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stringlengths 14
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6.32M
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cosmopolitan/libc/tinymath/signgam.c | /*-*- mode:c;indent-tabs-mode:nil;c-basic-offset:2;tab-width:8;coding:utf-8 -*-â
âvi: set net ft=c ts=2 sts=2 sw=2 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ¡
â Copyright 2021 Justine Alexandra Roberts Tunney â
â â
â Permission to use, copy, modify, and/or distribute this software for â
â any purpose with or without fee is hereby granted, provided that the â
â above copyright notice and this permission notice appear in all copies. â
â â
â THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL â
â WARRANTIES WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED â
â WARRANTIES OF MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE â
â AUTHOR BE LIABLE FOR ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL â
â DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR â
â PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER â
â TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR â
â PERFORMANCE OF THIS SOFTWARE. â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
int signgam;
| 1,850 | 21 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/catanh.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/complex.h"
#include "libc/math.h"
#include "libc/tinymath/complex.internal.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 */
/* atanh = -i atan(i z) */
double complex catanh(double complex z)
{
z = catan(CMPLX(-cimag(z), creal(z)));
return CMPLX(cimag(z), -creal(z));
}
| 3,008 | 47 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/ilogb.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/limits.h"
#include "libc/math.h"
#include "libc/tinymath/internal.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
/**
* Returns logâð¥ exponent part of double.
*/
int ilogb(double x)
{
// #pragma STDC FENV_ACCESS ON
union {double f; uint64_t i;} u = {x};
uint64_t i = u.i;
int e = i>>52 & 0x7ff;
if (!e) {
i <<= 12;
if (i == 0) {
FORCE_EVAL(0/0.0f);
return FP_ILOGB0;
}
/* subnormal x */
for (e = -0x3ff; i>>63 == 0; e--, i<<=1);
return e;
}
if (e == 0x7ff) {
FORCE_EVAL(0/0.0f);
return i<<12 ? FP_ILOGBNAN : INT_MAX;
}
return e - 0x3ff;
}
#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
__strong_reference(ilogb, ilogbl);
#endif
| 3,401 | 68 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/lrintl.c | /*-*- mode:c;indent-tabs-mode:nil;c-basic-offset:2;tab-width:8;coding:utf-8 -*-â
âvi: set net ft=c ts=2 sts=2 sw=2 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ¡
â Copyright 2023 Justine Alexandra Roberts Tunney â
â â
â Permission to use, copy, modify, and/or distribute this software for â
â any purpose with or without fee is hereby granted, provided that the â
â above copyright notice and this permission notice appear in all copies. â
â â
â THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL â
â WARRANTIES WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED â
â WARRANTIES OF MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE â
â AUTHOR BE LIABLE FOR ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL â
â DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR â
â PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER â
â TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR â
â PERFORMANCE OF THIS SOFTWARE. â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
#include "libc/runtime/fenv.h"
#if !(LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024)
/**
* Rounds to integer in current rounding mode.
*
* The floating-point exception `FE_INEXACT` is raised if the result is
* different from the input.
*/
long lrintl(long double x) {
fenv_t env;
long double y;
feholdexcept(&env);
y = rintl(x);
if (fetestexcept(FE_INVALID)) {
feclearexcept(FE_INEXACT);
}
feupdateenv(&env);
return y;
}
#endif /* long double is long */
| 2,337 | 42 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/ccosl.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/complex.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
long double complex ccosl(long double complex z) {
#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
return ccos(z);
#else
return ccoshl(CMPLXL(-cimagl(z), creall(z)));
#endif
}
| 2,966 | 43 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/rint.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
#include "libc/runtime/fenv.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
#if FLT_EVAL_METHOD==0 || FLT_EVAL_METHOD==1
#define EPS DBL_EPSILON
#elif FLT_EVAL_METHOD==2
#define EPS LDBL_EPSILON
#endif
static const double_t toint = 1/EPS;
/**
* Rounds to integer in current rounding mode.
*
* The floating-point exception `FE_INEXACT` is raised if the result is
* different from the input.
*/
double rint(double x)
{
union {double f; uint64_t i;} u = {x};
int e = u.i>>52 & 0x7ff;
int s = u.i>>63;
double_t y;
if (e >= 0x3ff+52)
return x;
if (s)
y = x - toint + toint;
else
y = x + toint - toint;
if (y == 0)
return s ? -0.0 : 0;
return y;
}
#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
__strong_reference(rint, rintl);
#endif
| 3,495 | 71 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/exp2f.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/intrin/likely.h"
#include "libc/math.h"
#include "libc/tinymath/exp2f_data.internal.h"
#include "libc/tinymath/internal.h"
asm(".ident\t\"\\n\\n\
Double-precision math functions (MIT License)\\n\
Copyright 2018 ARM Limited\"");
asm(".include \"libc/disclaimer.inc\"");
// clang-format off
/*
* Single-precision 2^x function.
*
* Copyright (c) 2017-2018, Arm Limited.
* SPDX-License-Identifier: MIT
*/
/*
EXP2F_TABLE_BITS = 5
EXP2F_POLY_ORDER = 3
ULP error: 0.502 (nearest rounding.)
Relative error: 1.69 * 2^-34 in [-1/64, 1/64] (before rounding.)
Wrong count: 168353 (all nearest rounding wrong results with fma.)
Non-nearest ULP error: 1 (rounded ULP error)
*/
#define N (1 << EXP2F_TABLE_BITS)
#define T __exp2f_data.tab
#define C __exp2f_data.poly
#define SHIFT __exp2f_data.shift_scaled
static inline uint32_t top12(float x)
{
return asuint(x) >> 20;
}
/**
* Returns 2^ð¥.
*/
float exp2f(float x)
{
uint32_t abstop;
uint64_t ki, t;
double_t kd, xd, z, r, r2, y, s;
xd = (double_t)x;
abstop = top12(x) & 0x7ff;
if (UNLIKELY(abstop >= top12(128.0f))) {
/* |x| >= 128 or x is nan. */
if (asuint(x) == asuint(-INFINITY))
return 0.0f;
if (abstop >= top12(INFINITY))
return x + x;
if (x > 0.0f)
return __math_oflowf(0);
if (x <= -150.0f)
return __math_uflowf(0);
}
/* x = k/N + r with r in [-1/(2N), 1/(2N)] and int k. */
kd = eval_as_double(xd + SHIFT);
ki = asuint64(kd);
kd -= SHIFT; /* k/N for int k. */
r = xd - kd;
/* exp2(x) = 2^(k/N) * 2^r ~= s * (C0*r^3 + C1*r^2 + C2*r + 1) */
t = T[ki % N];
t += ki << (52 - EXP2F_TABLE_BITS);
s = asdouble(t);
z = C[0] * r + C[1];
r2 = r * r;
y = C[2] * r + 1;
y = z * r2 + y;
y = y * s;
return eval_as_float(y);
}
| 4,343 | 106 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/ksin.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
#include "libc/tinymath/kernel.internal.h"
asm(".ident\t\"\\n\\n\
fdlibm (fdlibm license)\\n\
Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.\"");
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
/* origin: FreeBSD /usr/src/lib/msun/src/k_sin.c */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/* __sin( x, y, iy)
* kernel sin function on ~[-pi/4, pi/4] (except on -0), pi/4 ~ 0.7854
* Input x is assumed to be bounded by ~pi/4 in magnitude.
* Input y is the tail of x.
* Input iy indicates whether y is 0. (if iy=0, y assume to be 0).
*
* Algorithm
* 1. Since sin(-x) = -sin(x), we need only to consider positive x.
* 2. Callers must return sin(-0) = -0 without calling here since our
* odd polynomial is not evaluated in a way that preserves -0.
* Callers may do the optimization sin(x) ~ x for tiny x.
* 3. sin(x) is approximated by a polynomial of degree 13 on
* [0,pi/4]
* 3 13
* sin(x) ~ x + S1*x + ... + S6*x
* where
*
* |sin(x) 2 4 6 8 10 12 | -58
* |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x +S6*x )| <= 2
* | x |
*
* 4. sin(x+y) = sin(x) + sin'(x')*y
* ~ sin(x) + (1-x*x/2)*y
* For better accuracy, let
* 3 2 2 2 2
* r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6))))
* then 3 2
* sin(x) = x + (S1*x + (x *(r-y/2)+y))
*/
#define S1 -1.66666666666666324348e-01
#define S2 8.33333333332248946124e-03
#define S3 -1.98412698298579493134e-04
#define S4 2.75573137070700676789e-06
#define S5 -2.50507602534068634195e-08
#define S6 1.58969099521155010221e-10
double __sin(double x, double y, int iy)
{
double_t z,r,v,w;
z = x*x;
w = z*z;
r = S2 + z*(S3 + z*S4) + z*w*(S5 + z*S6);
v = z*x;
if (iy == 0)
return x + v*(S1 + z*r);
else
return x - ((z*(0.5*y - v*r) - y) - v*S1);
}
| 5,124 | 100 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/ccoshl.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/complex.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
//FIXME
long double complex ccoshl(long double complex z)
{
return ccosh(z);
}
| 2,868 | 41 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/ccos.c | /*-*- mode:c;indent-tabs-mode:nil;c-basic-offset:2;tab-width:8;coding:utf-8 -*-â
âvi: set net ft=c ts=2 sts=2 sw=2 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ¡
â Copyright 2023 Justine Alexandra Roberts Tunney â
â â
â Permission to use, copy, modify, and/or distribute this software for â
â any purpose with or without fee is hereby granted, provided that the â
â above copyright notice and this permission notice appear in all copies. â
â â
â THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL â
â WARRANTIES WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED â
â WARRANTIES OF MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE â
â AUTHOR BE LIABLE FOR ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL â
â DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR â
â PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER â
â TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR â
â PERFORMANCE OF THIS SOFTWARE. â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/complex.h"
#include "libc/math.h"
double complex ccos(double complex z) {
return ccosh(CMPLX(-cimag(z), creal(z)));
}
| 1,972 | 25 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/rempio2f.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/intrin/likely.h"
#include "libc/math.h"
#include "libc/runtime/fenv.h"
#include "libc/tinymath/kernel.internal.h"
asm(".ident\t\"\\n\\n\
fdlibm (fdlibm license)\\n\
Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.\"");
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 */
/* origin: FreeBSD /usr/src/lib/msun/src/e_rem_pio2f.c */
/*
* Conversion to float by Ian Lance Taylor, Cygnus Support, [email protected].
* Debugged and optimized by Bruce D. Evans.
*/
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/* __rem_pio2f(x,y)
*
* return the remainder of x rem pi/2 in *y
* use double precision for everything except passing x
* use __rem_pio2_large() for large x
*/
#if FLT_EVAL_METHOD==0 || FLT_EVAL_METHOD==1
#define EPS DBL_EPSILON
#elif FLT_EVAL_METHOD==2
#define EPS LDBL_EPSILON
#endif
/*
* invpio2: 53 bits of 2/pi
* pio2_1: first 25 bits of pi/2
* pio2_1t: pi/2 - pio2_1
*/
static const double
toint = 1.5/EPS,
pio4 = 0x1.921fb6p-1,
invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
pio2_1 = 1.57079631090164184570e+00, /* 0x3FF921FB, 0x50000000 */
pio2_1t = 1.58932547735281966916e-08; /* 0x3E5110b4, 0x611A6263 */
int __rem_pio2f(float x, double *y)
{
union {float f; uint32_t i;} u = {x};
double tx[1],ty[1];
double_t fn;
uint32_t ix;
int n, sign, e0;
ix = u.i & 0x7fffffff;
/* 25+53 bit pi is good enough for medium size */
if (ix < 0x4dc90fdb) { /* |x| ~< 2^28*(pi/2), medium size */
/* Use a specialized rint() to get fn. */
fn = (double_t)x*invpio2 + toint - toint;
n = (int32_t)fn;
*y = x - fn*pio2_1 - fn*pio2_1t;
/* Matters with directed rounding. */
if (UNLIKELY(*y < -pio4)) {
n--;
fn--;
*y = x - fn*pio2_1 - fn*pio2_1t;
} else if (UNLIKELY(*y > pio4)) {
n++;
fn++;
*y = x - fn*pio2_1 - fn*pio2_1t;
}
return n;
}
if(ix>=0x7f800000) { /* x is inf or NaN */
*y = x-x;
return 0;
}
/* scale x into [2^23, 2^24-1] */
sign = u.i>>31;
e0 = (ix>>23) - (0x7f+23); /* e0 = ilogb(|x|)-23, positive */
u.i = ix - (e0<<23);
tx[0] = u.f;
n = __rem_pio2_large(tx,ty,e0,1,0);
if (sign) {
*y = -ty[0];
return -n;
}
*y = ty[0];
return n;
}
| 5,229 | 126 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/__math_invalid.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/tinymath/internal.h"
// clang-format off
double __math_invalid(double x)
{
return (x - x) / (x - x);
}
| 2,722 | 35 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/log10l.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
#include "libc/tinymath/internal.h"
#if LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384
asm(".ident\t\"\\n\\n\
OpenBSD libm (ISC License)\\n\
Copyright (c) 2008 Stephen L. Moshier <[email protected]>\"");
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
/* origin: OpenBSD /usr/src/lib/libm/src/ld80/e_log10l.c */
/*
* Copyright (c) 2008 Stephen L. Moshier <[email protected]>
*
* Permission to use, copy, modify, and 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.
*/
/*
* Common logarithm, long double precision
*
*
* SYNOPSIS:
*
* long double x, y, log10l();
*
* y = log10l( x );
*
*
* DESCRIPTION:
*
* Returns the base 10 logarithm of x.
*
* The argument is separated into its exponent and fractional
* parts. If the exponent is between -1 and +1, the logarithm
* of the fraction is approximated by
*
* log(1+x) = x - 0.5 x**2 + x**3 P(x)/Q(x).
*
* Otherwise, setting z = 2(x-1)/x+1),
*
* log(x) = z + z**3 P(z)/Q(z).
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* IEEE 0.5, 2.0 30000 9.0e-20 2.6e-20
* IEEE exp(+-10000) 30000 6.0e-20 2.3e-20
*
* In the tests over the interval exp(+-10000), the logarithms
* of the random arguments were uniformly distributed over
* [-10000, +10000].
*
* ERROR MESSAGES:
*
* log singularity: x = 0; returns MINLOG
* log domain: x < 0; returns MINLOG
*/
/* Coefficients for log(1+x) = x - x**2/2 + x**3 P(x)/Q(x)
* 1/sqrt(2) <= x < sqrt(2)
* Theoretical peak relative error = 6.2e-22
*/
static const long double P[] = {
4.9962495940332550844739E-1L,
1.0767376367209449010438E1L,
7.7671073698359539859595E1L,
2.5620629828144409632571E2L,
4.2401812743503691187826E2L,
3.4258224542413922935104E2L,
1.0747524399916215149070E2L,
};
static const long double Q[] = {
/* 1.0000000000000000000000E0,*/
2.3479774160285863271658E1L,
1.9444210022760132894510E2L,
7.7952888181207260646090E2L,
1.6911722418503949084863E3L,
2.0307734695595183428202E3L,
1.2695660352705325274404E3L,
3.2242573199748645407652E2L,
};
/* Coefficients for log(x) = z + z^3 P(z^2)/Q(z^2),
* where z = 2(x-1)/(x+1)
* 1/sqrt(2) <= x < sqrt(2)
* Theoretical peak relative error = 6.16e-22
*/
static const long double R[4] = {
1.9757429581415468984296E-3L,
-7.1990767473014147232598E-1L,
1.0777257190312272158094E1L,
-3.5717684488096787370998E1L,
};
static const long double S[4] = {
/* 1.00000000000000000000E0L,*/
-2.6201045551331104417768E1L,
1.9361891836232102174846E2L,
-4.2861221385716144629696E2L,
};
/* log10(2) */
#define L102A 0.3125L
#define L102B -1.1470004336018804786261e-2L
/* log10(e) */
#define L10EA 0.5L
#define L10EB -6.5705518096748172348871e-2L
#define SQRTH 0.70710678118654752440L
/**
* Calculates logââð¥.
*/
long double log10l(long double x)
{
#ifdef __x86__
// asm improves performance 41ns â 21ns
// measurement made on an intel core i9
long double lg2;
asm("fldlg2" : "=t"(lg2));
asm("fyl2x"
: "=t"(x)
: "0"(x), "u"(lg2)
: "st(1)");
return x;
#else
long double y, z;
int e;
if (isnan(x))
return x;
if(x <= 0.0) {
if(x == 0.0)
return -1.0 / (x*x);
return (x - x) / 0.0;
}
if (x == INFINITY)
return INFINITY;
/* separate mantissa from exponent */
/* Note, frexp is used so that denormal numbers
* will be handled properly.
*/
x = frexpl(x, &e);
/* logarithm using log(x) = z + z**3 P(z)/Q(z),
* where z = 2(x-1)/x+1)
*/
if (e > 2 || e < -2) {
if (x < SQRTH) { /* 2(2x-1)/(2x+1) */
e -= 1;
z = x - 0.5;
y = 0.5 * z + 0.5;
} else { /* 2 (x-1)/(x+1) */
z = x - 0.5;
z -= 0.5;
y = 0.5 * x + 0.5;
}
x = z / y;
z = x*x;
y = x * (z * __polevll(z, R, 3) / __p1evll(z, S, 3));
goto done;
}
/* logarithm using log(1+x) = x - .5x**2 + x**3 P(x)/Q(x) */
if (x < SQRTH) {
e -= 1;
x = 2.0*x - 1.0;
} else {
x = x - 1.0;
}
z = x*x;
y = x * (z * __polevll(x, P, 6) / __p1evll(x, Q, 7));
y = y - 0.5*z;
done:
/* Multiply log of fraction by log10(e)
* and base 2 exponent by log10(2).
*
* ***CAUTION***
*
* This sequence of operations is critical and it may
* be horribly defeated by some compiler optimizers.
*/
z = y * (L10EB);
z += x * (L10EB);
z += e * (L102B);
z += y * (L10EA);
z += x * (L10EA);
z += e * (L102A);
return z;
#endif
}
#endif /* ieee80 */
| 7,780 | 238 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/tgammaf.c | /*-*- mode:c;indent-tabs-mode:nil;c-basic-offset:2;tab-width:8;coding:utf-8 -*-â
âvi: set net ft=c ts=2 sts=2 sw=2 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ¡
â Copyright 2021 Justine Alexandra Roberts Tunney â
â â
â Permission to use, copy, modify, and/or distribute this software for â
â any purpose with or without fee is hereby granted, provided that the â
â above copyright notice and this permission notice appear in all copies. â
â â
â THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL â
â WARRANTIES WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED â
â WARRANTIES OF MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE â
â AUTHOR BE LIABLE FOR ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL â
â DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR â
â PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER â
â TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR â
â PERFORMANCE OF THIS SOFTWARE. â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
float tgammaf(float x) {
return tgamma(x);
}
| 1,907 | 24 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/__math_uflow.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/tinymath/internal.h"
// clang-format off
double __math_uflow(uint32_t sign)
{
return __math_xflow(sign, 0x1p-767);
}
| 2,736 | 35 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/significandl.c | /*-*- mode:c;indent-tabs-mode:nil;c-basic-offset:2;tab-width:8;coding:utf-8 -*-â
âvi: set net ft=c ts=2 sts=2 sw=2 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ¡
â Copyright 2023 Justine Alexandra Roberts Tunney â
â â
â Permission to use, copy, modify, and/or distribute this software for â
â any purpose with or without fee is hereby granted, provided that the â
â above copyright notice and this permission notice appear in all copies. â
â â
â THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL â
â WARRANTIES WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED â
â WARRANTIES OF MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE â
â AUTHOR BE LIABLE FOR ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL â
â DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR â
â PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER â
â TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR â
â PERFORMANCE OF THIS SOFTWARE. â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
#if !(LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024)
/**
* Return mantissa of ð¥ scaled to range [1,2).
*/
long double significandl(long double x) {
return scalbnl(x, -ilogbl(x));
}
#endif /* long double is long */
| 2,080 | 30 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/expm1l.c | #include "libc/math.h"
#include "libc/tinymath/internal.h"
// clang-format off
#if !(LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024)
asm(".ident\t\"\\n\\n\
OpenBSD libm (ISC License)\\n\
Copyright (c) 2008 Stephen L. Moshier <[email protected]>\"");
asm(".include \"libc/disclaimer.inc\"");
/* origin: OpenBSD /usr/src/lib/libm/src/ld80/e_expm1l.c */
/*
* Copyright (c) 2008 Stephen L. Moshier <[email protected]>
*
* Permission to use, copy, modify, and 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.
*/
/*
* Exponential function, minus 1
* Long double precision
*
*
* SYNOPSIS:
*
* long double x, y, expm1l();
*
* y = expm1l( x );
*
*
* DESCRIPTION:
*
* Returns e (2.71828...) raised to the x power, minus 1.
*
* Range reduction is accomplished by separating the argument
* into an integer k and fraction f such that
*
* x k f
* e = 2 e.
*
* An expansion x + .5 x^2 + x^3 R(x) approximates exp(f) - 1
* in the basic range [-0.5 ln 2, 0.5 ln 2].
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* IEEE -45,+maxarg 200,000 1.2e-19 2.5e-20
*/
/* exp(x) - 1 = x + 0.5 x^2 + x^3 P(x)/Q(x)
-.5 ln 2 < x < .5 ln 2
Theoretical peak relative error = 3.4e-22 */
static const long double
P0 = -1.586135578666346600772998894928250240826E4L,
P1 = 2.642771505685952966904660652518429479531E3L,
P2 = -3.423199068835684263987132888286791620673E2L,
P3 = 1.800826371455042224581246202420972737840E1L,
P4 = -5.238523121205561042771939008061958820811E-1L,
Q0 = -9.516813471998079611319047060563358064497E4L,
Q1 = 3.964866271411091674556850458227710004570E4L,
Q2 = -7.207678383830091850230366618190187434796E3L,
Q3 = 7.206038318724600171970199625081491823079E2L,
Q4 = -4.002027679107076077238836622982900945173E1L,
/* Q5 = 1.000000000000000000000000000000000000000E0 */
/* C1 + C2 = ln 2 */
C1 = 6.93145751953125E-1L,
C2 = 1.428606820309417232121458176568075500134E-6L,
/* ln 2^-65 */
minarg = -4.5054566736396445112120088E1L,
/* ln 2^16384 */
maxarg = 1.1356523406294143949492E4L;
/**
* Returns ðË£-1.
*/
long double expm1l(long double x)
{
long double px, qx, xx;
int k;
if (isnan(x))
return x;
if (x > maxarg)
return x*0x1p16383L; /* overflow, unless x==inf */
if (x == 0.0)
return x;
if (x < minarg)
return -1.0;
xx = C1 + C2;
/* Express x = ln 2 (k + remainder), remainder not exceeding 1/2. */
px = floorl(0.5 + x / xx);
k = px;
/* remainder times ln 2 */
x -= px * C1;
x -= px * C2;
/* Approximate exp(remainder ln 2).*/
px = (((( P4 * x + P3) * x + P2) * x + P1) * x + P0) * x;
qx = (((( x + Q4) * x + Q3) * x + Q2) * x + Q1) * x + Q0;
xx = x * x;
qx = x + (0.5 * xx + xx * px / qx);
/* exp(x) = exp(k ln 2) exp(remainder ln 2) = 2^k exp(remainder ln 2).
We have qx = exp(remainder ln 2) - 1, so
exp(x) - 1 = 2^k (qx + 1) - 1 = 2^k qx + 2^k - 1. */
px = scalbnl(1.0, k);
x = px * qx + (px - 1.0);
return x;
}
#endif /* long double is long */
| 3,675 | 124 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/copysignl.c | /*-*- mode:c;indent-tabs-mode:nil;c-basic-offset:2;tab-width:8;coding:utf-8 -*-â
âvi: set net ft=c ts=2 sts=2 sw=2 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ¡
â Copyright 2023 Justine Alexandra Roberts Tunney â
â â
â Permission to use, copy, modify, and/or distribute this software for â
â any purpose with or without fee is hereby granted, provided that the â
â above copyright notice and this permission notice appear in all copies. â
â â
â THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL â
â WARRANTIES WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED â
â WARRANTIES OF MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE â
â AUTHOR BE LIABLE FOR ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL â
â DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR â
â PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER â
â TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR â
â PERFORMANCE OF THIS SOFTWARE. â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
#include "libc/tinymath/ldshape.internal.h"
#if !(LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024)
/**
* Returns ð¥ with same sign as ð¦.
*/
long double copysignl(long double x, long double y) {
union ldshape ux = {x}, uy = {y};
ux.i.se &= 0x7fff;
ux.i.se |= uy.i.se & 0x8000;
return ux.f;
}
#endif /* long double is long */
| 2,196 | 34 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/tgamma.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
#include "libc/tinymath/feval.internal.h"
#include "libc/tinymath/kernel.internal.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
/*
"A Precision Approximation of the Gamma Function" - Cornelius Lanczos (1964)
"Lanczos Implementation of the Gamma Function" - Paul Godfrey (2001)
"An Analysis of the Lanczos Gamma Approximation" - Glendon Ralph Pugh (2004)
approximation method:
(x - 0.5) S(x)
Gamma(x) = (x + g - 0.5) * ----------------
exp(x + g - 0.5)
with
a1 a2 a3 aN
S(x) ~= [ a0 + ----- + ----- + ----- + ... + ----- ]
x + 1 x + 2 x + 3 x + N
with a0, a1, a2, a3,.. aN constants which depend on g.
for x < 0 the following reflection formula is used:
Gamma(x)*Gamma(-x) = -pi/(x sin(pi x))
most ideas and constants are from boost and python
*/
static const double pi = 3.141592653589793238462643383279502884;
/* sin(pi x) with x > 0x1p-100, if sin(pi*x)==0 the sign is arbitrary */
static double sinpi(double x)
{
int n;
/* argument reduction: x = |x| mod 2 */
/* spurious inexact when x is odd int */
x = x * 0.5;
x = 2 * (x - floor(x));
/* reduce x into [-.25,.25] */
n = 4 * x;
n = (n+1)/2;
x -= n * 0.5;
x *= pi;
switch (n) {
default: /* case 4 */
case 0:
return __sin(x, 0, 0);
case 1:
return __cos(x, 0);
case 2:
return __sin(-x, 0, 0);
case 3:
return -__cos(x, 0);
}
}
#define N 12
//static const double g = 6.024680040776729583740234375;
static const double gmhalf = 5.524680040776729583740234375;
static const double Snum[N+1] = {
23531376880.410759688572007674451636754734846804940,
42919803642.649098768957899047001988850926355848959,
35711959237.355668049440185451547166705960488635843,
17921034426.037209699919755754458931112671403265390,
6039542586.3520280050642916443072979210699388420708,
1439720407.3117216736632230727949123939715485786772,
248874557.86205415651146038641322942321632125127801,
31426415.585400194380614231628318205362874684987640,
2876370.6289353724412254090516208496135991145378768,
186056.26539522349504029498971604569928220784236328,
8071.6720023658162106380029022722506138218516325024,
210.82427775157934587250973392071336271166969580291,
2.5066282746310002701649081771338373386264310793408,
};
static const double Sden[N+1] = {
0, 39916800, 120543840, 150917976, 105258076, 45995730, 13339535,
2637558, 357423, 32670, 1925, 66, 1,
};
/* n! for small integer n */
static const double fact[] = {
1, 1, 2, 6, 24, 120, 720, 5040.0, 40320.0, 362880.0, 3628800.0, 39916800.0,
479001600.0, 6227020800.0, 87178291200.0, 1307674368000.0, 20922789888000.0,
355687428096000.0, 6402373705728000.0, 121645100408832000.0,
2432902008176640000.0, 51090942171709440000.0, 1124000727777607680000.0,
};
/* S(x) rational function for positive x */
static double S(double x)
{
double_t num = 0, den = 0;
int i;
/* to avoid overflow handle large x differently */
if (x < 8)
for (i = N; i >= 0; i--) {
num = num * x + Snum[i];
den = den * x + Sden[i];
}
else
for (i = 0; i <= N; i++) {
num = num / x + Snum[i];
den = den / x + Sden[i];
}
return num/den;
}
/**
* Calculates gamma function of ð¥.
*/
double tgamma(double x)
{
union {double f; uint64_t i;} u = {x};
double absx, y;
double_t dy, z, r;
uint32_t ix = u.i>>32 & 0x7fffffff;
int sign = u.i>>63;
/* special cases */
if (ix >= 0x7ff00000)
/* tgamma(nan)=nan, tgamma(inf)=inf, tgamma(-inf)=nan with invalid */
return x + INFINITY;
if (ix < (0x3ff-54)<<20)
/* |x| < 2^-54: tgamma(x) ~ 1/x, +-0 raises div-by-zero */
return 1/x;
/* integer arguments */
/* raise inexact when non-integer */
if (x == floor(x)) {
if (sign)
return 0/0.0;
if (x <= sizeof fact/sizeof *fact)
return fact[(int)x - 1];
}
/* x >= 172: tgamma(x)=inf with overflow */
/* x =< -184: tgamma(x)=+-0 with underflow */
if (ix >= 0x40670000) { /* |x| >= 184 */
if (sign) {
fevalf(0x1p-126/x);
if (floor(x) * 0.5 == floor(x * 0.5))
return 0;
return -0.0;
}
x *= 0x1p1023;
return x;
}
absx = sign ? -x : x;
/* handle the error of x + g - 0.5 */
y = absx + gmhalf;
if (absx > gmhalf) {
dy = y - absx;
dy -= gmhalf;
} else {
dy = y - gmhalf;
dy -= absx;
}
z = absx - 0.5;
r = S(absx) * exp(-y);
if (x < 0) {
/* reflection formula for negative x */
/* sinpi(absx) is not 0, integers are already handled */
r = -pi / (sinpi(absx) * absx * r);
dy = -dy;
z = -z;
}
r += dy * (gmhalf+0.5) * r / y;
z = pow(y, 0.5*z);
y = r * z * z;
return y;
}
| 7,340 | 211 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/floorl.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
#include "libc/tinymath/internal.h"
#include "libc/tinymath/ldshape.internal.h"
#if !(LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024)
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
/**
* Returns largest integral value not greater than ð¥.
*/
long double floorl(long double x)
{
static const long double toint = 1/LDBL_EPSILON;
union ldshape u = {x};
int e = u.i.se & 0x7fff;
long double y;
if (e >= 0x3fff+LDBL_MANT_DIG-1 || x == 0)
return x;
/* y = int(x) - x, where int(x) is an integer neighbor of x */
if (u.i.se >> 15)
y = x - toint + toint - x;
else
y = x + toint - toint - x;
/* special case because of non-nearest rounding modes */
if (e <= 0x3fff-1) {
FORCE_EVAL(y);
return u.i.se >> 15 ? -1 : 0;
}
if (y > 0)
return x + y - 1;
return x + y;
}
#endif /* long double is long */
| 3,553 | 68 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/log2f_data.internal.h | #ifndef COSMOPOLITAN_LIBC_TINYMATH_LOG2F_DATA_INTERNAL_H_
#define COSMOPOLITAN_LIBC_TINYMATH_LOG2F_DATA_INTERNAL_H_
#define LOG2F_TABLE_BITS 4
#define LOG2F_POLY_ORDER 4
#if !(__ASSEMBLER__ + __LINKER__ + 0)
COSMOPOLITAN_C_START_
extern _Hide const struct log2f_data {
struct {
double invc, logc;
} tab[1 << LOG2F_TABLE_BITS];
double poly[LOG2F_POLY_ORDER];
} __log2f_data;
COSMOPOLITAN_C_END_
#endif /* !(__ASSEMBLER__ + __LINKER__ + 0) */
#endif /* COSMOPOLITAN_LIBC_TINYMATH_LOG2F_DATA_INTERNAL_H_ */
| 518 | 20 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/jnf.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
#include "libc/tinymath/complex.internal.h"
asm(".ident\t\"\\n\\n\
Double-precision math functions (MIT License)\\n\
Copyright 2018 ARM Limited\"");
asm(".include \"libc/disclaimer.inc\"");
// clang-format off
/* origin: FreeBSD /usr/src/lib/msun/src/e_jnf.c */
/*
* Conversion to float by Ian Lance Taylor, Cygnus Support, [email protected].
*/
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/**
* Returns Bessel function of ð¥ of first kind of order ð.
*/
float jnf(int n, float x)
{
uint32_t ix;
int nm1, sign, i;
float a, b, temp;
GET_FLOAT_WORD(ix, x);
sign = ix>>31;
ix &= 0x7fffffff;
if (ix > 0x7f800000) /* nan */
return x;
/* J(-n,x) = J(n,-x), use |n|-1 to avoid overflow in -n */
if (n == 0)
return j0f(x);
if (n < 0) {
nm1 = -(n+1);
x = -x;
sign ^= 1;
} else
nm1 = n-1;
if (nm1 == 0)
return j1f(x);
sign &= n; /* even n: 0, odd n: signbit(x) */
x = fabsf(x);
if (ix == 0 || ix == 0x7f800000) /* if x is 0 or inf */
b = 0.0f;
else if (nm1 < x) {
/* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */
a = j0f(x);
b = j1f(x);
for (i=0; i<nm1; ){
i++;
temp = b;
b = b*(2.0f*i/x) - a;
a = temp;
}
} else {
if (ix < 0x35800000) { /* x < 2**-20 */
/* x is tiny, return the first Taylor expansion of J(n,x)
* J(n,x) = 1/n!*(x/2)^n - ...
*/
if (nm1 > 8) /* underflow */
nm1 = 8;
temp = 0.5f * x;
b = temp;
a = 1.0f;
for (i=2; i<=nm1+1; i++) {
a *= (float)i; /* a = n! */
b *= temp; /* b = (x/2)^n */
}
b = b/a;
} else {
/* use backward recurrence */
/* x x^2 x^2
* J(n,x)/J(n-1,x) = ---- ------ ------ .....
* 2n - 2(n+1) - 2(n+2)
*
* 1 1 1
* (for large x) = ---- ------ ------ .....
* 2n 2(n+1) 2(n+2)
* -- - ------ - ------ -
* x x x
*
* Let w = 2n/x and h=2/x, then the above quotient
* is equal to the continued fraction:
* 1
* = -----------------------
* 1
* w - -----------------
* 1
* w+h - ---------
* w+2h - ...
*
* To determine how many terms needed, let
* Q(0) = w, Q(1) = w(w+h) - 1,
* Q(k) = (w+k*h)*Q(k-1) - Q(k-2),
* When Q(k) > 1e4 good for single
* When Q(k) > 1e9 good for double
* When Q(k) > 1e17 good for quadruple
*/
/* determine k */
float t,q0,q1,w,h,z,tmp,nf;
int k;
nf = nm1+1.0f;
w = 2*nf/x;
h = 2/x;
z = w+h;
q0 = w;
q1 = w*z - 1.0f;
k = 1;
while (q1 < 1.0e4f) {
k += 1;
z += h;
tmp = z*q1 - q0;
q0 = q1;
q1 = tmp;
}
for (t=0.0f, i=k; i>=0; i--)
t = 1.0f/(2*(i+nf)/x-t);
a = t;
b = 1.0f;
/* estimate log((2/x)^n*n!) = n*log(2/x)+n*ln(n)
* Hence, if n*(log(2n/x)) > ...
* single 8.8722839355e+01
* double 7.09782712893383973096e+02
* long double 1.1356523406294143949491931077970765006170e+04
* then recurrent value may overflow and the result is
* likely underflow to zero
*/
tmp = nf*logf(fabsf(w));
if (tmp < 88.721679688f) {
for (i=nm1; i>0; i--) {
temp = b;
b = 2.0f*i*b/x - a;
a = temp;
}
} else {
for (i=nm1; i>0; i--){
temp = b;
b = 2.0f*i*b/x - a;
a = temp;
/* scale b to avoid spurious overflow */
if (b > 0x1p60f) {
a /= b;
t /= b;
b = 1.0f;
}
}
}
z = j0f(x);
w = j1f(x);
if (fabsf(z) >= fabsf(w))
b = t*z/b;
else
b = t*w/a;
}
}
return sign ? -b : b;
}
/**
* Returns Bessel function of ð¥ of second kind of order ð.
*/
float ynf(int n, float x)
{
uint32_t ix, ib;
int nm1, sign, i;
float a, b, temp;
GET_FLOAT_WORD(ix, x);
sign = ix>>31;
ix &= 0x7fffffff;
if (ix > 0x7f800000) /* nan */
return x;
if (sign && ix != 0) /* x < 0 */
return 0/0.0f;
if (ix == 0x7f800000)
return 0.0f;
if (n == 0)
return y0f(x);
if (n < 0) {
nm1 = -(n+1);
sign = n&1;
} else {
nm1 = n-1;
sign = 0;
}
if (nm1 == 0)
return sign ? -y1f(x) : y1f(x);
a = y0f(x);
b = y1f(x);
/* quit if b is -inf */
GET_FLOAT_WORD(ib,b);
for (i = 0; i < nm1 && ib != 0xff800000; ) {
i++;
temp = b;
b = (2.0f*i/x)*b - a;
GET_FLOAT_WORD(ib, b);
a = temp;
}
return sign ? -b : b;
}
| 7,454 | 242 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/lgamma.c | /*-*- mode:c;indent-tabs-mode:nil;c-basic-offset:2;tab-width:8;coding:utf-8 -*-â
âvi: set net ft=c ts=2 sts=2 sw=2 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ¡
â Copyright 2022 Justine Alexandra Roberts Tunney â
â â
â Permission to use, copy, modify, and/or distribute this software for â
â any purpose with or without fee is hereby granted, provided that the â
â above copyright notice and this permission notice appear in all copies. â
â â
â THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL â
â WARRANTIES WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED â
â WARRANTIES OF MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE â
â AUTHOR BE LIABLE FOR ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL â
â DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR â
â PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER â
â TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR â
â PERFORMANCE OF THIS SOFTWARE. â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
#include "libc/tinymath/kernel.internal.h"
/**
* Returns natural logarithm of absolute value of gamma function.
*/
double lgamma(double x) {
return lgamma_r(x, &signgam);
}
| 2,037 | 28 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/scalbf.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2020 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
asm(".ident\t\"\\n\\n\
fdlibm (fdlibm license)\\n\
Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.\"");
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
float scalbf(float x, float fn)
{
if (isunordered(x, fn))
return x*fn;
if (!isfinite(fn)) {
if (fn > 0.0f)
return x*fn;
else
return x/(-fn);
}
if (rintf(fn) != fn) return (fn-fn)/(fn-fn);
if ( fn > 65000.0f) return scalbnf(x, 65000);
if (-fn > 65000.0f) return scalbnf(x,-65000);
return scalbnf(x,(int)fn);
}
| 3,235 | 54 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/ceilf.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
#include "libc/tinymath/internal.h"
#include "third_party/intel/smmintrin.internal.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
/**
* Returns smallest integral value not less than ð¥.
*/
float ceilf(float x)
{
#ifdef __aarch64__
asm("frintp\t%s0,%s1" : "=w"(x) : "w"(x));
return x;
#elif defined(__powerpc64__) && defined(_ARCH_PWR5X)
asm("frip\t%0,%1" : "=f"(x) : "f"(x));
return x;
#elif defined(__s390x__) && (defined(__HTM__) || __ARCH__ >= 9)
asm("fiebra\t%0,6,%1,4" : "=f"(x) : "f"(x));
return x;
#elif defined(__x86_64__) && defined(__SSE4_1__)
asm("roundss\t%2,%1,%0"
: "=x"(x)
: "x"(x), "i"(_MM_FROUND_TO_POS_INF | _MM_FROUND_NO_EXC));
return x;
#else
union {float f; uint32_t i;} u = {x};
int e = (int)(u.i >> 23 & 0xff) - 0x7f;
uint32_t m;
if (e >= 23)
return x;
if (e >= 0) {
m = 0x007fffff >> e;
if ((u.i & m) == 0)
return x;
FORCE_EVAL(x + 0x1p120f);
if (u.i >> 31 == 0)
u.i += m;
u.i &= ~m;
} else {
FORCE_EVAL(x + 0x1p120f);
if (u.i >> 31)
u.f = -0.0;
else if (u.i << 1)
u.f = 1.0;
}
return u.f;
#endif /* __aarch64__ */
}
| 3,853 | 92 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/expo2f.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.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
#define asfloat(i) ((union{uint32_t _i; float _f;}){i})._f
#define SET_FLOAT_WORD(d,w) \
do { \
(d) = asfloat(w); \
} while (0)
/* k is such that k*ln2 has minimal relative error and x - kln2 > log(FLT_MIN) */
static const int k = 235;
static const float kln2 = 0x1.45c778p+7f;
/* expf(x)/2 for x >= log(FLT_MAX), slightly better than 0.5f*expf(x/2)*expf(x/2) */
float __expo2f(float x, float sign)
{
float scale;
/* note that k is odd and scale*scale overflows */
SET_FLOAT_WORD(scale, (uint32_t)(0x7f + k/2) << 23);
/* exp(x - k ln2) * 2**(k-1) */
/* in directed rounding correct sign before rounding or overflow is important */
return expf(x - kln2) * (sign * scale) * scale;
}
| 3,574 | 57 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/carg.c | /*-*- mode:c;indent-tabs-mode:nil;c-basic-offset:2;tab-width:8;coding:utf-8 -*-â
âvi: set net ft=c ts=2 sts=2 sw=2 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ¡
â Copyright 2023 Justine Alexandra Roberts Tunney â
â â
â Permission to use, copy, modify, and/or distribute this software for â
â any purpose with or without fee is hereby granted, provided that the â
â above copyright notice and this permission notice appear in all copies. â
â â
â THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL â
â WARRANTIES WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED â
â WARRANTIES OF MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE â
â AUTHOR BE LIABLE FOR ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL â
â DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR â
â PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER â
â TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR â
â PERFORMANCE OF THIS SOFTWARE. â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/complex.h"
#include "libc/math.h"
double carg(double complex z) {
return atan2(cimag(z), creal(z));
}
#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
__strong_reference(carg, cargl);
#endif
| 2,045 | 29 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/logf_data.internal.h | #ifndef COSMOPOLITAN_LIBC_TINYMATH_LOGF_DATA_INTERNAL_H_
#define COSMOPOLITAN_LIBC_TINYMATH_LOGF_DATA_INTERNAL_H_
#define LOGF_TABLE_BITS 4
#define LOGF_POLY_ORDER 4
#if !(__ASSEMBLER__ + __LINKER__ + 0)
COSMOPOLITAN_C_START_
extern _Hide const struct logf_data {
struct {
double invc, logc;
} tab[1 << LOGF_TABLE_BITS];
double ln2;
double poly[LOGF_POLY_ORDER - 1]; /* First order coefficient is 1. */
} __logf_data;
COSMOPOLITAN_C_END_
#endif /* !(__ASSEMBLER__ + __LINKER__ + 0) */
#endif /* COSMOPOLITAN_LIBC_TINYMATH_LOGF_DATA_INTERNAL_H_ */
| 564 | 21 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/powf_data.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/tinymath/powf_data.internal.h"
asm(".ident\t\"\\n\\n\
Double-precision math functions (MIT License)\\n\
Copyright 2018 ARM Limited\"");
asm(".include \"libc/disclaimer.inc\"");
/* clang-format off */
/*
* Data definition for powf.
*
* Copyright (c) 2017-2018, Arm Limited.
* SPDX-License-Identifier: MIT
*/
const struct powf_log2_data __powf_log2_data = {
.tab = {
{ 0x1.661ec79f8f3bep+0, -0x1.efec65b963019p-2 * POWF_SCALE },
{ 0x1.571ed4aaf883dp+0, -0x1.b0b6832d4fca4p-2 * POWF_SCALE },
{ 0x1.49539f0f010bp+0, -0x1.7418b0a1fb77bp-2 * POWF_SCALE },
{ 0x1.3c995b0b80385p+0, -0x1.39de91a6dcf7bp-2 * POWF_SCALE },
{ 0x1.30d190c8864a5p+0, -0x1.01d9bf3f2b631p-2 * POWF_SCALE },
{ 0x1.25e227b0b8eap+0, -0x1.97c1d1b3b7afp-3 * POWF_SCALE },
{ 0x1.1bb4a4a1a343fp+0, -0x1.2f9e393af3c9fp-3 * POWF_SCALE },
{ 0x1.12358f08ae5bap+0, -0x1.960cbbf788d5cp-4 * POWF_SCALE },
{ 0x1.0953f419900a7p+0, -0x1.a6f9db6475fcep-5 * POWF_SCALE },
{ 0x1p+0, 0x0p+0 * POWF_SCALE },
{ 0x1.e608cfd9a47acp-1, 0x1.338ca9f24f53dp-4 * POWF_SCALE },
{ 0x1.ca4b31f026aap-1, 0x1.476a9543891bap-3 * POWF_SCALE },
{ 0x1.b2036576afce6p-1, 0x1.e840b4ac4e4d2p-3 * POWF_SCALE },
{ 0x1.9c2d163a1aa2dp-1, 0x1.40645f0c6651cp-2 * POWF_SCALE },
{ 0x1.886e6037841edp-1, 0x1.88e9c2c1b9ff8p-2 * POWF_SCALE },
{ 0x1.767dcf5534862p-1, 0x1.ce0a44eb17bccp-2 * POWF_SCALE },
},
.poly = {
0x1.27616c9496e0bp-2 * POWF_SCALE, -0x1.71969a075c67ap-2 * POWF_SCALE,
0x1.ec70a6ca7baddp-2 * POWF_SCALE, -0x1.7154748bef6c8p-1 * POWF_SCALE,
0x1.71547652ab82bp0 * POWF_SCALE,
}
};
| 4,183 | 68 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/atan2f.c | /*-*- mode:c;indent-tabs-mode:nil;c-basic-offset:2;tab-width:8;coding:utf-8 -*-â
âvi: set net ft=c ts=2 sts=2 sw=2 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Optimized Routines â
â Copyright (c) 1999-2022, Arm Limited. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/intrin/likely.h"
#include "libc/math.h"
#include "libc/tinymath/atanf_common.internal.h"
#include "libc/tinymath/internal.h"
asm(".ident\t\"\\n\\n\
Optimized Routines (MIT License)\\n\
Copyright 2022 ARM Limited\"");
asm(".include \"libc/disclaimer.inc\"");
// clang-format off
#define Pi (0x1.921fb6p+1f)
#define PiOver2 (0x1.921fb6p+0f)
#define PiOver4 (0x1.921fb6p-1f)
#define SignMask (0x80000000)
/* We calculate atan2f by P(n/d), where n and d are similar to the input
arguments, and P is a polynomial. The polynomial may underflow.
POLY_UFLOW_BOUND is the lower bound of the difference in exponents of n and d
for which P underflows, and is used to special-case such inputs. */
#define POLY_UFLOW_BOUND 24
static inline int32_t
biased_exponent (float f)
{
uint32_t fi = asuint (f);
int32_t ex = (int32_t) ((fi & 0x7f800000) >> 23);
if (UNLIKELY (ex == 0))
{
/* Subnormal case - we still need to get the exponent right for subnormal
numbers as division may take us back inside the normal range. */
return ex - __builtin_clz (fi << 9);
}
return ex;
}
/* Fast implementation of scalar atan2f. Largest observed error is
2.88ulps in [99.0, 101.0] x [99.0, 101.0]:
atan2f(0x1.9332d8p+6, 0x1.8cb6c4p+6) got 0x1.964646p-1
want 0x1.964640p-1. */
float
atan2f (float y, float x)
{
uint32_t ix = asuint (x);
uint32_t iy = asuint (y);
uint32_t sign_x = ix & SignMask;
uint32_t sign_y = iy & SignMask;
uint32_t iax = ix & ~SignMask;
uint32_t iay = iy & ~SignMask;
/* x or y is NaN. */
if ((iax > 0x7f800000) || (iay > 0x7f800000))
return x + y;
/* m = 2 * sign(x) + sign(y). */
uint32_t m = ((iy >> 31) & 1) | ((ix >> 30) & 2);
/* The following follows glibc ieee754 implementation, except
that we do not use +-tiny shifts (non-nearest rounding mode). */
int32_t exp_diff = biased_exponent (x) - biased_exponent (y);
/* Special case for (x, y) either on or very close to the x axis. Either y =
0, or y is tiny and x is huge (difference in exponents >=
POLY_UFLOW_BOUND). In the second case, we only want to use this special
case when x is negative (i.e. quadrants 2 or 3). */
if (UNLIKELY (iay == 0 || (exp_diff >= POLY_UFLOW_BOUND && m >= 2)))
{
switch (m)
{
case 0:
case 1:
return y; /* atan(+-0,+anything)=+-0. */
case 2:
return Pi; /* atan(+0,-anything) = pi. */
case 3:
return -Pi; /* atan(-0,-anything) =-pi. */
}
}
/* Special case for (x, y) either on or very close to the y axis. Either x =
0, or x is tiny and y is huge (difference in exponents >=
POLY_UFLOW_BOUND). */
if (UNLIKELY (iax == 0 || exp_diff <= -POLY_UFLOW_BOUND))
return sign_y ? -PiOver2 : PiOver2;
/* x is INF. */
if (iax == 0x7f800000)
{
if (iay == 0x7f800000)
{
switch (m)
{
case 0:
return PiOver4; /* atan(+INF,+INF). */
case 1:
return -PiOver4; /* atan(-INF,+INF). */
case 2:
return 3.0f * PiOver4; /* atan(+INF,-INF). */
case 3:
return -3.0f * PiOver4; /* atan(-INF,-INF). */
}
}
else
{
switch (m)
{
case 0:
return 0.0f; /* atan(+...,+INF). */
case 1:
return -0.0f; /* atan(-...,+INF). */
case 2:
return Pi; /* atan(+...,-INF). */
case 3:
return -Pi; /* atan(-...,-INF). */
}
}
}
/* y is INF. */
if (iay == 0x7f800000)
return sign_y ? -PiOver2 : PiOver2;
uint32_t sign_xy = sign_x ^ sign_y;
float ax = asfloat (iax);
float ay = asfloat (iay);
bool pred_aygtax = (ay > ax);
/* Set up z for call to atanf. */
float n = pred_aygtax ? -ax : ay;
float d = pred_aygtax ? ay : ax;
float z = n / d;
float ret;
if (UNLIKELY (m < 2 && exp_diff >= POLY_UFLOW_BOUND))
{
/* If (x, y) is very close to x axis and x is positive, the polynomial
will underflow and evaluate to z. */
ret = z;
}
else
{
/* Work out the correct shift. */
float shift = sign_x ? -2.0f : 0.0f;
shift = pred_aygtax ? shift + 1.0f : shift;
shift *= PiOver2;
ret = eval_poly (z, z, shift);
}
/* Account for the sign of x and y. */
return asfloat (asuint (ret) ^ sign_xy);
}
| 6,866 | 183 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/csqrt.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/complex.h"
#include "libc/math.h"
#include "libc/tinymath/complex.internal.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 */
/* origin: FreeBSD /usr/src/lib/msun/src/s_csqrt.c */
/*-
* Copyright (c) 2007 David Schultz <[email protected]>
* 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.
*/
/*
* gcc doesn't implement complex multiplication or division correctly,
* so we need to handle infinities specially. We turn on this pragma to
* notify conforming c99 compilers that the fast-but-incorrect code that
* gcc generates is acceptable, since the special cases have already been
* handled.
*/
// TODO(elimisteve): write test proving why we do / don't need it
// #pragma STDC CX_LIMITED_RANGE ON
/* We risk spurious overflow for components >= DBL_MAX / (1 + sqrt(2)). */
#define THRESH 0x1.a827999fcef32p+1022
/**
* Returns complex square root.
*/
complex double csqrt(complex double z)
{
complex double result;
double a, b;
double t;
int scale;
a = creal(z);
b = cimag(z);
/* Handle special cases. */
if (z == 0)
return CMPLX(0, b);
if (isinf(b))
return CMPLX(INFINITY, b);
if (isnan(a)) {
t = (b - b) / (b - b); /* raise invalid if b is not a NaN */
return CMPLX(a, t); /* return NaN + NaN i */
}
if (isinf(a)) {
/*
* csqrt(inf + NaN i) = inf + NaN i
* csqrt(inf + y i) = inf + 0 i
* csqrt(-inf + NaN i) = NaN +- inf i
* csqrt(-inf + y i) = 0 + inf i
*/
if (signbit(a))
return CMPLX(fabs(b - b), copysign(a, b));
else
return CMPLX(a, copysign(b - b, b));
}
/*
* The remaining special case (b is NaN) is handled just fine by
* the normal code path below.
*/
/* Scale to avoid overflow. */
if (fabs(a) >= THRESH || fabs(b) >= THRESH) {
a *= 0.25;
b *= 0.25;
scale = 1;
} else {
scale = 0;
}
/* Algorithm 312, CACM vol 10, Oct 1967. */
if (a >= 0) {
t = sqrt((a + hypot(a, b)) * 0.5);
result = CMPLX(t, b / (2 * t));
} else {
t = sqrt((-a + hypot(a, b)) * 0.5);
result = CMPLX(fabs(b) / (2 * t), copysign(t, b));
}
/* Rescale. */
if (scale)
result *= 2;
return result;
}
| 6,079 | 140 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/expl.c | /*-*- mode:c;indent-tabs-mode:nil;c-basic-offset:2;tab-width:8;coding:utf-8 -*-â
âvi: set net ft=c ts=2 sts=2 sw=2 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ¡
â Copyright 2023 Justine Alexandra Roberts Tunney â
â â
â Permission to use, copy, modify, and/or distribute this software for â
â any purpose with or without fee is hereby granted, provided that the â
â above copyright notice and this permission notice appear in all copies. â
â â
â THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL â
â WARRANTIES WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED â
â WARRANTIES OF MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE â
â AUTHOR BE LIABLE FOR ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL â
â DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR â
â PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER â
â TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR â
â PERFORMANCE OF THIS SOFTWARE. â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
#if LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384
#include "libc/tinymath/internal.h"
asm(".ident\t\"\\n\\n\
OpenBSD libm (ISC License)\\n\
Copyright (c) 2008 Stephen L. Moshier <[email protected]>\"");
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
/* origin: OpenBSD /usr/src/lib/libm/src/ld80/e_expl.c */
/*
* Copyright (c) 2008 Stephen L. Moshier <[email protected]>
*
* Permission to use, copy, modify, and 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.
*/
/*
* Exponential function, long double precision
*
*
* SYNOPSIS:
*
* long double x, y, expl();
*
* y = expl( x );
*
*
* DESCRIPTION:
*
* Returns e (2.71828...) raised to the x power.
*
* Range reduction is accomplished by separating the argument
* into an integer k and fraction f such that
*
* x k f
* e = 2 e.
*
* A Pade' form of degree 5/6 is used to approximate exp(f) - 1
* in the basic range [-0.5 ln 2, 0.5 ln 2].
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* IEEE +-10000 50000 1.12e-19 2.81e-20
*
*
* Error amplification in the exponential function can be
* a serious matter. The error propagation involves
* exp( X(1+delta) ) = exp(X) ( 1 + X*delta + ... ),
* which shows that a 1 lsb error in representing X produces
* a relative error of X times 1 lsb in the function.
* While the routine gives an accurate result for arguments
* that are exactly represented by a long double precision
* computer number, the result contains amplified roundoff
* error for large arguments not exactly represented.
*
*
* ERROR MESSAGES:
*
* message condition value returned
* exp underflow x < MINLOG 0.0
* exp overflow x > MAXLOG MAXNUM
*
*/
static const long double P[3] = {
1.2617719307481059087798E-4L,
3.0299440770744196129956E-2L,
9.9999999999999999991025E-1L,
};
static const long double Q[4] = {
3.0019850513866445504159E-6L,
2.5244834034968410419224E-3L,
2.2726554820815502876593E-1L,
2.0000000000000000000897E0L,
};
static const long double
LN2HI = 6.9314575195312500000000E-1L,
LN2LO = 1.4286068203094172321215E-6L,
LOG2E = 1.4426950408889634073599E0L;
/**
* Returns ðË£.
*/
long double expl(long double x)
{
long double px, xx;
int k;
if (isnan(x))
return x;
if (x > 11356.5234062941439488L) /* x > ln(2^16384 - 0.5) */
return x * 0x1p16383L;
if (x < -11399.4985314888605581L) /* x < ln(2^-16446) */
return -0x1p-16445L/x;
/* Express e**x = e**f 2**k
* = e**(f + k ln(2))
*/
px = floorl(LOG2E * x + 0.5);
k = px;
x -= px * LN2HI;
x -= px * LN2LO;
/* rational approximation of the fractional part:
* e**x = 1 + 2x P(x**2)/(Q(x**2) - x P(x**2))
*/
xx = x * x;
px = x * __polevll(xx, P, 2);
x = px/(__polevll(xx, Q, 3) - px);
x = 1.0 + 2.0 * x;
return scalbnl(x, k);
}
#elif LDBL_MANT_DIG == 113 && LDBL_MAX_EXP == 16384
#include "libc/tinymath/freebsd.internal.h"
asm(".ident\t\"\\n\\n\
FreeBSD libm (BSD-2 License)\\n\
Copyright (c) 2005-2011, Bruce D. Evans, Steven G. Kargl, David Schultz.\"");
asm(".ident\t\"\\n\\n\
fdlibm (fdlibm license)\\n\
Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.\"");
asm(".include \"libc/disclaimer.inc\"");
// clang-format off
/*-
* SPDX-License-Identifier: BSD-2-Clause-FreeBSD
*
* Copyright (c) 2009-2013 Steven G. Kargl
* 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 unmodified, 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 ``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.
*
* Optimized by Bruce D. Evans.
*/
/*
* ld128 version of s_expl.c. See ../ld80/s_expl.c for most comments.
*/
/* XXX Prevent compilers from erroneously constant folding these: */
static const volatile long double
huge = 0x1p10000L,
tiny = 0x1p-10000L;
static const long double
twom10000 = 0x1p-10000L;
static const long double
/* log(2**16384 - 0.5) rounded towards zero: */
/* log(2**16384 - 0.5 + 1) rounded towards zero for expm1l() is the same: */
o_threshold = 11356.523406294143949491931077970763428L,
/* log(2**(-16381-64-1)) rounded towards zero: */
u_threshold = -11433.462743336297878837243843452621503L;
static const double
/*
* ln2/INTERVALS = L1+L2 (hi+lo decomposition for multiplication). L1 must
* have at least 22 (= log2(|LDBL_MIN_EXP-extras|) + log2(INTERVALS)) lowest
* bits zero so that multiplication of it by n is exact.
*/
INV_L = 1.8466496523378731e+2, /* 0x171547652b82fe.0p-45 */
L2 = -1.0253670638894731e-29; /* -0x1.9ff0342542fc3p-97 */
static const long double
/* 0x1.62e42fefa39ef35793c768000000p-8 */
L1 = 5.41521234812457272982212595914567508e-3L;
/*
* XXX values in hex in comments have been lost (or were never present)
* from here.
*/
static const long double
/*
* Domain [-0.002708, 0.002708], range ~[-2.4021e-38, 2.4234e-38]:
* |exp(x) - p(x)| < 2**-124.9
* (0.002708 is ln2/(2*INTERVALS) rounded up a little).
*
* XXX the coeffs aren't very carefully rounded, and I get 3.6 more bits.
*/
A2 = 0.5,
A3 = 1.66666666666666666666666666651085500e-1L,
A4 = 4.16666666666666666666666666425885320e-2L,
A5 = 8.33333333333333333334522877160175842e-3L,
A6 = 1.38888888888888888889971139751596836e-3L;
static const double
A7 = 1.9841269841269470e-4, /* 0x1.a01a01a019f91p-13 */
A8 = 2.4801587301585286e-5, /* 0x1.71de3ec75a967p-19 */
A9 = 2.7557324277411235e-6, /* 0x1.71de3ec75a967p-19 */
A10 = 2.7557333722375069e-7; /* 0x1.27e505ab56259p-22 */
/**
* Returns ðË£.
*/
long double
expl(long double x)
{
union IEEEl2bits u;
long double hi, lo, t, twopk;
int k;
uint16_t hx, ix;
DOPRINT_START(&x);
/* Filter out exceptional cases. */
u.e = x;
hx = u.xbits.expsign;
ix = hx & 0x7fff;
if (ix >= BIAS + 13) { /* |x| >= 8192 or x is NaN */
if (ix == BIAS + LDBL_MAX_EXP) {
if (hx & 0x8000) /* x is -Inf or -NaN */
RETURNP(-1 / x);
RETURNP(x + x); /* x is +Inf or +NaN */
}
if (x > o_threshold)
RETURNP(huge * huge);
if (x < u_threshold)
RETURNP(tiny * tiny);
} else if (ix < BIAS - 114) { /* |x| < 0x1p-114 */
RETURN2P(1, x); /* 1 with inexact iff x != 0 */
}
ENTERI();
twopk = 1;
__k_expl(x, &hi, &lo, &k);
t = SUM2P(hi, lo);
/* Scale by 2**k. */
/*
* XXX sparc64 multiplication was so slow that scalbnl() is faster,
* but performance on aarch64 and riscv hasn't yet been quantified.
*/
if (k >= LDBL_MIN_EXP) {
if (k == LDBL_MAX_EXP)
RETURNI(t * 2 * 0x1p16383L);
SET_LDBL_EXPSIGN(twopk, BIAS + k);
RETURNI(t * twopk);
} else {
SET_LDBL_EXPSIGN(twopk, BIAS + k + 10000);
RETURNI(t * twopk * twom10000);
}
}
/*
* Our T1 and T2 are chosen to be approximately the points where method
* A and method B have the same accuracy. Tang's T1 and T2 are the
* points where method A's accuracy changes by a full bit. For Tang,
* this drop in accuracy makes method A immediately less accurate than
* method B, but our larger INTERVALS makes method A 2 bits more
* accurate so it remains the most accurate method significantly
* closer to the origin despite losing the full bit in our extended
* range for it.
*
* Split the interval [T1, T2] into two intervals [T1, T3] and [T3, T2].
* Setting T3 to 0 would require the |x| < 0x1p-113 condition to appear
* in both subintervals, so set T3 = 2**-5, which places the condition
* into the [T1, T3] interval.
*
* XXX we now do this more to (partially) balance the number of terms
* in the C and D polys than to avoid checking the condition in both
* intervals.
*
* XXX these micro-optimizations are excessive.
*/
static const double
T1 = -0.1659, /* ~-30.625/128 * log(2) */
T2 = 0.1659, /* ~30.625/128 * log(2) */
T3 = 0.03125;
/*
* Domain [-0.1659, 0.03125], range ~[2.9134e-44, 1.8404e-37]:
* |(exp(x)-1-x-x**2/2)/x - p(x)| < 2**-122.03
*
* XXX none of the long double C or D coeffs except C10 is correctly printed.
* If you re-print their values in %.35Le format, the result is always
* different. For example, the last 2 digits in C3 should be 59, not 67.
* 67 is apparently from rounding an extra-precision value to 36 decimal
* places.
*/
static const long double
C3 = 1.66666666666666666666666666666666667e-1L,
C4 = 4.16666666666666666666666666666666645e-2L,
C5 = 8.33333333333333333333333333333371638e-3L,
C6 = 1.38888888888888888888888888891188658e-3L,
C7 = 1.98412698412698412698412697235950394e-4L,
C8 = 2.48015873015873015873015112487849040e-5L,
C9 = 2.75573192239858906525606685484412005e-6L,
C10 = 2.75573192239858906612966093057020362e-7L,
C11 = 2.50521083854417203619031960151253944e-8L,
C12 = 2.08767569878679576457272282566520649e-9L,
C13 = 1.60590438367252471783548748824255707e-10L;
/*
* XXX this has 1 more coeff than needed.
* XXX can start the double coeffs but not the double mults at C10.
* With my coeffs (C10-C17 double; s = best_s):
* Domain [-0.1659, 0.03125], range ~[-1.1976e-37, 1.1976e-37]:
* |(exp(x)-1-x-x**2/2)/x - p(x)| ~< 2**-122.65
*/
static const double
C14 = 1.1470745580491932e-11, /* 0x1.93974a81dae30p-37 */
C15 = 7.6471620181090468e-13, /* 0x1.ae7f3820adab1p-41 */
C16 = 4.7793721460260450e-14, /* 0x1.ae7cd18a18eacp-45 */
C17 = 2.8074757356658877e-15, /* 0x1.949992a1937d9p-49 */
C18 = 1.4760610323699476e-16; /* 0x1.545b43aabfbcdp-53 */
/*
* Domain [0.03125, 0.1659], range ~[-2.7676e-37, -1.0367e-38]:
* |(exp(x)-1-x-x**2/2)/x - p(x)| < 2**-121.44
*/
static const long double
D3 = 1.66666666666666666666666666666682245e-1L,
D4 = 4.16666666666666666666666666634228324e-2L,
D5 = 8.33333333333333333333333364022244481e-3L,
D6 = 1.38888888888888888888887138722762072e-3L,
D7 = 1.98412698412698412699085805424661471e-4L,
D8 = 2.48015873015873015687993712101479612e-5L,
D9 = 2.75573192239858944101036288338208042e-6L,
D10 = 2.75573192239853161148064676533754048e-7L,
D11 = 2.50521083855084570046480450935267433e-8L,
D12 = 2.08767569819738524488686318024854942e-9L,
D13 = 1.60590442297008495301927448122499313e-10L;
/*
* XXX this has 1 more coeff than needed.
* XXX can start the double coeffs but not the double mults at D11.
* With my coeffs (D11-D16 double):
* Domain [0.03125, 0.1659], range ~[-1.1980e-37, 1.1980e-37]:
* |(exp(x)-1-x-x**2/2)/x - p(x)| ~< 2**-122.65
*/
static const double
D14 = 1.1470726176204336e-11, /* 0x1.93971dc395d9ep-37 */
D15 = 7.6478532249581686e-13, /* 0x1.ae892e3D16fcep-41 */
D16 = 4.7628892832607741e-14, /* 0x1.ad00Dfe41feccp-45 */
D17 = 3.0524857220358650e-15; /* 0x1.D7e8d886Df921p-49 */
/**
* Returns ðË£-1.
*/
long double
expm1l(long double x)
{
union IEEEl2bits u, v;
long double hx2_hi, hx2_lo, q, r, r1, t, twomk, twopk, x_hi;
long double x_lo, x2;
double dr, dx, fn, r2;
int k, n, n2;
uint16_t hx, ix;
DOPRINT_START(&x);
/* Filter out exceptional cases. */
u.e = x;
hx = u.xbits.expsign;
ix = hx & 0x7fff;
if (ix >= BIAS + 7) { /* |x| >= 128 or x is NaN */
if (ix == BIAS + LDBL_MAX_EXP) {
if (hx & 0x8000) /* x is -Inf or -NaN */
RETURNP(-1 / x - 1);
RETURNP(x + x); /* x is +Inf or +NaN */
}
if (x > o_threshold)
RETURNP(huge * huge);
/*
* expm1l() never underflows, but it must avoid
* unrepresentable large negative exponents. We used a
* much smaller threshold for large |x| above than in
* expl() so as to handle not so large negative exponents
* in the same way as large ones here.
*/
if (hx & 0x8000) /* x <= -128 */
RETURN2P(tiny, -1); /* good for x < -114ln2 - eps */
}
ENTERI();
if (T1 < x && x < T2) {
x2 = x * x;
dx = x;
if (x < T3) {
if (ix < BIAS - 113) { /* |x| < 0x1p-113 */
/* x (rounded) with inexact if x != 0: */
RETURNPI(x == 0 ? x :
(0x1p200 * x + fabsl(x)) * 0x1p-200);
}
q = x * x2 * C3 + x2 * x2 * (C4 + x * (C5 + x * (C6 +
x * (C7 + x * (C8 + x * (C9 + x * (C10 +
x * (C11 + x * (C12 + x * (C13 +
dx * (C14 + dx * (C15 + dx * (C16 +
dx * (C17 + dx * C18))))))))))))));
} else {
q = x * x2 * D3 + x2 * x2 * (D4 + x * (D5 + x * (D6 +
x * (D7 + x * (D8 + x * (D9 + x * (D10 +
x * (D11 + x * (D12 + x * (D13 +
dx * (D14 + dx * (D15 + dx * (D16 +
dx * D17)))))))))))));
}
x_hi = (float)x;
x_lo = x - x_hi;
hx2_hi = x_hi * x_hi / 2;
hx2_lo = x_lo * (x + x_hi) / 2;
if (ix >= BIAS - 7)
RETURN2PI(hx2_hi + x_hi, hx2_lo + x_lo + q);
else
RETURN2PI(x, hx2_lo + q + hx2_hi);
}
/* Reduce x to (k*ln2 + endpoint[n2] + r1 + r2). */
fn = rnint((double)x * INV_L);
n = irint(fn);
n2 = (unsigned)n % INTERVALS;
k = n >> LOG2_INTERVALS;
r1 = x - fn * L1;
r2 = fn * -L2;
r = r1 + r2;
/* Prepare scale factor. */
v.e = 1;
v.xbits.expsign = BIAS + k;
twopk = v.e;
/*
* Evaluate lower terms of
* expl(endpoint[n2] + r1 + r2) = kExplData[n2] * expl(r1 + r2).
*/
dr = r;
q = r2 + r * r * (A2 + r * (A3 + r * (A4 + r * (A5 + r * (A6 +
dr * (A7 + dr * (A8 + dr * (A9 + dr * A10))))))));
t = kExplData[n2].lo + kExplData[n2].hi;
if (k == 0) {
t = SUM2P(kExplData[n2].hi - 1, kExplData[n2].lo * (r1 + 1) + t * q +
kExplData[n2].hi * r1);
RETURNI(t);
}
if (k == -1) {
t = SUM2P(kExplData[n2].hi - 2, kExplData[n2].lo * (r1 + 1) + t * q +
kExplData[n2].hi * r1);
RETURNI(t / 2);
}
if (k < -7) {
t = SUM2P(kExplData[n2].hi, kExplData[n2].lo + t * (q + r1));
RETURNI(t * twopk - 1);
}
if (k > 2 * LDBL_MANT_DIG - 1) {
t = SUM2P(kExplData[n2].hi, kExplData[n2].lo + t * (q + r1));
if (k == LDBL_MAX_EXP)
RETURNI(t * 2 * 0x1p16383L - 1);
RETURNI(t * twopk - 1);
}
v.xbits.expsign = BIAS - k;
twomk = v.e;
if (k > LDBL_MANT_DIG - 1)
t = SUM2P(kExplData[n2].hi, kExplData[n2].lo - twomk + t * (q + r1));
else
t = SUM2P(kExplData[n2].hi - twomk, kExplData[n2].lo + t * (q + r1));
RETURNI(t * twopk);
}
#endif
| 17,577 | 522 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/clogf.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/complex.h"
#include "libc/math.h"
#include "libc/tinymath/complex.internal.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 */
// FIXME
float complex clogf(float complex z)
{
float r, phi;
r = cabsf(z);
phi = cargf(z);
return CMPLXF(logf(r), phi);
}
| 2,989 | 50 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/atan2l.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
#include "libc/tinymath/internal.h"
#include "libc/tinymath/invtrigl.internal.h"
#include "libc/tinymath/ldshape.internal.h"
#if !(LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024)
asm(".ident\t\"\\n\\n\
fdlibm (fdlibm license)\\n\
Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.\"");
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
/* origin: FreeBSD /usr/src/lib/msun/src/e_atan2l.c */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*
*/
/*
* See comments in atan2.c.
* Converted to long double by David Schultz <[email protected]>.
*/
/**
* Returns arc tangent of ð¦/ð¥.
*/
long double atan2l(long double y, long double x)
{
#ifdef __x86__
asm("fpatan"
: "=t"(x)
: "0"(x), "u"(y)
: "st(1)");
return x;
#else
union ldshape ux, uy;
long double z;
int m, ex, ey;
if (isunordered(x, y))
return x+y;
if (x == 1)
return atanl(y);
ux.f = x;
uy.f = y;
ex = ux.i.se & 0x7fff;
ey = uy.i.se & 0x7fff;
m = 2*(ux.i.se>>15) | uy.i.se>>15;
if (y == 0) {
switch(m) {
case 0:
case 1: return y; /* atan(+-0,+anything)=+-0 */
case 2: return 2*pio2_hi; /* atan(+0,-anything) = pi */
case 3: return -2*pio2_hi; /* atan(-0,-anything) =-pi */
}
}
if (x == 0)
return m&1 ? -pio2_hi : pio2_hi;
if (ex == 0x7fff) {
if (ey == 0x7fff) {
switch(m) {
case 0: return pio2_hi/2; /* atan(+INF,+INF) */
case 1: return -pio2_hi/2; /* atan(-INF,+INF) */
case 2: return 1.5*pio2_hi; /* atan(+INF,-INF) */
case 3: return -1.5*pio2_hi; /* atan(-INF,-INF) */
}
} else {
switch(m) {
case 0: return 0.0; /* atan(+...,+INF) */
case 1: return -0.0; /* atan(-...,+INF) */
case 2: return 2*pio2_hi; /* atan(+...,-INF) */
case 3: return -2*pio2_hi; /* atan(-...,-INF) */
}
}
}
if (ex+120 < ey || ey == 0x7fff)
return m&1 ? -pio2_hi : pio2_hi;
/* z = atan(|y/x|) without spurious underflow */
if ((m&2) && ey+120 < ex) /* |y/x| < 0x1p-120, x<0 */
z = 0.0;
else
z = atanl(fabsl(y/x));
switch (m) {
case 0: return z; /* atan(+,+) */
case 1: return -z; /* atan(-,+) */
case 2: return 2*pio2_hi-(z-2*pio2_lo); /* atan(+,-) */
default: /* case 3 */
return (z-2*pio2_lo)-2*pio2_hi; /* atan(-,-) */
}
#endif
}
#endif /* long double is long */
| 5,362 | 134 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/polevll.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2020 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
asm(".ident\t\"\\n\\n\
Musl libc (MIT License)\\n\
Copyright 2005-2014 Rich Felker, et. al.\"");
asm(".ident\t\"\\n\\n\
OpenBSD libm (ISC License)\\n\
Copyright (c) 2008 Stephen L. Moshier <[email protected]>\"");
asm(".include \"libc/disclaimer.inc\"");
// clang-format off
/* origin: OpenBSD /usr/src/lib/libm/src/polevll.c */
/*
* Copyright (c) 2008 Stephen L. Moshier <[email protected]>
*
* Permission to use, copy, modify, and 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.
*/
/*
* Evaluate polynomial
*
*
* SYNOPSIS:
*
* int N;
* long double x, y, coef[N+1], polevl[];
*
* y = polevll( x, coef, N );
*
*
* DESCRIPTION:
*
* Evaluates polynomial of degree N:
*
* 2 N
* y = C + C x + C x +...+ C x
* 0 1 2 N
*
* Coefficients are stored in reverse order:
*
* coef[0] = C , ..., coef[N] = C .
* N 0
*
* The function p1evll() assumes that coef[N] = 1.0 and is
* omitted from the array. Its calling arguments are
* otherwise the same as polevll().
*
*
* SPEED:
*
* In the interest of speed, there are no checks for out
* of bounds arithmetic. This routine is used by most of
* the functions in the library. Depending on available
* equipment features, the user may wish to rewrite the
* program in microcode or assembly language.
*
*/
#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
#else
/*
* Polynomial evaluator:
* P[0] x^n + P[1] x^(n-1) + ... + P[n]
*/
long double __polevll(long double x, const long double *P, int n)
{
long double y;
y = *P++;
do {
y = y * x + *P++;
} while (--n);
return y;
}
/*
* Polynomial evaluator:
* x^n + P[0] x^(n-1) + P[1] x^(n-2) + ... + P[n]
*/
long double __p1evll(long double x, const long double *P, int n)
{
long double y;
n -= 1;
y = x + *P++;
do {
y = y * x + *P++;
} while (--n);
return y;
}
#endif
| 5,188 | 130 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/ceill.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
#include "libc/tinymath/internal.h"
#include "libc/tinymath/ldshape.internal.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
/**
* Returns smallest integral value not less than ð¥.
*/
long double ceill(long double x) {
#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
return ceil(x);
#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
static const long double toint = 1/LDBL_EPSILON;
union ldshape u = {x};
int e = u.i.se & 0x7fff;
long double y;
if (e >= 0x3fff+LDBL_MANT_DIG-1 || x == 0)
return x;
/* y = int(x) - x, where int(x) is an integer neighbor of x */
if (u.i.se >> 15)
y = x - toint + toint - x;
else
y = x + toint - toint - x;
/* special case because of non-nearest rounding modes */
if (e <= 0x3fff-1) {
FORCE_EVAL(y);
return u.i.se >> 15 ? -0.0 : 1;
}
if (y < 0)
return x + y + 1;
return x + y;
#else
#error "architecture unsupported"
#endif
}
| 3,654 | 68 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/sinl.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
#include "libc/tinymath/internal.h"
#include "libc/tinymath/kernel.internal.h"
#include "libc/tinymath/ldshape.internal.h"
#if !(LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024)
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
/**
* Returns sine of ð¥.
*/
long double sinl(long double x)
{
union ldshape u = {x};
unsigned n;
long double y[2], hi, lo;
u.i.se &= 0x7fff;
if (u.i.se == 0x7fff)
return x - x;
if (u.f < M_PI_4) {
if (u.i.se < 0x3fff - LDBL_MANT_DIG/2) {
/* raise inexact if x!=0 and underflow if subnormal */
FORCE_EVAL(u.i.se == 0 ? x*0x1p-120f : x+0x1p120f);
return x;
}
return __sinl(x, 0.0, 0);
}
n = __rem_pio2l(x, y);
hi = y[0];
lo = y[1];
switch (n & 3) {
case 0:
return __sinl(hi, lo, 1);
case 1:
return __cosl(hi, lo);
case 2:
return -__sinl(hi, lo, 1);
case 3:
default:
return -__cosl(hi, lo);
}
}
#endif /* long double is long */
| 3,633 | 77 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/expm1f.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â FreeBSD lib/msun/src/s_expm1f.c â
â â
â Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. â
â â
â Developed at SunPro, a Sun Microsystems, Inc. business. â
â Permission to use, copy, modify, and distribute this â
â software is freely granted, provided that this notice â
â is preserved. â
â â
â Copyright (c) 1992-2023 The FreeBSD Project. â
â â
â Redistribution and use in source and binary forms, with or without â
â modification, are permitted provided that the following conditions â
â are met: â
â 1. Redistributions of source code must retain the above copyright â
â notice, this list of conditions and the following disclaimer. â
â 2. Redistributions in binary form must reproduce the above copyright â
â notice, this list of conditions and the following disclaimer in the â
â documentation and/or other materials provided with the distribution. â
â â
â THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND â
â ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE â
â IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE â
â ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE â
â FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL â
â DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS â
â OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) â
â HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT â
â LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY â
â OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF â
â SUCH DAMAGE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
#include "libc/tinymath/freebsd.internal.h"
asm(".ident\t\"\\n\\n\
FreeBSD libm (BSD-2 License)\\n\
Copyright (c) 2005-2011, Bruce D. Evans, Steven G. Kargl, David Schultz.\"");
asm(".ident\t\"\\n\\n\
fdlibm (fdlibm license)\\n\
Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.\"");
asm(".include \"libc/disclaimer.inc\"");
// clang-format off
static const float
one = 1.0,
tiny = 1.0e-30,
o_threshold = 8.8721679688e+01,/* 0x42b17180 */
ln2_hi = 6.9313812256e-01,/* 0x3f317180 */
ln2_lo = 9.0580006145e-06,/* 0x3717f7d1 */
invln2 = 1.4426950216e+00,/* 0x3fb8aa3b */
/*
* Domain [-0.34568, 0.34568], range ~[-6.694e-10, 6.696e-10]:
* |6 / x * (1 + 2 * (1 / (exp(x) - 1) - 1 / x)) - q(x)| < 2**-30.04
* Scaled coefficients: Qn_here = 2**n * Qn_for_q (see s_expm1.c):
*/
Q1 = -3.3333212137e-2, /* -0x888868.0p-28 */
Q2 = 1.5807170421e-3; /* 0xcf3010.0p-33 */
static volatile float huge = 1.0e+30;
/**
* Returns ðË£-1.
*/
float
expm1f(float x)
{
float y,hi,lo,c,t,e,hxs,hfx,r1,twopk;
int32_t k,xsb;
uint32_t hx;
GET_FLOAT_WORD(hx,x);
xsb = hx&0x80000000; /* sign bit of x */
hx &= 0x7fffffff; /* high word of |x| */
/* filter out huge and non-finite argument */
if(hx >= 0x4195b844) { /* if |x|>=27*ln2 */
if(hx >= 0x42b17218) { /* if |x|>=88.721... */
if(hx>0x7f800000)
return x+x; /* NaN */
if(hx==0x7f800000)
return (xsb==0)? x:-1.0;/* exp(+-inf)={inf,-1} */
if(x > o_threshold) return huge*huge; /* overflow */
}
if(xsb!=0) { /* x < -27*ln2, return -1.0 with inexact */
if(x+tiny<(float)0.0) /* raise inexact */
return tiny-one; /* return -1 */
}
}
/* argument reduction */
if(hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */
if(hx < 0x3F851592) { /* and |x| < 1.5 ln2 */
if(xsb==0)
{hi = x - ln2_hi; lo = ln2_lo; k = 1;}
else
{hi = x + ln2_hi; lo = -ln2_lo; k = -1;}
} else {
k = invln2*x+((xsb==0)?(float)0.5:(float)-0.5);
t = k;
hi = x - t*ln2_hi; /* t*ln2_hi is exact here */
lo = t*ln2_lo;
}
STRICT_ASSIGN(float, x, hi - lo);
c = (hi-x)-lo;
}
else if(hx < 0x33000000) { /* when |x|<2**-25, return x */
t = huge+x; /* return x with inexact flags when x!=0 */
return x - (t-(huge+x));
}
else k = 0;
/* x is now in primary range */
hfx = (float)0.5*x;
hxs = x*hfx;
r1 = one+hxs*(Q1+hxs*Q2);
t = (float)3.0-r1*hfx;
e = hxs*((r1-t)/((float)6.0 - x*t));
if(k==0) return x - (x*e-hxs); /* c is 0 */
else {
SET_FLOAT_WORD(twopk,((uint32_t)(0x7f+k))<<23); /* 2^k */
e = (x*(e-c)-c);
e -= hxs;
if(k== -1) return (float)0.5*(x-e)-(float)0.5;
if(k==1) {
if(x < (float)-0.25) return -(float)2.0*(e-(x+(float)0.5));
else return one+(float)2.0*(x-e);
}
if (k <= -2 || k>56) { /* suffice to return exp(x)-1 */
y = one-(e-x);
if (k == 128) y = y*2.0F*0x1p127F;
else y = y*twopk;
return y-one;
}
t = one;
if(k<23) {
SET_FLOAT_WORD(t,0x3f800000 - (0x1000000>>k)); /* t=1-2^-k */
y = t-(e-x);
y = y*twopk;
} else {
SET_FLOAT_WORD(t,((0x7f-k)<<23)); /* 2^-k */
y = x-(e+t);
y += one;
y = y*twopk;
}
}
return y;
}
| 6,728 | 154 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/invtrigl.internal.h | #ifndef COSMOPOLITAN_LIBC_TINYMATH_INVTRIGL_H_
#define COSMOPOLITAN_LIBC_TINYMATH_INVTRIGL_H_
#if !(__ASSEMBLER__ + __LINKER__ + 0)
COSMOPOLITAN_C_START_
/* shared by acosl, asinl and atan2l */
#define pio2_hi __pio2_hi
#define pio2_lo __pio2_lo
_Hide extern const long double pio2_hi, pio2_lo;
_Hide long double __invtrigl_R(long double z);
COSMOPOLITAN_C_END_
#endif /* !(__ASSEMBLER__ + __LINKER__ + 0) */
#endif /* COSMOPOLITAN_LIBC_TINYMATH_INVTRIGL_H_ */
| 465 | 17 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/remquo.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2020 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.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
/**
* Computes remainder and part of quotient.
*/
double remquo(double x, double y, int *quo)
{
union {double f; uint64_t i;} ux = {x}, uy = {y};
int ex = ux.i>>52 & 0x7ff;
int ey = uy.i>>52 & 0x7ff;
int sx = ux.i>>63;
int sy = uy.i>>63;
uint32_t q;
uint64_t i;
uint64_t uxi = ux.i;
*quo = 0;
if (uy.i<<1 == 0 || isnan(y) || ex == 0x7ff)
return (x*y)/(x*y);
if (ux.i<<1 == 0)
return x;
/* normalize x and y */
if (!ex) {
for (i = uxi<<12; i>>63 == 0; ex--, i <<= 1);
uxi <<= -ex + 1;
} else {
uxi &= -1ULL >> 12;
uxi |= 1ULL << 52;
}
if (!ey) {
for (i = uy.i<<12; i>>63 == 0; ey--, i <<= 1);
uy.i <<= -ey + 1;
} else {
uy.i &= -1ULL >> 12;
uy.i |= 1ULL << 52;
}
q = 0;
if (ex < ey) {
if (ex+1 == ey)
goto end;
return x;
}
/* x mod y */
for (; ex > ey; ex--) {
i = uxi - uy.i;
if (i >> 63 == 0) {
uxi = i;
q++;
}
uxi <<= 1;
q <<= 1;
}
i = uxi - uy.i;
if (i >> 63 == 0) {
uxi = i;
q++;
}
if (uxi == 0)
ex = -60;
else
for (; uxi>>52 == 0; uxi <<= 1, ex--);
end:
/* scale result and decide between |x| and |x|-|y| */
if (ex > 0) {
uxi -= 1ULL << 52;
uxi |= (uint64_t)ex << 52;
} else {
uxi >>= -ex + 1;
}
ux.i = uxi;
x = ux.f;
if (sy)
y = -y;
if (ex == ey || (ex+1 == ey && (2*x > y || (2*x == y && q%2)))) {
x -= y;
q++;
}
q &= 0x7fffffff;
*quo = sx^sy ? -(int)q : (int)q;
return sx ? -x : x;
}
#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
__strong_reference(remquo, remquol);
#endif
| 4,280 | 122 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/lroundl.c | /*-*- mode:c;indent-tabs-mode:nil;c-basic-offset:2;tab-width:8;coding:utf-8 -*-â
âvi: set net ft=c ts=2 sts=2 sw=2 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ¡
â Copyright 2023 Justine Alexandra Roberts Tunney â
â â
â Permission to use, copy, modify, and/or distribute this software for â
â any purpose with or without fee is hereby granted, provided that the â
â above copyright notice and this permission notice appear in all copies. â
â â
â THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL â
â WARRANTIES WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED â
â WARRANTIES OF MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE â
â AUTHOR BE LIABLE FOR ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL â
â DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR â
â PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER â
â TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR â
â PERFORMANCE OF THIS SOFTWARE. â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
#if !(LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024)
long lroundl(long double x) {
return roundl(x);
}
#endif /* long double is long */
| 1,997 | 27 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/log1pf_data.c | /*-*- mode:c;indent-tabs-mode:nil;c-basic-offset:2;tab-width:8;coding:utf-8 -*-â
âvi: set net ft=c ts=2 sts=2 sw=2 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Optimized Routines â
â Copyright (c) 1999-2022, Arm Limited. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/tinymath/log1pf_data.internal.h"
asm(".ident\t\"\\n\\n\
Optimized Routines (MIT License)\\n\
Copyright 2022 ARM Limited\"");
asm(".include \"libc/disclaimer.inc\"");
/* clang-format off */
/* Polynomial coefficients generated using floating-point minimax
algorithm, see tools/log1pf.sollya for details. */
const struct log1pf_data __log1pf_data
= {.coeffs = {-0x1p-1f, 0x1.5555aap-2f, -0x1.000038p-2f, 0x1.99675cp-3f,
-0x1.54ef78p-3f, 0x1.28a1f4p-3f, -0x1.0da91p-3f, 0x1.abcb6p-4f,
-0x1.6f0d5ep-5f}};
| 3,129 | 42 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/exp.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Optimized Routines â
â Copyright (c) 1999-2022, Arm Limited. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/intrin/likely.h"
#include "libc/math.h"
#include "libc/tinymath/exp_data.internal.h"
#include "libc/tinymath/internal.h"
asm(".ident\t\"\\n\\n\
Double-precision math functions (MIT License)\\n\
Copyright 2018 ARM Limited\"");
asm(".include \"libc/disclaimer.inc\"");
// clang-format off
/*
* Double-precision e^x function.
*
* Copyright (c) 2018, Arm Limited.
* SPDX-License-Identifier: MIT
*/
#define N (1 << EXP_TABLE_BITS)
#define InvLn2N __exp_data.invln2N
#define NegLn2hiN __exp_data.negln2hiN
#define NegLn2loN __exp_data.negln2loN
#define Shift __exp_data.shift
#define T __exp_data.tab
#define C2 __exp_data.poly[5 - EXP_POLY_ORDER]
#define C3 __exp_data.poly[6 - EXP_POLY_ORDER]
#define C4 __exp_data.poly[7 - EXP_POLY_ORDER]
#define C5 __exp_data.poly[8 - EXP_POLY_ORDER]
/* Handle cases that may overflow or underflow when computing the result that
is scale*(1+TMP) without intermediate rounding. The bit representation of
scale is in SBITS, however it has a computed exponent that may have
overflown into the sign bit so that needs to be adjusted before using it as
a double. (int32_t)KI is the k used in the argument reduction and exponent
adjustment of scale, positive k here means the result may overflow and
negative k means the result may underflow. */
static inline double specialcase(double_t tmp, uint64_t sbits, uint64_t ki)
{
double_t scale, y;
if ((ki & 0x80000000) == 0) {
/* k > 0, the exponent of scale might have overflowed by <= 460. */
sbits -= 1009ull << 52;
scale = asdouble(sbits);
y = 0x1p1009 * (scale + scale * tmp);
return eval_as_double(y);
}
/* k < 0, need special care in the subnormal range. */
sbits += 1022ull << 52;
scale = asdouble(sbits);
y = scale + scale * tmp;
if (y < 1.0) {
/* Round y to the right precision before scaling it into the subnormal
range to avoid double rounding that can cause 0.5+E/2 ulp error where
E is the worst-case ulp error outside the subnormal range. So this
is only useful if the goal is better than 1 ulp worst-case error. */
double_t hi, lo;
lo = scale - y + scale * tmp;
hi = 1.0 + y;
lo = 1.0 - hi + y + lo;
y = eval_as_double(hi + lo) - 1.0;
/* Avoid -0.0 with downward rounding. */
if (WANT_ROUNDING && y == 0.0)
y = 0.0;
/* The underflow exception needs to be signaled explicitly. */
fp_force_eval(fp_barrier(0x1p-1022) * 0x1p-1022);
}
y = 0x1p-1022 * y;
return eval_as_double(y);
}
/* Top 12 bits of a double (sign and exponent bits). */
static inline uint32_t top12(double x)
{
return asuint64(x) >> 52;
}
/**
* Returns ð^x.
*/
double exp(double x)
{
uint32_t abstop;
uint64_t ki, idx, top, sbits;
double_t kd, z, r, r2, scale, tail, tmp;
abstop = top12(x) & 0x7ff;
if (UNLIKELY(abstop - top12(0x1p-54) >= top12(512.0) - top12(0x1p-54))) {
if (abstop - top12(0x1p-54) >= 0x80000000)
/* Avoid spurious underflow for tiny x. */
/* Note: 0 is common input. */
return WANT_ROUNDING ? 1.0 + x : 1.0;
if (abstop >= top12(1024.0)) {
if (asuint64(x) == asuint64(-INFINITY))
return 0.0;
if (abstop >= top12(INFINITY))
return 1.0 + x;
if (asuint64(x) >> 63)
return __math_uflow(0);
else
return __math_oflow(0);
}
/* Large x is special cased below. */
abstop = 0;
}
/* exp(x) = 2^(k/N) * exp(r), with exp(r) in [2^(-1/2N),2^(1/2N)]. */
/* x = ln2/N*k + r, with int k and r in [-ln2/2N, ln2/2N]. */
z = InvLn2N * x;
#if TOINT_INTRINSICS
kd = roundtoint(z);
ki = converttoint(z);
#elif EXP_USE_TOINT_NARROW
/* z - kd is in [-0.5-2^-16, 0.5] in all rounding modes. */
kd = eval_as_double(z + Shift);
ki = asuint64(kd) >> 16;
kd = (double_t)(int32_t)ki;
#else
/* z - kd is in [-1, 1] in non-nearest rounding modes. */
kd = eval_as_double(z + Shift);
ki = asuint64(kd);
kd -= Shift;
#endif
r = x + kd * NegLn2hiN + kd * NegLn2loN;
/* 2^(k/N) ~= scale * (1 + tail). */
idx = 2 * (ki % N);
top = ki << (52 - EXP_TABLE_BITS);
tail = asdouble(T[idx]);
/* This is only a valid scale when -1023*N < k < 1024*N. */
sbits = T[idx + 1] + top;
/* exp(x) = 2^(k/N) * exp(r) ~= scale + scale * (tail + exp(r) - 1). */
/* Evaluation is optimized assuming superscalar pipelined execution. */
r2 = r * r;
/* Without fma the worst case error is 0.25/N ulp larger. */
/* Worst case error is less than 0.5+1.11/N+(abs poly error * 2^53) ulp. */
tmp = tail + r + r2 * (C2 + r * C3) + r2 * r2 * (C4 + r * C5);
if (UNLIKELY(abstop == 0))
return specialcase(tmp, sbits, ki);
scale = asdouble(sbits);
/* Note: tmp == 0 or |tmp| > 2^-200 and scale > 2^-739, so there
is no spurious underflow here even without fma. */
return eval_as_double(scale + scale * tmp);
}
#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
__strong_reference(exp, expl);
#endif
| 7,415 | 175 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/conj.c | /*-*- mode:c;indent-tabs-mode:nil;c-basic-offset:2;tab-width:8;coding:utf-8 -*-â
âvi: set net ft=c ts=2 sts=2 sw=2 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ¡
â Copyright 2023 Justine Alexandra Roberts Tunney â
â â
â Permission to use, copy, modify, and/or distribute this software for â
â any purpose with or without fee is hereby granted, provided that the â
â above copyright notice and this permission notice appear in all copies. â
â â
â THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL â
â WARRANTIES WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED â
â WARRANTIES OF MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE â
â AUTHOR BE LIABLE FOR ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL â
â DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR â
â PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER â
â TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR â
â PERFORMANCE OF THIS SOFTWARE. â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/complex.h"
double complex conj(double complex z) {
return CMPLX(creal(z), -cimag(z));
}
| 1,942 | 24 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/__math_oflow.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/tinymath/internal.h"
// clang-format off
double __math_oflow(uint32_t sign)
{
return __math_xflow(sign, 0x1p769);
}
| 2,735 | 35 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/asin.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2020 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.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
/* origin: FreeBSD /usr/src/lib/msun/src/e_asin.c */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/* asin(x)
* Method :
* Since asin(x) = x + x^3/6 + x^5*3/40 + x^7*15/336 + ...
* we approximate asin(x) on [0,0.5] by
* asin(x) = x + x*x^2*R(x^2)
* where
* R(x^2) is a rational approximation of (asin(x)-x)/x^3
* and its remez error is bounded by
* |(asin(x)-x)/x^3 - R(x^2)| < 2^(-58.75)
*
* For x in [0.5,1]
* asin(x) = pi/2-2*asin(sqrt((1-x)/2))
* Let y = (1-x), z = y/2, s := sqrt(z), and pio2_hi+pio2_lo=pi/2;
* then for x>0.98
* asin(x) = pi/2 - 2*(s+s*z*R(z))
* = pio2_hi - (2*(s+s*z*R(z)) - pio2_lo)
* For x<=0.98, let pio4_hi = pio2_hi/2, then
* f = hi part of s;
* c = sqrt(z) - f = (z-f*f)/(s+f) ...f+c=sqrt(z)
* and
* asin(x) = pi/2 - 2*(s+s*z*R(z))
* = pio4_hi+(pio4-2s)-(2s*z*R(z)-pio2_lo)
* = pio4_hi+(pio4-2f)-(2s*z*R(z)-(pio2_lo+2c))
*
* Special cases:
* if x is NaN, return x itself;
* if |x|>1, return NaN with invalid signal.
*
*/
static const double
pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */
pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */
/* coefficients for R(x^2) */
pS0 = 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */
pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */
pS2 = 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */
pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */
pS4 = 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */
pS5 = 3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */
qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */
qS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */
qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */
qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */
static double R(double z)
{
double_t p, q;
p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
q = 1.0+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
return p/q;
}
/**
* Returns arc sine of ð¥.
*
* @return value in range [-M_PI/2,M_PI/2]
* @return NAN if ð¥ â {NAN,+INFINITY,-INFINITY}
* @return NAN if ð¥ â [-1,1]
*/
double asin(double x)
{
int ng;
uint32_t ix,lx;
double z,r,s,f,c;
union {
double f;
int64_t s;
uint64_t i;
} u = {x};
ng = u.s < 0;
ix = (u.i & 0x7fffffff00000000) >> 32;
/* |x| >= 1 or nan */
if (ix >= 0x3ff00000) {
lx = u.i;
if (!(ix-0x3ff00000 | lx))
/* asin(1) = +-pi/2 with inexact */
return x*pio2_hi + 0x1p-120f;
return 0/(x-x);
}
/* |x| < 0.5 */
if (ix < 0x3fe00000) {
/* if 0x1p-1022 <= |x| < 0x1p-26, avoid raising underflow */
if (ix < 0x3e500000 && ix >= 0x00100000)
return x;
return x + x*R(x*x);
}
/* 1 > |x| >= 0.5 */
z = (1 - fabs(x))*0.5;
s = sqrt(z);
r = R(z);
if (ix >= 0x3fef3333) { /* if |x| > 0.975 */
x = pio2_hi-(2*(s+s*r)-pio2_lo);
} else {
/* f+c = sqrt(z) */
u.f = s;
u.i &= 0xffffffff00000000;
f = u.f;
c = (z-f*f)/(s+f);
x = 0.5*pio2_hi - (2*s*r - (pio2_lo-2*c) - (0.5*pio2_hi-2*f));
}
return ng ? -x : x;
}
#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
__strong_reference(asin, asinl);
#endif
| 6,467 | 154 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/nearbyintf.c | /*-*- mode:c;indent-tabs-mode:nil;c-basic-offset:2;tab-width:8;coding:utf-8 -*-â
âvi: set net ft=c ts=2 sts=2 sw=2 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ¡
â Copyright 2023 Justine Alexandra Roberts Tunney â
â â
â Permission to use, copy, modify, and/or distribute this software for â
â any purpose with or without fee is hereby granted, provided that the â
â above copyright notice and this permission notice appear in all copies. â
â â
â THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL â
â WARRANTIES WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED â
â WARRANTIES OF MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE â
â AUTHOR BE LIABLE FOR ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL â
â DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR â
â PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER â
â TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR â
â PERFORMANCE OF THIS SOFTWARE. â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
#include "libc/runtime/fenv.h"
/**
* Rounds to nearest integer.
*/
float nearbyintf(float x) {
#ifdef FE_INEXACT
// #pragma STDC FENV_ACCESS ON
int e;
e = fetestexcept(FE_INEXACT);
#endif
x = rintf(x);
#ifdef FE_INEXACT
if (!e) feclearexcept(FE_INEXACT);
#endif
return x;
}
| 2,148 | 37 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/floor.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
#include "libc/runtime/fenv.h"
#include "libc/tinymath/internal.h"
#include "third_party/intel/smmintrin.internal.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
#if FLT_EVAL_METHOD==0 || FLT_EVAL_METHOD==1
#define EPS DBL_EPSILON
#elif FLT_EVAL_METHOD==2
#define EPS LDBL_EPSILON
#endif
static const double_t toint = 1/EPS;
/**
* Returns largest integral value not greater than ð¥.
*/
double floor(double x)
{
#ifdef __aarch64__
asm("frintm\t%d0,%d1" : "=w"(x) : "w"(x));
return x;
#elif defined(__powerpc64__) && defined(_ARCH_PWR5X)
asm("frim\t%0,%1" : "=d"(x) : "d"(x));
return x;
#elif defined(__s390x__) && (defined(__HTM__) || __ARCH__ >= 9)
asm("fidbra\t%0,7,%1,4" : "=f"(x) : "f"(x));
return x;
#elif defined(__x86_64__) && defined(__SSE4_1__)
asm("roundsd\t%2,%1,%0"
: "=x"(x)
: "x"(x), "i"(_MM_FROUND_TO_NEG_INF | _MM_FROUND_NO_EXC));
return x;
#else
union {double f; uint64_t i;} u = {x};
int e = u.i >> 52 & 0x7ff;
double_t y;
if (e >= 0x3ff+52 || x == 0)
return x;
/* y = int(x) - x, where int(x) is an integer neighbor of x */
if (u.i >> 63)
y = x - toint + toint - x;
else
y = x + toint - toint - x;
/* special case because of non-nearest rounding modes */
if (e <= 0x3ff-1) {
FORCE_EVAL(y);
return u.i >> 63 ? -1 : 0;
}
if (y > 0)
return x + y - 1;
return x + y;
#endif /* __aarch64__ */
}
#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
__strong_reference(floor, floorl);
#endif
| 4,196 | 101 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/finitef.c | /*-*- mode:c;indent-tabs-mode:nil;c-basic-offset:2;tab-width:8;coding:utf-8 -*-â
âvi: set net ft=c ts=2 sts=2 sw=2 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ¡
â Copyright 2021 Justine Alexandra Roberts Tunney â
â â
â Permission to use, copy, modify, and/or distribute this software for â
â any purpose with or without fee is hereby granted, provided that the â
â above copyright notice and this permission notice appear in all copies. â
â â
â THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL â
â WARRANTIES WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED â
â WARRANTIES OF MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE â
â AUTHOR BE LIABLE FOR ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL â
â DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR â
â PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER â
â TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR â
â PERFORMANCE OF THIS SOFTWARE. â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
/**
* Returns nonzero if ð¥ isn't INFINITY or NAN.
*/
int finitef(float x) {
return isfinite(x);
}
| 1,965 | 27 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/cacosf.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/complex.h"
#include "libc/math.h"
#include "libc/tinymath/complex.internal.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 */
// FIXME
float complex cacosf(float complex z)
{
z = casinf(z);
return CMPLXF((float)M_PI_2 - crealf(z), -cimagf(z));
}
| 2,981 | 45 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/ceil.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
#include "libc/runtime/fenv.h"
#include "libc/tinymath/internal.h"
#include "third_party/intel/smmintrin.internal.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
#if FLT_EVAL_METHOD==0 || FLT_EVAL_METHOD==1
#define EPS DBL_EPSILON
#elif FLT_EVAL_METHOD==2
#define EPS LDBL_EPSILON
#endif
static const double_t toint = 1/EPS;
/**
* Returns smallest integral value not less than ð¥.
*/
double ceil(double x)
{
#ifdef __aarch64__
asm("frintp\t%d0,%d1" : "=w"(x) : "w"(x));
return x;
#elif defined(__powerpc64__) && defined(_ARCH_PWR5X)
asm("frip\t%0,%1" : "=d"(x) : "d"(x));
return x;
#elif defined(__s390x__) && (defined(__HTM__) || __ARCH__ >= 9)
asm("fidbra\t%0,6,%1,4" : "=f"(x) : "f"(x));
return x;
#elif defined(__x86_64__) && defined(__SSE4_1__)
asm("roundsd\t%2,%1,%0"
: "=x"(x)
: "x"(x), "i"(_MM_FROUND_TO_POS_INF | _MM_FROUND_NO_EXC));
return x;
#else
union {double f; uint64_t i;} u = {x};
int e = u.i >> 52 & 0x7ff;
double_t y;
if (e >= 0x3ff+52 || x == 0)
return x;
/* y = int(x) - x, where int(x) is an integer neighbor of x */
if (u.i >> 63)
y = x - toint + toint - x;
else
y = x + toint - toint - x;
/* special case because of non-nearest rounding modes */
if (e <= 0x3ff-1) {
FORCE_EVAL(y);
return u.i >> 63 ? -0.0 : 1;
}
if (y < 0)
return x + y + 1;
return x + y;
#endif /* __aarch64__ */
}
| 4,104 | 97 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/nexttoward.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2020 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
#include "libc/tinymath/feval.internal.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
double nexttoward(double x, long double y)
{
union {double f; uint64_t i;} ux = {x};
int e;
if (isunordered(x, y))
return x + y;
if (x == y)
return y;
if (x == 0) {
ux.i = 1;
if (signbit(y))
ux.i |= 1ULL<<63;
} else if (x < y) {
if (signbit(x))
ux.i--;
else
ux.i++;
} else {
if (signbit(x))
ux.i++;
else
ux.i--;
}
e = ux.i>>52 & 0x7ff;
/* raise overflow if ux.f is infinite and x is finite */
if (e == 0x7ff)
feval(x+x);
/* raise underflow if ux.f is subnormal or zero */
if (e == 0)
feval(x*x + ux.f*ux.f);
return ux.f;
}
| 3,400 | 70 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/__cexpf.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/complex.h"
#include "libc/math.h"
#include "libc/tinymath/complex.internal.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
/* origin: FreeBSD /usr/src/lib/msun/src/k_expf.c */
/*-
* Copyright (c) 2011 David Schultz <[email protected]>
* 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.
*/
static const uint32_t k = 235; /* constant for reduction */
static const float kln2 = 162.88958740F; /* k * ln2 */
/*
* See __cexp.c for details.
*
* Input: ln(FLT_MAX) <= x < ln(2 * FLT_MAX / FLT_MIN_DENORM) ~= 192.7
* Output: 2**127 <= y < 2**128
*/
static float __frexp_expf(float x, int *expt)
{
float exp_x;
uint32_t hx;
exp_x = expf(x - kln2);
GET_FLOAT_WORD(hx, exp_x);
*expt = (hx >> 23) - (0x7f + 127) + k;
SET_FLOAT_WORD(exp_x, (hx & 0x7fffff) | ((0x7f + 127) << 23));
return exp_x;
}
float complex __ldexp_cexpf(float complex z, int expt)
{
float x, y, exp_x, scale1, scale2;
int ex_expt, half_expt;
x = crealf(z);
y = cimagf(z);
exp_x = __frexp_expf(x, &ex_expt);
expt += ex_expt;
half_expt = expt / 2;
SET_FLOAT_WORD(scale1, (0x7f + half_expt) << 23);
half_expt = expt - half_expt;
SET_FLOAT_WORD(scale2, (0x7f + half_expt) << 23);
return CMPLXF(cosf(y) * exp_x * scale1 * scale2,
sinf(y) * exp_x * scale1 * scale2);
}
| 5,248 | 105 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/nanf.c | /*-*- mode:c;indent-tabs-mode:nil;c-basic-offset:2;tab-width:8;coding:utf-8 -*-â
âvi: set net ft=c ts=2 sts=2 sw=2 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ¡
â Copyright 2022 Justine Alexandra Roberts Tunney â
â â
â Permission to use, copy, modify, and/or distribute this software for â
â any purpose with or without fee is hereby granted, provided that the â
â above copyright notice and this permission notice appear in all copies. â
â â
â THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL â
â WARRANTIES WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED â
â WARRANTIES OF MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE â
â AUTHOR BE LIABLE FOR ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL â
â DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR â
â PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER â
â TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR â
â PERFORMANCE OF THIS SOFTWARE. â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
float nanf(const char *s) {
return NAN;
}
| 1,904 | 24 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/frexpl.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Copyright (c) 2004-2005 David Schultz <[email protected]> â
â All rights reserved. â
â â
â Redistribution and use in source and binary forms, with or without â
â modification, are permitted provided that the following conditions â
â are met: â
â 1. Redistributions of source code must retain the above copyright â
â notice, this list of conditions and the following disclaimer. â
â 2. Redistributions in binary form must reproduce the above copyright â
â notice, this list of conditions and the following disclaimer in the â
â documentation and/or other materials provided with the distribution. â
â â
â THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND â
â ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE â
â IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE â
â ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE â
â FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL â
â DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS â
â OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) â
â HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT â
â LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY â
â OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF â
â SUCH DAMAGE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
#include "libc/tinymath/freebsd.internal.h"
#if !(LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024)
asm(".ident\t\"\\n\\n\
FreeBSD libm (BSD-2 License)\\n\
Copyright (c) 2005-2011, Bruce D. Evans, Steven G. Kargl, David Schultz.\"");
asm(".include \"libc/disclaimer.inc\"");
// clang-format off
/**
* Splits number normalized fraction and exponent.
*/
long double
frexpl(long double x, int *ex)
{
union IEEEl2bits u;
u.e = x;
switch (u.bits.exp) {
case 0: /* 0 or subnormal */
if ((u.bits.manl | u.bits.manh) == 0) {
*ex = 0;
} else {
u.e *= 0x1.0p514;
*ex = u.bits.exp - 0x4200;
u.bits.exp = 0x3ffe;
}
break;
case 0x7fff: /* infinity or NaN; value of *ex is unspecified */
break;
default: /* normal */
*ex = u.bits.exp - 0x3ffe;
u.bits.exp = 0x3ffe;
break;
}
return (u.e);
}
#endif /* long double is long */
| 3,641 | 70 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/atan_data.internal.h | #ifndef COSMOPOLITAN_LIBC_TINYMATH_ATAN_DATA_H_
#define COSMOPOLITAN_LIBC_TINYMATH_ATAN_DATA_H_
#if !(__ASSEMBLER__ + __LINKER__ + 0)
COSMOPOLITAN_C_START_
#define ATAN_POLY_NCOEFFS 20
extern const struct atan_poly_data {
double poly[ATAN_POLY_NCOEFFS];
} __atan_poly_data _Hide;
COSMOPOLITAN_C_END_
#endif /* !(__ASSEMBLER__ + __LINKER__ + 0) */
#endif /* COSMOPOLITAN_LIBC_TINYMATH_ATAN_DATA_H_ */
| 404 | 14 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/powf.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/intrin/likely.h"
#include "libc/math.h"
#include "libc/tinymath/exp2f_data.internal.h"
#include "libc/tinymath/exp_data.internal.h"
#include "libc/tinymath/internal.h"
#include "libc/tinymath/powf_data.internal.h"
asm(".ident\t\"\\n\\n\
Double-precision math functions (MIT License)\\n\
Copyright 2018 ARM Limited\"");
asm(".include \"libc/disclaimer.inc\"");
// clang-format off
/*
* Copyright (c) 2017-2018, Arm Limited.
* SPDX-License-Identifier: MIT
*/
/*
POWF_LOG2_POLY_ORDER = 5
EXP2F_TABLE_BITS = 5
ULP error: 0.82 (~ 0.5 + relerr*2^24)
relerr: 1.27 * 2^-26 (Relative error ~= 128*Ln2*relerr_log2 + relerr_exp2)
relerr_log2: 1.83 * 2^-33 (Relative error of logx.)
relerr_exp2: 1.69 * 2^-34 (Relative error of exp2(ylogx).)
*/
#define N (1 << POWF_LOG2_TABLE_BITS)
#define T __powf_log2_data.tab
#define A __powf_log2_data.poly
#define OFF 0x3f330000
/* Subnormal input is normalized so ix has negative biased exponent.
Output is multiplied by N (POWF_SCALE) if TOINT_INTRINICS is set. */
static inline double_t log2_inline(uint32_t ix)
{
double_t z, r, r2, r4, p, q, y, y0, invc, logc;
uint32_t iz, top, tmp;
int k, i;
/* x = 2^k z; where z is in range [OFF,2*OFF] and exact.
The range is split into N subintervals.
The ith subinterval contains z and c is near its center. */
tmp = ix - OFF;
i = (tmp >> (23 - POWF_LOG2_TABLE_BITS)) % N;
top = tmp & 0xff800000;
iz = ix - top;
k = (int32_t)top >> (23 - POWF_SCALE_BITS); /* arithmetic shift */
invc = T[i].invc;
logc = T[i].logc;
z = (double_t)asfloat(iz);
/* log2(x) = log1p(z/c-1)/ln2 + log2(c) + k */
r = z * invc - 1;
y0 = logc + (double_t)k;
/* Pipelined polynomial evaluation to approximate log1p(r)/ln2. */
r2 = r * r;
y = A[0] * r + A[1];
p = A[2] * r + A[3];
r4 = r2 * r2;
q = A[4] * r + y0;
q = p * r2 + q;
y = y * r4 + q;
return y;
}
#undef N
#undef T
#define N (1 << EXP2F_TABLE_BITS)
#define T __exp2f_data.tab
#define SIGN_BIAS (1 << (EXP2F_TABLE_BITS + 11))
/* The output of log2 and thus the input of exp2 is either scaled by N
(in case of fast toint intrinsics) or not. The unscaled xd must be
in [-1021,1023], sign_bias sets the sign of the result. */
static inline float exp2_inline(double_t xd, uint32_t sign_bias)
{
uint64_t ki, ski, t;
double_t kd, z, r, r2, y, s;
#if TOINT_INTRINSICS
#define C __exp2f_data.poly_scaled
/* N*x = k + r with r in [-1/2, 1/2] */
kd = roundtoint(xd); /* k */
ki = converttoint(xd);
#else
#define C __exp2f_data.poly
#define SHIFT __exp2f_data.shift_scaled
/* x = k/N + r with r in [-1/(2N), 1/(2N)] */
kd = eval_as_double(xd + SHIFT);
ki = asuint64(kd);
kd -= SHIFT; /* k/N */
#endif
r = xd - kd;
/* exp2(x) = 2^(k/N) * 2^r ~= s * (C0*r^3 + C1*r^2 + C2*r + 1) */
t = T[ki % N];
ski = ki + sign_bias;
t += ski << (52 - EXP2F_TABLE_BITS);
s = asdouble(t);
z = C[0] * r + C[1];
r2 = r * r;
y = C[2] * r + 1;
y = z * r2 + y;
y = y * s;
return eval_as_float(y);
}
/* Returns 0 if not int, 1 if odd int, 2 if even int. The argument is
the bit representation of a non-zero finite floating-point value. */
static inline int checkint(uint32_t iy)
{
int e = iy >> 23 & 0xff;
if (e < 0x7f)
return 0;
if (e > 0x7f + 23)
return 2;
if (iy & ((1 << (0x7f + 23 - e)) - 1))
return 0;
if (iy & (1 << (0x7f + 23 - e)))
return 1;
return 2;
}
static inline int zeroinfnan(uint32_t ix)
{
return 2 * ix - 1 >= 2u * 0x7f800000 - 1;
}
/**
* Returns ð¥^ð¦.
* @note should take ~16ns
*/
float powf(float x, float y)
{
uint32_t sign_bias = 0;
uint32_t ix, iy;
ix = asuint(x);
iy = asuint(y);
if (UNLIKELY(ix - 0x00800000 >= 0x7f800000 - 0x00800000 ||
zeroinfnan(iy))) {
/* Either (x < 0x1p-126 or inf or nan) or (y is 0 or inf or nan). */
if (UNLIKELY(zeroinfnan(iy))) {
if (2 * iy == 0)
return issignalingf_inline(x) ? x + y : 1.0f;
if (ix == 0x3f800000)
return issignalingf_inline(y) ? x + y : 1.0f;
if (2 * ix > 2u * 0x7f800000 ||
2 * iy > 2u * 0x7f800000)
return x + y;
if (2 * ix == 2 * 0x3f800000)
return 1.0f;
if ((2 * ix < 2 * 0x3f800000) == !(iy & 0x80000000))
return 0.0f; /* |x|<1 && y==inf or |x|>1 && y==-inf. */
return y * y;
}
if (UNLIKELY(zeroinfnan(ix))) {
float_t x2 = x * x;
if (ix & 0x80000000 && checkint(iy) == 1)
x2 = -x2;
/* Without the barrier some versions of clang hoist the 1/x2 and
thus division by zero exception can be signaled spuriously. */
return iy & 0x80000000 ? fp_barrierf(1 / x2) : x2;
}
/* x and y are non-zero finite. */
if (ix & 0x80000000) {
/* Finite x < 0. */
int yint = checkint(iy);
if (yint == 0)
return __math_invalidf(x);
if (yint == 1)
sign_bias = SIGN_BIAS;
ix &= 0x7fffffff;
}
if (ix < 0x00800000) {
/* Normalize subnormal x so exponent becomes negative. */
ix = asuint(x * 0x1p23f);
ix &= 0x7fffffff;
ix -= 23 << 23;
}
}
double_t logx = log2_inline(ix);
double_t ylogx = y * logx; /* cannot overflow, y is single prec. */
if (UNLIKELY((asuint64(ylogx) >> 47 & 0xffff) >=
asuint64(126.0 * POWF_SCALE) >> 47)) {
/* |y*log(x)| >= 126. */
if (ylogx > 0x1.fffffffd1d571p+6 * POWF_SCALE)
return __math_oflowf(sign_bias);
if (ylogx <= -150.0 * POWF_SCALE)
return __math_uflowf(sign_bias);
}
return exp2_inline(ylogx, sign_bias);
}
__weak_reference(powf, __powf_finite);
| 8,026 | 226 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/ctanhf.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/complex.h"
#include "libc/math.h"
#include "libc/tinymath/complex.internal.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 */
/* origin: FreeBSD /usr/src/lib/msun/src/s_ctanhf.c */
/*-
* Copyright (c) 2011 David Schultz
* 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 unmodified, 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 ``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.
*/
/*
* Hyperbolic tangent of a complex argument z. See s_ctanh.c for details.
*/
float complex ctanhf(float complex z)
{
float x, y;
float t, beta, s, rho, denom;
uint32_t hx, ix;
x = crealf(z);
y = cimagf(z);
GET_FLOAT_WORD(hx, x);
ix = hx & 0x7fffffff;
if (ix >= 0x7f800000) {
if (ix & 0x7fffff)
return CMPLXF(x, (y == 0 ? y : x * y));
SET_FLOAT_WORD(x, hx - 0x40000000);
return CMPLXF(x, copysignf(0, isinf(y) ? y : sinf(y) * cosf(y)));
}
if (!isfinite(y))
return CMPLXF(ix ? y - y : x, y - y);
if (ix >= 0x41300000) { /* x >= 11 */
float exp_mx = expf(-fabsf(x));
return CMPLXF(copysignf(1, x), 4 * sinf(y) * cosf(y) * exp_mx * exp_mx);
}
t = tanf(y);
beta = 1.0 + t * t;
s = sinhf(x);
rho = sqrtf(1 + s * s);
denom = 1 + beta * s * s;
return CMPLXF((beta * rho * s) / denom, t / denom);
}
| 5,086 | 104 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/lroundf.c | /*-*- mode:c;indent-tabs-mode:nil;c-basic-offset:2;tab-width:8;coding:utf-8 -*-â
âvi: set net ft=c ts=2 sts=2 sw=2 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ¡
â Copyright 2023 Justine Alexandra Roberts Tunney â
â â
â Permission to use, copy, modify, and/or distribute this software for â
â any purpose with or without fee is hereby granted, provided that the â
â above copyright notice and this permission notice appear in all copies. â
â â
â THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL â
â WARRANTIES WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED â
â WARRANTIES OF MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE â
â AUTHOR BE LIABLE FOR ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL â
â DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR â
â PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER â
â TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR â
â PERFORMANCE OF THIS SOFTWARE. â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
/**
* Rounds ð¥ to nearest integer, away from zero.
*/
long lroundf(float x) {
long res;
#ifdef __aarch64__
asm("fcvtas\t%x0,%s1" : "=r"(res) : "w"(x));
#elif defined(__powerpc64__) && defined(__VSX__)
asm("xsrdpi\t%1,%1\n\t"
"fctid\t%0,%1"
: "=d"(res), "+f"(x));
#else
res = roundf(x);
#endif
return res;
}
| 2,194 | 37 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/tanhl.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â FreeBSD lib/msun/src/s_tanhl.c â
â Converted to long double by Bruce D. Evans â
â â
â Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. â
â â
â Developed at SunPro, a Sun Microsystems, Inc. business. â
â Permission to use, copy, modify, and distribute this â
â software is freely granted, provided that this notice â
â is preserved. â
â â
â Copyright (c) 1992-2023 The FreeBSD Project. â
â â
â Redistribution and use in source and binary forms, with or without â
â modification, are permitted provided that the following conditions â
â are met: â
â 1. Redistributions of source code must retain the above copyright â
â notice, this list of conditions and the following disclaimer. â
â 2. Redistributions in binary form must reproduce the above copyright â
â notice, this list of conditions and the following disclaimer in the â
â documentation and/or other materials provided with the distribution. â
â â
â THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND â
â ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE â
â IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE â
â ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE â
â FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL â
â DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS â
â OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) â
â HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT â
â LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY â
â OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF â
â SUCH DAMAGE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/intrin/likely.h"
#include "libc/math.h"
#include "libc/tinymath/freebsd.internal.h"
asm(".ident\t\"\\n\\n\
FreeBSD libm (BSD-2 License)\\n\
Copyright (c) 2005-2011, Bruce D. Evans, Steven G. Kargl, David Schultz.\"");
asm(".ident\t\"\\n\\n\
fdlibm (fdlibm license)\\n\
Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.\"");
asm(".include \"libc/disclaimer.inc\"");
// clang-format off
#if LDBL_MAX_EXP != 0x4000
/* We also require the usual expsign encoding. */
#error "Unsupported long double format"
#endif
#define BIAS (LDBL_MAX_EXP - 1)
static const volatile double tiny = 1.0e-300;
static const double one = 1.0;
#if LDBL_MANT_DIG == 64
/*
* Domain [-0.25, 0.25], range ~[-1.6304e-22, 1.6304e-22]:
* |tanh(x)/x - t(x)| < 2**-72.3
*/
static const union IEEEl2bits
T3u = LD80C(0xaaaaaaaaaaaaaa9f, -2, -3.33333333333333333017e-1L);
#define T3 T3u.e
static const double
T5 = 1.3333333333333314e-1, /* 0x1111111111110a.0p-55 */
T7 = -5.3968253968210485e-2, /* -0x1ba1ba1ba1a1a1.0p-57 */
T9 = 2.1869488531393817e-2, /* 0x1664f488172022.0p-58 */
T11 = -8.8632352345964591e-3, /* -0x1226e34bc138d5.0p-59 */
T13 = 3.5921169709993771e-3, /* 0x1d6d371d3e400f.0p-61 */
T15 = -1.4555786415756001e-3, /* -0x17d923aa63814d.0p-62 */
T17 = 5.8645267876296793e-4, /* 0x13378589b85aa7.0p-63 */
T19 = -2.1121033571392224e-4; /* -0x1baf0af80c4090.0p-65 */
#elif LDBL_MANT_DIG == 113
/*
* Domain [-0.25, 0.25], range ~[-2.4211e-37, 2.4211e-37]:
* |tanh(x)/x - t(x)| < 2**121.6
*/
static const long double
T3 = -3.33333333333333333333333333333332980e-1L, /* -0x1555555555555555555555555554e.0p-114L */
T5 = 1.33333333333333333333333333332707260e-1L, /* 0x1111111111111111111111110ab7b.0p-115L */
T7 = -5.39682539682539682539682535723482314e-2L, /* -0x1ba1ba1ba1ba1ba1ba1ba17b5fc98.0p-117L */
T9 = 2.18694885361552028218693591149061717e-2L, /* 0x1664f4882c10f9f32d6b1a12a25e5.0p-118L */
T11 = -8.86323552990219656883762347736381851e-3L, /* -0x1226e355e6c23c8f5a5a0f386cb4d.0p-119L */
T13 = 3.59212803657248101358314398220822722e-3L, /* 0x1d6d3d0e157ddfb403ad3637442c6.0p-121L */
T15 = -1.45583438705131796512568010348874662e-3L; /* -0x17da36452b75e150c44cc34253b34.0p-122L */
static const double
T17 = 5.9002744094556621e-4, /* 0x1355824803668e.0p-63 */
T19 = -2.3912911424260516e-4, /* -0x1f57d7734c8dde.0p-65 */
T21 = 9.6915379535512898e-5, /* 0x1967e18ad6a6ca.0p-66 */
T23 = -3.9278322983156353e-5, /* -0x1497d8e6b75729.0p-67 */
T25 = 1.5918887220143869e-5, /* 0x10b1319998cafa.0p-68 */
T27 = -6.4514295231630956e-6, /* -0x1b0f2b71b218eb.0p-70 */
T29 = 2.6120754043964365e-6, /* 0x15e963a3cf3a39.0p-71 */
T31 = -1.0407567231003314e-6, /* -0x1176041e656869.0p-72 */
T33 = 3.4744117554063574e-7; /* 0x1750fe732cab9c.0p-74 */
#endif /* LDBL_MANT_DIG == 64 */
static inline long double
divl(long double a, long double b, long double c, long double d,
long double e, long double f)
{
long double inv, r;
float fr, fw;
_2sumF(a, c);
b = b + c;
_2sumF(d, f);
e = e + f;
inv = 1 / (d + e);
r = (a + b) * inv;
fr = r;
r = fr;
fw = d + e;
e = d - fw + e;
d = fw;
r = r + (a - d * r + b - e * r) * inv;
return r;
}
/**
* Returns hyperbolic tangent of ð¥.
*/
long double
tanhl(long double x)
{
long double hi,lo,s,x2,x4,z;
#if LDBL_MANT_DIG == 113
double dx2;
#endif
int16_t jx,ix;
GET_LDBL_EXPSIGN(jx,x);
ix = jx&0x7fff;
/* x is INF or NaN */
if(ix>=0x7fff) {
if (jx>=0) return one/x+one; /* tanh(+-inf)=+-1 */
else return one/x-one; /* tanh(NaN) = NaN */
}
ENTERI();
/* |x| < 40 */
if (ix < 0x4004 || fabsl(x) < 40) { /* |x|<40 */
if (UNLIKELY(ix<BIAS-(LDBL_MANT_DIG+1)/2)) { /* |x|<TINY */
/* tanh(+-0) = +0; tanh(tiny) = tiny(-+) with inexact: */
return (x == 0 ? x : (0x1p200 * x - x) * 0x1p-200);
}
if (ix<0x3ffd) { /* |x|<0.25 */
x2 = x*x;
#if LDBL_MANT_DIG == 64
x4 = x2*x2;
RETURNI(((T19*x2 + T17)*x4 + (T15*x2 + T13))*(x2*x*x2*x4*x4) +
((T11*x2 + T9)*x4 + (T7*x2 + T5))*(x2*x*x2) +
T3*(x2*x) + x);
#elif LDBL_MANT_DIG == 113
dx2 = x2;
long double q = ((((((((((((((T33*dx2 + T31)*dx2 + T29)*dx2 + T27)*dx2 +
T25)*x2 + T23)*x2 + T21)*x2 + T19)*x2 + T17)*x2 +
T15)*x2 + T13)*x2 + T11)*x2 + T9)*x2 + T7)*x2 + T5)*
(x2*x*x2);
RETURNI(q + T3*(x2*x) + x);
#endif
}
k_hexpl(2*fabsl(x), &hi, &lo);
if (ix<0x4001 && fabsl(x) < 1.5) /* |x|<1.5 */
z = divl(hi, lo, -0.5, hi, lo, 0.5);
else
z = one - one/(lo+0.5+hi);
/* |x| >= 40, return +-1 */
} else {
z = one - tiny; /* raise inexact flag */
}
s = 1;
if (jx<0) s = -1;
RETURNI(s*z);
}
| 8,208 | 188 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/cprojl.c | /*-*- mode:c;indent-tabs-mode:nil;c-basic-offset:2;tab-width:8;coding:utf-8 -*-â
âvi: set net ft=c ts=2 sts=2 sw=2 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ¡
â Copyright 2023 Justine Alexandra Roberts Tunney â
â â
â Permission to use, copy, modify, and/or distribute this software for â
â any purpose with or without fee is hereby granted, provided that the â
â above copyright notice and this permission notice appear in all copies. â
â â
â THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL â
â WARRANTIES WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED â
â WARRANTIES OF MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE â
â AUTHOR BE LIABLE FOR ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL â
â DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR â
â PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER â
â TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR â
â PERFORMANCE OF THIS SOFTWARE. â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/complex.h"
#include "libc/math.h"
long double complex cprojl(long double complex z) {
#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
return cproj(z);
#else
if (isinf(creall(z)) || isinf(cimagl(z))) {
return CMPLXL(INFINITY, copysignl(0.0, cimagl(z)));
}
return z;
#endif
}
| 2,138 | 32 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/atan2.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â FreeBSD lib/msun/src/e_atan2.c â
â â
â Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. â
â â
â Developed at SunPro, a Sun Microsystems, Inc. business. â
â Permission to use, copy, modify, and distribute this â
â software is freely granted, provided that this notice â
â is preserved. â
â â
â Copyright (c) 1992-2023 The FreeBSD Project. â
â â
â Redistribution and use in source and binary forms, with or without â
â modification, are permitted provided that the following conditions â
â are met: â
â 1. Redistributions of source code must retain the above copyright â
â notice, this list of conditions and the following disclaimer. â
â 2. Redistributions in binary form must reproduce the above copyright â
â notice, this list of conditions and the following disclaimer in the â
â documentation and/or other materials provided with the distribution. â
â â
â THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND â
â ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE â
â IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE â
â ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE â
â FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL â
â DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS â
â OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) â
â HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT â
â LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY â
â OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF â
â SUCH DAMAGE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
#include "libc/tinymath/freebsd.internal.h"
asm(".ident\t\"\\n\\n\
FreeBSD libm (BSD-2 License)\\n\
Copyright (c) 2005-2011, Bruce D. Evans, Steven G. Kargl, David Schultz.\"");
asm(".ident\t\"\\n\\n\
fdlibm (fdlibm license)\\n\
Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.\"");
asm(".include \"libc/disclaimer.inc\"");
// clang-format off
/* atan2(y,x)
* Method :
* 1. Reduce y to positive by atan2(y,x)=-atan2(-y,x).
* 2. Reduce x to positive by (if x and y are unexceptional):
* ARG (x+iy) = arctan(y/x) ... if x > 0,
* ARG (x+iy) = pi - arctan[y/(-x)] ... if x < 0,
*
* Special cases:
*
* ATAN2((anything), NaN ) is NaN;
* ATAN2(NAN , (anything) ) is NaN;
* ATAN2(+-0, +(anything but NaN)) is +-0 ;
* ATAN2(+-0, -(anything but NaN)) is +-pi ;
* ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2;
* ATAN2(+-(anything but INF and NaN), +INF) is +-0 ;
* ATAN2(+-(anything but INF and NaN), -INF) is +-pi;
* ATAN2(+-INF,+INF ) is +-pi/4 ;
* ATAN2(+-INF,-INF ) is +-3pi/4;
* ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2;
*
* Constants:
* The hexadecimal values are the intended ones for the following
* constants. The decimal values may be used, provided that the
* compiler will convert from decimal to binary accurately enough
* to produce the hexadecimal values shown.
*/
static volatile double
tiny = 1.0e-300;
static const double
zero = 0.0,
pi_o_4 = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */
pi_o_2 = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */
pi = 3.1415926535897931160E+00; /* 0x400921FB, 0x54442D18 */
static volatile double
pi_lo = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */
/**
* Returns arc tangent of ð¦/ð¥.
*/
double
atan2(double y, double x)
{
double z;
int32_t k,m,hx,hy,ix,iy;
uint32_t lx,ly;
EXTRACT_WORDS(hx,lx,x);
ix = hx&0x7fffffff;
EXTRACT_WORDS(hy,ly,y);
iy = hy&0x7fffffff;
if(((ix|((lx|-lx)>>31))>0x7ff00000)||
((iy|((ly|-ly)>>31))>0x7ff00000)) /* x or y is NaN */
return nan_mix(x, y);
if(hx==0x3ff00000&&lx==0) return atan(y); /* x=1.0 */
m = ((hy>>31)&1)|((hx>>30)&2); /* 2*sign(x)+sign(y) */
/* when y = 0 */
if((iy|ly)==0) {
switch(m) {
case 0:
case 1: return y; /* atan(+-0,+anything)=+-0 */
case 2: return pi+tiny;/* atan(+0,-anything) = pi */
case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */
}
}
/* when x = 0 */
if((ix|lx)==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
/* when x is INF */
if(ix==0x7ff00000) {
if(iy==0x7ff00000) {
switch(m) {
case 0: return pi_o_4+tiny;/* atan(+INF,+INF) */
case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */
case 2: return 3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/
case 3: return -3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/
}
} else {
switch(m) {
case 0: return zero ; /* atan(+...,+INF) */
case 1: return -zero ; /* atan(-...,+INF) */
case 2: return pi+tiny ; /* atan(+...,-INF) */
case 3: return -pi-tiny ; /* atan(-...,-INF) */
}
}
}
/* when y is INF */
if(iy==0x7ff00000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
/* compute y/x */
k = (iy-ix)>>20;
if(k > 60) { /* |y/x| > 2**60 */
z=pi_o_2+0.5*pi_lo;
m&=1;
}
else if(hx<0&&k<-60) z=0.0; /* 0 > |y|/x > -2**-60 */
else z=atan(fabs(y/x)); /* safe to do y/x */
switch (m) {
case 0: return z ; /* atan(+,+) */
case 1: return -z ; /* atan(-,+) */
case 2: return pi-(z-pi_lo);/* atan(+,-) */
default: /* case 3 */
return (z-pi_lo)-pi;/* atan(-,-) */
}
}
#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
__strong_reference(atan2, atan2l);
#endif
| 7,155 | 160 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/sinhf.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
#include "libc/tinymath/expo.internal.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
/**
* Returns hyperbolic sine of ð¥.
*
* sinh(x) = (exp(x) - 1/exp(x))/2
* = (exp(x)-1 + (exp(x)-1)/exp(x))/2
* = x + x^3/6 + o(x^5)
*/
float sinhf(float x)
{
union {float f; uint32_t i;} u = {.f = x};
uint32_t w;
float t, h, absx;
h = 0.5;
if (u.i >> 31)
h = -h;
/* |x| */
u.i &= 0x7fffffff;
absx = u.f;
w = u.i;
/* |x| < log(FLT_MAX) */
if (w < 0x42b17217) {
t = expm1f(absx);
if (w < 0x3f800000) {
if (w < 0x3f800000 - (12<<23))
return x;
return h*(2*t - t*t/(t+1));
}
return h*(t + t/(t+1));
}
/* |x| > logf(FLT_MAX) or nan */
t = __expo2f(absx, 2*h);
return t;
}
| 3,468 | 73 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/atanf_common.internal.h | #ifndef COSMOPOLITAN_LIBC_TINYMATH_ATANF_COMMON_H_
#define COSMOPOLITAN_LIBC_TINYMATH_ATANF_COMMON_H_
#include "libc/tinymath/atanf_data.internal.h"
#include "libc/tinymath/estrin_wrap.internal.h"
#include "libc/tinymath/hornerf.internal.h"
#if !(__ASSEMBLER__ + __LINKER__ + 0)
COSMOPOLITAN_C_START_
// clang-format off
#if WANT_VMATH
#define FLT_T float32x4_t
#define P(i) v_f32 (__atanf_poly_data.poly[i])
#else
#define FLT_T float
#define P(i) __atanf_poly_data.poly[i]
#endif
/* Polynomial used in fast atanf(x) and atan2f(y,x) implementations
The order 7 polynomial P approximates (atan(sqrt(x))-sqrt(x))/x^(3/2). */
static inline FLT_T
eval_poly (FLT_T z, FLT_T az, FLT_T shift)
{
/* Use 2-level Estrin scheme for P(z^2) with deg(P)=7. However,
a standard implementation using z8 creates spurious underflow
in the very last fma (when z^8 is small enough).
Therefore, we split the last fma into a mul and and an fma.
Horner and single-level Estrin have higher errors that exceed
threshold. */
FLT_T z2 = z * z;
FLT_T z4 = z2 * z2;
/* Then assemble polynomial. */
FLT_T y = FMA (z4, z4 * ESTRIN_3_ (z2, z4, P, 4), ESTRIN_3 (z2, z4, P));
/* Finalize:
y = shift + z * P(z^2). */
return FMA (y, z2 * az, az) + shift;
}
COSMOPOLITAN_C_END_
#endif /* !(__ASSEMBLER__ + __LINKER__ + 0) */
#endif /* COSMOPOLITAN_LIBC_TINYMATH_ATANF_COMMON_H_ */
| 1,404 | 47 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/csinl.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/complex.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
#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
long double complex csinl(long double complex z)
{
return csin(z);
}
#else
long double complex csinl(long double complex z)
{
z = csinhl(CMPLXL(-cimagl(z), creall(z)));
return CMPLXL(cimagl(z), -creall(z));
}
#endif
| 3,055 | 48 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/hypotl.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
#include "libc/tinymath/ldshape.internal.h"
#if !(LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024)
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
#if LDBL_MANT_DIG == 64
#define SPLIT (0x1p32L+1)
#elif LDBL_MANT_DIG == 113
#define SPLIT (0x1p57L+1)
#endif
static void sq(long double *hi, long double *lo, long double x)
{
long double xh, xl, xc;
xc = x*SPLIT;
xh = x - xc + xc;
xl = x - xh;
*hi = x*x;
*lo = xh*xh - *hi + 2*xh*xl + xl*xl;
}
/**
* Returns euclidean distance.
*/
long double hypotl(long double x, long double y)
{
union ldshape ux = {x}, uy = {y};
int ex, ey;
long double hx, lx, hy, ly, z;
ux.i.se &= 0x7fff;
uy.i.se &= 0x7fff;
if (ux.i.se < uy.i.se) {
ex = uy.i.se;
ey = ux.i.se;
x = uy.f;
y = ux.f;
} else {
ex = ux.i.se;
ey = uy.i.se;
x = ux.f;
y = uy.f;
}
if (ex == 0x7fff && isinf(y))
return y;
if (ex == 0x7fff || y == 0)
return x;
if (ex - ey > LDBL_MANT_DIG)
return x + y;
z = 1;
if (ex > 0x3fff+8000) {
z = 0x1p10000L;
x *= 0x1p-10000L;
y *= 0x1p-10000L;
} else if (ey < 0x3fff-8000) {
z = 0x1p-10000L;
x *= 0x1p10000L;
y *= 0x1p10000L;
}
sq(&hx, &lx, x);
sq(&hy, &ly, y);
return z*sqrtl(ly+lx+hy+hx);
}
#endif /* long double is long */
| 3,962 | 100 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/magicu.c | /*-*- mode:c;indent-tabs-mode:nil;c-basic-offset:2;tab-width:8;coding:utf-8 -*-â
âvi: set net ft=c ts=2 sts=2 sw=2 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ¡
â Copyright 2023 Justine Alexandra Roberts Tunney â
â â
â Permission to use, copy, modify, and/or distribute this software for â
â any purpose with or without fee is hereby granted, provided that the â
â above copyright notice and this permission notice appear in all copies. â
â â
â THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL â
â WARRANTIES WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED â
â WARRANTIES OF MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE â
â AUTHOR BE LIABLE FOR ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL â
â DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR â
â PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER â
â TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR â
â PERFORMANCE OF THIS SOFTWARE. â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/tinymath/magicu.h"
#include "libc/assert.h"
/**
* Precomputes magic numbers for unsigned division by constant.
*
* The returned divisor may be passed to __magic_div() to perform
* unsigned integer division way faster than normal division e.g.
*
* assert(77 / 7 == __magicu_div(77, __magicu_get(7)));
*
* @param d is intended divisor, which must not be zero
* @return magic divisor (never zero)
*/
struct magicu __magicu_get(uint32_t d) {
// From Hacker's Delight by Henry S. Warren Jr., 9780321842688
// Figure 10â3. Simplified algorithm for magic number unsigned
int a, p;
struct magicu magu;
uint32_t p32, q, r, delta;
_npassert(d); // Can't divide by zero.
p32 = 0; // Avoid compiler warning.
a = 0; // Initialize "add" indicator.
p = 31; // Initialize p.
q = 0x7FFFFFFF / d; // Initialize q = (2**p - 1)/d.
r = 0x7FFFFFFF - q * d; // Init. r = rem(2**p - 1, d).
do {
p = p + 1;
if (p == 32) {
p32 = 1; // Set p32 = 2**(p-32).
} else {
p32 = 2 * p32;
}
if (r + 1 >= d - r) {
if (q >= 0x7FFFFFFF) a = 1;
q = 2 * q + 1; // Update q.
r = 2 * r + 1 - d; // Update r.
} else {
if (q >= 0x80000000) a = 1;
q = 2 * q;
r = 2 * r + 1;
}
delta = d - 1 - r;
} while (p < 64 && p32 < delta);
magu.M = q + 1; // Magic number and
magu.s = p - 32; // Shift amount to return
if (a) magu.s |= 64; // Sets "add" indicator
_npassert(magu.M || magu.s); // Never returns zero.
return magu;
}
| 3,470 | 69 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/acosl.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
#include "libc/tinymath/invtrigl.internal.h"
#include "libc/tinymath/ldshape.internal.h"
#if !(LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024)
asm(".ident\t\"\\n\\n\
fdlibm (fdlibm license)\\n\
Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.\"");
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
/* origin: FreeBSD /usr/src/lib/msun/src/e_acosl.c */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/*
* See comments in acos.c.
* Converted to long double by David Schultz <[email protected]>.
*/
#if LDBL_MANT_DIG == 64
#define CLEARBOTTOM(u) (u.i.m &= -1ULL << 32)
#elif LDBL_MANT_DIG == 113
#define CLEARBOTTOM(u) (u.i.lo = 0)
#endif
/**
* Returns arc cosine of ð¥.
*
* @define atan2(fabs(sqrt((1-ð¥)*(1+ð¥))),ð¥)
* @domain -1 ⤠ð¥ ⤠1
*/
long double acosl(long double x)
{
union ldshape u = {x};
long double z, s, c, f;
uint16_t e = u.i.se & 0x7fff;
/* |x| >= 1 or nan */
if (e >= 0x3fff) {
if (x == 1)
return 0;
if (x == -1)
return 2*pio2_hi + 0x1p-120f;
return 0/(x-x);
}
/* |x| < 0.5 */
if (e < 0x3fff - 1) {
if (e < 0x3fff - LDBL_MANT_DIG - 1)
return pio2_hi + 0x1p-120f;
return pio2_hi - (__invtrigl_R(x*x)*x - pio2_lo + x);
}
/* x < -0.5 */
if (u.i.se >> 15) {
z = (1 + x)*0.5;
s = sqrtl(z);
return 2*(pio2_hi - (__invtrigl_R(z)*s - pio2_lo + s));
}
/* x > 0.5 */
z = (1 - x)*0.5;
s = sqrtl(z);
u.f = s;
CLEARBOTTOM(u);
f = u.f;
c = (z - f*f)/(s + f);
return 2*(__invtrigl_R(z)*s + c + f);
}
#endif /* long double is long */
| 4,586 | 107 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/log2_data.internal.h | #ifndef COSMOPOLITAN_LIBC_TINYMATH_LOG2_DATA_INTERNAL_H_
#define COSMOPOLITAN_LIBC_TINYMATH_LOG2_DATA_INTERNAL_H_
#define LOG2_TABLE_BITS 6
#define LOG2_POLY_ORDER 7
#define LOG2_POLY1_ORDER 11
#if !(__ASSEMBLER__ + __LINKER__ + 0)
COSMOPOLITAN_C_START_
extern _Hide const struct log2_data {
double invln2hi;
double invln2lo;
double poly[LOG2_POLY_ORDER - 1];
double poly1[LOG2_POLY1_ORDER - 1];
struct {
double invc, logc;
} tab[1 << LOG2_TABLE_BITS];
#if !__FP_FAST_FMA
struct {
double chi, clo;
} tab2[1 << LOG2_TABLE_BITS];
#endif
} __log2_data;
COSMOPOLITAN_C_END_
#endif /* !(__ASSEMBLER__ + __LINKER__ + 0) */
#endif /* COSMOPOLITAN_LIBC_TINYMATH_LOG2_DATA_INTERNAL_H_ */
| 709 | 29 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/cabsf.c | /*-*- mode:c;indent-tabs-mode:nil;c-basic-offset:2;tab-width:8;coding:utf-8 -*-â
âvi: set net ft=c ts=2 sts=2 sw=2 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ¡
â Copyright 2023 Justine Alexandra Roberts Tunney â
â â
â Permission to use, copy, modify, and/or distribute this software for â
â any purpose with or without fee is hereby granted, provided that the â
â above copyright notice and this permission notice appear in all copies. â
â â
â THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL â
â WARRANTIES WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED â
â WARRANTIES OF MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE â
â AUTHOR BE LIABLE FOR ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL â
â DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR â
â PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER â
â TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR â
â PERFORMANCE OF THIS SOFTWARE. â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/complex.h"
#include "libc/math.h"
/**
* Returns absolute value of complex number.
*/
float cabsf(float complex z) {
return hypotf(crealf(z), cimagf(z));
}
| 2,011 | 28 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/creal.c | /*-*- mode:c;indent-tabs-mode:nil;c-basic-offset:2;tab-width:8;coding:utf-8 -*-â
âvi: set net ft=c ts=2 sts=2 sw=2 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ¡
â Copyright 2023 Justine Alexandra Roberts Tunney â
â â
â Permission to use, copy, modify, and/or distribute this software for â
â any purpose with or without fee is hereby granted, provided that the â
â above copyright notice and this permission notice appear in all copies. â
â â
â THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL â
â WARRANTIES WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED â
â WARRANTIES OF MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE â
â AUTHOR BE LIABLE FOR ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL â
â DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR â
â PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER â
â TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR â
â PERFORMANCE OF THIS SOFTWARE. â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/complex.h"
double(creal)(double complex z) {
return creal(z);
}
| 1,918 | 24 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/cbrtf.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2020 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
asm(".ident\t\"\\n\\n\
fdlibm (fdlibm license)\\n\
Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.\"");
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
/* origin: FreeBSD /usr/src/lib/msun/src/s_cbrtf.c */
/*
* Conversion to float by Ian Lance Taylor, Cygnus Support, [email protected].
* Debugged and optimized by Bruce D. Evans.
*/
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
static const unsigned
B1 = 709958130, /* B1 = (127-127.0/3-0.03306235651)*2**23 */
B2 = 642849266; /* B2 = (127-127.0/3-24/3-0.03306235651)*2**23 */
/**
* Returns cube root of ð¥.
*/
float cbrtf(float x)
{
double_t r,T;
union {float f; uint32_t i;} u = {x};
uint32_t hx = u.i & 0x7fffffff;
if (hx >= 0x7f800000) /* cbrt(NaN,INF) is itself */
return x + x;
/* rough cbrt to 5 bits */
if (hx < 0x00800000) { /* zero or subnormal? */
if (hx == 0)
return x; /* cbrt(+-0) is itself */
u.f = x*0x1p24f;
hx = u.i & 0x7fffffff;
hx = hx/3 + B2;
} else
hx = hx/3 + B1;
u.i &= 0x80000000;
u.i |= hx;
/*
* First step Newton iteration (solving t*t-x/t == 0) to 16 bits. In
* double precision so that its terms can be arranged for efficiency
* without causing overflow or underflow.
*/
T = u.f;
r = T*T*T;
T = T*((double_t)x+x+r)/(x+r+r);
/*
* Second step Newton iteration to 47 bits. In double precision for
* efficiency and accuracy.
*/
r = T*T*T;
T = T*((double_t)x+x+r)/(x+r+r);
/* rounding to 24 bits is perfect in round-to-nearest mode */
return T;
}
| 4,575 | 102 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/fma.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2020 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.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
#define ASUINT64(x) ((union {double f; uint64_t i;}){x}).i
#define ZEROINFNAN (0x7ff-0x3ff-52-1)
static inline int a_clz_64(uint64_t x)
{
#ifdef __GNUC__
if (!x) return 63;
return __builtin_clzll(x);
#else
uint32_t y;
int r;
if (x>>32) y=x>>32, r=0; else y=x, r=32;
if (y>>16) y>>=16; else r |= 16;
if (y>>8) y>>=8; else r |= 8;
if (y>>4) y>>=4; else r |= 4;
if (y>>2) y>>=2; else r |= 2;
return r | !(y>>1);
#endif
}
struct num { uint64_t m; int e; int sign; };
static struct num normalize(double x)
{
uint64_t ix = ASUINT64(x);
int e = ix>>52;
int sign = e & 0x800;
e &= 0x7ff;
if (!e) {
ix = ASUINT64(x*0x1p63);
e = ix>>52 & 0x7ff;
e = e ? e-63 : 0x800;
}
ix &= (1ull<<52)-1;
ix |= 1ull<<52;
ix <<= 1;
e -= 0x3ff + 52 + 1;
return (struct num){ix,e,sign};
}
static void mul(uint64_t *hi, uint64_t *lo, uint64_t x, uint64_t y)
{
uint64_t t1,t2,t3;
uint64_t xlo = (uint32_t)x, xhi = x>>32;
uint64_t ylo = (uint32_t)y, yhi = y>>32;
t1 = xlo*ylo;
t2 = xlo*yhi + xhi*ylo;
t3 = xhi*yhi;
*lo = t1 + (t2<<32);
*hi = t3 + (t2>>32) + (t1 > *lo);
}
/**
* Performs fused multiply add.
*
* @return `ð¥ * ð¦ + ð§` rounded as one ternary operation
*/
double fma(double x, double y, double z)
{
#if defined(__x86_64__) && defined(__FMA__) && defined(__FAST_MATH__)
// Intel Haswell+ (c. 2013)
// AMD Piledriver+ (c. 2011)
asm("vfmadd132sd\t%1,%2,%0" : "+x"(x) : "x"(y), "x"(z));
return x;
#elif defined(__x86_64__) && defined(__FMA4__) && defined(__FAST_MATH__)
// AMD Bulldozer+ (c. 2011)
asm("vfmaddsd\t%3,%2,%1,%0" : "=x"(x) : "x"(x), "x"(y), "x"(z));
return x;
#elif defined(__aarch64__) && defined(__FAST_MATH__)
asm("fmadd\t%d0,%d1,%d2,%d3" : "=w"(x) : "w"(x), "w"(y), "w"(z));
return x;
#elif defined(__powerpc64__) && defined(__FAST_MATH__)
asm("fmadd\t%0,%1,%2,%3" : "=d"(x) : "d"(x), "d"(y), "d"(z));
return x;
#elif defined(__riscv) && __riscv_flen >= 64 && defined(__FAST_MATH__)
asm("fmadd.d\t%0,%1,%2,%3" : "=f"(x) : "f"(x), "f"(y), "f"(z));
return x;
#elif defined(__s390x__) && defined(__FAST_MATH__)
asm("madbr\t%0,\t%1,\t%2" : "+f"(z) : "f"(x), "f"(y));
return z;
#else
// #pragma STDC FENV_ACCESS ON
/* normalize so top 10bits and last bit are 0 */
struct num nx, ny, nz;
nx = normalize(x);
ny = normalize(y);
nz = normalize(z);
if (nx.e >= ZEROINFNAN || ny.e >= ZEROINFNAN)
return x*y + z;
if (nz.e >= ZEROINFNAN) {
if (nz.e > ZEROINFNAN) /* z==0 */
return x*y + z;
return z;
}
/* mul: r = x*y */
uint64_t rhi, rlo, zhi, zlo;
mul(&rhi, &rlo, nx.m, ny.m);
/* either top 20 or 21 bits of rhi and last 2 bits of rlo are 0 */
/* align exponents */
int e = nx.e + ny.e;
int d = nz.e - e;
/* shift bits z<<=kz, r>>=kr, so kz+kr == d, set e = e+kr (== ez-kz) */
if (d > 0) {
if (d < 64) {
zlo = nz.m<<d;
zhi = nz.m>>64-d;
} else {
zlo = 0;
zhi = nz.m;
e = nz.e - 64;
d -= 64;
if (d == 0) {
} else if (d < 64) {
rlo = rhi<<64-d | rlo>>d | !!(rlo<<64-d);
rhi = rhi>>d;
} else {
rlo = 1;
rhi = 0;
}
}
} else {
zhi = 0;
d = -d;
if (d == 0) {
zlo = nz.m;
} else if (d < 64) {
zlo = nz.m>>d | !!(nz.m<<64-d);
} else {
zlo = 1;
}
}
/* add */
int sign = nx.sign^ny.sign;
int samesign = !(sign^nz.sign);
int nonzero = 1;
if (samesign) {
/* r += z */
rlo += zlo;
rhi += zhi + (rlo < zlo);
} else {
/* r -= z */
uint64_t t = rlo;
rlo -= zlo;
rhi = rhi - zhi - (t < rlo);
if (rhi>>63) {
rlo = -rlo;
rhi = -rhi-!!rlo;
sign = !sign;
}
nonzero = !!rhi;
}
/* set rhi to top 63bit of the result (last bit is sticky) */
if (nonzero) {
e += 64;
d = a_clz_64(rhi)-1;
/* note: d > 0 */
rhi = rhi<<d | rlo>>64-d | !!(rlo<<d);
} else if (rlo) {
d = a_clz_64(rlo)-1;
if (d < 0)
rhi = rlo>>1 | (rlo&1);
else
rhi = rlo<<d;
} else {
/* exact +-0 */
return x*y + z;
}
e -= d;
/* convert to double */
int64_t i = rhi; /* i is in [1<<62,(1<<63)-1] */
if (sign)
i = -i;
double r = i; /* |r| is in [0x1p62,0x1p63] */
if (e < -1022-62) {
/* result is subnormal before rounding */
if (e == -1022-63) {
double c = 0x1p63;
if (sign)
c = -c;
if (r == c) {
/* min normal after rounding, underflow depends
on arch behaviour which can be imitated by
a double to float conversion */
float fltmin = 0x0.ffffff8p-63*FLT_MIN * r;
return DBL_MIN/FLT_MIN * fltmin;
}
/* one bit is lost when scaled, add another top bit to
only round once at conversion if it is inexact */
if (rhi << 53) {
i = rhi>>1 | (rhi&1) | 1ull<<62;
if (sign)
i = -i;
r = i;
r = 2*r - c; /* remove top bit */
/* raise underflow portably, such that it
cannot be optimized away */
{
double_t tiny = DBL_MIN/FLT_MIN * r;
r += (double)(tiny*tiny) * (r-r);
}
}
} else {
/* only round once when scaled */
d = 10;
i = ( rhi>>d | !!(rhi<<64-d) ) << d;
if (sign)
i = -i;
r = i;
}
}
return scalbn(r, e);
#endif /* __x86_64__ */
}
| 7,827 | 271 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/atan_common.internal.h | #ifndef COSMOPOLITAN_LIBC_TINYMATH_ATAN_COMMON_H_
#define COSMOPOLITAN_LIBC_TINYMATH_ATAN_COMMON_H_
#include "libc/tinymath/atan_data.internal.h"
#include "libc/tinymath/estrin_wrap.internal.h"
#include "libc/tinymath/horner.internal.h"
#if !(__ASSEMBLER__ + __LINKER__ + 0)
COSMOPOLITAN_C_START_
// clang-format off
/*
* Double-precision polynomial evaluation function for scalar and vector atan(x)
* and atan2(y,x).
*
* Copyright (c) 2021-2023, Arm Limited.
* SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
*/
#if WANT_VMATH
#define DBL_T float64x2_t
#define P(i) v_f64 (__atan_poly_data.poly[i])
#else
#define DBL_T double
#define P(i) __atan_poly_data.poly[i]
#endif
/* Polynomial used in fast atan(x) and atan2(y,x) implementations
The order 19 polynomial P approximates (atan(sqrt(x))-sqrt(x))/x^(3/2). */
static inline DBL_T
eval_poly (DBL_T z, DBL_T az, DBL_T shift)
{
/* Use split Estrin scheme for P(z^2) with deg(P)=19. Use split instead of
full scheme to avoid underflow in x^16. */
DBL_T z2 = z * z;
DBL_T x2 = z2 * z2;
DBL_T x4 = x2 * x2;
DBL_T x8 = x4 * x4;
DBL_T y
= FMA (ESTRIN_11_ (z2, x2, x4, x8, P, 8), x8, ESTRIN_7 (z2, x2, x4, P));
/* Finalize. y = shift + z + z^3 * P(z^2). */
y = FMA (y, z2 * az, az);
y = y + shift;
return y;
}
#undef DBL_T
#undef FMA
#undef P
COSMOPOLITAN_C_END_
#endif /* !(__ASSEMBLER__ + __LINKER__ + 0) */
#endif /* COSMOPOLITAN_LIBC_TINYMATH_ATAN_COMMON_H_ */
| 1,476 | 58 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/expm1.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
#include "libc/tinymath/internal.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
/* origin: FreeBSD /usr/src/lib/msun/src/s_expm1.c */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/* expm1(x)
* Returns exp(x)-1, the exponential of x minus 1.
*
* Method
* 1. Argument reduction:
* Given x, find r and integer k such that
*
* x = k*ln2 + r, |r| <= 0.5*ln2 ~ 0.34658
*
* Here a correction term c will be computed to compensate
* the error in r when rounded to a floating-point number.
*
* 2. Approximating expm1(r) by a special rational function on
* the interval [0,0.34658]:
* Since
* r*(exp(r)+1)/(exp(r)-1) = 2+ r^2/6 - r^4/360 + ...
* we define R1(r*r) by
* r*(exp(r)+1)/(exp(r)-1) = 2+ r^2/6 * R1(r*r)
* That is,
* R1(r**2) = 6/r *((exp(r)+1)/(exp(r)-1) - 2/r)
* = 6/r * ( 1 + 2.0*(1/(exp(r)-1) - 1/r))
* = 1 - r^2/60 + r^4/2520 - r^6/100800 + ...
* We use a special Remez algorithm on [0,0.347] to generate
* a polynomial of degree 5 in r*r to approximate R1. The
* maximum error of this polynomial approximation is bounded
* by 2**-61. In other words,
* R1(z) ~ 1.0 + Q1*z + Q2*z**2 + Q3*z**3 + Q4*z**4 + Q5*z**5
* where Q1 = -1.6666666666666567384E-2,
* Q2 = 3.9682539681370365873E-4,
* Q3 = -9.9206344733435987357E-6,
* Q4 = 2.5051361420808517002E-7,
* Q5 = -6.2843505682382617102E-9;
* z = r*r,
* with error bounded by
* | 5 | -61
* | 1.0+Q1*z+...+Q5*z - R1(z) | <= 2
* | |
*
* expm1(r) = exp(r)-1 is then computed by the following
* specific way which minimize the accumulation rounding error:
* 2 3
* r r [ 3 - (R1 + R1*r/2) ]
* expm1(r) = r + --- + --- * [--------------------]
* 2 2 [ 6 - r*(3 - R1*r/2) ]
*
* To compensate the error in the argument reduction, we use
* expm1(r+c) = expm1(r) + c + expm1(r)*c
* ~ expm1(r) + c + r*c
* Thus c+r*c will be added in as the correction terms for
* expm1(r+c). Now rearrange the term to avoid optimization
* screw up:
* ( 2 2 )
* ({ ( r [ R1 - (3 - R1*r/2) ] ) } r )
* expm1(r+c)~r - ({r*(--- * [--------------------]-c)-c} - --- )
* ({ ( 2 [ 6 - r*(3 - R1*r/2) ] ) } 2 )
* ( )
*
* = r - E
* 3. Scale back to obtain expm1(x):
* From step 1, we have
* expm1(x) = either 2^k*[expm1(r)+1] - 1
* = or 2^k*[expm1(r) + (1-2^-k)]
* 4. Implementation notes:
* (A). To save one multiplication, we scale the coefficient Qi
* to Qi*2^i, and replace z by (x^2)/2.
* (B). To achieve maximum accuracy, we compute expm1(x) by
* (i) if x < -56*ln2, return -1.0, (raise inexact if x!=inf)
* (ii) if k=0, return r-E
* (iii) if k=-1, return 0.5*(r-E)-0.5
* (iv) if k=1 if r < -0.25, return 2*((r+0.5)- E)
* else return 1.0+2.0*(r-E);
* (v) if (k<-2||k>56) return 2^k(1-(E-r)) - 1 (or exp(x)-1)
* (vi) if k <= 20, return 2^k((1-2^-k)-(E-r)), else
* (vii) return 2^k(1-((E+2^-k)-r))
*
* Special cases:
* expm1(INF) is INF, expm1(NaN) is NaN;
* expm1(-INF) is -1, and
* for finite argument, only expm1(0)=0 is exact.
*
* Accuracy:
* according to an error analysis, the error is always less than
* 1 ulp (unit in the last place).
*
* Misc. info.
* For IEEE double
* if x > 7.09782712893383973096e+02 then expm1(x) overflow
*
* Constants:
* The hexadecimal values are the intended ones for the following
* constants. The decimal values may be used, provided that the
* compiler will convert from decimal to binary accurately enough
* to produce the hexadecimal values shown.
*/
static const double
o_threshold = 7.09782712893383973096e+02, /* 0x40862E42, 0xFEFA39EF */
ln2_hi = 6.93147180369123816490e-01, /* 0x3fe62e42, 0xfee00000 */
ln2_lo = 1.90821492927058770002e-10, /* 0x3dea39ef, 0x35793c76 */
invln2 = 1.44269504088896338700e+00, /* 0x3ff71547, 0x652b82fe */
/* Scaled Q's: Qn_here = 2**n * Qn_above, for R(2*z) where z = hxs = x*x/2: */
Q1 = -3.33333333333331316428e-02, /* BFA11111 111110F4 */
Q2 = 1.58730158725481460165e-03, /* 3F5A01A0 19FE5585 */
Q3 = -7.93650757867487942473e-05, /* BF14CE19 9EAADBB7 */
Q4 = 4.00821782732936239552e-06, /* 3ED0CFCA 86E65239 */
Q5 = -2.01099218183624371326e-07; /* BE8AFDB7 6E09C32D */
/**
* Returns ð^ð¥-ð·.
*/
double expm1(double x)
{
double_t y,hi,lo,c,t,e,hxs,hfx,r1,twopk;
union {double f; uint64_t i;} u = {x};
uint32_t hx = u.i>>32 & 0x7fffffff;
int k, sign = u.i>>63;
/* filter out huge and non-finite argument */
if (hx >= 0x4043687A) { /* if |x|>=56*ln2 */
if (isnan(x))
return x;
if (sign)
return -1;
if (x > o_threshold) {
x *= 0x1p1023;
return x;
}
}
/* argument reduction */
if (hx > 0x3fd62e42) { /* if |x| > 0.5 ln2 */
if (hx < 0x3FF0A2B2) { /* and |x| < 1.5 ln2 */
if (!sign) {
hi = x - ln2_hi;
lo = ln2_lo;
k = 1;
} else {
hi = x + ln2_hi;
lo = -ln2_lo;
k = -1;
}
} else {
k = invln2*x + (sign ? -0.5 : 0.5);
t = k;
hi = x - t*ln2_hi; /* t*ln2_hi is exact here */
lo = t*ln2_lo;
}
x = hi-lo;
c = (hi-x)-lo;
} else if (hx < 0x3c900000) { /* |x| < 2**-54, return x */
if (hx < 0x00100000)
FORCE_EVAL((float)x);
return x;
} else
k = 0;
/* x is now in primary range */
hfx = 0.5*x;
hxs = x*hfx;
r1 = 1.0+hxs*(Q1+hxs*(Q2+hxs*(Q3+hxs*(Q4+hxs*Q5))));
t = 3.0-r1*hfx;
e = hxs*((r1-t)/(6.0 - x*t));
if (k == 0) /* c is 0 */
return x - (x*e-hxs);
e = x*(e-c) - c;
e -= hxs;
/* exp(x) ~ 2^k (x_reduced - e + 1) */
if (k == -1)
return 0.5*(x-e) - 0.5;
if (k == 1) {
if (x < -0.25)
return -2.0*(e-(x+0.5));
return 1.0+2.0*(x-e);
}
u.i = (uint64_t)(0x3ff + k)<<52; /* 2^k */
twopk = u.f;
if (k < 0 || k > 56) { /* suffice to return exp(x)-1 */
y = x - e + 1.0;
if (k == 1024)
y = y*2.0*0x1p1023;
else
y = y*twopk;
return y - 1.0;
}
u.i = (uint64_t)(0x3ff - k)<<52; /* 2^-k */
if (k < 20)
y = (x-e+(1-u.f))*twopk;
else
y = (x-(e+u.f)+1)*twopk;
return y;
}
#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
__strong_reference(expm1, expm1l);
#endif
| 9,892 | 243 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/log10.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/intrin/likely.h"
#include "libc/math.h"
#include "libc/tinymath/complex.internal.h"
#include "libc/tinymath/internal.h"
#include "libc/tinymath/log2_data.internal.h"
asm(".ident\t\"\\n\\n\
fdlibm (fdlibm license)\\n\
Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.\"");
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
/* origin: FreeBSD /usr/src/lib/msun/src/e_log10.c */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/*
* Return the base 10 logarithm of x. See log.c for most comments.
*
* Reduce x to 2^k (1+f) and calculate r = log(1+f) - f + f*f/2
* as in log.c, then combine and scale in extra precision:
* log10(x) = (f - f*f/2 + r)/log(10) + k*log10(2)
*/
static const double
ivln10hi = 4.34294481878168880939e-01, /* 0x3fdbcb7b, 0x15200000 */
ivln10lo = 2.50829467116452752298e-11, /* 0x3dbb9438, 0xca9aadd5 */
log10_2hi = 3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */
log10_2lo = 3.69423907715893078616e-13, /* 0x3D59FEF3, 0x11F12B36 */
Lg1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */
Lg2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */
Lg3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */
Lg4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */
Lg5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */
Lg6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */
Lg7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */
/**
* Calculates logââð¥.
*/
double log10(double x)
{
union {double f; uint64_t i;} u = {x};
double_t hfsq,f,s,z,R,w,t1,t2,dk,y,hi,lo,val_hi,val_lo;
uint32_t hx;
int k;
hx = u.i>>32;
k = 0;
if (hx < 0x00100000 || hx>>31) {
if (u.i<<1 == 0)
return -1/(x*x); /* log(+-0)=-inf */
if (hx>>31)
return (x-x)/0.0; /* log(-#) = NaN */
/* subnormal number, scale x up */
k -= 54;
x *= 0x1p54;
u.f = x;
hx = u.i>>32;
} else if (hx >= 0x7ff00000) {
return x;
} else if (hx == 0x3ff00000 && u.i<<32 == 0)
return 0;
/* reduce x into [sqrt(2)/2, sqrt(2)] */
hx += 0x3ff00000 - 0x3fe6a09e;
k += (int)(hx>>20) - 0x3ff;
hx = (hx&0x000fffff) + 0x3fe6a09e;
u.i = (uint64_t)hx<<32 | (u.i&0xffffffff);
x = u.f;
f = x - 1.0;
hfsq = 0.5*f*f;
s = f/(2.0+f);
z = s*s;
w = z*z;
t1 = w*(Lg2+w*(Lg4+w*Lg6));
t2 = z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7)));
R = t2 + t1;
/* See log2.c for details. */
/* hi+lo = f - hfsq + s*(hfsq+R) ~ log(1+f) */
hi = f - hfsq;
u.f = hi;
u.i &= (uint64_t)-1<<32;
hi = u.f;
lo = f - hi - hfsq + s*(hfsq+R);
/* val_hi+val_lo ~ log10(1+f) + k*log10(2) */
val_hi = hi*ivln10hi;
dk = k;
y = dk*log10_2hi;
val_lo = dk*log10_2lo + (lo+hi)*ivln10lo + lo*ivln10hi;
/*
* Extra precision in for adding y is not strictly needed
* since there is no very large cancellation near x = sqrt(2) or
* x = 1/sqrt(2), but we do it anyway since it costs little on CPUs
* with some parallelism and it reduces the error for many args.
*/
w = y + val_hi;
val_lo += (y - w) + val_hi;
val_hi = w;
return val_lo + val_hi;
}
#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
__strong_reference(log10, log10l);
#endif
| 6,122 | 148 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/exp2.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/intrin/likely.h"
#include "libc/math.h"
#include "libc/tinymath/exp_data.internal.h"
#include "libc/tinymath/internal.h"
asm(".ident\t\"\\n\\n\
Double-precision math functions (MIT License)\\n\
Copyright 2018 ARM Limited\"");
asm(".include \"libc/disclaimer.inc\"");
/* clang-format off */
/*
* Double-precision 2^x function.
*
* Copyright (c) 2018, Arm Limited.
* SPDX-License-Identifier: MIT
*/
#define N (1 << EXP_TABLE_BITS)
#define Shift __exp_data.exp2_shift
#define T __exp_data.tab
#define C1 __exp_data.exp2_poly[0]
#define C2 __exp_data.exp2_poly[1]
#define C3 __exp_data.exp2_poly[2]
#define C4 __exp_data.exp2_poly[3]
#define C5 __exp_data.exp2_poly[4]
/* Handle cases that may overflow or underflow when computing the result that
is scale*(1+TMP) without intermediate rounding. The bit representation of
scale is in SBITS, however it has a computed exponent that may have
overflown into the sign bit so that needs to be adjusted before using it as
a double. (int32_t)KI is the k used in the argument reduction and exponent
adjustment of scale, positive k here means the result may overflow and
negative k means the result may underflow. */
static inline double specialcase(double_t tmp, uint64_t sbits, uint64_t ki)
{
double_t scale, y;
if ((ki & 0x80000000) == 0) {
/* k > 0, the exponent of scale might have overflowed by 1. */
sbits -= 1ull << 52;
scale = asdouble(sbits);
y = 2 * (scale + scale * tmp);
return eval_as_double(y);
}
/* k < 0, need special care in the subnormal range. */
sbits += 1022ull << 52;
scale = asdouble(sbits);
y = scale + scale * tmp;
if (y < 1.0) {
/* Round y to the right precision before scaling it into the subnormal
range to avoid double rounding that can cause 0.5+E/2 ulp error where
E is the worst-case ulp error outside the subnormal range. So this
is only useful if the goal is better than 1 ulp worst-case error. */
double_t hi, lo;
lo = scale - y + scale * tmp;
hi = 1.0 + y;
lo = 1.0 - hi + y + lo;
y = eval_as_double(hi + lo) - 1.0;
/* Avoid -0.0 with downward rounding. */
if (WANT_ROUNDING && y == 0.0)
y = 0.0;
/* The underflow exception needs to be signaled explicitly. */
fp_force_eval(fp_barrier(0x1p-1022) * 0x1p-1022);
}
y = 0x1p-1022 * y;
return eval_as_double(y);
}
/* Top 12 bits of a double (sign and exponent bits). */
static inline uint32_t top12(double x)
{
return asuint64(x) >> 52;
}
/**
* Returns 2^ð¥.
*/
double exp2(double x)
{
uint32_t abstop;
uint64_t ki, idx, top, sbits;
double_t kd, r, r2, scale, tail, tmp;
abstop = top12(x) & 0x7ff;
if (UNLIKELY(abstop - top12(0x1p-54) >= top12(512.0) - top12(0x1p-54))) {
if (abstop - top12(0x1p-54) >= 0x80000000)
/* Avoid spurious underflow for tiny x. */
/* Note: 0 is common input. */
return WANT_ROUNDING ? 1.0 + x : 1.0;
if (abstop >= top12(1024.0)) {
if (asuint64(x) == asuint64(-INFINITY))
return 0.0;
if (abstop >= top12(INFINITY))
return 1.0 + x;
if (!(asuint64(x) >> 63))
return __math_oflow(0);
else if (asuint64(x) >= asuint64(-1075.0))
return __math_uflow(0);
}
if (2 * asuint64(x) > 2 * asuint64(928.0))
/* Large x is special cased below. */
abstop = 0;
}
/* exp2(x) = 2^(k/N) * 2^r, with 2^r in [2^(-1/2N),2^(1/2N)]. */
/* x = k/N + r, with int k and r in [-1/2N, 1/2N]. */
kd = eval_as_double(x + Shift);
ki = asuint64(kd); /* k. */
kd -= Shift; /* k/N for int k. */
r = x - kd;
/* 2^(k/N) ~= scale * (1 + tail). */
idx = 2 * (ki % N);
top = ki << (52 - EXP_TABLE_BITS);
tail = asdouble(T[idx]);
/* This is only a valid scale when -1023*N < k < 1024*N. */
sbits = T[idx + 1] + top;
/* exp2(x) = 2^(k/N) * 2^r ~= scale + scale * (tail + 2^r - 1). */
/* Evaluation is optimized assuming superscalar pipelined execution. */
r2 = r * r;
/* Without fma the worst case error is 0.5/N ulp larger. */
/* Worst case error is less than 0.5+0.86/N+(abs poly error * 2^53) ulp. */
tmp = tail + r * C1 + r2 * (C2 + r * C3) + r2 * r2 * (C4 + r * C5);
if (UNLIKELY(abstop == 0))
return specialcase(tmp, sbits, ki);
scale = asdouble(sbits);
/* Note: tmp == 0 or |tmp| > 2^-65 and scale > 2^-928, so there
is no spurious underflow here even without fma. */
return eval_as_double(scale + scale * tmp);
}
#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
__strong_reference(exp2, exp2l);
#endif
| 7,032 | 162 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/LICENSE.freebsd | # @(#)COPYRIGHT 8.2 (Berkeley) 3/21/94
The compilation of software known as FreeBSD is distributed under the
following terms:
Copyright (c) 1992-2023 The FreeBSD Project.
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.
The 4.4BSD and 4.4BSD-Lite software is distributed under the following
terms:
All of the documentation and software included in the 4.4BSD and 4.4BSD-Lite
Releases is copyrighted by The Regents of the University of California.
Copyright 1979, 1980, 1983, 1986, 1988, 1989, 1991, 1992, 1993, 1994
The Regents of the University of California. 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.
3. All advertising materials mentioning features or use of this software
must display the following acknowledgement:
This product includes software developed by the University of
California, Berkeley and its contributors.
4. Neither the name of the University nor the names of its contributors
may be used to endorse or promote products derived from this software
without specific prior written permission.
THIS SOFTWARE IS PROVIDED BY THE REGENTS 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 REGENTS 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.
The Institute of Electrical and Electronics Engineers and the American
National Standards Committee X3, on Information Processing Systems have
given us permission to reprint portions of their documentation.
In the following statement, the phrase ``this text'' refers to portions
of the system documentation.
Portions of this text are reprinted and reproduced in electronic form in
the second BSD Networking Software Release, from IEEE Std 1003.1-1988, IEEE
Standard Portable Operating System Interface for Computer Environments
(POSIX), copyright C 1988 by the Institute of Electrical and Electronics
Engineers, Inc. In the event of any discrepancy between these versions
and the original IEEE Standard, the original IEEE Standard is the referee
document.
In the following statement, the phrase ``This material'' refers to portions
of the system documentation.
This material is reproduced with permission from American National
Standards Committee X3, on Information Processing Systems. Computer and
Business Equipment Manufacturers Association (CBEMA), 311 First St., NW,
Suite 500, Washington, DC 20001-2178. The developmental work of
Programming Language C was completed by the X3J11 Technical Committee.
The views and conclusions contained in the software and documentation are
those of the authors and should not be interpreted as representing official
policies, either expressed or implied, of the Regents of the University
of California.
NOTE: The copyright of UC Berkeley's Berkeley Software Distribution ("BSD")
source has been updated. The copyright addendum may be found at
ftp://ftp.cs.berkeley.edu/pub/4bsd/README.Impt.License.Change and is
included below.
July 22, 1999
To All Licensees, Distributors of Any Version of BSD:
As you know, certain of the Berkeley Software Distribution ("BSD") source
code files require that further distributions of products containing all or
portions of the software, acknowledge within their advertising materials
that such products contain software developed by UC Berkeley and its
contributors.
Specifically, the provision reads:
" * 3. All advertising materials mentioning features or use of this software
* must display the following acknowledgement:
* This product includes software developed by the University of
* California, Berkeley and its contributors."
Effective immediately, licensees and distributors are no longer required to
include the acknowledgement within advertising materials. Accordingly, the
foregoing paragraph of those BSD Unix files containing it is hereby deleted
in its entirety.
William Hoskins
Director, Office of Technology Licensing
University of California, Berkeley
| 6,109 | 126 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/fabsl.c | /*-*- mode:c;indent-tabs-mode:nil;c-basic-offset:2;tab-width:8;coding:utf-8 -*-â
âvi: set net ft=c ts=2 sts=2 sw=2 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ¡
â Copyright 2023 Justine Alexandra Roberts Tunney â
â â
â Permission to use, copy, modify, and/or distribute this software for â
â any purpose with or without fee is hereby granted, provided that the â
â above copyright notice and this permission notice appear in all copies. â
â â
â THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL â
â WARRANTIES WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED â
â WARRANTIES OF MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE â
â AUTHOR BE LIABLE FOR ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL â
â DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR â
â PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER â
â TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR â
â PERFORMANCE OF THIS SOFTWARE. â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
#include "libc/tinymath/ldshape.internal.h"
#if !(LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024)
/**
* Returns absolute value of floating point number.
*/
long double fabsl(long double x) {
union ldshape u = {x};
u.i.se &= 0x7fff;
return u.f;
}
#endif /* long double is long */
| 2,145 | 33 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/LICENSE.openbsd | OpenBSD Copyright Policy
https://www.openbsd.org/policy.html
Goal
Copyright law is complex, OpenBSD policy is simple â OpenBSD
strives to provide code that can be freely used, copied, modified,
and distributed by anyone and for any purpose. This maintains the
spirit of the original Berkeley Software Distribution. The
preferred wording of a license to be applied to new code can be
found in the license template.
OpenBSD can exist as it does today because of the example set by
the Computer Systems Research Group at Berkeley and the battles
which they and others fought to create a Unix source distribution
un-encumbered by proprietary code and commercial licensing.
The ability of a freely redistributable "Berkeley" Unix to move
forward on a competitive basis with other operating systems
depends on the willingness of the various development groups to
exchange code amongst themselves and with other projects.
Understanding the legal issues surrounding copyright is
fundamental to the ability to exchange and re-distribute code,
while honoring the spirit of the copyright and concept of
attribution is fundamental to promoting the cooperation of the
people involved.
The Berkeley Copyright
The original Berkeley copyright poses no restrictions on private
or commercial use of the software and imposes only simple and
uniform requirements for maintaining copyright notices in
redistributed versions and crediting the originator of the
material only in advertising.
For instance:
* Copyright (c) 1982, 1986, 1990, 1991, 1993
* The Regents of the University of California. 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.
* 3. All advertising materials mentioning features or use of this software
* must display the following acknowledgement:
* This product includes software developed by the University of
* California, Berkeley and its contributors.
* 4. Neither the name of the University nor the names of its contributors
* may be used to endorse or promote products derived from this software
* without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE REGENTS 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 REGENTS 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.
*
Berkeley rescinded the 3rd term (the advertising term) on 22 July
1999. Verbatim copies of the Berkeley license in the OpenBSD tree
have that term removed. In addition, many 3rd-party BSD-style
licenses consist solely of the first two terms.
Because the OpenBSD copyright imposes no conditions beyond those
imposed by the Berkeley copyright, OpenBSD can hope to share the
same wide distribution and applicability as the Berkeley
distributions. It follows however, that OpenBSD cannot include
material which includes copyrights which are more restrictive than
the Berkeley copyright, or must relegate this material to a
secondary status, i.e. OpenBSD as a whole is freely
redistributable, but some optional components may not be.
Copyright Law
While the overall subject of copyright law is far beyond the scope
of this document, some basics are in order. Under the current
copyright law, copyrights are implicit in the creation of a new
work and reside with the creator. In general the copyright applies
only to the new work, not the material the work was derived from,
nor those portions of the derivative material included in the new
work.
Copyright law admits to three general categories of works:
Original Work
A new work that is not derived from an existing work.
Derivative Work
Work that is derived from, includes or amends existing
works.
Compilation
A work that is a compilation of existing new and
derivative works.
The fundamental concept is that there is primacy of the copyright,
that is a copyright of a derivative work does not affect the
rights held by the owner of the copyright of the original work,
rather only the part added. Likewise the copyright of a
compilation does not affect the rights of the owner of the
included works, only the compilation as an entity.
It is vitally important to understand that copyrights are broad
protections as defined by national and international copyright
law. The "copyright notices" usually included in source files are
not copyrights, but rather notices that a party asserts that they
hold copyright to the material or to part of the material.
Typically these notices are associated with license terms which
grant permissions subject to copyright law and with disclaimers
that state the position of the copyright holder/distributor with
respect to liability surrounding use of the material.
By international law, specifically the Berne Convention for the
Protection of Literary and Artistic Works, part of the author's
copyright, the so-called moral rights, are inalienable. This
includes the author's right "to claim authorship of the work and
to object to any distortion, mutilation or other modification of,
or other derogatory action in relation to, the said work, which
would be prejudicial to his honor or reputation". In some
countries, the law reserves additional inalienable moral rights to
the author. On the other hand, the author is free to transfer
other parts of his copyright, the so-called economic rights, in
particular the rights to use, copy, modify, distribute, and
license the work.
Permissions â the flip side
Because copyrights arise from the creation of a work, rather than
through a registration process, there needs to be a practical way
to extend permission to use a work beyond what might be allowed by
"fair use" provisions of the copyright laws.
This permission typically takes the form of a "release" or
"license" included in the work, which grants the additional uses
beyond those granted by copyright law, usually subject to a
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the originator asserts that he imposes no restrictions on use of
the material, at the other restrictive clauses that actually grant
no additional rights or impose restrictive, discriminatory or
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Note that a license is not to be confused with a copyright
transfer. While a transfer would give the new copyright holder
exclusive rights to use the code and take these rights away from
the author, a license typically grants additional people
non-exclusive rights to use the code, while the authors retain all
their rights.
The above observations regarding moral rights imply that putting
code under an ISC or two-clause BSD license essentially makes the
code as free as it can possibly get. Modifying the wording of
these licenses can only result in one of the three following
effects:
* making the code less free by adding additional restrictions
regarding its use, copying, modification or distribution;
* or effectively not changing anything by merely changing the
wording, but not changing anything substantial regarding the
legal content;
* or making the license illegal by attempting to deprive the
authors of rights they cannot legally give away.
Again, an important point to note is that the release and
conditions can only apply to the portion of the work that was
originated by the copyright holderâthe holder of a copyright on a
derivative work can neither grant additional permissions for use
of the original work, nor impose more restrictive conditions for
use of that work.
Because copyright arises from the creation of a work and not the
text or a registration process, removing or altering a copyright
notice or associated release terms has no bearing on the existence
of the copyright, rather all that is accomplished is to cast doubt
upon whatever rights the person making the modifications had to
use the material in the first place. Likewise, adding terms and
conditions in conflict with the original terms and conditions does
not supersede them, rather it casts doubts on the rights of the
person making the amendments to use the material and creates
confusion as to whether anyone can use the amended version or
derivatives thereof.
Finally, releases are generally binding on the material that they
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distributes that work with a release granting certain permissions,
those permissions apply as stated, without discrimination, to all
persons legitimately possessing a copy of the work. That means
that having granted a permission, the copyright holder can not
retroactively say that an individual or class of individuals are
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holder decide to "go commercial" he can not revoke permissions
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Specific Cases
This section attempts to summarize the position of OpenBSD
relative to some commonly encountered copyrights.
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copyright. It retains the rights of the copyright holder,
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or copyrights closely adhering to the Berkeley model can
generally be included in OpenBSD.
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AT&T copyright notice on some of the files in 4.4BSD lite
and lite2. The terms of this license are identical to the
standard Berkeley license.
Additionally, OpenBSD includes some other AT&T code with
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implementation of awk.
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The original Unix code (AT&T versions 1 through 7 UNIX,
including 32V) was freed by Caldera, Inc. on 23 January
2002 and is now available under a 4-term BSD-style
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to incorporate original Unix code into OpenBSD. However,
that code is now so old that it does not satisfy today's
interface and quality standards.
DEC, Sun, other manufacturers/software houses.
In general OpenBSD does not include material copyrighted
by manufacturers or software houses. Material may be
included where the copyright owner has granted general
permission for reuse without conditions, with terms
similar to the Berkeley copyright, or where the material
is the product of an employee and the employer's copyright
notice effectively releases any rights they might have to
the work.
Carnegie-Mellon (CMU, Mach)
The Carnegie-Mellon copyright is similar to the Berkeley
copyright, except that it requests that derivative works
be made available to Carnegie-Mellon. Because this is only
a request and not a condition, such material can still be
included in OpenBSD. It should be noted that existing
versions of Mach are still subject to AT&T copyrights,
which prevents the general distribution of Mach sources.
Apache
The original Apache license was similar to the Berkeley
license, but source code published under version 2 of the
Apache license is subject to additional restrictions and
cannot be included into OpenBSD. In particular, if you use
code under the Apache 2 license, some of your rights will
terminate if you claim in court that the code violates a
patent.
A license can only be considered fully permissive if it
allows use by anyone for all the future without giving up
any of their rights. If there are conditions that might
terminate any rights in the future, or if you have to give
up a right that you would otherwise have, even if
exercising that right could reasonably be regarded as
morally objectionable, the code is not free.
In addition, the clause about the patent license is
problematic because a patent license cannot be granted
under Copyright law, but only under contract law, which
drags the whole license into the domain of contract law.
But while Copyright law is somewhat standardized by
international agreements, contract law differs wildly
among jurisdictions. So what the license means in
different jurisdictions may vary and is hard to predict.
ISC
The ISC copyright is functionally equivalent to a two-term
BSD copyright with language removed that is made
unnecessary by the Berne convention. This is the preferred
license for new code incorporated into OpenBSD. A sample
license is available in the file
/usr/share/misc/license.template.
GNU General Public License, GPL, LGPL, copyleft, etc.
The GNU Public License and licenses modeled on it impose
the restriction that source code must be distributed or
made available for all works that are derivatives of the
GNU copyrighted code.
While this may superficially look like a noble strategy,
it is a condition that is typically unacceptable for
commercial use of software. So in practice, it usually
ends up hindering free sharing and reuse of code and ideas
rather than encouraging it. As a consequence, no
additional software bound by the GPL terms will be
considered for inclusion into the OpenBSD base system.
For historical reasons, the OpenBSD base system still
includes the following GPL-licensed components: the GNU
compiler collection (GCC) with supporting binutils and
libraries, GNU CVS, GNU texinfo, the mkhybrid file system
creation tool, and the readline library. Replacement by
equivalent, more freely licensed tools is a long-term
desideratum.
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Much of OpenBSD is originally based on and evolved from
NetBSD, since some of the OpenBSD developers were involved
in the NetBSD project. The general NetBSD license terms
are compatible with the Berkeley license and permit such
use. Material subject only to the general NetBSD license
can generally be included in OpenBSD.
In the past, NetBSD has included material copyrighted by
individuals who have imposed license conditions beyond
that of the general NetBSD license, but granted the NetBSD
Foundation license to distribute the material. Such
material can not be included in OpenBSD as long as the
conditions imposed are at odds with the OpenBSD license
terms or releases from those terms are offered on a
discriminatory basis.
FreeBSD
Most of FreeBSD is also based on Berkeley licensed
material or includes copyright notices based on the
Berkeley model. Such material can be included in OpenBSD,
while those parts that are subject to GPL or various
individual copyright terms that are at odds with the
OpenBSD license can not be included in OpenBSD.
Linux
Most of Linux is subject to GPL style licensing terms and
therefore can not be included in OpenBSD. Individual
components may be eligible, subject to the terms of the
originator's copyright notices. Note that Linux
"distributions" may also be subject to additional
copyright claims of the distributing organization, either
as a compilation or on material included that is not part
of the Linux core.
X.Org
The X.Org Foundation maintains and distributes the X
Window System under a modified MIT license, which is quite
similar to the BSD license and additionally allows
sublicensing. Under the name of Xenocara, the OpenBSD base
system includes an improved and actively maintained
version of the X.Org code.
Shareware, Charityware, Freeware, etc.
Most "shareware" copyright notices impose conditions for
redistribution, use or visibility that are at conflict
with the OpenBSD project goals. Review on a case-by-case
basis is required as to whether the wording of the
conditions is acceptable in terms of conditions being
requested vs. demanded and whether the spirit of the
conditions is compatible with goals of the OpenBSD
project.
Public Domain
While material that is truly entered into the "public
domain" can be included in OpenBSD, review is required on
a case by case basis. Frequently the "public domain"
assertion is made by someone who does not really hold all
rights under copyright law to grant that status or there
are a variety of conditions imposed on use. For a work to
be truly in the "public domain" all rights are abandoned
and the material is offered without restrictions.
In some jurisdictions, it is doubtful whether voluntarily
placing one's own work into the public domain is legally
possible. For that reason, to make any substantial body of
code free, it is preferable to state the copyright and put
it under an ISC or BSD license instead of attempting to
release it into the public domain.
| 19,445 | 395 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/atanhf.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
#include "libc/tinymath/feval.internal.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 */
/**
* Returns inverse hyperbolic tangent of ð¥.
* @define x ? log1p(2 * x / (1 - x)) / 2 : x
*/
float atanhf(float x)
{
union {float f; uint32_t i;} u = {.f = x};
unsigned s = u.i >> 31;
float_t y;
/* |x| */
u.i &= 0x7fffffff;
y = u.f;
if (u.i < 0x3f800000 - (1<<23)) {
if (u.i < 0x3f800000 - (32<<23)) {
/* handle underflow */
if (u.i < (1<<23))
fevalf(y*y);
} else {
/* |x| < 0.5, up to 1.7ulp error */
y = 0.5f*log1pf(2*y + 2*y*y/(1-y));
}
} else {
/* avoid overflow */
y = 0.5f*log1pf(2*(y/(1-y)));
}
return s ? -y : y;
}
| 3,399 | 66 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/fsumf.c | /*-*- mode:c;indent-tabs-mode:nil;c-basic-offset:2;tab-width:8;coding:utf-8 -*-â
âvi: set net ft=c ts=2 sts=2 sw=2 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ¡
â Copyright 2021 Justine Alexandra Roberts Tunney â
â â
â Permission to use, copy, modify, and/or distribute this software for â
â any purpose with or without fee is hereby granted, provided that the â
â above copyright notice and this permission notice appear in all copies. â
â â
â THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL â
â WARRANTIES WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED â
â WARRANTIES OF MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE â
â AUTHOR BE LIABLE FOR ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL â
â DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR â
â PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER â
â TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR â
â PERFORMANCE OF THIS SOFTWARE. â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
/**
* Adds floats in array.
*/
double fsumf(const float *p, size_t n) {
double s;
size_t i;
if (n > 8) return fsumf(p, n / 2) + fsumf(p + n / 2, n - n / 2);
for (s = i = 0; i < n; ++i) s += p[i];
return s;
}
| 2,080 | 31 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/csinf.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/complex.h"
#include "libc/math.h"
#include "libc/tinymath/complex.internal.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 */
float complex csinf(float complex z)
{
z = csinhf(CMPLXF(-cimagf(z), crealf(z)));
return CMPLXF(cimagf(z), -crealf(z));
}
| 2,984 | 45 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/cos.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
#include "libc/tinymath/feval.internal.h"
#include "libc/tinymath/kernel.internal.h"
asm(".ident\t\"\\n\\n\
fdlibm (fdlibm license)\\n\
Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.\"");
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
/* origin: FreeBSD /usr/src/lib/msun/src/s_cos.c */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/* cos(x)
* Return cosine function of x.
*
* kernel function:
* __sin ... sine function on [-pi/4,pi/4]
* __cos ... cosine function on [-pi/4,pi/4]
* __rem_pio2 ... argument reduction routine
*
* Method.
* Let S,C and T denote the sin, cos and tan respectively on
* [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
* in [-pi/4 , +pi/4], and let n = k mod 4.
* We have
*
* n sin(x) cos(x) tan(x)
* ----------------------------------------------------------
* 0 S C T
* 1 C -S -1/T
* 2 -S -C T
* 3 -C S -1/T
* ----------------------------------------------------------
*
* Special cases:
* Let trig be any of sin, cos, or tan.
* trig(+-INF) is NaN, with signals;
* trig(NaN) is that NaN;
*
* Accuracy:
* TRIG(x) returns trig(x) nearly rounded
*/
#define asuint64(f) ((union{double _f; uint64_t _i;}){f})._i
#define gethighw(hi,d) (hi) = asuint64(d) >> 32
/**
* Returns cosine of ð¥.
* @note should take ~5ns
*/
double cos(double x)
{
double y[2];
uint32_t ix;
unsigned n;
gethighw(ix, x);
ix &= 0x7fffffff;
/* |x| ~< pi/4 */
if (ix <= 0x3fe921fb) {
if (ix < 0x3e46a09e) { /* |x| < 2**-27 * sqrt(2) */
/* raise inexact if x!=0 */
feval(x + 0x1p120f);
return 1.0;
}
return __cos(x, 0);
}
/* cos(Inf or NaN) is NaN */
if (ix >= 0x7ff00000)
return x-x;
/* argument reduction */
n = __rem_pio2(x, y);
switch (n&3) {
case 0: return __cos(y[0], y[1]);
case 1: return -__sin(y[0], y[1], 1);
case 2: return -__cos(y[0], y[1]);
default:
return __sin(y[0], y[1], 1);
}
}
#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
__strong_reference(cos, cosl);
#endif
| 5,332 | 127 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/sincosf.internal.h | #ifndef COSMOPOLITAN_LIBC_TINYMATH_SINCOSF_INTERNAL_H_
#define COSMOPOLITAN_LIBC_TINYMATH_SINCOSF_INTERNAL_H_
#include "libc/tinymath/internal.h"
#if !(__ASSEMBLER__ + __LINKER__ + 0)
COSMOPOLITAN_C_START_
// clang-format off
/*
* Header for sinf, cosf and sincosf.
*
* Copyright (c) 2018-2021, Arm Limited.
* SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
*/
/* 2PI * 2^-64. */
static const double pi63 = 0x1.921FB54442D18p-62;
/* PI / 4. */
static const float pio4f = 0x1.921FB6p-1f;
/* The constants and polynomials for sine and cosine. */
typedef struct
{
double sign[4]; /* Sign of sine in quadrants 0..3. */
double hpi_inv; /* 2 / PI ( * 2^24 if !TOINT_INTRINSICS). */
double hpi; /* PI / 2. */
double c0, c1, c2, c3, c4; /* Cosine polynomial. */
double s1, s2, s3; /* Sine polynomial. */
} sincos_t;
/* Polynomial data (the cosine polynomial is negated in the 2nd entry). */
extern const sincos_t __sincosf_table[2] _Hide;
/* Table with 4/PI to 192 bit precision. */
extern const uint32_t __inv_pio4[] _Hide;
/* Top 12 bits of the float representation with the sign bit cleared. */
static inline uint32_t
abstop12 (float x)
{
return (asuint (x) >> 20) & 0x7ff;
}
/* Compute the sine and cosine of inputs X and X2 (X squared), using the
polynomial P and store the results in SINP and COSP. N is the quadrant,
if odd the cosine and sine polynomials are swapped. */
static inline void
sincosf_poly (double x, double x2, const sincos_t *p, int n, float *sinp,
float *cosp)
{
double x3, x4, x5, x6, s, c, c1, c2, s1;
x4 = x2 * x2;
x3 = x2 * x;
c2 = p->c3 + x2 * p->c4;
s1 = p->s2 + x2 * p->s3;
/* Swap sin/cos result based on quadrant. */
float *tmp = (n & 1 ? cosp : sinp);
cosp = (n & 1 ? sinp : cosp);
sinp = tmp;
c1 = p->c0 + x2 * p->c1;
x5 = x3 * x2;
x6 = x4 * x2;
s = x + x3 * p->s1;
c = c1 + x4 * p->c2;
*sinp = s + x5 * s1;
*cosp = c + x6 * c2;
}
/* Return the sine of inputs X and X2 (X squared) using the polynomial P.
N is the quadrant, and if odd the cosine polynomial is used. */
static inline float
sinf_poly (double x, double x2, const sincos_t *p, int n)
{
double x3, x4, x6, x7, s, c, c1, c2, s1;
if ((n & 1) == 0)
{
x3 = x * x2;
s1 = p->s2 + x2 * p->s3;
x7 = x3 * x2;
s = x + x3 * p->s1;
return s + x7 * s1;
}
else
{
x4 = x2 * x2;
c2 = p->c3 + x2 * p->c4;
c1 = p->c0 + x2 * p->c1;
x6 = x4 * x2;
c = c1 + x4 * p->c2;
return c + x6 * c2;
}
}
/* Fast range reduction using single multiply-subtract. Return the modulo of
X as a value between -PI/4 and PI/4 and store the quadrant in NP.
The values for PI/2 and 2/PI are accessed via P. Since PI/2 as a double
is accurate to 55 bits and the worst-case cancellation happens at 6 * PI/4,
the result is accurate for |X| <= 120.0. */
static inline double
reduce_fast (double x, const sincos_t *p, int *np)
{
double r;
#if TOINT_INTRINSICS
/* Use fast round and lround instructions when available. */
r = x * p->hpi_inv;
*np = converttoint (r);
return x - roundtoint (r) * p->hpi;
#else
/* Use scaled float to int conversion with explicit rounding.
hpi_inv is prescaled by 2^24 so the quadrant ends up in bits 24..31.
This avoids inaccuracies introduced by truncating negative values. */
r = x * p->hpi_inv;
int n = ((int32_t)r + 0x800000) >> 24;
*np = n;
return x - n * p->hpi;
#endif
}
/* Reduce the range of XI to a multiple of PI/2 using fast integer arithmetic.
XI is a reinterpreted float and must be >= 2.0f (the sign bit is ignored).
Return the modulo between -PI/4 and PI/4 and store the quadrant in NP.
Reduction uses a table of 4/PI with 192 bits of precision. A 32x96->128 bit
multiply computes the exact 2.62-bit fixed-point modulo. Since the result
can have at most 29 leading zeros after the binary point, the double
precision result is accurate to 33 bits. */
static inline double
reduce_large (uint32_t xi, int *np)
{
const uint32_t *arr = &__inv_pio4[(xi >> 26) & 15];
int shift = (xi >> 23) & 7;
uint64_t n, res0, res1, res2;
xi = (xi & 0xffffff) | 0x800000;
xi <<= shift;
res0 = xi * arr[0];
res1 = (uint64_t)xi * arr[4];
res2 = (uint64_t)xi * arr[8];
res0 = (res2 >> 32) | (res0 << 32);
res0 += res1;
n = (res0 + (1ULL << 61)) >> 62;
res0 -= n << 62;
double x = (int64_t)res0;
*np = n;
return x * pi63;
}
COSMOPOLITAN_C_END_
#endif /* !(__ASSEMBLER__ + __LINKER__ + 0) */
#endif /* COSMOPOLITAN_LIBC_TINYMATH_SINCOSF_INTERNAL_H_ */
| 4,624 | 161 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/tinymath.h | 0 | 1 | jart/cosmopolitan | false |
|
cosmopolitan/libc/tinymath/truncl.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
#include "libc/tinymath/internal.h"
#include "libc/tinymath/ldshape.internal.h"
#if !(LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024)
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
/**
* Rounds to integer, towards zero.
*/
long double truncl(long double x)
{
static const long double toint = 1/LDBL_EPSILON;
union ldshape u = {x};
int e = u.i.se & 0x7fff;
int s = u.i.se >> 15;
long double y;
if (e >= 0x3fff+LDBL_MANT_DIG-1)
return x;
if (e <= 0x3fff-1) {
FORCE_EVAL(x + 0x1p120f);
return x*0;
}
/* y = int(|x|) - |x|, where int(|x|) is an integer neighbor of |x| */
if (s)
x = -x;
y = x + toint - toint - x;
if (y > 0)
y -= 1;
x += y;
return s ? -x : x;
}
#endif /* long double is long */
| 3,455 | 68 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/jn.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
#include "libc/tinymath/complex.internal.h"
asm(".ident\t\"\\n\\n\
Double-precision math functions (MIT License)\\n\
Copyright 2018 ARM Limited\"");
asm(".include \"libc/disclaimer.inc\"");
// clang-format off
/* origin: FreeBSD /usr/src/lib/msun/src/e_jn.c */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/*
* jn(n, x), yn(n, x)
* floating point Bessel's function of the 1st and 2nd kind
* of order n
*
* Special cases:
* y0(0)=y1(0)=yn(n,0) = -inf with division by zero signal;
* y0(-ve)=y1(-ve)=yn(n,-ve) are NaN with invalid signal.
* Note 2. About jn(n,x), yn(n,x)
* For n=0, j0(x) is called,
* for n=1, j1(x) is called,
* for n<=x, forward recursion is used starting
* from values of j0(x) and j1(x).
* for n>x, a continued fraction approximation to
* j(n,x)/j(n-1,x) is evaluated and then backward
* recursion is used starting from a supposed value
* for j(n,x). The resulting value of j(0,x) is
* compared with the actual value to correct the
* supposed value of j(n,x).
*
* yn(n,x) is similar in all respects, except
* that forward recursion is used for all
* values of n>1.
*/
static const double invsqrtpi = 5.64189583547756279280e-01; /* 0x3FE20DD7, 0x50429B6D */
/**
* Returns Bessel function of ð¥ of first kind of order ð.
*/
double jn(int n, double x)
{
uint32_t ix, lx;
int nm1, i, sign;
double a, b, temp;
EXTRACT_WORDS(ix, lx, x);
sign = ix>>31;
ix &= 0x7fffffff;
if ((ix | (lx|-lx)>>31) > 0x7ff00000) /* nan */
return x;
/* J(-n,x) = (-1)^n * J(n, x), J(n, -x) = (-1)^n * J(n, x)
* Thus, J(-n,x) = J(n,-x)
*/
/* nm1 = |n|-1 is used instead of |n| to handle n==INT_MIN */
if (n == 0)
return j0(x);
if (n < 0) {
nm1 = -(n+1);
x = -x;
sign ^= 1;
} else
nm1 = n-1;
if (nm1 == 0)
return j1(x);
sign &= n; /* even n: 0, odd n: signbit(x) */
x = fabs(x);
if ((ix|lx) == 0 || ix == 0x7ff00000) /* if x is 0 or inf */
b = 0.0;
else if (nm1 < x) {
/* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */
if (ix >= 0x52d00000) { /* x > 2**302 */
/* (x >> n**2)
* Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi)
* Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi)
* Let s=sin(x), c=cos(x),
* xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then
*
* n sin(xn)*sqt2 cos(xn)*sqt2
* ----------------------------------
* 0 s-c c+s
* 1 -s-c -c+s
* 2 -s+c -c-s
* 3 s+c c-s
*/
switch(nm1&3) {
case 0: temp = -cos(x)+sin(x); break;
case 1: temp = -cos(x)-sin(x); break;
case 2: temp = cos(x)-sin(x); break;
default:
case 3: temp = cos(x)+sin(x); break;
}
b = invsqrtpi*temp/sqrt(x);
} else {
a = j0(x);
b = j1(x);
for (i=0; i<nm1; ) {
i++;
temp = b;
b = b*(2.0*i/x) - a; /* avoid underflow */
a = temp;
}
}
} else {
if (ix < 0x3e100000) { /* x < 2**-29 */
/* x is tiny, return the first Taylor expansion of J(n,x)
* J(n,x) = 1/n!*(x/2)^n - ...
*/
if (nm1 > 32) /* underflow */
b = 0.0;
else {
temp = x*0.5;
b = temp;
a = 1.0;
for (i=2; i<=nm1+1; i++) {
a *= (double)i; /* a = n! */
b *= temp; /* b = (x/2)^n */
}
b = b/a;
}
} else {
/* use backward recurrence */
/* x x^2 x^2
* J(n,x)/J(n-1,x) = ---- ------ ------ .....
* 2n - 2(n+1) - 2(n+2)
*
* 1 1 1
* (for large x) = ---- ------ ------ .....
* 2n 2(n+1) 2(n+2)
* -- - ------ - ------ -
* x x x
*
* Let w = 2n/x and h=2/x, then the above quotient
* is equal to the continued fraction:
* 1
* = -----------------------
* 1
* w - -----------------
* 1
* w+h - ---------
* w+2h - ...
*
* To determine how many terms needed, let
* Q(0) = w, Q(1) = w(w+h) - 1,
* Q(k) = (w+k*h)*Q(k-1) - Q(k-2),
* When Q(k) > 1e4 good for single
* When Q(k) > 1e9 good for double
* When Q(k) > 1e17 good for quadruple
*/
/* determine k */
double t,q0,q1,w,h,z,tmp,nf;
int k;
nf = nm1 + 1.0;
w = 2*nf/x;
h = 2/x;
z = w+h;
q0 = w;
q1 = w*z - 1.0;
k = 1;
while (q1 < 1.0e9) {
k += 1;
z += h;
tmp = z*q1 - q0;
q0 = q1;
q1 = tmp;
}
for (t=0.0, i=k; i>=0; i--)
t = 1/(2*(i+nf)/x - t);
a = t;
b = 1.0;
/* estimate log((2/x)^n*n!) = n*log(2/x)+n*ln(n)
* Hence, if n*(log(2n/x)) > ...
* single 8.8722839355e+01
* double 7.09782712893383973096e+02
* long double 1.1356523406294143949491931077970765006170e+04
* then recurrent value may overflow and the result is
* likely underflow to zero
*/
tmp = nf*log(fabs(w));
if (tmp < 7.09782712893383973096e+02) {
for (i=nm1; i>0; i--) {
temp = b;
b = b*(2.0*i)/x - a;
a = temp;
}
} else {
for (i=nm1; i>0; i--) {
temp = b;
b = b*(2.0*i)/x - a;
a = temp;
/* scale b to avoid spurious overflow */
if (b > 0x1p500) {
a /= b;
t /= b;
b = 1.0;
}
}
}
z = j0(x);
w = j1(x);
if (fabs(z) >= fabs(w))
b = t*z/b;
else
b = t*w/a;
}
}
return sign ? -b : b;
}
/**
* Returns Bessel function of ð¥ of second kind of order ð.
*/
double yn(int n, double x)
{
uint32_t ix, lx, ib;
int nm1, sign, i;
double a, b, temp;
EXTRACT_WORDS(ix, lx, x);
sign = ix>>31;
ix &= 0x7fffffff;
if ((ix | (lx|-lx)>>31) > 0x7ff00000) /* nan */
return x;
if (sign && (ix|lx)!=0) /* x < 0 */
return 0/0.0;
if (ix == 0x7ff00000)
return 0.0;
if (n == 0)
return y0(x);
if (n < 0) {
nm1 = -(n+1);
sign = n&1;
} else {
nm1 = n-1;
sign = 0;
}
if (nm1 == 0)
return sign ? -y1(x) : y1(x);
if (ix >= 0x52d00000) { /* x > 2**302 */
/* (x >> n**2)
* Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi)
* Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi)
* Let s=sin(x), c=cos(x),
* xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then
*
* n sin(xn)*sqt2 cos(xn)*sqt2
* ----------------------------------
* 0 s-c c+s
* 1 -s-c -c+s
* 2 -s+c -c-s
* 3 s+c c-s
*/
switch(nm1&3) {
case 0: temp = -sin(x)-cos(x); break;
case 1: temp = -sin(x)+cos(x); break;
case 2: temp = sin(x)+cos(x); break;
default:
case 3: temp = sin(x)-cos(x); break;
}
b = invsqrtpi*temp/sqrt(x);
} else {
a = y0(x);
b = y1(x);
/* quit if b is -inf */
GET_HIGH_WORD(ib, b);
for (i=0; i<nm1 && ib!=0xfff00000; ){
i++;
temp = b;
b = (2.0*i/x)*b - a;
GET_HIGH_WORD(ib, b);
a = temp;
}
}
return sign ? -b : b;
}
| 10,092 | 320 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/catanl.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â OpenBSD /usr/src/lib/libm/src/s_catanl.c â
â â
â Copyright (c) 2008 Stephen L. Moshier <[email protected]> â
â â
â Permission to use, copy, modify, and distribute this software for any â
â purpose with or without fee is hereby granted, provided that the above â
â copyright notice and this permission notice appear in all copies. â
â â
â THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES â
â WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF â
â MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR â
â ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES â
â WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN â
â ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/complex.h"
#include "libc/math.h"
#include "libc/tinymath/complex.internal.h"
#if !(LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024)
asm(".ident\t\"\\n\\n\
OpenBSD libm (ISC License)\\n\
Copyright (c) 2008 Stephen L. Moshier <[email protected]>\"");
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
/*
* Complex circular arc tangent
*
*
* SYNOPSIS:
*
* long double complex catanl();
* long double complex z, w;
*
* w = catanl( z );
*
*
* DESCRIPTION:
*
* If
* z = x + iy,
*
* then
* 1 ( 2x )
* Re w = - arctan(-----------) + k PI
* 2 ( 2 2)
* (1 - x - y )
*
* ( 2 2)
* 1 (x + (y+1) )
* Im w = - log(------------)
* 4 ( 2 2)
* (x + (y-1) )
*
* Where k is an arbitrary integer.
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* DEC -10,+10 5900 1.3e-16 7.8e-18
* IEEE -10,+10 30000 2.3e-15 8.5e-17
* The check catan( ctan(z) ) = z, with |x| and |y| < PI/2,
* had peak relative error 1.5e-16, rms relative error
* 2.9e-17. See also clog().
*/
static const long double PIL = 3.141592653589793238462643383279502884197169L;
static const long double DP1 = 3.14159265358979323829596852490908531763125L;
static const long double DP2 = 1.6667485837041756656403424829301998703007e-19L;
static const long double DP3 = 1.8830410776607851167459095484560349402753e-39L;
static long double redupil(long double x)
{
long double t;
long i;
t = x / PIL;
if (t >= 0.0L)
t += 0.5L;
else
t -= 0.5L;
i = t; /* the multiple */
t = i;
t = ((x - t * DP1) - t * DP2) - t * DP3;
return t;
}
long double complex catanl(long double complex z)
{
long double complex w;
long double a, t, x, x2, y;
x = creall(z);
y = cimagl(z);
x2 = x * x;
a = 1.0L - x2 - (y * y);
t = atan2l(2.0L * x, a) * 0.5L;
w = redupil(t);
t = y - 1.0L;
a = x2 + (t * t);
t = y + 1.0L;
a = (x2 + (t * t)) / a;
w = CMPLXF(w, 0.25L * logl(a));
return w;
}
#endif /* long double is long */
| 4,300 | 124 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/hypotf.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.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
float hypotf(float x, float y)
{
union {float f; uint32_t i;} ux = {x}, uy = {y}, ut;
float_t z;
ux.i &= -1U>>1;
uy.i &= -1U>>1;
if (ux.i < uy.i) {
ut = ux;
ux = uy;
uy = ut;
}
x = ux.f;
y = uy.f;
if (uy.i == 0xff<<23)
return y;
if (ux.i >= 0xff<<23 || uy.i == 0 || ux.i - uy.i >= 25<<23)
return x + y;
z = 1;
if (ux.i >= (0x7f+60)<<23) {
z = 0x1p90f;
x *= 0x1p-90f;
y *= 0x1p-90f;
} else if (uy.i < (0x7f-60)<<23) {
z = 0x1p-90f;
x *= 0x1p90f;
y *= 0x1p90f;
}
return z*sqrtf((double)x*x + (double)y*y);
}
| 3,331 | 68 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/roundl.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
#include "libc/tinymath/internal.h"
#include "libc/tinymath/ldshape.internal.h"
#if !(LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024)
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
/**
* Rounds ð¥ to nearest integer, away from zero.
*/
long double roundl(long double x)
{
static const long double toint = 1/LDBL_EPSILON;
union ldshape u = {x};
int e = u.i.se & 0x7fff;
long double y;
if (e >= 0x3fff+LDBL_MANT_DIG-1)
return x;
if (u.i.se >> 15)
x = -x;
if (e < 0x3fff-1) {
FORCE_EVAL(x + toint);
return 0*u.f;
}
y = x + toint - toint - x;
if (y > 0.5)
y = y + x - 1;
else if (y <= -0.5)
y = y + x + 1;
else
y = y + x;
if (u.i.se >> 15)
y = -y;
return y;
}
#endif /* long double is long */
| 3,461 | 71 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/exp2f_data.internal.h | #ifndef COSMOPOLITAN_LIBC_TINYMATH_EXP2F_DATA_INTERNAL_H_
#define COSMOPOLITAN_LIBC_TINYMATH_EXP2F_DATA_INTERNAL_H_
#define EXP2F_TABLE_BITS 5
#define EXP2F_POLY_ORDER 3
#if !(__ASSEMBLER__ + __LINKER__ + 0)
COSMOPOLITAN_C_START_
extern _Hide const struct exp2f_data {
uint64_t tab[1 << EXP2F_TABLE_BITS];
double shift_scaled;
double poly[EXP2F_POLY_ORDER];
double shift;
double invln2_scaled;
double poly_scaled[EXP2F_POLY_ORDER];
} __exp2f_data;
COSMOPOLITAN_C_END_
#endif /* !(__ASSEMBLER__ + __LINKER__ + 0) */
#endif /* COSMOPOLITAN_LIBC_TINYMATH_EXP2F_DATA_INTERNAL_H_ */
| 594 | 22 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/emodl.h | #ifndef COSMOPOLITAN_LIBC_TINYMATH_EMODL_H_
#define COSMOPOLITAN_LIBC_TINYMATH_EMODL_H_
#include "libc/math.h"
#if !(__ASSEMBLER__ + __LINKER__ + 0)
/**
* Returns Euclidean floating-point division remainder.
*
* @return (ð¥ mod ð¦) â [0.,ð¦)
* @see fmodl()
*/
#define emodl(x, y) \
({ \
long double __x = x; \
long double __y = y; \
__x - fabsl(__y) * floorl(__x / fabsl(__y)); \
})
#endif /* !(__ASSEMBLER__ + __LINKER__ + 0) */
#endif /* COSMOPOLITAN_LIBC_TINYMATH_EMODL_H_ */
| 631 | 21 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/clog.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/complex.h"
#include "libc/math.h"
#include "libc/tinymath/complex.internal.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 */
// FIXME
/* log(z) = log(|z|) + i arg(z) */
double complex clog(double complex z)
{
double r, phi;
r = cabs(z);
phi = carg(z);
return CMPLX(log(r), phi);
}
| 3,023 | 52 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/casinl.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/complex.h"
#if !(LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024)
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
long double complex casinl(long double complex z)
{
long double complex w;
long double x, y;
x = creall(z);
y = cimagl(z);
w = CMPLXL(1.0 - (x - y)*(x + y), -2.0*x*y);
long double complex r = clogl(CMPLXL(-y, x) + csqrtl(w));
return CMPLXL(cimagl(r), -creall(r));
}
#endif /* long double is long */
| 3,146 | 49 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/csqrtl.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/complex.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
//FIXME
long double complex csqrtl(long double complex z)
{
return csqrt(z);
}
| 2,868 | 41 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/atan_data.c | /*-*- mode:c;indent-tabs-mode:nil;c-basic-offset:2;tab-width:8;coding:utf-8 -*-â
âvi: set net ft=c ts=2 sts=2 sw=2 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Optimized Routines â
â Copyright (c) 1999-2022, Arm Limited. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/tinymath/atan_data.internal.h"
asm(".ident\t\"\\n\\n\
Optimized Routines (MIT License)\\n\
Copyright 2022 ARM Limited\"");
asm(".include \"libc/disclaimer.inc\"");
/* clang-format off */
const struct atan_poly_data __atan_poly_data = {
.poly = {/* Coefficients of polynomial P such that atan(x)~x+x*P(x^2) on
[2**-1022, 1.0]. See atan.sollya for details of how these were
generated. */
-0x1.5555555555555p-2, 0x1.99999999996c1p-3, -0x1.2492492478f88p-3,
0x1.c71c71bc3951cp-4, -0x1.745d160a7e368p-4, 0x1.3b139b6a88ba1p-4,
-0x1.11100ee084227p-4, 0x1.e1d0f9696f63bp-5, -0x1.aebfe7b418581p-5,
0x1.842dbe9b0d916p-5, -0x1.5d30140ae5e99p-5, 0x1.338e31eb2fbbcp-5,
-0x1.00e6eece7de8p-5, 0x1.860897b29e5efp-6, -0x1.0051381722a59p-6,
0x1.14e9dc19a4a4ep-7, -0x1.d0062b42fe3bfp-9, 0x1.17739e210171ap-10,
-0x1.ab24da7be7402p-13, 0x1.358851160a528p-16}};
| 3,516 | 47 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/lgammaf.c | /*-*- mode:c;indent-tabs-mode:nil;c-basic-offset:2;tab-width:8;coding:utf-8 -*-â
âvi: set net ft=c ts=2 sts=2 sw=2 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ¡
â Copyright 2022 Justine Alexandra Roberts Tunney â
â â
â Permission to use, copy, modify, and/or distribute this software for â
â any purpose with or without fee is hereby granted, provided that the â
â above copyright notice and this permission notice appear in all copies. â
â â
â THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL â
â WARRANTIES WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED â
â WARRANTIES OF MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE â
â AUTHOR BE LIABLE FOR ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL â
â DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR â
â PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER â
â TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR â
â PERFORMANCE OF THIS SOFTWARE. â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
#include "libc/tinymath/kernel.internal.h"
float lgammaf(float x) {
return lgammaf_r(x, &signgam);
}
| 1,963 | 25 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/j1f.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
#include "libc/tinymath/complex.internal.h"
asm(".ident\t\"\\n\\n\
Double-precision math functions (MIT License)\\n\
Copyright 2018 ARM Limited\"");
asm(".include \"libc/disclaimer.inc\"");
// clang-format off
/* origin: FreeBSD /usr/src/lib/msun/src/e_j1f.c */
/*
* Conversion to float by Ian Lance Taylor, Cygnus Support, [email protected].
*/
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
static float ponef(float), qonef(float);
static const float
invsqrtpi = 5.6418961287e-01, /* 0x3f106ebb */
tpi = 6.3661974669e-01; /* 0x3f22f983 */
static float common(uint32_t ix, float x, int y1, int sign)
{
double z,s,c,ss,cc;
s = sinf(x);
if (y1)
s = -s;
c = cosf(x);
cc = s-c;
if (ix < 0x7f000000) {
ss = -s-c;
z = cosf(2*x);
if (s*c > 0)
cc = z/ss;
else
ss = z/cc;
if (ix < 0x58800000) {
if (y1)
ss = -ss;
cc = ponef(x)*cc-qonef(x)*ss;
}
}
if (sign)
cc = -cc;
return invsqrtpi*cc/sqrtf(x);
}
/* R0/S0 on [0,2] */
static const float
r00 = -6.2500000000e-02, /* 0xbd800000 */
r01 = 1.4070566976e-03, /* 0x3ab86cfd */
r02 = -1.5995563444e-05, /* 0xb7862e36 */
r03 = 4.9672799207e-08, /* 0x335557d2 */
s01 = 1.9153760746e-02, /* 0x3c9ce859 */
s02 = 1.8594678841e-04, /* 0x3942fab6 */
s03 = 1.1771846857e-06, /* 0x359dffc2 */
s04 = 5.0463624390e-09, /* 0x31ad6446 */
s05 = 1.2354227016e-11; /* 0x2d59567e */
float j1f(float x)
{
float z,r,s;
uint32_t ix;
int sign;
GET_FLOAT_WORD(ix, x);
sign = ix>>31;
ix &= 0x7fffffff;
if (ix >= 0x7f800000)
return 1/(x*x);
if (ix >= 0x40000000) /* |x| >= 2 */
return common(ix, fabsf(x), 0, sign);
if (ix >= 0x39000000) { /* |x| >= 2**-13 */
z = x*x;
r = z*(r00+z*(r01+z*(r02+z*r03)));
s = 1+z*(s01+z*(s02+z*(s03+z*(s04+z*s05))));
z = 0.5f + r/s;
} else
z = 0.5f;
return z*x;
}
static const float U0[5] = {
-1.9605709612e-01, /* 0xbe48c331 */
5.0443872809e-02, /* 0x3d4e9e3c */
-1.9125689287e-03, /* 0xbafaaf2a */
2.3525259166e-05, /* 0x37c5581c */
-9.1909917899e-08, /* 0xb3c56003 */
};
static const float V0[5] = {
1.9916731864e-02, /* 0x3ca3286a */
2.0255257550e-04, /* 0x3954644b */
1.3560879779e-06, /* 0x35b602d4 */
6.2274145840e-09, /* 0x31d5f8eb */
1.6655924903e-11, /* 0x2d9281cf */
};
float y1f(float x)
{
float z,u,v;
uint32_t ix;
GET_FLOAT_WORD(ix, x);
if ((ix & 0x7fffffff) == 0)
return -1/0.0f;
if (ix>>31)
return 0/0.0f;
if (ix >= 0x7f800000)
return 1/x;
if (ix >= 0x40000000) /* |x| >= 2.0 */
return common(ix,x,1,0);
if (ix < 0x33000000) /* x < 2**-25 */
return -tpi/x;
z = x*x;
u = U0[0]+z*(U0[1]+z*(U0[2]+z*(U0[3]+z*U0[4])));
v = 1.0f+z*(V0[0]+z*(V0[1]+z*(V0[2]+z*(V0[3]+z*V0[4]))));
return x*(u/v) + tpi*(j1f(x)*logf(x)-1.0f/x);
}
/* For x >= 8, the asymptotic expansions of pone is
* 1 + 15/128 s^2 - 4725/2^15 s^4 - ..., where s = 1/x.
* We approximate pone by
* pone(x) = 1 + (R/S)
* where R = pr0 + pr1*s^2 + pr2*s^4 + ... + pr5*s^10
* S = 1 + ps0*s^2 + ... + ps4*s^10
* and
* | pone(x)-1-R/S | <= 2 ** ( -60.06)
*/
static const float pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
0.0000000000e+00, /* 0x00000000 */
1.1718750000e-01, /* 0x3df00000 */
1.3239480972e+01, /* 0x4153d4ea */
4.1205184937e+02, /* 0x43ce06a3 */
3.8747453613e+03, /* 0x45722bed */
7.9144794922e+03, /* 0x45f753d6 */
};
static const float ps8[5] = {
1.1420736694e+02, /* 0x42e46a2c */
3.6509309082e+03, /* 0x45642ee5 */
3.6956207031e+04, /* 0x47105c35 */
9.7602796875e+04, /* 0x47bea166 */
3.0804271484e+04, /* 0x46f0a88b */
};
static const float pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
1.3199052094e-11, /* 0x2d68333f */
1.1718749255e-01, /* 0x3defffff */
6.8027510643e+00, /* 0x40d9b023 */
1.0830818176e+02, /* 0x42d89dca */
5.1763616943e+02, /* 0x440168b7 */
5.2871520996e+02, /* 0x44042dc6 */
};
static const float ps5[5] = {
5.9280597687e+01, /* 0x426d1f55 */
9.9140142822e+02, /* 0x4477d9b1 */
5.3532670898e+03, /* 0x45a74a23 */
7.8446904297e+03, /* 0x45f52586 */
1.5040468750e+03, /* 0x44bc0180 */
};
static const float pr3[6] = {
3.0250391081e-09, /* 0x314fe10d */
1.1718686670e-01, /* 0x3defffab */
3.9329774380e+00, /* 0x407bb5e7 */
3.5119403839e+01, /* 0x420c7a45 */
9.1055007935e+01, /* 0x42b61c2a */
4.8559066772e+01, /* 0x42423c7c */
};
static const float ps3[5] = {
3.4791309357e+01, /* 0x420b2a4d */
3.3676245117e+02, /* 0x43a86198 */
1.0468714600e+03, /* 0x4482dbe3 */
8.9081134033e+02, /* 0x445eb3ed */
1.0378793335e+02, /* 0x42cf936c */
};
static const float pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
1.0771083225e-07, /* 0x33e74ea8 */
1.1717621982e-01, /* 0x3deffa16 */
2.3685150146e+00, /* 0x401795c0 */
1.2242610931e+01, /* 0x4143e1bc */
1.7693971634e+01, /* 0x418d8d41 */
5.0735230446e+00, /* 0x40a25a4d */
};
static const float ps2[5] = {
2.1436485291e+01, /* 0x41ab7dec */
1.2529022980e+02, /* 0x42fa9499 */
2.3227647400e+02, /* 0x436846c7 */
1.1767937469e+02, /* 0x42eb5bd7 */
8.3646392822e+00, /* 0x4105d590 */
};
static float ponef(float x)
{
const float *p,*q;
float_t z,r,s;
uint32_t ix;
GET_FLOAT_WORD(ix, x);
ix &= 0x7fffffff;
if (ix >= 0x41000000){p = pr8; q = ps8;}
else if (ix >= 0x409173eb){p = pr5; q = ps5;}
else if (ix >= 0x4036d917){p = pr3; q = ps3;}
else /*ix >= 0x40000000*/ {p = pr2; q = ps2;}
z = 1.0f/(x*x);
r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
s = 1.0f+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4]))));
return 1.0f + r/s;
}
/* For x >= 8, the asymptotic expansions of qone is
* 3/8 s - 105/1024 s^3 - ..., where s = 1/x.
* We approximate pone by
* qone(x) = s*(0.375 + (R/S))
* where R = qr1*s^2 + qr2*s^4 + ... + qr5*s^10
* S = 1 + qs1*s^2 + ... + qs6*s^12
* and
* | qone(x)/s -0.375-R/S | <= 2 ** ( -61.13)
*/
static const float qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
0.0000000000e+00, /* 0x00000000 */
-1.0253906250e-01, /* 0xbdd20000 */
-1.6271753311e+01, /* 0xc1822c8d */
-7.5960174561e+02, /* 0xc43de683 */
-1.1849806641e+04, /* 0xc639273a */
-4.8438511719e+04, /* 0xc73d3683 */
};
static const float qs8[6] = {
1.6139537048e+02, /* 0x43216537 */
7.8253862305e+03, /* 0x45f48b17 */
1.3387534375e+05, /* 0x4802bcd6 */
7.1965775000e+05, /* 0x492fb29c */
6.6660125000e+05, /* 0x4922be94 */
-2.9449025000e+05, /* 0xc88fcb48 */
};
static const float qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
-2.0897993405e-11, /* 0xadb7d219 */
-1.0253904760e-01, /* 0xbdd1fffe */
-8.0564479828e+00, /* 0xc100e736 */
-1.8366960144e+02, /* 0xc337ab6b */
-1.3731937256e+03, /* 0xc4aba633 */
-2.6124443359e+03, /* 0xc523471c */
};
static const float qs5[6] = {
8.1276550293e+01, /* 0x42a28d98 */
1.9917987061e+03, /* 0x44f8f98f */
1.7468484375e+04, /* 0x468878f8 */
4.9851425781e+04, /* 0x4742bb6d */
2.7948074219e+04, /* 0x46da5826 */
-4.7191835938e+03, /* 0xc5937978 */
};
static const float qr3[6] = {
-5.0783124372e-09, /* 0xb1ae7d4f */
-1.0253783315e-01, /* 0xbdd1ff5b */
-4.6101160049e+00, /* 0xc0938612 */
-5.7847221375e+01, /* 0xc267638e */
-2.2824453735e+02, /* 0xc3643e9a */
-2.1921012878e+02, /* 0xc35b35cb */
};
static const float qs3[6] = {
4.7665153503e+01, /* 0x423ea91e */
6.7386511230e+02, /* 0x4428775e */
3.3801528320e+03, /* 0x45534272 */
5.5477290039e+03, /* 0x45ad5dd5 */
1.9031191406e+03, /* 0x44ede3d0 */
-1.3520118713e+02, /* 0xc3073381 */
};
static const float qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
-1.7838172539e-07, /* 0xb43f8932 */
-1.0251704603e-01, /* 0xbdd1f475 */
-2.7522056103e+00, /* 0xc0302423 */
-1.9663616180e+01, /* 0xc19d4f16 */
-4.2325313568e+01, /* 0xc2294d1f */
-2.1371921539e+01, /* 0xc1aaf9b2 */
};
static const float qs2[6] = {
2.9533363342e+01, /* 0x41ec4454 */
2.5298155212e+02, /* 0x437cfb47 */
7.5750280762e+02, /* 0x443d602e */
7.3939318848e+02, /* 0x4438d92a */
1.5594900513e+02, /* 0x431bf2f2 */
-4.9594988823e+00, /* 0xc09eb437 */
};
static float qonef(float x)
{
const float *p,*q;
float_t s,r,z;
uint32_t ix;
GET_FLOAT_WORD(ix, x);
ix &= 0x7fffffff;
if (ix >= 0x41000000){p = qr8; q = qs8;}
else if (ix >= 0x409173eb){p = qr5; q = qs5;}
else if (ix >= 0x4036d917){p = qr3; q = qs3;}
else /*ix >= 0x40000000*/ {p = qr2; q = qs2;}
z = 1.0f/(x*x);
r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
s = 1.0f+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5])))));
return (.375f + r/s)/x;
}
| 11,431 | 344 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/acoshf.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.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 */
/**
* Returns inverse hyperbolic cosine of ð¥.
* @define acosh(x) = log(x + sqrt(x*x-1))
*/
float acoshf(float x)
{
union {float f; uint32_t i;} u = {x};
uint32_t a = u.i & 0x7fffffff;
if (a < 0x3f800000+(1<<23))
/* |x| < 2, invalid if x < 1 */
/* up to 2ulp error in [1,1.125] */
return log1pf(x-1 + sqrtf((x-1)*(x-1)+2*(x-1)));
if (u.i < 0x3f800000+(12<<23))
/* 2 <= x < 0x1p12 */
return logf(2*x - 1/(x+sqrtf(x*x-1)));
/* x >= 0x1p12 or x <= -2 or nan */
return logf(x) + 0.693147180559945309417232121458176568f;
}
| 3,328 | 55 | jart/cosmopolitan | false |
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