From 8a236433a26437059ec8d3a31b75bf08b5fd22d5 Mon Sep 17 00:00:00 2001 From: dosisod <39638017+dosisod@users.noreply.github.com> Date: Wed, 17 Mar 2021 20:05:12 -0700 Subject: [PATCH] Add more math functions (#128) --- libc/tinymath/erff.c | 220 +++++++++++++++++++++++++++++++++++ libc/tinymath/fdim.c | 45 ++++++++ libc/tinymath/fdimf.c | 45 ++++++++ libc/tinymath/fdiml.c | 45 ++++++++ libc/tinymath/fma.c | 225 ++++++++++++++++++++++++++++++++++++ libc/tinymath/frexpf.c | 57 +++++++++ libc/tinymath/frexpl.c | 65 +++++++++++ libc/tinymath/nexttoward.c | 76 ++++++++++++ libc/tinymath/nexttowardf.c | 76 ++++++++++++ libc/tinymath/nexttowardl.c | 41 +++++++ libc/tinymath/remquo.c | 116 +++++++++++++++++++ libc/tinymath/remquof.c | 116 +++++++++++++++++++ libc/tinymath/remquol.c | 122 +++++++++++++++++++ 13 files changed, 1249 insertions(+) create mode 100644 libc/tinymath/erff.c create mode 100644 libc/tinymath/fdim.c create mode 100644 libc/tinymath/fdimf.c create mode 100644 libc/tinymath/fdiml.c create mode 100644 libc/tinymath/fma.c create mode 100644 libc/tinymath/frexpf.c create mode 100644 libc/tinymath/frexpl.c create mode 100644 libc/tinymath/nexttoward.c create mode 100644 libc/tinymath/nexttowardf.c create mode 100644 libc/tinymath/nexttowardl.c create mode 100644 libc/tinymath/remquo.c create mode 100644 libc/tinymath/remquof.c create mode 100644 libc/tinymath/remquol.c diff --git a/libc/tinymath/erff.c b/libc/tinymath/erff.c new file mode 100644 index 000000000..1e0e1361c --- /dev/null +++ b/libc/tinymath/erff.c @@ -0,0 +1,220 @@ +/*-*- mode:c;indent-tabs-mode:nil;c-basic-offset:2;tab-width:8;coding:utf-8 -*-│ +│vi: set net ft=c ts=2 sts=2 sw=2 fenc=utf-8 :vi│ +╚──────────────────────────────────────────────────────────────────────────────╝ +│ │ +│ Musl Libc │ +│ Copyright © 2005-2020 Rich Felker, et al. │ +│ │ +│ Permission is hereby granted, free of charge, to any person obtaining │ +│ a copy of this software and associated documentation files (the │ +│ "Software"), to deal in the Software without restriction, including │ +│ without limitation the rights to use, copy, modify, merge, publish, │ +│ distribute, sublicense, and/or sell copies of the Software, and to │ +│ permit persons to whom the Software is furnished to do so, subject to │ +│ the following conditions: │ +│ │ +│ The above copyright notice and this permission notice shall be │ +│ included in all copies or substantial portions of the Software. │ +│ │ +│ THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, │ +│ EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF │ +│ MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. │ +│ IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY │ +│ CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, │ +│ TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE │ +│ SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. │ +│ │ +╚─────────────────────────────────────────────────────────────────────────────*/ + +#include "libc/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 2005-2020 Rich Felker, et. al.\""); +asm(".include \"libc/disclaimer.inc\""); + +/* clang-format off */ +/* origin: FreeBSD /usr/src/lib/msun/src/s_erff.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. + * ==================================================== + */ + +#define asuint(f) ((union{float _f; uint32_t _i;}){f})._i +#define asfloat(i) ((union{uint32_t _i; float _f;}){i})._f + +static const float +erx = 8.4506291151e-01, /* 0x3f58560b */ +/* + * Coefficients for approximation to erf on [0,0.84375] + */ +efx8 = 1.0270333290e+00, /* 0x3f8375d4 */ +pp0 = 1.2837916613e-01, /* 0x3e0375d4 */ +pp1 = -3.2504209876e-01, /* 0xbea66beb */ +pp2 = -2.8481749818e-02, /* 0xbce9528f */ +pp3 = -5.7702702470e-03, /* 0xbbbd1489 */ +pp4 = -2.3763017452e-05, /* 0xb7c756b1 */ +qq1 = 3.9791721106e-01, /* 0x3ecbbbce */ +qq2 = 6.5022252500e-02, /* 0x3d852a63 */ +qq3 = 5.0813062117e-03, /* 0x3ba68116 */ +qq4 = 1.3249473704e-04, /* 0x390aee49 */ +qq5 = -3.9602282413e-06, /* 0xb684e21a */ +/* + * Coefficients for approximation to erf in [0.84375,1.25] + */ +pa0 = -2.3621185683e-03, /* 0xbb1acdc6 */ +pa1 = 4.1485610604e-01, /* 0x3ed46805 */ +pa2 = -3.7220788002e-01, /* 0xbebe9208 */ +pa3 = 3.1834661961e-01, /* 0x3ea2fe54 */ +pa4 = -1.1089469492e-01, /* 0xbde31cc2 */ +pa5 = 3.5478305072e-02, /* 0x3d1151b3 */ +pa6 = -2.1663755178e-03, /* 0xbb0df9c0 */ +qa1 = 1.0642088205e-01, /* 0x3dd9f331 */ +qa2 = 5.4039794207e-01, /* 0x3f0a5785 */ +qa3 = 7.1828655899e-02, /* 0x3d931ae7 */ +qa4 = 1.2617121637e-01, /* 0x3e013307 */ +qa5 = 1.3637083583e-02, /* 0x3c5f6e13 */ +qa6 = 1.1984500103e-02, /* 0x3c445aa3 */ +/* + * Coefficients for approximation to erfc in [1.25,1/0.35] + */ +ra0 = -9.8649440333e-03, /* 0xbc21a093 */ +ra1 = -6.9385856390e-01, /* 0xbf31a0b7 */ +ra2 = -1.0558626175e+01, /* 0xc128f022 */ +ra3 = -6.2375331879e+01, /* 0xc2798057 */ +ra4 = -1.6239666748e+02, /* 0xc322658c */ +ra5 = -1.8460508728e+02, /* 0xc3389ae7 */ +ra6 = -8.1287437439e+01, /* 0xc2a2932b */ +ra7 = -9.8143291473e+00, /* 0xc11d077e */ +sa1 = 1.9651271820e+01, /* 0x419d35ce */ +sa2 = 1.3765776062e+02, /* 0x4309a863 */ +sa3 = 4.3456588745e+02, /* 0x43d9486f */ +sa4 = 6.4538726807e+02, /* 0x442158c9 */ +sa5 = 4.2900814819e+02, /* 0x43d6810b */ +sa6 = 1.0863500214e+02, /* 0x42d9451f */ +sa7 = 6.5702495575e+00, /* 0x40d23f7c */ +sa8 = -6.0424413532e-02, /* 0xbd777f97 */ +/* + * Coefficients for approximation to erfc in [1/.35,28] + */ +rb0 = -9.8649431020e-03, /* 0xbc21a092 */ +rb1 = -7.9928326607e-01, /* 0xbf4c9dd4 */ +rb2 = -1.7757955551e+01, /* 0xc18e104b */ +rb3 = -1.6063638306e+02, /* 0xc320a2ea */ +rb4 = -6.3756646729e+02, /* 0xc41f6441 */ +rb5 = -1.0250950928e+03, /* 0xc480230b */ +rb6 = -4.8351919556e+02, /* 0xc3f1c275 */ +sb1 = 3.0338060379e+01, /* 0x41f2b459 */ +sb2 = 3.2579251099e+02, /* 0x43a2e571 */ +sb3 = 1.5367296143e+03, /* 0x44c01759 */ +sb4 = 3.1998581543e+03, /* 0x4547fdbb */ +sb5 = 2.5530502930e+03, /* 0x451f90ce */ +sb6 = 4.7452853394e+02, /* 0x43ed43a7 */ +sb7 = -2.2440952301e+01; /* 0xc1b38712 */ + +static float erfc1(float x) +{ + float_t s,P,Q; + + s = fabsf(x) - 1; + P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6))))); + Q = 1+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6))))); + return 1 - erx - P/Q; +} + +static float erfc2(uint32_t ix, float x) +{ + float_t s,R,S; + float z; + + if (ix < 0x3fa00000) /* |x| < 1.25 */ + return erfc1(x); + + x = fabsf(x); + s = 1/(x*x); + if (ix < 0x4036db6d) { /* |x| < 1/0.35 */ + R = ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*( + ra5+s*(ra6+s*ra7)))))); + S = 1.0f+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*( + sa5+s*(sa6+s*(sa7+s*sa8))))))); + } else { /* |x| >= 1/0.35 */ + R = rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*( + rb5+s*rb6))))); + S = 1.0f+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*( + sb5+s*(sb6+s*sb7)))))); + } + ix = asuint(x); + z = asfloat(ix&0xffffe000); + return expf(-z*z - 0.5625f) * expf((z-x)*(z+x) + R/S)/x; +} + +float erff(float x) +{ + float r,s,z,y; + uint32_t ix; + int sign; + + ix = asuint(x); + sign = ix>>31; + ix &= 0x7fffffff; + if (ix >= 0x7f800000) { + /* erf(nan)=nan, erf(+-inf)=+-1 */ + return 1-2*sign + 1/x; + } + if (ix < 0x3f580000) { /* |x| < 0.84375 */ + if (ix < 0x31800000) { /* |x| < 2**-28 */ + /*avoid underflow */ + return 0.125f*(8*x + efx8*x); + } + z = x*x; + r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4))); + s = 1+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5)))); + y = r/s; + return x + x*y; + } + if (ix < 0x40c00000) /* |x| < 6 */ + y = 1 - erfc2(ix,x); + else + y = 1 - 0x1p-120f; + return sign ? -y : y; +} + +float erfcf(float x) +{ + float r,s,z,y; + uint32_t ix; + int sign; + + ix = asuint(x); + sign = ix>>31; + ix &= 0x7fffffff; + if (ix >= 0x7f800000) { + /* erfc(nan)=nan, erfc(+-inf)=0,2 */ + return 2*sign + 1/x; + } + + if (ix < 0x3f580000) { /* |x| < 0.84375 */ + if (ix < 0x23800000) /* |x| < 2**-56 */ + return 1.0f - x; + z = x*x; + r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4))); + s = 1.0f+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5)))); + y = r/s; + if (sign || ix < 0x3e800000) /* x < 1/4 */ + return 1.0f - (x+x*y); + return 0.5f - (x - 0.5f + x*y); + } + if (ix < 0x41e00000) { /* |x| < 28 */ + return sign ? 2 - erfc2(ix,x) : erfc2(ix,x); + } + return sign ? 2 - 0x1p-120f : 0x1p-120f*0x1p-120f; +} diff --git a/libc/tinymath/fdim.c b/libc/tinymath/fdim.c new file mode 100644 index 000000000..94889578f --- /dev/null +++ b/libc/tinymath/fdim.c @@ -0,0 +1,45 @@ +/*-*- mode:c;indent-tabs-mode:nil;c-basic-offset:2;tab-width:8;coding:utf-8 -*-│ +│vi: set net ft=c ts=2 sts=2 sw=2 fenc=utf-8 :vi│ +╚──────────────────────────────────────────────────────────────────────────────╝ +│ │ +│ Musl Libc │ +│ Copyright © 2005-2020 Rich Felker, et al. │ +│ │ +│ Permission is hereby granted, free of charge, to any person obtaining │ +│ a copy of this software and associated documentation files (the │ +│ "Software"), to deal in the Software without restriction, including │ +│ without limitation the rights to use, copy, modify, merge, publish, │ +│ distribute, sublicense, and/or sell copies of the Software, and to │ +│ permit persons to whom the Software is furnished to do so, subject to │ +│ the following conditions: │ +│ │ +│ The above copyright notice and this permission notice shall be │ +│ included in all copies or substantial portions of the Software. │ +│ │ +│ THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, │ +│ EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF │ +│ MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. │ +│ IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY │ +│ CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, │ +│ TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE │ +│ SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. │ +│ │ +╚─────────────────────────────────────────────────────────────────────────────*/ + +#include "libc/math.h" + +asm(".ident\t\"\\n\\n\ +Musl libc (MIT License)\\n\ +Copyright 2005-2020 Rich Felker, et. al.\""); +asm(".include \"libc/disclaimer.inc\""); + +/* clang-format off */ + +double fdim(double x, double y) +{ + if (isnan(x)) + return x; + if (isnan(y)) + return y; + return x > y ? x - y : 0; +} diff --git a/libc/tinymath/fdimf.c b/libc/tinymath/fdimf.c new file mode 100644 index 000000000..1985ac1b2 --- /dev/null +++ b/libc/tinymath/fdimf.c @@ -0,0 +1,45 @@ +/*-*- mode:c;indent-tabs-mode:nil;c-basic-offset:2;tab-width:8;coding:utf-8 -*-│ +│vi: set net ft=c ts=2 sts=2 sw=2 fenc=utf-8 :vi│ +╚──────────────────────────────────────────────────────────────────────────────╝ +│ │ +│ Musl Libc │ +│ Copyright © 2005-2020 Rich Felker, et al. │ +│ │ +│ Permission is hereby granted, free of charge, to any person obtaining │ +│ a copy of this software and associated documentation files (the │ +│ "Software"), to deal in the Software without restriction, including │ +│ without limitation the rights to use, copy, modify, merge, publish, │ +│ distribute, sublicense, and/or sell copies of the Software, and to │ +│ permit persons to whom the Software is furnished to do so, subject to │ +│ the following conditions: │ +│ │ +│ The above copyright notice and this permission notice shall be │ +│ included in all copies or substantial portions of the Software. │ +│ │ +│ THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, │ +│ EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF │ +│ MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. │ +│ IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY │ +│ CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, │ +│ TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE │ +│ SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. │ +│ │ +╚─────────────────────────────────────────────────────────────────────────────*/ + +#include "libc/math.h" + +asm(".ident\t\"\\n\\n\ +Musl libc (MIT License)\\n\ +Copyright 2005-2020 Rich Felker, et. al.\""); +asm(".include \"libc/disclaimer.inc\""); + +/* clang-format off */ + +float fdimf(float x, float y) +{ + if (isnan(x)) + return x; + if (isnan(y)) + return y; + return x > y ? x - y : 0; +} diff --git a/libc/tinymath/fdiml.c b/libc/tinymath/fdiml.c new file mode 100644 index 000000000..2ad277391 --- /dev/null +++ b/libc/tinymath/fdiml.c @@ -0,0 +1,45 @@ +/*-*- mode:c;indent-tabs-mode:nil;c-basic-offset:2;tab-width:8;coding:utf-8 -*-│ +│vi: set net ft=c ts=2 sts=2 sw=2 fenc=utf-8 :vi│ +╚──────────────────────────────────────────────────────────────────────────────╝ +│ │ +│ Musl Libc │ +│ Copyright © 2005-2020 Rich Felker, et al. │ +│ │ +│ Permission is hereby granted, free of charge, to any person obtaining │ +│ a copy of this software and associated documentation files (the │ +│ "Software"), to deal in the Software without restriction, including │ +│ without limitation the rights to use, copy, modify, merge, publish, │ +│ distribute, sublicense, and/or sell copies of the Software, and to │ +│ permit persons to whom the Software is furnished to do so, subject to │ +│ the following conditions: │ +│ │ +│ The above copyright notice and this permission notice shall be │ +│ included in all copies or substantial portions of the Software. │ +│ │ +│ THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, │ +│ EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF │ +│ MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. │ +│ IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY │ +│ CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, │ +│ TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE │ +│ SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. │ +│ │ +╚─────────────────────────────────────────────────────────────────────────────*/ + +#include "libc/math.h" + +asm(".ident\t\"\\n\\n\ +Musl libc (MIT License)\\n\ +Copyright 2005-2020 Rich Felker, et. al.\""); +asm(".include \"libc/disclaimer.inc\""); + +/* clang-format off */ + +long double fdiml(long double x, long double y) +{ + if (isnan(x)) + return x; + if (isnan(y)) + return y; + return x > y ? x - y : 0; +} diff --git a/libc/tinymath/fma.c b/libc/tinymath/fma.c new file mode 100644 index 000000000..071da700d --- /dev/null +++ b/libc/tinymath/fma.c @@ -0,0 +1,225 @@ +/*-*- mode:c;indent-tabs-mode:nil;c-basic-offset:2;tab-width:8;coding:utf-8 -*-│ +│vi: set net ft=c ts=2 sts=2 sw=2 fenc=utf-8 :vi│ +╚──────────────────────────────────────────────────────────────────────────────╝ +│ │ +│ Musl Libc │ +│ Copyright © 2005-2020 Rich Felker, et al. │ +│ │ +│ Permission is hereby granted, free of charge, to any person obtaining │ +│ a copy of this software and associated documentation files (the │ +│ "Software"), to deal in the Software without restriction, including │ +│ without limitation the rights to use, copy, modify, merge, publish, │ +│ distribute, sublicense, and/or sell copies of the Software, and to │ +│ permit persons to whom the Software is furnished to do so, subject to │ +│ the following conditions: │ +│ │ +│ The above copyright notice and this permission notice shall be │ +│ included in all copies or substantial portions of the Software. │ +│ │ +│ THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, │ +│ EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF │ +│ MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. │ +│ IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY │ +│ CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, │ +│ TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE │ +│ SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. │ +│ │ +╚─────────────────────────────────────────────────────────────────────────────*/ + +#include "libc/math.h" + +asm(".ident\t\"\\n\\n\ +Musl libc (MIT License)\\n\ +Copyright 2005-2020 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) +{ + 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); +} + +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); +} + +double fma(double x, double y, double z) +{ + /* 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<>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<>64-d | !!(rlo<>1 | (rlo&1); + else + rhi = rlo<>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); +} diff --git a/libc/tinymath/frexpf.c b/libc/tinymath/frexpf.c new file mode 100644 index 000000000..bdeaf208d --- /dev/null +++ b/libc/tinymath/frexpf.c @@ -0,0 +1,57 @@ +/*-*- mode:c;indent-tabs-mode:nil;c-basic-offset:2;tab-width:8;coding:utf-8 -*-│ +│vi: set net ft=c ts=2 sts=2 sw=2 fenc=utf-8 :vi│ +╚──────────────────────────────────────────────────────────────────────────────╝ +│ │ +│ Musl Libc │ +│ Copyright © 2005-2020 Rich Felker, et al. │ +│ │ +│ Permission is hereby granted, free of charge, to any person obtaining │ +│ a copy of this software and associated documentation files (the │ +│ "Software"), to deal in the Software without restriction, including │ +│ without limitation the rights to use, copy, modify, merge, publish, │ +│ distribute, sublicense, and/or sell copies of the Software, and to │ +│ permit persons to whom the Software is furnished to do so, subject to │ +│ the following conditions: │ +│ │ +│ The above copyright notice and this permission notice shall be │ +│ included in all copies or substantial portions of the Software. │ +│ │ +│ THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, │ +│ EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF │ +│ MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. │ +│ IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY │ +│ CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, │ +│ TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE │ +│ SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. │ +│ │ +╚─────────────────────────────────────────────────────────────────────────────*/ + +#include "libc/math.h" + +asm(".ident\t\"\\n\\n\ +Musl libc (MIT License)\\n\ +Copyright 2005-2020 Rich Felker, et. al.\""); +asm(".include \"libc/disclaimer.inc\""); + +/* clang-format off */ + +float frexpf(float x, int *e) +{ + union { float f; uint32_t i; } y = { x }; + int ee = y.i>>23 & 0xff; + + if (!ee) { + if (x) { + x = frexpf(x*0x1p64, e); + *e -= 64; + } else *e = 0; + return x; + } else if (ee == 0xff) { + return x; + } + + *e = ee - 0x7e; + y.i &= 0x807ffffful; + y.i |= 0x3f000000ul; + return y.f; +} diff --git a/libc/tinymath/frexpl.c b/libc/tinymath/frexpl.c new file mode 100644 index 000000000..b8a044efb --- /dev/null +++ b/libc/tinymath/frexpl.c @@ -0,0 +1,65 @@ +/*-*- mode:c;indent-tabs-mode:nil;c-basic-offset:2;tab-width:8;coding:utf-8 -*-│ +│vi: set net ft=c ts=2 sts=2 sw=2 fenc=utf-8 :vi│ +╚──────────────────────────────────────────────────────────────────────────────╝ +│ │ +│ Musl Libc │ +│ Copyright © 2005-2014 Rich Felker, et al. │ +│ │ +│ Permission is hereby granted, free of charge, to any person obtaining │ +│ a copy of this software and associated documentation files (the │ +│ "Software"), to deal in the Software without restriction, including │ +│ without limitation the rights to use, copy, modify, merge, publish, │ +│ distribute, sublicense, and/or sell copies of the Software, and to │ +│ permit persons to whom the Software is furnished to do so, subject to │ +│ the following conditions: │ +│ │ +│ The above copyright notice and this permission notice shall be │ +│ included in all copies or substantial portions of the Software. │ +│ │ +│ THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, │ +│ EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF │ +│ MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. │ +│ IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY │ +│ CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, │ +│ TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE │ +│ SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. │ +│ │ +╚─────────────────────────────────────────────────────────────────────────────*/ + +#include "libc/math.h" + +asm(".ident\t\"\\n\\n\ +Musl libc (MIT License)\\n\ +Copyright 2005-2020 Rich Felker, et. al.\""); +asm(".include \"libc/disclaimer.inc\""); + +/* clang-format off */ + +union ldshape { + long double f; + struct { + uint64_t m; + uint16_t se; + } i; +}; + +long double frexpl(long double x, int *e) +{ + union ldshape u = {x}; + int ee = u.i.se & 0x7fff; + + if (!ee) { + if (x) { + x = frexpl(x*0x1p120, e); + *e -= 120; + } else *e = 0; + return x; + } else if (ee == 0x7fff) { + return x; + } + + *e = ee - 0x3ffe; + u.i.se &= 0x8000; + u.i.se |= 0x3ffe; + return u.f; +} diff --git a/libc/tinymath/nexttoward.c b/libc/tinymath/nexttoward.c new file mode 100644 index 000000000..757645835 --- /dev/null +++ b/libc/tinymath/nexttoward.c @@ -0,0 +1,76 @@ +/*-*- mode:c;indent-tabs-mode:nil;c-basic-offset:2;tab-width:8;coding:utf-8 -*-│ +│vi: set net ft=c ts=2 sts=2 sw=2 fenc=utf-8 :vi│ +╚──────────────────────────────────────────────────────────────────────────────╝ +│ │ +│ Musl Libc │ +│ Copyright © 2005-2020 Rich Felker, et al. │ +│ │ +│ Permission is hereby granted, free of charge, to any person obtaining │ +│ a copy of this software and associated documentation files (the │ +│ "Software"), to deal in the Software without restriction, including │ +│ without limitation the rights to use, copy, modify, merge, publish, │ +│ distribute, sublicense, and/or sell copies of the Software, and to │ +│ permit persons to whom the Software is furnished to do so, subject to │ +│ the following conditions: │ +│ │ +│ The above copyright notice and this permission notice shall be │ +│ included in all copies or substantial portions of the Software. │ +│ │ +│ THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, │ +│ EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF │ +│ MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. │ +│ IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY │ +│ CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, │ +│ TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE │ +│ SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. │ +│ │ +╚─────────────────────────────────────────────────────────────────────────────*/ + +#include "libc/math.h" + +asm(".ident\t\"\\n\\n\ +Musl libc (MIT License)\\n\ +Copyright 2005-2020 Rich Felker, et. al.\""); +asm(".include \"libc/disclaimer.inc\""); + +/* clang-format off */ + +static inline void fp_force_eval(double x) +{ + volatile double y; + y = x; +} + +double nexttoward(double x, long double y) +{ + union {double f; uint64_t i;} ux = {x}; + int e; + + if (isnan(x) || isnan(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) + fp_force_eval(x+x); + /* raise underflow if ux.f is subnormal or zero */ + if (e == 0) + fp_force_eval(x*x + ux.f*ux.f); + return ux.f; +} diff --git a/libc/tinymath/nexttowardf.c b/libc/tinymath/nexttowardf.c new file mode 100644 index 000000000..721832cef --- /dev/null +++ b/libc/tinymath/nexttowardf.c @@ -0,0 +1,76 @@ +/*-*- mode:c;indent-tabs-mode:nil;c-basic-offset:2;tab-width:8;coding:utf-8 -*-│ +│vi: set net ft=c ts=2 sts=2 sw=2 fenc=utf-8 :vi│ +╚──────────────────────────────────────────────────────────────────────────────╝ +│ │ +│ Musl Libc │ +│ Copyright © 2005-2020 Rich Felker, et al. │ +│ │ +│ Permission is hereby granted, free of charge, to any person obtaining │ +│ a copy of this software and associated documentation files (the │ +│ "Software"), to deal in the Software without restriction, including │ +│ without limitation the rights to use, copy, modify, merge, publish, │ +│ distribute, sublicense, and/or sell copies of the Software, and to │ +│ permit persons to whom the Software is furnished to do so, subject to │ +│ the following conditions: │ +│ │ +│ The above copyright notice and this permission notice shall be │ +│ included in all copies or substantial portions of the Software. │ +│ │ +│ THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, │ +│ EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF │ +│ MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. │ +│ IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY │ +│ CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, │ +│ TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE │ +│ SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. │ +│ │ +╚─────────────────────────────────────────────────────────────────────────────*/ + +#include "libc/math.h" + +asm(".ident\t\"\\n\\n\ +Musl libc (MIT License)\\n\ +Copyright 2005-2020 Rich Felker, et. al.\""); +asm(".include \"libc/disclaimer.inc\""); + +/* clang-format off */ + +static inline void fp_force_evalf(float x) +{ + volatile float y; + y = x; +} + +float nexttowardf(float x, long double y) +{ + union {float f; uint32_t i;} ux = {x}; + uint32_t e; + + if (isnan(x) || isnan(y)) + return x + y; + if (x == y) + return y; + if (x == 0) { + ux.i = 1; + if (signbit(y)) + ux.i |= 0x80000000; + } else if (x < y) { + if (signbit(x)) + ux.i--; + else + ux.i++; + } else { + if (signbit(x)) + ux.i++; + else + ux.i--; + } + e = ux.i & 0x7f800000; + /* raise overflow if ux.f is infinite and x is finite */ + if (e == 0x7f800000) + fp_force_evalf(x+x); + /* raise underflow if ux.f is subnormal or zero */ + if (e == 0) + fp_force_evalf(x*x + ux.f*ux.f); + return ux.f; +} diff --git a/libc/tinymath/nexttowardl.c b/libc/tinymath/nexttowardl.c new file mode 100644 index 000000000..a4e443801 --- /dev/null +++ b/libc/tinymath/nexttowardl.c @@ -0,0 +1,41 @@ +/*-*- mode:c;indent-tabs-mode:nil;c-basic-offset:2;tab-width:8;coding:utf-8 -*-│ +│vi: set net ft=c ts=2 sts=2 sw=2 fenc=utf-8 :vi│ +╚──────────────────────────────────────────────────────────────────────────────╝ +│ │ +│ Musl Libc │ +│ Copyright © 2005-2020 Rich Felker, et al. │ +│ │ +│ Permission is hereby granted, free of charge, to any person obtaining │ +│ a copy of this software and associated documentation files (the │ +│ "Software"), to deal in the Software without restriction, including │ +│ without limitation the rights to use, copy, modify, merge, publish, │ +│ distribute, sublicense, and/or sell copies of the Software, and to │ +│ permit persons to whom the Software is furnished to do so, subject to │ +│ the following conditions: │ +│ │ +│ The above copyright notice and this permission notice shall be │ +│ included in all copies or substantial portions of the Software. │ +│ │ +│ THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, │ +│ EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF │ +│ MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. │ +│ IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY │ +│ CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, │ +│ TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE │ +│ SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. │ +│ │ +╚─────────────────────────────────────────────────────────────────────────────*/ + +#include "libc/math.h" + +asm(".ident\t\"\\n\\n\ +Musl libc (MIT License)\\n\ +Copyright 2005-2020 Rich Felker, et. al.\""); +asm(".include \"libc/disclaimer.inc\""); + +/* clang-format off */ + +long double nexttowardl(long double x, long double y) +{ + return nextafterl(x, y); +} diff --git a/libc/tinymath/remquo.c b/libc/tinymath/remquo.c new file mode 100644 index 000000000..9fb2d714c --- /dev/null +++ b/libc/tinymath/remquo.c @@ -0,0 +1,116 @@ +/*-*- mode:c;indent-tabs-mode:nil;c-basic-offset:2;tab-width:8;coding:utf-8 -*-│ +│vi: set net ft=c ts=2 sts=2 sw=2 fenc=utf-8 :vi│ +╚──────────────────────────────────────────────────────────────────────────────╝ +│ │ +│ Musl Libc │ +│ Copyright © 2005-2020 Rich Felker, et al. │ +│ │ +│ Permission is hereby granted, free of charge, to any person obtaining │ +│ a copy of this software and associated documentation files (the │ +│ "Software"), to deal in the Software without restriction, including │ +│ without limitation the rights to use, copy, modify, merge, publish, │ +│ distribute, sublicense, and/or sell copies of the Software, and to │ +│ permit persons to whom the Software is furnished to do so, subject to │ +│ the following conditions: │ +│ │ +│ The above copyright notice and this permission notice shall be │ +│ included in all copies or substantial portions of the Software. │ +│ │ +│ THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, │ +│ EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF │ +│ MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. │ +│ IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY │ +│ CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, │ +│ TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE │ +│ SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. │ +│ │ +╚─────────────────────────────────────────────────────────────────────────────*/ + +#include "libc/math.h" + +asm(".ident\t\"\\n\\n\ +Musl libc (MIT License)\\n\ +Copyright 2005-2020 Rich Felker, et. al.\""); +asm(".include \"libc/disclaimer.inc\""); + +/* clang-format off */ + +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; +} diff --git a/libc/tinymath/remquof.c b/libc/tinymath/remquof.c new file mode 100644 index 000000000..a7f738f4e --- /dev/null +++ b/libc/tinymath/remquof.c @@ -0,0 +1,116 @@ +/*-*- mode:c;indent-tabs-mode:nil;c-basic-offset:2;tab-width:8;coding:utf-8 -*-│ +│vi: set net ft=c ts=2 sts=2 sw=2 fenc=utf-8 :vi│ +╚──────────────────────────────────────────────────────────────────────────────╝ +│ │ +│ Musl Libc │ +│ Copyright © 2005-2020 Rich Felker, et al. │ +│ │ +│ Permission is hereby granted, free of charge, to any person obtaining │ +│ a copy of this software and associated documentation files (the │ +│ "Software"), to deal in the Software without restriction, including │ +│ without limitation the rights to use, copy, modify, merge, publish, │ +│ distribute, sublicense, and/or sell copies of the Software, and to │ +│ permit persons to whom the Software is furnished to do so, subject to │ +│ the following conditions: │ +│ │ +│ The above copyright notice and this permission notice shall be │ +│ included in all copies or substantial portions of the Software. │ +│ │ +│ THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, │ +│ EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF │ +│ MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. │ +│ IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY │ +│ CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, │ +│ TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE │ +│ SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. │ +│ │ +╚─────────────────────────────────────────────────────────────────────────────*/ + +#include "libc/math.h" + +asm(".ident\t\"\\n\\n\ +Musl libc (MIT License)\\n\ +Copyright 2005-2020 Rich Felker, et. al.\""); +asm(".include \"libc/disclaimer.inc\""); + +/* clang-format off */ + +float remquof(float x, float y, int *quo) +{ + union {float f; uint32_t i;} ux = {x}, uy = {y}; + int ex = ux.i>>23 & 0xff; + int ey = uy.i>>23 & 0xff; + int sx = ux.i>>31; + int sy = uy.i>>31; + uint32_t q; + uint32_t i; + uint32_t uxi = ux.i; + + *quo = 0; + if (uy.i<<1 == 0 || isnan(y) || ex == 0xff) + return (x*y)/(x*y); + if (ux.i<<1 == 0) + return x; + + /* normalize x and y */ + if (!ex) { + for (i = uxi<<9; i>>31 == 0; ex--, i <<= 1); + uxi <<= -ex + 1; + } else { + uxi &= -1U >> 9; + uxi |= 1U << 23; + } + if (!ey) { + for (i = uy.i<<9; i>>31 == 0; ey--, i <<= 1); + uy.i <<= -ey + 1; + } else { + uy.i &= -1U >> 9; + uy.i |= 1U << 23; + } + + 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 >> 31 == 0) { + uxi = i; + q++; + } + uxi <<= 1; + q <<= 1; + } + i = uxi - uy.i; + if (i >> 31 == 0) { + uxi = i; + q++; + } + if (uxi == 0) + ex = -30; + else + for (; uxi>>23 == 0; uxi <<= 1, ex--); +end: + /* scale result and decide between |x| and |x|-|y| */ + if (ex > 0) { + uxi -= 1U << 23; + uxi |= (uint32_t)ex << 23; + } 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; +} diff --git a/libc/tinymath/remquol.c b/libc/tinymath/remquol.c new file mode 100644 index 000000000..be879bade --- /dev/null +++ b/libc/tinymath/remquol.c @@ -0,0 +1,122 @@ +/*-*- mode:c;indent-tabs-mode:nil;c-basic-offset:2;tab-width:8;coding:utf-8 -*-│ +│vi: set net ft=c ts=2 sts=2 sw=2 fenc=utf-8 :vi│ +╚──────────────────────────────────────────────────────────────────────────────╝ +│ │ +│ Musl Libc │ +│ Copyright © 2005-2020 Rich Felker, et al. │ +│ │ +│ Permission is hereby granted, free of charge, to any person obtaining │ +│ a copy of this software and associated documentation files (the │ +│ "Software"), to deal in the Software without restriction, including │ +│ without limitation the rights to use, copy, modify, merge, publish, │ +│ distribute, sublicense, and/or sell copies of the Software, and to │ +│ permit persons to whom the Software is furnished to do so, subject to │ +│ the following conditions: │ +│ │ +│ The above copyright notice and this permission notice shall be │ +│ included in all copies or substantial portions of the Software. │ +│ │ +│ THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, │ +│ EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF │ +│ MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. │ +│ IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY │ +│ CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, │ +│ TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE │ +│ SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. │ +│ │ +╚─────────────────────────────────────────────────────────────────────────────*/ + +#include "libc/math.h" + +union ldshape { + long double f; + struct { + uint64_t m; + uint16_t se; + } i; +}; + +asm(".ident\t\"\\n\\n\ +Musl libc (MIT License)\\n\ +Copyright 2005-2020 Rich Felker, et. al.\""); +asm(".include \"libc/disclaimer.inc\""); + +/* clang-format off */ + +long double remquol(long double x, long double y, int *quo) +{ + union ldshape ux = {x}, uy = {y}; + int ex = ux.i.se & 0x7fff; + int ey = uy.i.se & 0x7fff; + int sx = ux.i.se >> 15; + int sy = uy.i.se >> 15; + uint32_t q; + + *quo = 0; + if (y == 0 || isnan(y) || ex == 0x7fff) + return (x*y)/(x*y); + if (x == 0) + return x; + + /* normalize x and y */ + if (!ex) { + ux.i.se = ex; + ux.f *= 0x1p120f; + ex = ux.i.se - 120; + } + if (!ey) { + uy.i.se = ey; + uy.f *= 0x1p120f; + ey = uy.i.se - 120; + } + + q = 0; + if (ex >= ey) { + /* x mod y */ + uint64_t i, mx, my; + mx = ux.i.m; + my = uy.i.m; + for (; ex > ey; ex--) { + i = mx - my; + if (mx >= my) { + mx = 2*i; + q++; + q <<= 1; + } else if (2*mx < mx) { + mx = 2*mx - my; + q <<= 1; + q++; + } else { + mx = 2*mx; + q <<= 1; + } + } + i = mx - my; + if (mx >= my) { + mx = i; + q++; + } + if (mx == 0) + ex = -120; + else + for (; mx >> 63 == 0; mx *= 2, ex--); + ux.i.m = mx; + } + + /* scale result and decide between |x| and |x|-|y| */ + if (ex <= 0) { + ux.i.se = ex + 120; + ux.f *= 0x1p-120f; + } else + ux.i.se = ex; + 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; +}