“of“ëMZ–¹–sw“rhoº,‘êSusing–Œ‡the“methoAÇd“of“sec-ޤ ‘íºâtion‘T3.5.3.ŽŸ ‘íºâFinally‘ÿ:«,‘¾Pthe–¨ëMAConstr“ºcase.‘ø.Although“sections“3.5.1“and“3.5.2Ž¡‘íºâcompletely–r doAÇcumenš¾9t“abstract“v‘ÿ|ralue“and“con˜text“ o˜wsŽ¡‘íºâthrough–ŽÌconstructors,‘í*wš¾9e“as“y˜et“ha˜v˜e“no“w˜a˜y“of“creatingŽ¡‘íºâabstract–bûv‘ÿ|ralues“for“constructors.‘fStarting“from“a“generalŽ¡‘íºâconstructor‘Tapplicationޤ\‘ûç¤ëMC–¹–e1“...“enŽ¡‘íºâºw¾9e–Tdesire“to“buildŽ¡‘ûç¤ëMFval–¹–(\c1“->“f1“(FncC^n“c1))ޤ ‘‡’(\a1–¹–->“Fval“(\c2“->“f2“(FncC^(n-1)“c2))Ž¡‘‡’(\a2–¹–->“...Ž¡‘9TB...Ž¡‘9TB...–¹–->“Fval“(\cn“->“fn“(FncC^1“cn))Ž¡‘rJ(\an–¹–->“aresultant)“...))Ž©\‘íºâºwhere–-ñëMFncC^i‘¹–e“ºmeans“ëMFncC‘-êºapplied“ëMi“ºtimes“to“ëMe.“ºObserv¾9eŽ¡‘íºâthat–j¢eac¾9h“use“of“ëMFncC‘jŒºhere“is“of“the“form“ëMFncC^i‘¹–cj“ºwhereŽ¡‘íºâëMi–¹–+“j“==“n“+“1º,‘»Fand–šso“all“these“terms“simply“denote“theŽ¡‘íºâcon¾9text–`on“the“result“of“the“constructor“application.‘üÇWhatŽ¡‘íºâsection–P3.5.2“proš¾9vides“is“a“w˜a˜y“to“compute“the“ëMn“ºcon˜textŽ¡‘íºâmaps,‘ý÷ëMf1–¹–...“fnº.‘±-Section–œ>3.5.1“generates“a“term“of“theŽ¡‘íºâformަ‘ûç¤ëM\a1–¹–...“\an“->“aresultantަ‘íºâºand›+ÁbAÇet•¾9w“een˜them,‘ñ\that's˜all˜that's˜needed.‘ _¸As˜thisŽ¡‘íºâis–ìÈrather“confusing,‘¢¤here's“a“couple“of“examples.‘ ¢ËF‘ÿ:«orŽ¡‘íºâëM(:)–¹–::“Int“->“[Int]“->“[Int]:ަ‘ûç¤Fval–¹–(\c1“->“DropUU“1“(FncC“(FncC“c1)))Ž¡‘‡’(\a1–¹–->“Fval“(\c2“->“ZapWHNF“(FncC“c2))Ž¡‘Pô0(\a2–¹–->“ARec“[ANonRec“[]]))ަ‘íºâºF‘ÿ:«or‘TëM(,)–¹–::“Int“->“Int“->“(Int,“Int)º:ަ‘ûç¤ëMFval–¹–(\c1“->“DropU“1“(FncC“(FncC“c1)))Ž¡‘‡’(\a1–¹–->“Fval“(\c2“->“DropU“2“(FncC“c2))Ž¡‘Pô0(\a2–¹–->“ANonRec“[ANonRec“[],Ž¡’¡G&ANonRec‘¹–[]]))ŽŸìù‘íºâ¹3.6.2Ž‘ úíDe nition–LÎof“ëMCŽŸm‘íºâºPropagation–Tof“a“conš¾9text“on˜to“a“constan˜t“has“no“e ect:ަ‘ûç¤ëMC–¹–x“(tau,“ALit“n)“rho“alphaŽ¡‘ f=–¹–bot“(domain-of-x)ަ‘íºâºThe–Tv‘ÿ|rariable“case“is:ަ‘ûç¤ëMC–¹–x“(tau,“AVar“v)“rho“alphaŽ¡‘ f=–¹–if‘æXx“==“vŽ¡‘‡’then‘ s,alphaŽ¡‘‡’else‘ s,bot‘¹–(domain-of-x)ަ‘íºâºAs–ØbšAÇefore,‘9the“application“and“lam¾9b˜da“cases“are“a“bit“mindŽ¡‘íºâbAÇending.ަ‘ûç¤ëMC–¹–x“(tau,“ALam“[y]“e)“rho“alphaŽ¡‘ f=–¹–C“x“e“rho2“(FncC“alpha)Ž¡‘‡’whereŽ¡‘!´Trho2–¹–=“rho“{y“->“FncA“alpha}ŽŽŽ ý€’õºâºHere,‘9OëMalpha–2ºis“a“function“con¾9text“bAÇeing“applied“to“ëM(\y.e).ޤ ’õºâºAssuming–@ßthat“ëMx“ºand“ëMy“ºare“not“the“same“v‘ÿ|rariable“(theŽ¡’õºâlamš¾9bAÇda-lifter–Ðassures“this),‘ÿIcon˜text“on“ëMx“ºin“ëM(\y.e)“ºcan“bAÇeŽ¡’õºâfound– Ïfrom“the“con¾9text“on“ëMx“ºin“ëMeº.‘™Since“ëMalpha“ºis“a“functionŽ¡’õºâconš¾9text,‘€¢ëMFncA‘¹–alpha–k,ºis“an“abstract“v‘ÿ|ralue“whic˜h“ëMy“ºis“bAÇoundŽ¡’õºâto,–Tgenerating“ëMrho2.“FncC‘¹–alpha“ºis“the“con¾9text“on“ëMe“ºitself.Ž©ÐO’ç¤ëMC–¹–x“(tau,“AAp“f“e)“rho“alphaŽ¡’f=–¹–CJoin“[“C“x“f“alpha_f“rho,Ž¡’ATBC–¹–x“e“alpha_e“rho“]Ž¡’‡’whereŽ¡’)´Talpha_f–¹–=“Fnc“(Z“e“rho)“alphaŽ¡’)´Talpha_e–¹–=“CtxAp“(FvalC“(Z“f“rho))“alpha_fަ’õºâºT‘ÿ:«o–·Òdeal“with“applications,‘ʆobservš¾9e“that“ëMx“ºma˜y“ošAÇccur“in“b˜othŽ¡’õºâthe–ª°function“and“argumenš¾9t“expressions,‘Ðso“w˜e“need“to“col-Ž¡’õºâlect–¿up“the“con¾9texts“from“ëMf“ºand“ëMeº,‘ÐUand“\add“them“together"Ž¡’õºâusing–©ëMCJoinº.‘ópThe“only“problem“is“ guring“out“what“con-Ž¡’õºâtext–v®propagates“to“ëMf“ºand“ëMeº.‘@~Recall“that“a“function“con-Ž¡’õºâtext–ú˜consists“of“the“abstract“v‘ÿ|ralue“of“the“argumen¾9t,‘ÿñand“theŽ¡’õºâconš¾9text–x1on“the“result.‘EHence,‘Ðèthe“con˜text“on“ëMf“ºm˜ust“bAÇeŽ¡’õºâëMFnc–¹–(Z“e“rho)“alphaº.‘ PThe–dôcon¾9text“on“ëMe“ºis“equal“to“theŽ¡’õºâconš¾9text–lythat“ëMf“ºw˜ould“propagate“to“its“argumen˜t,‘ÂBand“w˜eŽ¡’õºâknoš¾9w–Ôthat“the“con˜text“on“ëMf“ºis“ëMalpha_f.“ºSo,‘C4w˜e“build“theŽ¡’õºâabstract–í˜in¾9terpretation“for“ëMf“ºwith“ëMZ–¹–f“rhoº,‘õŠextract–í˜the“con-Ž¡’õºâtext–ìUmap“using“ëMFvalCº,“and“apply“that“to“ëMalpha_fº.‘ÆAll“told,Ž¡’õºâthat's‘TëMCtx–¹–(FvalC“(Z“f“rho))“alpha_fº.ŽŸ ’õºâDue–ëWto“the“heroic“e orts“of“section“3.5.4,‘ó½the“rather“compli-Ž¡’õºâcated–TëMcase“ºclause“is“stated“quite“succinctly:ަ’ç¤ëMC–¹–x“(tau,“ACase“sw“[(cname1,“(pars1,“rhs1))“...Ž¡’bg\(cnamen,–¹–(parsn,“rhsn))])Ž¡’Íürho‘¹–alphaŽ¡’f=–¹–CJoin“[“C“x“sw“rho“alpha_sw,Ž¡’ATBCMeet–¹–[“C“x“rhs1“rho1“alpha“...Ž¡’g òC–¹–x“rhsn“rhon“alphaŽ¡’]­Æ]Ž¡’7á]ަ’õºâºHere,‘Ý"ëMalpha_sw–µ,ºis“the“conš¾9text“on“ëMsw,“ºgiv˜en“ëMalpha“ºcon˜textŽ¡’õºâon–¦Åthe“ëMcase“ºexpression“itself,‘¼âas“computed“b¾9y“the“methoAÇd“ofŽ¡’õºâsection‘T3.5.4.Ž© ’õºâAs–¸…bAÇefore,‘Ëthe“ëMrhoi“(1–¹–<=“i“<=“n)–¸…ºare“obtained“b¾9y“extend-Ž¡’õºâing–œëMrho“ºto“pro¾9vide“bindings“for“ëMparsi“ºin“view“of“the“v‘ÿ|ralueŽ¡’õºâof›TëMZ–¹–sw“rhoº,˜using˜the˜methoAÇd˜of˜section˜3.5.3.ަ’õºâV‘ÿ:«ariable– ëMx“ºcan“appšAÇear“in“b˜oth“the“switc¾9h“expression,‘J[andŽ¡’õºâanš¾9y–&¯of“the“alternativ˜es.‘ P€T‘ÿ:«o“deal“with“the“former,‘«con-Ž¡’õºâtext–»on“ëMsw“ºis“computed“as“pAÇer“section“3.5.4,‘äand“this“con-Ž¡’õºâtext–b0propagated“inš¾9to“ëMsw.“ºCon˜text“for“ëMx“ºin“alterativ˜e“ëMi“ºisŽ¡’õºâëMC–¹–x“rhsi“rhoi“alphaº,‘Ìpbut–§Ñsince“wš¾9e“can't“sa˜y“whic˜h“alter-Ž¡’õºâativš¾9e–:Ÿwill“actually“bAÇe“selected,‘ƒñw˜e“m˜ust“tak˜e“the“greatestŽ¡’õºâlo•¾9w“er–è'bAÇound“o•¾9v“er–è'all“alternativš¾9es.‘”éFinally‘ÿ:«,‘Ûthe“switc˜h“andŽ¡’õºâalterativ•¾9e›àcon“texts˜are˜once˜again˜\added"˜using˜ëMCJoinº.‘IAsŽ¡’õºâwith–5‘the“ëMZ‘5‰ºclause“for“ëMcase“ºrho“is“extended“to“pro¾9vide“bind-Ž¡’õºâings–Tfor“the“v‘ÿ|rariables“assoAÇciated“with“eac¾9h“constructor.ަ’õºâFinally‘ÿ:«,‘Dµthe–ëMAConstr“ºcase.‘ôŒAll“the“actual“w¾9ork“of“dealingŽ¡’õºâwith–ÚÞconš¾9text“ o˜w“through“constructors“is“done“in“the“corre-Ž¡’õºâspAÇonding–?³ëMZ‘?¨ºclause.‘›All“wš¾9e“need“do“here“is“observ˜e“that“ëMx“ºisŽ¡’õºânevš¾9er–Tfree“in“an˜y“constructor,“and“so“return“zero“con˜text:ŽŸÐO’ç¤ëMC–¹–x“(tau,“AConstr“c)“rho“alphaŽ¡’f=–¹–bot“(domain-of-x)ŽŽŽŽŽŸ’åäº16ŽŽŒ‹š •ºâ ý? £ ý€‘íºâ¹4Ž‘ü”The–LÎterm“rewriting“systemŽŸ†´‘íºâ4.1Ž‘G·IntroFfductionŽŸm‘íºâºF‘ÿ:«or–*eacš¾9h“Core“function,‘o=the“abstract“in˜terpreter“proAÇducesޤ ‘íºâan–¡EëMAbsVal“ºterm.‘õÀRecursivš¾9e“groups“of“terms“require“ xpAÇoin˜t-Ž¡‘íºâing,‘-jwhicš¾9h–(™is“done“in“a“straigh˜tforw˜ard“manner.‘V>The“initialŽ¡‘íºâappro¾9ximation–vÿfor“a“function“in“domain“ëMD‘v¤ºis“ëMatop(D)º,“soŽ¡‘íºâthe–hé xpšAÇoin¾9ting“pro˜duces“the“greatest“ xp˜oin¾9t.‘/Although“itŽ¡‘íºâmighš¾9t–ôÒseem“a“little“un˜usual“to“seek“the“greatest“ xed“pAÇoin˜t,Ž¡‘íºâbAÇear–»”in“mind“that“this“approacš¾9h“represen˜ts“starting“o “fromŽ¡‘íºâa–)ôdangerous“v‘ÿ|ralue,‘YëMatop(D)‘)¸ºand“iterating“one's“w•¾9a“y–)ôto“safet¾9y‘ÿ:«.Ž¡‘íºâIn–Ôôforwš¾9ard“analyses“in“the“st˜yle“of“[Sew91Ž‘/],‘Ûdanger“is“rep-Ž¡‘íºâresen•¾9ted›I:b“y˜the˜least˜pAÇoin“t˜in˜the˜domains,‘V3and˜ xpAÇoin“tingŽ¡‘íºâyields–³/the“least“ xed“pAÇoinš¾9t.‘öIn“an˜y“case,‘Ú¦this“discussion“isŽ¡‘íºârather–W¨academic,‘h>since“w¾9e“can“claim“to“bšAÇe“lo˜oking“for“leastŽ¡‘íºâ xpšAÇoin¾9ts–¯Uhere“to˜o“simply“b¾9y“turning“all“the“domains“upside-Ž¡‘íºâdo¾9wn–pñ{“as“they“are“ nite,›‡Ùcomplete“lattices,˜sucš¾9h“a“tric˜k“isŽ¡‘íºâquite‘Tallo•¾9w“able.Ž© ‘íºâThe–‘)term“rewriter“exists“bAÇecause“of“the“need“to“compare“ap-Ž¡‘íºâproš¾9ximations–Xduring“ xpAÇoin˜ting.‘é}F‘ÿ:«or“non-recursiv˜e“terms,Ž¡‘íºâthere–ºóis,›Ístrictly“spAÇeaking,˜no“need“to“use“the“rewriter.‘þPNev-Ž¡‘íºâertheless,‘‘bAÇecause–²Rwhat“emerges“from“the“abstract“in¾9ter-Ž¡‘íºâpreter–fˆis“usually“grossly“redundan¾9t,‘ºÔall“terms“are“sub‘ƒŽjectŽ¡‘íºâto–JBrewriting,‘—}and“the“recursivš¾9e“ones“are“subsequen˜tly“ x-Ž¡‘íºâpAÇoin¾9ted.ަ‘íºâWhat–•the“rewriter“došAÇes“is“to“transform“eac¾9h“p˜ossible“termŽ¡‘íºâinš¾9to–Â}a“normal“form,‘Ósuc˜h“that“seman˜tically“equiv‘ÿ|ralen˜t“formsŽ¡‘íºâmap–9ðto“the“same“normal“form.‘ŠEDetection“of“ xed“pAÇoin¾9tsŽ¡‘íºâis–;Úthen“a“simple“matter“of“detecting“synš¾9tactic“equalit˜y“ofŽ¡‘íºâthe–normal“forms.‘%øF›ÿ:«or“higher“order“terms,‘YLunfortunately˜,Ž¡‘íºâthis–ximplies“an“abilitš¾9y“to“solv˜e“the“halting“problem.‘D‹W‘ÿ:«eŽ¡‘íºâtherefore–Vdeal“with“higher“order“functions“as“describAÇed“inŽ¡‘íºâsection–j¦5,‘ŒÉand“restrict“ourselv¾9es“to“generating“unique“normalŽ¡‘íºâforms–)Ôfor“the“abstract“in¾9terpretations“of“ rst“order“functions,Ž¡‘íºâsomething–Twhic¾9h“is,“fortunately‘ÿ:«,“decidable.ަ‘íºâThe–Ñáterm“rewriter“propšAÇer“is“an“elab˜orate“system“whic¾9h“gen-Ž¡‘íºâerates–a,normal“forms“bš¾9y“applying“man˜y“loAÇcal“transformationsŽ¡‘íºâto–v¥a“term.‘@bWhen“no“more“transformations“can“bAÇe“applied,Ž¡‘íºâthe–Mäterm“is“deemed“to“bAÇe“in“normal“form.‘Æ!Eac¾9h“kind“of“al-Ž¡‘íºâlo•¾9w“able–jÓtransformation“is“encapsulated“in“a“so-called“rewriteŽ¡‘íºârule.‘óÜEacš¾9h–]#rule“m˜ust“implemen˜t“a“seman˜tically“in˜v‘ÿ|rarian˜tŽ¡‘íºâtransformation.‘ »¸Section–õ3.2“in¾9troAÇduced“a“few“equalities,Ž¡‘íºâwhicš¾9h,–Twhen“giv˜en“a“directionalit˜y‘ÿ:«,“bAÇecome“rewrite“rules:Ž©ÐO‘ûç¤ëMFncA–¹–(Fnc“a“c)‘Ÿî===>‘,ÂaŽ¡‘ûç¤FncC–¹–(Fnc“a“c)‘Ÿî===>‘,ÂcŽ¡‘ûç¤FvalA–¹–(Fval“c“a)–,Â===>“aŽ¡‘ûç¤FvalC–¹–(Fval“c“a)–,Â===>“cަ‘íºâºMost–(×rules“are“complicated“b¾9y“the“presence“of“side-Ž¡‘íºâconditions:ަ‘ûç¤ëMFnc–¹–(FncA“c1)“(FncC“c2)–,Â===>“c1Ž¡‘ûç¤providedŽ¡‘ fc1–¹–==“c2ަ‘íºâºThese–6yexamples“illustrate“the“problem“of“whether“to“simplifyŽ¡‘íºâterms–~starting“from“the“lea•¾9v“es–~(innermost- rst)“or“from“theŽ¡‘íºâroAÇot–MÁ(outermost- rst).‘Å·Since,››Üin“the“second“example,˜theŽ¡‘íºârule–F¾only“applies“if“subterms“ëMc1“ºand“ëMc2“ºare“pro¾9v‘ÿ|rably“equal,Ž¡‘íºâinnermost- rst–Æ9rewriting“seems“necessary‘ÿ:«.‘ /But“the“sameŽ¡‘íºâstrategy–Jµapplied“to“ëMFvalC–¹–(Fval“c“a))–Jµºcould“w¾9aste“a“lotŽŽŽ ý€’õºâof–Û¯e ort“simplifying“ëMa,“ºonly“to“throš¾9w“it“a˜w˜a˜y‘ÿ:«,‘ç7so“outermost-ޤ ’õºâ rst–Tmighš¾9t“giv˜e“bšAÇetter“p˜erformance.Ž© ’õºâProš¾9viding–ÚDthe“rules“are“ nitely“con uen˜t“and“terminating,Ž¡’õºâbAÇoth–:‡approacš¾9hes“still“giv˜e“the“same“normal“forms.‘ŒObserv˜eŽ¡’õºâho•¾9w“ev“er–˜ðthat“whatevš¾9er“approac˜h“is“used,‘ù×m˜ultiple“passesŽ¡’õºâo•¾9v“er–'the“tree“will,›Zin“general,˜bAÇe“needed“to“arriv¾9e“at“nor-Ž¡’õºâmal–ÿçform.‘Ü)The“decision“can“therefore“bAÇe“based“purely“onŽ¡’õºâwhic•¾9hev“er›žœsc“heme˜giv“es˜b•AÇetter˜p“erformance.‘¸HExp“erimen¾9ta-Ž¡’õºâtion›~"sho•¾9w“ed˜that˜outermost- rst˜rewriting˜w“as˜up˜to˜tenŽ¡’õºâtimes›ZDslo•¾9w“er˜than˜innermost- rst˜for˜realistically˜sized˜termsŽ¡’õºâemitted–•?bš¾9y“the“abstract“in˜terpreter.‘œ1Although“it“w˜ould“bAÇeŽ¡’õºâfoAÇolish–Boto“claim“that“this“is“alw•¾9a“ys–Boso,‘lthe“evidence“suggestedŽ¡’õºâan–b innermost- rst“scš¾9heme“w˜ould“usually“bAÇe“m˜uc˜h“quic˜k˜er,‘…÷soŽ¡’õºâan–Tinnermost- rst“sc•¾9hemeŸü-=ó*¹Aa¨cmr6Õ1ŽŽ‘?ûºw“as‘Tadopted.ŽŸ5’õºâ¹4.2Ž’ G·P•¹™erfo“rming–LÎa“single“simpli cation“passŽŸm’õºâºBecause–¿¾the“ëMAbsVal“ºand“ëMContext“ºtš¾9ypAÇes“are“m˜utually“re-Ž¡’õºâcursivš¾9e,‘ÖËthe–°term“rewriter“propAÇer“consists“of“t˜w˜o“functionsŽ¡’õºâof–ÂGtš¾9ypAÇe“ëMAbsVal–¹–->“AbsVal–ÂGºand“ëMContext–¹–->“Contextº,‘í„eac˜hŽ¡’õºâof–qwhicš¾9h“pAÇerforms“m˜ultiple“innermost- rst“simpli cationŽ¡’õºâpasses–N¦with“an“auxiliary“function.‘Ú6When“stabilitš¾9y“is“reac˜hed,Ž¡’õºâit–gômeans“normal“form“has“bAÇeen“ac•¾9hiev“ed.‘OThis–gôsection“dis-Ž¡’õºâcusses–ÛWhoš¾9w“those“auxiliary“functions“w˜ork.‘nxF‘ÿ:«or“simplicit˜y‘ÿ:«,Ž¡’õºâthey–¬!are“treated“as“a“single“function,›ÑÔcalled“ëMsimpº,˜w¾9orkingŽ¡’õºâon–Tthe“union“of“ëMAbsVal“ºand“ëMContextº,“called“ëMTermº.ަ’õºâT‘ÿ:«o–iþmaximise“pAÇerformance,‘)eac¾9h“pass“of“ëMsimp“ºtries“to“do“asŽ¡’õºâm•¾9uc“h–éÑas“pšAÇossible,‘ðso“as“to“minimise“the“n•¾9um“b˜er–éÑof“passesŽ¡’õºârequired.‘€AMeasuremen•¾9ts›6šsho“w“ed˜the˜v‘ÿ|rast˜ma‘ƒŽjorit“y˜of˜termsŽ¡’õºâreac¾9h–Å#normal“form“in“one“pass,‘ñand“no“term“has“bAÇeen“ob-Ž¡’õºâserv¾9ed–Tto“require“more“than“three“passes.ަ’õºâThe–L?individual“rewrite“rules“are“classi ed“in¾9to“groups“(rep-Ž¡’õºâresenš¾9ted–Åïas“lists)“b˜y“the“roAÇot“sym˜bAÇol“of“the“term“whic˜h“theyŽ¡’õºârewrite.‘¼±The–J¿mecš¾9hanism“whic˜h“directs“the“application“ofŽ¡’õºârewrite–ðÖrules“ensures“that“eac¾9h“rule“is“only“applied“to“termsŽ¡’õºâpšAÇossessing–xÈthe“relev‘ÿ|ran¾9t“ro˜ot“sym•¾9b˜ol.‘FÌEac“h–xÈrule“is“imple-Ž¡’õºâmenš¾9ted–Tas“a“function“of“t˜ypAÇe“ëMTerm–¹–->“Maybe“Termº,‘Twhere:ޤÐO’ç¤ëMdata–¹–Maybe“a“=“Nothing“|“Just“aŽ¡’õºâºAs–•bAÇecomes“clear“shortly‘ÿ:«,‘ "wš¾9e“need“to“kno˜w“whether“the“ap-ޤ ’õºâplication–q¡of“a“rewrite“rule“has“had“an¾9y“e ect.‘1VW‘ÿ:«e“couldŽ¡’õºâmak•¾9e›ì6eac“h˜rule˜ha“v“e˜t“ypAÇe˜ëMTerm–¹–->“Term˜ºand˜compare˜theŽ¡’õºâterm–­ bšAÇefore“and“after“application,‘öbut“this“seems“ab˜om-Ž¡’õºâinably–.Œinecienš¾9t,‘tÚbAÇecause“the“rule“itself“\kno˜ws"“when“itŽ¡’õºâhas–¹`made“a“c•¾9hange.‘”Therefore,‘âcw“e–¹`encoAÇde“that“kno¾9wledgeŽ¡’õºâin–³Ythe“return“v‘ÿ|ralue“bš¾9y“passing“bac˜k“ëMNothing“ºif“there“is“noŽ¡’õºâc•¾9hange.‘֎Observ“e–S^that“the“returned“ëMMaybe‘¹–Term“ºv‘ÿ|ralue“is“in-Ž¡’õºâstan•¾9tly›¨“disassem“bled˜using˜a˜Hask“ell˜case˜expression,‘¾Sto˜ ndŽ¡’õºâout–¹whether“the“rule“has“succeeded.‘ä Therefore,‘>a“Hask¾9ellŽ¡’õºâimplemen•¾9tation›íŽwhic“h˜returns˜constructors˜in˜registers,‘õ‚lik“eŽ¡’õºâGlasgo•¾9w›—¦Hask“ell˜[PJ92Ž‘L ],‘¸:nev“er˜actually˜builds˜the˜ëMNothingŽ¡’õºâºor–TëMJust“ºclosure“in“the“heap,“a“pleasing“little“eciency‘ÿ:«.ަ’õºâLet–9oëMt“ºdenote“a“term,‘‚uand“ëMrulesfor(t)“ºdenote“the“list“ofŽ’õºâŸ@‰ff_ÿ Ÿ× ‘ r}Ÿüûró†›Zcmr5°1ŽŽ‘Y±One–5of“the“sharp7er“wits“in“the“functional“programming“commÈãu-ޤnitšÈãy‘ÿZª,–±Èon“reading“an“early“draft,“commen˜ted:ŽŸ ‘€HošÈãw–%could“y˜ou“let“suc˜h“a“w˜onderful“example“of“self-Ž¡‘€reference–Aègo“bšÈãy“unremark˜ed?‘hðI‘AÌthough˜t“it“w˜as“absolutelyŽ¡‘€marvšÈãelous–:that“y˜ou“decided“to“use“an“innermost- rstŽ¡‘€scšÈãheme–A¥in“the“term“rewriter“whic˜h“is,›Xafter“all,˜the“wholeŽ¡‘€p7oinÈãt–øof“Anna's“existance“in“the“Real“W‘ÿZªorld“outside“it-Ž¡‘€self‘!Ž¡ŽŽŽŽŸ’åäº17ŽŽŒ‹²È •ºâ ý? £ ý€‘íºâºrewrite–Мrules“relev‘ÿ|ranš¾9t“to“the“roAÇot“sym˜bAÇol“of“ëMt.“simp(t)“ºisޤ ‘íºâcomputed–Tas“follo¾9ws:Ž©ÐO‘ûç¤ëMsimp(t)Ž¡‘ f=‘¹–schedule(t_inner_simp)Ž¡‘‡’whereŽ¡‘!´Tt_inner_simpŽ¡‘/á=–¹–t“with“simp“applied“to“t's“subtermsŽ¡¡‘ûç¤schedule(t)Ž¡‘ f=–¹–rewrite_with(rulesfor(t),“t)Ž¡¡‘ûç¤rewrite_with([],‘¹–t)Ž¡‘ f=‘¹–tŽ¡¡‘ûç¤rewrite_with((rule:rules),‘¹–t)Ž¡‘ f=–¹–case“(rule“t)“ofŽ¡‘!´TNothing–¹–->“rewrite_with(rules,t)Ž¡‘!´TJust–¹–t2“->“schedule(t2)ަ‘íºâºFirstly‘ÿ:«,›6$ëMtº's–üasubterms“are“simpli ed,˜giving“ëMt_inner_simp.Ž¡‘íºâºThis–"óis“passed“to“inš¾9termediary“ëMscheduleº,‘f[whic˜h“examinesŽ¡‘íºâthe–ƒ¼rošAÇot“sym¾9b˜ol“to“determine“the“relev‘ÿ|ran¾9t“list“of“rewriteŽ¡‘íºârules.‘ )OëMschedule–ÄIºpasses“the“rules“and“its“argumen¾9t“toŽ¡‘íºâëMrewrite_withº,‘™¬whic•¾9h›zÂw“orks˜its˜w“a“y˜through˜the˜list˜of˜rules.Ž¡‘íºâIf–2ºit“runs“out“of“rules,‘` it“simply“returns“the“term.‘ÐçBut“if“thereŽ¡‘íºâis–Þ a“rule,‘é‘it“is“applied“to“the“term.‘ 4This“either“has“no“e ect,Ž¡‘íºâin–÷whic¾9h“case“the“next“rule“is“tried,‘/‚or“it“proAÇduces“a“newŽ¡‘íºâterm–'eëMt2º.‘R¢Noš¾9w“ëMt2“ºma˜y“w˜ell“ha˜v˜e“a“di eren˜t“roAÇot“sym˜bAÇol,Ž¡‘íºâwhic•¾9h›¶Ýw“ould˜in“v‘ÿ|ralidate˜all˜the˜remaining˜rules.‘üóSo˜rewritingŽ¡‘íºâof–TëMt2“ºis“con•¾9tin“ued›Tb“y˜passing˜it˜bac“k˜to˜ëMscheduleº.ŽŸ ‘íºâThe–mnet“e ect“of“ëMschedule(t)“ºis“thš¾9us“to“k˜eep“applyingŽ¡‘íºârewrite–¯„rules“to“the“roAÇot“of“ëMt“ºun¾9til“no“applicable“rules“canŽ¡‘íºâbšAÇe–5¢found.‘ }ZThis“pro˜cess“deals“prop˜erly“with“c¾9hanges“inŽ¡‘íºâthe–ôrošAÇot“sym•¾9b˜ol.‘¸®Observ“e–ôthat“the“call“to“ëMschedule“ºfromŽ¡‘íºâëMrewrite_with–HSºis“not“necessary“for“correctness.‘µmW‘ÿ:«e“couldŽ¡‘íºâsimply–+´return“ëMt2“ºat“this“pAÇoinš¾9t.‘ΐWhat“this“w˜ould“mean“is“thatŽ¡‘íºâanš¾9y–8ípAÇossible“rewrites“of“ëMt2“ºw˜ould“bAÇe“dela˜y˜ed“un˜til“the“nextŽ¡‘íºâsimpli cation–7Îpass,‘drather“than“bAÇeing“done“straighš¾9t“a˜w˜a˜y‘ÿ:«.‘ҙSoŽ¡‘íºâomitting–~the“re-sc¾9hedule“implies“more“simpli cation“passesŽ¡‘íºâand–Ta“serious“loss“of“eciency‘ÿ:«.ŽŸ5‘íºâ¹4.3Ž‘G·Dealing–LÎwith“lambFfdas“and“applicationsŽŸm‘íºâºThe–éŸpresence“of“ëMAbsLamº,‘^²ëMAbsAp“ºand“ëMAbsVar“ºterms“in¾9tro-Ž¡‘íºâduces–Ö?the“need“to“pšAÇerform“lam¾9b˜da“calculus-lik¾9e“substi-Ž¡‘íºâtution.‘ *What–çfollo¾9ws“applies“equally“to“the“dual“con-Ž¡‘íºâstructions–°ªëMCtxLamº,‘—ëMCtxAp“ºand“ëMCtxVarº.‘îsIn“particular,Ž¡‘íºâëMsimp–|Uºneeds“to“bAÇe“able“to“deal“with“terms“of“the“formŽ¡‘íºâëM(AbsAp–¹–(AbsLam“v“e)“a)º.‘ pNaturally‘ÿ:«,‘‚wš¾9e–Ûàcan“reac˜h“di-Ž¡‘íºârectly–Béfor“the“blunderbuss“solution:‘ w™devise“a“functionŽ¡‘íºâëMsubst(e,v,a)–Xžºto“replace“free“oAÇccurrences“of“ëMv“ºin“ëMe“ºwith“ëMa,Ž¡‘íºâºand–Templo¾9y“it“in“the“rewrite“rule:ަ‘ûç¤ëMAbsAp–¹–(AbsLam“v“e)“a–,Â===>“subst(e,v,a)ަ‘íºâºTwš¾9o–Adefects“are“apparen˜t.‘ ðFirstly‘ÿ:«,‘L‰since“ëMsimp“ºis“committedŽ¡‘íºâto–8Ðdoing“innermost- rst“simpli cation,‘dëbAÇoth“function“and“ar-Ž¡‘íºâgumenš¾9t–B–are“simpli ed“extensiv˜ely“bšAÇefore“substitution“b˜egins.Ž¡‘íºâOur–­ßhands“are“noš¾9w“tied:‘èµw˜e“cannot“mak˜e“the“lam˜bAÇda/applyŽ¡‘íºâterm–ãereduction“an¾9y“lazier.‘†¤Ineciency“is“the“second“com-Ž¡‘íºâplain•¾9t.‘0‹This›q]sc“heme˜demands˜a˜complete˜substitution˜passŽ¡‘íºâo•¾9v“er–TëMe“ºfor“evš¾9ery“argumen˜t.ŽŽŽ ý€’õºâAn–R±altogether“nicer“solution“is“to“forget“abAÇout“ëMsubst“ºand“theޤ ’õºârewrite–»drule.‘ŸInstead,‘äèwš¾9e“equip“ëMsimp“ºwith“an“en˜vironmen˜tŽ¡’õºâëMenv–?oºwhic¾9h“binds“ëMAbsº-v›ÿ|rariables“to“v˜alues.‘šÀNo•¾9w,‘‰õgiv“e‘?oëMsimpŽ¡’õºâºa–©couple“of“spAÇecial“cases.‘ØöThese“omit“the“usual“simpli ca-Ž¡’õºâtion–›·of“subterms,‘½Oand“bš¾9ypass“the“general“rewriting“mec˜ha-Ž¡’õºânism.‘¥6In–˜Athis“w•¾9a“y›˜Aw“e˜regain˜precise˜con“trol˜o“v“er˜the˜orderŽ¡’õºâof–ý×rewrites,‘‰and“no“separate“substitution“passes“are“needed.Ž¡’õºâV‘ÿ:«ariables–Tare“simply“loAÇok¾9ed“up:ޤÐO’ç¤ëMsimp–¹–env“(AbsVar“v)“=“env“vŽ¡’õºâºOn–Ýencounš¾9tering“ëM(AbsAp–¹–f“a)º,‘îw˜e–Ýneed“to“try“and“turn“ëMfޤ ’õºâºinš¾9to– ³an“ëM(AbsLam–¹–v“e)º.‘>The– ³ob˜vious“w˜a˜y“to“do“this“is“b˜yŽ¡’õºâapplying–ôÒëMsimp“ºto“ëMfº,‘ûSbut“this“wš¾9ould“bAÇe“a“big“w˜aste“of“time“ifŽ¡’õºâëMf–×ãºis“in“that“form“already‘ÿ:«.‘õSo“there“is“a“spAÇecial“c•¾9hec“k–×ãfor“thisŽ¡’õºâcase.‘‰¼The›ämen•¾9vironmen“t˜is˜then˜augmen“ted˜with˜a˜bindingŽ¡’õºâfor–³¹ëMvº,‘ÛRand“simpli cation“con•¾9tin“ues–³¹with“ëMeº.‘÷žBy“c¾9hoAÇosing“toŽ¡’õºâbind–íÉëMv“ºto“ëMa“ºor“ëMsimp–¹–env“aº,‘õ²w¾9e–íÉcan“again“v‘ÿ|rary“the“strictnessŽ¡’õºâof–y;the“scš¾9heme.‘H$The“latter“c˜hoice“giv˜es“bšAÇetter“p˜erformance,Ž¡’õºâso–Tthe“spAÇecial“case“for“ëM(AbsAp–¹–f“a)‘Tºis:Ž©ÐO’ç¤ëMsimp–¹–env“(AbsAp“f“a)Ž¡’f=–¹–let“sa“=“simp“env“aŽ¡’.mêsf–¹–=“simp“env“fŽ¡’‡’inŽ¡’‡’case–¹–f“ofŽ¡’)´TAbsLam–¹–v“eŽ¡’7á->–¹–simp“env{v“:->“sa}“eŽ¡’)´TotherŽ¡’7á->–¹–case“sf“ofŽ¡’T:šAbsLam–¹–v2“e2Ž¡’bg\->–¹–simp“env{v2“:->“sa}“e2Ž¡’T:šotherŽ¡’bg\->–¹–AbsAp“sf“saަ’õºâºIf–òÁëMf“ºsimply“refuses“to“bAÇe“rewritten“in¾9to“an“ëMAbsLamº,‘ù«the“termŽ¡’õºâhas–,òits“subterms“simpli ed“and“is“then“returned“as-is.‘cJThisŽ¡’õºâis–Dzconsistenš¾9t“with“ho˜w“normal“cases“are“dealt“with,‘CsinceŽ¡’õºâthere–Tare“no“more“ëMAbsAp“ºrewrite“rules.ŽŸ ’õºâAn–—-ëMAbsVar“ºconstruct“can“refer“not“just“to“v‘ÿ|rariables“bAÇoundŽ¡’õºâb¾9y–=‹a“surrounding“ëMAbsLamº,‘‡˜but“also“to“the“abstract“v‘ÿ|raluesŽ¡’õºâof–6/other“functions.‘T‘ÿ:«o“deal“with“these,‘~fw¾9e“\preload"“theŽ¡’õºâëMAbsº-en•¾9vironmen“t–°Fwith“suitable“bindings“bAÇefore“starting“sim-Ž¡’õºâpli cation.‘}òFinally‘ÿ:«,‘èŸnote–‹*that“the“dual“ëMCtxº-constructionsŽ¡’õºâare–ü¿dealt“with“in“the“same“w•¾9a“y‘ÿ:«,‘6™so–ü¿ëMsimp“ºcarries“t•¾9w“o‘ü¿en“vi-Ž¡’õºâronmen¾9ts,‘HËrather–>€than“just“one.‘—óThe“only“di erence“is“thatŽ¡’õºâa–þëMCtxVar“ºcan“only“refer“to“ëMCtxLam“ºbAÇound“v‘ÿ|rariables.‘nTheseŽ¡’õºât•¾9w“o›rÙen“vironmen“ts˜are˜henceforth˜referred˜to˜as˜ëMaenv˜ºandŽ¡’õºâëMcenv‘TºrespAÇectiv¾9ely‘ÿ:«.ŽŸ5’õºâ¹4.4Ž’ G·Avoiding–LÎin nite“b¹™ranchingޤm’õºâ4.4.1Ž’úíA–LÎnaive“app¹™roachŽ¡’õºâºSection–323.4“in¾9troAÇduced“the“ëMCaseU›3*ºand“ëMCaseUU˜ºconstructionsޤ ’õºâas–¹yone“of“the“fundamenš¾9tal“mec˜hanisms“for“disassem˜blingŽ¡’õºâconš¾9texts.‘uA‘‡Øserious–ˆ8problem“whic˜h“bAÇecomes“apparen˜t“asŽ¡’õºâsošAÇon–UÄas“one“starts“ xp˜oin¾9ting“is“the“p˜oten¾9tial“for“in niteŽ¡’õºâbranc•¾9hing.‘pFixpšAÇoin“ting–Tpro˜duces“expressions“lik¾9eަ’ç¤ëMCaseU–¹–e“(CaseU“e“w“x)“(CaseU“e“y“z)ަ’õºâºwhicš¾9h–Tis“equiv‘ÿ|ralen˜t“to:ŽŽŽŽŽŸ’åä18ŽŽŒ‹Ó¦ •ºâ ý? £ ý€‘ûç¤ëMCaseU–¹–e“w“zŽ©ÐO‘íºâºW‘ÿ:«e–¶©can“get“round“this“b¾9y“designing“the“normal“form“so“thatޤ ‘íºâfor– ±a“term“ëM(CaseU–¹–e“a“b)º,‘ Ÿneither– ±subterm“ëMa“ºnor“ëMb“ºma¾9y“doŽ¡‘íºâa–fÕëMCaseU‘fÀºon“ëMeº.‘òT‘ÿ:«o“ac•¾9hiev“e–fÕthis“normalisation“requires“usingŽ¡‘íºâpartial–˜fkno¾9wledge“abAÇout“the“v‘ÿ|ralue“of“ëMe“ºwhen“simplifying“ëMaŽ¡‘íºâºand‘TëMbº.ŽŸ ‘íºâT‘ÿ:«o–@óimplemenš¾9t“this,‘‹Úw˜e“could“adopt“the“follo˜wing“sc˜heme.Ž¡‘íºâGivš¾9e–^#ëMsimp“ºy˜et“another“en˜vironmen˜t,–°VëMselenvº,“whic˜h‘^#mapsŽ¡‘íºâswitc¾9h–…expressions“seen“in“surrounding“ëMCaseU‘„ÿºand“ëMCaseUUsŽ¡‘íºâºto–N"partial“information“abAÇout“their“v‘ÿ|ralue.‘ÆÚWhen“a“nestedŽ¡‘íºâëMCase–s ºexpression“is“encounš¾9tered,‘‹3loAÇok“up“its“switc˜h“v‘ÿ|ralue“inŽ¡‘íºâëMselenvº.‘`¥If–,there“is“a“correspAÇonding“en¾9try‘ÿ:«,‘1¿this“ëMCase“ºexpres-Ž¡‘íºâsion–¿›mš¾9ust“bAÇe“examining“a“con˜text“whic˜h“has“already“bAÇeenŽ¡‘íºâloAÇokš¾9ed–—Öat,‘¸vso“the“ëMCase“ºexpression“is“replaced“b˜y“whic˜hev˜erŽ¡‘íºâarm–é;the“table“enš¾9try“sa˜ys“is“correct.‘˜$F‘ÿ:«or“example,‘4giv˜en“aŽ¡‘íºâcallަ‘ûç¤ëMsimp–¹–selenv“(CaseU“e“(CaseU“e“w“x)“(CaseU“e“y“z))ަ‘íºâºsimpli cation–,Ëof“ëM(CaseU–¹–e“w“x)–,˺is“done“with“ëMselenv“ºbindingŽ¡‘íºâëMe–/ƒºto“ëMStop1º,‘]zand“simpli cation“of“ëM(CaseU–¹–e“y“z)–/ƒºis“done“withŽ¡‘íºâëMselenv–`Lºbinding“ëMe“ºto“some“v‘ÿ|ralue“of“the“form“ëMUp1‘¹–[...]º.‘àThisŽ¡‘íºâpartial–_$information“abAÇout“ëMe“ºimmediately“allo¾9ws“the“systemŽ¡‘íºâto–‡(reduce“the“t•¾9w“o–‡(subterms“to“ëMw“ºand“ëMz“ºrespAÇectiv¾9ely‘ÿ:«.‘qìProp-Ž¡‘íºâagation–ûìof“information“abAÇout“ëMCaseUU‘ûåºselector“v‘ÿ|ralues“is“doneŽ¡‘íºâanalogously‘ÿ:«.ŽŸ ‘íºâëMselenv–(cºis“augmenš¾9ted“eac˜h“time“a“ëMCaseU›(^ºor“ëMCaseUU˜ºis“\goneŽ¡‘íºâpast".‘ ?îA‘Ë problem–ËÓis“what“happAÇens“when“w¾9e“go“pastŽ¡‘íºâa›ÙÍëM(CtxLam–¹–v“e)º,‘Jësince˜this˜w•¾9ould˜in“v‘ÿ|ralidate˜an“y˜k“eys˜inŽ¡‘íºâëMselenv–9ºconš¾9taining“free“v‘ÿ|rariable“ëMvº.‘" Remem˜bAÇer“that“the“k˜eysŽ¡‘íºâare–üarbitrary“expressions,‘5²rather“than“mere“v‘ÿ|rariables.‘ІAnŽ¡‘íºâexpAÇensivš¾9e–£Wsolution“is“to“ lter“out“all“(k˜ey‘ÿ:«,‘º$v‘ÿ|ralue)“pairs“whic˜hŽ¡‘íºârefer–àœto“ëMvº,‘nbut“that's“o•¾9v“erkill.‘~HIt–àœis“c¾9heapAÇer“to“completelyŽ¡‘íºâemptš¾9y–{°ëMselenv“ºat“ev˜ery“ëMCtxLamº.‘O„This“doAÇesn't“lose“informa-Ž¡‘íºâtion–kbAÇecause“the“abstract“inš¾9terpreter“nev˜er“builds“con˜textŽ¡‘íºâexpressions–÷ewhere“wš¾9e“need“to“main˜tain“selector“informationŽ¡‘íºâacross–”’ëMCtxLam“ºbAÇoundaries.‘ñ…F‘ÿ:«or“example,‘®Sit“nevš¾9er“builds“an˜y-Ž¡‘íºâthing‘Tlik¾9e:ަ‘ûç¤ëMCaseU–¹–s1“(\c1“->“...“(CaseU“s2“....))Ž¡‘&mê(\c2–¹–->“...“(CaseU“s2“....))ŽŸ5‘íºâ¹4.4.2Ž‘ úíGeneralising–LÎthe“schemeŽŸm‘íºâºA‘œ›little–œ¾thoughš¾9t“sho˜ws“our“solution,‘¾˜whilst“pAÇerfectly“w˜ork-Ž¡‘íºâable,‘µDis–@toAÇo“wš¾9eak.‘ôiW‘ÿ:«e“need“a“more“general“w˜a˜y“to“propagateŽ¡‘íºâso-called–ëá\ëMselenv“ºinformation"“around,‘!„as“can“bAÇe“seen“b¾9yŽ¡‘íºâconsidering:ަ‘ûç¤ëMCMeet–¹–[e,“UpUp2“[Stop1,“Stop1]]ަ‘íºâºInitially‘ÿ:«,‘Òit–¬UlošAÇoks“lik¾9e“nothing“more“can“b˜e“done“with“this.Ž¡‘íºâBut–®if,›ab¾9y“loAÇoking“in“ëMselenvº,˜wš¾9e“can“sho˜w“that“ëMe“ºhas“anŽ¡‘íºâëMUpUp2‘¹–[...]–Tºv‘ÿ|ralue,“then:ަ‘ZÐëMCMeet–¹–[e,“UpUp2“[Stop1,“Stop1]]Ž¡‘ûç¤=–¹–UpUp2“[Stop1,“Stop1]ަ‘íºâºWhat–}twš¾9e“really“need“is“a“general“mec˜hanism“for“propagat-Ž¡‘íºâing–ÓTëMselenv“ºinformation.‘VqT‘ÿ:«o“bAÇe“fully“general,‘Ôwš¾9e“will“ha˜v˜eŽ¡‘íºâto–W¯searcš¾9h“ëMselenv“ºfor“eac˜h“term“ëMsimp“ºencoun˜ters.‘ã€This“pro-Ž¡‘íºâcess–ÆÀcan“bAÇe“rolled“inš¾9to“the“general“mec˜hanism“of“ëMsimpº,‘ób˜yŽŽŽ ý€’õºâsearc¾9hing–«ÄëMselenv“ºafter“ëMsimp“ºruns“out“of“applicable“rewriteޤ ’õºârules.‘5ÂW‘ÿ:«e–ÅexpšAÇect“to“disco•¾9v“er–Ånothing“ab˜out“the“v‘ÿ|rast“ma-Ž¡’õºâjoritš¾9y–Xµof“terms,‘iin“whic˜h“case“ëMsimp“ºacts“as“bAÇefore.‘æ’But,‘iforŽ¡’õºâa–luc¾9ky“few,‘? ëMselenv“ºtells“us“a“little“abAÇout“the“term:‘øÉit“isŽ¡’õºâeither›>jëMStop1º,–ˆ°ëMStop2º,“ëMUp2º,“ëMUp1–¹–[...]˜ºor˜ëMUpUp2“[...]º.‘—³InŽ¡’õºâthe–¼Ô rst“three“cases,‘·wš¾9e“can“ob˜viously“replace“the“term“withŽ¡’õºâthe–relev›ÿ|ran¾9t“v˜alue,‘õbut“the“other“t•¾9w“o–are“problematic.‘'Ho¾9wŽ¡’õºâcan–y wš¾9e“exploit“partial“information“lik˜e“this?‘G™Conceptually‘ÿ:«,Ž¡’õºâwš¾9e–%need“to“add“a“foAÇotnote“to“the“v‘ÿ|ralue“sa˜ying,‘ ûfor“example,Ž¡’õºâ\P‘ÿ:«.S.–)£This“v‘ÿ|ralue“is“kno¾9wn“to“bšAÇe“ëMUpUp2‘¹–[...]º",‘.·and“mo˜difyŽ¡’õºâthe–Trewrite“rules“to“takš¾9e“accoun˜t“of“suc˜h“foAÇotnotes.ŽŸ ’õºâThis–LHall“sounds“rather“clumsy‘ÿ:«,‘Zbut“there“is“a“neat“solution.Ž¡’õºâRecall– qsection“3.4“in¾9troAÇduced“ëMDefU‘ 1ºand“ëMDefUUº.“ëMDefºs“standŽ¡’õºâfor–Ÿg\de nitely",‘¶ýand“are“inš¾9tended“as“a“w˜a˜y“of“attac˜hing“suc˜hŽ¡’õºâa–TèfoAÇotnote“to“a“v‘ÿ|ralue.‘Û-The“in•¾9tuitiv“e–Tèreading“of“ëM(DefU‘¹–e)“ºisŽ¡’õºâ\I'm–†not“sure“what“the“exact“v‘ÿ|ralue“of“ëMe“ºis,‘¢¾but“I‘…ódo“kno¾9w“it'sŽ¡’õºâan–zòëMUp1‘¹–[...]“ºv‘ÿ|ralue".‘MISo“noš¾9w,‘”Yon“disco˜v˜ering“from“ëMselenvŽ¡’õºâºthat–x¶a“term“ëMc“ºhas“an“ëMUp1›¹–[...]“ºor“ëMUpUp2˜[...]“ºv‘ÿ|ralue,‘‘Žw¾9eŽ¡’õºâmerely–èµneed“to“wrap“ëMc“ºin“ëMDefU›è~ºor“ëMDefUU˜ºrespAÇectiv¾9ely‘ÿ:«.‘–“AllŽ¡’õºâthat–’/remains“to“do“is“moAÇdify“rewrite“rules“to“takš¾9e“accoun˜t“ofŽ¡’õºâëMDefU–BHºand›BTëMDefUU“ºas˜appropriate.‘£pThis˜mec¾9hanism˜subsumesŽ¡’õºâthe–Tprevious“one.‘pConsider“again:Ž©½ì’ç¤ëMsimp‘¹–selenvŽ¡’‡’(CaseU–¹–e“(CaseU“e“w“x)“(CaseU“e“y“z))ަ’õºâºIgnoring–‚ÀpAÇossible“c¾9hanges“to“ëMwº,–žëMxº,“ëMy–‚Àºand“ëMzº,‘žëMsimp“ºtranformsŽ¡’õºâthis‘Tto:ަ’ç¤ëMCaseU–¹–e“(CaseU“Stop1“w“x)“(CaseU“(DefU“e)“y“z)ަ’õºâºApplication–Tof“the“rewrite“rulesަ’ç¤ëMCaseU–¹–Stop1‘æXa“b–,Â===>“aŽ¡’ç¤CaseU–¹–(DefU“e)“a“b–,Â===>“bަ’õºâºyields–Tthe“desired“result:ަ’ç¤ëMCaseU–¹–e“w“zަ’õºâºRecall–&the“other“example,‘j,in“whic¾9h“ëMselenv“ºbinds“ëMe“ºto“anŽ¡’õºâëMUpUp2‘¹–[...]‘Tºv‘ÿ|ralue:ަ’ç¤ëMCMeet–¹–[e,“UpUp2“[Stop1,“Stop1]]ަ’õºâºAfter–Î}wrapping“ëMDefUU‘ÎMºaround“ëMeº,‘üÇthe“follo¾9wing“sequence“ofŽ¡’õºârewrites–Tis“pAÇossible:ަ’ ZÐëMCMeet–¹–[DefUU“e,“UpUp2“[Stop1,“Stop1]]Ž¡¡’ç¤=–¹–UpUp2“[“CMeet“[SelUU“1“e,“Stop1],Ž¡’3'€CMeet–¹–[SelUU“2“e,“Stop1]“]Ž¡¡’ç¤=–¹–UpUp2“[Stop1,“Stop1]ަ’õºâºAgain,‘ôåthe–È/desired“result“is“obtained.‘5All“w¾9e“had“to“do“isŽ¡’õºâinclude–Ta“rewrite“rule“deriv¾9ed“from“this:ަ’ç¤ëMCMeet–¹–[“UpUp2“[x1,“x2],‘ s,UpUp2“[y1,“y2]“]Ž¡’f===>‘,ÂUpUp2–¹–[“CMeet“[x1,“y1],Ž¡’Xô0CMeet–¹–[x2,“y2]“]ަ’õºâºBy–\ŸmoAÇdifying“the“rule“so“that“one“of“the“initial“terms“isŽ¡’õºâëM(DefUU‘¹–e)º,‘ÛHand–ÌÄbAÇearing“in“mind“the“meanings“of“ëMDefUU‘̲ºandŽ¡’õºâëMSelUU–Tº(see“section“3.4),“one“can“easily“sho¾9w“that:ŽŽŽŽŽŸ’åä19ŽŽŒ‹îs •ºâ ý? £ ý€‘ûç¤ëMCMeet–¹–[“DefUU“e,‘ s,UpUp2“[y1,“y2]“]ޤ ‘ f===>‘,ÂUpUp2–¹–[“CMeet“[SelUU“1“e,“y1],Ž¡‘Pô0CMeet–¹–[SelUU“2“e,“y2]“]Ž©ÐO‘íºâºAll–™in“all,‘ú‰a“rather“eleganš¾9t“solution“to“a“tric˜ky“problem.Ž¡‘íºâThere–Tis“just“one“ nal“ca•¾9v“eat.‘pConsider:ަ‘ûç¤ëMsimp–¹–selenv“(CaseU“e“a“b)ަ‘íºâºIf–ùFw¾9e“cannot“ nd“a“v‘ÿ|ralue“for“ëMe“ºin“ëMselenvº,‘þãthe“ëMCaseU‘ù?ºexpres-Ž¡‘íºâsion–͗maš¾9y“still“bAÇe“remo˜v‘ÿ|rable“b˜y“the“follo˜wing“means.‘E:FindŽ¡‘íºâin–ÔëMselenv“ºa“kš¾9ey“ëMk“ºfor“whic˜h“w˜e“can“pro˜v˜e“that“ëMkŽ‘ëPv‘zgëMeŽ‘ 3ýº,Ž¡‘íºâand–æ(for“whic¾9h“ëMk“ºis“bAÇound“to“some“ëMUp1‘¹–[...]“ºv‘ÿ|ralue.‘ŽìSo“ëMeŽ¡‘íºâºmš¾9ust–&also“bind“to“some“ëMUp1‘¹–[...]“ºv‘ÿ|ralue,‘*Cso“w˜e“can“replaceŽ¡‘íºâëM(CaseU–¹–e“a“b)–àºb¾9y“ëM(CaseU–¹–(DefU“e)“a“b)º.‘'ëMCaseUUºs‘àare,‘ÃasŽ¡‘íºâev•¾9er,‘W¬analogous.‘»ªSo›Jgw“e˜migh“t˜bAÇe˜able˜to˜do˜just˜a˜little˜bitŽ¡‘íºâbAÇetter– ¼mš¾9y“taking“monotonicit˜y“of“k˜eys“in˜to“accoun˜t“whenŽ¡‘íºâsearc¾9hing‘TëMselenvº.ŽŸ5‘íºâ¹4.5Ž‘G·Avoiding–LÎan“expFfonential“explosionŽŸm‘íºâºAlthough–4¶wš¾9e“ha˜v˜e“a˜v˜oided“non-termination“via“in niteŽ¡‘íºâbrancš¾9hing,‘ïŠanother–³insidious“problem“lurks:‘.terms“whic˜hŽ¡‘íºâexpand–™,expšAÇonen¾9tially“for“a“while,‘º"b˜efore“shrinking“bac¾9k“toŽ¡‘íºâa–#compact“normal“form.‘ÝSucš¾9h“bAÇeha˜viour“causes“the“termŽ¡‘íºârewriter–Âlto“run“out“of“memory“simplifying“seemingly“in-Ž¡‘íºâsigni can¾9t–¸expressions.‘yThe“problem“manifests“itself,‘à­onceŽ¡‘íºâagain,‘nŸwith–\ÃëMCaseU›\±ºand“ëMCaseUU˜ºterms.‘ò¾The“normal“form“re-Ž¡‘íºâquires–ª¸that“the“switc¾9h“expression“cannot“itself“bAÇe“a“ëMCaseU‘ªºorŽ¡‘íºâëMCaseUUº,–Tgiving“rise“to“some“rules“of“the“form:ަ‘ûç¤ëMCaseUU–¹–(CaseUU“a“b“c“d)“e“f“gŽ¡‘ûç¤===>Ž¡‘ûç¤CaseUU–¹–a“(CaseUU“b“e“f“g)Ž¡‘&mê(CaseUU–¹–c“e“f“g)Ž¡‘&mê(CaseUU–¹–d“e“f“g)ަ‘íºâºThe–Ðzproblem“ošAÇccurs“b˜ecause“of“the“w•¾9a“y–ÐzëMrewrite_with“ºat-Ž¡‘íºâtempts–ž5to“apply“rewrite“rules“to“the“roAÇot“term“un¾9til“no“moreŽ¡‘íºâcan–ËbAÇe“found.‘óÔIf“ëMa“ºis“itself“a“ëMCaseUU‘Œºterm,‘DhëMrewrite_withŽ¡‘íºâºwill–îéimmediately“reapply“the“rule,‘¥Mtrebling“the“expres-Ž¡‘íºâsion–Æÿsize“again.‘ 1rIt“w¾9ould“bšAÇe“b˜etter“to“lo˜ok“to“see“ifŽ¡‘íºâw¾9e–åâcan“do“some“simpli cations“on“the“ëM(CaseUU–¹–b“e“f“g)º,Ž¡‘íºâëM(CaseUU–¹–c“e“f“g)–køºand“ëM(CaseUU–¹–d“e“f“g)–køºterms“ëRb•‡efor“e‘køºse-Ž¡‘íºâlecting–FÖanother“rewrite“rule“for“the“roAÇot“term.‘°öThere's“aŽ¡‘íºâv¾9ery›yZgo•AÇo“d˜c•¾9hance˜w“e˜can,‘˜bAÇecause˜it˜is˜lik“ely˜that˜w“e˜alreadyŽ¡‘íºâkno¾9w–üËenough“abšAÇout“ëMbº,‘³ëMc“ºand“ëMd“ºto“eliminate“their“asso˜ciatedŽ¡‘íºâëMCaseUUºs.‘iÙIt–/"ma¾9y“also“turn“out“that“ëMa“ºis“the“same“as“ëMbº,‘5•ëMc“ºorŽ¡‘íºâëMdº,–Tand“this“is“helpful“toAÇo.ŽŸ ‘íºâImplemenš¾9ting–oÍthis“is“not“only“easy‘ÿ:«,‘Æjbut“essen˜tial.‘+ÚWhenŽ¡‘íºâëMrewrite_with–I$ºdetects“that“a“rewrite“rule“has“created“aŽ¡‘íºâëMCaseUU‘3ºterm,‘»Îit–4doAÇes“not“immediately“seek“out“anotherŽ¡‘íºârewrite–àarule“for“the“roAÇot“term.‘}–Instead,‘$it“tries“to“rewriteŽ¡‘íºâthe–’subterms“as“m•¾9uc“h–’as“pšAÇossible,‘¬Âand“only“then“lo˜oks“againŽ¡‘íºâat–3<the“rošAÇot“term.‘v'This“minor“mo˜di cation“pro•¾9v“es›3<v“ery˜suc-Ž¡‘íºâcessful–Tat“a•¾9v“oiding›TexpAÇonen“tial˜explosions.ŽŸ5‘íºâ¹4.6Ž‘G·T‘ÿ,Ìyp•Ffe-sp“eci c–LÎëMAbsVal“¹optimisationŽŸm‘íºâºThe–ì abstract“v‘ÿ|ralues“(ëMAbsValsº)“of“all“non-function-space“ob-Ž¡‘íºâjects–—‘are“pšAÇoin¾9ts“in“a“one“p˜oinš¾9t“domain.‘£(Therefore,‘¸ for“an˜yŽ¡‘íºâëMAbsVal– Xºat“all,‘ ‹if“w¾9e“can“determine“that“the“ob‘ƒŽject's“domainŽ¡‘íºâis–È+non-functional,‘ôàwš¾9e“can“man˜ufacture“an“equiv‘ÿ|ralen˜t“v‘ÿ|ralueŽŽŽ ý€’õºâfrom–)@ëMARec“ºand“ëMANonRecº.›X3This“is“extremely“useful.˜The“def-ޤ ’õºâinition–/cof“ëMAbsValº,›5çpresen¾9ted“in“section“3.3,˜is“augmen¾9ted“soŽ¡’õºâwš¾9e–¥.can“iden˜tify“the“domain“for“an˜y“term.‘ËÿThis“is“done“b˜yŽ¡’õºâtagging–^Æeacš¾9h“ëMAbsVal“ºwith“a“con˜text“domain“v‘ÿ|ralue,‘ƒJexcept“forŽ¡’õºâthe–TëMARec“ºand“ëMANonRec“ºcases,“where“the“domain“is“ob¾9vious.ŽŸ ’õºâThe–•žëMsimp“ºaction“for“ëMAbsValºs“noš¾9w“bAÇegins“b˜y“extracting“theŽ¡’õºâconš¾9text–®domain,‘¯and“building“a“literal“replacemen˜t“if“appro-Ž¡’õºâpriate.‘pLet–TëMdomainof(a)“ºbAÇe“the“domain“of“ëMaº.Ž©7’’ç¤ëMsimp‘¹–aŽ¡’f=–¹–let“a_ctx_domain“=“domainof(a)Ž¡’‡’inŽ¡’‡’if‘æXunitary_ctx_domain(a_ctx_domain)Ž¡’‡’then‘ s,unit_value(a_ctx_domain)Ž¡’‡’else‘ s,(...–¹–do“as“before“...)Ž¡¡’ç¤unitary_ctx_domain–¹–(Lift‘ s,(D1“x“...“x“Dn))Ž¡’f=–¹–unitary_ctx_domain(D1)“&&“...“&&Ž¡’‡’unitary_ctx_domain(Dn)Ž¡¡’ç¤unitary_ctx_domain–¹–(Lift2“(D1“x“...“x“Dn))Ž¡’f=–¹–unitary_ctx_domain(D1)“&&“...“&&Ž¡’‡’unitary_ctx_domain(Dn)Ž¡¡’ç¤unitary_ctx_domain–¹–(Ds“->“Dt)Ž¡’f=‘¹–FalseŽ¡¡’ç¤unit_value–¹–(Lift‘ s,(D1“x“...“x“Dn))Ž¡’f=–¹–ANonRec“[unit_value(D1)“...“unit_value(Dn)]Ž¡¡’ç¤unit_value–¹–(Lift2“(D1“x“...“x“Dn))Ž¡’f=–¹–ARec‘æX[unit_value(D1)“...“unit_value(Dn)]ަ’õºâºThis–T—wš¾9orks“ ne,–¤gbut,“as‘T—usual,“w˜e–T—can“do“a“little“bAÇetter.Ž¡’õºâPresenš¾9ted–&with“a“term“already“compAÇosed“en˜tirely“of“ëMARecŽ¡’õºâºand–•øëMANonRecºs,‘¯qthe“scš¾9heme“returns“a“cop˜y“of“the“term,‘¯qgivingŽ¡’õºâa–k pšAÇoten¾9tial“loss“of“sharing.‘‘A‘j±small“mo˜di cation“detectsŽ¡’õºâsuc¾9h–Tterms“and“returns“them“as-is.ŽŸ€’õºâ¹4.7Ž’ G·Impš¹™roving–LÎthe“rep˜resentation“of“contexts:‘fhëMApplyETŽŸm’õºâºF‘ÿ:«or–;tmanš¾9y“trivial-loAÇoking“functions,‘Düthe“abstract“in˜terpreterŽ¡’õºâemits–wa“remark‘ÿ|rably“cumš¾9bAÇersome“and“unin˜tuitiv˜e-loAÇokingŽ¡’õºâterm.‘ÝÂExamination–YJof“terms“from“ rst“order“functions“sho¾9wsŽ¡’õºâa›èsw•¾9a“y˜to˜cut˜do“wn˜their˜sizes.‘ zSince˜all˜abstract˜v‘ÿ|ralues˜pAÇer-Ž¡’õºâtaining–à¶to“the“argumen¾9ts“and“result“of“a“ rst“order“functionŽ¡’õºâare–H unitary‘ÿ:«,‘T·the“only“thing“one“can“ask“abAÇout“it“is“ho¾9w“theŽ¡’õºâconš¾9text–˜ùon“the“result“propagates“to“eac˜h“argumen˜t.‘òüSuppAÇos-Ž¡’õºâing–“Õwš¾9e“ha˜v˜e“ëMfº,‘­¼a“ rst“order“function“of“óO5ùž" cmmi9ëOm“ºargumen˜ts,‘­¼and“w˜eŽ¡’õºâw•¾9an“t–^to“knoš¾9w“what“con˜text“propagates“to“the“ëOnº'th“argumen˜tŽ¡’õºâif–aØthe“result“is“demanded“in“conš¾9text“ëMalphaº.‘ýA˜t“presen˜t,‘túw˜eŽ¡’õºâget–Ta“large“term“of“the“form:ަ’ç¤ëMCtxAp‘ s,(FvalC–¹–(AbsAp“(GetA“...“(AbsAp“(FvalA“f)Ž¡’¼-~a1)Ž¡’ƒzv...Ž¡’kڈai)Ž¡’$ú¾))Ž¡¡’$ú¾(Fnc–¹–aj“...“(Fnc“am“alpha)“...)ަ’õºâºwhere‘“áëMiŽ› ²(º=‘d±ëOn–b–ëP“º1–“áand“ëMjŽ˜º=‘d±ëOn–b–º+“1.‘˜What–“áthis“doAÇes“it“to“useŽ¡’õºâthe›©ªëM(AbsAp–¹–(GetA“...))˜ºconstruction˜ëOn–6äëP“º1˜times˜to˜supplyŽ¡’õºâthe–w rst“ëOn–OëP“º1–wabstract“v‘ÿ|ralue“argumen•¾9ts,‘€whic“h–wexpAÇoses“theŽŽŽŽŽŸ’åä20ŽŽŒ‹ Ö •ºâ ý? £ þ§þ ÿi€‘íºâ ÿefg‰fföÌ̟ÿþÌÍ )³4„0³2ff þäÿþ‘33ëMFsqDiffޤ ‘ ìÉ=–¹–(Fval“(\c1“->“(CJOINŽ¡‘^ùU(ApplyET#0–¹–F+“(ApplyET#1“F*“(FncC“(FncC“c1))))Ž¡‘^ùU(ApplyET#0–¹–F-“(ApplyET#0“F*“(FncC“(FncC“c1))))))Ž¡‘/¹y(\a1–¹–->“(Fval“(\c2“->“(CJOINŽ¡’¡‰(ApplyET#1–¹–F+“(ApplyET#1“F*“(FncC“c2)))Ž¡’¡‰(ApplyET#1–¹–F-“(ApplyET#0“F*“(FncC“c2)))))Ž¡‘qß­(\a2–¹–->“(ANonRec“[])))))Ž¡¡‘33FsqDiffŽ¡‘ ìÉ=–¹–(Fval“(\c1“->“(CJOINŽ¡‘^ùU{(FvalC‘¹–F+)Ž¡‘c²ë(Fnc–¹–(ANonRec“[])“(Fnc“(ANonRec“[])“{(FvalC“{*(FvalA“F*)“(ANonRec“[])*})Ž¡’…™(Fnc–¹–(ANonRec“[])“(FncC“(FncC“c1)))}))}Ž¡‘^ùU{(FvalC‘¹–F-)Ž¡‘c²ë(Fnc–¹–(ANonRec“[])“(Fnc“(ANonRec“[])“{(FvalC“F*)Ž¡’…™(Fnc–¹–(ANonRec“[])“(Fnc“(ANonRec“[])Ž¡’2(FncC–¹–(FncC“c1))))}))}))Ž¡‘/¹y(\a1–¹–->“(Fval“(\c2“->“(CJOINŽ¡’¡‰{(FvalC–¹–{*(FvalA“F+)“(ANonRec“[])*})Ž¡’¥Ù(Fnc–¹–(ANonRec“[])“{(FvalC“{*(FvalA“F*)“(ANonRec“[])*})Ž¡’ÿŸA(Fnc–¹–(ANonRec“[])“(FncC“c2))})}Ž¡’¡‰{(FvalC–¹–{*(FvalA“F-)“(ANonRec“[])*})Ž¡’¥Ù(Fnc–¹–(ANonRec“[])“{(FvalC“F*)Ž¡’ÿŸA(Fnc–¹–(ANonRec“[])“(Fnc“(ANonRec“[])“(FncC“c2)))})}))Ž¡‘qß­(\a2–¹–->“(ANonRec“[])))))ŽŸ‘^®rºFigure–T1:‘pAbstract“in¾9terpretation“of“ëMsqDiffº,“with“and“without“using“ëMApplyETŽŽ¡Ž’öff„0³2ffŽŽ *š‰fföÌ̎ŽŽŽ X€ þÃþ‘íºâëOnº'th–ªcon¾9text“map.‘ÚxThis“is“then“applied“to“ëMalpha“ºwrappAÇedޤ ‘íºâup–NÍin“a“cš¾9hain“of“ëM(Fnc‘¹–...)“ºconstructions“whic˜h“supply“theŽ¡‘íºâremaining›TëOm–8ëP“ëOn“ëP“º1˜abstract˜v‘ÿ|ralue˜argumen¾9ts.Ž© ‘íºâThis–^seems“an“enormously“wš¾9asteful“w˜a˜y“to“sa˜y“what“amoun˜tsŽ¡‘íºâto:ޤڍ‘ûç¤ëMApplyET–¹–n“f“alphaŽ¡‘íºâºThat–##is,‘S”\extract“the“ëOnº'th“con¾9text“map“from“ëMf“ºand“apply“it“toޤ ‘íºâthe–M¯con¾9text“ëMalphaº".–ŁW‘ÿ:«ell,›[Æalmost.“In–M¯fact,˜ëMfº's“ëOnº'th“con¾9textŽ¡‘íºâmap–ïHexpšAÇects“to“b˜e“applied“not“directly“to“ëMalphaº,‘öäbut“to“theŽ¡‘íºâterm›œèëM(Fnc–¹–aj“...“(Fnc“am“alpha)“...)º.‘³+It˜loAÇoks˜at˜ rstŽ¡‘íºâlik•¾9e›‚~w“e˜need˜to˜include˜the˜abstract˜v‘ÿ|ralues˜ëMaj˜ºto˜ëMam˜ºin˜theŽ¡‘íºâëMApplyET‘=šºterm.‘–'F–ÿ:«ortunately“,‘ˆ that–=æis“a•¾9v“oidable:‘m”since‘=ætheyŽ¡‘íºâare–9vall“unitary‘ÿ:«,‘‚~wš¾9e“should“nev˜er“need“to“kno˜w“what“theyŽ¡‘íºâare.‘’÷Instead,‘†·wš¾9e–<Ösimply“record“in“the“ëMApplyET‘<Šºterm“ho˜wŽ¡‘íºâmanš¾9y–8Iof“these“\trailing"“argumen˜ts“there“are.‘…OWhen“theŽ¡‘íºâterm–ê%rewriter“ nally“gets“hold“of“ëMfº's“ëOnº'th“con¾9text“map,‘ZitŽ¡‘íºâuses–Tthis“n•¾9um“bAÇer–Tto“build“a“suitable“\dumm¾9y“term"ޤڍ‘ûç¤ëM(Fnc–¹–Error“...“(Fnc“Error“alpha)“...)Ž¡‘íºâºto–~üwhicš¾9h“it“applies“the“relev‘ÿ|ran˜t“con˜text“map.‘YhIn“e ect,‘™fw˜eޤ ‘íºâa•¾9v“oided–9storing“those“trailing“argumenš¾9ts,‘ïand“fak˜ed“themŽ¡‘íºâinstead,›F using–<^ëMError“ºterms,˜bAÇecause“wš¾9e“can“guaran˜tee“theyŽ¡‘íºâwill–žònevš¾9er“bAÇe“used.‘¹JF‘ÿ:«rom“this“it“follo˜ws“that“it“is“an“errorŽ¡‘íºâfor–TëMError“ºto“appAÇear“in“the“normal“form“of“an¾9y“term.ަ‘íºâUse–î°of“ëMApplyET‘îwºshrinks“man¾9y“terms“dramatically‘ÿ:«,‘%and“en-Ž¡‘íºâhances– Çthe“time“and“space“pAÇerformance“of“the“analyser.‘>ÉAsŽ¡‘íºâan–Texample,“Figure“1“shoš¾9ws“the“abstract“in˜terpretation“ofŽŸڍ‘ûç¤ëMsqDiff–¹–x“y“=“(x“+“y)“*“(x“-“y)ŽŽŽ þÃþ’õºâºwith–LÎand“without“using“ëMApplyETº.“Of“course,‘Z­when“the“de -ޤ ’õºânitions–Öof“ëM(+)º,›®vëM(-)“ºand“ëM(*)“ºare“substituted“in,˜bAÇoth“termsŽ¡’õºâreduce–'Zto“the“same“thing.‘RNote“that“ëM(CtxAp–¹–e1“e2)‘'ZºandŽ¡’õºâëM(AbsAp–¹–e1“e2)–õoºare“written“as“ëPfëMe1›¹–e2ëPg“ºand“ëPfëM*e1˜e2*ëPg“ºre-Ž¡’õºâspAÇectiv¾9ely‘ÿ:«.ŽŸ5’õºâ¹4.8Ž’ G·No•¹™rmal›LÎfo“rms˜and˜termination˜p“ropFfertiesŽ©m’õºâºShoš¾9wing–÷that“the“term“rewriting“system“alw˜a˜ys“terminates,Ž¡’õºâand–\`prošAÇduces“normal“forms,‘^is“imp˜ortan¾9t.‘ÞÉF‘ÿ:«or“a“system“withŽ¡’õºâas–B½man¾9y“rewrite“rules“and“complications“as“this,‘NproAÇducingŽ¡’õºâa– ªcorrectness“argumen¾9t“is“a“formidable“task.‘ùrW‘ÿ:«e“hopAÇe“toŽ¡’õºâinclude–›¦one“in“a“later“v¾9ersion“of“this“papšAÇer.‘¯fAlso“to“b˜eŽ¡’õºâincluded–Ewill“bAÇe“a“listing“of“the“rewrite“rules,‘‘ along“withŽ¡’õºâtheir–D€assošAÇciated“pro˜ofs“of“correctness.‘©ôThere“are“at“presen¾9tŽ¡’õºâin–Tthe“region“of“sixt¾9y“rewrite“rules.ŽŸ-’õºâ¹5Ž’”Firsti cation–LÎand“monomo¹™rphisationŽŸ†´’õºâ5.1Ž’ G·IntroFfductionަ’õºâºAlthough–¹· rst“order“functions“are“easily“handled“b¾9y“term-Ž¡’õºârewriting–­ based“ xpAÇoinš¾9ting,‘Áøhigher“order“recursiv˜e“functionsŽ¡’õºâgivš¾9e–Ttrouble,“as“t˜ypi ed“b˜y“foldr:Ž©ÐO’ç¤ëMfoldr–¹–f“a“[]‘Y„=“aŽ¡’ç¤foldr–¹–f“a“(x:xs)‘ s,=“f“x“(foldr“f“a“xs)ަ’õºâºNaiv•¾9ely›\Í xpAÇoin“ting˜this˜giv“es˜an˜series˜of˜appro“ximationsŽ¡’õºâin–­whicš¾9h“a“term“in˜v˜olving“functional“parameter“ëMf“ºis“appliedŽ¡’õºâev¾9er–J(more“times“to“an“initial“term.‘Ø·The“term“rewriter“cannotŽŽŽŽŽŽŸ’åä21ŽŽŒ‹% •ºâ ý? £ ý€‘íºâºshoš¾9w–Õ½that“t˜w˜o“appro˜ximations“are“the“same,‘Öso“a“ xpAÇoin˜tޤ ‘íºâis–-œapparenš¾9tly“nev˜er“reac˜hed.‘eHWhat's“really“going“on“is“thatŽ¡‘íºâthe–T xpšAÇoin¾9t“of“ëMfoldr“ºdep˜ends“on“the“ xp˜oin¾9t“of“ëMfº.Ž© ‘íºâThere– lare“only“t•¾9w“o› lw“a“ys˜round˜this.‘=¸The˜ rst˜is˜to˜iter-Ž¡‘íºâate–Ÿenough“times“to“bšAÇe“sure“that“the“ xp˜oin¾9t“is“certainlyŽ¡‘íºâreac•¾9hed.‘ЂW‘ÿ:«ork›QZb“y˜Nielson˜and˜Nielson˜[NN92Ž‘>]˜giv“es˜safeŽ¡‘íºâlo•¾9w“er–ö™bšAÇounds“on“the“n•¾9um“b˜er–ö™of“iterations“needed.‘À>Unfor-Ž¡‘íºâtunately‘ÿ:«,‘Wthe–¼expAÇense“of“doing“this“makš¾9es“it“unattractiv˜e.Ž¡‘íºâNote–Talso“that“this“approac¾9h“demands“monomorphisation.ަ‘íºâThe–M9second“solution“requires“us“to“supply“a“v‘ÿ|ralue“for“ëMf“ºbAÇe-Ž¡‘íºâfore–š% xpAÇoinš¾9ting“ëMfoldr,“ºso“that“w˜e“are,›»Yin“e ect,˜no“longerŽ¡‘íºâdealing–¿xwith“a“higher-order“function.‘ÜThere“are“n¾9umerousŽ¡‘íºâw•¾9a“ys–T¾to“do“this,‘d™some“rather“obscure“in“that“they“partiallyŽ¡‘íºâsubstitute–g?in“functional“parameters“as“part“of“the“ xpAÇoin¾9t-Ž¡‘íºâing–¶hproAÇcess“[ëN?Ž‘sº].‘ÿ­By“con¾9trast,‘­Anna“adopts“a“completelyŽ¡‘íºâstraigh•¾9tforw“ard›päapproac“h:‘ӑtransform˜the˜source˜program.Ž¡‘íºâProgram–ñvtransformation“is“a“pAÇopular“sub‘ƒŽject,‘(~and“v‘ÿ|rariousŽ¡‘íºâpap•AÇers›—¶describ“e˜higher-order˜function˜remo•¾9v‘ÿ|ral˜(also˜kno“wnŽ¡‘íºâas–М rsti cation“or“spAÇecialisation)“[CD91Ž‘þä]‘¡8[NelŽ‘ žº].‘ˆThe“sc¾9hemeŽ¡‘íºâpresen•¾9ted›TbAÇelo“w˜is˜based˜on˜w“ork˜b“y˜George˜Nelan˜[NelŽ‘ žº].ަ‘íºâNot–Àall“functional“parameters“can“bAÇe“remo•¾9v“ed.‘ÇF‘ÿ:«or‘Àexam-Ž¡‘íºâple,‘õrecursivš¾9e–ífunctions“whic˜h“ha˜v˜e“accum˜ulating“functionalŽ¡‘íºâparameters–Iare“not“transformable,‘Æat“least“with“the“sc¾9hemeŽ¡‘íºâbAÇelo¾9w:Ž©:¢‘ûç¤ëMf–¹–g“x“=“if‘æXx“==“0Ž¡‘!´Tthen‘ s,g‘¹–1Ž¡‘!´Telse‘ s,x–¹–*“f“(\y“->“g“x“+“y)“(x-1)ަ‘íºâºW‘ÿ:«e– _justify“this“design“decision“on“the“basis“that“the“v‘ÿ|rastŽ¡‘íºâma‘ƒŽjorit¾9y–Yof“functions“that“pšAÇeople“really“write“can“b˜e“ rsti-Ž¡‘íºâ ed,‘T‰and–Gåthe“v‘ÿ|rast“ma‘ƒŽjoritš¾9y“of“the“rest“can“bAÇe“handled“b˜y“aŽ¡‘íºâsecondary–=§mec¾9hanism“outlined“in“section“6.4.‘•jIn“doing“thisŽ¡‘íºâwš¾9e–±Yimplicitly“appAÇeal“to“the“measuremen˜t-lead“approac˜h“toŽ¡‘íºâdesign–Ô¼discussed“in“the“in¾9troAÇduction.‘Z©W‘ÿ:«e“only“need“to“re-Ž¡‘íºâmo•¾9v“e–PÛfunctional“parameters“for“recursiv¾9e“functions,–_½but,“asŽ¡‘íºâbAÇecomes–’fclear,‘¬–this“means“ rstifying“non-recursiv¾9e“functionsŽ¡‘íºâtoAÇo.ŽŸæ‘íºâ¹5.2Ž‘G·Firsti cation–LÎb¹™y“examplesŽŸm‘íºâºF‘ÿ:«or–þcthe“momen¾9t,‘x§let's“use“ëMfoldr“ºas“a“running“example.Ž¡‘íºâGivš¾9en–Ta“use“of“ëMfoldrº,“lik˜eަ‘ûç¤ëMsum–¹–xs“=“foldr“(+)“0“xsަ‘íºâºwš¾9e–½can“unfold“functional“parameter“ëM(+)“ºand“iden˜tit˜y“ëM0“ºin˜toŽ¡‘íºâëMfoldrº,–Tgiving“a“new“function“ëMfoldrSpecº:ަ‘ûç¤ëMsum–¹–xs“=“foldrSpec“xsŽ¡¡‘ûç¤foldrSpec–¹–[]‘Y„=“0Ž¡‘ûç¤foldrSpec–¹–(x:xs)‘ s,=“x“+“foldr“(+)“0“xsަ‘íºâºAnd–noš¾9w,‘E%folding“the“b•AÇo“dy–of“ëMfoldrSpec“ºgiv˜es“what“w˜e“reallyŽ¡‘íºâw•¾9an“t:ަ‘ûç¤ëMsum–¹–xs“=“foldrSpec“xsŽ¡¡‘ûç¤foldrSpec–¹–[]‘Y„=“0Ž¡‘ûç¤foldrSpec–¹–(x:xs)‘ s,=“x“+“foldrSpec“xsަ‘íºâºThe–h5kš¾9ey“to“success“here“is“the“ease“with“whic˜h“that“lastŽ¡‘íºâfold–4wš¾9as“done.‘xÈIn“general,‘;Îfolding“is“a“tric˜ky“business,‘;ÎwithŽŽŽ ý€’õºâno–4`guaranš¾9tee“of“termination.‘y“Ho˜w˜ev˜er,‘|"b˜y“restricting“theޤ ’õºâfunctions–s‘wš¾9e“deal“with,‘‹ w˜e“can“guaran˜tee“to“mak˜e“the“foldŽ¡’õºâstep–¶ˆterminating,‘ÞÔand“trivial“to“carry“out.‘ The“restrictionŽ¡’õºâis–ÒPthat“the“function“mš¾9ust“pass“along“all“parameters“whic˜hŽ¡’õºâw•¾9e›¹w“an“t˜to˜sp•AÇecialise˜in˜the˜same˜p“osition˜in˜recursiv¾9e˜callsŽ¡’õºâas–ythey“appAÇeared“in“the“argumen¾9ts.‘+ßF‘ÿ:«or“example,‘Âin“ëMfoldrº,Ž¡’õºâbAÇoth–TëMa“ºand“ëMf“ºsatisfy“this.ŽŸ ’õºâIn–³fact,‘Ÿ:wš¾9e“only“w˜an˜t“to“substitute“in“functional“parameters.Ž¡’õºâSo–Tthe“transformation“of“ëMsum“ºis“really:Ž©ÐO’ç¤ëMsum–¹–xs“=“foldrSpec“0“xsŽ¡¡’ç¤foldrSpec–¹–a“[]‘Y„=“aŽ¡’ç¤foldrSpec–¹–a“(x:xs)‘ s,=“x“+“foldrSpec“a“xsަ’õºâºA‘ºlittle–ûterminology‘ÿ:«.‘ƨThe“function“or“recursiv¾9e“group“of“func-Ž¡’õºâtions–¯3-“for“example,‘àëMfoldr“º-“for“whic¾9h“functional“parametersŽ¡’õºâare–Ý·bAÇeing“remo•¾9v“ed–Ý·is“called“the“ëNtarget‘LÂgroupº.‘ æAnd“a“func-Ž¡’õºâtion–Tcon¾9taining“a“call“to“a“target“group“is“called“a“ëNsourceº.ŽŸ ’õºâThe–Oxrestriction“on“v‘ÿ|ralid“targets“seems“to“bAÇe“this:‘·the“func-Ž¡’õºâtion–Ímš¾9ust“pass“along“all“functional“parameters“unc˜hanged“inŽ¡’õºâall–~recursivš¾9e“calls.‘´ïGeneralising“this“to“deal“with“m˜utuallyŽ¡’õºârecursiv¾9e–ÃRtargets“requires“the“notion“of“a“ëNconstan´Ct‘Uargu-Ž¡’õºâmen´Ct‘Œßsetº.‘¨Calling–ga“recursiv¾9e“group“in“general“causes“callsŽ¡’õºâwithin–'the“group,‘œand“a“constanš¾9t“argumen˜t“set“gathers“to-Ž¡’õºâgether–&margumenš¾9ts“whic˜h“are“guaran˜teed“to“ha˜v˜e“the“sameŽ¡’õºâv‘ÿ|ralue–Tfor“evš¾9ery“sub-call.‘pF‘ÿ:«or“example,“giv˜enަ’ç¤ëMf–¹–x“y“z‘ s,=“f“y“y“z“+“g“z“xŽ¡’ç¤g–¹–a“b‘æX=“f“a“b“a“+“g“a“bަ’õºâºa–æÔlittle“thoughš¾9t“sho˜ws“ëMfº's“third“argumen˜t“and“ëMgº's“ rst“argu-Ž¡’õºâmenš¾9t–•sare“alw˜a˜ys“the“same,‘µ{giving“a“constan˜t“argumen˜t“setŽ¡’õºâwritten–g ëM{f.3,‘¹–g.1}º.‘–A‘fögroup“can“ha•¾9v“e–g more“than“one“set,Ž¡’õºâas–Tthe“folloš¾9wing“trivial“example“sho˜ws:ަ’ç¤ëMf–¹–x“y‘ s,=“g“x“yŽ¡’ç¤g–¹–a“b‘ s,=“f“a“bަ’õºâºConstan•¾9t›mïargumen“t˜sets˜can˜bAÇe˜computed˜using˜a˜simpleŽ¡’õºâabstract–Ë>in¾9terpretation“describšAÇed“b˜elo¾9w.‘¾What“is“imp˜ortan¾9tŽ¡’õºâhere– Iis“that“for“a“recursiv¾9e“target“group“to“bšAÇe“sp˜ecialisable,Ž¡’õºâall–ñbfunctional“parameters“in“the“group“mš¾9ust“bAÇe“constan˜t“ar-Ž¡’õºâgumenš¾9ts.‘ýCertain–µ‹other“constrain˜ts“also“apply–ÿ:«.‘ýW“e‘µ‹returnŽ¡’õºâto–Tthese“later.ŽŸ ’õºâThe–Tfolloš¾9wing“example“breaks“our“nice“sc˜heme:ަ’ç¤ëMmap–¹–f“[]‘Y„=“[]Ž¡’ç¤map–¹–f“(x:xs)‘ s,=“f“x“:“map“f“xsŽ¡¡’ç¤addN–¹–n“xs“=“map“(+“n)“xsަ’õºâºF‘ÿ:«olding–Tand“unfolding“as“abAÇo•¾9v“e‘Tgiv“esަ’ç¤ëMaddN–¹–n“xs“=“mapSpec“xsŽ¡¡’ç¤mapSpec–¹–[]‘Y„=“[]Ž¡’ç¤mapSpec–¹–(x:xs)‘ s,=“(x+n)“:“mapSpec“xsަ’õºâºwhic¾9h–ۆis“clearly“wrong“bAÇecause“ëMn“ºis“unde ned“in“ëMmapSpecº.Ž¡’õºâWhat–?jwš¾9e“need“to“do“is“pass“along“all“free“lam˜b•AÇda-b“oundŽ¡’õºâv›ÿ|rariables–Ѹin“the“spAÇecialising“v˜alue“ëM(+‘¹–n)“ºas“new“parameters,Ž¡’õºâin–Ta“stš¾9yle“reminiscen˜t“of“lam˜bAÇda-lifting:ŽŽŽŽŽŸ’åä22ŽŽŒ‹8— •ºâ ý? £ ý€‘ûç¤ëMaddN–¹–n“xs“=“mapSpec“n“xsޤ ¡‘ûç¤mapSpec–¹–n“[]‘Y„=“[]Ž¡‘ûç¤mapSpec–¹–n“(x:xs)‘ s,=“(x+n)“:“mapSpec“n“xsŽ©å‘íºâºNevš¾9ertheless–PØthis“still“allo˜ws“us“to“get“our“knic˜k˜ers“in“a“t˜wist.Ž¡‘íºâIn–d%the“folloš¾9wing“(admittedly“con˜triv˜ed)“example,‘·Ùw˜e“ma˜yŽ¡‘íºâselect–Teither“ëMinc“ºor“ëMg“ºas“a“source“to“transform“ rst:ަ‘ûç¤ëMapply–¹–f“x‘ s,=“f“xŽ¡‘ûç¤g–¹–a“b‘Y„=“apply“a“bŽ¡¡‘ûç¤inc–¹–y‘Y„=“g“(+“1)“yަ‘íºâºDoing–Tg“ rst“giv¾9es:ަ‘ûç¤ëMapplySpec–¹–x‘ s,=“a“xŽ¡‘ûç¤g–¹–a“b‘%̰=“applySpec“bŽ¡¡‘ûç¤inc–¹–y‘%̰=“g“(+“1)“yަ‘íºâºNo•¾9w›mÅw“e˜need˜to˜in“tro•AÇduce˜free˜v‘ÿ|rariables˜of˜the˜sp“ecialisingŽ¡‘íºâv‘ÿ|ralue–TëMa“ºas“a“new“parameter“to“ëMapplySpecº:ަ‘ûç¤ëMapplySpec–¹–a“x‘ s,=“a“xŽ¡‘ûç¤g–¹–a“b‘/?Ü=“applySpec“a“bŽ¡¡‘ûç¤inc–¹–y‘/?Ü=“g“(+“1)“yަ‘íºâºWhereupšAÇon–uit“should“b˜e“eminenš¾9tly“clear“that“w˜e'v˜e“ac˜hiev˜edŽ¡‘íºâexactly–Ànothing!‘…µOur“mistakš¾9e“w˜as“to“select“a“source“forŽ¡‘íºâwhic¾9h–çúthe“spAÇecialising“v›ÿ|ralue“had“function-v˜alued“free“v˜ari-Ž¡‘íºâables,‘˜ since–}åpassing“them“as“new“parameters“to“ëMapplySpecŽ¡‘íºâºmeans–œõëMapplySpec“ºis“still“a“higher-order“function.‘ôPThe“moralŽ¡‘íºâis–bTclear:‘¶qonly“transform“sources“for“whicš¾9h“the“free“lam˜bAÇda-Ž¡‘íºâbšAÇound–Òrv‘ÿ|rariables“of“the“sp˜ecialising“v‘ÿ|ralue“are“not“higher-Ž¡‘íºâorder.‘ÅA‘¿šsecond–¿Æobš¾9vious“constrain˜t“on“source“calls“is“thatŽ¡‘íºâthe–¿call“should“bAÇe“sucien¾9tly“applied“for“all“function-v‘ÿ|raluedŽ¡‘íºâparameters–Tto“bAÇe“visible.Ž© ‘íºâIn–5ïwhat“follo•¾9ws,‘bžw“e–5ïassume“that“naming“issues“are“dealt“withŽ¡‘íºâcorrectly‘ÿ:«.‘T=In–'îparticular,‘,”the“free“v‘ÿ|rariables“in“an“spAÇecialisingŽ¡‘íºâv‘ÿ|ralue–ΐneed“to“bšAÇe“renamed“b˜efore“they“can“b˜e“safely“insertedŽ¡‘íºâas–Tnew“parameters“of“the“spAÇecialised“target.ަ‘íºâThe–²4algorithm“bšAÇelo¾9w“requires“the“program“to“b˜e“strati edŽ¡‘íºâinš¾9to–øminimal“m˜utually“recursiv˜e“groups,‘;áand“topAÇologicallyŽ¡‘íºâsorted.‘% W‘ÿ:«e–2adopt“the“usual“con•¾9v“en“tion–2that“the“programŽ¡‘íºâis–bIwritten“top-to-bAÇottom,‘u†with“anš¾9y“giv˜en“function“referringŽ¡‘íºâonly–‘oto“its“oš¾9wn“group,‘«Ðif“recursiv˜e,‘«Ðand“groups“abAÇo˜v˜e“it.‘ðyTheŽ¡‘íºârošAÇot–Texpression“is“righ¾9t“at“the“b˜ottom.ަ‘íºâSpAÇecialisation–(of“target“groups“ma¾9y“result“in“some“groupsŽ¡‘íºâbšAÇecoming–•Ðunreac¾9hable“from“ëMmainº.‘ãThese“groups“should“b˜eŽ¡‘íºâremo•¾9v“ed.‘í4A‘°more–°@dicult“problem“is“ho¾9w“to“insert“a“newŽ¡‘íºâgroup,‘ûÍresulting–š‚from“spAÇecialisation“of“an“existing“group,Ž¡‘íºâinš¾9to– –the“program“so“as“to“main˜tain“depAÇendancy‘ÿ:«.‘ÿ7It“turnsŽ¡‘íºâout– ðthat“t•¾9w“o› ðdi eren“t˜bAÇeha“viours˜are˜pAÇossible.‘?EIn˜the˜usualŽ¡‘íºâcase,–Tthe“new“group“\splits"“a•¾9w“a“y–Tfrom“the“source“group:ŽŸå‘ûç¤ëMletrec‘æXmap–¹–f“[]‘Y„=“[]Ž¡‘+'€map–¹–f“(x:xs)‘ s,=“f“x“:“map“f“xsŽ¡‘ûç¤in‘¹–letŽ¡‘+'€square–¹–x‘Y„=“x“*“xŽ¡‘ûç¤in‘¹–letŽ¡‘+'€squareList–¹–xs“=“map“square“xsŽ¡‘ûç¤in‘¹–...ŽŽŽ ý€’õºâºSince–L®the“spAÇecialised“target“ëMmapSpec“ºrefers“to“ëMsquareº,‘š…w¾9eޤ ’õºâmš¾9ust–‡place“it“after“ëMsquareº.‘sKT‘ÿ:«aking“this“argumen˜t“to“itsŽ¡’õºâconclusion–üEshoš¾9ws“w˜e“should“place“an˜y“\splitting"“group“im-Ž¡’õºâmediately–TbAÇefore“the“source“group:Ž©ÐO’ç¤ëMlet‘!square–¹–x‘%̰=“x“*“xŽ¡’ç¤in‘¹–letrecŽ¡’3'€mapSpec–¹–[]‘Y„=“[]Ž¡’3'€mapSpec–¹–(x:xs)‘ s,=“square“x“:Ž¡’ˆ4 mapSpec‘¹–xsŽ¡’ç¤in‘¹–letŽ¡’3'€squarelist–¹–xs‘,Â=“mapSpec“xsŽ¡’ç¤in‘¹–...ަ’õºâºSources–Tgiving“rise“to“\joining"“spAÇecialisations“are“un¾9usual:ަ’ç¤ëMletrec‘æXmap–¹–f“[]‘Y„=“[]Ž¡’3'€map–¹–f“(x:xs)‘ s,=“f“x“:“map“f“xsŽ¡’ç¤in‘¹–letrecŽ¡’3'€squareList‘¹–xsŽ¡’ATB=–¹–map“(head.squareList.unit)“xsŽ¡’ç¤in‘¹–...ަ’õºâºHere,›~ the–X8de nitions“of“ëM(.)º,˜ëMhead“ºand“ëMunit“ºare“unimpAÇortan¾9t.Ž¡’õºâBecause–ºthe“spAÇecialising“v‘ÿ|ralue“ëM(head.squareList.unit)Ž¡’õºâºrefers–z¶to“the“source“group“from“whic¾9h“it“originates,‘”the“re-Ž¡’õºâsulting–âáspAÇecialisation“of“ëMmap“ºwill“also“refer“to“ëMsquareListº,Ž¡’õºâand–âKthat“in“turn“means“the“spšAÇecialisation“should“b˜e“mergedŽ¡’õºâin¾9to–Tthe“source“group:ަ’ç¤ëMletrecŽ¡’fsquareList–¹–xs‘,Â=“mapSpec“xsŽ¡’fmapSpec–¹–[]‘Y„=“[]Ž¡’fmapSpec–¹–(x:xs)‘ s,=“(head.squareList.unit)“x“:Ž¡’g òmapSpec‘¹–xsŽ¡’ç¤in‘¹–...ަ’õºâºSince–{·only“recursivš¾9e“source“groups“can“refer“to“themselv˜es,Ž¡’õºâsp•AÇecialisations›Bcorresp“onding˜to˜sources˜in˜non-recursiv¾9eŽ¡’õºâgroups–Tnevš¾9er“exhibit“this“\joining"“bAÇeha˜viour.ŽŸ5’õºâ¹5.3Ž’ G·An‘LÎalgo¹™rithmŽŸm’õºâºThe–PùprošAÇcedure“b˜elo¾9w“is“rep˜eated“un¾9til“no“more“v‘ÿ|ralid“(source,Ž¡’õºâtarget)–җpairs“can“bAÇe“found.‘T9As“shoš¾9wn“b˜y“Nelan“[NelŽ‘ žº],‘ètheŽ¡’õºâorder–)in“whicš¾9h“these“pairs“are“selected“mak˜es“no“di erence.Ž¡’õºâUn¾9used––Õtargets“should“bšAÇe“deleted,‘°"but“again“it“do˜esn't“mak¾9eŽ¡’õºâanš¾9y–Tdi erence“when.‘pAs“a“running“example,“w˜e“tak˜e:ަ’ÿ.ëMletrecŽ¡’ ZÐmap1–¹–f“g“(x:y:xys)‘ s,=“f“x“:“g“y“:“map2“g“f“xysŽ¡’ ZÐmap1–¹–f“g“_‘/?Ü=“[]Ž¡¡’ ZÐmap2–¹–g“f“(x:y:xys)‘ s,=“g“x“:“f“y“:“map1“f“g“xysŽ¡’ ZÐmap2–¹–g“f“_‘/?Ü=“[]Ž¡’ÿ.in‘¹–letŽ¡’ ZÐaddmul–¹–p“q“xs‘!=“map1“(+“p)“(*“q)“xsŽŸÐO’‰º1.ŽŽŽ’ :âFind–&´a“v›ÿ|ralid“target“group,‘k and“a“v˜alid“source“groupŽ¡’ :âwhic¾9h–Trefers“to“the“target“group.ŽŸÌ͍’g¤ëMTarget–¹–group‘,Â=“{map1,“map2}Ž¡’g¤Source–¹–group‘,Â=“{addmul},“refers“to“map1ŽŽŽŽŽŸ’åäº23ŽŽŒ‹Rè •ºâ ý? £ ý€‘ø‰º2.ŽŽŽ‘:âIf–‡dthe“target“group“is“recursivš¾9e,‘£çcompute“its“constan˜tޤ ‘:âargumenš¾9t–½Ðsets“(see“section“5.4).‘ãIn“realit˜y‘ÿ:«,‘çîthis“com-Ž¡‘:âputation–É$has“to“bšAÇe“p˜erformed“at“step“(1).‘ 7áIf“non-Ž¡‘:ârecursiv•¾9e,‘¿$man“ufacture–iûa“\fak¾9e"“singleton“set“listingŽ¡‘:âall–Thigher-order“parameters“as“constan¾9t.Ž©ª_‘g¤ëMConst–¹–arg“sets‘ s,=“{“{map1.1,“map2.2},Ž¡‘pç\{map1.2,–¹–map2.1}“}ަ‘ø‰º3.ŽŽŽ‘:âIn•¾9v“en“t–Aa“new“set“of“names“for“the“spAÇecialised“targetŽ¡‘:âgroup.ަ‘g¤ëMNew–¹–names‘ s,=“{map1Spec,“map2Spec}ަ‘ø‰º4.ŽŽŽ‘:âDetermine,‘çfrom–Ûlthe“constanš¾9t“argumen˜t“set,‘çwhic˜h“ar-Ž¡‘:âgumen¾9ts–¿Yin“the“source“call“site“are“the“spAÇecialising“v‘ÿ|ral-Ž¡‘:âues.‘²Extract–G8their“free“lam¾9b•AÇda-b“ound–G8v‘ÿ|rariables“andŽ¡‘:ârename.ަ‘g¤ëMOriginal:Ž¡‘!:specialising–¹–values“=“{(+“p),“(*“q)}Ž¡‘!:free–¹–variables‘Y„=“{p,“q}Ž¡¡‘g¤Renamed:Ž¡‘!:specialising–¹–values“=“{(+“pnew),“(*“qnew)}Ž¡‘!:free–¹–variables‘Y„=“{pnew,“qnew}ަ‘ø‰º5.ŽŽŽ‘:âRebuild–­½the“source“call“b¾9y“deleting“the“spAÇecialisationŽ¡‘:âv›ÿ|ralues,‘Åninserting–±tfree“v˜ariables“as“new“parameters,‘ÅnandŽ¡‘:âc¾9hanging–À+the“called“function“to“its“new“name,‘êáas“de-Ž¡‘:âtermined–Tin“step“(3).ަ‘g¤ëMRebuilt–¹–source“call‘ s,=“map1Spec“p“q“xsަ‘ø‰º6.ŽŽŽ‘:âBuild–2vthe“spAÇecialised“target“group,‘_Östarting“with“a“cop¾9yŽ¡‘:âof–$šthe“original“target“group.‘JAF‘ÿ:«or“eacš¾9h“recursiv˜e“callŽ¡‘:âinside–Táthe“group,‘dÄmoAÇdify“that“call“in“a“similar“w•¾9a“y‘TátoŽ¡‘:âhoš¾9w–Tthe“source“call“w˜as“moAÇdi ed“in“step“(5).ަ‘:âëMRebuilt–¹–target“group:Ž¡¡‘g¤map1Spec–¹–pnew“qnew“(x:y:xys)Ž¡‘ ”f=–¹–(x“+“pnew)“:“(y“*“qnew)“:Ž¡‘gt0map2Spec–¹–pnew“qnew“restŽ¡‘g¤map1Spec–¹–pnew“qnew“_Ž¡‘ ”f=‘¹–[]Ž¡¡‘g¤map2Spec–¹–pnew“qnew“(x:y:xys)Ž¡‘ ”f=–¹–(x“*“qnew)“:“(y“+“pnew)“:Ž¡‘gt0map1Spec–¹–pnew“qnew“restŽ¡‘g¤map2Spec–¹–pnew“qnew“_Ž¡‘ ”f=‘¹–[]ަ‘ø‰º7.ŽŽŽ‘:âDetermine–Zgwhether“the“spAÇecialised“target“group“shouldŽ¡‘:âsplit–»or“join,‘¦b¾9y“ nding“out“whether“the“spAÇecialisationŽ¡‘:âv‘ÿ|ralues–“fconš¾9tained“an˜y“reference“to“the“source“group.Ž¡‘:âAugmen¾9t–Tprogram“appropriately‘ÿ:«.ަ‘g¤ëMSpecialisation–¹–vals“{(+“p),“(*“q)}“don'tŽ¡‘g¤refer–¹–to“{addmul},“so“new“group“splits.ŽŸ­â‘íºâºA‘qùv‘ÿ|ralid–rnon-recursivš¾9e“target“group“m˜ust“consist“of“a“singleŽ¡‘íºâhigher–HØorder“function.‘¶ûA‘HÊv‘ÿ|ralid“recursiv¾9e“target“group“satis-Ž¡‘íºâ es–Tall“the“follo¾9wing:ŽŽŽ ý€’äëPŽŽŽ’ :âºAll–ږfunctions“in“the“group“ha•¾9v“e–ږat“least“one“functionalޤ ’ :âparameter.Ž©8’äëPŽŽŽ’ :âºEacš¾9h–¤lfunctional“parameter“in“the“group“is“a“mem˜bAÇerŽ¡’ :âof–s“exactly“one“of“the“group's“constanš¾9t“argumen˜t“sets.Ž¡’ :âThis–|implies“that“all“inš¾9tra-group“calls“m˜ust“bAÇe“su-Ž¡’ :âcienš¾9tly–Tapplied“to“expAÇose“all“functional“argumen˜ts.ަ’äëPŽŽŽ’ :âºEac•¾9h›¦âconstan“t˜argumen“t˜set˜m“ust˜men“tion˜exactly˜oneŽ¡’ :âargumenš¾9t–¤Çfor“eac˜h“function“in“the“group.‘ÊÊThis“disal-Ž¡’ :âloš¾9ws–'Úcertain“con˜triv˜ed“pathological“cases“whic˜h“w˜ouldŽ¡’ :âotherwise–Tseriously“complicate“the“algorithm.ޤšW’õºâA–Tv‘ÿ|ralid“source“call“site“satis es“the“follo¾9wing:Ž¡’äëPŽŽŽ’ :âºThe–Tsite“is“a“call“to“a“v‘ÿ|ralid“target“group.ަ’äëPŽŽŽ’ :âºThe–Bpapplication“mš¾9ust“ha˜v˜e“sucien˜t“argumen˜ts“to“sup-ޤ ’ :âply–Tall“higher“order“(spAÇecialisable)“argumen¾9ts.ަ’äëPŽŽŽ’ :âºF‘ÿ:«or–Û7eacš¾9h“spAÇecialisable“argumen˜t,‘Œ¯none“of“the“freeŽ¡’ :âlamš¾9b•AÇda-b“ound–&v‘ÿ|rariables“ma˜y“bAÇe,‘jNor“con˜tain,‘jNa“func-Ž¡’ :âtion‘Tspace.Ž©šW’õºâAlthough–/it“lošAÇoks“easy“on“pap˜er,‘uqimplemen¾9ting“this“algo-Ž¡’õºârithm–s3is“tricš¾9ky–ÿ:«.‘6 T“aking–s3in˜to“accoun˜t“the“mec˜hanisms“forŽ¡’õºâdetecting–ëbconstanš¾9t“argumen˜ts“and“main˜taining“t˜ypAÇe“anno-Ž¡’õºâtations,‘Íthe–èèHaskš¾9ell“implemen˜tation“approac˜hes“1500“linesŽ¡’õºâof‘TcoAÇde.ŽŸ*£’õºâ¹5.4Ž’ G·Computing–LÎconstant“a¹™rgument“setsŽŸm’õºâºA‘õ¦simple–õ®abstract“inš¾9terpretation“is“used.‘ãEac˜h“function“callŽ¡’õºâin–kÏthe“group“is“abstracted“to“expAÇose“the“parameters“it“passesŽ¡’õºâalong:ަ’ç¤ëMf–¹–x“y“z‘ s,=“f“y“y“z“+“g“z“xŽ¡’ç¤g–¹–a“b‘æX=“f“a“b“a“+“g“a“bަ’õºâºPhrased–Tabstractly‘ÿ:«,“this“bAÇecomes:ަ’ç¤ëMf:–¹–calls“f“[#2,“#2,“#3]Ž¡’fcalls–¹–g“[#3,“#1]Ž¡¡’ç¤g:–¹–calls“f“[#1,“#2,“#1]Ž¡’fcalls–¹–g“[#1,“#2]ަ’õºâºNo•¾9w›è;w“e˜iterate˜to˜a˜ xed˜pAÇoin“t,‘ñ@gathering˜a˜complete˜set˜ofŽ¡’õºâthe–‡opAÇossible“v‘ÿ|ralues“of“eacš¾9h“argumen˜t.‘í$There“is“a“list“for“eac˜hŽ¡’õºâfunction,‘£ƒand–‡eacš¾9h“list“con˜tains“a“set“of“pAÇossible“v‘ÿ|ralues“forŽ¡’õºâeac•¾9h›Targumen“t.‘pInitially‘ÿ:«,˜eac“h˜argumen“t˜can˜only˜bAÇe˜itself:ަ’ç¤ëMF0–¹–=“[“{f.1},“{f.2},“{f.3}“]Ž¡’ç¤G0–¹–=“[“{g.1},“{g.2}“]ަ’õºâºA•¾9t›å¹eac“h˜iteration,‘ï?new˜appro“ximations˜are˜computed˜b“y˜us-Ž¡’õºâing–EÉthe“abstract“v¾9ersions“of“functions“to“lošAÇok“up“p˜ossibleŽ¡’õºâargumenš¾9t–\sets“in“the“existing“appro˜ximation.‘ð¥Also,‘m¿the“ex-Ž¡’õºâisting–Tappro¾9ximation“is“merged“in“wholesale:ަ’ç¤ëMF1–¹–=“F0“U“[“{f.2},“{f.2},“{f.3}“]Ž¡’)´TU–¹–[“{g.1},“{g.2},“{g.1}“]Ž¡’f=–¹–[“{f.1,“f.2,“g.1},“{f.2,“g.2},“{f.3,“g.1}“]Ž¡¡’ç¤G1–¹–=“G0“U“[“{f.3},“{f.1}“]ŽŽŽŽŽŸ’åäº24ŽŽŒ‹i •ºâ ý? £ ý€‘!´TëMU–¹–[“{g.1},“{g.2}“]ޤ ‘ f=–¹–[“{f.3,“g.1},“{f.1,“g.2}“]Ž¡¡‘ûç¤F2–¹–=“F1“U“[“{f.2,“g.2},“{f.2,“g.2},“{f.3,“g.1}“]Ž¡‘+'€[–¹–{f.3,“g.1},“{f.1,“g.2},“{f.3,“g.1}“]Ž¡‘ f=–¹–[“{f.1,“f.2,“f.3,“g.1,“g.2},Ž¡‘ú¾{f.1,–¹–f.2,“g.2},“{f.3,“g.1}“]Ž¡¡‘ûç¤G2–¹–=“G1“U“[“{f.3,“g.1},“{f.1,“f.2,“g.1}“]Ž¡‘!´TU–¹–[“{f.3,“g.1},“{f.1,“g.2}“]Ž¡‘ f=–¹–[“{f.3,“g.1},“{f.1,“f.2,“g.1,“g.2}“]Ž©Y‘íºâºEv•¾9en“tually–g<this“prošAÇcess“stabilises,‘{¶giving“the“follo¾9wing“p˜os-Ž¡‘íºâsible–Targumen¾9t“v‘ÿ|ralues:ަ‘ûç¤ëMf.1› s,could–¹–have“value˜f.1,“f.2,“f.3,“g.1,“g.2Ž¡‘ûç¤f.2› s,could–¹–have“value˜f.1,“f.2,“f.3,“g.1,“g.2Ž¡‘ûç¤f.3› s,could–¹–have“value˜f.3,“g.1Ž¡‘ûç¤g.1› s,could–¹–have“value˜f.3,“g.1Ž¡‘ûç¤g.2› s,could–¹–have“value˜f.1,“f.2,“f.3,“g.1,“g.2ަ‘íºâºSo–E3wš¾9e“ha˜v˜e“t˜w˜o“candidate“constan˜t“argumen˜t“sets:Ž¡‘íºâëM{f.1,–¹–f.2,“f.3,“g.1,“g.2}–‚­ºand“ëM{f.3,‘¹–g.1}º.‘d{W‘ÿ:«e“rejectŽ¡‘íºâthe–` 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xpAÇoinš¾9ting,‘EÊëMUnknown“ºannihilates“an˜y“other“v‘ÿ|ralues“in“aŽ¡‘íºâset.‘ÐF‘ÿ:«or–;Éexample,‘Efa“set“ëM{f.1,–¹–g.2,“Unknown}–;ɺis“equiv‘ÿ|ralen¾9tŽ¡‘íºâsimply–to“ëM{Unknown}º.‘îžëMUnknown“ºrepresenš¾9ts“an“argumen˜t“ofŽ¡‘íºâuncertain–\Êorigin,‘n¨so“wš¾9e“disallo˜w“an˜y“constan˜t“argumen˜t“setŽ¡‘íºâcon¾9taining‘Tit.ŽŸ¥‘íºâ¹5.5Ž‘G·Preserving–LÎt¹™ypFfe“annotationsŽŸm‘íºâºSince–gAnna“wš¾9orks“with“t˜ypAÇe“annotated“Core“expressions,Ž¡‘íºâw¾9e–Åòneed“to“go“to“a“little“trouble“to“transform“the“annota-Ž¡‘íºâtions–-gtošAÇo.‘dªA¾9t“ rst“glance,‘3lthis“lo˜oks“lik¾9e“a“simple“matter“ofŽ¡‘íºâmošAÇdifying–Fhfunction“t¾9yp˜es“p˜ertaining“to“sp˜ecialised“functions,Ž¡‘íºâbš¾9y–ɚdeleting“t˜ypšAÇes“of“sp˜ecialised“argumen¾9ts“and“inserting“theŽ¡‘íºât¾9ypšAÇes–’Jof“free“v‘ÿ|rariables“b˜eing“passed“as“extra“parameters.Ž¡‘íºâThis–.is“indeed“correct,‘M¤but“there's“more“to“it.‘ þRecall“theŽ¡‘íºâprevious–Tde 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rst“searc˜h“fromŽ¡’õºâëMmain–d©ºto“disco•¾9v“er–d©all“required“instances.‘ nThe“second“passŽ¡’õºâclones–Á×coAÇde,‘,÷c¾9hanges“function“names“accordingly“and“re-Ž¡’õºâstores–TdepAÇendancy“order.ަ’õºâ¹5.6.1Ž’úíCollecting–LÎthe“instancesŽŸm’õºâºI‘õÓam–ö indebted“to“Mark“Jones“for“suggesting“the“follo¾9wingŽ¡’õºâalgorithm.‘GYW‘ÿ:«e–x÷carry“a“set“ëMinstances“ºto“accum¾9ulate“theŽ¡’õºâev•¾9en“tual–g|result,‘¼and“a“stacš¾9k“ëMtoVisit“ºrecording“places“w˜eŽ¡’õºâneed–ÒLto“visit.‘Elemen¾9ts“of“ëMinstances“ºand“ëMtoVisit“ºare“pairsŽ¡’õºâof–”z(function“name,‘ôCt¾9ypšAÇe“expression)“sp˜ecifying“a“particu-Ž¡’õºâlar–C—instance“of“a“function.‘§8The“tš¾9ypAÇe“expressions“are“alw˜a˜ysŽ¡’õºâmonomorphic.ŽŸ ’õºâSince–B ëMmain“ºmaš¾9y“bAÇe“of“an˜y“t˜ypAÇe,‘Í6w˜e“trivially“monomor-Ž¡’õºâphise–£zit“bš¾9y“substituting“an˜y“t˜ypAÇe“v‘ÿ|rariables“with“ëMIntº.‘ÆáThisŽ¡’õºâgiv¾9es–ªa“single“initial“v‘ÿ|ralue“for“ëMtoVisitº,‘!with“ëMinstances“ºini-Ž¡’õºâtially–H bAÇeing“empt¾9y‘ÿ:«.‘´The“ nal“v‘ÿ|ralue“of“ëMinstances“ºis“thenŽ¡’õºâëMsearch(instances,‘¹–toVisit)º,‘Twhere:ŽŸÐO’õºâëMsearch(instances,‘¹–toVisit)Ž¡’ç¤=–¹–if‘æX[toVisit“is“empty]Ž¡’ ZÐthen‘ s,instancesŽ¡’ ZÐelseŽ¡’ ZÐlet‘,Ânext–¹–=“head“toVisitŽ¡’ ZÐin–æXif“next–¹–`elem`“instancesŽ¡’F Ø[We've–¹–already“been“here]Ž¡’ ZÐthen‘ s,search(instances,–¹–tail“toVisit)Ž¡’ ZÐelse‘ s,[Get–¹–the“function“specified“by“next.Ž¡’.mêFind–¹–out“what“instances“of“otherŽŽŽŽŽŸ’åäº25ŽŽŒ‹~ •ºâ ý? £ ý€‘&mêëMfunctions–¹–are“called.‘ s,Add“theseޤ ‘&mêinstances–¹–to“(tail“toVisit)“givingŽ¡‘&mêtoVisitAug,–¹–and“then“do]Ž¡‘&mêsearch({next}–¹–U“instances,“toVisitAug)ޤzÁ‘íºâºF‘ÿ:«or–Texample,“giv¾9enŽ¡‘ûç¤ëMid–¹–x‘ s,=“xޤ ‘ûç¤f–¹–x‘,Â=“id“xŽ¡‘ûç¤main‘ s,=–¹–id“42“+“ord“(f“'c')ޤzÁ‘íºâºthe–Talgorithm“runs“through“these“states:Ž¡‘ fëMinstances‘YÆ"toVisitޤ ‘íºâ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~Ž¡‘íºâ{}‘zÙ<[(main,‘¹–Int)]Ž¡¡‘íºâ{(main,–¹–Int)}‘FßÊ[(id,‘,ÂInt“->“Int),Ž¡‘vÀà(f,‘æXChar–¹–->“Char)]Ž¡¡‘íºâ{(main,–¹–Int),‘FßÊ[(f,‘æXChar“->“Char)]Ž¡‘òtx(id,‘,ÂInt–¹–->“Int)}Ž¡¡‘íºâ{(main,–¹–Int),‘FßÊ[(id,‘,ÂChar“->“Char)]Ž¡‘òtx(id,‘,ÂInt–¹–->“Int),Ž¡‘òtx(f,‘æXChar–¹–->“Char)}Ž¡¡‘íºâ{(main,‘¹–Int),‘FßÊ[]Ž¡‘òtx(id,‘,ÂInt–¹–->“Int),Ž¡‘òtx(id,‘,ÂChar–¹–->“Char),Ž¡‘òtx(f,‘æXChar–¹–->“Char)}ŽŸzÁ‘íºâºThis–™givš¾9es“t˜w˜o“instances“for“ëMidº.‘ÜBecause“the“abstract“in˜ter-Ž¡‘íºâpretation–´Œof“t¾9ypšAÇes“maps“b˜oth“ëMInt“ºand“ëMChar“ºto“the“t•¾9w“o‘´Œp˜oin“tŽ¡‘íºâdomain,‘¥only–Ó.one“of“those“instances“is“needed“for“analysisŽ¡‘íºâpurpAÇoses.‘ú In–_9general,‘±²wš¾9e“can“exploit“the“fact“that“man˜yŽ¡‘íºâdi eren•¾9t›@Rt“ypAÇes˜are˜assigned˜the˜same˜domain˜to˜reduce˜theŽ¡‘íºâprogram–•±expansion“caused“b¾9y“monomorphisation.‘†F‘ÿ:«ar“andŽ¡‘íºâa•¾9w“a“y–èŒthe“easiest“w•¾9a“y–èŒto“do“this“is“to“transform“the“t¾9ypAÇe“an-Ž¡‘íºânotations–ñnto“domain“annotations“bAÇefore“monomorphisation,Ž¡‘íºâusing–ùýthe“results“of“section“2.2.5.‘ST¾9ypAÇe“v‘ÿ|rariables“are“simplyŽ¡‘íºâreplaced–Tb¾9y“domain“v‘ÿ|rariables.ŽŸò덍‘íºâ¹5.6.2Ž‘ úíCloning‘LÎcoFfdeŽŸm‘íºâºThis–¨èis“fairly“trivial.‘×+Eac¾9h“function“is“duplicated“once“pAÇerŽ¡‘íºâinstance,‘ܶwith–´Öappropriate“new“names.‘úõThe“function“b•AÇo“d-Ž¡‘íºâies›#\ha•¾9v“e˜their˜call˜sites˜moAÇdi ed˜to˜refer˜to˜appropriatelyŽ¡‘íºânamed–_2instances“in“previous“groups,›qªand“this“one,˜if“recur-Ž¡‘íºâsivš¾9e.‘\Then–Ðthe“b•AÇo“dies–Ðha˜v˜e“the“t˜ypAÇe“v‘ÿ|rariables“in“their“anno-Ž¡‘íºâtations–çãsubstituted“appropriately“for“eacš¾9h“di eren˜t“instanceŽ¡‘íºârequired.‘¶eThe–ûen¾9tire“program“can“bšAÇe“pro˜cessed“in“a“singleŽ¡‘íºâtop-to-bAÇottom‘Tpass.Ž© ‘íºâThe–ŠËonly“slighš¾9tly“tric˜ky“problem“is“rebuilding“recursiv˜eŽ¡‘íºâgroups–”0so“as“to“mainš¾9tain“depAÇendancy–ÿ:«.‘™F“or‘”0non-recursiv˜eŽ¡‘íºâclones,›/this–Åis“easy‘ÿ:«,˜but“bAÇecause“of“the“existance“of“cer-Ž¡‘íºâtain›2Äcon•¾9triv“ed˜recursiv“e˜functions,‘: main“taining˜depAÇendancyŽ¡‘íºâin–ó«the“recursivš¾9e“case“can“bAÇe“complicated.‘·vW‘ÿ:«e“a˜v˜oid“theseŽ¡‘íºâproblems–"dbš¾9y“lumping“all“the“clones“arising“from“a“recursiv˜eŽ¡‘íºâfunction–ÿ‹group“in¾9to“a“single“ëMletrecº,‘:and“passing“the“pro-Ž¡‘íºâgram–Ta“third“time“though“the“depAÇendancy“analyser.ަ‘íºâDespite–8hthese“complications,‘,the“monomorphiser“is“ex-Ž¡‘íºâtremely–aÞquicš¾9k“and“doAÇes“not“pro˜v˜e“a“signi can˜t“limitationŽ¡‘íºâon‘TpAÇerformance.ŽŽŽ ý€’õºâ¹6Ž’”DiscussionŽŸ†´’õºâºThis–ÙÎsection“draš¾9ws“together“the“detailed“tec˜hnical“threadsޤ ’õºâexpAÇounded–‡in“the“previous“three“sections,‘š“bš¾9y“presen˜tingŽ¡’õºâsome–äkpšAÇerformance“results,‘1and“lo˜oking“at“related“and“fur-Ž¡’õºâther–Èxwš¾9ork.‘5ÜBut“w˜e“bAÇegin“b˜y“lošAÇoking“at“some“p˜erformanceŽ¡’õºâissues.ŽŸtŠ’õºâ¹6.1Ž’ G·Putting–LÎit“all“togetherŽŸm’õºâºThro¾9wing–°realistically“sized“programs“at“the“analyser“re-Ž¡’õºâvš¾9ealed–½psome“pAÇerformance“problems“whic˜h“w˜ere“traced“toŽ¡’õºâniceties–Xüin“the“inš¾9terface“bAÇet˜w˜een“the“abstract“in˜terpreter“andŽ¡’õºâthe–Tterm“rewriter.Ž© ’õºâP¾9erformance–òrproblems“appAÇear“when“the“term“rewriting“sys-Ž¡’õºâtem–u,is“fed“a“giganš¾9tic“term“to“simplify–ÿ:«.‘;ùUsually“,‘"suc˜h‘u,termsŽ¡’õºâreduce–-œto“something“quite“trivial.‘eHIt“is“impAÇortan¾9t“to“realiseŽ¡’õºâthat–}0the“abstract“in¾9terpreter“will“generate“absolutely“enor-Ž¡’õºâmous–úUterms,‘3–espAÇecially“from“source“text“whic¾9h“has“deeplyŽ¡’õºânested–BÊfunction“calls“or“deeply“nested“ëMcase“ºexpressions,‘læbAÇothŽ¡’õºâof–ˁwhic¾9h“are“quite“common.‘>÷F‘ÿ:«or“example,‘ù the“bigger“pro-Ž¡’õºâgrams–2menš¾9tioned“in“section“6.2“generated“terms“whic˜h,‘_êwhenŽ¡’õºâprett•¾9y-prin“ted–#in“the“stš¾9yle“used“in“this“papAÇer,‘&„co˜v˜ered“liter-Ž¡’õºâally–Ttens“of“A4“pages.ަ’õºâAnalysis–²¾of“a“program“proAÇceeds“as“follo¾9ws.‘ô­First,‘Úthe“pro-Ž¡’õºâgram–L•is“passed“in“its“en•¾9tiret“y–L•through“the“abstract“in¾9ter-Ž¡’õºâpreter,‘0generating–Ä«a“correspAÇonding“collection“of“recursiv¾9eŽ¡’õºâequations–\õ(or“terms).‘óTThese“equations“are“h¾9ugely“redun-Ž¡’õºâdan¾9t–`Ðand“are“simpli ed“individually‘ÿ:«,‘³®without“reference“toŽ¡’õºâeacš¾9h–“nother.‘–¾Finally‘ÿ:«,‘òôthe“ xpAÇoin˜ting“system“tra˜v˜els“alongŽ¡’õºâthe–_úgroups“of“equations,‘²£accumš¾9ulating“an“en˜vironmen˜t“ofŽ¡’õºâ\solv•¾9ed"›˜Ìequations.‘¦×A‘˜ªsolv“ed˜equation˜is˜self-con“tained:‘#_itŽ¡’õºâdoAÇes–2ònot“refer“to“the“abstract“inš¾9terpretation“of“an˜y“otherŽ¡’õºâfunction.‘ëÌSolving–ƒgnon-recursiv¾9e“equations“is“a“simple“matterŽ¡’õºâof–Ê\substituting“in“the“abstract“in¾9terpretations“of“other“func-Ž¡’õºâtions,›7and–Ösimplifying.‘,öF‘ÿ:«or“recursiv¾9e“functions,˜this“stage“isŽ¡’õºâfollo•¾9w“ed›Tb“y˜ xpAÇoin“ting.ަ’õºâWhat–Ðreally“ruins“pšAÇerformance“is“not“ xp˜oin¾9ting,‘C.but“theŽ¡’õºâinitial–úsimpli cation“of“terms“whic¾9h“emerge“from“the“ab-Ž¡’õºâstract–èeinš¾9terpreter.‘•¤This“problem“w˜as“largely“alleviated“b˜yŽ¡’õºâgiving–wªthe“abstract“inš¾9terpreter“a“little“more“in˜telligence,‘?inŽ¡’õºâthe–Tform“of:ŽŸît’äëPŽŽŽ’ :âºThe›#žt¾9yp•AÇe-sp“eci c˜ëMAbsVal˜ºrewrites˜describ“ed˜in˜sec-Ž¡’ :âtion‘T4.6.ŽŸBF’äëPŽŽŽ’ :âºA‘ëknoš¾9wledge–€Iof“k˜ey“ëMContext“ºrewrite“rules.‘]PIn“par-Ž¡’ :âticular,‘~9the–6 rules“for“ëMcase“ºstatemen¾9ts“generate“largeŽ¡’ :âexpressions›xin•¾9v“olving˜ëMCMeetº,–"ëMCJoinº,“ëMStop1˜ºand˜ëMStop2º.Ž¡’ :âA‘Ôhandful–Ôyof“rules“emš¾9b•AÇo“dying–Ôysimple“facts“suc˜h“asŽ¡’ :âëMCMeet–¹–[...“Stop2“...]“==“Stop2–Tºw¾9ere“added.ŽŸ ¡#’ :âBet•¾9w“een–Yêthem,‘gthe“sizes“of“terms“generated“w¾9ere“some-Ž¡’ :âtimes–قcut“bš¾9y“t˜w˜o“orders“of“magnitude,‘Jand“pAÇerfor-Ž¡’ :âmance–Twš¾9as“m˜uc˜h“impro˜v˜ed.ŽŸîu’õºâA‘m†second–m±pAÇerformance“problem“w¾9as“traced“to“the“initial“sim-Ž¡’õºâpli cation–M²of“terms“emerging“from“the“abstract“in¾9terpreter.Ž¡’õºâThese–=¬terms“are“simpli ed“without“reference“to“eac¾9h“other.Ž¡’õºâIt–ïÚturns“out“to“bšAÇe“b˜etter“to“simplify“a“term“only“whenŽ¡’õºâw•¾9e›ñxkno“w˜the˜solv“ed˜v‘ÿ|ralues˜of˜the˜other˜terms˜it˜refers˜to,Ž¡’õºâbAÇecause–V”knoš¾9wing“these“v‘ÿ|ralues“mak˜es“the“ nal“term“m˜uc˜hŽ¡’õºâsmaller.‘рIn–§e 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ffŽ’"±0.586‘TM‘33Ÿ„ ff‘fg„ ffŽ’Y+ú0.92‘Ts‘33Ÿ„ ffŽ’²Ò19‘T%‘33Ÿ„ ff‘fg„ ffŽŽ¡“¤„ ff‘fg„ ff‘33Ÿüÿþzip3‘ ô ¡„ ffŽ‘?ìëO<‘Tº10‘33Ÿ„ ff‘fg„ ffŽ‘iL©0.52‘Ts‘33Ÿ„ ffŽ’”†1.793‘TM‘33Ÿ„ ffŽ’É4´56.1‘Tk‘33Ÿ„ ff‘fg„ ffŽ’÷w"0.17‘Ts‘33Ÿ„ ffŽ’"±0.570‘TM‘33Ÿ„ ff‘fg„ ffŽ’Y+ú1.00‘Ts‘33Ÿ„ ffŽ’²Ò17‘T%‘33Ÿ„ ff‘fg„ ffŽŽ¡“¤„ ff‘fg„ ff‘33Ÿüÿþw¾9ang‘•Ó¡„ ffŽ‘E“385‘33Ÿ„ ff‘fg„ ffŽ‘d¬«23.62‘Ts‘33Ÿ„ ffŽ’æ‘85.396‘TM‘33Ÿ„ ffŽ’Ä”¶908.8‘Tk‘33Ÿ„ ff‘fg„ ffŽ’÷w"9.15‘Ts‘33Ÿ„ ffŽ’ 15.861‘TM‘33Ÿ„ ff‘fg„ ffŽ’T‹ü43.61‘Ts‘33Ÿ„ ffŽ’²Ò21‘T%‘33Ÿ„ ff‘fg„ ffŽŽ¡“¤„ ff‘fg„ ff›33Ÿüÿþw•¾9a“v“e4main˜¡„ ffŽ‘E“619‘33Ÿ„ ff‘fg„ ffŽ‘d¬«43.40‘Ts‘33Ÿ„ ffŽ’‹F“116.207‘TM‘33Ÿ„ ffŽ’¿ô¸2897.7‘Tk‘33Ÿ„ ff‘fg„ ffŽ’ò×$21.62‘Ts‘33Ÿ„ ffŽ’ 43.239‘TM‘33Ÿ„ ff‘fg„ ffŽ’Oëþ199.29‘Ts‘33Ÿ„ ffŽ’²Ò11‘T%‘33Ÿ„ ff‘fg„ ffŽŽ¡“¤„ ff‘fg„ ff‘33Ÿüÿþag2hs‘¼:¡„ ffŽ‘@ó1047‘33Ÿ„ ff‘fg„ ffŽ‘` ­208.95‘Ts‘33Ÿ„ ffŽ’‹F“275.245‘TM‘33Ÿ„ ffŽ’¿ô¸9653.8‘Tk‘33Ÿ„ ff‘fg„ ffŽ’î7&126.42‘Ts‘33Ÿ„ ffŽ’q 135.335‘TM‘33Ÿ„ ff‘fg„ ffŽ’Oëþ100.68‘Ts‘33Ÿ„ ffŽ’­hÔ126‘T%‘33Ÿ„ ff‘fg„ ffŽŽ¡“Ÿ„ ff‘fg„ ff‘6˜ý„ ffŽ‘X¦GŸ„ ff‘fg„ ffŽ’…¬úŸ„ ffŽ’º[Ÿ„ ffŽ’æÐÀŸ„ ff‘fg„ ffŽ’×sŸ„ ffŽ’H…˜Ÿ„ ff‘fg„ ffŽ’uŒKŸ„ ffŽ’ËF§Ÿ„ ff‘fg„ ffŽŽŸfh‰ffÍF§ŽŽŽŸEÌ̍’Ÿ¸/T‘ÿ:«able–T2:‘pSome“pAÇerformance“ gures“for“ëNAnnaŽŽŸ Ž’öff„’Ù˜ffŽŽ Œ@‰fföÌ̎ŽŽŽ öYœ þ%¦d‘íºâ¹6.2Ž‘G·Absolute–LÎpFferfo¹™rmance“resultsŽŸm‘íºâºFivš¾9e–ÿWtest“programs“w˜ere“used.‘ÚxThe“ rst“t˜w˜o,‘9×ëMconcat“ºandޤ ‘íºâëMzip3º,‘ZŠare–utterly“trivial“and“w¾9ere“included“as“comparisonŽ¡‘íºâagainst–Ûì gures“presen¾9ted“in“[Sew93Ž‘/].‘p7ëMwang“ºand“ëMwave4mainŽ¡‘íºâºare–‡Htakš¾9en“from“Pieter“Hartel's“bAÇenc˜hmark“suite“[HL92Ž‘÷l].‘íTheŽ¡‘íºâbiggest›²›one,–ÙíëMag2hsº,“is˜preproAÇcessor˜for˜a˜dialect˜of˜Hask¾9ellŽ¡‘íºâaugmen¾9ted–ˆðwith“attribute“grammar“[Joh87Ž‘Ä9]“facilities,‘¥Öwrit-Ž¡‘íºâten–Ãbš¾9y“Da˜vid“Rushall.‘ %ŸThe“analyser“w˜as“compiled“withŽ¡‘íºâChalmers–ÙîHask¾9ell-B‘Ù»0.999.4,‘ with“ ags“ëM-fpbu‘¹–-Oº,“and“runŽ¡‘íºâusing–èçan“eighš¾9t“megab˜yte“heap“for“all“except“ëMag2hsº,‘Ëwhic˜hŽ¡‘íºârequired–~¢a“sixteen“megab¾9yte“heap.‘XYA‘~‡generational“garbageŽ¡‘íºâcollector–W×wš¾9as“emplo˜y˜ed.‘ãøT‘ÿ:«ests“w˜ere“run“on“a“ligh˜tly“loadedŽ¡‘íºâSun–ˆ¨Sparc“10/31,‘¤Ëand“eacš¾9h“test“w˜as“pAÇerformed“at“least“threeŽ¡‘íºâtimes.‘pTimes–Tare“user“CPU“seconds.Ž© ‘íºâSimply–Ãmeasuring“o•¾9v“erall–Ãrun“times“is“not“particularly“help-Ž¡‘íºâful,‘mbAÇecause–[†wš¾9e“really“w˜an˜t“to“establish“ho˜w“expAÇensiv˜e“thisŽ¡‘íºâanalyser–Š¢wš¾9ould“bAÇe“if“emplo˜y˜ed“in“a“Hask˜ell“compiler.‘|ZItŽ¡‘íºâseems–v²reasonable“to“consider“the“\bšAÇorder"“b˜et•¾9w“een–v²the“fron¾9tŽ¡‘íºâend–”and“the“analyser“itself“as“the“pAÇoinš¾9t“where“the“t˜ypAÇe-Ž¡‘íºâc•¾9hec“k“er–ØÁprošAÇduces“a“t¾9yp˜e-annotated“Core“tree,–äÞsince,“at‘ØÁleastŽ¡‘íºâin–q±Glasgoš¾9w“Hask˜ell,‘ÈÈthe“compiler“proAÇduces“this“tree“an˜y-Ž¡‘íºâw•¾9a“y‘ÿ:«.‘€So›ƒw“e˜presen“t˜ gures˜not˜only˜for˜a˜complete˜run,‘butŽ¡‘íºâalso– §for“the“analysis“phase“propAÇer.‘6The“latter“category“co¾9v-Ž¡‘íºâers›Ç_ rsti cation,–Öömonomorphisation,“abstract˜in¾9terpretationŽ¡‘íºâand–¼ xpAÇoinš¾9ting,‘DÛall“of“whic˜h“are“legitimate“analysis“expAÇenses.ަ‘íºâT‘ÿ:«o–assess“whether“or“not“wš¾9e“are“approac˜hing“the“righ˜t“ball-Ž¡‘íºâpark,‘C§wš¾9e–;timed“Glasgo˜w“Hask˜ell“0.10“compiling“the“programsŽ¡‘íºâin¾9to–®*C,“and“compared“those“times“with“the“analysis“phaseŽ¡‘íºâtime–á^of“Anna.‘ The“compiler“options“w¾9ere“ëM-O2‘¹–-Cº.“CompilerŽ¡‘íºâsemispace–Œ¡sizes“wš¾9ere“3“megab˜ytes“for“the“small“t˜w˜o,‘ªsand“8Ž¡‘íºâmegabš¾9ytes–¸¡for“the“big“three:‘c this“turned“out“to“bAÇe“plen˜t˜y‘ÿ:«.Ž¡‘íºâThe–¢times“repAÇorted“for“Glasgoš¾9w“Hask˜ell“are“for“the“compilerŽ¡‘íºâpropAÇer,–£(that›†œis,“that˜part˜of˜the˜compiler˜whic¾9h˜is˜itself˜writ-Ž¡‘íºâten–fin“Haskš¾9ell,‘ëand“whic˜h“translates“the“output“of“the“Y‘ÿ:«accŽ¡‘íºâparser–Tin¾9to“C.ަ‘íºâT‘ÿ:«able–¿À2“presenš¾9ts“the“ gures.‘µThe“maxim˜um“residency“ g-Ž¡‘íºâures–½wš¾9ere“obtained“using“a“cop˜ying“collector“with“heap“sizesŽ¡‘íºâset–¯only“just“big“enough.‘êðThis“quan•¾9tit“y–¯is“omitted“for“theŽ¡‘íºâanalysis-only–° gures“bAÇecause“of“the“diculties“of“decidingŽ¡‘íºâon– Èho¾9w“to“divide“space“expšAÇenses“b˜et•¾9w“een– Èthe“fron¾9t“end“andŽ¡‘íºâthe–Tanalysis“phase.ަ‘íºâF‘ÿ:«or–¯{the“big“three,›Ötimes“are,˜v¾9ery“roughly‘ÿ:«,˜divided“equallyŽ¡‘íºâbAÇet•¾9w“een–âÿthe“fron¾9t“end“and“analysis“phases.‘ ©ëMag2hs“ºhas“a“rel-Ž¡‘íºâativ¾9ely–؈large“analysis“time“in“comparison“to“its“size.‘f ThisŽ¡‘íºâis–4bAÇecause“it“makš¾9es“considerable“use“of“lazy“pattern“matc˜h-Ž¡‘íºâing,‘FÆwhicš¾9h– °translates“to“a“large“quan˜tit˜y“of“complex“CoreŽŽŽ þ%¦d’õºâexpressions.‘ÓìThese–R}in“turn“generate“some“large,‘¡Çcomplexޤ ’õºâsets–(zof“equations“for“the“ xpAÇoinš¾9ter“to“solv˜e.‘UâA‘(3tec˜hniqueŽ¡’õºâmenš¾9tioned–9ìin“section“6.4“migh˜t“help“here.‘Š9F‘ÿ:«or“the“largerŽ¡’õºâproblems,›—¢space–x4consumption“is“of“concern.‘èMuc¾9h,˜if“not“theŽ¡’õºâma‘ƒŽjoritš¾9y‘ÿ:«,‘©@of–‹«the“space“used“is“related“to“fron˜t-end“proAÇcess-Ž¡’õºâing,‘›+and–€fit“seems“likš¾9ely“that“the“analysis“itself“is“relativ˜elyŽ¡’õºâcš¾9heap–Þon“space.‘¶F‘ÿ:«urther“in˜v˜estigation“with“a“heap“pro lerŽ¡’õºâis‘Tnecessary‘ÿ:«.Ž© ’õºâThe–±results“of“comparing“analysis“time“with“a“run“of“Glasgo¾9wŽ¡’õºâHaskš¾9ell–Ueon“the“same“program“are“in˜triguing.‘ÜvThe“tests“are“atŽ¡’õºâleast–øfair“in“the“sense“that“bAÇoth“Anna“and“the“Hask¾9ell“com-Ž¡’õºâpiler–Äare“written“in“Hask¾9ell,‘ {so“neither“has“an“unfair“adv‘ÿ|ran-Ž¡’õºâtage.‘ñàJust–•£bš¾9y“themselv˜es,‘¯-it“is“a“little“un˜usual“that“ëMghc“ºcom-Ž¡’õºâpiled–šÍëMag2hs“ºin“almost“half“the“time“it“toAÇok“for“ëMwave4mainº.Ž¡’õºâIt–’+maš¾9y“bAÇe“that“the“hea˜vy“use“of“n˜umeric“o˜v˜erloading“in“ëMwangŽ¡’õºâºand–еëMwave4main“ºhas“slo•¾9w“ed›еdo“wn˜ëMghc˜ºas˜it˜will˜ha“v“e˜hadŽ¡’õºâto–îûgenerate“and“optimise“large“quan¾9tities“of“dictionary“han-Ž¡’õºâdling–bdcoAÇde.‘àËëMag2hsº,›†.b¾9y“comparison,˜is“mostly“string“handling:Ž¡’õºâthere–ÜÌis“little“o•¾9v“erloading–ÜÌin“it.‘rÙAnna“has“a“naiv¾9e“view“ofŽ¡’õºâthe–ÐKHaskš¾9ell“n˜um˜bAÇers“{“it“only“kno˜ws“abAÇout“ëMIntº,‘ÿso“it“willŽ¡’õºânot›)ôha•¾9v“e˜seen˜an“y˜suc“h˜n“umeric˜o“v“erloading.‘ZQIn˜order˜toŽ¡’õºâmakš¾9e–¨Anna“accept“these“t˜w˜o“programs,‘Ëw˜e“had“to“strip“outŽ¡’õºâthe–‘äextensivš¾9e“t˜ypAÇe“signatures“whic˜h“had“bAÇeen“placed“thereŽ¡’õºâexpressely–vxto“eliminate“nš¾9umeric“o˜v˜erloading.‘?ÝThese“factorsŽ¡’õºâma•¾9y›8·w“ell˜ha“v“e˜conspired˜to˜giv“e˜Anna˜a˜remark‘ÿ|rably˜go•AÇo“d˜rel-Ž¡’õºâativ•¾9e›Š#sho“wing˜for˜ëMwang˜ºand˜ëMwave4mainº,‘§Walthough˜it˜is˜hardŽ¡’õºâto–ÂèbAÇelievš¾9e“they“accoun˜t“for“all“the“di 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xp˜oin¾9ting“a“single“large“group“of“ab˜out“t•¾9w“en“t“yŽ¡’õºâfunctions–µÀwhicš¾9h“arose“from“the“extensiv˜e“use“of“lazy“patternŽ¡’õºâmatc¾9hing.‘~ÀIt–6seems“plausible“that“this“particular“group“didŽ¡’õºânot–œãcause“anš¾9y“similar“dicult˜y“to“ëMghcº,‘¾Çand“it“ma˜y“also“bAÇeŽ¡’õºâpšAÇossible–x£that“ëMghcº's“desugarer“did“a“b˜etter“job“than“Anna'sŽ¡’õºâin–qCtranslating“the“pattern“matc•¾9hing.‘0<Nev“ertheless,‘ˆ>the‘qCdis-Ž¡’õºâparitš¾9y–çin“relativ˜e“analysis/compile“costs“bAÇet˜w˜een“ëMag2hs“ºandŽ¡’õºâthe–òÔother“t•¾9w“o–òÔbig“examples“is“a“wš¾9arning“that“w˜e“should“notŽ¡’õºâread–¡\toAÇo“m•¾9uc“h›¡\in“to˜these˜measuremen“ts˜bAÇey“ond˜the˜pAÇerhapsŽ¡’õºâheartening–ò]conclusion“that“wš¾9e“are“indeed“approac˜hing“theŽ¡’õºârigh¾9t–Tballpark“for“analyser“pAÇerformance.ŽŽŽŽŽŽŸ’åä27ŽŽŒ‹´† •ºâ ý? £ ý€‘íºâ¹6.3Ž‘G·Related‘LÎw•¹™o“rkŽŸm‘íºâºMycroft's–òoriginal“wš¾9ork“[Myc80Ž‘¸|]“on“applying“abstract“in˜ter-ޤ 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nition“strictnessŽ¡‘íºâanalysis–päfor“an¾9ything“other“than“trivial“inputs,‘‘Èand“there“areŽ¡‘íºâgo•AÇo“d–¬õtheoretical“reasons“for“bAÇelieving“the“situation“cannotŽ¡‘íºâbAÇe‘Timpro•¾9v“ed.Ž© ‘íºâStarting–{at“around“the“same“time,‘™íanother“scš¾9hoAÇol“of“though˜tŽ¡‘íºâw•¾9as›þÐdev“eloping˜bac“kw“ards,–Qor˜pro‘ƒŽjection,“analyses.‘ïA‘þÊbac¾9k-Ž¡‘íºâwš¾9ards–·analysis“sho˜ws“ho˜w“the“seman˜tic“quan˜tit˜y“in“questionŽ¡‘íºâ-–Jphere,‘W·demand“for“ev‘ÿ|raluation“-“propagates“from“a“functionŽ¡‘íºâapplication–@to“the“individual“argumen¾9ts.‘Õ\Hughes“[Hug90Ž‘ó']“ar-Ž¡‘íºâgues–¼Ûthat“bac•¾9kw“ards–¼Ûanalyses“are“inherenš¾9tly“more“ecien˜tŽ¡‘íºâthan–U[forwš¾9ard“ones,‘e]bAÇecause“the“function“spaces“with“whic˜hŽ¡‘íºâthe–¯Àanalyses“deal“are“smaller“in“the“bac•¾9kw“ards‘¯Àcase.‘ú”Pro‘ƒŽjec-Ž¡‘íºâtion–êãanalysis“deals“easily“with“sum-of-prošAÇducts“t¾9yp˜es,‘ GandŽ¡‘íºâcaptures–ÔZcertain“propAÇerties,›Dsuc¾9h“as“head-strictness,˜thatŽ¡‘íºâseem–žto“elude“forw¾9ard“analyses.‘¶ˆA‘ãgo•AÇo“d–žreference“for“pro-Ž¡‘íºâjection–Þanalysis“is“[WH87Ž‘±].‘v¯Later“wš¾9ork“sho˜w˜ed“ho˜w“to“doŽ¡‘íºâmak¾9e–+únon- at“pro‘ƒŽjection“analysis“pAÇolymorphic“[HugŽ‘³+],‘q¤andŽ¡‘íºâa–Úñsuccessful“non- at,‘ WpAÇolymorphic“pro‘ƒŽjection“analyser“w¾9asŽ¡‘íºâbuilt–Tinš¾9to“Glasgo˜w“Hask˜ell“[KHL91Ž‘(Ô].ަ‘íºâDespite–ãÔthese“successes,‘tpro‘ƒŽjection“analyses“ha•¾9v“e–ãÔa“funda-Ž¡‘íºâmen•¾9tal› #inabilit“y˜to˜deal˜with˜higher˜order˜functions.‘÷ÞF‘ÿ:«ol-Ž¡‘íºâloš¾9wing–˜the“lead“of“W‘ÿ:«ra˜y“[W‘ÿ:«ra85Ž‘:C],‘ù.Hughes“de ned“a“mixedŽ¡‘íºâanalysis–ô|whicš¾9h“w˜as“forw˜ards“for“the“higher“order“bits“andŽ¡‘íºâbac•¾9kw“ards–SŠfor“evš¾9erything“else“[Hug87Ž‘ó'].‘×Doing“this“giv˜es“anŽ¡‘íºâanalysis–r+whic¾9h“deals“with“higher-orderness“whilst“retainingŽ¡‘íºâthe–‡äinherenš¾9t“eciency“of“bac˜kw˜ard“analysis.‘íKRecen˜tly‘ÿ:«,‘¤.otherŽ¡‘íºâw•¾9ork“ers›ÌQha“v“e˜b•AÇegun˜to˜explore˜the˜relationship˜b“et•¾9w“een˜for-Ž¡‘íºâwš¾9ard–ÒÉand“bac˜kw˜ard“analysis“[Bur90Ž‘Žã]“[HL90Ž‘÷l]“[D˜W90Ž‘N].‘TÐTheŽ¡‘íºâanalysis–³ÁdescribšAÇed“in“this“pap˜er“is“a“mo˜di cation“of“Hughes'Ž¡‘íºâoriginal–Tmixed“analysis.ަ‘íºâMean•¾9while,‘=pAÇeople›xha“v“e˜b•AÇeen˜lo“oking˜at˜other˜w•¾9a“ys˜of˜solv-Ž¡‘íºâing–vÝrecursiv¾9e“domain“equations.‘A There“has“bAÇeen“a“discern-Ž¡‘íºâable–Jƒshift“to•¾9w“ards–Jƒterm“orienš¾9ted“approac˜hes.‘»üF‘ÿ:«erguson“andŽ¡‘íºâHughes–ö#dev¾9elopAÇed“\concrete“data“structures"“(CDSs)“[ëN?Ž‘sº]Ž¡‘íºâbased–7…on“Curien's“wš¾9ork“on“sequen˜tial“algorithms“[Cur86Ž‘¯õ].Ž¡‘íºâCDSs–‚Îdeal“with“higher-orderness“b¾9y“regarding“a“higher“or-Ž¡‘íºâder–#%function“as“conš¾9taining“a“CDS‘#!in˜terpreter“for“eac˜h“func-Ž¡‘íºâtional–®0parameter.‘çThis“is“really“a“disguised“w•¾9a“y–®0of“substi-Ž¡‘íºâtuting–‡in“functional“parameters“bšAÇefore“ xp˜oin¾9ting.‘ìÿWhetherŽ¡‘íºâor–not“CDSs“can“delivš¾9er“a“viable“ xpAÇoin˜ting“mec˜hanism“re-Ž¡‘íºâmains–þto“bAÇe“seen.‘îmEarly“implemenš¾9tations“hin˜ted“at“spaceŽ¡‘íºâproblems,‘€but–®Dthese“maš¾9y“no˜w“ha˜v˜e“bAÇeen“solv˜ed“[Hug93Ž‘ó'].Ž¡‘íºâCDSs–/·can“also“bAÇe“view¾9ed“as“a“higher-order“generalisationŽ¡‘íºâof–ÁÁthe“minimal“function“graph“sc¾9heme“originally“describAÇedŽ¡‘íºâb¾9y–E§Neil“Jones“[JM86Ž‘zú].‘­jMinimal“function“graphs“are“usedŽ¡‘íºâin–=Äthe“Semanš¾9tique“analyser“[KHL91Ž‘(Ô]“built“in˜to“Glasgo˜wŽ¡‘íºâHask¾9ell‘T[PHHP93Ž‘#µø].ަ‘íºâThe–ü“term“rewriting“based“ xpšAÇoin¾9ter“describ˜ed“here“w¾9as,ŽŽŽ ý€’õºâin–œÅpart,‘¾¡inspired“b¾9y“Charles“Consel's“strictness“analyser“inޤ ’õºâthe–G¿Y‘ÿ:«ale“Hask¾9ell“compiler“[Gro92Ž‘ÀP].‘³±Consel's“papAÇer“[Con91Ž‘±¼],Ž¡’õºâwhicš¾9h–Îseems“to“ha˜v˜e“passed“b˜y“almost“unnoticed,‘µdescribAÇedŽ¡’õºâa–7#successful,›–if“simple,˜strictness“analyser“solving“ xpAÇoin¾9tŽ¡’õºâequations–•Ybš¾9y“term“rewriting.‘œIn“view“of“ho˜w“w˜ell“this“andŽ¡’õºâConsel's–}ásystem“wš¾9ork,‘œ,it“is“pAÇerhaps“a“pit˜y“that“P˜eyton“JonesŽ¡’õºâet–;al“made“disparaging“remarks“abšAÇout“term-based“ xp˜oin¾9t-Ž¡’õºâing–Tin“their“seminal“fron¾9tiers“papAÇer“[PC87Ž‘9].ŽŸ5’õºâ¹6.4Ž’ G·F•¹™urther‘LÎw“o“rkŽŸm’õºâºAnna's–N¾pAÇerformance“is“encouraging.‘È­Nev¾9ertheless,‘there'sŽ¡’õºâstill–ê¿a“long“w•¾9a“y–ê¿to“go“bAÇefore“ev‘ÿ|raluation“transformer“infor-Ž¡’õºâmation–BÙcan“bšAÇe“generated“automatically“in“pro˜duction“com-Ž¡’õºâpilers.‘pThree›Ta•¾9v“en“ues˜of˜dev“elopmen“t˜need˜to˜b•AÇe˜p“ersued.ŽŸÐO’äëPŽŽŽ’ :âëNEnhancemenš´Ct–jeof“applicabilit˜y‘ÿÌ.‘È]ºAnna's–most“w¾9orry-Ž¡’ :âing–®alimitation“is“her“inabilit¾9y“to“deal“with“higher“orderŽ¡’ :âfunctions–Ûwhic¾9h“cannot“bšAÇe“ rsti ed.‘ôA‘½p˜ossible“partialŽ¡’ :âsolution–ÉMis“to“iterate“these“(or,›؂more“precisely‘ÿ:«,˜just“theŽ¡’ :ânastš¾9y–Âwbits)“as“man˜y“times“as“is“necessary“to“guaran-Ž¡’ :âtee–GÔa“ xpAÇoinš¾9t.‘×ðThe“w˜ork“of“Nielson“and“Nielson“[NN92Ž‘>]Ž¡’ :âgivš¾9es–7ethe“magic“n˜um˜bAÇer“of“iterations“needed.‘ÒvF‘ÿ:«or“man˜yŽ¡’ :âcommon–’'forms,›ñ[this“n•¾9um“bAÇer–’'is“reasonably“lo¾9w,˜andŽ¡’ :âit–Zseems“reasonable“to“expAÇect“this“approac¾9h“to“yieldŽ¡’ :âw•¾9orth“while‘Tresults.Ž© ™š’ :âIt–·eis“also“necessary“to“remo•¾9v“e–·esome“of“the“excessiv¾9e“re-Ž¡’ :âstrictions–Jion“user-de ned“data“t¾9ypAÇes“discussed“in“sec-Ž¡’ :âtion–\ô2.2.6.‘óQThis“došAÇes“not“app˜ear“to“b˜e“particularlyŽ¡’ :âdicult.‘òKubiak–\Šet“al“[KHL91Ž‘(Ô]“managed“this“quiteŽ¡’ :âsuccessfully‘ÿ:«.ŽŸ34’äëPŽŽŽ’ :âëNEnhancemen´Ct–gof“pK¼erformance.‘÷ÙºThe–§Žre nemen¾9ts“ofŽ¡’ :âsection–=Œ6.1“ha•¾9v“e–=Œdone“a“lot“to“impro•¾9v“e–=Œthe“system'sŽ¡’ :âpAÇerformance.‘¡Nevš¾9ertheless,‘Œ˜some–A‹programs“w˜e“triedŽ¡’ :ârecen¾9tly–›Ö-“in“excess“of“a“thousand“lines“-“run“moreŽ¡’ :âsloš¾9wly–îÀthan“one“w˜ould“lik˜e.‘¨µIn˜v˜estigations“are“bAÇeingŽ¡’ :âmade.ަ’ :âFixpAÇoin¾9ting–L½large“groups“of“functions“could“conciev-Ž¡’ :âably–ðbAÇe“accelerated“b¾9y“reducing“the“group“to“a“\mini-Ž¡’ :âmal–Tform"“ rst.‘pF‘ÿ:«or“example,“giv¾9enŽ©Ì͍’g¤ëMa–¹–=“...“a“...“b“...Ž¡’g¤b–¹–=“...“c“...Ž¡’g¤c–¹–=“...“c“...“d“...Ž¡’g¤d–¹–=“...“a“...ަ’ :âºwš¾9e–`®can“remo˜v˜e“ëMb“ºand“ëMd“ºb˜y“substituting“them“in˜to“ëMa“ºandŽ¡’ :âëMc– åºrespAÇectivš¾9ely‘ÿ:«.‘ This“halv˜es“the“n˜um˜bAÇer“of“functions“inŽ¡’ :âthe–ÿ2group“bšAÇeing“ xp˜oin¾9ted.‘Ú Once“the“solutions“to“ëMaŽ¡’ :âºand–ÆlëMc“ºha•¾9v“e–ÆlbAÇeen“generated,‘Ö4w¾9e“obtain“v‘ÿ|ralues“for“ëMb“ºandŽ¡’ :âëMd–Tºbš¾9y“straigh˜tforw˜ard“bac˜k-substitution.ŽŸ ™š’ :âNote–G that“this“tecš¾9hnique“ma˜y“bAÇe“used“in“an˜y“situa-Ž¡’ :âtion›¥¿in•¾9v“olving˜ xpAÇoin“ting˜m“utually˜recursiv“e˜groups˜ofŽ¡’ :âequations.‘µÆThe–Æidea“stems“from“an“analogy“with“theŽ¡’ :âGauss-Jordan–„¨methoAÇd“for“solving“sim¾9ultaneous“linearŽ¡’ :âequations.‘zíIn–4Óthis“case,‘<³a“recursiv¾9e“group“can“only“bAÇeŽ¡’ :âreduced–Ito“the“pAÇoinš¾9t“where“ev˜ery“equation“in“the“groupŽ¡’ :ârefers–öœdirectly“to“itself“{“no“further.‘ÀHAfter“that,‘.î x-Ž¡’ :âpAÇoinš¾9ting–x is“una˜v˜oidable.‘DWhether“or“not“this“rendersŽ¡’ :âa–ŸspšAÇeedup“dep˜ends“on“the“relativ¾9e“costs“of“substitution,Ž¡’ :âbacš¾9k–Tsubstitution“and“ xpAÇoin˜ting.ŽŽŽŽŽŸ’åä28ŽŽŒ‹ÜÑ •ºâ ý? £ ý€‘ûäëPŽŽŽ‘:âëNDealing–¦with“moK¼dulesº.‘ 5MoAÇdules–ÈZare“an“unmiti-ޤ ‘:âgated–†Çnš¾9uisance“for“man˜y“kinds“of“high“pAÇo˜w˜ered“seman-Ž¡‘:âtic–xManalyses“and“optimisations.‘E\In“particular,‘Ñ moAÇd-Ž¡‘:âules–Ñcause“big“diculties“for“an¾9y“kind“of“what“JohnŽ¡‘:âY›ÿ:«oung–(termed“\collecting“in¾9terpretations"“[Y˜ou89Ž‘-Ò].‘TÂAŽ¡‘:âcollecting–‘Tinš¾9terpretation“is“essen˜tially“a“global“anal-Ž¡‘:âysis.‘ vøMan¾9y–Þ,compile“time“optimisations“are“limitedŽ¡‘:âb¾9y–$the“moAÇdule“structure.‘IøF‘ÿ:«or“example,‘hMsome“of“theŽ¡‘:âmore–Äirecenš¾9t“sc˜hemes“for“compiling“o˜v˜erloading“ef-Ž¡‘:â cien¾9tly–[Jon93Ž‘Ä9]“[Aug93Ž‘ó']“require“global“analysis“forŽ¡‘:âfull–Ê=applicabilitš¾9y‘ÿ:«.‘ ;,The“pAÇoin˜t“of“all“this“is“that“theŽ¡‘:âmonomorphisation–+œand“ rsti cation“transformationsŽ¡‘:âused–Tin“Anna“also“require“a“global“view.ŽŸ Ûk‘:âThere–”"is“an“urgen¾9t“need“to“devise“sophisticated“com-Ž¡‘:âpilation–×wsystems“whicš¾9h“main˜tain“enough“in˜termoAÇduleŽ¡‘:âcommš¾9unication–?™to“mak˜e“global“analyses“pAÇossible.‘›?De-Ž¡‘:âv•¾9elopmen“t–»fof“sucš¾9h“a“framew˜ork“w˜ould“bAÇene t“not“onlyŽ¡‘:âstrictness–oªanalysis,‘†@but“man¾9y“aspAÇects“of“compile“timeŽ¡‘:âoptimisation.‘©¨Sucš¾9h–™¼a“compiler“migh˜t“w˜ork“b˜y“dump-Ž¡‘:âing–^øa“lot“of“information“inš¾9to“a“moAÇdule's“in˜terface“ le,Ž¡‘:âenough–A‚to“do“whatevš¾9er“analyses“w˜e“need.‘ úThis“w˜ouldŽ¡‘:âreally–©„just“bAÇe“an“extension“of“the“sc¾9hemes“used“al-Ž¡‘:âready–a in“the“Chalmers“and“Glasgoš¾9w“compilers,‘sûwhic˜hŽ¡‘:âdump–ù{function“aritš¾9y“and“rudimen˜tary“strictness“infor-Ž¡‘:âmation–¯inš¾9to“in˜terface“ les.‘µThe“question“is“not“re-Ž¡‘:âally–@ whether“wš¾9e“could“construct“suc˜h“a“system,‘ŠÓbutŽ¡‘:âwhether–ˆ¯the“quan•¾9tit“y–ˆ¯of“information“dumpAÇed“in¾9to“in-Ž¡‘:âterface–3ú les“could“bAÇe“limited“sucien¾9tly“to“render“theŽ¡‘:âsc¾9heme‘Tpractical.Ž©™µ‘íºâ¹Ackno¹™wledgementsŽŸ†´‘íºâºThanks–9Íto“Bill“Mitc¾9hell“for“advice“on“building“term“rewrit-Ž¡‘íºâing– ‚systems,‘ ¬and“to“Barney“Hilkš¾9en“for“an“in˜v‘ÿ|raluable“insigh˜tŽ¡‘íºâregarding–separate“compilation“systems.‘ê Mark“Jones“pro-Ž¡‘íºâvided–ñmanš¾9y“in˜teresting“commen˜ts“abAÇout“monomorphisationŽ¡‘íºâand–Oz rsti cation,‘^and“outlined“the“instance-collecting“algo-Ž¡‘íºârithm–߯of“Section“5.6.1.‘ ŽGeo rey“Burn“and“Denis“Ho•¾9w“e‘߯w“ereŽ¡‘íºâsucien•¾9tly›8Öbra“v“e˜to˜expAÇerimen“t˜with˜the˜implemen“tation,Ž¡‘íºâand–Tproš¾9vided“useful“feedbac˜k.ŽŸ ‘íºâDenis›Û³Ho•¾9w“e˜read˜an˜early˜draft˜in˜min“ute˜detail.‘ :His˜exten-Ž¡‘íºâsivš¾9e–³|and“sometimes“am˜usingŸü-=Õ2ŽŽ‘Þ#ºcommen˜ts“pro˜v˜ed“v˜ery“helpfulŽ¡‘íºâin–Tmaking“the“presen¾9tation“clearer.ަ‘íºâ¹ReferencesŽŸÅ‘íºâº[Aug87]ŽŽ‘fL.‘|Augustsson.‘ŠëRCompiling–J´Lš‡azy“F‘ÿJªunctional“L˜an-Ž¡‘fguages,‘l’Part‘f€IIº.‘h€PhD‘/¶thesis,‘6WChalmers‘/¼T‘ÿ:«eknisk‘ÿ|raŽ¡‘fH–û`ogsk¾9ola,›TG“otebAÇorg,˜Sw¾9eden,˜1987.Ž©¶Ö‘íºâ[Aug93]ŽŽ‘fLennart–¤êAugustsson.‘bImplemenš¾9ting“hask˜ell“o˜v˜er-Ž¡‘floading.‘-ðIn‘ÍëRPr•‡o“c“e“e“dings–AEof“the“F‘ÿJªunctional“Pr‡o-Ž¡‘fgr•‡amming›•`L“anguages˜and˜Computer˜AÃŽr“chite“ctur“eŽ¡‘fConfer•‡enc“e,›N<Cop“enhagen,˜Denmarkº,–TJune“1993.ަ‘íºâ[Bar91]ŽŽ‘fG.–³úBaraki.‘íuA‘³Žnote“on“abstract“in¾9terpretationŽ¡‘fof–äQpAÇolymorphic“functions.‘ }„In“R.J.M.“Hughes,Ž¡‘feditor,‘÷íëRPr•‡o“c“e“e“dings–ôÑof“the“ fth“AÃŽCM‘ô§c•‡onfer“enc“eŽ¡‘fon–6¨F‘ÿJªunctional“Lš‡anguages“and“Computer“AÃŽr˜chi-Ž¡‘fte•‡ctur“eº,‘„Fn•¾9um“bAÇer–:ã523“in“Lecture“Notes“in“Com-Ž¡‘fputer–{–Science,›•&pages“367{378,˜Cam¾9bridge,˜Mas-Ž¡‘fsac•¾9h“usetts,–T26{30“August“1991.“Springer-V‘ÿ:«erlag.Ž‘íºâŸâ‰ff_ÿ Ÿ× ‘ r}Ÿüûr°2ŽŽ‘Y±See–±Èthe“other“fo7otnote.ŽŽŽ ý€’õºâº[BHA85]ŽŽ’#fG.L.–0Burn,›ܧC.L.“Hankin,˜and“S.“Abramsky‘ÿ:«.ޤ ’#fThe–‘àtheory“of“strictness“analysis“for“higher-orderŽ¡’#ffunctions.‘MŒIn‘~QëRPr•‡o“c“e“e“dings–™õof“the“Workshop“onŽ¡’#fPr•‡o“gr“ams–È÷as“Data“Obje‡ctsº,–¼Fpages‘šâ42{62,“DIKU,Ž¡’#fCopšAÇenhagen,–ÚøDenmark,“17{19–ØOctob˜er“1985.Ž¡’#fSpringer-V‘ÿ:«erlag–TLNCS“217.Ž©ÕV’õºâ[Bur87]ŽŽ’#fG.L.‘ìüBurn.‘Ø ëRAÃŽbstr•‡act›))Interpr“etation˜and˜the˜Par-Ž¡’#falxälel–þìEvaluation“of“F‘ÿJªunctional“L‡anguagesº.‘VÉPhDŽ¡’#fthesis,–ÏImpAÇerial›7PCollege,“Univ•¾9ersit“y˜of˜London,Ž¡’#fMarc¾9h‘T1987.ަ’õºâ[Bur90]ŽŽ’#fG.L.–}ÃBurn.‘QA‘}¨relationship“bAÇet•¾9w“een–}Ãabstract“in-Ž¡’#fterpretation–k{and“pro‘ƒŽjection“analysis.‘òIn“ëR17th‘²)AÃŽn-Ž¡’#fnual–F×AÃŽCM‘FÕSympš‡osium“on“the“Principles“of“Pr˜o-Ž¡’#fgr•‡amming‘ŽkL“anguagesº,–l¢pages›[,151{156,“San˜F‘ÿ:«ran-Ž¡’#fcisco,–T17{19“Janš¾9uary“1990.“A˜CM.ަ’õºâ[Bur91]ŽŽ’#fG.L.‘yoBurn.‘°ëRLš‡azy–¾úF‘ÿJªunctional“L˜anguages:‘øbAÃŽbstr˜actŽ¡’#fInterpr‡etation–“<and“Compilationº.‘ÎResearc¾9h‘IÔMono-Ž¡’#fgraphs–in“P¾9arallel“and“Distributed“Computing.Ž¡’#fPitman–ÝÈin“assoAÇciation“with“MIT‘ݺPress,‘èå1991.‘¿CT‘ÿ:«oŽ¡’#fappAÇear.ަ’õºâ[CD91]ŽŽ’#fW‘ÿ:«ei-Ngan–¸Chin“and“John“Darlington.‘¸Remo¾9vingŽ¡’#fhigher-order–Pþexpressions“b¾9y“program“transforma-Ž¡’#ftion.‘Chin– zis“at“NUS,“SingapAÇore“and“DarlingtonŽ¡’#fat–<|ImpAÇerial,›FFLondon.“P¾9ossibly“published,˜F‘ÿ:«ebru-Ž¡’#fary‘T1991.ަ’õºâ[Con91]ŽŽ’#fCharles–íÏConsel.‘ ”®F‘ÿ:«ast“strictness“analysis“viaŽ¡’#fsymš¾9b•AÇolic‘JU xp“oin˜t–JUiteration.‘²¤Unpublished.“Y‘ÿ:«aleŽ¡’#fUniv•¾9ersit“y‘ÿ:«,‘9Departmen“t–˜[of“Computer“Science,Ž¡’#fSeptem¾9bAÇer‘T1991.ަ’õºâ[Cur86]ŽŽ’#fP‘ÿ:«.-L.‘Z˜Curien.‘è8ëRCate•‡goric“al‘ãCombinators,‘ÍSe“quen-Ž¡’#ftial–—ùAšÃŽlgorithms“A˜nd“F‘ÿJªunctional“Pr•‡o“gr“ammingº.Ž¡’#fResearc¾9h–\¼Notes“in“Theoretical“Computer“Sci-Ž¡’#fence–—›series.“Pitman“Publishing“Limited,‘°ÀLondon,Ž¡’#f1986.ަ’õºâ[D¾9W90]ŽŽ’#fKei–¬UDa¾9vis“and“Philip“W‘ÿ:«adler.‘n¨Strictness“analysisŽ¡’#fin–¢Ü4d.‘_7In“ëRIn›å pr•‡o“c“e“e“dings˜of˜the˜1990˜Glasgow˜AyrŽ¡’#fFP–N<Workshop“(??)º,‘T1990.ަ’õºâ[Gro92]ŽŽ’#fThe–JÝY‘ÿ:«ale“Haskš¾9ell“Group.‘¹WThe“y˜ale“hask˜ell“usersŽ¡’#fman•¾9ual,›Tv“ersion˜y2.0-bAÇeta,˜August˜1992.ަ’õºâ[HH91]ŽŽ’#fSebastian–²Hunš¾9t“and“Chris“Hankin.‘#ØFixed“pAÇoin˜tsŽ¡’#fand–çæfronš¾9tiers:‘Á“a“new“p•AÇersp“ectiv˜e.‘ ˆ/ëRJournal‘úüofŽ¡’#fF‘ÿJªunctional‘ò-Pr•‡o“gr“ammingº,›Å01(1):91–±&{“120,˜Jan¾9uaryŽ¡’#f1991.ަ’õºâ[HH92]ŽŽ’#fSebastian–¸7Hunš¾9t“and“Chris“Hankin.‘‚Appro˜ximateŽ¡’#f 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jart/cosmopolitan
false
cosmopolitan/third_party/bzip2/spewG.c
#include "libc/stdio/rand.h" #include "libc/stdio/stdio.h" /* clang-format off */ /* spew out a thoroughly gigantic file designed so that bzip2 can compress it reasonably rapidly. This is to help test support for large files (> 2GB) in a reasonable amount of time. I suggest you use the undocumented --exponential option to bzip2 when compressing the resulting file; this saves a bit of time. Note: *don't* bother with --exponential when compressing Real Files; it'll just waste a lot of CPU time :-) (but is otherwise harmless). */ /* ------------------------------------------------------------------ This file is part of bzip2/libbzip2, a program and library for lossless, block-sorting data compression. bzip2/libbzip2 version 1.0.8 of 13 July 2019 Copyright (C) 1996-2019 Julian Seward <[email protected]> Please read the WARNING, DISCLAIMER and PATENTS sections in the README file. This program is released under the terms of the license contained in the file LICENSE. ------------------------------------------------------------------ */ #define _FILE_OFFSET_BITS 64 /* The number of megabytes of junk to spew out (roughly) */ #define MEGABYTES 5000 #define N_BUF 1000000 char buf[N_BUF]; int main ( int argc, char** argv ) { int ii, kk, p; srandom(1); setbuffer ( stdout, buf, N_BUF ); for (kk = 0; kk < MEGABYTES * 515; kk+=3) { p = 25+random()%50; for (ii = 0; ii < p; ii++) printf ( "aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa" ); for (ii = 0; ii < p-1; ii++) printf ( "bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb" ); for (ii = 0; ii < p+1; ii++) printf ( "ccccccccccccccccccccccccccccccccccccc" ); } fflush(stdout); return 0; }
1,767
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jart/cosmopolitan
false
cosmopolitan/third_party/bzip2/words3
If you got this far and the 'cmp's didn't complain, it looks like you're in business. To install in /usr/local/bin, /usr/local/lib, /usr/local/man and /usr/local/include, type make install To install somewhere else, eg, /xxx/yyy/{bin,lib,man,include}, type make install PREFIX=/xxx/yyy If you are (justifiably) paranoid and want to see what 'make install' is going to do, you can first do make -n install or make -n install PREFIX=/xxx/yyy respectively. The -n instructs make to show the commands it would execute, but not actually execute them. Instructions for use are in the preformatted manual page, in the file bzip2.txt. For more detailed documentation, read the full manual. It is available in Postscript form (manual.ps), PDF form (manual.pdf), and HTML form (manual.html). You can also do "bzip2 --help" to see some helpful information. "bzip2 -L" displays the software license.
945
31
jart/cosmopolitan
false
cosmopolitan/third_party/bzip2/bzlib_private.inc
#include "third_party/bzip2/bzlib.h" #define BZ_NO_STDIO /* clang-format off */ /*-------------------------------------------------------------*/ /*--- Private header file for the library. ---*/ /*--- bzlib_private.h ---*/ /*-------------------------------------------------------------*/ /* ------------------------------------------------------------------ This file is part of bzip2/libbzip2, a program and library for lossless, block-sorting data compression. bzip2/libbzip2 version 1.0.8 of 13 July 2019 Copyright (C) 1996-2019 Julian Seward <[email protected]> Please read the WARNING, DISCLAIMER and PATENTS sections in the README file. This program is released under the terms of the license contained in the file LICENSE. ------------------------------------------------------------------ */ /*-- General stuff. --*/ #define BZ_VERSION "1.0.8, 13-Jul-2019" typedef char Char; typedef unsigned char Bool; typedef unsigned char UChar; typedef int Int32; typedef unsigned int UInt32; typedef short Int16; typedef unsigned short UInt16; #define True ((Bool)1) #define False ((Bool)0) #ifndef __GNUC__ #define __inline__ /* */ #endif #ifndef BZ_NO_STDIO extern void BZ2_bz__AssertH__fail ( int errcode ); #define AssertH(cond,errcode) \ { if (!(cond)) BZ2_bz__AssertH__fail ( errcode ); } #if BZ_DEBUG #define AssertD(cond,msg) \ { if (!(cond)) { \ fprintf ( stderr, \ "\n\nlibbzip2(debug build): internal error\n\t%s\n", msg );\ exit(1); \ }} #else #define AssertD(cond,msg) /* */ #endif /* BZ_DEBUG */ #define VPrintf0(zf) \ fprintf(stderr,zf) #define VPrintf1(zf,za1) \ fprintf(stderr,zf,za1) #define VPrintf2(zf,za1,za2) \ fprintf(stderr,zf,za1,za2) #define VPrintf3(zf,za1,za2,za3) \ fprintf(stderr,zf,za1,za2,za3) #define VPrintf4(zf,za1,za2,za3,za4) \ fprintf(stderr,zf,za1,za2,za3,za4) #define VPrintf5(zf,za1,za2,za3,za4,za5) \ fprintf(stderr,zf,za1,za2,za3,za4,za5) #else /* BZ_NO_STDIO */ extern void bz_internal_error ( int errcode ); #define AssertH(cond,errcode) \ { if (!(cond)) bz_internal_error ( errcode ); } #define AssertD(cond,msg) do { } while (0) #define VPrintf0(zf) do { } while (0) #define VPrintf1(zf,za1) do { } while (0) #define VPrintf2(zf,za1,za2) do { } while (0) #define VPrintf3(zf,za1,za2,za3) do { } while (0) #define VPrintf4(zf,za1,za2,za3,za4) do { } while (0) #define VPrintf5(zf,za1,za2,za3,za4,za5) do { } while (0) #endif /* BZ_NO_STDIO */ #define BZALLOC(nnn) (strm->bzalloc)(strm->opaque,(nnn),1) #define BZFREE(ppp) (strm->bzfree)(strm->opaque,(ppp)) /*-- Header bytes. --*/ #define BZ_HDR_B 0x42 /* 'B' */ #define BZ_HDR_Z 0x5a /* 'Z' */ #define BZ_HDR_h 0x68 /* 'h' */ #define BZ_HDR_0 0x30 /* '0' */ /*-- Constants for the back end. --*/ #define BZ_MAX_ALPHA_SIZE 258 #define BZ_MAX_CODE_LEN 23 #define BZ_RUNA 0 #define BZ_RUNB 1 #define BZ_N_GROUPS 6 #define BZ_G_SIZE 50 #define BZ_N_ITERS 4 #define BZ_MAX_SELECTORS (2 + (900000 / BZ_G_SIZE)) /*-- Stuff for randomising repetitive blocks. --*/ extern Int32 BZ2_rNums[512]; #define BZ_RAND_DECLS \ Int32 rNToGo; \ Int32 rTPos \ #define BZ_RAND_INIT_MASK \ s->rNToGo = 0; \ s->rTPos = 0 \ #define BZ_RAND_MASK ((s->rNToGo == 1) ? 1 : 0) #define BZ_RAND_UPD_MASK \ if (s->rNToGo == 0) { \ s->rNToGo = BZ2_rNums[s->rTPos]; \ s->rTPos++; \ if (s->rTPos == 512) s->rTPos = 0; \ } \ s->rNToGo--; /*-- Stuff for doing CRCs. --*/ extern UInt32 BZ2_crc32Table[256]; #define BZ_INITIALISE_CRC(crcVar) \ { \ crcVar = 0xffffffffL; \ } #define BZ_FINALISE_CRC(crcVar) \ { \ crcVar = ~(crcVar); \ } #define BZ_UPDATE_CRC(crcVar,cha) \ { \ crcVar = (crcVar << 8) ^ \ BZ2_crc32Table[(crcVar >> 24) ^ \ ((UChar)cha)]; \ } /*-- States and modes for compression. --*/ #define BZ_M_IDLE 1 #define BZ_M_RUNNING 2 #define BZ_M_FLUSHING 3 #define BZ_M_FINISHING 4 #define BZ_S_OUTPUT 1 #define BZ_S_INPUT 2 #define BZ_N_RADIX 2 #define BZ_N_QSORT 12 #define BZ_N_SHELL 18 #define BZ_N_OVERSHOOT (BZ_N_RADIX + BZ_N_QSORT + BZ_N_SHELL + 2) /*-- Structure holding all the compression-side stuff. --*/ typedef struct { /* pointer back to the struct bz_stream */ bz_stream* strm; /* mode this stream is in, and whether inputting */ /* or outputting data */ Int32 mode; Int32 state; /* remembers avail_in when flush/finish requested */ UInt32 avail_in_expect; /* for doing the block sorting */ UInt32* arr1; UInt32* arr2; UInt32* ftab; Int32 origPtr; /* aliases for arr1 and arr2 */ UInt32* ptr; UChar* block; UInt16* mtfv; UChar* zbits; /* for deciding when to use the fallback sorting algorithm */ Int32 workFactor; /* run-length-encoding of the input */ UInt32 state_in_ch; Int32 state_in_len; BZ_RAND_DECLS; /* input and output limits and current posns */ Int32 nblock; Int32 nblockMAX; Int32 numZ; Int32 state_out_pos; /* map of bytes used in block */ Int32 nInUse; Bool inUse[256]; UChar unseqToSeq[256]; /* the buffer for bit stream creation */ UInt32 bsBuff; Int32 bsLive; /* block and combined CRCs */ UInt32 blockCRC; UInt32 combinedCRC; /* misc administratium */ Int32 verbosity; Int32 blockNo; Int32 blockSize100k; /* stuff for coding the MTF values */ Int32 nMTF; Int32 mtfFreq [BZ_MAX_ALPHA_SIZE]; UChar selector [BZ_MAX_SELECTORS]; UChar selectorMtf[BZ_MAX_SELECTORS]; UChar len [BZ_N_GROUPS][BZ_MAX_ALPHA_SIZE]; Int32 code [BZ_N_GROUPS][BZ_MAX_ALPHA_SIZE]; Int32 rfreq [BZ_N_GROUPS][BZ_MAX_ALPHA_SIZE]; /* second dimension: only 3 needed; 4 makes index calculations faster */ UInt32 len_pack[BZ_MAX_ALPHA_SIZE][4]; } EState; /*-- externs for compression. --*/ extern void BZ2_blockSort ( EState* ); extern void BZ2_compressBlock ( EState*, Bool ); extern void BZ2_bsInitWrite ( EState* ); extern void BZ2_hbAssignCodes ( Int32*, UChar*, Int32, Int32, Int32 ); extern void BZ2_hbMakeCodeLengths ( UChar*, Int32*, Int32, Int32 ); /*-- states for decompression. --*/ #define BZ_X_IDLE 1 #define BZ_X_OUTPUT 2 #define BZ_X_MAGIC_1 10 #define BZ_X_MAGIC_2 11 #define BZ_X_MAGIC_3 12 #define BZ_X_MAGIC_4 13 #define BZ_X_BLKHDR_1 14 #define BZ_X_BLKHDR_2 15 #define BZ_X_BLKHDR_3 16 #define BZ_X_BLKHDR_4 17 #define BZ_X_BLKHDR_5 18 #define BZ_X_BLKHDR_6 19 #define BZ_X_BCRC_1 20 #define BZ_X_BCRC_2 21 #define BZ_X_BCRC_3 22 #define BZ_X_BCRC_4 23 #define BZ_X_RANDBIT 24 #define BZ_X_ORIGPTR_1 25 #define BZ_X_ORIGPTR_2 26 #define BZ_X_ORIGPTR_3 27 #define BZ_X_MAPPING_1 28 #define BZ_X_MAPPING_2 29 #define BZ_X_SELECTOR_1 30 #define BZ_X_SELECTOR_2 31 #define BZ_X_SELECTOR_3 32 #define BZ_X_CODING_1 33 #define BZ_X_CODING_2 34 #define BZ_X_CODING_3 35 #define BZ_X_MTF_1 36 #define BZ_X_MTF_2 37 #define BZ_X_MTF_3 38 #define BZ_X_MTF_4 39 #define BZ_X_MTF_5 40 #define BZ_X_MTF_6 41 #define BZ_X_ENDHDR_2 42 #define BZ_X_ENDHDR_3 43 #define BZ_X_ENDHDR_4 44 #define BZ_X_ENDHDR_5 45 #define BZ_X_ENDHDR_6 46 #define BZ_X_CCRC_1 47 #define BZ_X_CCRC_2 48 #define BZ_X_CCRC_3 49 #define BZ_X_CCRC_4 50 /*-- Constants for the fast MTF decoder. --*/ #define MTFA_SIZE 4096 #define MTFL_SIZE 16 /*-- Structure holding all the decompression-side stuff. --*/ typedef struct { /* pointer back to the struct bz_stream */ bz_stream* strm; /* state indicator for this stream */ Int32 state; /* for doing the final run-length decoding */ UChar state_out_ch; Int32 state_out_len; Bool blockRandomised; BZ_RAND_DECLS; /* the buffer for bit stream reading */ UInt32 bsBuff; Int32 bsLive; /* misc administratium */ Int32 blockSize100k; Bool smallDecompress; Int32 currBlockNo; Int32 verbosity; /* for undoing the Burrows-Wheeler transform */ Int32 origPtr; UInt32 tPos; Int32 k0; Int32 unzftab[256]; Int32 nblock_used; Int32 cftab[257]; Int32 cftabCopy[257]; /* for undoing the Burrows-Wheeler transform (FAST) */ UInt32 *tt; /* for undoing the Burrows-Wheeler transform (SMALL) */ UInt16 *ll16; UChar *ll4; /* stored and calculated CRCs */ UInt32 storedBlockCRC; UInt32 storedCombinedCRC; UInt32 calculatedBlockCRC; UInt32 calculatedCombinedCRC; /* map of bytes used in block */ Int32 nInUse; Bool inUse[256]; Bool inUse16[16]; UChar seqToUnseq[256]; /* for decoding the MTF values */ UChar mtfa [MTFA_SIZE]; Int32 mtfbase[256 / MTFL_SIZE]; UChar selector [BZ_MAX_SELECTORS]; UChar selectorMtf[BZ_MAX_SELECTORS]; UChar len [BZ_N_GROUPS][BZ_MAX_ALPHA_SIZE]; Int32 limit [BZ_N_GROUPS][BZ_MAX_ALPHA_SIZE]; Int32 base [BZ_N_GROUPS][BZ_MAX_ALPHA_SIZE]; Int32 perm [BZ_N_GROUPS][BZ_MAX_ALPHA_SIZE]; Int32 minLens[BZ_N_GROUPS]; /* save area for scalars in the main decompress code */ Int32 save_i; Int32 save_j; Int32 save_t; Int32 save_alphaSize; Int32 save_nGroups; Int32 save_nSelectors; Int32 save_EOB; Int32 save_groupNo; Int32 save_groupPos; Int32 save_nextSym; Int32 save_nblockMAX; Int32 save_nblock; Int32 save_es; Int32 save_N; Int32 save_curr; Int32 save_zt; Int32 save_zn; Int32 save_zvec; Int32 save_zj; Int32 save_gSel; Int32 save_gMinlen; Int32* save_gLimit; Int32* save_gBase; Int32* save_gPerm; } DState; /*-- Macros for decompression. --*/ #define BZ_GET_FAST(cccc) \ /* c_tPos is unsigned, hence test < 0 is pointless. */ \ if (s->tPos >= (UInt32)100000 * (UInt32)s->blockSize100k) return True; \ s->tPos = s->tt[s->tPos]; \ cccc = (UChar)(s->tPos & 0xff); \ s->tPos >>= 8; #define BZ_GET_FAST_C(cccc) \ /* c_tPos is unsigned, hence test < 0 is pointless. */ \ if (c_tPos >= (UInt32)100000 * (UInt32)ro_blockSize100k) return True; \ c_tPos = c_tt[c_tPos]; \ cccc = (UChar)(c_tPos & 0xff); \ c_tPos >>= 8; #define SET_LL4(i,n) \ { if (((i) & 0x1) == 0) \ s->ll4[(i) >> 1] = (s->ll4[(i) >> 1] & 0xf0) | (n); else \ s->ll4[(i) >> 1] = (s->ll4[(i) >> 1] & 0x0f) | ((n) << 4); \ } #define GET_LL4(i) \ ((((UInt32)(s->ll4[(i) >> 1])) >> (((i) << 2) & 0x4)) & 0xF) #define SET_LL(i,n) \ { s->ll16[i] = (UInt16)(n & 0x0000ffff); \ SET_LL4(i, n >> 16); \ } #define GET_LL(i) \ (((UInt32)s->ll16[i]) | (GET_LL4(i) << 16)) #define BZ_GET_SMALL(cccc) \ /* c_tPos is unsigned, hence test < 0 is pointless. */ \ if (s->tPos >= (UInt32)100000 * (UInt32)s->blockSize100k) return True; \ cccc = BZ2_indexIntoF ( s->tPos, s->cftab ); \ s->tPos = GET_LL(s->tPos); /*-- externs for decompression. --*/ extern Int32 BZ2_indexIntoF ( Int32, Int32* ); extern Int32 BZ2_decompress ( DState* ); extern void BZ2_hbCreateDecodeTables ( Int32*, Int32*, Int32*, UChar*, Int32, Int32, Int32 );
12,848
482
jart/cosmopolitan
false
cosmopolitan/third_party/bzip2/decompress.c
/* clang-format off */ /*-------------------------------------------------------------*/ /*--- Decompression machinery ---*/ /*--- decompress.c ---*/ /*-------------------------------------------------------------*/ /* ------------------------------------------------------------------ This file is part of bzip2/libbzip2, a program and library for lossless, block-sorting data compression. bzip2/libbzip2 version 1.0.8 of 13 July 2019 Copyright (C) 1996-2019 Julian Seward <[email protected]> Please read the WARNING, DISCLAIMER and PATENTS sections in the README file. This program is released under the terms of the license contained in the file LICENSE. ------------------------------------------------------------------ */ #include "third_party/bzip2/bzlib_private.inc" /*---------------------------------------------------*/ static void makeMaps_d ( DState* s ) { Int32 i; s->nInUse = 0; for (i = 0; i < 256; i++) if (s->inUse[i]) { s->seqToUnseq[s->nInUse] = i; s->nInUse++; } } /*---------------------------------------------------*/ #define RETURN(rrr) \ { retVal = rrr; goto save_state_and_return; }; #define GET_BITS(lll,vvv,nnn) \ case lll: s->state = lll; \ while (True) { \ if (s->bsLive >= nnn) { \ UInt32 v; \ v = (s->bsBuff >> \ (s->bsLive-nnn)) & ((1 << nnn)-1); \ s->bsLive -= nnn; \ vvv = v; \ break; \ } \ if (s->strm->avail_in == 0) RETURN(BZ_OK); \ s->bsBuff \ = (s->bsBuff << 8) | \ ((UInt32) \ (*((UChar*)(s->strm->next_in)))); \ s->bsLive += 8; \ s->strm->next_in++; \ s->strm->avail_in--; \ s->strm->total_in_lo32++; \ if (s->strm->total_in_lo32 == 0) \ s->strm->total_in_hi32++; \ } #define GET_UCHAR(lll,uuu) \ GET_BITS(lll,uuu,8) #define GET_BIT(lll,uuu) \ GET_BITS(lll,uuu,1) /*---------------------------------------------------*/ #define GET_MTF_VAL(label1,label2,lval) \ { \ if (groupPos == 0) { \ groupNo++; \ if (groupNo >= nSelectors) \ RETURN(BZ_DATA_ERROR); \ groupPos = BZ_G_SIZE; \ gSel = s->selector[groupNo]; \ gMinlen = s->minLens[gSel]; \ gLimit = &(s->limit[gSel][0]); \ gPerm = &(s->perm[gSel][0]); \ gBase = &(s->base[gSel][0]); \ } \ groupPos--; \ zn = gMinlen; \ GET_BITS(label1, zvec, zn); \ while (1) { \ if (zn > 20 /* the longest code */) \ RETURN(BZ_DATA_ERROR); \ if (zvec <= gLimit[zn]) break; \ zn++; \ GET_BIT(label2, zj); \ zvec = (zvec << 1) | zj; \ }; \ if (zvec - gBase[zn] < 0 \ || zvec - gBase[zn] >= BZ_MAX_ALPHA_SIZE) \ RETURN(BZ_DATA_ERROR); \ lval = gPerm[zvec - gBase[zn]]; \ } /*---------------------------------------------------*/ Int32 BZ2_decompress ( DState* s ) { UChar uc; Int32 retVal; Int32 minLen, maxLen; bz_stream* strm = s->strm; /* stuff that needs to be saved/restored */ Int32 i; Int32 j; Int32 t; Int32 alphaSize; Int32 nGroups; Int32 nSelectors; Int32 EOB; Int32 groupNo; Int32 groupPos; Int32 nextSym; Int32 nblockMAX; Int32 nblock; Int32 es; Int32 N; Int32 curr; Int32 zt; Int32 zn; Int32 zvec; Int32 zj; Int32 gSel; Int32 gMinlen; Int32* gLimit; Int32* gBase; Int32* gPerm; if (s->state == BZ_X_MAGIC_1) { /*initialise the save area*/ s->save_i = 0; s->save_j = 0; s->save_t = 0; s->save_alphaSize = 0; s->save_nGroups = 0; s->save_nSelectors = 0; s->save_EOB = 0; s->save_groupNo = 0; s->save_groupPos = 0; s->save_nextSym = 0; s->save_nblockMAX = 0; s->save_nblock = 0; s->save_es = 0; s->save_N = 0; s->save_curr = 0; s->save_zt = 0; s->save_zn = 0; s->save_zvec = 0; s->save_zj = 0; s->save_gSel = 0; s->save_gMinlen = 0; s->save_gLimit = NULL; s->save_gBase = NULL; s->save_gPerm = NULL; } /*restore from the save area*/ i = s->save_i; j = s->save_j; t = s->save_t; alphaSize = s->save_alphaSize; nGroups = s->save_nGroups; nSelectors = s->save_nSelectors; EOB = s->save_EOB; groupNo = s->save_groupNo; groupPos = s->save_groupPos; nextSym = s->save_nextSym; nblockMAX = s->save_nblockMAX; nblock = s->save_nblock; es = s->save_es; N = s->save_N; curr = s->save_curr; zt = s->save_zt; zn = s->save_zn; zvec = s->save_zvec; zj = s->save_zj; gSel = s->save_gSel; gMinlen = s->save_gMinlen; gLimit = s->save_gLimit; gBase = s->save_gBase; gPerm = s->save_gPerm; retVal = BZ_OK; switch (s->state) { GET_UCHAR(BZ_X_MAGIC_1, uc); if (uc != BZ_HDR_B) RETURN(BZ_DATA_ERROR_MAGIC); GET_UCHAR(BZ_X_MAGIC_2, uc); if (uc != BZ_HDR_Z) RETURN(BZ_DATA_ERROR_MAGIC); GET_UCHAR(BZ_X_MAGIC_3, uc) if (uc != BZ_HDR_h) RETURN(BZ_DATA_ERROR_MAGIC); GET_BITS(BZ_X_MAGIC_4, s->blockSize100k, 8) if (s->blockSize100k < (BZ_HDR_0 + 1) || s->blockSize100k > (BZ_HDR_0 + 9)) RETURN(BZ_DATA_ERROR_MAGIC); s->blockSize100k -= BZ_HDR_0; if (s->smallDecompress) { s->ll16 = BZALLOC( s->blockSize100k * 100000 * sizeof(UInt16) ); s->ll4 = BZALLOC( ((1 + s->blockSize100k * 100000) >> 1) * sizeof(UChar) ); if (s->ll16 == NULL || s->ll4 == NULL) RETURN(BZ_MEM_ERROR); } else { s->tt = BZALLOC( s->blockSize100k * 100000 * sizeof(Int32) ); if (s->tt == NULL) RETURN(BZ_MEM_ERROR); } GET_UCHAR(BZ_X_BLKHDR_1, uc); if (uc == 0x17) goto endhdr_2; if (uc != 0x31) RETURN(BZ_DATA_ERROR); GET_UCHAR(BZ_X_BLKHDR_2, uc); if (uc != 0x41) RETURN(BZ_DATA_ERROR); GET_UCHAR(BZ_X_BLKHDR_3, uc); if (uc != 0x59) RETURN(BZ_DATA_ERROR); GET_UCHAR(BZ_X_BLKHDR_4, uc); if (uc != 0x26) RETURN(BZ_DATA_ERROR); GET_UCHAR(BZ_X_BLKHDR_5, uc); if (uc != 0x53) RETURN(BZ_DATA_ERROR); GET_UCHAR(BZ_X_BLKHDR_6, uc); if (uc != 0x59) RETURN(BZ_DATA_ERROR); s->currBlockNo++; if (s->verbosity >= 2) VPrintf1 ( "\n [%d: huff+mtf ", s->currBlockNo ); s->storedBlockCRC = 0; GET_UCHAR(BZ_X_BCRC_1, uc); s->storedBlockCRC = (s->storedBlockCRC << 8) | ((UInt32)uc); GET_UCHAR(BZ_X_BCRC_2, uc); s->storedBlockCRC = (s->storedBlockCRC << 8) | ((UInt32)uc); GET_UCHAR(BZ_X_BCRC_3, uc); s->storedBlockCRC = (s->storedBlockCRC << 8) | ((UInt32)uc); GET_UCHAR(BZ_X_BCRC_4, uc); s->storedBlockCRC = (s->storedBlockCRC << 8) | ((UInt32)uc); GET_BITS(BZ_X_RANDBIT, s->blockRandomised, 1); s->origPtr = 0; GET_UCHAR(BZ_X_ORIGPTR_1, uc); s->origPtr = (s->origPtr << 8) | ((Int32)uc); GET_UCHAR(BZ_X_ORIGPTR_2, uc); s->origPtr = (s->origPtr << 8) | ((Int32)uc); GET_UCHAR(BZ_X_ORIGPTR_3, uc); s->origPtr = (s->origPtr << 8) | ((Int32)uc); if (s->origPtr < 0) RETURN(BZ_DATA_ERROR); if (s->origPtr > 10 + 100000*s->blockSize100k) RETURN(BZ_DATA_ERROR); /*--- Receive the mapping table ---*/ for (i = 0; i < 16; i++) { GET_BIT(BZ_X_MAPPING_1, uc); if (uc == 1) s->inUse16[i] = True; else s->inUse16[i] = False; } for (i = 0; i < 256; i++) s->inUse[i] = False; for (i = 0; i < 16; i++) if (s->inUse16[i]) for (j = 0; j < 16; j++) { GET_BIT(BZ_X_MAPPING_2, uc); if (uc == 1) s->inUse[i * 16 + j] = True; } makeMaps_d ( s ); if (s->nInUse == 0) RETURN(BZ_DATA_ERROR); alphaSize = s->nInUse+2; /*--- Now the selectors ---*/ GET_BITS(BZ_X_SELECTOR_1, nGroups, 3); if (nGroups < 2 || nGroups > BZ_N_GROUPS) RETURN(BZ_DATA_ERROR); GET_BITS(BZ_X_SELECTOR_2, nSelectors, 15); if (nSelectors < 1) RETURN(BZ_DATA_ERROR); for (i = 0; i < nSelectors; i++) { j = 0; while (True) { GET_BIT(BZ_X_SELECTOR_3, uc); if (uc == 0) break; j++; if (j >= nGroups) RETURN(BZ_DATA_ERROR); } /* Having more than BZ_MAX_SELECTORS doesn't make much sense since they will never be used, but some implementations might "round up" the number of selectors, so just ignore those. */ if (i < BZ_MAX_SELECTORS) s->selectorMtf[i] = j; } if (nSelectors > BZ_MAX_SELECTORS) nSelectors = BZ_MAX_SELECTORS; /*--- Undo the MTF values for the selectors. ---*/ { UChar pos[BZ_N_GROUPS], tmp, v; for (v = 0; v < nGroups; v++) pos[v] = v; for (i = 0; i < nSelectors; i++) { v = s->selectorMtf[i]; tmp = pos[v]; while (v > 0) { pos[v] = pos[v-1]; v--; } pos[0] = tmp; s->selector[i] = tmp; } } /*--- Now the coding tables ---*/ for (t = 0; t < nGroups; t++) { GET_BITS(BZ_X_CODING_1, curr, 5); for (i = 0; i < alphaSize; i++) { while (True) { if (curr < 1 || curr > 20) RETURN(BZ_DATA_ERROR); GET_BIT(BZ_X_CODING_2, uc); if (uc == 0) break; GET_BIT(BZ_X_CODING_3, uc); if (uc == 0) curr++; else curr--; } s->len[t][i] = curr; } } /*--- Create the Huffman decoding tables ---*/ for (t = 0; t < nGroups; t++) { minLen = 32; maxLen = 0; for (i = 0; i < alphaSize; i++) { if (s->len[t][i] > maxLen) maxLen = s->len[t][i]; if (s->len[t][i] < minLen) minLen = s->len[t][i]; } BZ2_hbCreateDecodeTables ( &(s->limit[t][0]), &(s->base[t][0]), &(s->perm[t][0]), &(s->len[t][0]), minLen, maxLen, alphaSize ); s->minLens[t] = minLen; } /*--- Now the MTF values ---*/ EOB = s->nInUse+1; nblockMAX = 100000 * s->blockSize100k; groupNo = -1; groupPos = 0; for (i = 0; i <= 255; i++) s->unzftab[i] = 0; /*-- MTF init --*/ { Int32 ii, jj, kk; kk = MTFA_SIZE-1; for (ii = 256 / MTFL_SIZE - 1; ii >= 0; ii--) { for (jj = MTFL_SIZE-1; jj >= 0; jj--) { s->mtfa[kk] = (UChar)(ii * MTFL_SIZE + jj); kk--; } s->mtfbase[ii] = kk + 1; } } /*-- end MTF init --*/ nblock = 0; GET_MTF_VAL(BZ_X_MTF_1, BZ_X_MTF_2, nextSym); while (True) { if (nextSym == EOB) break; if (nextSym == BZ_RUNA || nextSym == BZ_RUNB) { es = -1; N = 1; do { /* Check that N doesn't get too big, so that es doesn't go negative. The maximum value that can be RUNA/RUNB encoded is equal to the block size (post the initial RLE), viz, 900k, so bounding N at 2 million should guard against overflow without rejecting any legitimate inputs. */ if (N >= 2*1024*1024) RETURN(BZ_DATA_ERROR); if (nextSym == BZ_RUNA) es = es + (0+1) * N; else if (nextSym == BZ_RUNB) es = es + (1+1) * N; N = N * 2; GET_MTF_VAL(BZ_X_MTF_3, BZ_X_MTF_4, nextSym); } while (nextSym == BZ_RUNA || nextSym == BZ_RUNB); es++; uc = s->seqToUnseq[ s->mtfa[s->mtfbase[0]] ]; s->unzftab[uc] += es; if (s->smallDecompress) while (es > 0) { if (nblock >= nblockMAX) RETURN(BZ_DATA_ERROR); s->ll16[nblock] = (UInt16)uc; nblock++; es--; } else while (es > 0) { if (nblock >= nblockMAX) RETURN(BZ_DATA_ERROR); s->tt[nblock] = (UInt32)uc; nblock++; es--; }; continue; } else { if (nblock >= nblockMAX) RETURN(BZ_DATA_ERROR); /*-- uc = MTF ( nextSym-1 ) --*/ { Int32 ii, jj, kk, pp, lno, off; UInt32 nn; nn = (UInt32)(nextSym - 1); if (nn < MTFL_SIZE) { /* avoid general-case expense */ pp = s->mtfbase[0]; uc = s->mtfa[pp+nn]; while (nn > 3) { Int32 z = pp+nn; s->mtfa[(z) ] = s->mtfa[(z)-1]; s->mtfa[(z)-1] = s->mtfa[(z)-2]; s->mtfa[(z)-2] = s->mtfa[(z)-3]; s->mtfa[(z)-3] = s->mtfa[(z)-4]; nn -= 4; } while (nn > 0) { s->mtfa[(pp+nn)] = s->mtfa[(pp+nn)-1]; nn--; }; s->mtfa[pp] = uc; } else { /* general case */ lno = nn / MTFL_SIZE; off = nn % MTFL_SIZE; pp = s->mtfbase[lno] + off; uc = s->mtfa[pp]; while (pp > s->mtfbase[lno]) { s->mtfa[pp] = s->mtfa[pp-1]; pp--; }; s->mtfbase[lno]++; while (lno > 0) { s->mtfbase[lno]--; s->mtfa[s->mtfbase[lno]] = s->mtfa[s->mtfbase[lno-1] + MTFL_SIZE - 1]; lno--; } s->mtfbase[0]--; s->mtfa[s->mtfbase[0]] = uc; if (s->mtfbase[0] == 0) { kk = MTFA_SIZE-1; for (ii = 256 / MTFL_SIZE-1; ii >= 0; ii--) { for (jj = MTFL_SIZE-1; jj >= 0; jj--) { s->mtfa[kk] = s->mtfa[s->mtfbase[ii] + jj]; kk--; } s->mtfbase[ii] = kk + 1; } } } } /*-- end uc = MTF ( nextSym-1 ) --*/ s->unzftab[s->seqToUnseq[uc]]++; if (s->smallDecompress) s->ll16[nblock] = (UInt16)(s->seqToUnseq[uc]); else s->tt[nblock] = (UInt32)(s->seqToUnseq[uc]); nblock++; GET_MTF_VAL(BZ_X_MTF_5, BZ_X_MTF_6, nextSym); continue; } } /* Now we know what nblock is, we can do a better sanity check on s->origPtr. */ if (s->origPtr < 0 || s->origPtr >= nblock) RETURN(BZ_DATA_ERROR); /*-- Set up cftab to facilitate generation of T^(-1) --*/ /* Check: unzftab entries in range. */ for (i = 0; i <= 255; i++) { if (s->unzftab[i] < 0 || s->unzftab[i] > nblock) RETURN(BZ_DATA_ERROR); } /* Actually generate cftab. */ s->cftab[0] = 0; for (i = 1; i <= 256; i++) s->cftab[i] = s->unzftab[i-1]; for (i = 1; i <= 256; i++) s->cftab[i] += s->cftab[i-1]; /* Check: cftab entries in range. */ for (i = 0; i <= 256; i++) { if (s->cftab[i] < 0 || s->cftab[i] > nblock) { /* s->cftab[i] can legitimately be == nblock */ RETURN(BZ_DATA_ERROR); } } /* Check: cftab entries non-descending. */ for (i = 1; i <= 256; i++) { if (s->cftab[i-1] > s->cftab[i]) { RETURN(BZ_DATA_ERROR); } } s->state_out_len = 0; s->state_out_ch = 0; BZ_INITIALISE_CRC ( s->calculatedBlockCRC ); s->state = BZ_X_OUTPUT; if (s->verbosity >= 2) VPrintf0 ( "rt+rld" ); if (s->smallDecompress) { /*-- Make a copy of cftab, used in generation of T --*/ for (i = 0; i <= 256; i++) s->cftabCopy[i] = s->cftab[i]; /*-- compute the T vector --*/ for (i = 0; i < nblock; i++) { uc = (UChar)(s->ll16[i]); SET_LL(i, s->cftabCopy[uc]); s->cftabCopy[uc]++; } /*-- Compute T^(-1) by pointer reversal on T --*/ i = s->origPtr; j = GET_LL(i); do { Int32 tmp = GET_LL(j); SET_LL(j, i); i = j; j = tmp; } while (i != s->origPtr); s->tPos = s->origPtr; s->nblock_used = 0; if (s->blockRandomised) { BZ_RAND_INIT_MASK; BZ_GET_SMALL(s->k0); s->nblock_used++; BZ_RAND_UPD_MASK; s->k0 ^= BZ_RAND_MASK; } else { BZ_GET_SMALL(s->k0); s->nblock_used++; } } else { /*-- compute the T^(-1) vector --*/ for (i = 0; i < nblock; i++) { uc = (UChar)(s->tt[i] & 0xff); s->tt[s->cftab[uc]] |= (i << 8); s->cftab[uc]++; } s->tPos = s->tt[s->origPtr] >> 8; s->nblock_used = 0; if (s->blockRandomised) { BZ_RAND_INIT_MASK; BZ_GET_FAST(s->k0); s->nblock_used++; BZ_RAND_UPD_MASK; s->k0 ^= BZ_RAND_MASK; } else { BZ_GET_FAST(s->k0); s->nblock_used++; } } RETURN(BZ_OK); endhdr_2: GET_UCHAR(BZ_X_ENDHDR_2, uc); if (uc != 0x72) RETURN(BZ_DATA_ERROR); GET_UCHAR(BZ_X_ENDHDR_3, uc); if (uc != 0x45) RETURN(BZ_DATA_ERROR); GET_UCHAR(BZ_X_ENDHDR_4, uc); if (uc != 0x38) RETURN(BZ_DATA_ERROR); GET_UCHAR(BZ_X_ENDHDR_5, uc); if (uc != 0x50) RETURN(BZ_DATA_ERROR); GET_UCHAR(BZ_X_ENDHDR_6, uc); if (uc != 0x90) RETURN(BZ_DATA_ERROR); s->storedCombinedCRC = 0; GET_UCHAR(BZ_X_CCRC_1, uc); s->storedCombinedCRC = (s->storedCombinedCRC << 8) | ((UInt32)uc); GET_UCHAR(BZ_X_CCRC_2, uc); s->storedCombinedCRC = (s->storedCombinedCRC << 8) | ((UInt32)uc); GET_UCHAR(BZ_X_CCRC_3, uc); s->storedCombinedCRC = (s->storedCombinedCRC << 8) | ((UInt32)uc); GET_UCHAR(BZ_X_CCRC_4, uc); s->storedCombinedCRC = (s->storedCombinedCRC << 8) | ((UInt32)uc); s->state = BZ_X_IDLE; RETURN(BZ_STREAM_END); default: AssertH ( False, 4001 ); } AssertH ( False, 4002 ); save_state_and_return: s->save_i = i; s->save_j = j; s->save_t = t; s->save_alphaSize = alphaSize; s->save_nGroups = nGroups; s->save_nSelectors = nSelectors; s->save_EOB = EOB; s->save_groupNo = groupNo; s->save_groupPos = groupPos; s->save_nextSym = nextSym; s->save_nblockMAX = nblockMAX; s->save_nblock = nblock; s->save_es = es; s->save_N = N; s->save_curr = curr; s->save_zt = zt; s->save_zn = zn; s->save_zvec = zvec; s->save_zj = zj; s->save_gSel = gSel; s->save_gMinlen = gMinlen; s->save_gLimit = gLimit; s->save_gBase = gBase; s->save_gPerm = gPerm; return retVal; } /*-------------------------------------------------------------*/ /*--- end decompress.c ---*/ /*-------------------------------------------------------------*/
21,301
654
jart/cosmopolitan
false
cosmopolitan/third_party/bzip2/format.pl
#!/usr/bin/perl -w # # ------------------------------------------------------------------ # This file is part of bzip2/libbzip2, a program and library for # lossless, block-sorting data compression. # # bzip2/libbzip2 version 1.0.8 of 13 July 2019 # Copyright (C) 1996-2019 Julian Seward <[email protected]> # # Please read the WARNING, DISCLAIMER and PATENTS sections in the # README file. # # This program is released under the terms of the license contained # in the file LICENSE. # ------------------------------------------------------------------ # use strict; # get command line values: if ( $#ARGV !=1 ) { die "Usage: $0 xml_infile xml_outfile\n"; } my $infile = shift; # check infile exists die "Can't find file \"$infile\"" unless -f $infile; # check we can read infile if (! -r $infile) { die "Can't read input $infile\n"; } # check we can open infile open( INFILE,"<$infile" ) or die "Can't input $infile $!"; #my $outfile = 'fmt-manual.xml'; my $outfile = shift; #print "Infile: $infile, Outfile: $outfile\n"; # check we can write to outfile open( OUTFILE,">$outfile" ) or die "Can't output $outfile $! for writing"; my ($prev, $curr, $str); $prev = ''; $curr = ''; while ( <INFILE> ) { print OUTFILE $prev; $prev = $curr; $curr = $_; $str = ''; if ( $prev =~ /<programlisting>$|<screen>$/ ) { chomp $prev; $curr = join( '', $prev, "<![CDATA[", $curr ); $prev = ''; next; } elsif ( $curr =~ /<\/programlisting>|<\/screen>/ ) { chomp $prev; $curr = join( '', $prev, "]]>", $curr ); $prev = ''; next; } } print OUTFILE $curr; close INFILE; close OUTFILE; exit;
1,684
69
jart/cosmopolitan
false
cosmopolitan/third_party/bzip2/bzip2.1
.PU .TH bzip2 1 .SH NAME bzip2, bunzip2 \- a block-sorting file compressor, v1.0.8 .br bzcat \- decompresses files to stdout .br bzip2recover \- recovers data from damaged bzip2 files .SH SYNOPSIS .ll +8 .B bzip2 .RB [ " \-cdfkqstvzVL123456789 " ] [ .I "filenames \&..." ] .ll -8 .br .B bunzip2 .RB [ " \-fkvsVL " ] [ .I "filenames \&..." ] .br .B bzcat .RB [ " \-s " ] [ .I "filenames \&..." ] .br .B bzip2recover .I "filename" .SH DESCRIPTION .I bzip2 compresses files using the Burrows-Wheeler block sorting text compression algorithm, and Huffman coding. Compression is generally considerably better than that achieved by more conventional LZ77/LZ78-based compressors, and approaches the performance of the PPM family of statistical compressors. The command-line options are deliberately very similar to those of .I GNU gzip, but they are not identical. .I bzip2 expects a list of file names to accompany the command-line flags. Each file is replaced by a compressed version of itself, with the name "original_name.bz2". Each compressed file has the same modification date, permissions, and, when possible, ownership as the corresponding original, so that these properties can be correctly restored at decompression time. File name handling is naive in the sense that there is no mechanism for preserving original file names, permissions, ownerships or dates in filesystems which lack these concepts, or have serious file name length restrictions, such as MS-DOS. .I bzip2 and .I bunzip2 will by default not overwrite existing files. If you want this to happen, specify the \-f flag. If no file names are specified, .I bzip2 compresses from standard input to standard output. In this case, .I bzip2 will decline to write compressed output to a terminal, as this would be entirely incomprehensible and therefore pointless. .I bunzip2 (or .I bzip2 \-d) decompresses all specified files. Files which were not created by .I bzip2 will be detected and ignored, and a warning issued. .I bzip2 attempts to guess the filename for the decompressed file from that of the compressed file as follows: filename.bz2 becomes filename filename.bz becomes filename filename.tbz2 becomes filename.tar filename.tbz becomes filename.tar anyothername becomes anyothername.out If the file does not end in one of the recognised endings, .I .bz2, .I .bz, .I .tbz2 or .I .tbz, .I bzip2 complains that it cannot guess the name of the original file, and uses the original name with .I .out appended. As with compression, supplying no filenames causes decompression from standard input to standard output. .I bunzip2 will correctly decompress a file which is the concatenation of two or more compressed files. The result is the concatenation of the corresponding uncompressed files. Integrity testing (\-t) of concatenated compressed files is also supported. You can also compress or decompress files to the standard output by giving the \-c flag. Multiple files may be compressed and decompressed like this. The resulting outputs are fed sequentially to stdout. Compression of multiple files in this manner generates a stream containing multiple compressed file representations. Such a stream can be decompressed correctly only by .I bzip2 version 0.9.0 or later. Earlier versions of .I bzip2 will stop after decompressing the first file in the stream. .I bzcat (or .I bzip2 -dc) decompresses all specified files to the standard output. .I bzip2 will read arguments from the environment variables .I BZIP2 and .I BZIP, in that order, and will process them before any arguments read from the command line. This gives a convenient way to supply default arguments. Compression is always performed, even if the compressed file is slightly larger than the original. Files of less than about one hundred bytes tend to get larger, since the compression mechanism has a constant overhead in the region of 50 bytes. Random data (including the output of most file compressors) is coded at about 8.05 bits per byte, giving an expansion of around 0.5%. As a self-check for your protection, .I bzip2 uses 32-bit CRCs to make sure that the decompressed version of a file is identical to the original. This guards against corruption of the compressed data, and against undetected bugs in .I bzip2 (hopefully very unlikely). The chances of data corruption going undetected is microscopic, about one chance in four billion for each file processed. Be aware, though, that the check occurs upon decompression, so it can only tell you that something is wrong. It can't help you recover the original uncompressed data. You can use .I bzip2recover to try to recover data from damaged files. Return values: 0 for a normal exit, 1 for environmental problems (file not found, invalid flags, I/O errors, &c), 2 to indicate a corrupt compressed file, 3 for an internal consistency error (eg, bug) which caused .I bzip2 to panic. .SH OPTIONS .TP .B \-c --stdout Compress or decompress to standard output. .TP .B \-d --decompress Force decompression. .I bzip2, .I bunzip2 and .I bzcat are really the same program, and the decision about what actions to take is done on the basis of which name is used. This flag overrides that mechanism, and forces .I bzip2 to decompress. .TP .B \-z --compress The complement to \-d: forces compression, regardless of the invocation name. .TP .B \-t --test Check integrity of the specified file(s), but don't decompress them. This really performs a trial decompression and throws away the result. .TP .B \-f --force Force overwrite of output files. Normally, .I bzip2 will not overwrite existing output files. Also forces .I bzip2 to break hard links to files, which it otherwise wouldn't do. bzip2 normally declines to decompress files which don't have the correct magic header bytes. If forced (-f), however, it will pass such files through unmodified. This is how GNU gzip behaves. .TP .B \-k --keep Keep (don't delete) input files during compression or decompression. .TP .B \-s --small Reduce memory usage, for compression, decompression and testing. Files are decompressed and tested using a modified algorithm which only requires 2.5 bytes per block byte. This means any file can be decompressed in 2300k of memory, albeit at about half the normal speed. During compression, \-s selects a block size of 200k, which limits memory use to around the same figure, at the expense of your compression ratio. In short, if your machine is low on memory (8 megabytes or less), use \-s for everything. See MEMORY MANAGEMENT below. .TP .B \-q --quiet Suppress non-essential warning messages. Messages pertaining to I/O errors and other critical events will not be suppressed. .TP .B \-v --verbose Verbose mode -- show the compression ratio for each file processed. Further \-v's increase the verbosity level, spewing out lots of information which is primarily of interest for diagnostic purposes. .TP .B \-L --license -V --version Display the software version, license terms and conditions. .TP .B \-1 (or \-\-fast) to \-9 (or \-\-best) Set the block size to 100 k, 200 k .. 900 k when compressing. Has no effect when decompressing. See MEMORY MANAGEMENT below. The \-\-fast and \-\-best aliases are primarily for GNU gzip compatibility. In particular, \-\-fast doesn't make things significantly faster. And \-\-best merely selects the default behaviour. .TP .B \-- Treats all subsequent arguments as file names, even if they start with a dash. This is so you can handle files with names beginning with a dash, for example: bzip2 \-- \-myfilename. .TP .B \--repetitive-fast --repetitive-best These flags are redundant in versions 0.9.5 and above. They provided some coarse control over the behaviour of the sorting algorithm in earlier versions, which was sometimes useful. 0.9.5 and above have an improved algorithm which renders these flags irrelevant. .SH MEMORY MANAGEMENT .I bzip2 compresses large files in blocks. The block size affects both the compression ratio achieved, and the amount of memory needed for compression and decompression. The flags \-1 through \-9 specify the block size to be 100,000 bytes through 900,000 bytes (the default) respectively. At decompression time, the block size used for compression is read from the header of the compressed file, and .I bunzip2 then allocates itself just enough memory to decompress the file. Since block sizes are stored in compressed files, it follows that the flags \-1 to \-9 are irrelevant to and so ignored during decompression. Compression and decompression requirements, in bytes, can be estimated as: Compression: 400k + ( 8 x block size ) Decompression: 100k + ( 4 x block size ), or 100k + ( 2.5 x block size ) Larger block sizes give rapidly diminishing marginal returns. Most of the compression comes from the first two or three hundred k of block size, a fact worth bearing in mind when using .I bzip2 on small machines. It is also important to appreciate that the decompression memory requirement is set at compression time by the choice of block size. For files compressed with the default 900k block size, .I bunzip2 will require about 3700 kbytes to decompress. To support decompression of any file on a 4 megabyte machine, .I bunzip2 has an option to decompress using approximately half this amount of memory, about 2300 kbytes. Decompression speed is also halved, so you should use this option only where necessary. The relevant flag is -s. In general, try and use the largest block size memory constraints allow, since that maximises the compression achieved. Compression and decompression speed are virtually unaffected by block size. Another significant point applies to files which fit in a single block -- that means most files you'd encounter using a large block size. The amount of real memory touched is proportional to the size of the file, since the file is smaller than a block. For example, compressing a file 20,000 bytes long with the flag -9 will cause the compressor to allocate around 7600k of memory, but only touch 400k + 20000 * 8 = 560 kbytes of it. Similarly, the decompressor will allocate 3700k but only touch 100k + 20000 * 4 = 180 kbytes. Here is a table which summarises the maximum memory usage for different block sizes. Also recorded is the total compressed size for 14 files of the Calgary Text Compression Corpus totalling 3,141,622 bytes. This column gives some feel for how compression varies with block size. These figures tend to understate the advantage of larger block sizes for larger files, since the Corpus is dominated by smaller files. Compress Decompress Decompress Corpus Flag usage usage -s usage Size -1 1200k 500k 350k 914704 -2 2000k 900k 600k 877703 -3 2800k 1300k 850k 860338 -4 3600k 1700k 1100k 846899 -5 4400k 2100k 1350k 845160 -6 5200k 2500k 1600k 838626 -7 6100k 2900k 1850k 834096 -8 6800k 3300k 2100k 828642 -9 7600k 3700k 2350k 828642 .SH RECOVERING DATA FROM DAMAGED FILES .I bzip2 compresses files in blocks, usually 900kbytes long. Each block is handled independently. If a media or transmission error causes a multi-block .bz2 file to become damaged, it may be possible to recover data from the undamaged blocks in the file. The compressed representation of each block is delimited by a 48-bit pattern, which makes it possible to find the block boundaries with reasonable certainty. Each block also carries its own 32-bit CRC, so damaged blocks can be distinguished from undamaged ones. .I bzip2recover is a simple program whose purpose is to search for blocks in .bz2 files, and write each block out into its own .bz2 file. You can then use .I bzip2 \-t to test the integrity of the resulting files, and decompress those which are undamaged. .I bzip2recover takes a single argument, the name of the damaged file, and writes a number of files "rec00001file.bz2", "rec00002file.bz2", etc, containing the extracted blocks. The output filenames are designed so that the use of wildcards in subsequent processing -- for example, "bzip2 -dc rec*file.bz2 > recovered_data" -- processes the files in the correct order. .I bzip2recover should be of most use dealing with large .bz2 files, as these will contain many blocks. It is clearly futile to use it on damaged single-block files, since a damaged block cannot be recovered. If you wish to minimise any potential data loss through media or transmission errors, you might consider compressing with a smaller block size. .SH PERFORMANCE NOTES The sorting phase of compression gathers together similar strings in the file. Because of this, files containing very long runs of repeated symbols, like "aabaabaabaab ..." (repeated several hundred times) may compress more slowly than normal. Versions 0.9.5 and above fare much better than previous versions in this respect. The ratio between worst-case and average-case compression time is in the region of 10:1. For previous versions, this figure was more like 100:1. You can use the \-vvvv option to monitor progress in great detail, if you want. Decompression speed is unaffected by these phenomena. .I bzip2 usually allocates several megabytes of memory to operate in, and then charges all over it in a fairly random fashion. This means that performance, both for compressing and decompressing, is largely determined by the speed at which your machine can service cache misses. Because of this, small changes to the code to reduce the miss rate have been observed to give disproportionately large performance improvements. I imagine .I bzip2 will perform best on machines with very large caches. .SH CAVEATS I/O error messages are not as helpful as they could be. .I bzip2 tries hard to detect I/O errors and exit cleanly, but the details of what the problem is sometimes seem rather misleading. This manual page pertains to version 1.0.8 of .I bzip2. Compressed data created by this version is entirely forwards and backwards compatible with the previous public releases, versions 0.1pl2, 0.9.0, 0.9.5, 1.0.0, 1.0.1, 1.0.2 and above, but with the following exception: 0.9.0 and above can correctly decompress multiple concatenated compressed files. 0.1pl2 cannot do this; it will stop after decompressing just the first file in the stream. .I bzip2recover versions prior to 1.0.2 used 32-bit integers to represent bit positions in compressed files, so they could not handle compressed files more than 512 megabytes long. Versions 1.0.2 and above use 64-bit ints on some platforms which support them (GNU supported targets, and Windows). To establish whether or not bzip2recover was built with such a limitation, run it without arguments. In any event you can build yourself an unlimited version if you can recompile it with MaybeUInt64 set to be an unsigned 64-bit integer. .SH AUTHOR Julian Seward, [email protected]. https://sourceware.org/bzip2/ The ideas embodied in .I bzip2 are due to (at least) the following people: Michael Burrows and David Wheeler (for the block sorting transformation), David Wheeler (again, for the Huffman coder), Peter Fenwick (for the structured coding model in the original .I bzip, and many refinements), and Alistair Moffat, Radford Neal and Ian Witten (for the arithmetic coder in the original .I bzip). I am much indebted for their help, support and advice. See the manual in the source distribution for pointers to sources of documentation. Christian von Roques encouraged me to look for faster sorting algorithms, so as to speed up compression. Bela Lubkin encouraged me to improve the worst-case compression performance. Donna Robinson XMLised the documentation. The bz* scripts are derived from those of GNU gzip. Many people sent patches, helped with portability problems, lent machines, gave advice and were generally helpful.
16,266
455
jart/cosmopolitan
false
cosmopolitan/third_party/bzip2/words0
If compilation produces errors, or a large number of warnings, please read README.COMPILATION.PROBLEMS -- you might be able to adjust the flags in this Makefile to improve matters. Also in README.COMPILATION.PROBLEMS are some hints that may help if your build produces an executable which is unable to correctly handle so-called 'large files' -- files of size 2GB or more.
376
10
jart/cosmopolitan
false
cosmopolitan/third_party/bzip2/bzdiff.1
\"Shamelessly copied from zmore.1 by Philippe Troin <[email protected]> \"for Debian GNU/Linux .TH BZDIFF 1 .SH NAME bzcmp, bzdiff \- compare bzip2 compressed files .SH SYNOPSIS .B bzcmp [ cmp_options ] file1 [ file2 ] .br .B bzdiff [ diff_options ] file1 [ file2 ] .SH DESCRIPTION .I Bzcmp and .I bzdiff are used to invoke the .I cmp or the .I diff program on bzip2 compressed files. All options specified are passed directly to .I cmp or .IR diff "." If only 1 file is specified, then the files compared are .I file1 and an uncompressed .IR file1 ".bz2." If two files are specified, then they are uncompressed if necessary and fed to .I cmp or .IR diff "." The exit status from .I cmp or .I diff is preserved. .SH "SEE ALSO" cmp(1), diff(1), bzmore(1), bzless(1), bzgrep(1), bzip2(1) .SH BUGS Messages from the .I cmp or .I diff programs refer to temporary filenames instead of those specified.
897
48
jart/cosmopolitan
false
cosmopolitan/third_party/bzip2/sample2.bz2
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73,732
572
jart/cosmopolitan
false
cosmopolitan/third_party/bzip2/bzip2.mk
#-*-mode:makefile-gmake;indent-tabs-mode:t;tab-width:8;coding:utf-8-*-┐ #───vi: set et ft=make ts=8 tw=8 fenc=utf-8 :vi───────────────────────┘ PKGS += THIRD_PARTY_BZIP2 THIRD_PARTY_BZIP2_ARTIFACTS += THIRD_PARTY_BZIP2_A THIRD_PARTY_BZIP2 = $(THIRD_PARTY_BZIP2_A_DEPS) $(THIRD_PARTY_BZIP2_A) THIRD_PARTY_BZIP2_A = o/$(MODE)/third_party/bzip2/bzip2.a THIRD_PARTY_BZIP2_A_FILES := $(wildcard third_party/bzip2/*) THIRD_PARTY_BZIP2_A_HDRS = $(filter %.h,$(THIRD_PARTY_BZIP2_A_FILES)) THIRD_PARTY_BZIP2_A_INCS = $(filter %.inc,$(THIRD_PARTY_BZIP2_A_FILES)) THIRD_PARTY_BZIP2_A_SRCS = $(filter %.c,$(THIRD_PARTY_BZIP2_A_FILES)) THIRD_PARTY_BZIP2_A_OBJS = $(THIRD_PARTY_BZIP2_A_SRCS:%.c=o/$(MODE)/%.o) THIRD_PARTY_BZIP2_BINS = $(THIRD_PARTY_BZIP2_COMS) $(THIRD_PARTY_BZIP2_COMS:%=%.dbg) THIRD_PARTY_BZIP2_COMS = \ o/$(MODE)/third_party/bzip2/bzip2.com \ o/$(MODE)/third_party/bzip2/bzip2recover.com THIRD_PARTY_BZIP2_A_CHECKS = \ $(THIRD_PARTY_BZIP2_A).pkg \ $(THIRD_PARTY_BZIP2_A_HDRS:%=o/$(MODE)/%.ok) THIRD_PARTY_BZIP2_A_DIRECTDEPS = \ LIBC_CALLS \ LIBC_FMT \ LIBC_INTRIN \ LIBC_LOG \ LIBC_MEM \ LIBC_NEXGEN32E \ LIBC_RUNTIME \ LIBC_STDIO \ LIBC_STR \ LIBC_STUBS \ LIBC_SYSV THIRD_PARTY_BZIP2_A_DEPS := \ $(call uniq,$(foreach x,$(THIRD_PARTY_BZIP2_A_DIRECTDEPS),$($(x)))) $(THIRD_PARTY_BZIP2_A): \ third_party/bzip2/ \ $(THIRD_PARTY_BZIP2_A).pkg \ $(THIRD_PARTY_BZIP2_A_OBJS) $(THIRD_PARTY_BZIP2_A).pkg: \ $(THIRD_PARTY_BZIP2_A_OBJS) \ $(foreach x,$(THIRD_PARTY_BZIP2_A_DIRECTDEPS),$($(x)_A).pkg) o/$(MODE)/third_party/bzip2/bzip2.com.dbg: \ $(THIRD_PARTY_BZIP2) \ o/$(MODE)/third_party/bzip2/bzip2.o \ o/$(MODE)/third_party/bzip2/bzip2.a.pkg \ $(CRT) \ $(APE_NO_MODIFY_SELF) @$(APELINK) o/$(MODE)/third_party/bzip2/bzip2recover.com.dbg: \ $(THIRD_PARTY_BZIP2) \ o/$(MODE)/third_party/bzip2/bzip2recover.o \ o/$(MODE)/third_party/bzip2/bzip2.a.pkg \ $(CRT) \ $(APE_NO_MODIFY_SELF) @$(APELINK) $(THIRD_PARTY_BZIP2_A_OBJS): private \ OVERRIDE_CFLAGS += \ -ffunction-sections \ -fdata-sections THIRD_PARTY_BZIP2_LIBS = $(foreach x,$(THIRD_PARTY_BZIP2_ARTIFACTS),$($(x))) THIRD_PARTY_BZIP2_SRCS = $(foreach x,$(THIRD_PARTY_BZIP2_ARTIFACTS),$($(x)_SRCS)) THIRD_PARTY_BZIP2_HDRS = $(foreach x,$(THIRD_PARTY_BZIP2_ARTIFACTS),$($(x)_HDRS)) THIRD_PARTY_BZIP2_INCS = $(foreach x,$(THIRD_PARTY_BZIP2_ARTIFACTS),$($(x)_INCS)) THIRD_PARTY_BZIP2_BINS = $(foreach x,$(THIRD_PARTY_BZIP2_ARTIFACTS),$($(x)_BINS)) THIRD_PARTY_BZIP2_CHECKS = $(foreach x,$(THIRD_PARTY_BZIP2_ARTIFACTS),$($(x)_CHECKS)) THIRD_PARTY_BZIP2_OBJS = $(foreach x,$(THIRD_PARTY_BZIP2_ARTIFACTS),$($(x)_OBJS)) $(THIRD_PARTY_BZIP2_OBJS): $(BUILD_FILES) third_party/bzip2/bzip2.mk .PHONY: o/$(MODE)/third_party/bzip2 o/$(MODE)/third_party/bzip2: \ $(THIRD_PARTY_BZIP2_COMS) \ $(THIRD_PARTY_BZIP2_CHECKS) # TODO(jart): write regression test # master jart@nightmare:~/cosmo$ o//third_party/bzip2/bzip2.com -1 <third_party/bzip2/sample1.ref >a # master jart@nightmare:~/cosmo$ cmp -s third_party/bzip2/sample1.bz2 a
3,215
87
jart/cosmopolitan
false
cosmopolitan/third_party/bzip2/bzmore.1
.\"Shamelessly copied from zmore.1 by Philippe Troin <[email protected]> .\"for Debian GNU/Linux .TH BZMORE 1 .SH NAME bzmore, bzless \- file perusal filter for crt viewing of bzip2 compressed text .SH SYNOPSIS .B bzmore [ name ... ] .br .B bzless [ name ... ] .SH NOTE In the following description, .I bzless and .I less can be used interchangeably with .I bzmore and .I more. .SH DESCRIPTION .I Bzmore is a filter which allows examination of compressed or plain text files one screenful at a time on a soft-copy terminal. .I bzmore works on files compressed with .I bzip2 and also on uncompressed files. If a file does not exist, .I bzmore looks for a file of the same name with the addition of a .bz2 suffix. .PP .I Bzmore normally pauses after each screenful, printing --More-- at the bottom of the screen. If the user then types a carriage return, one more line is displayed. If the user hits a space, another screenful is displayed. Other possibilities are enumerated later. .PP .I Bzmore looks in the file .I /etc/termcap to determine terminal characteristics, and to determine the default window size. On a terminal capable of displaying 24 lines, the default window size is 22 lines. Other sequences which may be typed when .I bzmore pauses, and their effects, are as follows (\fIi\fP is an optional integer argument, defaulting to 1) : .PP .IP \fIi\|\fP<space> display .I i more lines, (or another screenful if no argument is given) .PP .IP ^D display 11 more lines (a ``scroll''). If .I i is given, then the scroll size is set to \fIi\|\fP. .PP .IP d same as ^D (control-D) .PP .IP \fIi\|\fPz same as typing a space except that \fIi\|\fP, if present, becomes the new window size. Note that the window size reverts back to the default at the end of the current file. .PP .IP \fIi\|\fPs skip \fIi\|\fP lines and print a screenful of lines .PP .IP \fIi\|\fPf skip \fIi\fP screenfuls and print a screenful of lines .PP .IP "q or Q" quit reading the current file; go on to the next (if any) .PP .IP "e or q" When the prompt --More--(Next file: .IR file ) is printed, this command causes bzmore to exit. .PP .IP s When the prompt --More--(Next file: .IR file ) is printed, this command causes bzmore to skip the next file and continue. .PP .IP = Display the current line number. .PP .IP \fIi\|\fP/expr search for the \fIi\|\fP-th occurrence of the regular expression \fIexpr.\fP If the pattern is not found, .I bzmore goes on to the next file (if any). Otherwise, a screenful is displayed, starting two lines before the place where the expression was found. The user's erase and kill characters may be used to edit the regular expression. Erasing back past the first column cancels the search command. .PP .IP \fIi\|\fPn search for the \fIi\|\fP-th occurrence of the last regular expression entered. .PP .IP !command invoke a shell with \fIcommand\|\fP. The character `!' in "command" are replaced with the previous shell command. The sequence "\\!" is replaced by "!". .PP .IP ":q or :Q" quit reading the current file; go on to the next (if any) (same as q or Q). .PP .IP . (dot) repeat the previous command. .PP The commands take effect immediately, i.e., it is not necessary to type a carriage return. Up to the time when the command character itself is given, the user may hit the line kill character to cancel the numerical argument being formed. In addition, the user may hit the erase character to redisplay the --More-- message. .PP At any time when output is being sent to the terminal, the user can hit the quit key (normally control\-\\). .I Bzmore will stop sending output, and will display the usual --More-- prompt. The user may then enter one of the above commands in the normal manner. Unfortunately, some output is lost when this is done, due to the fact that any characters waiting in the terminal's output queue are flushed when the quit signal occurs. .PP The terminal is set to .I noecho mode by this program so that the output can be continuous. What you type will thus not show on your terminal, except for the / and ! commands. .PP If the standard output is not a teletype, then .I bzmore acts just like .I bzcat, except that a header is printed before each file. .SH FILES .DT /etc/termcap Terminal data base .SH "SEE ALSO" more(1), less(1), bzip2(1), bzdiff(1), bzgrep(1)
4,310
153
jart/cosmopolitan
false
cosmopolitan/third_party/bzip2/sample3.bz2
BZh31AY&SYºÍ3É:¶ß€@e0 ?ïÞà0ÚÛCS™'Ꙧ£OHmM‚MC £@"Qé4щ hÓJ™oޙÑTAeS<í|îÛé8–ß'Cβ­µ÷O¸=Áxž¯µa{»â•^ý2底n°VêƒB·ïuU‰©´`†Û2 ªÉçI%@¯@ ±ž€ ‹¾Œàý £^‘1 ˯ðú£¦Ç“º™€•)„ëô·alèDh3H¯‘Ú\mIL´hiiȕB°RóXV_ÅܑN$.³Lò@
235
3
jart/cosmopolitan
false
cosmopolitan/third_party/bzip2/bzip2.1.txt
bzip2(1) bzip2(1) 𝐍𝐀𝐌𝐄 bzip2, bunzip2 − a block-sorting file compressor, v1.0.8 bzcat − decompresses files to stdout bzip2recover − recovers data from damaged bzip2 files 𝐒𝐘𝐍𝐎𝐏𝐒𝐈𝐒 𝗯𝘇𝗶𝗽𝟮 [ −𝗰𝗱𝗳𝗸𝗾𝘀𝘁𝘃𝘇𝐕𝐋𝟭𝟮𝟯𝟰𝟱𝟲𝟳𝟴𝟵 ] [ f̲i̲l̲e̲n̲a̲m̲e̲s̲ .̲.̲.̲ ] 𝗯𝘂𝗻𝘇𝗶𝗽𝟮 [ −𝗳𝗸𝘃𝘀𝐕𝐋 ] [ f̲i̲l̲e̲n̲a̲m̲e̲s̲ .̲.̲.̲ ] 𝗯𝘇𝗰𝗮𝘁 [ −𝘀 ] [ f̲i̲l̲e̲n̲a̲m̲e̲s̲ .̲.̲.̲ ] 𝗯𝘇𝗶𝗽𝟮𝗿𝗲𝗰𝗼𝘃𝗲𝗿 f̲i̲l̲e̲n̲a̲m̲e̲ 𝐃𝐄𝐒𝐂𝐑𝐈𝐏𝐓𝐈𝐎𝐍 b̲z̲i̲p̲2̲ compresses files using the Burrows-Wheeler block sorting text compression algorithm, and Huffman coding. Compression is generally considerably better than that achieved by more conventional LZ77/LZ78-based compressors, and approaches the performance of the PPM family of sta- tistical compressors. The command-line options are deliberately very similar to those of G̲N̲U̲ g̲z̲i̲p̲,̲ but they are not identical. b̲z̲i̲p̲2̲ expects a list of file names to accompany the com- mand-line flags. Each file is replaced by a compressed version of itself, with the name "original_name.bz2". Each compressed file has the same modification date, per- missions, and, when possible, ownership as the correspond- ing original, so that these properties can be correctly restored at decompression time. File name handling is naive in the sense that there is no mechanism for preserv- ing original file names, permissions, ownerships or dates in filesystems which lack these concepts, or have serious file name length restrictions, such as MS-DOS. b̲z̲i̲p̲2̲ and b̲u̲n̲z̲i̲p̲2̲ will by default not overwrite existing files. If you want this to happen, specify the −f flag. If no file names are specified, b̲z̲i̲p̲2̲ compresses from standard input to standard output. In this case, b̲z̲i̲p̲2̲ will decline to write compressed output to a terminal, as this would be entirely incomprehensible and therefore pointless. b̲u̲n̲z̲i̲p̲2̲ (or b̲z̲i̲p̲2̲ −̲d̲)̲ decompresses all specified files. Files which were not created by b̲z̲i̲p̲2̲ will be detected and ignored, and a warning issued. b̲z̲i̲p̲2̲ attempts to guess the filename for the decompressed file from that of the compressed file as follows: filename.bz2 becomes filename filename.bz becomes filename filename.tbz2 becomes filename.tar filename.tbz becomes filename.tar anyothername becomes anyothername.out If the file does not end in one of the recognised endings, .̲b̲z̲2̲,̲ .̲b̲z̲,̲ .̲t̲b̲z̲2̲ or .̲t̲b̲z̲,̲ b̲z̲i̲p̲2̲ complains that it cannot guess the name of the original file, and uses the original name with .̲o̲u̲t̲ appended. As with compression, supplying no filenames causes decom- pression from standard input to standard output. b̲u̲n̲z̲i̲p̲2̲ will correctly decompress a file which is the con- catenation of two or more compressed files. The result is the concatenation of the corresponding uncompressed files. Integrity testing (−t) of concatenated compressed files is also supported. You can also compress or decompress files to the standard output by giving the −c flag. Multiple files may be com- pressed and decompressed like this. The resulting outputs are fed sequentially to stdout. Compression of multiple files in this manner generates a stream containing multi- ple compressed file representations. Such a stream can be decompressed correctly only by b̲z̲i̲p̲2̲ version 0.9.0 or later. Earlier versions of b̲z̲i̲p̲2̲ will stop after decom- pressing the first file in the stream. b̲z̲c̲a̲t̲ (or b̲z̲i̲p̲2̲ -̲d̲c̲)̲ decompresses all specified files to the standard output. b̲z̲i̲p̲2̲ will read arguments from the environment variables B̲Z̲I̲P̲2̲ and B̲Z̲I̲P̲,̲ in that order, and will process them before any arguments read from the command line. This gives a convenient way to supply default arguments. Compression is always performed, even if the compressed file is slightly larger than the original. Files of less than about one hundred bytes tend to get larger, since the compression mechanism has a constant overhead in the region of 50 bytes. Random data (including the output of most file compressors) is coded at about 8.05 bits per byte, giving an expansion of around 0.5%. As a self-check for your protection, b̲z̲i̲p̲2̲ uses 32-bit CRCs to make sure that the decompressed version of a file is identical to the original. This guards against corrup- tion of the compressed data, and against undetected bugs in b̲z̲i̲p̲2̲ (hopefully very unlikely). The chances of data corruption going undetected is microscopic, about one chance in four billion for each file processed. Be aware, though, that the check occurs upon decompression, so it can only tell you that something is wrong. It can’t help you recover the original uncompressed data. You can use b̲z̲i̲p̲2̲r̲e̲c̲o̲v̲e̲r̲ to try to recover data from damaged files. Return values: 0 for a normal exit, 1 for environmental problems (file not found, invalid flags, I/O errors, &c), 2 to indicate a corrupt compressed file, 3 for an internal consistency error (eg, bug) which caused b̲z̲i̲p̲2̲ to panic. 𝐎𝐏𝐓𝐈𝐎𝐍𝐒 −𝗰 --𝘀𝘁𝗱𝗼𝘂𝘁 Compress or decompress to standard output. −𝗱 --𝗱𝗲𝗰𝗼𝗺𝗽𝗿𝗲𝘀𝘀 Force decompression. b̲z̲i̲p̲2̲,̲ b̲u̲n̲z̲i̲p̲2̲ and b̲z̲c̲a̲t̲ are really the same program, and the decision about what actions to take is done on the basis of which name is used. This flag overrides that mechanism, and forces b̲z̲i̲p̲2̲ to decompress. −𝘇 --𝗰𝗼𝗺𝗽𝗿𝗲𝘀𝘀 The complement to −d: forces compression, regardless of the invocation name. −𝘁 --𝘁𝗲𝘀𝘁 Check integrity of the specified file(s), but don’t decompress them. This really performs a trial decompression and throws away the result. −𝗳 --𝗳𝗼𝗿𝗰𝗲 Force overwrite of output files. Normally, b̲z̲i̲p̲2̲ will not overwrite existing output files. Also forces b̲z̲i̲p̲2̲ to break hard links to files, which it otherwise wouldn’t do. bzip2 normally declines to decompress files which don’t have the correct magic header bytes. If forced (-f), however, it will pass such files through unmodified. This is how GNU gzip behaves. −𝗸 --𝗸𝗲𝗲𝗽 Keep (don’t delete) input files during compression or decompression. −𝘀 --𝘀𝗺𝗮𝗹𝗹 Reduce memory usage, for compression, decompression and testing. Files are decompressed and tested using a modified algorithm which only requires 2.5 bytes per block byte. This means any file can be decompressed in 2300k of memory, albeit at about half the normal speed. During compression, −s selects a block size of 200k, which limits memory use to around the same figure, at the expense of your compression ratio. In short, if your machine is low on memory (8 megabytes or less), use −s for everything. See MEMORY MANAGEMENT below. −𝗾 --𝗾𝘂𝗶𝗲𝘁 Suppress non-essential warning messages. Messages pertaining to I/O errors and other critical events will not be suppressed. −𝘃 --𝘃𝗲𝗿𝗯𝗼𝘀𝗲 Verbose mode -- show the compression ratio for each file processed. Further −v’s increase the ver- bosity level, spewing out lots of information which is primarily of interest for diagnostic purposes. −𝐋 --𝗹𝗶𝗰𝗲𝗻𝘀𝗲 -𝐕 --𝘃𝗲𝗿𝘀𝗶𝗼𝗻 Display the software version, license terms and conditions. −𝟭 (𝗼𝗿 −−𝗳𝗮𝘀𝘁) 𝘁𝗼 −𝟵 (𝗼𝗿 −−𝗯𝗲𝘀𝘁) Set the block size to 100 k, 200 k .. 900 k when compressing. Has no effect when decompressing. See MEMORY MANAGEMENT below. The −−fast and −−best aliases are primarily for GNU gzip compatibility. In particular, −−fast doesn’t make things signifi- cantly faster. And −−best merely selects the default behaviour. −- Treats all subsequent arguments as file names, even if they start with a dash. This is so you can han- dle files with names beginning with a dash, for example: bzip2 −- −myfilename. −-𝗿𝗲𝗽𝗲𝘁𝗶𝘁𝗶𝘃𝗲-𝗳𝗮𝘀𝘁 --𝗿𝗲𝗽𝗲𝘁𝗶𝘁𝗶𝘃𝗲-𝗯𝗲𝘀𝘁 These flags are redundant in versions 0.9.5 and above. They provided some coarse control over the behaviour of the sorting algorithm in earlier ver- sions, which was sometimes useful. 0.9.5 and above have an improved algorithm which renders these flags irrelevant. 𝐌𝐄𝐌𝐎𝐑𝐘 𝐌𝐀𝐍𝐀𝐆𝐄𝐌𝐄𝐍𝐓 b̲z̲i̲p̲2̲ compresses large files in blocks. The block size affects both the compression ratio achieved, and the amount of memory needed for compression and decompression. The flags −1 through −9 specify the block size to be 100,000 bytes through 900,000 bytes (the default) respec- tively. At decompression time, the block size used for compression is read from the header of the compressed file, and b̲u̲n̲z̲i̲p̲2̲ then allocates itself just enough memory to decompress the file. Since block sizes are stored in compressed files, it follows that the flags −1 to −9 are irrelevant to and so ignored during decompression. Compression and decompression requirements, in bytes, can be estimated as: Compression: 400k + ( 8 x block size ) Decompression: 100k + ( 4 x block size ), or 100k + ( 2.5 x block size ) Larger block sizes give rapidly diminishing marginal returns. Most of the compression comes from the first two or three hundred k of block size, a fact worth bearing in mind when using b̲z̲i̲p̲2̲ on small machines. It is also important to appreciate that the decompression memory requirement is set at compression time by the choice of block size. For files compressed with the default 900k block size, b̲u̲n̲z̲i̲p̲2̲ will require about 3700 kbytes to decompress. To support decompression of any file on a 4 megabyte machine, b̲u̲n̲z̲i̲p̲2̲ has an option to decompress using approximately half this amount of memory, about 2300 kbytes. Decompres- sion speed is also halved, so you should use this option only where necessary. The relevant flag is -s. In general, try and use the largest block size memory con- straints allow, since that maximises the compression achieved. Compression and decompression speed are virtu- ally unaffected by block size. Another significant point applies to files which fit in a single block -- that means most files you’d encounter using a large block size. The amount of real memory touched is proportional to the size of the file, since the file is smaller than a block. For example, compressing a file 20,000 bytes long with the flag -9 will cause the compressor to allocate around 7600k of memory, but only touch 400k + 20000 * 8 = 560 kbytes of it. Similarly, the decompressor will allocate 3700k but only touch 100k + 20000 * 4 = 180 kbytes. Here is a table which summarises the maximum memory usage for different block sizes. Also recorded is the total compressed size for 14 files of the Calgary Text Compres- sion Corpus totalling 3,141,622 bytes. This column gives some feel for how compression varies with block size. These figures tend to understate the advantage of larger block sizes for larger files, since the Corpus is domi- nated by smaller files. Compress Decompress Decompress Corpus Flag usage usage -s usage Size -1 1200k 500k 350k 914704 -2 2000k 900k 600k 877703 -3 2800k 1300k 850k 860338 -4 3600k 1700k 1100k 846899 -5 4400k 2100k 1350k 845160 -6 5200k 2500k 1600k 838626 -7 6100k 2900k 1850k 834096 -8 6800k 3300k 2100k 828642 -9 7600k 3700k 2350k 828642 𝐑𝐄𝐂𝐎𝐕𝐄𝐑𝐈𝐍𝐆 𝐃𝐀𝐓𝐀 𝐅𝐑𝐎𝐌 𝐃𝐀𝐌𝐀𝐆𝐄𝐃 𝐅𝐈𝐋𝐄𝐒 b̲z̲i̲p̲2̲ compresses files in blocks, usually 900kbytes long. Each block is handled independently. If a media or trans- mission error causes a multi-block .bz2 file to become damaged, it may be possible to recover data from the undamaged blocks in the file. The compressed representation of each block is delimited by a 48-bit pattern, which makes it possible to find the block boundaries with reasonable certainty. Each block also carries its own 32-bit CRC, so damaged blocks can be distinguished from undamaged ones. b̲z̲i̲p̲2̲r̲e̲c̲o̲v̲e̲r̲ is a simple program whose purpose is to search for blocks in .bz2 files, and write each block out into its own .bz2 file. You can then use b̲z̲i̲p̲2̲ −t to test the integrity of the resulting files, and decompress those which are undamaged. b̲z̲i̲p̲2̲r̲e̲c̲o̲v̲e̲r̲ takes a single argument, the name of the dam- aged file, and writes a number of files "rec00001file.bz2", "rec00002file.bz2", etc, containing the extracted blocks. The output filenames are designed so that the use of wildcards in subsequent pro- cessing -- for example, "bzip2 -dc rec*file.bz2 > recov- ered_data" -- processes the files in the correct order. b̲z̲i̲p̲2̲r̲e̲c̲o̲v̲e̲r̲ should be of most use dealing with large .bz2 files, as these will contain many blocks. It is clearly futile to use it on damaged single-block files, since a damaged block cannot be recovered. If you wish to min- imise any potential data loss through media or transmis- sion errors, you might consider compressing with a smaller block size. 𝐏𝐄𝐑𝐅𝐎𝐑𝐌𝐀𝐍𝐂𝐄 𝐍𝐎𝐓𝐄𝐒 The sorting phase of compression gathers together similar strings in the file. Because of this, files containing very long runs of repeated symbols, like "aabaabaabaab ..." (repeated several hundred times) may compress more slowly than normal. Versions 0.9.5 and above fare much better than previous versions in this respect. The ratio between worst-case and average-case compression time is in the region of 10:1. For previous versions, this figure was more like 100:1. You can use the −vvvv option to mon- itor progress in great detail, if you want. Decompression speed is unaffected by these phenomena. b̲z̲i̲p̲2̲ usually allocates several megabytes of memory to operate in, and then charges all over it in a fairly ran- dom fashion. This means that performance, both for com- pressing and decompressing, is largely determined by the speed at which your machine can service cache misses. Because of this, small changes to the code to reduce the miss rate have been observed to give disproportionately large performance improvements. I imagine b̲z̲i̲p̲2̲ will per- form best on machines with very large caches. 𝐂𝐀𝐕𝐄𝐀𝐓𝐒 I/O error messages are not as helpful as they could be. b̲z̲i̲p̲2̲ tries hard to detect I/O errors and exit cleanly, but the details of what the problem is sometimes seem rather misleading. This manual page pertains to version 1.0.8 of b̲z̲i̲p̲2̲.̲ Com- pressed data created by this version is entirely forwards and backwards compatible with the previous public releases, versions 0.1pl2, 0.9.0, 0.9.5, 1.0.0, 1.0.1, 1.0.2 and above, but with the following exception: 0.9.0 and above can correctly decompress multiple concatenated compressed files. 0.1pl2 cannot do this; it will stop after decompressing just the first file in the stream. b̲z̲i̲p̲2̲r̲e̲c̲o̲v̲e̲r̲ versions prior to 1.0.2 used 32-bit integers to represent bit positions in compressed files, so they could not handle compressed files more than 512 megabytes long. Versions 1.0.2 and above use 64-bit ints on some platforms which support them (GNU supported targets, and Windows). To establish whether or not bzip2recover was built with such a limitation, run it without arguments. In any event you can build yourself an unlimited version if you can recompile it with MaybeUInt64 set to be an unsigned 64-bit integer. 𝐀𝐔𝐓𝐇𝐎𝐑 Julian Seward, [email protected]. https://sourceware.org/bzip2/ The ideas embodied in b̲z̲i̲p̲2̲ are due to (at least) the fol- lowing people: Michael Burrows and David Wheeler (for the block sorting transformation), David Wheeler (again, for the Huffman coder), Peter Fenwick (for the structured cod- ing model in the original b̲z̲i̲p̲,̲ and many refinements), and Alistair Moffat, Radford Neal and Ian Witten (for the arithmetic coder in the original b̲z̲i̲p̲)̲.̲ I am much indebted for their help, support and advice. See the man- ual in the source distribution for pointers to sources of documentation. Christian von Roques encouraged me to look for faster sorting algorithms, so as to speed up compres- sion. Bela Lubkin encouraged me to improve the worst-case compression performance. Donna Robinson XMLised the docu- mentation. The bz* scripts are derived from those of GNU gzip. Many people sent patches, helped with portability problems, lent machines, gave advice and were generally helpful. bzip2(1)
20,840
400
jart/cosmopolitan
false
cosmopolitan/third_party/bzip2/libbz2.dsp
# Microsoft Developer Studio Project File - Name="libbz2" - Package Owner=<4> # Microsoft Developer Studio Generated Build File, Format Version 5.00 # ** •ҏW‚µ‚È‚¢‚Å‚­‚¾‚³‚¢ ** # TARGTYPE "Win32 (x86) Dynamic-Link Library" 0x0102 CFG=libbz2 - Win32 Debug !MESSAGE ‚±‚ê‚Í—LŒø‚ÈÒ²¸Ì§²Ù‚ł͂ ‚è‚Ü‚¹‚ñB ‚±‚ÌÌßÛ¼Þª¸Ä‚ðËÞÙÄނ·‚邽‚ß‚É‚Í NMAKE ‚ðŽg—p‚µ‚Ä‚­‚¾‚³‚¢B !MESSAGE [Ò²¸Ì§²Ù‚Ì´¸½Îß°Ä] ºÏÝÄނðŽg—p‚µ‚ÄŽÀs‚µ‚Ä‚­‚¾‚³‚¢ !MESSAGE !MESSAGE NMAKE /f "libbz2.mak". !MESSAGE !MESSAGE NMAKE ‚ÌŽÀsŽž‚ɍ\¬‚ðŽw’è‚Å‚«‚Ü‚· !MESSAGE ºÏÝÄÞ ×²Ýã‚Åϸۂ̐ݒè‚ð’è‹`‚µ‚Ü‚·B—á: !MESSAGE !MESSAGE NMAKE /f "libbz2.mak" CFG="libbz2 - Win32 Debug" !MESSAGE !MESSAGE ‘I‘ð‰Â”\‚ÈËÞÙÄÞ Ó°ÄÞ: !MESSAGE !MESSAGE "libbz2 - Win32 Release" ("Win32 (x86) Dynamic-Link Library" —p) !MESSAGE "libbz2 - Win32 Debug" ("Win32 (x86) Dynamic-Link Library" —p) !MESSAGE # Begin Project # PROP Scc_ProjName "" # PROP Scc_LocalPath "" CPP=cl.exe MTL=midl.exe RSC=rc.exe !IF "$(CFG)" == "libbz2 - Win32 Release" # PROP BASE Use_MFC 0 # PROP BASE Use_Debug_Libraries 0 # PROP BASE Output_Dir "Release" # PROP BASE Intermediate_Dir "Release" # PROP BASE Target_Dir "" # PROP Use_MFC 0 # PROP Use_Debug_Libraries 0 # PROP Output_Dir "Release" # PROP Intermediate_Dir "Release" # PROP Ignore_Export_Lib 0 # PROP Target_Dir "" # ADD BASE CPP /nologo /MT /W3 /GX /O2 /D "WIN32" /D "NDEBUG" /D "_WINDOWS" /YX /FD /c # ADD CPP /nologo /MT /W3 /GX /O2 /D "WIN32" /D "NDEBUG" /D "_WINDOWS" /YX /FD /c # ADD BASE MTL /nologo /D "NDEBUG" /mktyplib203 /o NUL /win32 # ADD MTL /nologo /D "NDEBUG" /mktyplib203 /o NUL /win32 # ADD BASE RSC /l 0x411 /d "NDEBUG" # ADD RSC /l 0x411 /d "NDEBUG" BSC32=bscmake.exe # ADD BASE BSC32 /nologo # ADD BSC32 /nologo LINK32=link.exe # ADD BASE LINK32 kernel32.lib user32.lib gdi32.lib winspool.lib comdlg32.lib advapi32.lib shell32.lib ole32.lib oleaut32.lib uuid.lib odbc32.lib odbccp32.lib /nologo /subsystem:windows /dll /machine:I386 # ADD LINK32 kernel32.lib user32.lib gdi32.lib winspool.lib comdlg32.lib advapi32.lib shell32.lib ole32.lib oleaut32.lib uuid.lib odbc32.lib odbccp32.lib /nologo /subsystem:windows /dll /machine:I386 /out:"libbz2.dll" !ELSEIF "$(CFG)" == "libbz2 - Win32 Debug" # PROP BASE Use_MFC 0 # PROP BASE Use_Debug_Libraries 1 # PROP BASE Output_Dir "Debug" # PROP BASE Intermediate_Dir "Debug" # PROP BASE Target_Dir "" # PROP Use_MFC 0 # PROP Use_Debug_Libraries 1 # PROP Output_Dir "Debug" # PROP Intermediate_Dir "Debug" # PROP Ignore_Export_Lib 0 # PROP Target_Dir "" # ADD BASE CPP /nologo /MTd /W3 /Gm /GX /Zi /Od /D "WIN32" /D "_DEBUG" /D "_WINDOWS" /YX /FD /c # ADD CPP /nologo /MTd /W3 /Gm /GX /Zi /Od /D "WIN32" /D "_DEBUG" /D "_WINDOWS" /YX /FD /c # ADD BASE MTL /nologo /D "_DEBUG" /mktyplib203 /o NUL /win32 # ADD MTL /nologo /D "_DEBUG" /mktyplib203 /o NUL /win32 # ADD BASE RSC /l 0x411 /d "_DEBUG" # ADD RSC /l 0x411 /d "_DEBUG" BSC32=bscmake.exe # ADD BASE BSC32 /nologo # ADD BSC32 /nologo LINK32=link.exe # ADD BASE LINK32 kernel32.lib user32.lib gdi32.lib winspool.lib comdlg32.lib advapi32.lib shell32.lib ole32.lib oleaut32.lib uuid.lib odbc32.lib odbccp32.lib /nologo /subsystem:windows /dll /debug /machine:I386 /pdbtype:sept # ADD LINK32 kernel32.lib user32.lib gdi32.lib winspool.lib comdlg32.lib advapi32.lib shell32.lib ole32.lib oleaut32.lib uuid.lib odbc32.lib odbccp32.lib /nologo /subsystem:windows /dll /debug /machine:I386 /out:"libbz2.dll" /pdbtype:sept !ENDIF # Begin Target # Name "libbz2 - Win32 Release" # Name "libbz2 - Win32 Debug" # Begin Source File SOURCE=.\blocksort.c # End Source File # Begin Source File SOURCE=.\bzlib.c # End Source File # Begin Source File SOURCE=.\bzlib.h # End Source File # Begin Source File SOURCE=.\bzlib_private.h # End Source File # Begin Source File SOURCE=.\compress.c # End Source File # Begin Source File SOURCE=.\crctable.c # End Source File # Begin Source File SOURCE=.\decompress.c # End Source File # Begin Source File SOURCE=.\huffman.c # End Source File # Begin Source File SOURCE=.\libbz2.def # End Source File # Begin Source File SOURCE=.\randtable.c # End Source File # End Target # End Project
4,124
131
jart/cosmopolitan
false
cosmopolitan/third_party/bzip2/sample3.ref
This file is exceedingly boring. If you find yourself reading it, please (1) take it from me that you can safely guess what the rest of the file says, and (2) seek professional help. ps. there are no further sarcastic remarks in this file. ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh ugh 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120,244
30,008
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294
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jart/cosmopolitan
false
cosmopolitan/third_party/bzip2/randtable.c
/* clang-format off */ /*-------------------------------------------------------------*/ /*--- Table for randomising repetitive blocks ---*/ /*--- randtable.c ---*/ /*-------------------------------------------------------------*/ /* ------------------------------------------------------------------ This file is part of bzip2/libbzip2, a program and library for lossless, block-sorting data compression. bzip2/libbzip2 version 1.0.8 of 13 July 2019 Copyright (C) 1996-2019 Julian Seward <[email protected]> Please read the WARNING, DISCLAIMER and PATENTS sections in the README file. This program is released under the terms of the license contained in the file LICENSE. ------------------------------------------------------------------ */ #include "third_party/bzip2/bzlib_private.inc" /*---------------------------------------------*/ Int32 BZ2_rNums[512] = { 619, 720, 127, 481, 931, 816, 813, 233, 566, 247, 985, 724, 205, 454, 863, 491, 741, 242, 949, 214, 733, 859, 335, 708, 621, 574, 73, 654, 730, 472, 419, 436, 278, 496, 867, 210, 399, 680, 480, 51, 878, 465, 811, 169, 869, 675, 611, 697, 867, 561, 862, 687, 507, 283, 482, 129, 807, 591, 733, 623, 150, 238, 59, 379, 684, 877, 625, 169, 643, 105, 170, 607, 520, 932, 727, 476, 693, 425, 174, 647, 73, 122, 335, 530, 442, 853, 695, 249, 445, 515, 909, 545, 703, 919, 874, 474, 882, 500, 594, 612, 641, 801, 220, 162, 819, 984, 589, 513, 495, 799, 161, 604, 958, 533, 221, 400, 386, 867, 600, 782, 382, 596, 414, 171, 516, 375, 682, 485, 911, 276, 98, 553, 163, 354, 666, 933, 424, 341, 533, 870, 227, 730, 475, 186, 263, 647, 537, 686, 600, 224, 469, 68, 770, 919, 190, 373, 294, 822, 808, 206, 184, 943, 795, 384, 383, 461, 404, 758, 839, 887, 715, 67, 618, 276, 204, 918, 873, 777, 604, 560, 951, 160, 578, 722, 79, 804, 96, 409, 713, 940, 652, 934, 970, 447, 318, 353, 859, 672, 112, 785, 645, 863, 803, 350, 139, 93, 354, 99, 820, 908, 609, 772, 154, 274, 580, 184, 79, 626, 630, 742, 653, 282, 762, 623, 680, 81, 927, 626, 789, 125, 411, 521, 938, 300, 821, 78, 343, 175, 128, 250, 170, 774, 972, 275, 999, 639, 495, 78, 352, 126, 857, 956, 358, 619, 580, 124, 737, 594, 701, 612, 669, 112, 134, 694, 363, 992, 809, 743, 168, 974, 944, 375, 748, 52, 600, 747, 642, 182, 862, 81, 344, 805, 988, 739, 511, 655, 814, 334, 249, 515, 897, 955, 664, 981, 649, 113, 974, 459, 893, 228, 433, 837, 553, 268, 926, 240, 102, 654, 459, 51, 686, 754, 806, 760, 493, 403, 415, 394, 687, 700, 946, 670, 656, 610, 738, 392, 760, 799, 887, 653, 978, 321, 576, 617, 626, 502, 894, 679, 243, 440, 680, 879, 194, 572, 640, 724, 926, 56, 204, 700, 707, 151, 457, 449, 797, 195, 791, 558, 945, 679, 297, 59, 87, 824, 713, 663, 412, 693, 342, 606, 134, 108, 571, 364, 631, 212, 174, 643, 304, 329, 343, 97, 430, 751, 497, 314, 983, 374, 822, 928, 140, 206, 73, 263, 980, 736, 876, 478, 430, 305, 170, 514, 364, 692, 829, 82, 855, 953, 676, 246, 369, 970, 294, 750, 807, 827, 150, 790, 288, 923, 804, 378, 215, 828, 592, 281, 565, 555, 710, 82, 896, 831, 547, 261, 524, 462, 293, 465, 502, 56, 661, 821, 976, 991, 658, 869, 905, 758, 745, 193, 768, 550, 608, 933, 378, 286, 215, 979, 792, 961, 61, 688, 793, 644, 986, 403, 106, 366, 905, 644, 372, 567, 466, 434, 645, 210, 389, 550, 919, 135, 780, 773, 635, 389, 707, 100, 626, 958, 165, 504, 920, 176, 193, 713, 857, 265, 203, 50, 668, 108, 645, 990, 626, 197, 510, 357, 358, 850, 858, 364, 936, 638 }; /*-------------------------------------------------------------*/ /*--- end randtable.c ---*/ /*-------------------------------------------------------------*/
3,898
86
jart/cosmopolitan
false
cosmopolitan/third_party/bzip2/huffman.c
/* clang-format off */ /*-------------------------------------------------------------*/ /*--- Huffman coding low-level stuff ---*/ /*--- huffman.c ---*/ /*-------------------------------------------------------------*/ /* ------------------------------------------------------------------ This file is part of bzip2/libbzip2, a program and library for lossless, block-sorting data compression. bzip2/libbzip2 version 1.0.8 of 13 July 2019 Copyright (C) 1996-2019 Julian Seward <[email protected]> Please read the WARNING, DISCLAIMER and PATENTS sections in the README file. This program is released under the terms of the license contained in the file LICENSE. ------------------------------------------------------------------ */ #include "libc/mem/gc.internal.h" #include "libc/mem/mem.h" #include "third_party/bzip2/bzlib_private.inc" /*---------------------------------------------------*/ #define WEIGHTOF(zz0) ((zz0) & 0xffffff00) #define DEPTHOF(zz1) ((zz1) & 0x000000ff) #define MYMAX(zz2,zz3) ((zz2) > (zz3) ? (zz2) : (zz3)) #define ADDWEIGHTS(zw1,zw2) \ (WEIGHTOF(zw1)+WEIGHTOF(zw2)) | \ (1 + MYMAX(DEPTHOF(zw1),DEPTHOF(zw2))) #define UPHEAP(z) \ { \ Int32 zz, tmp; \ zz = z; tmp = heap[zz]; \ while (weight[tmp] < weight[heap[zz >> 1]]) { \ heap[zz] = heap[zz >> 1]; \ zz >>= 1; \ } \ heap[zz] = tmp; \ } #define DOWNHEAP(z) \ { \ Int32 zz, yy, tmp; \ zz = z; tmp = heap[zz]; \ while (True) { \ yy = zz << 1; \ if (yy > nHeap) break; \ if (yy < nHeap && \ weight[heap[yy+1]] < weight[heap[yy]]) \ yy++; \ if (weight[tmp] < weight[heap[yy]]) break; \ heap[zz] = heap[yy]; \ zz = yy; \ } \ heap[zz] = tmp; \ } /*---------------------------------------------------*/ void BZ2_hbMakeCodeLengths ( UChar *len, Int32 *freq, Int32 alphaSize, Int32 maxLen ) { /*-- Nodes and heap entries run from 1. Entry 0 for both the heap and nodes is a sentinel. --*/ Int32 nNodes, nHeap, n1, n2, i, j, k; Bool tooLong; Int32 *heap = gc(calloc(BZ_MAX_ALPHA_SIZE + 2, 4)); Int32 *weight = gc(calloc(BZ_MAX_ALPHA_SIZE * 2, 4)); Int32 *parent = gc(calloc(BZ_MAX_ALPHA_SIZE * 2, 4)); for (i = 0; i < alphaSize; i++) weight[i+1] = (freq[i] == 0 ? 1 : freq[i]) << 8; while (True) { nNodes = alphaSize; nHeap = 0; heap[0] = 0; weight[0] = 0; parent[0] = -2; for (i = 1; i <= alphaSize; i++) { parent[i] = -1; nHeap++; heap[nHeap] = i; UPHEAP(nHeap); } AssertH( nHeap < (BZ_MAX_ALPHA_SIZE+2), 2001 ); while (nHeap > 1) { n1 = heap[1]; heap[1] = heap[nHeap]; nHeap--; DOWNHEAP(1); n2 = heap[1]; heap[1] = heap[nHeap]; nHeap--; DOWNHEAP(1); nNodes++; parent[n1] = parent[n2] = nNodes; weight[nNodes] = ADDWEIGHTS(weight[n1], weight[n2]); parent[nNodes] = -1; nHeap++; heap[nHeap] = nNodes; UPHEAP(nHeap); } AssertH( nNodes < (BZ_MAX_ALPHA_SIZE * 2), 2002 ); tooLong = False; for (i = 1; i <= alphaSize; i++) { j = 0; k = i; while (parent[k] >= 0) { k = parent[k]; j++; } len[i-1] = j; if (j > maxLen) tooLong = True; } if (! tooLong) break; /* 17 Oct 04: keep-going condition for the following loop used to be 'i < alphaSize', which missed the last element, theoretically leading to the possibility of the compressor looping. However, this count-scaling step is only needed if one of the generated Huffman code words is longer than maxLen, which up to and including version 1.0.2 was 20 bits, which is extremely unlikely. In version 1.0.3 maxLen was changed to 17 bits, which has minimal effect on compression ratio, but does mean this scaling step is used from time to time, enough to verify that it works. This means that bzip2-1.0.3 and later will only produce Huffman codes with a maximum length of 17 bits. However, in order to preserve backwards compatibility with bitstreams produced by versions pre-1.0.3, the decompressor must still handle lengths of up to 20. */ for (i = 1; i <= alphaSize; i++) { j = weight[i] >> 8; j = 1 + (j / 2); weight[i] = j << 8; } } } /*---------------------------------------------------*/ void BZ2_hbAssignCodes ( Int32 *code, UChar *length, Int32 minLen, Int32 maxLen, Int32 alphaSize ) { Int32 n, vec, i; vec = 0; for (n = minLen; n <= maxLen; n++) { for (i = 0; i < alphaSize; i++) if (length[i] == n) { code[i] = vec; vec++; }; vec <<= 1; } } /*---------------------------------------------------*/ void BZ2_hbCreateDecodeTables ( Int32 *limit, Int32 *base, Int32 *perm, UChar *length, Int32 minLen, Int32 maxLen, Int32 alphaSize ) { Int32 pp, i, j, vec; pp = 0; for (i = minLen; i <= maxLen; i++) for (j = 0; j < alphaSize; j++) if (length[j] == i) { perm[pp] = j; pp++; }; for (i = 0; i < BZ_MAX_CODE_LEN; i++) base[i] = 0; for (i = 0; i < alphaSize; i++) base[length[i]+1]++; for (i = 1; i < BZ_MAX_CODE_LEN; i++) base[i] += base[i-1]; for (i = 0; i < BZ_MAX_CODE_LEN; i++) limit[i] = 0; vec = 0; for (i = minLen; i <= maxLen; i++) { vec += (base[i+1] - base[i]); limit[i] = vec-1; vec <<= 1; } for (i = minLen + 1; i <= maxLen; i++) base[i] = ((limit[i-1] + 1) << 1) - base[i]; } /*-------------------------------------------------------------*/ /*--- end huffman.c ---*/ /*-------------------------------------------------------------*/
7,130
209
jart/cosmopolitan
false
cosmopolitan/third_party/bzip2/prepare-release.sh
#!/bin/bash # Script to run to prepare a new release. # It will update the release number and tell you to update the # CHANGES file and to double check everything looks before doing # the release commit and tagging. # Afterwards you probably want to run release-update.sh to upload # the release and update the website at https://sourceware.org/bzip2/ # Any error is fatal set -e # We take one argument, the version (e.g. 1.0.7) if [ $# -ne 1 ]; then echo "$0 <version> (e.g. 1.0.7)" exit 1 fi LANG=C VERSION="$1" DATE=$(date +"%d %B %Y") DAY=$(date +"%d") MONTH=$(date +"%B") SHORTMONTH=$(date +"%b") YEAR=$(date +"%Y") # Replace the version strings and date ranges in the comments VER_PREFIX="bzip2/libbzip2 version " sed -i -e "s@${VER_PREFIX}[0-9].*@${VER_PREFIX}${VERSION} of ${DATE}@" \ -e "s@ (C) \([0-9]\+\)-[0-9]\+ @ (C) \1-$YEAR @" \ CHANGES LICENSE Makefile* README* *.c *.h *.pl *.sh # Add an entry to the README printf "%2s %8s %s\n" "$DAY" "$MONTH" "$YEAR (bzip2, version $VERSION)" \ >> README # Update manual sed -i -e "s@ENTITY bz-version \".*\"@ENTITY bz-version \"$VERSION\"@" \ -e "s@ENTITY bz-date \".*\"@ENTITY bz-date \"$DAY $MONTH $YEAR\"@" \ -e "s@ENTITY bz-lifespan \"\([0-9]\+\)-[0-9]\+\"@ENTITY bz-lifespan \"\1-$YEAR\"@"\ entities.xml # bzip2.1 should really be generated from the manual.xml, but currently # isn't, so explicitly change it here too. sed -i -e "s@This manual page pertains to version .* of@This manual page pertains to version $VERSION of@" \ -e "s@sorting file compressor, v.*@sorting file compressor, v$VERSION@" \ bzip2.1* bzip2.txt # Update sources. All sources, use bzlib_private. # Except bzip2recover, which embeds a version string... sed -i -e "s@^#define BZ_VERSION \".*\"@#define BZ_VERSION \"${VERSION}, ${DAY}-${SHORTMONTH}-${YEAR}\"@" \ bzlib_private.h sed -i -e "s@\"bzip2recover .*: extracts blocks from damaged@\"bzip2recover ${VERSION}: extracts blocks from damaged@" \ bzip2recover.c # And finally update the version/dist/so_name in the Makefiles. sed -i -e "s@^DISTNAME=bzip2-.*@DISTNAME=bzip2-${VERSION}@" \ Makefile sed -i -e "s@libbz2\.so\.[0-9]\.[0-9]\.[0-9]*@libbz2\.so\.${VERSION}@" \ Makefile-libbz2_so echo "Now make sure the diff looks correct:" echo " git diff" echo echo "And make sure there is a $VERSION section in the CHANGES file." echo echo "Double check:" echo " make clean && make dist && make clean && make -f Makefile-libbz2_so" echo echo "Does everything look fine?" echo echo "git commit -a -m \"Prepare for $VERSION release.\"" echo "git push" echo echo "Wait for the buildbot to give the all green!" echo "Then..." echo echo "git tag -s -m \"bzip2 $VERSION release\" bzip2-$VERSION" echo "git push --tags" echo echo "./release-update.sh"
2,790
83
jart/cosmopolitan
false
cosmopolitan/third_party/musl/crypt.h
#ifndef COSMOPOLITAN_THIRD_PARTY_MUSL_CRYPT_H_ #define COSMOPOLITAN_THIRD_PARTY_MUSL_CRYPT_H_ #if !(__ASSEMBLER__ + __LINKER__ + 0) COSMOPOLITAN_C_START_ struct crypt_data { int initialized; char __buf[256]; }; void encrypt(char *, int); void setkey(const char *); char *crypt(const char *, const char *); char *crypt_r(const char *, const char *, struct crypt_data *); COSMOPOLITAN_C_END_ #endif /* !(__ASSEMBLER__ + __LINKER__ + 0) */ #endif /* COSMOPOLITAN_THIRD_PARTY_MUSL_CRYPT_H_ */
496
19
jart/cosmopolitan
false
cosmopolitan/third_party/musl/strfmon.c
/*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-│ │vi: set et ft=c ts=8 tw=8 fenc=utf-8 :vi│ ╚──────────────────────────────────────────────────────────────────────────────╝ │ │ │ Musl Libc │ │ Copyright © 2005-2014 Rich Felker, et al. │ │ │ │ Permission is hereby granted, free of charge, to any person obtaining │ │ a copy of this software and associated documentation files (the │ │ "Software"), to deal in the Software without restriction, including │ │ without limitation the rights to use, copy, modify, merge, publish, │ │ distribute, sublicense, and/or sell copies of the Software, and to │ │ permit persons to whom the Software is furnished to do so, subject to │ │ the following conditions: │ │ │ │ The above copyright notice and this permission notice shall be │ │ included in all copies or substantial portions of the Software. │ │ │ │ THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, │ │ EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF │ │ MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. │ │ IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY │ │ CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, │ │ TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE │ │ SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. │ │ │ ╚─────────────────────────────────────────────────────────────────────────────*/ #include "libc/errno.h" #include "libc/fmt/fmt.h" #include "libc/str/locale.h" #include "libc/str/str.h" #include "libc/thread/tls.h" asm(".ident\t\"\\n\\n\ Musl libc (MIT License)\\n\ Copyright 2005-2014 Rich Felker, et. al.\""); asm(".include \"libc/disclaimer.inc\""); // clang-format off static ssize_t vstrfmon_l(char *s, size_t n, locale_t loc, const char *fmt, va_list ap) { size_t l; double x; int fill, nogrp, negpar, nosym, left, intl; int lp, rp, w, fw; char *s0=s; for (; n && *fmt; ) { if (*fmt != '%') { literal: *s++ = *fmt++; n--; continue; } fmt++; if (*fmt == '%') goto literal; fill = ' '; nogrp = 0; negpar = 0; nosym = 0; left = 0; for (; ; fmt++) { switch (*fmt) { case '=': fill = *++fmt; continue; case '^': nogrp = 1; continue; case '(': negpar = 1; case '+': continue; case '!': nosym = 1; continue; case '-': left = 1; continue; } break; } for (fw=0; isdigit(*fmt); fmt++) fw = 10*fw + (*fmt-'0'); lp = 0; rp = 2; if (*fmt=='#') for (lp=0, fmt++; isdigit(*fmt); fmt++) lp = 10*lp + (*fmt-'0'); if (*fmt=='.') for (rp=0, fmt++; isdigit(*fmt); fmt++) rp = 10*rp + (*fmt-'0'); intl = *fmt++ == 'i'; w = lp + 1 + rp; if (!left && fw>w) w = fw; x = va_arg(ap, double); l = snprintf(s, n, "%*.*f", w, rp, x); if (l >= n) { errno = E2BIG; return -1; } s += l; n -= l; } return s-s0; } ssize_t strfmon_l(char *restrict s, size_t n, locale_t loc, const char *restrict fmt, ...) { va_list ap; ssize_t ret; va_start(ap, fmt); ret = vstrfmon_l(s, n, loc, fmt, ap); va_end(ap); return ret; } ssize_t strfmon(char *restrict s, size_t n, const char *restrict fmt, ...) { va_list ap; ssize_t ret; va_start(ap, fmt); ret = vstrfmon_l(s, n, (locale_t)__get_tls()->tib_locale, fmt, ap); va_end(ap); return ret; }
4,500
134
jart/cosmopolitan
false
cosmopolitan/third_party/musl/ftw.h
#ifndef COSMOPOLITAN_THIRD_PARTY_MUSL_FTW_H_ #define COSMOPOLITAN_THIRD_PARTY_MUSL_FTW_H_ #include "libc/calls/struct/stat.h" #if !(__ASSEMBLER__ + __LINKER__ + 0) COSMOPOLITAN_C_START_ #define FTW_F 1 /* file */ #define FTW_D 2 /* directory */ #define FTW_DNR 3 /* directory that cannot be read */ #define FTW_NS 4 /* not a symbolic link and stat failed */ #define FTW_SL 5 /* symbolic link */ #define FTW_DP 6 /* directory and FTW_DEPTH was specified */ #define FTW_SLN 7 /* symbolic link pointing to nonexistent file */ #define FTW_PHYS 1 #define FTW_MOUNT 2 #define FTW_CHDIR 4 #define FTW_DEPTH 8 struct FTW { int base; int level; }; int ftw(const char *, int (*)(const char *, const struct stat *, int), int); int nftw(const char *, int (*)(const char *, const struct stat *, int, struct FTW *), int, int); COSMOPOLITAN_C_END_ #endif /* !(__ASSEMBLER__ + __LINKER__ + 0) */ #endif /* COSMOPOLITAN_THIRD_PARTY_MUSL_FTW_H_ */
965
33
jart/cosmopolitan
false
cosmopolitan/third_party/musl/rand48.c
/*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-│ │vi: set et ft=c ts=8 tw=8 fenc=utf-8 :vi│ ╚──────────────────────────────────────────────────────────────────────────────╝ │ │ │ Musl Libc │ │ Copyright © 2005-2014 Rich Felker, et al. │ │ │ │ Permission is hereby granted, free of charge, to any person obtaining │ │ a copy of this software and associated documentation files (the │ │ "Software"), to deal in the Software without restriction, including │ │ without limitation the rights to use, copy, modify, merge, publish, │ │ distribute, sublicense, and/or sell copies of the Software, and to │ │ permit persons to whom the Software is furnished to do so, subject to │ │ the following conditions: │ │ │ │ The above copyright notice and this permission notice shall be │ │ included in all copies or substantial portions of the Software. │ │ │ │ THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, │ │ EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF │ │ MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. │ │ IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY │ │ CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, │ │ TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE │ │ SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. │ │ │ ╚─────────────────────────────────────────────────────────────────────────────*/ #include "libc/str/str.h" #include "third_party/musl/rand48.h" asm(".ident\t\"\\n\\n\ Musl libc (MIT License)\\n\ Copyright 2005-2014 Rich Felker, et. al.\""); asm(".include \"libc/disclaimer.inc\""); // clang-format off static unsigned short __seed48[7] = { 0, 0, 0, 0xe66d, 0xdeec, 0x5, 0xb }; static uint64_t __rand48_step(unsigned short *xi, unsigned short *lc) { uint64_t a, x; x = xi[0] | xi[1]+0U<<16 | xi[2]+0ULL<<32; a = lc[0] | lc[1]+0U<<16 | lc[2]+0ULL<<32; x = a*x + lc[3]; xi[0] = x; xi[1] = x>>16; xi[2] = x>>32; return x & 0xffffffffffffull; } double erand48(unsigned short s[3]) { union { uint64_t u; double f; } x = { 0x3ff0000000000000ULL | __rand48_step(s, __seed48+3)<<4 }; return x.f - 1.0; } double drand48(void) { return erand48(__seed48); } void lcong48(unsigned short p[7]) { memcpy(__seed48, p, sizeof __seed48); } long nrand48(unsigned short s[3]) { return __rand48_step(s, __seed48+3) >> 17; } long lrand48(void) { return nrand48(__seed48); } long jrand48(unsigned short s[3]) { return (int32_t)(__rand48_step(s, __seed48+3) >> 16); } long mrand48(void) { return jrand48(__seed48); } unsigned short *seed48(unsigned short *s) { static unsigned short p[3]; memcpy(p, __seed48, sizeof p); memcpy(__seed48, s, sizeof p); return p; } void srand48(long seed) { seed48((unsigned short [3]){ 0x330e, seed, seed>>16 }); }
3,982
102
jart/cosmopolitan
false
cosmopolitan/third_party/musl/crypt_des.internal.h
// clang-format off #ifndef CRYPT_DES_H #define CRYPT_DES_H #include "libc/limits.h" #include "libc/literal.h" struct expanded_key { uint32_t l[16], r[16]; }; _Hide void __des_setkey(const unsigned char *, struct expanded_key *); _Hide void __do_des(uint32_t, uint32_t, uint32_t *, uint32_t *, uint32_t, uint32_t, const struct expanded_key *); #endif
377
17
jart/cosmopolitan
false
cosmopolitan/third_party/musl/crypt_md5.c
/*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-│ │vi: set et ft=c ts=8 tw=8 fenc=utf-8 :vi│ ╚──────────────────────────────────────────────────────────────────────────────╝ │ │ │ Musl Libc │ │ Copyright © 2005-2014 Rich Felker, et al. │ │ │ │ Permission is hereby granted, free of charge, to any person obtaining │ │ a copy of this software and associated documentation files (the │ │ "Software"), to deal in the Software without restriction, including │ │ without limitation the rights to use, copy, modify, merge, publish, │ │ distribute, sublicense, and/or sell copies of the Software, and to │ │ permit persons to whom the Software is furnished to do so, subject to │ │ the following conditions: │ │ │ │ The above copyright notice and this permission notice shall be │ │ included in all copies or substantial portions of the Software. │ │ │ │ THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, │ │ EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF │ │ MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. │ │ IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY │ │ CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, │ │ TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE │ │ SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. │ │ │ ╚─────────────────────────────────────────────────────────────────────────────*/ #include "libc/mem/alg.h" #include "libc/limits.h" #include "libc/literal.h" #include "libc/str/str.h" #include "third_party/musl/crypt.internal.h" #pragma GCC diagnostic ignored "-Wmissing-braces" asm(".ident\t\"\\n\\n\ Musl libc (MIT License)\\n\ Copyright 2005-2014 Rich Felker, et. al.\""); asm(".include \"libc/disclaimer.inc\""); // clang-format off /* * md5 crypt implementation * * original md5 crypt design is from Poul-Henning Kamp * this implementation was created based on the code in freebsd * at least 32bit int is assumed, key is limited and $1$ prefix is mandatory, * on error "*" is returned */ /* public domain md5 implementation based on rfc1321 and libtomcrypt */ struct md5 { uint64_t len; /* processed message length */ uint32_t h[4]; /* hash state */ uint8_t buf[64]; /* message block buffer */ }; static uint32_t rol(uint32_t n, int k) { return (n << k) | (n >> (32-k)); } #define F(x,y,z) (z ^ (x & (y ^ z))) #define G(x,y,z) (y ^ (z & (y ^ x))) #define H(x,y,z) (x ^ y ^ z) #define I(x,y,z) (y ^ (x | ~z)) #define FF(a,b,c,d,w,s,t) a += F(b,c,d) + w + t; a = rol(a,s) + b #define GG(a,b,c,d,w,s,t) a += G(b,c,d) + w + t; a = rol(a,s) + b #define HH(a,b,c,d,w,s,t) a += H(b,c,d) + w + t; a = rol(a,s) + b #define II(a,b,c,d,w,s,t) a += I(b,c,d) + w + t; a = rol(a,s) + b static const uint32_t tab[64] = { 0xd76aa478, 0xe8c7b756, 0x242070db, 0xc1bdceee, 0xf57c0faf, 0x4787c62a, 0xa8304613, 0xfd469501, 0x698098d8, 0x8b44f7af, 0xffff5bb1, 0x895cd7be, 0x6b901122, 0xfd987193, 0xa679438e, 0x49b40821, 0xf61e2562, 0xc040b340, 0x265e5a51, 0xe9b6c7aa, 0xd62f105d, 0x02441453, 0xd8a1e681, 0xe7d3fbc8, 0x21e1cde6, 0xc33707d6, 0xf4d50d87, 0x455a14ed, 0xa9e3e905, 0xfcefa3f8, 0x676f02d9, 0x8d2a4c8a, 0xfffa3942, 0x8771f681, 0x6d9d6122, 0xfde5380c, 0xa4beea44, 0x4bdecfa9, 0xf6bb4b60, 0xbebfbc70, 0x289b7ec6, 0xeaa127fa, 0xd4ef3085, 0x04881d05, 0xd9d4d039, 0xe6db99e5, 0x1fa27cf8, 0xc4ac5665, 0xf4292244, 0x432aff97, 0xab9423a7, 0xfc93a039, 0x655b59c3, 0x8f0ccc92, 0xffeff47d, 0x85845dd1, 0x6fa87e4f, 0xfe2ce6e0, 0xa3014314, 0x4e0811a1, 0xf7537e82, 0xbd3af235, 0x2ad7d2bb, 0xeb86d391 }; static void processblock(struct md5 *s, const uint8_t *buf) { uint32_t i, W[16], a, b, c, d; for (i = 0; i < 16; i++) { W[i] = buf[4*i]; W[i] |= (uint32_t)buf[4*i+1]<<8; W[i] |= (uint32_t)buf[4*i+2]<<16; W[i] |= (uint32_t)buf[4*i+3]<<24; } a = s->h[0]; b = s->h[1]; c = s->h[2]; d = s->h[3]; i = 0; while (i < 16) { FF(a,b,c,d, W[i], 7, tab[i]); i++; FF(d,a,b,c, W[i], 12, tab[i]); i++; FF(c,d,a,b, W[i], 17, tab[i]); i++; FF(b,c,d,a, W[i], 22, tab[i]); i++; } while (i < 32) { GG(a,b,c,d, W[(5*i+1)%16], 5, tab[i]); i++; GG(d,a,b,c, W[(5*i+1)%16], 9, tab[i]); i++; GG(c,d,a,b, W[(5*i+1)%16], 14, tab[i]); i++; GG(b,c,d,a, W[(5*i+1)%16], 20, tab[i]); i++; } while (i < 48) { HH(a,b,c,d, W[(3*i+5)%16], 4, tab[i]); i++; HH(d,a,b,c, W[(3*i+5)%16], 11, tab[i]); i++; HH(c,d,a,b, W[(3*i+5)%16], 16, tab[i]); i++; HH(b,c,d,a, W[(3*i+5)%16], 23, tab[i]); i++; } while (i < 64) { II(a,b,c,d, W[7*i%16], 6, tab[i]); i++; II(d,a,b,c, W[7*i%16], 10, tab[i]); i++; II(c,d,a,b, W[7*i%16], 15, tab[i]); i++; II(b,c,d,a, W[7*i%16], 21, tab[i]); i++; } s->h[0] += a; s->h[1] += b; s->h[2] += c; s->h[3] += d; } static void pad(struct md5 *s) { unsigned r = s->len % 64; s->buf[r++] = 0x80; if (r > 56) { memset(s->buf + r, 0, 64 - r); r = 0; processblock(s, s->buf); } memset(s->buf + r, 0, 56 - r); s->len *= 8; s->buf[56] = s->len; s->buf[57] = s->len >> 8; s->buf[58] = s->len >> 16; s->buf[59] = s->len >> 24; s->buf[60] = s->len >> 32; s->buf[61] = s->len >> 40; s->buf[62] = s->len >> 48; s->buf[63] = s->len >> 56; processblock(s, s->buf); } static void md5_init(struct md5 *s) { s->len = 0; s->h[0] = 0x67452301; s->h[1] = 0xefcdab89; s->h[2] = 0x98badcfe; s->h[3] = 0x10325476; } static void md5_sum(struct md5 *s, uint8_t *md) { int i; pad(s); for (i = 0; i < 4; i++) { md[4*i] = s->h[i]; md[4*i+1] = s->h[i] >> 8; md[4*i+2] = s->h[i] >> 16; md[4*i+3] = s->h[i] >> 24; } } static void md5_update(struct md5 *s, const void *m, unsigned long len) { const uint8_t *p = m; unsigned r = s->len % 64; s->len += len; if (r) { if (len < 64 - r) { memcpy(s->buf + r, p, len); return; } memcpy(s->buf + r, p, 64 - r); len -= 64 - r; p += 64 - r; processblock(s, s->buf); } for (; len >= 64; len -= 64, p += 64) processblock(s, p); memcpy(s->buf, p, len); } /*- * Copyright (c) 2003 Poul-Henning Kamp * All rights reserved. * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions * are met: * 1. Redistributions of source code must retain the above copyright * notice, this list of conditions and the following disclaimer. * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in the * documentation and/or other materials provided with the distribution. * * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF * SUCH DAMAGE. */ /* key limit is not part of the original design, added for DoS protection */ #define KEY_MAX 30000 #define SALT_MAX 8 static const unsigned char b64[] = "./0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz"; static char *to64(char *s, unsigned int u, int n) { while (--n >= 0) { *s++ = b64[u % 64]; u /= 64; } return s; } static char *md5crypt(const char *key, const char *setting, char *output) { struct md5 ctx; unsigned char md[16]; unsigned int i, klen, slen; const char *salt; char *p; /* reject large keys */ klen = strnlen(key, KEY_MAX+1); if (klen > KEY_MAX) return 0; /* setting: $1$salt$ (closing $ is optional) */ if (strncmp(setting, "$1$", 3) != 0) return 0; salt = setting + 3; for (i = 0; i < SALT_MAX && salt[i] && salt[i] != '$'; i++); slen = i; /* md5(key salt key) */ md5_init(&ctx); md5_update(&ctx, key, klen); md5_update(&ctx, salt, slen); md5_update(&ctx, key, klen); md5_sum(&ctx, md); /* md5(key $1$ salt repeated-md weird-key[0]-0) */ md5_init(&ctx); md5_update(&ctx, key, klen); md5_update(&ctx, setting, 3 + slen); for (i = klen; i > sizeof md; i -= sizeof md) md5_update(&ctx, md, sizeof md); md5_update(&ctx, md, i); md[0] = 0; for (i = klen; i; i >>= 1) if (i & 1) md5_update(&ctx, md, 1); else md5_update(&ctx, key, 1); md5_sum(&ctx, md); /* md = f(md, key, salt) iteration */ for (i = 0; i < 1000; i++) { md5_init(&ctx); if (i % 2) md5_update(&ctx, key, klen); else md5_update(&ctx, md, sizeof md); if (i % 3) md5_update(&ctx, salt, slen); if (i % 7) md5_update(&ctx, key, klen); if (i % 2) md5_update(&ctx, md, sizeof md); else md5_update(&ctx, key, klen); md5_sum(&ctx, md); } /* output is $1$salt$hash */ memcpy(output, setting, 3 + slen); p = output + 3 + slen; *p++ = '$'; static const unsigned char perm[][3] = { 0,6,12,1,7,13,2,8,14,3,9,15,4,10,5 }; for (i=0; i<5; i++) p = to64(p, (md[perm[i][0]]<<16)|(md[perm[i][1]]<<8)|md[perm[i][2]], 4); p = to64(p, md[11], 2); *p = 0; return output; } char *__crypt_md5(const char *key, const char *setting, char *output) { static const char testkey[] = "Xy01@#\x01\x02\x80\x7f\xff\r\n\x81\t !"; static const char testsetting[] = "$1$abcd0123$"; static const char testhash[] = "$1$abcd0123$9Qcg8DyviekV3tDGMZynJ1"; char testbuf[64]; char *p, *q; p = md5crypt(key, setting, output); /* self test and stack cleanup */ q = md5crypt(testkey, testsetting, testbuf); if (!p || q != testbuf || memcmp(testbuf, testhash, sizeof testhash)) return "*"; return p; }
11,042
325
jart/cosmopolitan
false
cosmopolitan/third_party/musl/ftw.c
/*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-│ │vi: set et ft=c ts=8 tw=8 fenc=utf-8 :vi│ ╚──────────────────────────────────────────────────────────────────────────────╝ │ │ │ Musl Libc │ │ Copyright © 2005-2014 Rich Felker, et al. │ │ │ │ Permission is hereby granted, free of charge, to any person obtaining │ │ a copy of this software and associated documentation files (the │ │ "Software"), to deal in the Software without restriction, including │ │ without limitation the rights to use, copy, modify, merge, publish, │ │ distribute, sublicense, and/or sell copies of the Software, and to │ │ permit persons to whom the Software is furnished to do so, subject to │ │ the following conditions: │ │ │ │ The above copyright notice and this permission notice shall be │ │ included in all copies or substantial portions of the Software. │ │ │ │ THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, │ │ EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF │ │ MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. │ │ IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY │ │ CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, │ │ TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE │ │ SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. │ │ │ ╚─────────────────────────────────────────────────────────────────────────────*/ #include "third_party/musl/ftw.h" asm(".ident\t\"\\n\\n\ Musl libc (MIT License)\\n\ Copyright 2005-2014 Rich Felker, et. al.\""); asm(".include \"libc/disclaimer.inc\""); /* clang-format off */ /** * Walks file tree. * * @see examples/walk.c for example * @see nftw() */ int ftw(const char *path, int (*fn)(const char *, const struct stat *, int), int fd_limit) { /* The following cast assumes that calling a function with one * argument more than it needs behaves as expected. This is * actually undefined, but works on all real-world machines. */ return nftw(path, (int (*)())fn, fd_limit, FTW_PHYS); }
3,222
50
jart/cosmopolitan
false
cosmopolitan/third_party/musl/glob.c
/*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-│ │vi: set et ft=c ts=8 tw=8 fenc=utf-8 :vi│ ╚──────────────────────────────────────────────────────────────────────────────╝ │ │ │ Musl Libc │ │ Copyright © 2005-2014 Rich Felker, et al. │ │ │ │ Permission is hereby granted, free of charge, to any person obtaining │ │ a copy of this software and associated documentation files (the │ │ "Software"), to deal in the Software without restriction, including │ │ without limitation the rights to use, copy, modify, merge, publish, │ │ distribute, sublicense, and/or sell copies of the Software, and to │ │ permit persons to whom the Software is furnished to do so, subject to │ │ the following conditions: │ │ │ │ The above copyright notice and this permission notice shall be │ │ included in all copies or substantial portions of the Software. │ │ │ │ THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, │ │ EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF │ │ MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. │ │ IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY │ │ CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, │ │ TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE │ │ SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. │ │ │ ╚─────────────────────────────────────────────────────────────────────────────*/ #include "libc/mem/alg.h" #include "libc/calls/calls.h" #include "libc/calls/struct/dirent.h" #include "libc/calls/struct/stat.h" #include "libc/errno.h" #include "libc/mem/mem.h" #include "libc/str/str.h" #include "libc/sysv/consts/dt.h" #include "libc/sysv/consts/s.h" #include "third_party/musl/fnmatch.h" #include "third_party/musl/glob.h" #define MAXPATH 1024 asm(".ident\t\"\\n\\n\ Musl libc (MIT License)\\n\ Copyright 2005-2014 Rich Felker, et. al.\""); asm(".include \"libc/disclaimer.inc\""); struct GlobList { struct GlobList *next; char name[]; }; static int AppendGlob(struct GlobList **tail, const char *name, size_t len, int mark) { struct GlobList *new; if ((new = malloc(sizeof(struct GlobList) + len + 2))) { (*tail)->next = new; new->next = NULL; memcpy(new->name, name, len + 1); if (mark && len && name[len - 1] != '/') { new->name[len] = '/'; new->name[len + 1] = 0; } *tail = new; return 0; } else { return -1; } } static int PerformGlob(char *buf, size_t pos, int type, char *pat, int flags, int (*errfunc)(const char *path, int err), struct GlobList **tail) { DIR *dir; size_t l; char *p, *p2; char saved_sep; ptrdiff_t i, j; struct stat st; struct dirent *de; int r, readerr, in_bracket, overflow, old_errno, fnm_flags; /* If GLOB_MARK is unused, we don't care about type. */ if (!type && !(flags & GLOB_MARK)) type = DT_REG; /* Special-case the remaining pattern being all slashes, in * which case we can use caller-passed type if it's a dir. */ if (*pat && type != DT_DIR) type = 0; while (pos + 1 < MAXPATH && *pat == '/') { buf[pos++] = *pat++; } /* Consume maximal [escaped-]literal prefix of pattern, copying * and un-escaping it to the running buffer as we go. */ i = 0; j = 0; overflow = 0; in_bracket = 0; for (; pat[i] != '*' && pat[i] != '?' && (!in_bracket || pat[i] != ']'); i++) { if (!pat[i]) { if (overflow) return 0; pat += i; pos += j; i = j = 0; break; } else if (pat[i] == '[') { in_bracket = 1; } else if (pat[i] == '\\' && !(flags & GLOB_NOESCAPE)) { /* Backslashes inside a bracket are (at least by * our interpretation) non-special, so if next * char is ']' we have a complete expression. */ if (in_bracket && pat[i + 1] == ']') break; /* Unpaired final backslash never matches. */ if (!pat[i + 1]) return 0; i++; } if (pat[i] == '/') { if (overflow) return 0; in_bracket = 0; pat += i + 1; i = -1; pos += j + 1; j = -1; } /* Only store a character if it fits in the buffer, but if * a potential bracket expression is open, the overflow * must be remembered and handled later only if the bracket * is unterminated (and thereby a literal), so as not to * disallow long bracket expressions with short matches. */ if (pos + (j + 1) < MAXPATH) { buf[pos + j++] = pat[i]; } else if (in_bracket) { overflow = 1; } else { return 0; } /* If we consume any new components, the caller-passed type * or dummy type from above is no longer valid. */ type = 0; } buf[pos] = 0; if (!*pat) { /* If we consumed any components above, or if GLOB_MARK is * requested and we don't yet know if the match is a dir, * we must call stat to confirm the file exists and/or * determine its type. */ if ((flags & GLOB_MARK) && type == DT_LNK) type = 0; if (!type && stat(buf, &st)) { if (errno != ENOENT && (errfunc(buf, errno) || (flags & GLOB_ERR))) { return GLOB_ABORTED; } return 0; } if (!type && S_ISDIR(st.st_mode)) type = DT_DIR; if (AppendGlob(tail, buf, pos, (flags & GLOB_MARK) && type == DT_DIR)) { return GLOB_NOSPACE; } return 0; } p2 = strchr(pat, '/'); saved_sep = '/'; /* Check if the '/' was escaped and, if so, remove the escape char * so that it will not be unpaired when passed to fnmatch. */ if (p2 && !(flags & GLOB_NOESCAPE)) { for (p = p2; p > pat && p[-1] == '\\'; p--) ; if ((p2 - p) % 2) { p2--; saved_sep = '\\'; } } dir = opendir(pos ? buf : "."); if (!dir) { if (errfunc(buf, errno) || (flags & GLOB_ERR)) return GLOB_ABORTED; return 0; } old_errno = errno; while (errno = 0, de = readdir(dir)) { /* Quickly skip non-directories when there's pattern left. */ if (p2 && de->d_type && de->d_type != DT_DIR && de->d_type != DT_LNK) { continue; } l = strlen(de->d_name); if (l >= MAXPATH - pos) continue; if (p2) *p2 = 0; fnm_flags = ((flags & GLOB_NOESCAPE) ? FNM_NOESCAPE : 0) | ((!(flags & GLOB_PERIOD)) ? FNM_PERIOD : 0); if (fnmatch(pat, de->d_name, fnm_flags)) continue; /* With GLOB_PERIOD don't allow matching . or .. unless fnmatch() * would match them with FNM_PERIOD rules in effect. */ if (p2 && (flags & GLOB_PERIOD) && de->d_name[0] == '.' && (!de->d_name[1] || de->d_name[1] == '.' && !de->d_name[2]) && fnmatch(pat, de->d_name, fnm_flags | FNM_PERIOD)) { continue; } memcpy(buf + pos, de->d_name, l + 1); if (p2) *p2 = saved_sep; r = PerformGlob(buf, pos + l, de->d_type, p2 ? p2 : "", flags, errfunc, tail); if (r) { closedir(dir); return r; } } readerr = errno; if (p2) *p2 = saved_sep; closedir(dir); if (readerr && (errfunc(buf, errno) || (flags & GLOB_ERR))) { return GLOB_ABORTED; } errno = old_errno; return 0; } static int IgnoreGlobError(const char *path, int err) { return 0; } static void FreeGlobList(struct GlobList *head) { struct GlobList *match, *next; for (match = head->next; match; match = next) { next = match->next; free(match); } } static int GlobPredicate(const void *a, const void *b) { return strcmp(*(const char **)a, *(const char **)b); } /** * Finds pathnames matching pattern. * * For example: * * glob_t g = {.gl_offs = 2}; * glob("*.*", GLOB_DOOFFS, NULL, &g); * glob("../.*", GLOB_DOOFFS | GLOB_APPEND, NULL, &g); * g.gl_pathv[0] = "ls"; * g.gl_pathv[1] = "-l"; * execvp("ls", &g.gl_pathv[0]); * globfree(g); * * @param pat can have star wildcard see fnmatch() * @param g will receive matching entries and needs globfree() * @return 0 on success or GLOB_NOMATCH, GLOB_NOSPACE on OOM, or * GLOB_ABORTED on read error */ int glob(const char *pat, int flags, int errfunc(const char *path, int err), glob_t *g) { int error = 0; size_t cnt, i; char *p, **pathv, buf[MAXPATH]; struct GlobList head = {.next = NULL}, *tail = &head; size_t offs = (flags & GLOB_DOOFFS) ? g->gl_offs : 0; if (!errfunc) errfunc = IgnoreGlobError; if (!(flags & GLOB_APPEND)) { g->gl_offs = offs; g->gl_pathc = 0; g->gl_pathv = NULL; } if (*pat) { char *p = strdup(pat); if (!p) return GLOB_NOSPACE; buf[0] = 0; error = PerformGlob(buf, 0, 0, p, flags, errfunc, &tail); free(p); } if (error == GLOB_NOSPACE) { FreeGlobList(&head); return error; } for (cnt = 0, tail = head.next; tail; tail = tail->next, cnt++) ; if (!cnt) { if (flags & GLOB_NOCHECK) { tail = &head; if (AppendGlob(&tail, pat, strlen(pat), 0)) { return GLOB_NOSPACE; } cnt++; } else return GLOB_NOMATCH; } if (flags & GLOB_APPEND) { pathv = realloc(g->gl_pathv, (offs + g->gl_pathc + cnt + 1) * sizeof(char *)); if (!pathv) { FreeGlobList(&head); return GLOB_NOSPACE; } g->gl_pathv = pathv; offs += g->gl_pathc; } else { g->gl_pathv = malloc((offs + cnt + 1) * sizeof(char *)); if (!g->gl_pathv) { FreeGlobList(&head); return GLOB_NOSPACE; } for (i = 0; i < offs; i++) { g->gl_pathv[i] = NULL; } } for (i = 0, tail = head.next; i < cnt; tail = tail->next, i++) { g->gl_pathv[offs + i] = tail->name; } g->gl_pathv[offs + i] = NULL; g->gl_pathc += cnt; if (!(flags & GLOB_NOSORT)) { qsort(g->gl_pathv + offs, cnt, sizeof(char *), GlobPredicate); } return error; } /** * Frees entries allocated by glob(). */ void globfree(glob_t *g) { size_t i; for (i = 0; i < g->gl_pathc; i++) { free(g->gl_pathv[g->gl_offs + i] - offsetof(struct GlobList, name)); } free(g->gl_pathv); g->gl_pathc = 0; g->gl_pathv = NULL; }
11,180
324
jart/cosmopolitan
false