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Add more math functions (#128)
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dosisod
GitHub
parent
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commit
8a236433a2
13 changed files with 1249 additions and 0 deletions
220
libc/tinymath/erff.c
Normal file
220
libc/tinymath/erff.c
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@ -0,0 +1,220 @@
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/*-*- mode:c;indent-tabs-mode:nil;c-basic-offset:2;tab-width:8;coding:utf-8 -*-│
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│vi: set net ft=c ts=2 sts=2 sw=2 fenc=utf-8 :vi│
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╚──────────────────────────────────────────────────────────────────────────────╝
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│ │
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│ Musl Libc │
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│ Copyright © 2005-2020 Rich Felker, et al. │
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│ │
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│ Permission is hereby granted, free of charge, to any person obtaining │
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│ a copy of this software and associated documentation files (the │
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│ "Software"), to deal in the Software without restriction, including │
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│ without limitation the rights to use, copy, modify, merge, publish, │
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│ distribute, sublicense, and/or sell copies of the Software, and to │
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│ permit persons to whom the Software is furnished to do so, subject to │
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│ the following conditions: │
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│ │
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│ The above copyright notice and this permission notice shall be │
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│ included in all copies or substantial portions of the Software. │
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│ │
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│ THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, │
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│ EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF │
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│ MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. │
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│ IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY │
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│ CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, │
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│ TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE │
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│ SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. │
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│ │
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╚─────────────────────────────────────────────────────────────────────────────*/
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#include "libc/math.h"
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asm(".ident\t\"\\n\\n\
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fdlibm (fdlibm license)\\n\
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Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.\"");
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asm(".ident\t\"\\n\\n\
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Musl libc (MIT License)\\n\
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Copyright 2005-2020 Rich Felker, et. al.\"");
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asm(".include \"libc/disclaimer.inc\"");
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/* clang-format off */
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/* origin: FreeBSD /usr/src/lib/msun/src/s_erff.c */
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/*
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* ====================================================
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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*
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* Developed at SunPro, a Sun Microsystems, Inc. business.
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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* is preserved.
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* ====================================================
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*/
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#define asuint(f) ((union{float _f; uint32_t _i;}){f})._i
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#define asfloat(i) ((union{uint32_t _i; float _f;}){i})._f
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static const float
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erx = 8.4506291151e-01, /* 0x3f58560b */
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/*
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* Coefficients for approximation to erf on [0,0.84375]
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*/
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efx8 = 1.0270333290e+00, /* 0x3f8375d4 */
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pp0 = 1.2837916613e-01, /* 0x3e0375d4 */
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pp1 = -3.2504209876e-01, /* 0xbea66beb */
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pp2 = -2.8481749818e-02, /* 0xbce9528f */
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pp3 = -5.7702702470e-03, /* 0xbbbd1489 */
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pp4 = -2.3763017452e-05, /* 0xb7c756b1 */
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qq1 = 3.9791721106e-01, /* 0x3ecbbbce */
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qq2 = 6.5022252500e-02, /* 0x3d852a63 */
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qq3 = 5.0813062117e-03, /* 0x3ba68116 */
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qq4 = 1.3249473704e-04, /* 0x390aee49 */
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qq5 = -3.9602282413e-06, /* 0xb684e21a */
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/*
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* Coefficients for approximation to erf in [0.84375,1.25]
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*/
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pa0 = -2.3621185683e-03, /* 0xbb1acdc6 */
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pa1 = 4.1485610604e-01, /* 0x3ed46805 */
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pa2 = -3.7220788002e-01, /* 0xbebe9208 */
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pa3 = 3.1834661961e-01, /* 0x3ea2fe54 */
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pa4 = -1.1089469492e-01, /* 0xbde31cc2 */
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pa5 = 3.5478305072e-02, /* 0x3d1151b3 */
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pa6 = -2.1663755178e-03, /* 0xbb0df9c0 */
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qa1 = 1.0642088205e-01, /* 0x3dd9f331 */
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qa2 = 5.4039794207e-01, /* 0x3f0a5785 */
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qa3 = 7.1828655899e-02, /* 0x3d931ae7 */
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qa4 = 1.2617121637e-01, /* 0x3e013307 */
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qa5 = 1.3637083583e-02, /* 0x3c5f6e13 */
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qa6 = 1.1984500103e-02, /* 0x3c445aa3 */
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/*
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* Coefficients for approximation to erfc in [1.25,1/0.35]
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*/
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ra0 = -9.8649440333e-03, /* 0xbc21a093 */
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ra1 = -6.9385856390e-01, /* 0xbf31a0b7 */
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ra2 = -1.0558626175e+01, /* 0xc128f022 */
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ra3 = -6.2375331879e+01, /* 0xc2798057 */
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ra4 = -1.6239666748e+02, /* 0xc322658c */
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ra5 = -1.8460508728e+02, /* 0xc3389ae7 */
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ra6 = -8.1287437439e+01, /* 0xc2a2932b */
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ra7 = -9.8143291473e+00, /* 0xc11d077e */
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sa1 = 1.9651271820e+01, /* 0x419d35ce */
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sa2 = 1.3765776062e+02, /* 0x4309a863 */
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sa3 = 4.3456588745e+02, /* 0x43d9486f */
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sa4 = 6.4538726807e+02, /* 0x442158c9 */
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sa5 = 4.2900814819e+02, /* 0x43d6810b */
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sa6 = 1.0863500214e+02, /* 0x42d9451f */
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sa7 = 6.5702495575e+00, /* 0x40d23f7c */
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sa8 = -6.0424413532e-02, /* 0xbd777f97 */
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/*
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* Coefficients for approximation to erfc in [1/.35,28]
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*/
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rb0 = -9.8649431020e-03, /* 0xbc21a092 */
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rb1 = -7.9928326607e-01, /* 0xbf4c9dd4 */
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rb2 = -1.7757955551e+01, /* 0xc18e104b */
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rb3 = -1.6063638306e+02, /* 0xc320a2ea */
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rb4 = -6.3756646729e+02, /* 0xc41f6441 */
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rb5 = -1.0250950928e+03, /* 0xc480230b */
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rb6 = -4.8351919556e+02, /* 0xc3f1c275 */
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sb1 = 3.0338060379e+01, /* 0x41f2b459 */
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sb2 = 3.2579251099e+02, /* 0x43a2e571 */
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sb3 = 1.5367296143e+03, /* 0x44c01759 */
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sb4 = 3.1998581543e+03, /* 0x4547fdbb */
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sb5 = 2.5530502930e+03, /* 0x451f90ce */
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sb6 = 4.7452853394e+02, /* 0x43ed43a7 */
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sb7 = -2.2440952301e+01; /* 0xc1b38712 */
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static float erfc1(float x)
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{
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float_t s,P,Q;
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s = fabsf(x) - 1;
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P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6)))));
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Q = 1+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6)))));
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return 1 - erx - P/Q;
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}
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static float erfc2(uint32_t ix, float x)
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{
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float_t s,R,S;
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float z;
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if (ix < 0x3fa00000) /* |x| < 1.25 */
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return erfc1(x);
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x = fabsf(x);
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s = 1/(x*x);
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if (ix < 0x4036db6d) { /* |x| < 1/0.35 */
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R = ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*(
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ra5+s*(ra6+s*ra7))))));
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S = 1.0f+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(
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sa5+s*(sa6+s*(sa7+s*sa8)))))));
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} else { /* |x| >= 1/0.35 */
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R = rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(
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rb5+s*rb6)))));
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S = 1.0f+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*(
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sb5+s*(sb6+s*sb7))))));
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}
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ix = asuint(x);
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z = asfloat(ix&0xffffe000);
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return expf(-z*z - 0.5625f) * expf((z-x)*(z+x) + R/S)/x;
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}
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float erff(float x)
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{
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float r,s,z,y;
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uint32_t ix;
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int sign;
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ix = asuint(x);
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sign = ix>>31;
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ix &= 0x7fffffff;
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if (ix >= 0x7f800000) {
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/* erf(nan)=nan, erf(+-inf)=+-1 */
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return 1-2*sign + 1/x;
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}
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if (ix < 0x3f580000) { /* |x| < 0.84375 */
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if (ix < 0x31800000) { /* |x| < 2**-28 */
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/*avoid underflow */
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return 0.125f*(8*x + efx8*x);
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}
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z = x*x;
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r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4)));
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s = 1+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))));
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y = r/s;
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return x + x*y;
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}
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if (ix < 0x40c00000) /* |x| < 6 */
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y = 1 - erfc2(ix,x);
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else
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y = 1 - 0x1p-120f;
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return sign ? -y : y;
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}
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float erfcf(float x)
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{
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float r,s,z,y;
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uint32_t ix;
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int sign;
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ix = asuint(x);
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sign = ix>>31;
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ix &= 0x7fffffff;
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if (ix >= 0x7f800000) {
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/* erfc(nan)=nan, erfc(+-inf)=0,2 */
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return 2*sign + 1/x;
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}
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if (ix < 0x3f580000) { /* |x| < 0.84375 */
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if (ix < 0x23800000) /* |x| < 2**-56 */
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return 1.0f - x;
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z = x*x;
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r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4)));
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s = 1.0f+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))));
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y = r/s;
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if (sign || ix < 0x3e800000) /* x < 1/4 */
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return 1.0f - (x+x*y);
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return 0.5f - (x - 0.5f + x*y);
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}
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if (ix < 0x41e00000) { /* |x| < 28 */
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return sign ? 2 - erfc2(ix,x) : erfc2(ix,x);
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}
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return sign ? 2 - 0x1p-120f : 0x1p-120f*0x1p-120f;
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}
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45
libc/tinymath/fdim.c
Normal file
45
libc/tinymath/fdim.c
Normal file
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@ -0,0 +1,45 @@
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/*-*- mode:c;indent-tabs-mode:nil;c-basic-offset:2;tab-width:8;coding:utf-8 -*-│
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│vi: set net ft=c ts=2 sts=2 sw=2 fenc=utf-8 :vi│
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╚──────────────────────────────────────────────────────────────────────────────╝
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│ │
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│ Musl Libc │
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│ Copyright © 2005-2020 Rich Felker, et al. │
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│ │
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│ Permission is hereby granted, free of charge, to any person obtaining │
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│ a copy of this software and associated documentation files (the │
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│ "Software"), to deal in the Software without restriction, including │
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│ without limitation the rights to use, copy, modify, merge, publish, │
|
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│ distribute, sublicense, and/or sell copies of the Software, and to │
|
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│ permit persons to whom the Software is furnished to do so, subject to │
|
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│ the following conditions: │
|
||||||
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│ │
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||||||
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│ The above copyright notice and this permission notice shall be │
|
||||||
|
│ included in all copies or substantial portions of the Software. │
|
||||||
|
│ │
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│ 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 │
|
||||||
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│ SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. │
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│ │
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╚─────────────────────────────────────────────────────────────────────────────*/
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#include "libc/math.h"
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asm(".ident\t\"\\n\\n\
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Musl libc (MIT License)\\n\
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Copyright 2005-2020 Rich Felker, et. al.\"");
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asm(".include \"libc/disclaimer.inc\"");
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/* clang-format off */
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double fdim(double x, double y)
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{
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if (isnan(x))
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return x;
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if (isnan(y))
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return y;
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return x > y ? x - y : 0;
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}
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45
libc/tinymath/fdimf.c
Normal file
45
libc/tinymath/fdimf.c
Normal file
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@ -0,0 +1,45 @@
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/*-*- mode:c;indent-tabs-mode:nil;c-basic-offset:2;tab-width:8;coding:utf-8 -*-│
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│vi: set net ft=c ts=2 sts=2 sw=2 fenc=utf-8 :vi│
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╚──────────────────────────────────────────────────────────────────────────────╝
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│ │
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│ Musl Libc │
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│ Copyright © 2005-2020 Rich Felker, et al. │
|
||||||
|
│ │
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│ Permission is hereby granted, free of charge, to any person obtaining │
|
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|
│ 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: │
|
||||||
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│ │
|
||||||
|
│ 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. │
|
||||||
|
│ │
|
||||||
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╚─────────────────────────────────────────────────────────────────────────────*/
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#include "libc/math.h"
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asm(".ident\t\"\\n\\n\
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Musl libc (MIT License)\\n\
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|
Copyright 2005-2020 Rich Felker, et. al.\"");
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asm(".include \"libc/disclaimer.inc\"");
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/* clang-format off */
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float fdimf(float x, float y)
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{
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if (isnan(x))
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return x;
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if (isnan(y))
|
||||||
|
return y;
|
||||||
|
return x > y ? x - y : 0;
|
||||||
|
}
|
||||||
45
libc/tinymath/fdiml.c
Normal file
45
libc/tinymath/fdiml.c
Normal file
|
|
@ -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;
|
||||||
|
}
|
||||||
225
libc/tinymath/fma.c
Normal file
225
libc/tinymath/fma.c
Normal file
|
|
@ -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<<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);
|
||||||
|
}
|
||||||
57
libc/tinymath/frexpf.c
Normal file
57
libc/tinymath/frexpf.c
Normal file
|
|
@ -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;
|
||||||
|
}
|
||||||
65
libc/tinymath/frexpl.c
Normal file
65
libc/tinymath/frexpl.c
Normal file
|
|
@ -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;
|
||||||
|
}
|
||||||
76
libc/tinymath/nexttoward.c
Normal file
76
libc/tinymath/nexttoward.c
Normal file
|
|
@ -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;
|
||||||
|
}
|
||||||
76
libc/tinymath/nexttowardf.c
Normal file
76
libc/tinymath/nexttowardf.c
Normal file
|
|
@ -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;
|
||||||
|
}
|
||||||
41
libc/tinymath/nexttowardl.c
Normal file
41
libc/tinymath/nexttowardl.c
Normal file
|
|
@ -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);
|
||||||
|
}
|
||||||
116
libc/tinymath/remquo.c
Normal file
116
libc/tinymath/remquo.c
Normal file
|
|
@ -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;
|
||||||
|
}
|
||||||
116
libc/tinymath/remquof.c
Normal file
116
libc/tinymath/remquof.c
Normal file
|
|
@ -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;
|
||||||
|
}
|
||||||
122
libc/tinymath/remquol.c
Normal file
122
libc/tinymath/remquol.c
Normal file
|
|
@ -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;
|
||||||
|
}
|
||||||
Loading…
Add table
Add a link
Reference in a new issue