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| from mpmath.libmp import * | |
| from mpmath import mpf, mp | |
| from random import randint, choice, seed | |
| all_modes = [round_floor, round_ceiling, round_down, round_up, round_nearest] | |
| fb = from_bstr | |
| fi = from_int | |
| ff = from_float | |
| def test_div_1_3(): | |
| a = fi(1) | |
| b = fi(3) | |
| c = fi(-1) | |
| # floor rounds down, ceiling rounds up | |
| assert mpf_div(a, b, 7, round_floor) == fb('0.01010101') | |
| assert mpf_div(a, b, 7, round_ceiling) == fb('0.01010110') | |
| assert mpf_div(a, b, 7, round_down) == fb('0.01010101') | |
| assert mpf_div(a, b, 7, round_up) == fb('0.01010110') | |
| assert mpf_div(a, b, 7, round_nearest) == fb('0.01010101') | |
| # floor rounds up, ceiling rounds down | |
| assert mpf_div(c, b, 7, round_floor) == fb('-0.01010110') | |
| assert mpf_div(c, b, 7, round_ceiling) == fb('-0.01010101') | |
| assert mpf_div(c, b, 7, round_down) == fb('-0.01010101') | |
| assert mpf_div(c, b, 7, round_up) == fb('-0.01010110') | |
| assert mpf_div(c, b, 7, round_nearest) == fb('-0.01010101') | |
| def test_mpf_divi_1_3(): | |
| a = 1 | |
| b = fi(3) | |
| c = -1 | |
| assert mpf_rdiv_int(a, b, 7, round_floor) == fb('0.01010101') | |
| assert mpf_rdiv_int(a, b, 7, round_ceiling) == fb('0.01010110') | |
| assert mpf_rdiv_int(a, b, 7, round_down) == fb('0.01010101') | |
| assert mpf_rdiv_int(a, b, 7, round_up) == fb('0.01010110') | |
| assert mpf_rdiv_int(a, b, 7, round_nearest) == fb('0.01010101') | |
| assert mpf_rdiv_int(c, b, 7, round_floor) == fb('-0.01010110') | |
| assert mpf_rdiv_int(c, b, 7, round_ceiling) == fb('-0.01010101') | |
| assert mpf_rdiv_int(c, b, 7, round_down) == fb('-0.01010101') | |
| assert mpf_rdiv_int(c, b, 7, round_up) == fb('-0.01010110') | |
| assert mpf_rdiv_int(c, b, 7, round_nearest) == fb('-0.01010101') | |
| def test_div_300(): | |
| q = fi(1000000) | |
| a = fi(300499999) # a/q is a little less than a half-integer | |
| b = fi(300500000) # b/q exactly a half-integer | |
| c = fi(300500001) # c/q is a little more than a half-integer | |
| # Check nearest integer rounding (prec=9 as 2**8 < 300 < 2**9) | |
| assert mpf_div(a, q, 9, round_down) == fi(300) | |
| assert mpf_div(b, q, 9, round_down) == fi(300) | |
| assert mpf_div(c, q, 9, round_down) == fi(300) | |
| assert mpf_div(a, q, 9, round_up) == fi(301) | |
| assert mpf_div(b, q, 9, round_up) == fi(301) | |
| assert mpf_div(c, q, 9, round_up) == fi(301) | |
| # Nearest even integer is down | |
| assert mpf_div(a, q, 9, round_nearest) == fi(300) | |
| assert mpf_div(b, q, 9, round_nearest) == fi(300) | |
| assert mpf_div(c, q, 9, round_nearest) == fi(301) | |
| # Nearest even integer is up | |
| a = fi(301499999) | |
| b = fi(301500000) | |
| c = fi(301500001) | |
| assert mpf_div(a, q, 9, round_nearest) == fi(301) | |
| assert mpf_div(b, q, 9, round_nearest) == fi(302) | |
| assert mpf_div(c, q, 9, round_nearest) == fi(302) | |
| def test_tight_integer_division(): | |
| # Test that integer division at tightest possible precision is exact | |
| N = 100 | |
| seed(1) | |
| for i in range(N): | |
| a = choice([1, -1]) * randint(1, 1<<randint(10, 100)) | |
| b = choice([1, -1]) * randint(1, 1<<randint(10, 100)) | |
| p = a * b | |
| width = bitcount(abs(b)) - trailing(b) | |
| a = fi(a); b = fi(b); p = fi(p) | |
| for mode in all_modes: | |
| assert mpf_div(p, a, width, mode) == b | |
| def test_epsilon_rounding(): | |
| # Verify that mpf_div uses infinite precision; this result will | |
| # appear to be exactly 0.101 to a near-sighted algorithm | |
| a = fb('0.101' + ('0'*200) + '1') | |
| b = fb('1.10101') | |
| c = mpf_mul(a, b, 250, round_floor) # exact | |
| assert mpf_div(c, b, bitcount(a[1]), round_floor) == a # exact | |
| assert mpf_div(c, b, 2, round_down) == fb('0.10') | |
| assert mpf_div(c, b, 3, round_down) == fb('0.101') | |
| assert mpf_div(c, b, 2, round_up) == fb('0.11') | |
| assert mpf_div(c, b, 3, round_up) == fb('0.110') | |
| assert mpf_div(c, b, 2, round_floor) == fb('0.10') | |
| assert mpf_div(c, b, 3, round_floor) == fb('0.101') | |
| assert mpf_div(c, b, 2, round_ceiling) == fb('0.11') | |
| assert mpf_div(c, b, 3, round_ceiling) == fb('0.110') | |
| # The same for negative numbers | |
| a = fb('-0.101' + ('0'*200) + '1') | |
| b = fb('1.10101') | |
| c = mpf_mul(a, b, 250, round_floor) | |
| assert mpf_div(c, b, bitcount(a[1]), round_floor) == a | |
| assert mpf_div(c, b, 2, round_down) == fb('-0.10') | |
| assert mpf_div(c, b, 3, round_up) == fb('-0.110') | |
| # Floor goes up, ceiling goes down | |
| assert mpf_div(c, b, 2, round_floor) == fb('-0.11') | |
| assert mpf_div(c, b, 3, round_floor) == fb('-0.110') | |
| assert mpf_div(c, b, 2, round_ceiling) == fb('-0.10') | |
| assert mpf_div(c, b, 3, round_ceiling) == fb('-0.101') | |
| def test_mod(): | |
| mp.dps = 15 | |
| assert mpf(234) % 1 == 0 | |
| assert mpf(-3) % 256 == 253 | |
| assert mpf(0.25) % 23490.5 == 0.25 | |
| assert mpf(0.25) % -23490.5 == -23490.25 | |
| assert mpf(-0.25) % 23490.5 == 23490.25 | |
| assert mpf(-0.25) % -23490.5 == -0.25 | |
| # Check that these cases are handled efficiently | |
| assert mpf('1e10000000000') % 1 == 0 | |
| assert mpf('1.23e-1000000000') % 1 == mpf('1.23e-1000000000') | |
| # test __rmod__ | |
| assert 3 % mpf('1.75') == 1.25 | |
| def test_div_negative_rnd_bug(): | |
| mp.dps = 15 | |
| assert (-3) / mpf('0.1531879017645047') == mpf('-19.583791966887116') | |
| assert mpf('-2.6342475750861301') / mpf('0.35126216427941814') == mpf('-7.4993775104985909') | |