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cosmopolitan/libc/tinymath/finite.c | /*-*- mode:c;indent-tabs-mode:nil;c-basic-offset:2;tab-width:8;coding:utf-8 -*-â
âvi: set net ft=c ts=2 sts=2 sw=2 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ¡
â Copyright 2021 Justine Alexandra Roberts Tunney â
â â
â Permission to use, copy, modify, and/or distribute this software for â
â any purpose with or without fee is hereby granted, provided that the â
â above copyright notice and this permission notice appear in all copies. â
â â
â THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL â
â WARRANTIES WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED â
â WARRANTIES OF MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE â
â AUTHOR BE LIABLE FOR ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL â
â DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR â
â PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER â
â TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR â
â PERFORMANCE OF THIS SOFTWARE. â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
/**
* Returns nonzero if ð¥ isn't INFINITY or NAN.
*/
int finite(double x) {
return isfinite(x);
}
| 1,965 | 27 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/scalb.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2020 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
asm(".ident\t\"\\n\\n\
fdlibm (fdlibm license)\\n\
Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.\"");
asm(".ident\t\"\\n\\n\
Musl libc (MIT License)\\n\
Copyright 2005-2014 Rich Felker, et. al.\"");
asm(".include \"libc/disclaimer.inc\"");
// clang-format off
/* origin: FreeBSD /usr/src/lib/msun/src/e_scalb.c */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/*
* scalb(x, fn) is provide for
* passing various standard test suite. One
* should use scalbn() instead.
*/
/**
* Returns ð¥ à 2ʸ.
*/
double scalb(double x, double y)
{
if (isunordered(x, y))
return x*y;
if (!isfinite(y)) {
if (y > 0.0)
return x*y;
else
return x/(-y);
}
if (rint(y) != y) return (y-y)/(y-y);
if ( y > 65000.0) return scalbn(x, 65000);
if (-y > 65000.0) return scalbn(x,-65000);
return scalbn(x,(int)y);
}
| 3,796 | 74 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/erf.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
asm(".ident\t\"\\n\\n\
fdlibm (fdlibm license)\\n\
Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.\"");
asm(".ident\t\"\\n\\n\
Musl libc (MIT License)\\n\
Copyright 2005-2014 Rich Felker, et. al.\"");
asm(".include \"libc/disclaimer.inc\"");
/* clang-format off */
/* origin: FreeBSD /usr/src/lib/msun/src/s_erf.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.
* ====================================================
*/
/* double erf(double x)
* double erfc(double x)
* x
* 2 |\
* erf(x) = --------- | exp(-t*t)dt
* sqrt(pi) \|
* 0
*
* erfc(x) = 1-erf(x)
* Note that
* erf(-x) = -erf(x)
* erfc(-x) = 2 - erfc(x)
*
* Method:
* 1. For |x| in [0, 0.84375]
* erf(x) = x + x*R(x^2)
* erfc(x) = 1 - erf(x) if x in [-.84375,0.25]
* = 0.5 + ((0.5-x)-x*R) if x in [0.25,0.84375]
* where R = P/Q where P is an odd poly of degree 8 and
* Q is an odd poly of degree 10.
* -57.90
* | R - (erf(x)-x)/x | <= 2
*
*
* Remark. The formula is derived by noting
* erf(x) = (2/sqrt(pi))*(x - x^3/3 + x^5/10 - x^7/42 + ....)
* and that
* 2/sqrt(pi) = 1.128379167095512573896158903121545171688
* is close to one. The interval is chosen because the fix
* point of erf(x) is near 0.6174 (i.e., erf(x)=x when x is
* near 0.6174), and by some experiment, 0.84375 is chosen to
* guarantee the error is less than one ulp for erf.
*
* 2. For |x| in [0.84375,1.25], let s = |x| - 1, and
* c = 0.84506291151 rounded to single (24 bits)
* erf(x) = sign(x) * (c + P1(s)/Q1(s))
* erfc(x) = (1-c) - P1(s)/Q1(s) if x > 0
* 1+(c+P1(s)/Q1(s)) if x < 0
* |P1/Q1 - (erf(|x|)-c)| <= 2**-59.06
* Remark: here we use the taylor series expansion at x=1.
* erf(1+s) = erf(1) + s*Poly(s)
* = 0.845.. + P1(s)/Q1(s)
* That is, we use rational approximation to approximate
* erf(1+s) - (c = (single)0.84506291151)
* Note that |P1/Q1|< 0.078 for x in [0.84375,1.25]
* where
* P1(s) = degree 6 poly in s
* Q1(s) = degree 6 poly in s
*
* 3. For x in [1.25,1/0.35(~2.857143)],
* erfc(x) = (1/x)*exp(-x*x-0.5625+R1/S1)
* erf(x) = 1 - erfc(x)
* where
* R1(z) = degree 7 poly in z, (z=1/x^2)
* S1(z) = degree 8 poly in z
*
* 4. For x in [1/0.35,28]
* erfc(x) = (1/x)*exp(-x*x-0.5625+R2/S2) if x > 0
* = 2.0 - (1/x)*exp(-x*x-0.5625+R2/S2) if -6<x<0
* = 2.0 - tiny (if x <= -6)
* erf(x) = sign(x)*(1.0 - erfc(x)) if x < 6, else
* erf(x) = sign(x)*(1.0 - tiny)
* where
* R2(z) = degree 6 poly in z, (z=1/x^2)
* S2(z) = degree 7 poly in z
*
* Note1:
* To compute exp(-x*x-0.5625+R/S), let s be a single
* precision number and s := x; then
* -x*x = -s*s + (s-x)*(s+x)
* exp(-x*x-0.5626+R/S) =
* exp(-s*s-0.5625)*exp((s-x)*(s+x)+R/S);
* Note2:
* Here 4 and 5 make use of the asymptotic series
* exp(-x*x)
* erfc(x) ~ ---------- * ( 1 + Poly(1/x^2) )
* x*sqrt(pi)
* We use rational approximation to approximate
* g(s)=f(1/x^2) = log(erfc(x)*x) - x*x + 0.5625
* Here is the error bound for R1/S1 and R2/S2
* |R1/S1 - f(x)| < 2**(-62.57)
* |R2/S2 - f(x)| < 2**(-61.52)
*
* 5. For inf > x >= 28
* erf(x) = sign(x) *(1 - tiny) (raise inexact)
* erfc(x) = tiny*tiny (raise underflow) if x > 0
* = 2 - tiny if x<0
*
* 7. Special case:
* erf(0) = 0, erf(inf) = 1, erf(-inf) = -1,
* erfc(0) = 1, erfc(inf) = 0, erfc(-inf) = 2,
* erfc/erf(NaN) is NaN
*/
static const double
erx = 8.45062911510467529297e-01, /* 0x3FEB0AC1, 0x60000000 */
/*
* Coefficients for approximation to erf on [0,0.84375]
*/
efx8 = 1.02703333676410069053e+00, /* 0x3FF06EBA, 0x8214DB69 */
pp0 = 1.28379167095512558561e-01, /* 0x3FC06EBA, 0x8214DB68 */
pp1 = -3.25042107247001499370e-01, /* 0xBFD4CD7D, 0x691CB913 */
pp2 = -2.84817495755985104766e-02, /* 0xBF9D2A51, 0xDBD7194F */
pp3 = -5.77027029648944159157e-03, /* 0xBF77A291, 0x236668E4 */
pp4 = -2.37630166566501626084e-05, /* 0xBEF8EAD6, 0x120016AC */
qq1 = 3.97917223959155352819e-01, /* 0x3FD97779, 0xCDDADC09 */
qq2 = 6.50222499887672944485e-02, /* 0x3FB0A54C, 0x5536CEBA */
qq3 = 5.08130628187576562776e-03, /* 0x3F74D022, 0xC4D36B0F */
qq4 = 1.32494738004321644526e-04, /* 0x3F215DC9, 0x221C1A10 */
qq5 = -3.96022827877536812320e-06, /* 0xBED09C43, 0x42A26120 */
/*
* Coefficients for approximation to erf in [0.84375,1.25]
*/
pa0 = -2.36211856075265944077e-03, /* 0xBF6359B8, 0xBEF77538 */
pa1 = 4.14856118683748331666e-01, /* 0x3FDA8D00, 0xAD92B34D */
pa2 = -3.72207876035701323847e-01, /* 0xBFD7D240, 0xFBB8C3F1 */
pa3 = 3.18346619901161753674e-01, /* 0x3FD45FCA, 0x805120E4 */
pa4 = -1.10894694282396677476e-01, /* 0xBFBC6398, 0x3D3E28EC */
pa5 = 3.54783043256182359371e-02, /* 0x3FA22A36, 0x599795EB */
pa6 = -2.16637559486879084300e-03, /* 0xBF61BF38, 0x0A96073F */
qa1 = 1.06420880400844228286e-01, /* 0x3FBB3E66, 0x18EEE323 */
qa2 = 5.40397917702171048937e-01, /* 0x3FE14AF0, 0x92EB6F33 */
qa3 = 7.18286544141962662868e-02, /* 0x3FB2635C, 0xD99FE9A7 */
qa4 = 1.26171219808761642112e-01, /* 0x3FC02660, 0xE763351F */
qa5 = 1.36370839120290507362e-02, /* 0x3F8BEDC2, 0x6B51DD1C */
qa6 = 1.19844998467991074170e-02, /* 0x3F888B54, 0x5735151D */
/*
* Coefficients for approximation to erfc in [1.25,1/0.35]
*/
ra0 = -9.86494403484714822705e-03, /* 0xBF843412, 0x600D6435 */
ra1 = -6.93858572707181764372e-01, /* 0xBFE63416, 0xE4BA7360 */
ra2 = -1.05586262253232909814e+01, /* 0xC0251E04, 0x41B0E726 */
ra3 = -6.23753324503260060396e+01, /* 0xC04F300A, 0xE4CBA38D */
ra4 = -1.62396669462573470355e+02, /* 0xC0644CB1, 0x84282266 */
ra5 = -1.84605092906711035994e+02, /* 0xC067135C, 0xEBCCABB2 */
ra6 = -8.12874355063065934246e+01, /* 0xC0545265, 0x57E4D2F2 */
ra7 = -9.81432934416914548592e+00, /* 0xC023A0EF, 0xC69AC25C */
sa1 = 1.96512716674392571292e+01, /* 0x4033A6B9, 0xBD707687 */
sa2 = 1.37657754143519042600e+02, /* 0x4061350C, 0x526AE721 */
sa3 = 4.34565877475229228821e+02, /* 0x407B290D, 0xD58A1A71 */
sa4 = 6.45387271733267880336e+02, /* 0x40842B19, 0x21EC2868 */
sa5 = 4.29008140027567833386e+02, /* 0x407AD021, 0x57700314 */
sa6 = 1.08635005541779435134e+02, /* 0x405B28A3, 0xEE48AE2C */
sa7 = 6.57024977031928170135e+00, /* 0x401A47EF, 0x8E484A93 */
sa8 = -6.04244152148580987438e-02, /* 0xBFAEEFF2, 0xEE749A62 */
/*
* Coefficients for approximation to erfc in [1/.35,28]
*/
rb0 = -9.86494292470009928597e-03, /* 0xBF843412, 0x39E86F4A */
rb1 = -7.99283237680523006574e-01, /* 0xBFE993BA, 0x70C285DE */
rb2 = -1.77579549177547519889e+01, /* 0xC031C209, 0x555F995A */
rb3 = -1.60636384855821916062e+02, /* 0xC064145D, 0x43C5ED98 */
rb4 = -6.37566443368389627722e+02, /* 0xC083EC88, 0x1375F228 */
rb5 = -1.02509513161107724954e+03, /* 0xC0900461, 0x6A2E5992 */
rb6 = -4.83519191608651397019e+02, /* 0xC07E384E, 0x9BDC383F */
sb1 = 3.03380607434824582924e+01, /* 0x403E568B, 0x261D5190 */
sb2 = 3.25792512996573918826e+02, /* 0x40745CAE, 0x221B9F0A */
sb3 = 1.53672958608443695994e+03, /* 0x409802EB, 0x189D5118 */
sb4 = 3.19985821950859553908e+03, /* 0x40A8FFB7, 0x688C246A */
sb5 = 2.55305040643316442583e+03, /* 0x40A3F219, 0xCEDF3BE6 */
sb6 = 4.74528541206955367215e+02, /* 0x407DA874, 0xE79FE763 */
sb7 = -2.24409524465858183362e+01; /* 0xC03670E2, 0x42712D62 */
#define asuint(f) ((union{float _f; uint32_t _i;}){f})._i
#define asfloat(i) ((union{uint32_t _i; float _f;}){i})._f
#define asuint64(f) ((union{double _f; uint64_t _i;}){f})._i
#define asdouble(i) ((union{uint64_t _i; double _f;}){i})._f
#define INSERT_WORDS(d,hi,lo) \
do { \
(d) = asdouble(((uint64_t)(hi)<<32) | (uint32_t)(lo)); \
} while (0)
#define GET_HIGH_WORD(hi,d) \
do { \
(hi) = asuint64(d) >> 32; \
} while (0)
#define GET_LOW_WORD(lo,d) \
do { \
(lo) = (uint32_t)asuint64(d); \
} while (0)
#define SET_HIGH_WORD(d,hi) \
INSERT_WORDS(d, hi, (uint32_t)asuint64(d))
#define SET_LOW_WORD(d,lo) \
INSERT_WORDS(d, asuint64(d)>>32, lo)
static double erfc1(double x)
{
double_t s,P,Q;
s = fabs(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 double erfc2(uint32_t ix, double x)
{
double_t s,R,S;
double z;
if (ix < 0x3ff40000) /* |x| < 1.25 */
return erfc1(x);
x = fabs(x);
s = 1/(x*x);
if (ix < 0x4006db6d) { /* |x| < 1/.35 ~ 2.85714 */
R = ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*(
ra5+s*(ra6+s*ra7))))));
S = 1.0+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(
sa5+s*(sa6+s*(sa7+s*sa8)))))));
} else { /* |x| > 1/.35 */
R = rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(
rb5+s*rb6)))));
S = 1.0+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*(
sb5+s*(sb6+s*sb7))))));
}
z = x;
SET_LOW_WORD(z,0);
return exp(-z*z-0.5625)*exp((z-x)*(z+x)+R/S)/x;
}
/**
* Returns error function of ð¥.
*/
double erf(double x)
{
double r,s,z,y;
uint32_t ix;
int sign;
GET_HIGH_WORD(ix, x);
sign = ix>>31;
ix &= 0x7fffffff;
if (ix >= 0x7ff00000) {
/* erf(nan)=nan, erf(+-inf)=+-1 */
return 1-2*sign + 1/x;
}
if (ix < 0x3feb0000) { /* |x| < 0.84375 */
if (ix < 0x3e300000) { /* |x| < 2**-28 */
/* avoid underflow */
return 0.125*(8*x + efx8*x);
}
z = x*x;
r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4)));
s = 1.0+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))));
y = r/s;
return x + x*y;
}
if (ix < 0x40180000) /* 0.84375 <= |x| < 6 */
y = 1 - erfc2(ix,x);
else
y = 1 - 0x1p-1022;
return sign ? -y : y;
}
/**
* Returns complementary error function of ð¥.
*/
double erfc(double x)
{
double r,s,z,y;
uint32_t ix;
int sign;
GET_HIGH_WORD(ix, x);
sign = ix>>31;
ix &= 0x7fffffff;
if (ix >= 0x7ff00000) {
/* erfc(nan)=nan, erfc(+-inf)=0,2 */
return 2*sign + 1/x;
}
if (ix < 0x3feb0000) { /* |x| < 0.84375 */
if (ix < 0x3c700000) /* |x| < 2**-56 */
return 1.0 - x;
z = x*x;
r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4)));
s = 1.0+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))));
y = r/s;
if (sign || ix < 0x3fd00000) { /* x < 1/4 */
return 1.0 - (x+x*y);
}
return 0.5 - (x - 0.5 + x*y);
}
if (ix < 0x403c0000) { /* 0.84375 <= |x| < 28 */
return sign ? 2 - erfc2(ix,x) : erfc2(ix,x);
}
return sign ? 2 - 0x1p-1022 : 0x1p-1022*0x1p-1022;
}
| 14,276 | 337 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/sindf.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2020 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
#include "libc/tinymath/kernel.internal.h"
asm(".ident\t\"\\n\\n\
fdlibm (fdlibm license)\\n\
Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.\"");
asm(".ident\t\"\\n\\n\
Musl libc (MIT License)\\n\
Copyright 2005-2014 Rich Felker, et. al.\"");
asm(".include \"libc/disclaimer.inc\"");
// clang-format off
/* origin: FreeBSD /usr/src/lib/msun/src/k_sinf.c */
/*
* Conversion to float by Ian Lance Taylor, Cygnus Support, [email protected].
* Optimized by Bruce D. Evans.
*/
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/* |sin(x)/x - s(x)| < 2**-37.5 (~[-4.89e-12, 4.824e-12]). */
static const double
S1 = -0x15555554cbac77.0p-55, /* -0.166666666416265235595 */
S2 = 0x111110896efbb2.0p-59, /* 0.0083333293858894631756 */
S3 = -0x1a00f9e2cae774.0p-65, /* -0.000198393348360966317347 */
S4 = 0x16cd878c3b46a7.0p-71; /* 0.0000027183114939898219064 */
noinstrument float __sindf(double x)
{
double_t r, s, w, z;
/* Try to optimize for parallel evaluation as in __tandf.c. */
z = x*x;
w = z*z;
r = S3 + z*S4;
s = z*x;
return (x + s*(S1 + z*S2)) + s*w*r;
}
| 4,045 | 74 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/scalbln.c | /*-*- mode:c;indent-tabs-mode:nil;c-basic-offset:2;tab-width:8;coding:utf-8 -*-â
âvi: set net ft=c ts=2 sts=2 sw=2 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ¡
â Copyright 2022 Justine Alexandra Roberts Tunney â
â â
â Permission to use, copy, modify, and/or distribute this software for â
â any purpose with or without fee is hereby granted, provided that the â
â above copyright notice and this permission notice appear in all copies. â
â â
â THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL â
â WARRANTIES WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED â
â WARRANTIES OF MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE â
â AUTHOR BE LIABLE FOR ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL â
â DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR â
â PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER â
â TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR â
â PERFORMANCE OF THIS SOFTWARE. â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
/**
* Returns ð¥ à 2ʸ.
*/
double scalbln(double x, long n) {
return scalbn(x, n > 65536 ? 65536 : n < -65536 ? -65536 : (int)n);
}
#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
__strong_reference(scalbln, scalblnl);
#endif
| 2,094 | 31 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/ccosf.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/complex.h"
#include "libc/math.h"
#include "libc/tinymath/complex.internal.h"
asm(".ident\t\"\\n\\n\
Musl libc (MIT License)\\n\
Copyright 2005-2014 Rich Felker, et. al.\"");
asm(".include \"libc/disclaimer.inc\"");
/* clang-format off */
float complex ccosf(float complex z)
{
return ccoshf(CMPLXF(-cimagf(z), crealf(z)));
}
| 2,948 | 44 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/remainderl.c | /*-*- mode:c;indent-tabs-mode:nil;c-basic-offset:2;tab-width:8;coding:utf-8 -*-â
âvi: set net ft=c ts=2 sts=2 sw=2 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ¡
â Copyright 2023 Justine Alexandra Roberts Tunney â
â â
â Permission to use, copy, modify, and/or distribute this software for â
â any purpose with or without fee is hereby granted, provided that the â
â above copyright notice and this permission notice appear in all copies. â
â â
â THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL â
â WARRANTIES WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED â
â WARRANTIES OF MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE â
â AUTHOR BE LIABLE FOR ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL â
â DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR â
â PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER â
â TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR â
â PERFORMANCE OF THIS SOFTWARE. â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
#if !(LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024)
/**
* Returns remainder of dividing ð¥ by ð¦.
*/
long double remainderl(long double x, long double y) {
int q;
return remquol(x, y, &q);
}
#endif /* long double is long */
| 2,094 | 31 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/asinh.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
#include "libc/tinymath/feval.internal.h"
#include "libc/tinymath/freebsd.internal.h"
asm(".ident\t\"\\n\\n\
Musl libc (MIT License)\\n\
Copyright 2005-2014 Rich Felker, et. al.\"");
asm(".include \"libc/disclaimer.inc\"");
// clang-format off
/**
* Returns inverse hyperbolic sine of ð¥.
* @define asinh(x) = sign(x)*log(|x|+sqrt(x*x+1)) ~= x - x^3/6 + o(x^5)
*/
double asinh(double x)
{
union {double f; uint64_t i;} u = {.f = x};
unsigned e = u.i >> 52 & 0x7ff;
unsigned s = u.i >> 63;
/* |x| */
u.i &= (uint64_t)-1/2;
x = u.f;
if (e >= 0x3ff + 26) {
/* |x| >= 0x1p26 or inf or nan */
x = log(x) + 0.693147180559945309417232121458176568;
} else if (e >= 0x3ff + 1) {
/* |x| >= 2 */
x = log(2*x + 1/(sqrt(x*x+1)+x));
} else if (e >= 0x3ff - 26) {
/* |x| >= 0x1p-26, up to 1.6ulp error in [0.125,0.5] */
x = log1p(x + x*x/(sqrt(x*x+1)+1));
} else {
/* |x| < 0x1p-26, raise inexact if x != 0 */
feval(x + 0x1p120f);
}
return s ? -x : x;
}
#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
__strong_reference(asinh, asinhl);
#endif
| 3,692 | 71 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/rempio2.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/intrin/likely.h"
#include "libc/math.h"
#include "libc/runtime/fenv.h"
#include "libc/tinymath/kernel.internal.h"
asm(".ident\t\"\\n\\n\
fdlibm (fdlibm license)\\n\
Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.\"");
asm(".ident\t\"\\n\\n\
Musl libc (MIT License)\\n\
Copyright 2005-2014 Rich Felker, et. al.\"");
asm(".include \"libc/disclaimer.inc\"");
/* clang-format off */
/* origin: FreeBSD /usr/src/lib/msun/src/e_rem_pio2.c */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*
* Optimized by Bruce D. Evans.
*/
/* __rem_pio2(x,y)
*
* return the remainder of x rem pi/2 in y[0]+y[1]
* use __rem_pio2_large() for large x
*/
#if FLT_EVAL_METHOD==0 || FLT_EVAL_METHOD==1
#define EPS DBL_EPSILON
#elif FLT_EVAL_METHOD==2
#define EPS LDBL_EPSILON
#endif
/*
* invpio2: 53 bits of 2/pi
* pio2_1: first 33 bit of pi/2
* pio2_1t: pi/2 - pio2_1
* pio2_2: second 33 bit of pi/2
* pio2_2t: pi/2 - (pio2_1+pio2_2)
* pio2_3: third 33 bit of pi/2
* pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3)
*/
#define toint (1.5/EPS)
#define pio4 0x1.921fb54442d18p-1
#define invpio2 6.36619772367581382433e-01
#define pio2_1 1.57079632673412561417e+00
#define pio2_1t 6.07710050650619224932e-11
#define pio2_2 6.07710050630396597660e-11
#define pio2_2t 2.02226624879595063154e-21
#define pio2_3 2.02226624871116645580e-21
#define pio2_3t 8.47842766036889956997e-32
/* caller must handle the case when reduction is not needed: |x| ~<= pi/4 */
int __rem_pio2(double x, double *y)
{
union {double f; uint64_t i;} u = {x};
double_t z,w,t,r,fn;
double tx[3],ty[2];
uint32_t ix;
int sign, n, ex, ey, i;
sign = u.i>>63;
ix = u.i>>32 & 0x7fffffff;
if (ix <= 0x400f6a7a) { /* |x| ~<= 5pi/4 */
if ((ix & 0xfffff) == 0x921fb) /* |x| ~= pi/2 or 2pi/2 */
goto medium; /* cancellation -- use medium case */
if (ix <= 0x4002d97c) { /* |x| ~<= 3pi/4 */
if (!sign) {
z = x - pio2_1; /* one round good to 85 bits */
y[0] = z - pio2_1t;
y[1] = (z-y[0]) - pio2_1t;
return 1;
} else {
z = x + pio2_1;
y[0] = z + pio2_1t;
y[1] = (z-y[0]) + pio2_1t;
return -1;
}
} else {
if (!sign) {
z = x - 2*pio2_1;
y[0] = z - 2*pio2_1t;
y[1] = (z-y[0]) - 2*pio2_1t;
return 2;
} else {
z = x + 2*pio2_1;
y[0] = z + 2*pio2_1t;
y[1] = (z-y[0]) + 2*pio2_1t;
return -2;
}
}
}
if (ix <= 0x401c463b) { /* |x| ~<= 9pi/4 */
if (ix <= 0x4015fdbc) { /* |x| ~<= 7pi/4 */
if (ix == 0x4012d97c) /* |x| ~= 3pi/2 */
goto medium;
if (!sign) {
z = x - 3*pio2_1;
y[0] = z - 3*pio2_1t;
y[1] = (z-y[0]) - 3*pio2_1t;
return 3;
} else {
z = x + 3*pio2_1;
y[0] = z + 3*pio2_1t;
y[1] = (z-y[0]) + 3*pio2_1t;
return -3;
}
} else {
if (ix == 0x401921fb) /* |x| ~= 4pi/2 */
goto medium;
if (!sign) {
z = x - 4*pio2_1;
y[0] = z - 4*pio2_1t;
y[1] = (z-y[0]) - 4*pio2_1t;
return 4;
} else {
z = x + 4*pio2_1;
y[0] = z + 4*pio2_1t;
y[1] = (z-y[0]) + 4*pio2_1t;
return -4;
}
}
}
if (ix < 0x413921fb) { /* |x| ~< 2^20*(pi/2), medium size */
medium:
/* rint(x/(pi/2)) */
fn = (double_t)x*invpio2 + toint - toint;
n = (int32_t)fn;
r = x - fn*pio2_1;
w = fn*pio2_1t; /* 1st round, good to 85 bits */
/* Matters with directed rounding. */
if (UNLIKELY(r - w < -pio4)) {
n--;
fn--;
r = x - fn*pio2_1;
w = fn*pio2_1t;
} else if (UNLIKELY(r - w > pio4)) {
n++;
fn++;
r = x - fn*pio2_1;
w = fn*pio2_1t;
}
y[0] = r - w;
u.f = y[0];
ey = u.i>>52 & 0x7ff;
ex = ix>>20;
if (ex - ey > 16) { /* 2nd round, good to 118 bits */
t = r;
w = fn*pio2_2;
r = t - w;
w = fn*pio2_2t - ((t-r)-w);
y[0] = r - w;
u.f = y[0];
ey = u.i>>52 & 0x7ff;
if (ex - ey > 49) { /* 3rd round, good to 151 bits, covers all cases */
t = r;
w = fn*pio2_3;
r = t - w;
w = fn*pio2_3t - ((t-r)-w);
y[0] = r - w;
}
}
y[1] = (r - y[0]) - w;
return n;
}
/*
* all other (large) arguments
*/
if (ix >= 0x7ff00000) { /* x is inf or NaN */
y[0] = y[1] = x - x;
return 0;
}
/* set z = scalbn(|x|,-ilogb(x)+23) */
u.f = x;
u.i &= (uint64_t)-1>>12;
u.i |= (uint64_t)(0x3ff + 23)<<52;
z = u.f;
for (i=0; i < 2; i++) {
tx[i] = (double)(int32_t)z;
z = (z-tx[i])*0x1p24;
}
tx[i] = z;
/* skip zero terms, first term is non-zero */
while (tx[i] == 0.0)
i--;
n = __rem_pio2_large(tx,ty,(int)(ix>>20)-(0x3ff+23),i+1,1);
if (sign) {
y[0] = -ty[0];
y[1] = -ty[1];
return -n;
}
y[0] = ty[0];
y[1] = ty[1];
return n;
}
| 7,524 | 228 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/README.cosmo | README
This folder provides libm scalar math functions, sourced from Musl
Libc, FreeBSD, OpenBSD, and ARM's Optimized Routines project.
LICENSE
All code is covered by notice licenses (e.g. BSD, MIT) which are
documented on a file-by-file basis.
ORIGIN
git://git.musl-libc.org/musl
commit f5f55d6589940fd2c2188d76686efe3a530e64e0
Author: Rich Felker <[email protected]>
Date: Mon May 1 23:39:41 2023 -0400
release 1.2.4
[email protected]:ARM-software/optimized-routines.git
commit f9f58aa37edc3486f18b1dd8701b74b5e3873699
Author: Joe Ramsay <[email protected]>
Date: Fri May 5 14:19:06 2023 +0100
math: Cleanup Neon cos and cosf
| 674 | 26 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/nextafterf.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
#include "libc/tinymath/feval.internal.h"
asm(".ident\t\"\\n\\n\
Musl libc (MIT License)\\n\
Copyright 2005-2014 Rich Felker, et. al.\"");
asm(".include \"libc/disclaimer.inc\"");
// clang-format off
float nextafterf(float x, float y)
{
union {float f; uint32_t i;} ux={x}, uy={y};
uint32_t ax, ay, e;
if (isunordered(x, y))
return x + y;
if (ux.i == uy.i)
return y;
ax = ux.i & 0x7fffffff;
ay = uy.i & 0x7fffffff;
if (ax == 0) {
if (ay == 0)
return y;
ux.i = (uy.i & 0x80000000) | 1;
} else if (ax > ay || ((ux.i ^ uy.i) & 0x80000000))
ux.i--;
else
ux.i++;
e = ux.i & 0x7f800000;
/* raise overflow if ux.f is infinite and x is finite */
if (e == 0x7f800000)
feval(x+x);
/* raise underflow if ux.f is subnormal or zero */
if (e == 0)
feval(x*x + ux.f*ux.f);
return ux.f;
}
| 3,435 | 65 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/kcosl.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
#include "libc/tinymath/kernel.internal.h"
asm(".ident\t\"\\n\\n\
FreeBSD libm (BSD-2 License)\\n\
Copyright (c) 2005-2011, Bruce D. Evans, Steven G. Kargl, David Schultz.\"");
asm(".ident\t\"\\n\\n\
fdlibm (fdlibm license)\\n\
Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.\"");
asm(".ident\t\"\\n\\n\
Musl libc (MIT License)\\n\
Copyright 2005-2014 Rich Felker, et. al.\"");
asm(".include \"libc/disclaimer.inc\"");
// clang-format off
/* origin: FreeBSD /usr/src/lib/msun/ld80/k_cosl.c */
/* origin: FreeBSD /usr/src/lib/msun/ld128/k_cosl.c */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
* Copyright (c) 2008 Steven G. Kargl, David Schultz, Bruce D. Evans.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
#if (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
#if LDBL_MANT_DIG == 64
/*
* ld80 version of __cos.c. See __cos.c for most comments.
*/
/*
* Domain [-0.7854, 0.7854], range ~[-2.43e-23, 2.425e-23]:
* |cos(x) - c(x)| < 2**-75.1
*
* The coefficients of c(x) were generated by a pari-gp script using
* a Remez algorithm that searches for the best higher coefficients
* after rounding leading coefficients to a specified precision.
*
* Simpler methods like Chebyshev or basic Remez barely suffice for
* cos() in 64-bit precision, because we want the coefficient of x^2
* to be precisely -0.5 so that multiplying by it is exact, and plain
* rounding of the coefficients of a good polynomial approximation only
* gives this up to about 64-bit precision. Plain rounding also gives
* a mediocre approximation for the coefficient of x^4, but a rounding
* error of 0.5 ulps for this coefficient would only contribute ~0.01
* ulps to the final error, so this is unimportant. Rounding errors in
* higher coefficients are even less important.
*
* In fact, coefficients above the x^4 one only need to have 53-bit
* precision, and this is more efficient. We get this optimization
* almost for free from the complications needed to search for the best
* higher coefficients.
*/
static const long double
C1 = 0.0416666666666666666136L; /* 0xaaaaaaaaaaaaaa9b.0p-68 */
static const double
C2 = -0.0013888888888888874, /* -0x16c16c16c16c10.0p-62 */
C3 = 0.000024801587301571716, /* 0x1a01a01a018e22.0p-68 */
C4 = -0.00000027557319215507120, /* -0x127e4fb7602f22.0p-74 */
C5 = 0.0000000020876754400407278, /* 0x11eed8caaeccf1.0p-81 */
C6 = -1.1470297442401303e-11, /* -0x19393412bd1529.0p-89 */
C7 = 4.7383039476436467e-14; /* 0x1aac9d9af5c43e.0p-97 */
#define POLY(z) (z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*(C6+z*C7)))))))
#elif LDBL_MANT_DIG == 113
/*
* ld128 version of __cos.c. See __cos.c for most comments.
*/
/*
* Domain [-0.7854, 0.7854], range ~[-1.80e-37, 1.79e-37]:
* |cos(x) - c(x))| < 2**-122.0
*
* 113-bit precision requires more care than 64-bit precision, since
* simple methods give a minimax polynomial with coefficient for x^2
* that is 1 ulp below 0.5, but we want it to be precisely 0.5. See
* above for more details.
*/
static const long double
C1 = 0.04166666666666666666666666666666658424671L,
C2 = -0.001388888888888888888888888888863490893732L,
C3 = 0.00002480158730158730158730158600795304914210L,
C4 = -0.2755731922398589065255474947078934284324e-6L,
C5 = 0.2087675698786809897659225313136400793948e-8L,
C6 = -0.1147074559772972315817149986812031204775e-10L,
C7 = 0.4779477332386808976875457937252120293400e-13L;
static const double
C8 = -0.1561920696721507929516718307820958119868e-15,
C9 = 0.4110317413744594971475941557607804508039e-18,
C10 = -0.8896592467191938803288521958313920156409e-21,
C11 = 0.1601061435794535138244346256065192782581e-23;
#define POLY(z) (z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*(C6+z*(C7+ \
z*(C8+z*(C9+z*(C10+z*C11)))))))))))
#endif
long double __cosl(long double x, long double y)
{
long double hz,z,r,w;
z = x*x;
r = POLY(z);
hz = 0.5*z;
w = 1.0-hz;
return w + (((1.0-w)-hz) + (z*r-x*y));
}
#endif
| 6,919 | 136 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/coshf.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
#include "libc/tinymath/expo.internal.h"
#include "libc/tinymath/feval.internal.h"
asm(".ident\t\"\\n\\n\
Musl libc (MIT License)\\n\
Copyright 2005-2014 Rich Felker, et. al.\"");
asm(".include \"libc/disclaimer.inc\"");
/* clang-format off */
/**
* Returns hyperbolic cosine of ð¥.
*
* cosh(x) = (exp(x) + 1/exp(x))/2
* = 1 + 0.5*(exp(x)-1)*(exp(x)-1)/exp(x)
* = 1 + x*x/2 + o(x^4)
*/
float coshf(float x)
{
union {float f; uint32_t i;} u = {.f = x};
uint32_t w;
float t;
/* |x| */
u.i &= 0x7fffffff;
x = u.f;
w = u.i;
/* |x| < log(2) */
if (w < 0x3f317217) {
if (w < 0x3f800000 - (12<<23)) {
feval(x + 0x1p120f);
return 1;
}
t = expm1f(x);
return 1 + t*t/(2*(1+t));
}
/* |x| < log(FLT_MAX) */
if (w < 0x42b17217) {
t = expf(x);
return 0.5f*(t + 1/t);
}
/* |x| > log(FLT_MAX) or nan */
t = __expo2f(x, 1.0f);
return t;
}
| 3,523 | 76 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/__math_xflowf.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/tinymath/internal.h"
// clang-format off
float __math_xflowf(uint32_t sign, float y)
{
return eval_as_float(fp_barrierf(sign ? -y : y) * y);
}
| 2,762 | 35 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/log1pf_data.internal.h | #ifndef COSMOPOLITAN_LIBC_TINYMATH_LOG1PF_DATA_H_
#define COSMOPOLITAN_LIBC_TINYMATH_LOG1PF_DATA_H_
#if !(__ASSEMBLER__ + __LINKER__ + 0)
COSMOPOLITAN_C_START_
#define LOG1PF_2U5
#define V_LOG1PF_2U5
#define LOG1PF_NCOEFFS 9
extern const struct log1pf_data {
float coeffs[LOG1PF_NCOEFFS];
} __log1pf_data _Hide;
COSMOPOLITAN_C_END_
#endif /* !(__ASSEMBLER__ + __LINKER__ + 0) */
#endif /* COSMOPOLITAN_LIBC_TINYMATH_LOG1PF_DATA_H_ */
| 438 | 16 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/tanl.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
#include "libc/tinymath/internal.h"
#include "libc/tinymath/kernel.internal.h"
#include "libc/tinymath/ldshape.internal.h"
#if !(LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024)
asm(".ident\t\"\\n\\n\
Musl libc (MIT License)\\n\
Copyright 2005-2014 Rich Felker, et. al.\"");
asm(".include \"libc/disclaimer.inc\"");
// clang-format off
/**
* Returns tangent of x.
*/
long double tanl(long double x)
{
union ldshape u = {x};
long double y[2];
unsigned n;
u.i.se &= 0x7fff;
if (u.i.se == 0x7fff)
return x - x;
if (u.f < M_PI_4) {
if (u.i.se < 0x3fff - LDBL_MANT_DIG/2) {
/* raise inexact if x!=0 and underflow if subnormal */
FORCE_EVAL(u.i.se == 0 ? x*0x1p-120f : x+0x1p120f);
return x;
}
return __tanl(x, 0, 0);
}
n = __rem_pio2l(x, y);
return __tanl(y[0], y[1], n&1);
}
#endif /* long double is long */
| 3,457 | 65 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/logb.c | /*-*- mode:c;indent-tabs-mode:nil;c-basic-offset:2;tab-width:8;coding:utf-8 -*-â
âvi: set net ft=c ts=2 sts=2 sw=2 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ¡
â Copyright 2023 Justine Alexandra Roberts Tunney â
â â
â Permission to use, copy, modify, and/or distribute this software for â
â any purpose with or without fee is hereby granted, provided that the â
â above copyright notice and this permission notice appear in all copies. â
â â
â THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL â
â WARRANTIES WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED â
â WARRANTIES OF MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE â
â AUTHOR BE LIABLE FOR ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL â
â DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR â
â PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER â
â TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR â
â PERFORMANCE OF THIS SOFTWARE. â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
double logb(double x) {
if (!isfinite(x)) return x * x;
if (!x) return -1 / (x * x);
return ilogb(x);
}
| 1,970 | 26 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/sincosf.c | /*-*- mode:c;indent-tabs-mode:nil;c-basic-offset:2;tab-width:8;coding:utf-8 -*-â
âvi: set net ft=c ts=2 sts=2 sw=2 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Optimized Routines â
â Copyright (c) 1999-2022, Arm Limited. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/intrin/likely.h"
#include "libc/math.h"
#include "libc/tinymath/sincosf.internal.h"
asm(".ident\t\"\\n\\n\
Optimized Routines (MIT License)\\n\
Copyright 2022 ARM Limited\"");
asm(".include \"libc/disclaimer.inc\"");
// clang-format off
/* Fast sincosf implementation. Worst-case ULP is 0.5607, maximum relative
error is 0.5303 * 2^-23. A single-step range reduction is used for
small values. Large inputs have their range reduced using fast integer
arithmetic. */
void
sincosf (float y, float *sinp, float *cosp)
{
double x = y;
double s;
int n;
const sincos_t *p = &__sincosf_table[0];
if (abstop12 (y) < abstop12 (pio4f))
{
double x2 = x * x;
if (UNLIKELY (abstop12 (y) < abstop12 (0x1p-12f)))
{
if (UNLIKELY (abstop12 (y) < abstop12 (0x1p-126f)))
/* Force underflow for tiny y. */
FORCE_EVAL (x2);
*sinp = y;
*cosp = 1.0f;
return;
}
sincosf_poly (x, x2, p, 0, sinp, cosp);
}
else if (abstop12 (y) < abstop12 (120.0f))
{
x = reduce_fast (x, p, &n);
/* Setup the signs for sin and cos. */
s = p->sign[n & 3];
if (n & 2)
p = &__sincosf_table[1];
sincosf_poly (x * s, x * x, p, n, sinp, cosp);
}
else if (LIKELY (abstop12 (y) < abstop12 (INFINITY)))
{
uint32_t xi = asuint (y);
int sign = xi >> 31;
x = reduce_large (xi, &n);
/* Setup signs for sin and cos - include original sign. */
s = p->sign[(n + sign) & 3];
if ((n + sign) & 2)
p = &__sincosf_table[1];
sincosf_poly (x * s, x * x, p, n, sinp, cosp);
}
else
{
/* Return NaN if Inf or NaN for both sin and cos. */
*sinp = *cosp = y - y;
#if WANT_ERRNO
/* Needed to set errno for +-Inf, the add is a hack to work
around a gcc register allocation issue: just passing y
affects code generation in the fast path. */
__math_invalidf (y + y);
#endif
}
}
| 4,540 | 105 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/cpowf.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/complex.h"
#include "libc/math.h"
#include "libc/tinymath/complex.internal.h"
asm(".ident\t\"\\n\\n\
Musl libc (MIT License)\\n\
Copyright 2005-2014 Rich Felker, et. al.\"");
asm(".include \"libc/disclaimer.inc\"");
/* clang-format off */
float complex cpowf(float complex z, float complex c)
{
return cexpf(c * clogf(z));
}
| 2,947 | 44 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/LICENSE.musl | musl as a whole is licensed under the following standard MIT license:
----------------------------------------------------------------------
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.
----------------------------------------------------------------------
Authors/contributors include:
A. Wilcox
Ada Worcester
Alex Dowad
Alex Suykov
Alexander Monakov
Andre McCurdy
Andrew Kelley
Anthony G. Basile
Aric Belsito
Arvid Picciani
Bartosz Brachaczek
Benjamin Peterson
Bobby Bingham
Boris Brezillon
Brent Cook
Chris Spiegel
Clément Vasseur
Daniel Micay
Daniel Sabogal
Daurnimator
David Carlier
David Edelsohn
Denys Vlasenko
Dmitry Ivanov
Dmitry V. Levin
Drew DeVault
Emil Renner Berthing
Fangrui Song
Felix Fietkau
Felix Janda
Gianluca Anzolin
Hauke Mehrtens
He X
Hiltjo Posthuma
Isaac Dunham
Jaydeep Patil
Jens Gustedt
Jeremy Huntwork
Jo-Philipp Wich
Joakim Sindholt
John Spencer
Julien Ramseier
Justin Cormack
Kaarle Ritvanen
Khem Raj
Kylie McClain
Leah Neukirchen
Luca Barbato
Luka Perkov
M Farkas-Dyck (Strake)
Mahesh Bodapati
Markus Wichmann
Masanori Ogino
Michael Clark
Michael Forney
Mikhail Kremnyov
Natanael Copa
Nicholas J. Kain
orc
Pascal Cuoq
Patrick Oppenlander
Petr Hosek
Petr Skocik
Pierre Carrier
Reini Urban
Rich Felker
Richard Pennington
Ryan Fairfax
Samuel Holland
Segev Finer
Shiz
sin
Solar Designer
Stefan Kristiansson
Stefan O'Rear
Szabolcs Nagy
Timo Teräs
Trutz Behn
Valentin Ochs
Will Dietz
William Haddon
William Pitcock
Portions of this software are derived from third-party works licensed
under terms compatible with the above MIT license:
The TRE regular expression implementation (src/regex/reg* and
src/regex/tre*) is Copyright © 2001-2008 Ville Laurikari and licensed
under a 2-clause BSD license (license text in the source files). The
included version has been heavily modified by Rich Felker in 2012, in
the interests of size, simplicity, and namespace cleanliness.
Much of the math library code (src/math/* and src/complex/*) is
Copyright © 1993,2004 Sun Microsystems or
Copyright © 2003-2011 David Schultz or
Copyright © 2003-2009 Steven G. Kargl or
Copyright © 2003-2009 Bruce D. Evans or
Copyright © 2008 Stephen L. Moshier or
Copyright © 2017-2018 Arm Limited
and labelled as such in comments in the individual source files. All
have been licensed under extremely permissive terms.
The ARM memcpy code (src/string/arm/memcpy.S) is Copyright © 2008
The Android Open Source Project and is licensed under a two-clause BSD
license. It was taken from Bionic libc, used on Android.
The AArch64 memcpy and memset code (src/string/aarch64/*) are
Copyright © 1999-2019, Arm Limited.
The implementation of DES for crypt (src/crypt/crypt_des.c) is
Copyright © 1994 David Burren. It is licensed under a BSD license.
The implementation of blowfish crypt (src/crypt/crypt_blowfish.c) was
originally written by Solar Designer and placed into the public
domain. The code also comes with a fallback permissive license for use
in jurisdictions that may not recognize the public domain.
The smoothsort implementation (src/stdlib/qsort.c) is Copyright © 2011
Valentin Ochs and is licensed under an MIT-style license.
The x86_64 port was written by Nicholas J. Kain and is licensed under
the standard MIT terms.
The mips and microblaze ports were originally written by Richard
Pennington for use in the ellcc project. The original code was adapted
by Rich Felker for build system and code conventions during upstream
integration. It is licensed under the standard MIT terms.
The mips64 port was contributed by Imagination Technologies and is
licensed under the standard MIT terms.
The powerpc port was also originally written by Richard Pennington,
and later supplemented and integrated by John Spencer. It is licensed
under the standard MIT terms.
All other files which have no copyright comments are original works
produced specifically for use as part of this library, written either
by Rich Felker, the main author of the library, or by one or more
contibutors listed above. Details on authorship of individual files
can be found in the git version control history of the project. The
omission of copyright and license comments in each file is in the
interest of source tree size.
In addition, permission is hereby granted for all public header files
(include/* and arch/*/bits/*) and crt files intended to be linked into
applications (crt/*, ldso/dlstart.c, and arch/*/crt_arch.h) to omit
the copyright notice and permission notice otherwise required by the
license, and to use these files without any requirement of
attribution. These files include substantial contributions from:
Bobby Bingham
John Spencer
Nicholas J. Kain
Rich Felker
Richard Pennington
Stefan Kristiansson
Szabolcs Nagy
all of whom have explicitly granted such permission.
This file previously contained text expressing a belief that most of
the files covered by the above exception were sufficiently trivial not
to be subject to copyright, resulting in confusion over whether it
negated the permissions granted in the license. In the spirit of
permissive licensing, and of not having licensing issues being an
obstacle to adoption, that text has been removed.
| 6,204 | 194 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/log2f_data.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/tinymath/log2f_data.internal.h"
asm(".ident\t\"\\n\\n\
Double-precision math functions (MIT License)\\n\
Copyright 2018 ARM Limited\"");
asm(".include \"libc/disclaimer.inc\"");
/* clang-format off */
/*
* Data definition for log2f.
*
* Copyright (c) 2017-2018, Arm Limited.
* SPDX-License-Identifier: MIT
*/
const struct log2f_data __log2f_data = {
.tab = {
{ 0x1.661ec79f8f3bep+0, -0x1.efec65b963019p-2 },
{ 0x1.571ed4aaf883dp+0, -0x1.b0b6832d4fca4p-2 },
{ 0x1.49539f0f010bp+0, -0x1.7418b0a1fb77bp-2 },
{ 0x1.3c995b0b80385p+0, -0x1.39de91a6dcf7bp-2 },
{ 0x1.30d190c8864a5p+0, -0x1.01d9bf3f2b631p-2 },
{ 0x1.25e227b0b8eap+0, -0x1.97c1d1b3b7afp-3 },
{ 0x1.1bb4a4a1a343fp+0, -0x1.2f9e393af3c9fp-3 },
{ 0x1.12358f08ae5bap+0, -0x1.960cbbf788d5cp-4 },
{ 0x1.0953f419900a7p+0, -0x1.a6f9db6475fcep-5 },
{ 0x1p+0, 0x0p+0 },
{ 0x1.e608cfd9a47acp-1, 0x1.338ca9f24f53dp-4 },
{ 0x1.ca4b31f026aap-1, 0x1.476a9543891bap-3 },
{ 0x1.b2036576afce6p-1, 0x1.e840b4ac4e4d2p-3 },
{ 0x1.9c2d163a1aa2dp-1, 0x1.40645f0c6651cp-2 },
{ 0x1.886e6037841edp-1, 0x1.88e9c2c1b9ff8p-2 },
{ 0x1.767dcf5534862p-1, 0x1.ce0a44eb17bccp-2 },
},
.poly = {
-0x1.712b6f70a7e4dp-2, 0x1.ecabf496832ep-2, -0x1.715479ffae3dep-1,
0x1.715475f35c8b8p0,
}
};
| 3,879 | 67 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/log10f.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
asm(".ident\t\"\\n\\n\
fdlibm (fdlibm license)\\n\
Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.\"");
asm(".ident\t\"\\n\\n\
Musl libc (MIT License)\\n\
Copyright 2005-2014 Rich Felker, et. al.\"");
asm(".include \"libc/disclaimer.inc\"");
// clang-format off
/* origin: FreeBSD /usr/src/lib/msun/src/e_log10f.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.
* ====================================================
*/
/*
* See comments in log10.c.
*/
static const float
ivln10hi = 4.3432617188e-01, /* 0x3ede6000 */
ivln10lo = -3.1689971365e-05, /* 0xb804ead9 */
log10_2hi = 3.0102920532e-01, /* 0x3e9a2080 */
log10_2lo = 7.9034151668e-07, /* 0x355427db */
/* |(log(1+s)-log(1-s))/s - Lg(s)| < 2**-34.24 (~[-4.95e-11, 4.97e-11]). */
Lg1 = 0xaaaaaa.0p-24, /* 0.66666662693 */
Lg2 = 0xccce13.0p-25, /* 0.40000972152 */
Lg3 = 0x91e9ee.0p-25, /* 0.28498786688 */
Lg4 = 0xf89e26.0p-26; /* 0.24279078841 */
/**
* Calculates logââð¥.
*/
float log10f(float x)
{
union {float f; uint32_t i;} u = {x};
float_t hfsq,f,s,z,R,w,t1,t2,dk,hi,lo;
uint32_t ix;
int k;
ix = u.i;
k = 0;
if (ix < 0x00800000 || ix>>31) { /* x < 2**-126 */
if (ix<<1 == 0)
return -1/(x*x); /* log(+-0)=-inf */
if (ix>>31)
return (x-x)/0.0f; /* log(-#) = NaN */
/* subnormal number, scale up x */
k -= 25;
x *= 0x1p25f;
u.f = x;
ix = u.i;
} else if (ix >= 0x7f800000) {
return x;
} else if (ix == 0x3f800000)
return 0;
/* reduce x into [sqrt(2)/2, sqrt(2)] */
ix += 0x3f800000 - 0x3f3504f3;
k += (int)(ix>>23) - 0x7f;
ix = (ix&0x007fffff) + 0x3f3504f3;
u.i = ix;
x = u.f;
f = x - 1.0f;
s = f/(2.0f + f);
z = s*s;
w = z*z;
t1= w*(Lg2+w*Lg4);
t2= z*(Lg1+w*Lg3);
R = t2 + t1;
hfsq = 0.5f*f*f;
hi = f - hfsq;
u.f = hi;
u.i &= 0xfffff000;
hi = u.f;
lo = f - hi - hfsq + s*(hfsq+R);
dk = k;
return dk*log10_2lo + (lo+hi)*ivln10lo + lo*ivln10hi + hi*ivln10hi + dk*log10_2hi;
}
| 4,833 | 116 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/rempio2l.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2020 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/intrin/likely.h"
#include "libc/math.h"
#include "libc/tinymath/kernel.internal.h"
#include "libc/tinymath/ldshape.internal.h"
asm(".ident\t\"\\n\\n\
FreeBSD libm (BSD-2 License)\\n\
Copyright (c) 2005-2011, Bruce D. Evans, Steven G. Kargl, David Schultz.\"");
asm(".ident\t\"\\n\\n\
fdlibm (fdlibm license)\\n\
Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.\"");
asm(".ident\t\"\\n\\n\
Musl libc (MIT License)\\n\
Copyright 2005-2014 Rich Felker, et. al.\"");
asm(".include \"libc/disclaimer.inc\"");
// clang-format off
/* origin: FreeBSD /usr/src/lib/msun/ld80/e_rem_pio2.c */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
* Copyright (c) 2008 Steven G. Kargl, David Schultz, Bruce D. Evans.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*
* Optimized by Bruce D. Evans.
*/
#if (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
/* ld80 and ld128 version of __rem_pio2(x,y)
*
* return the remainder of x rem pi/2 in y[0]+y[1]
* use __rem_pio2_large() for large x
*/
static const long double toint = 1.5/LDBL_EPSILON;
#if LDBL_MANT_DIG == 64
/* u ~< 0x1p25*pi/2 */
#define SMALL(u) (((u.i.se & 0x7fffU)<<16 | u.i.m>>48) < ((0x3fff + 25)<<16 | 0x921f>>1 | 0x8000))
#define QUOBITS(x) ((uint32_t)(int32_t)x & 0x7fffffff)
#define ROUND1 22
#define ROUND2 61
#define NX 3
#define NY 2
/*
* invpio2: 64 bits of 2/pi
* pio2_1: first 39 bits of pi/2
* pio2_1t: pi/2 - pio2_1
* pio2_2: second 39 bits of pi/2
* pio2_2t: pi/2 - (pio2_1+pio2_2)
* pio2_3: third 39 bits of pi/2
* pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3)
*/
static const double
pio2_1 = 1.57079632679597125389e+00, /* 0x3FF921FB, 0x54444000 */
pio2_2 = -1.07463465549783099519e-12, /* -0x12e7b967674000.0p-92 */
pio2_3 = 6.36831716351370313614e-25; /* 0x18a2e037074000.0p-133 */
static const long double
pio4 = 0x1.921fb54442d1846ap-1L,
invpio2 = 6.36619772367581343076e-01L, /* 0xa2f9836e4e44152a.0p-64 */
pio2_1t = -1.07463465549719416346e-12L, /* -0x973dcb3b399d747f.0p-103 */
pio2_2t = 6.36831716351095013979e-25L, /* 0xc51701b839a25205.0p-144 */
pio2_3t = -2.75299651904407171810e-37L; /* -0xbb5bf6c7ddd660ce.0p-185 */
#elif LDBL_MANT_DIG == 113
/* u ~< 0x1p45*pi/2 */
#define SMALL(u) (((u.i.se & 0x7fffU)<<16 | u.i.top) < ((0x3fff + 45)<<16 | 0x921f))
#define QUOBITS(x) ((uint32_t)(int64_t)x & 0x7fffffff)
#define ROUND1 51
#define ROUND2 119
#define NX 5
#define NY 3
static const long double
pio4 = 0x1.921fb54442d18469898cc51701b8p-1L,
invpio2 = 6.3661977236758134307553505349005747e-01L, /* 0x145f306dc9c882a53f84eafa3ea6a.0p-113 */
pio2_1 = 1.5707963267948966192292994253909555e+00L, /* 0x1921fb54442d18469800000000000.0p-112 */
pio2_1t = 2.0222662487959507323996846200947577e-21L, /* 0x13198a2e03707344a4093822299f3.0p-181 */
pio2_2 = 2.0222662487959507323994779168837751e-21L, /* 0x13198a2e03707344a400000000000.0p-181 */
pio2_2t = 2.0670321098263988236496903051604844e-43L, /* 0x127044533e63a0105df531d89cd91.0p-254 */
pio2_3 = 2.0670321098263988236499468110329591e-43L, /* 0x127044533e63a0105e00000000000.0p-254 */
pio2_3t = -2.5650587247459238361625433492959285e-65L; /* -0x159c4ec64ddaeb5f78671cbfb2210.0p-327 */
#endif
int __rem_pio2l(long double x, long double *y)
{
union ldshape u,uz;
long double z,w,t,r,fn;
double tx[NX],ty[NY];
int ex,ey,n,i;
u.f = x;
ex = u.i.se & 0x7fff;
if (SMALL(u)) {
/* rint(x/(pi/2)) */
fn = x*invpio2 + toint - toint;
n = QUOBITS(fn);
r = x-fn*pio2_1;
w = fn*pio2_1t; /* 1st round good to 102/180 bits (ld80/ld128) */
/* Matters with directed rounding. */
if (UNLIKELY(r - w < -pio4)) {
n--;
fn--;
r = x - fn*pio2_1;
w = fn*pio2_1t;
} else if (UNLIKELY(r - w > pio4)) {
n++;
fn++;
r = x - fn*pio2_1;
w = fn*pio2_1t;
}
y[0] = r-w;
u.f = y[0];
ey = u.i.se & 0x7fff;
if (ex - ey > ROUND1) { /* 2nd iteration needed, good to 141/248 (ld80/ld128) */
t = r;
w = fn*pio2_2;
r = t-w;
w = fn*pio2_2t-((t-r)-w);
y[0] = r-w;
u.f = y[0];
ey = u.i.se & 0x7fff;
if (ex - ey > ROUND2) { /* 3rd iteration, good to 180/316 bits */
t = r; /* will cover all possible cases (not verified for ld128) */
w = fn*pio2_3;
r = t-w;
w = fn*pio2_3t-((t-r)-w);
y[0] = r-w;
}
}
y[1] = (r - y[0]) - w;
return n;
}
/*
* all other (large) arguments
*/
if (ex == 0x7fff) { /* x is inf or NaN */
y[0] = y[1] = x - x;
return 0;
}
/* set z = scalbn(|x|,-ilogb(x)+23) */
uz.f = x;
uz.i.se = 0x3fff + 23;
z = uz.f;
for (i=0; i < NX - 1; i++) {
tx[i] = (double)(int32_t)z;
z = (z-tx[i])*0x1p24;
}
tx[i] = z;
while (tx[i] == 0)
i--;
n = __rem_pio2_large(tx, ty, ex-0x3fff-23, i+1, NY);
w = ty[1];
if (NY == 3)
w += ty[2];
r = ty[0] + w;
/* TODO: for ld128 this does not follow the recommendation of the
comments of __rem_pio2_large which seem wrong if |ty[0]| > |ty[1]+ty[2]| */
w -= r - ty[0];
if (u.i.se >> 15) {
y[0] = -r;
y[1] = -w;
return -n;
}
y[0] = r;
y[1] = w;
return n;
}
#else
#error "architecture unsupported"
#endif
| 7,979 | 203 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/__math_xflow.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/tinymath/internal.h"
// clang-format off
double __math_xflow(uint32_t sign, double y)
{
return eval_as_double(fp_barrier(sign ? -y : y) * y);
}
| 2,763 | 35 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/expo.internal.h | #ifndef COSMOPOLITAN_LIBC_TINYMATH_EXPO_H_
#define COSMOPOLITAN_LIBC_TINYMATH_EXPO_H_
#if !(__ASSEMBLER__ + __LINKER__ + 0)
COSMOPOLITAN_C_START_
double __expo2(double, double);
float __expo2f(float, float);
COSMOPOLITAN_C_END_
#endif /* !(__ASSEMBLER__ + __LINKER__ + 0) */
#endif /* COSMOPOLITAN_LIBC_TINYMATH_EXPO_H_ */
| 325 | 12 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/horner.internal.h | #ifndef COSMOPOLITAN_LIBC_TINYMATH_HORNER_INTERNAL_H_
#define COSMOPOLITAN_LIBC_TINYMATH_HORNER_INTERNAL_H_
#include "libc/math.h"
#if !(__ASSEMBLER__ + __LINKER__ + 0)
COSMOPOLITAN_C_START_
#if WANT_VMATH
#define FMA(x, y, z) vfmaq_f64(z, x, y)
#else
#define FMA fma
#endif
#include "libc/tinymath/horner_wrap.internal.h"
COSMOPOLITAN_C_END_
#endif /* !(__ASSEMBLER__ + __LINKER__ + 0) */
#endif /* COSMOPOLITAN_LIBC_TINYMATH_HORNER_INTERNAL_H_ */
| 452 | 18 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/remquof.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2020 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
asm(".ident\t\"\\n\\n\
Musl libc (MIT License)\\n\
Copyright 2005-2014 Rich Felker, et. al.\"");
asm(".include \"libc/disclaimer.inc\"");
// clang-format off
/**
* Computes remainder and part of quotient.
*/
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;
}
| 4,167 | 118 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/fsum.c | /*-*- mode:c;indent-tabs-mode:nil;c-basic-offset:2;tab-width:8;coding:utf-8 -*-â
âvi: set net ft=c ts=2 sts=2 sw=2 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ¡
â Copyright 2021 Justine Alexandra Roberts Tunney â
â â
â Permission to use, copy, modify, and/or distribute this software for â
â any purpose with or without fee is hereby granted, provided that the â
â above copyright notice and this permission notice appear in all copies. â
â â
â THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL â
â WARRANTIES WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED â
â WARRANTIES OF MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE â
â AUTHOR BE LIABLE FOR ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL â
â DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR â
â PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER â
â TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR â
â PERFORMANCE OF THIS SOFTWARE. â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
/**
* Adds doubles in array.
*/
double fsum(const double *p, size_t n) {
size_t i;
double err, sum, t, y;
sum = err = 0;
for (i = 0; i < n; ++i) {
y = p[i] - err;
t = sum + y;
err = (t - sum) - y;
sum = t;
}
return sum;
}
| 2,112 | 36 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/acos.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2020 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
asm(".ident\t\"\\n\\n\
Musl libc (MIT License)\\n\
Copyright 2005-2014 Rich Felker, et. al.\"");
asm(".include \"libc/disclaimer.inc\"");
// clang-format off
/* origin: FreeBSD /usr/src/lib/msun/src/e_acos.c */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/* acos(x)
* Method :
* acos(x) = pi/2 - asin(x)
* acos(-x) = pi/2 + asin(x)
* For |x|<=0.5
* acos(x) = pi/2 - (x + x*x^2*R(x^2)) (see asin.c)
* For x>0.5
* acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2)))
* = 2asin(sqrt((1-x)/2))
* = 2s + 2s*z*R(z) ...z=(1-x)/2, s=sqrt(z)
* = 2f + (2c + 2s*z*R(z))
* where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term
* for f so that f+c ~ sqrt(z).
* For x<-0.5
* acos(x) = pi - 2asin(sqrt((1-|x|)/2))
* = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z)
*
* Special cases:
* if x is NaN, return x itself;
* if |x|>1, return NaN with invalid signal.
*
* Function needed: sqrt
*/
static const double
pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */
pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */
pS0 = 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */
pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */
pS2 = 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */
pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */
pS4 = 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */
pS5 = 3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */
qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */
qS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */
qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */
qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */
static double R(double z)
{
double_t p, q;
p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
q = 1.0+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
return p/q;
}
/**
* Returns arc cosine of ð¥.
*
* @return value in range [0,M_PI]
* @return NAN if ð¥ â {NAN,+INFINITY,-INFINITY}
* @return NAN if ð¥ â [-1,1]
*/
double acos(double x)
{
double z,w,s,c,df;
uint32_t hx,lx,ix;
union {
double f;
uint64_t i;
} u = {x};
hx = u.i >> 32;
ix = hx & 0x7fffffff;
/* |x| >= 1 or nan */
if (ix >= 0x3ff00000) {
lx = u.i;
if ((ix-0x3ff00000 | lx) == 0) {
/* acos(1)=0, acos(-1)=pi */
if (hx >> 31)
return 2*pio2_hi + 0x1p-120f;
return 0;
}
return 0/(x-x);
}
/* |x| < 0.5 */
if (ix < 0x3fe00000) {
if (ix <= 0x3c600000) /* |x| < 2**-57 */
return pio2_hi + 0x1p-120f;
return pio2_hi - (x - (pio2_lo-x*R(x*x)));
}
/* x < -0.5 */
if (hx >> 31) {
z = (1.0+x)*0.5;
s = sqrt(z);
w = R(z)*s-pio2_lo;
return 2*(pio2_hi - (s+w));
}
/* x > 0.5 */
z = (1.0-x)*0.5;
s = sqrt(z);
u.f = s;
u.i &= 0xffffffff00000000;
df = u.f;
c = (z-df*df)/(s+df);
w = R(z)*s+c;
return 2*(df+w);
}
#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
__strong_reference(acos, acosl);
#endif
| 5,986 | 148 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/measureentropy.c | /*-*- mode:c;indent-tabs-mode:nil;c-basic-offset:2;tab-width:8;coding:utf-8 -*-â
âvi: set net ft=c ts=2 sts=2 sw=2 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ¡
â Copyright 2021 Justine Alexandra Roberts Tunney â
â â
â Permission to use, copy, modify, and/or distribute this software for â
â any purpose with or without fee is hereby granted, provided that the â
â above copyright notice and this permission notice appear in all copies. â
â â
â THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL â
â WARRANTIES WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED â
â WARRANTIES OF MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE â
â AUTHOR BE LIABLE FOR ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL â
â DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR â
â PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER â
â TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR â
â PERFORMANCE OF THIS SOFTWARE. â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
#include "libc/stdio/rand.h"
#include "libc/str/str.h"
/**
* Returns Shannon entropy of array.
*
* This gives you an idea of the density of information. Cryptographic
* random should be in the ballpark of 7.9 whereas plaintext will be
* more like 4.5.
*
* @param p is treated as binary octets
* @param n should be at least 1000
* @return number between 0 and 8
*/
double MeasureEntropy(const char *p, size_t n) {
size_t i;
double e, x;
long h[256];
e = 0;
if (n) {
bzero(h, sizeof(h));
for (i = 0; i < n; ++i) {
++h[p[i] & 255];
}
for (i = 0; i < 256; i++) {
if (h[i]) {
x = h[i];
x /= n;
e += x * log(x);
}
}
e = -(e / M_LN2);
}
return e;
}
| 2,592 | 55 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/frexpf.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2020 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
asm(".ident\t\"\\n\\n\
Musl libc (MIT License)\\n\
Copyright 2005-2014 Rich Felker, et. al.\"");
asm(".include \"libc/disclaimer.inc\"");
/* clang-format off */
/**
* Splits number normalized fraction and exponent.
*/
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;
}
| 3,160 | 59 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/lgammaf_r.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2020 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
#include "libc/tinymath/kernel.internal.h"
asm(".ident\t\"\\n\\n\
fdlibm (fdlibm license)\\n\
Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.\"");
asm(".ident\t\"\\n\\n\
Musl libc (MIT License)\\n\
Copyright 2005-2014 Rich Felker, et. al.\"");
asm(".include \"libc/disclaimer.inc\"");
// clang-format off
/* origin: FreeBSD /usr/src/lib/msun/src/e_lgammaf_r.c */
/*
* Conversion to float by Ian Lance Taylor, Cygnus Support, [email protected].
*/
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
static const float
pi = 3.1415927410e+00, /* 0x40490fdb */
a0 = 7.7215664089e-02, /* 0x3d9e233f */
a1 = 3.2246702909e-01, /* 0x3ea51a66 */
a2 = 6.7352302372e-02, /* 0x3d89f001 */
a3 = 2.0580807701e-02, /* 0x3ca89915 */
a4 = 7.3855509982e-03, /* 0x3bf2027e */
a5 = 2.8905137442e-03, /* 0x3b3d6ec6 */
a6 = 1.1927076848e-03, /* 0x3a9c54a1 */
a7 = 5.1006977446e-04, /* 0x3a05b634 */
a8 = 2.2086278477e-04, /* 0x39679767 */
a9 = 1.0801156895e-04, /* 0x38e28445 */
a10 = 2.5214456400e-05, /* 0x37d383a2 */
a11 = 4.4864096708e-05, /* 0x383c2c75 */
tc = 1.4616321325e+00, /* 0x3fbb16c3 */
tf = -1.2148628384e-01, /* 0xbdf8cdcd */
/* tt = -(tail of tf) */
tt = 6.6971006518e-09, /* 0x31e61c52 */
t0 = 4.8383611441e-01, /* 0x3ef7b95e */
t1 = -1.4758771658e-01, /* 0xbe17213c */
t2 = 6.4624942839e-02, /* 0x3d845a15 */
t3 = -3.2788541168e-02, /* 0xbd064d47 */
t4 = 1.7970675603e-02, /* 0x3c93373d */
t5 = -1.0314224288e-02, /* 0xbc28fcfe */
t6 = 6.1005386524e-03, /* 0x3bc7e707 */
t7 = -3.6845202558e-03, /* 0xbb7177fe */
t8 = 2.2596477065e-03, /* 0x3b141699 */
t9 = -1.4034647029e-03, /* 0xbab7f476 */
t10 = 8.8108185446e-04, /* 0x3a66f867 */
t11 = -5.3859531181e-04, /* 0xba0d3085 */
t12 = 3.1563205994e-04, /* 0x39a57b6b */
t13 = -3.1275415677e-04, /* 0xb9a3f927 */
t14 = 3.3552918467e-04, /* 0x39afe9f7 */
u0 = -7.7215664089e-02, /* 0xbd9e233f */
u1 = 6.3282704353e-01, /* 0x3f2200f4 */
u2 = 1.4549225569e+00, /* 0x3fba3ae7 */
u3 = 9.7771751881e-01, /* 0x3f7a4bb2 */
u4 = 2.2896373272e-01, /* 0x3e6a7578 */
u5 = 1.3381091878e-02, /* 0x3c5b3c5e */
v1 = 2.4559779167e+00, /* 0x401d2ebe */
v2 = 2.1284897327e+00, /* 0x4008392d */
v3 = 7.6928514242e-01, /* 0x3f44efdf */
v4 = 1.0422264785e-01, /* 0x3dd572af */
v5 = 3.2170924824e-03, /* 0x3b52d5db */
s0 = -7.7215664089e-02, /* 0xbd9e233f */
s1 = 2.1498242021e-01, /* 0x3e5c245a */
s2 = 3.2577878237e-01, /* 0x3ea6cc7a */
s3 = 1.4635047317e-01, /* 0x3e15dce6 */
s4 = 2.6642270386e-02, /* 0x3cda40e4 */
s5 = 1.8402845599e-03, /* 0x3af135b4 */
s6 = 3.1947532989e-05, /* 0x3805ff67 */
r1 = 1.3920053244e+00, /* 0x3fb22d3b */
r2 = 7.2193557024e-01, /* 0x3f38d0c5 */
r3 = 1.7193385959e-01, /* 0x3e300f6e */
r4 = 1.8645919859e-02, /* 0x3c98bf54 */
r5 = 7.7794247773e-04, /* 0x3a4beed6 */
r6 = 7.3266842264e-06, /* 0x36f5d7bd */
w0 = 4.1893854737e-01, /* 0x3ed67f1d */
w1 = 8.3333335817e-02, /* 0x3daaaaab */
w2 = -2.7777778450e-03, /* 0xbb360b61 */
w3 = 7.9365057172e-04, /* 0x3a500cfd */
w4 = -5.9518753551e-04, /* 0xba1c065c */
w5 = 8.3633989561e-04, /* 0x3a5b3dd2 */
w6 = -1.6309292987e-03; /* 0xbad5c4e8 */
/* sin(pi*x) assuming x > 2^-100, if sin(pi*x)==0 the sign is arbitrary */
static float sin_pi(float x)
{
double_t y;
int n;
/* spurious inexact if odd int */
x = 2*(x*0.5f - floorf(x*0.5f)); /* x mod 2.0 */
n = (int)(x*4);
n = (n+1)/2;
y = x - n*0.5f;
y *= 3.14159265358979323846;
switch (n) {
default: /* case 4: */
case 0: return __sindf(y);
case 1: return __cosdf(y);
case 2: return __sindf(-y);
case 3: return -__cosdf(y);
}
}
/**
* Returns natural logarithm of absolute value of Gamma function.
*/
float lgammaf_r(float x, int *signgamp)
{
union {float f; uint32_t i;} u = {x};
float t,y,z,nadj,p,p1,p2,p3,q,r,w;
uint32_t ix;
int i,sign;
/* purge off +-inf, NaN, +-0, tiny and negative arguments */
*signgamp = 1;
sign = u.i>>31;
ix = u.i & 0x7fffffff;
if (ix >= 0x7f800000)
return x*x;
if (ix < 0x35000000) { /* |x| < 2**-21, return -log(|x|) */
if (sign) {
*signgamp = -1;
x = -x;
}
return -logf(x);
}
if (sign) {
x = -x;
t = sin_pi(x);
if (t == 0.0f) /* -integer */
return 1.0f/(x-x);
if (t > 0.0f)
*signgamp = -1;
else
t = -t;
nadj = logf(pi/(t*x));
}
/* purge off 1 and 2 */
if (ix == 0x3f800000 || ix == 0x40000000)
r = 0;
/* for x < 2.0 */
else if (ix < 0x40000000) {
if (ix <= 0x3f666666) { /* lgamma(x) = lgamma(x+1)-log(x) */
r = -logf(x);
if (ix >= 0x3f3b4a20) {
y = 1.0f - x;
i = 0;
} else if (ix >= 0x3e6d3308) {
y = x - (tc-1.0f);
i = 1;
} else {
y = x;
i = 2;
}
} else {
r = 0.0f;
if (ix >= 0x3fdda618) { /* [1.7316,2] */
y = 2.0f - x;
i = 0;
} else if (ix >= 0x3F9da620) { /* [1.23,1.73] */
y = x - tc;
i = 1;
} else {
y = x - 1.0f;
i = 2;
}
}
switch(i) {
case 0:
z = y*y;
p1 = a0+z*(a2+z*(a4+z*(a6+z*(a8+z*a10))));
p2 = z*(a1+z*(a3+z*(a5+z*(a7+z*(a9+z*a11)))));
p = y*p1+p2;
r += p - 0.5f*y;
break;
case 1:
z = y*y;
w = z*y;
p1 = t0+w*(t3+w*(t6+w*(t9 +w*t12))); /* parallel comp */
p2 = t1+w*(t4+w*(t7+w*(t10+w*t13)));
p3 = t2+w*(t5+w*(t8+w*(t11+w*t14)));
p = z*p1-(tt-w*(p2+y*p3));
r += (tf + p);
break;
case 2:
p1 = y*(u0+y*(u1+y*(u2+y*(u3+y*(u4+y*u5)))));
p2 = 1.0f+y*(v1+y*(v2+y*(v3+y*(v4+y*v5))));
r += -0.5f*y + p1/p2;
}
} else if (ix < 0x41000000) { /* x < 8.0 */
i = (int)x;
y = x - (float)i;
p = y*(s0+y*(s1+y*(s2+y*(s3+y*(s4+y*(s5+y*s6))))));
q = 1.0f+y*(r1+y*(r2+y*(r3+y*(r4+y*(r5+y*r6)))));
r = 0.5f*y+p/q;
z = 1.0f; /* lgamma(1+s) = log(s) + lgamma(s) */
switch (i) {
case 7: z *= y + 6.0f; /* FALLTHRU */
case 6: z *= y + 5.0f; /* FALLTHRU */
case 5: z *= y + 4.0f; /* FALLTHRU */
case 4: z *= y + 3.0f; /* FALLTHRU */
case 3: z *= y + 2.0f; /* FALLTHRU */
r += logf(z);
break;
}
} else if (ix < 0x5c800000) { /* 8.0 <= x < 2**58 */
t = logf(x);
z = 1.0f/x;
y = z*z;
w = w0+z*(w1+y*(w2+y*(w3+y*(w4+y*(w5+y*w6)))));
r = (x-0.5f)*(t-1.0f)+w;
} else /* 2**58 <= x <= inf */
r = x*(logf(x)-1.0f);
if (sign)
r = nadj - r;
return r;
}
| 9,202 | 257 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/casin.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/complex.h"
#include "libc/math.h"
#include "libc/tinymath/complex.internal.h"
asm(".ident\t\"\\n\\n\
Musl libc (MIT License)\\n\
Copyright 2005-2014 Rich Felker, et. al.\"");
asm(".include \"libc/disclaimer.inc\"");
// clang-format off
// FIXME
/* asin(z) = -i log(i z + sqrt(1 - z*z)) */
double complex casin(double complex z)
{
double complex w;
double x, y;
x = creal(z);
y = cimag(z);
w = CMPLX(1.0 - (x - y)*(x + y), -2.0*x*y);
double complex r = clog(CMPLX(-y, x) + csqrt(w));
return CMPLX(cimag(r), -creal(r));
}
#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
__strong_reference(casin, casinl);
#endif
| 3,240 | 57 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/sinh.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
#include "libc/tinymath/expo.internal.h"
#include "libc/tinymath/freebsd.internal.h"
asm(".ident\t\"\\n\\n\
Musl libc (MIT License)\\n\
Copyright 2005-2014 Rich Felker, et. al.\"");
asm(".include \"libc/disclaimer.inc\"");
// clang-format off
/**
* Returns hyperbolic sine of ð¥.
*
* sinh(x) = (exp(x) - 1/exp(x))/2
* = (exp(x)-1 + (exp(x)-1)/exp(x))/2
* = x + x^3/6 + o(x^5)
*/
double sinh(double x)
{
union {double f; uint64_t i;} u = {.f = x};
uint32_t w;
double t, h, absx;
h = 0.5;
if (u.i >> 63)
h = -h;
/* |x| */
u.i &= (uint64_t)-1/2;
absx = u.f;
w = u.i >> 32;
/* |x| < log(DBL_MAX) */
if (w < 0x40862e42) {
t = expm1(absx);
if (w < 0x3ff00000) {
if (w < 0x3ff00000 - (26<<20))
/* note: inexact and underflow are raised by expm1 */
/* note: this branch avoids spurious underflow */
return x;
return h*(2*t - t*t/(t+1));
}
/* note: |x|>log(0x1p26)+eps could be just h*exp(x) */
return h*(t + t/(t+1));
}
/* |x| > log(DBL_MAX) or nan */
/* note: the result is stored to handle overflow */
t = __expo2(absx, 2*h);
return t;
}
| 3,744 | 78 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/ctan.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/complex.h"
#include "libc/math.h"
#include "libc/tinymath/complex.internal.h"
asm(".ident\t\"\\n\\n\
Musl libc (MIT License)\\n\
Copyright 2005-2014 Rich Felker, et. al.\"");
asm(".include \"libc/disclaimer.inc\"");
/* clang-format off */
/* tan(z) = -i tanh(i z) */
double complex ctan(double complex z)
{
z = ctanh(CMPLX(-cimag(z), creal(z)));
return CMPLX(cimag(z), -creal(z));
}
| 3,007 | 47 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/ksinl.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
#include "libc/tinymath/kernel.internal.h"
asm(".ident\t\"\\n\\n\
FreeBSD libm (BSD-2 License)\\n\
Copyright (c) 2005-2011, Bruce D. Evans, Steven G. Kargl, David Schultz.\"");
asm(".ident\t\"\\n\\n\
fdlibm (fdlibm license)\\n\
Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.\"");
asm(".ident\t\"\\n\\n\
Musl libc (MIT License)\\n\
Copyright 2005-2014 Rich Felker, et. al.\"");
asm(".include \"libc/disclaimer.inc\"");
// clang-format off
/* origin: FreeBSD /usr/src/lib/msun/ld80/k_sinl.c */
/* origin: FreeBSD /usr/src/lib/msun/ld128/k_sinl.c */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
* Copyright (c) 2008 Steven G. Kargl, David Schultz, Bruce D. Evans.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
#if (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
#if LDBL_MANT_DIG == 64
/*
* ld80 version of __sin.c. See __sin.c for most comments.
*/
/*
* Domain [-0.7854, 0.7854], range ~[-1.89e-22, 1.915e-22]
* |sin(x)/x - s(x)| < 2**-72.1
*
* See __cosl.c for more details about the polynomial.
*/
static const long double
S1 = -0.166666666666666666671L; /* -0xaaaaaaaaaaaaaaab.0p-66 */
static const double
S2 = 0.0083333333333333332, /* 0x11111111111111.0p-59 */
S3 = -0.00019841269841269427, /* -0x1a01a01a019f81.0p-65 */
S4 = 0.0000027557319223597490, /* 0x171de3a55560f7.0p-71 */
S5 = -0.000000025052108218074604, /* -0x1ae64564f16cad.0p-78 */
S6 = 1.6059006598854211e-10, /* 0x161242b90243b5.0p-85 */
S7 = -7.6429779983024564e-13, /* -0x1ae42ebd1b2e00.0p-93 */
S8 = 2.6174587166648325e-15; /* 0x179372ea0b3f64.0p-101 */
#define POLY(z) (S2+z*(S3+z*(S4+z*(S5+z*(S6+z*(S7+z*S8))))))
#elif LDBL_MANT_DIG == 113
/*
* ld128 version of __sin.c. See __sin.c for most comments.
*/
/*
* Domain [-0.7854, 0.7854], range ~[-1.53e-37, 1.659e-37]
* |sin(x)/x - s(x)| < 2**-122.1
*
* See __cosl.c for more details about the polynomial.
*/
static const long double
S1 = -0.16666666666666666666666666666666666606732416116558L,
S2 = 0.0083333333333333333333333333333331135404851288270047L,
S3 = -0.00019841269841269841269841269839935785325638310428717L,
S4 = 0.27557319223985890652557316053039946268333231205686e-5L,
S5 = -0.25052108385441718775048214826384312253862930064745e-7L,
S6 = 0.16059043836821614596571832194524392581082444805729e-9L,
S7 = -0.76471637318198151807063387954939213287488216303768e-12L,
S8 = 0.28114572543451292625024967174638477283187397621303e-14L;
static const double
S9 = -0.82206352458348947812512122163446202498005154296863e-17,
S10 = 0.19572940011906109418080609928334380560135358385256e-19,
S11 = -0.38680813379701966970673724299207480965452616911420e-22,
S12 = 0.64038150078671872796678569586315881020659912139412e-25;
#define POLY(z) (S2+z*(S3+z*(S4+z*(S5+z*(S6+z*(S7+z*(S8+ \
z*(S9+z*(S10+z*(S11+z*S12))))))))))
#endif
long double __sinl(long double x, long double y, int iy)
{
long double z,r,v;
z = x*x;
v = z*x;
r = POLY(z);
if (iy == 0)
return x+v*(S1+z*r);
return x-((z*(0.5*y-v*r)-y)-v*S1);
}
#endif
| 5,955 | 119 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/log_data.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/tinymath/log_data.internal.h"
asm(".ident\t\"\\n\\n\
Double-precision math functions (MIT License)\\n\
Copyright 2018 ARM Limited\"");
asm(".include \"libc/disclaimer.inc\"");
/* clang-format off */
/*
* Data for log.
*
* Copyright (c) 2018, Arm Limited.
* SPDX-License-Identifier: MIT
*/
#define N (1 << LOG_TABLE_BITS)
const struct log_data __log_data = {
.ln2hi = 0x1.62e42fefa3800p-1,
.ln2lo = 0x1.ef35793c76730p-45,
.poly1 = {
// relative error: 0x1.c04d76cp-63
// in -0x1p-4 0x1.09p-4 (|log(1+x)| > 0x1p-4 outside the interval)
-0x1p-1,
0x1.5555555555577p-2,
-0x1.ffffffffffdcbp-3,
0x1.999999995dd0cp-3,
-0x1.55555556745a7p-3,
0x1.24924a344de3p-3,
-0x1.fffffa4423d65p-4,
0x1.c7184282ad6cap-4,
-0x1.999eb43b068ffp-4,
0x1.78182f7afd085p-4,
-0x1.5521375d145cdp-4,
},
.poly = {
// relative error: 0x1.926199e8p-56
// abs error: 0x1.882ff33p-65
// in -0x1.fp-9 0x1.fp-9
-0x1.0000000000001p-1,
0x1.555555551305bp-2,
-0x1.fffffffeb459p-3,
0x1.999b324f10111p-3,
-0x1.55575e506c89fp-3,
},
/* Algorithm:
x = 2^k z
log(x) = k ln2 + log(c) + log(z/c)
log(z/c) = poly(z/c - 1)
where z is in [1.6p-1; 1.6p0] which is split into N subintervals and z falls
into the ith one, then table entries are computed as
tab[i].invc = 1/c
tab[i].logc = (double)log(c)
tab2[i].chi = (double)c
tab2[i].clo = (double)(c - (double)c)
where c is near the center of the subinterval and is chosen by trying +-2^29
floating point invc candidates around 1/center and selecting one for which
1) the rounding error in 0x1.8p9 + logc is 0,
2) the rounding error in z - chi - clo is < 0x1p-66 and
3) the rounding error in (double)log(c) is minimized (< 0x1p-66).
Note: 1) ensures that k*ln2hi + logc can be computed without rounding error,
2) ensures that z/c - 1 can be computed as (z - chi - clo)*invc with close to
a single rounding error when there is no fast fma for z*invc - 1, 3) ensures
that logc + poly(z/c - 1) has small error, however near x == 1 when
|log(x)| < 0x1p-4, this is not enough so that is special cased. */
.tab = {
{0x1.734f0c3e0de9fp+0, -0x1.7cc7f79e69000p-2},
{0x1.713786a2ce91fp+0, -0x1.76feec20d0000p-2},
{0x1.6f26008fab5a0p+0, -0x1.713e31351e000p-2},
{0x1.6d1a61f138c7dp+0, -0x1.6b85b38287800p-2},
{0x1.6b1490bc5b4d1p+0, -0x1.65d5590807800p-2},
{0x1.69147332f0cbap+0, -0x1.602d076180000p-2},
{0x1.6719f18224223p+0, -0x1.5a8ca86909000p-2},
{0x1.6524f99a51ed9p+0, -0x1.54f4356035000p-2},
{0x1.63356aa8f24c4p+0, -0x1.4f637c36b4000p-2},
{0x1.614b36b9ddc14p+0, -0x1.49da7fda85000p-2},
{0x1.5f66452c65c4cp+0, -0x1.445923989a800p-2},
{0x1.5d867b5912c4fp+0, -0x1.3edf439b0b800p-2},
{0x1.5babccb5b90dep+0, -0x1.396ce448f7000p-2},
{0x1.59d61f2d91a78p+0, -0x1.3401e17bda000p-2},
{0x1.5805612465687p+0, -0x1.2e9e2ef468000p-2},
{0x1.56397cee76bd3p+0, -0x1.2941b3830e000p-2},
{0x1.54725e2a77f93p+0, -0x1.23ec58cda8800p-2},
{0x1.52aff42064583p+0, -0x1.1e9e129279000p-2},
{0x1.50f22dbb2bddfp+0, -0x1.1956d2b48f800p-2},
{0x1.4f38f4734ded7p+0, -0x1.141679ab9f800p-2},
{0x1.4d843cfde2840p+0, -0x1.0edd094ef9800p-2},
{0x1.4bd3ec078a3c8p+0, -0x1.09aa518db1000p-2},
{0x1.4a27fc3e0258ap+0, -0x1.047e65263b800p-2},
{0x1.4880524d48434p+0, -0x1.feb224586f000p-3},
{0x1.46dce1b192d0bp+0, -0x1.f474a7517b000p-3},
{0x1.453d9d3391854p+0, -0x1.ea4443d103000p-3},
{0x1.43a2744b4845ap+0, -0x1.e020d44e9b000p-3},
{0x1.420b54115f8fbp+0, -0x1.d60a22977f000p-3},
{0x1.40782da3ef4b1p+0, -0x1.cc00104959000p-3},
{0x1.3ee8f5d57fe8fp+0, -0x1.c202956891000p-3},
{0x1.3d5d9a00b4ce9p+0, -0x1.b81178d811000p-3},
{0x1.3bd60c010c12bp+0, -0x1.ae2c9ccd3d000p-3},
{0x1.3a5242b75dab8p+0, -0x1.a45402e129000p-3},
{0x1.38d22cd9fd002p+0, -0x1.9a877681df000p-3},
{0x1.3755bc5847a1cp+0, -0x1.90c6d69483000p-3},
{0x1.35dce49ad36e2p+0, -0x1.87120a645c000p-3},
{0x1.34679984dd440p+0, -0x1.7d68fb4143000p-3},
{0x1.32f5cceffcb24p+0, -0x1.73cb83c627000p-3},
{0x1.3187775a10d49p+0, -0x1.6a39a9b376000p-3},
{0x1.301c8373e3990p+0, -0x1.60b3154b7a000p-3},
{0x1.2eb4ebb95f841p+0, -0x1.5737d76243000p-3},
{0x1.2d50a0219a9d1p+0, -0x1.4dc7b8fc23000p-3},
{0x1.2bef9a8b7fd2ap+0, -0x1.4462c51d20000p-3},
{0x1.2a91c7a0c1babp+0, -0x1.3b08abc830000p-3},
{0x1.293726014b530p+0, -0x1.31b996b490000p-3},
{0x1.27dfa5757a1f5p+0, -0x1.2875490a44000p-3},
{0x1.268b39b1d3bbfp+0, -0x1.1f3b9f879a000p-3},
{0x1.2539d838ff5bdp+0, -0x1.160c8252ca000p-3},
{0x1.23eb7aac9083bp+0, -0x1.0ce7f57f72000p-3},
{0x1.22a012ba940b6p+0, -0x1.03cdc49fea000p-3},
{0x1.2157996cc4132p+0, -0x1.f57bdbc4b8000p-4},
{0x1.201201dd2fc9bp+0, -0x1.e370896404000p-4},
{0x1.1ecf4494d480bp+0, -0x1.d17983ef94000p-4},
{0x1.1d8f5528f6569p+0, -0x1.bf9674ed8a000p-4},
{0x1.1c52311577e7cp+0, -0x1.adc79202f6000p-4},
{0x1.1b17c74cb26e9p+0, -0x1.9c0c3e7288000p-4},
{0x1.19e010c2c1ab6p+0, -0x1.8a646b372c000p-4},
{0x1.18ab07bb670bdp+0, -0x1.78d01b3ac0000p-4},
{0x1.1778a25efbcb6p+0, -0x1.674f145380000p-4},
{0x1.1648d354c31dap+0, -0x1.55e0e6d878000p-4},
{0x1.151b990275fddp+0, -0x1.4485cdea1e000p-4},
{0x1.13f0ea432d24cp+0, -0x1.333d94d6aa000p-4},
{0x1.12c8b7210f9dap+0, -0x1.22079f8c56000p-4},
{0x1.11a3028ecb531p+0, -0x1.10e4698622000p-4},
{0x1.107fbda8434afp+0, -0x1.ffa6c6ad20000p-5},
{0x1.0f5ee0f4e6bb3p+0, -0x1.dda8d4a774000p-5},
{0x1.0e4065d2a9fcep+0, -0x1.bbcece4850000p-5},
{0x1.0d244632ca521p+0, -0x1.9a1894012c000p-5},
{0x1.0c0a77ce2981ap+0, -0x1.788583302c000p-5},
{0x1.0af2f83c636d1p+0, -0x1.5715e67d68000p-5},
{0x1.09ddb98a01339p+0, -0x1.35c8a49658000p-5},
{0x1.08cabaf52e7dfp+0, -0x1.149e364154000p-5},
{0x1.07b9f2f4e28fbp+0, -0x1.e72c082eb8000p-6},
{0x1.06ab58c358f19p+0, -0x1.a55f152528000p-6},
{0x1.059eea5ecf92cp+0, -0x1.63d62cf818000p-6},
{0x1.04949cdd12c90p+0, -0x1.228fb8caa0000p-6},
{0x1.038c6c6f0ada9p+0, -0x1.c317b20f90000p-7},
{0x1.02865137932a9p+0, -0x1.419355daa0000p-7},
{0x1.0182427ea7348p+0, -0x1.81203c2ec0000p-8},
{0x1.008040614b195p+0, -0x1.0040979240000p-9},
{0x1.fe01ff726fa1ap-1, 0x1.feff384900000p-9},
{0x1.fa11cc261ea74p-1, 0x1.7dc41353d0000p-7},
{0x1.f6310b081992ep-1, 0x1.3cea3c4c28000p-6},
{0x1.f25f63ceeadcdp-1, 0x1.b9fc114890000p-6},
{0x1.ee9c8039113e7p-1, 0x1.1b0d8ce110000p-5},
{0x1.eae8078cbb1abp-1, 0x1.58a5bd001c000p-5},
{0x1.e741aa29d0c9bp-1, 0x1.95c8340d88000p-5},
{0x1.e3a91830a99b5p-1, 0x1.d276aef578000p-5},
{0x1.e01e009609a56p-1, 0x1.07598e598c000p-4},
{0x1.dca01e577bb98p-1, 0x1.253f5e30d2000p-4},
{0x1.d92f20b7c9103p-1, 0x1.42edd8b380000p-4},
{0x1.d5cac66fb5ccep-1, 0x1.606598757c000p-4},
{0x1.d272caa5ede9dp-1, 0x1.7da76356a0000p-4},
{0x1.cf26e3e6b2ccdp-1, 0x1.9ab434e1c6000p-4},
{0x1.cbe6da2a77902p-1, 0x1.b78c7bb0d6000p-4},
{0x1.c8b266d37086dp-1, 0x1.d431332e72000p-4},
{0x1.c5894bd5d5804p-1, 0x1.f0a3171de6000p-4},
{0x1.c26b533bb9f8cp-1, 0x1.067152b914000p-3},
{0x1.bf583eeece73fp-1, 0x1.147858292b000p-3},
{0x1.bc4fd75db96c1p-1, 0x1.2266ecdca3000p-3},
{0x1.b951e0c864a28p-1, 0x1.303d7a6c55000p-3},
{0x1.b65e2c5ef3e2cp-1, 0x1.3dfc33c331000p-3},
{0x1.b374867c9888bp-1, 0x1.4ba366b7a8000p-3},
{0x1.b094b211d304ap-1, 0x1.5933928d1f000p-3},
{0x1.adbe885f2ef7ep-1, 0x1.66acd2418f000p-3},
{0x1.aaf1d31603da2p-1, 0x1.740f8ec669000p-3},
{0x1.a82e63fd358a7p-1, 0x1.815c0f51af000p-3},
{0x1.a5740ef09738bp-1, 0x1.8e92954f68000p-3},
{0x1.a2c2a90ab4b27p-1, 0x1.9bb3602f84000p-3},
{0x1.a01a01393f2d1p-1, 0x1.a8bed1c2c0000p-3},
{0x1.9d79f24db3c1bp-1, 0x1.b5b515c01d000p-3},
{0x1.9ae2505c7b190p-1, 0x1.c2967ccbcc000p-3},
{0x1.9852ef297ce2fp-1, 0x1.cf635d5486000p-3},
{0x1.95cbaeea44b75p-1, 0x1.dc1bd3446c000p-3},
{0x1.934c69de74838p-1, 0x1.e8c01b8cfe000p-3},
{0x1.90d4f2f6752e6p-1, 0x1.f5509c0179000p-3},
{0x1.8e6528effd79dp-1, 0x1.00e6c121fb800p-2},
{0x1.8bfce9fcc007cp-1, 0x1.071b80e93d000p-2},
{0x1.899c0dabec30ep-1, 0x1.0d46b9e867000p-2},
{0x1.87427aa2317fbp-1, 0x1.13687334bd000p-2},
{0x1.84f00acb39a08p-1, 0x1.1980d67234800p-2},
{0x1.82a49e8653e55p-1, 0x1.1f8ffe0cc8000p-2},
{0x1.8060195f40260p-1, 0x1.2595fd7636800p-2},
{0x1.7e22563e0a329p-1, 0x1.2b9300914a800p-2},
{0x1.7beb377dcb5adp-1, 0x1.3187210436000p-2},
{0x1.79baa679725c2p-1, 0x1.377266dec1800p-2},
{0x1.77907f2170657p-1, 0x1.3d54ffbaf3000p-2},
{0x1.756cadbd6130cp-1, 0x1.432eee32fe000p-2},
},
#if !__FP_FAST_FMA
.tab2 = {
{0x1.61000014fb66bp-1, 0x1.e026c91425b3cp-56},
{0x1.63000034db495p-1, 0x1.dbfea48005d41p-55},
{0x1.650000d94d478p-1, 0x1.e7fa786d6a5b7p-55},
{0x1.67000074e6fadp-1, 0x1.1fcea6b54254cp-57},
{0x1.68ffffedf0faep-1, -0x1.c7e274c590efdp-56},
{0x1.6b0000763c5bcp-1, -0x1.ac16848dcda01p-55},
{0x1.6d0001e5cc1f6p-1, 0x1.33f1c9d499311p-55},
{0x1.6efffeb05f63ep-1, -0x1.e80041ae22d53p-56},
{0x1.710000e86978p-1, 0x1.bff6671097952p-56},
{0x1.72ffffc67e912p-1, 0x1.c00e226bd8724p-55},
{0x1.74fffdf81116ap-1, -0x1.e02916ef101d2p-57},
{0x1.770000f679c9p-1, -0x1.7fc71cd549c74p-57},
{0x1.78ffffa7ec835p-1, 0x1.1bec19ef50483p-55},
{0x1.7affffe20c2e6p-1, -0x1.07e1729cc6465p-56},
{0x1.7cfffed3fc9p-1, -0x1.08072087b8b1cp-55},
{0x1.7efffe9261a76p-1, 0x1.dc0286d9df9aep-55},
{0x1.81000049ca3e8p-1, 0x1.97fd251e54c33p-55},
{0x1.8300017932c8fp-1, -0x1.afee9b630f381p-55},
{0x1.850000633739cp-1, 0x1.9bfbf6b6535bcp-55},
{0x1.87000204289c6p-1, -0x1.bbf65f3117b75p-55},
{0x1.88fffebf57904p-1, -0x1.9006ea23dcb57p-55},
{0x1.8b00022bc04dfp-1, -0x1.d00df38e04b0ap-56},
{0x1.8cfffe50c1b8ap-1, -0x1.8007146ff9f05p-55},
{0x1.8effffc918e43p-1, 0x1.3817bd07a7038p-55},
{0x1.910001efa5fc7p-1, 0x1.93e9176dfb403p-55},
{0x1.9300013467bb9p-1, 0x1.f804e4b980276p-56},
{0x1.94fffe6ee076fp-1, -0x1.f7ef0d9ff622ep-55},
{0x1.96fffde3c12d1p-1, -0x1.082aa962638bap-56},
{0x1.98ffff4458a0dp-1, -0x1.7801b9164a8efp-55},
{0x1.9afffdd982e3ep-1, -0x1.740e08a5a9337p-55},
{0x1.9cfffed49fb66p-1, 0x1.fce08c19bep-60},
{0x1.9f00020f19c51p-1, -0x1.a3faa27885b0ap-55},
{0x1.a10001145b006p-1, 0x1.4ff489958da56p-56},
{0x1.a300007bbf6fap-1, 0x1.cbeab8a2b6d18p-55},
{0x1.a500010971d79p-1, 0x1.8fecadd78793p-55},
{0x1.a70001df52e48p-1, -0x1.f41763dd8abdbp-55},
{0x1.a90001c593352p-1, -0x1.ebf0284c27612p-55},
{0x1.ab0002a4f3e4bp-1, -0x1.9fd043cff3f5fp-57},
{0x1.acfffd7ae1ed1p-1, -0x1.23ee7129070b4p-55},
{0x1.aefffee510478p-1, 0x1.a063ee00edea3p-57},
{0x1.b0fffdb650d5bp-1, 0x1.a06c8381f0ab9p-58},
{0x1.b2ffffeaaca57p-1, -0x1.9011e74233c1dp-56},
{0x1.b4fffd995badcp-1, -0x1.9ff1068862a9fp-56},
{0x1.b7000249e659cp-1, 0x1.aff45d0864f3ep-55},
{0x1.b8ffff987164p-1, 0x1.cfe7796c2c3f9p-56},
{0x1.bafffd204cb4fp-1, -0x1.3ff27eef22bc4p-57},
{0x1.bcfffd2415c45p-1, -0x1.cffb7ee3bea21p-57},
{0x1.beffff86309dfp-1, -0x1.14103972e0b5cp-55},
{0x1.c0fffe1b57653p-1, 0x1.bc16494b76a19p-55},
{0x1.c2ffff1fa57e3p-1, -0x1.4feef8d30c6edp-57},
{0x1.c4fffdcbfe424p-1, -0x1.43f68bcec4775p-55},
{0x1.c6fffed54b9f7p-1, 0x1.47ea3f053e0ecp-55},
{0x1.c8fffeb998fd5p-1, 0x1.383068df992f1p-56},
{0x1.cb0002125219ap-1, -0x1.8fd8e64180e04p-57},
{0x1.ccfffdd94469cp-1, 0x1.e7ebe1cc7ea72p-55},
{0x1.cefffeafdc476p-1, 0x1.ebe39ad9f88fep-55},
{0x1.d1000169af82bp-1, 0x1.57d91a8b95a71p-56},
{0x1.d30000d0ff71dp-1, 0x1.9c1906970c7dap-55},
{0x1.d4fffea790fc4p-1, -0x1.80e37c558fe0cp-58},
{0x1.d70002edc87e5p-1, -0x1.f80d64dc10f44p-56},
{0x1.d900021dc82aap-1, -0x1.47c8f94fd5c5cp-56},
{0x1.dafffd86b0283p-1, 0x1.c7f1dc521617ep-55},
{0x1.dd000296c4739p-1, 0x1.8019eb2ffb153p-55},
{0x1.defffe54490f5p-1, 0x1.e00d2c652cc89p-57},
{0x1.e0fffcdabf694p-1, -0x1.f8340202d69d2p-56},
{0x1.e2fffdb52c8ddp-1, 0x1.b00c1ca1b0864p-56},
{0x1.e4ffff24216efp-1, 0x1.2ffa8b094ab51p-56},
{0x1.e6fffe88a5e11p-1, -0x1.7f673b1efbe59p-58},
{0x1.e9000119eff0dp-1, -0x1.4808d5e0bc801p-55},
{0x1.eafffdfa51744p-1, 0x1.80006d54320b5p-56},
{0x1.ed0001a127fa1p-1, -0x1.002f860565c92p-58},
{0x1.ef00007babcc4p-1, -0x1.540445d35e611p-55},
{0x1.f0ffff57a8d02p-1, -0x1.ffb3139ef9105p-59},
{0x1.f30001ee58ac7p-1, 0x1.a81acf2731155p-55},
{0x1.f4ffff5823494p-1, 0x1.a3f41d4d7c743p-55},
{0x1.f6ffffca94c6bp-1, -0x1.202f41c987875p-57},
{0x1.f8fffe1f9c441p-1, 0x1.77dd1f477e74bp-56},
{0x1.fafffd2e0e37ep-1, -0x1.f01199a7ca331p-57},
{0x1.fd0001c77e49ep-1, 0x1.181ee4bceacb1p-56},
{0x1.feffff7e0c331p-1, -0x1.e05370170875ap-57},
{0x1.00ffff465606ep+0, -0x1.a7ead491c0adap-55},
{0x1.02ffff3867a58p+0, -0x1.77f69c3fcb2ep-54},
{0x1.04ffffdfc0d17p+0, 0x1.7bffe34cb945bp-54},
{0x1.0700003cd4d82p+0, 0x1.20083c0e456cbp-55},
{0x1.08ffff9f2cbe8p+0, -0x1.dffdfbe37751ap-57},
{0x1.0b000010cda65p+0, -0x1.13f7faee626ebp-54},
{0x1.0d00001a4d338p+0, 0x1.07dfa79489ff7p-55},
{0x1.0effffadafdfdp+0, -0x1.7040570d66bcp-56},
{0x1.110000bbafd96p+0, 0x1.e80d4846d0b62p-55},
{0x1.12ffffae5f45dp+0, 0x1.dbffa64fd36efp-54},
{0x1.150000dd59ad9p+0, 0x1.a0077701250aep-54},
{0x1.170000f21559ap+0, 0x1.dfdf9e2e3deeep-55},
{0x1.18ffffc275426p+0, 0x1.10030dc3b7273p-54},
{0x1.1b000123d3c59p+0, 0x1.97f7980030188p-54},
{0x1.1cffff8299eb7p+0, -0x1.5f932ab9f8c67p-57},
{0x1.1effff48ad4p+0, 0x1.37fbf9da75bebp-54},
{0x1.210000c8b86a4p+0, 0x1.f806b91fd5b22p-54},
{0x1.2300003854303p+0, 0x1.3ffc2eb9fbf33p-54},
{0x1.24fffffbcf684p+0, 0x1.601e77e2e2e72p-56},
{0x1.26ffff52921d9p+0, 0x1.ffcbb767f0c61p-56},
{0x1.2900014933a3cp+0, -0x1.202ca3c02412bp-56},
{0x1.2b00014556313p+0, -0x1.2808233f21f02p-54},
{0x1.2cfffebfe523bp+0, -0x1.8ff7e384fdcf2p-55},
{0x1.2f0000bb8ad96p+0, -0x1.5ff51503041c5p-55},
{0x1.30ffffb7ae2afp+0, -0x1.10071885e289dp-55},
{0x1.32ffffeac5f7fp+0, -0x1.1ff5d3fb7b715p-54},
{0x1.350000ca66756p+0, 0x1.57f82228b82bdp-54},
{0x1.3700011fbf721p+0, 0x1.000bac40dd5ccp-55},
{0x1.38ffff9592fb9p+0, -0x1.43f9d2db2a751p-54},
{0x1.3b00004ddd242p+0, 0x1.57f6b707638e1p-55},
{0x1.3cffff5b2c957p+0, 0x1.a023a10bf1231p-56},
{0x1.3efffeab0b418p+0, 0x1.87f6d66b152bp-54},
{0x1.410001532aff4p+0, 0x1.7f8375f198524p-57},
{0x1.4300017478b29p+0, 0x1.301e672dc5143p-55},
{0x1.44fffe795b463p+0, 0x1.9ff69b8b2895ap-55},
{0x1.46fffe80475ep+0, -0x1.5c0b19bc2f254p-54},
{0x1.48fffef6fc1e7p+0, 0x1.b4009f23a2a72p-54},
{0x1.4afffe5bea704p+0, -0x1.4ffb7bf0d7d45p-54},
{0x1.4d000171027dep+0, -0x1.9c06471dc6a3dp-54},
{0x1.4f0000ff03ee2p+0, 0x1.77f890b85531cp-54},
{0x1.5100012dc4bd1p+0, 0x1.004657166a436p-57},
{0x1.530001605277ap+0, -0x1.6bfcece233209p-54},
{0x1.54fffecdb704cp+0, -0x1.902720505a1d7p-55},
{0x1.56fffef5f54a9p+0, 0x1.bbfe60ec96412p-54},
{0x1.5900017e61012p+0, 0x1.87ec581afef9p-55},
{0x1.5b00003c93e92p+0, -0x1.f41080abf0ccp-54},
{0x1.5d0001d4919bcp+0, -0x1.8812afb254729p-54},
{0x1.5efffe7b87a89p+0, -0x1.47eb780ed6904p-54},
},
#endif
};
| 16,722 | 362 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/j0f.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
#include "libc/tinymath/complex.internal.h"
asm(".ident\t\"\\n\\n\
Double-precision math functions (MIT License)\\n\
Copyright 2018 ARM Limited\"");
asm(".include \"libc/disclaimer.inc\"");
// clang-format off
/* origin: FreeBSD /usr/src/lib/msun/src/e_j0f.c */
/*
* Conversion to float by Ian Lance Taylor, Cygnus Support, [email protected].
*/
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
static float pzerof(float), qzerof(float);
static const float
invsqrtpi = 5.6418961287e-01, /* 0x3f106ebb */
tpi = 6.3661974669e-01; /* 0x3f22f983 */
static float common(uint32_t ix, float x, int y0)
{
float z,s,c,ss,cc;
/*
* j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x)
* y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x)
*/
s = sinf(x);
c = cosf(x);
if (y0)
c = -c;
cc = s+c;
if (ix < 0x7f000000) {
ss = s-c;
z = -cosf(2*x);
if (s*c < 0)
cc = z/ss;
else
ss = z/cc;
if (ix < 0x58800000) {
if (y0)
ss = -ss;
cc = pzerof(x)*cc-qzerof(x)*ss;
}
}
return invsqrtpi*cc/sqrtf(x);
}
/* R0/S0 on [0, 2.00] */
static const float
R02 = 1.5625000000e-02, /* 0x3c800000 */
R03 = -1.8997929874e-04, /* 0xb947352e */
R04 = 1.8295404516e-06, /* 0x35f58e88 */
R05 = -4.6183270541e-09, /* 0xb19eaf3c */
S01 = 1.5619102865e-02, /* 0x3c7fe744 */
S02 = 1.1692678527e-04, /* 0x38f53697 */
S03 = 5.1354652442e-07, /* 0x3509daa6 */
S04 = 1.1661400734e-09; /* 0x30a045e8 */
float j0f(float x)
{
float z,r,s;
uint32_t ix;
GET_FLOAT_WORD(ix, x);
ix &= 0x7fffffff;
if (ix >= 0x7f800000)
return 1/(x*x);
x = fabsf(x);
if (ix >= 0x40000000) { /* |x| >= 2 */
/* large ulp error near zeros */
return common(ix, x, 0);
}
if (ix >= 0x3a000000) { /* |x| >= 2**-11 */
/* up to 4ulp error near 2 */
z = x*x;
r = z*(R02+z*(R03+z*(R04+z*R05)));
s = 1+z*(S01+z*(S02+z*(S03+z*S04)));
return (1+x/2)*(1-x/2) + z*(r/s);
}
if (ix >= 0x21800000) /* |x| >= 2**-60 */
x = 0.25f*x*x;
return 1 - x;
}
static const float
u00 = -7.3804296553e-02, /* 0xbd9726b5 */
u01 = 1.7666645348e-01, /* 0x3e34e80d */
u02 = -1.3818567619e-02, /* 0xbc626746 */
u03 = 3.4745343146e-04, /* 0x39b62a69 */
u04 = -3.8140706238e-06, /* 0xb67ff53c */
u05 = 1.9559013964e-08, /* 0x32a802ba */
u06 = -3.9820518410e-11, /* 0xae2f21eb */
v01 = 1.2730483897e-02, /* 0x3c509385 */
v02 = 7.6006865129e-05, /* 0x389f65e0 */
v03 = 2.5915085189e-07, /* 0x348b216c */
v04 = 4.4111031494e-10; /* 0x2ff280c2 */
float y0f(float x)
{
float z,u,v;
uint32_t ix;
GET_FLOAT_WORD(ix, x);
if ((ix & 0x7fffffff) == 0)
return -1/0.0f;
if (ix>>31)
return 0/0.0f;
if (ix >= 0x7f800000)
return 1/x;
if (ix >= 0x40000000) { /* |x| >= 2.0 */
/* large ulp error near zeros */
return common(ix,x,1);
}
if (ix >= 0x39000000) { /* x >= 2**-13 */
/* large ulp error at x ~= 0.89 */
z = x*x;
u = u00+z*(u01+z*(u02+z*(u03+z*(u04+z*(u05+z*u06)))));
v = 1+z*(v01+z*(v02+z*(v03+z*v04)));
return u/v + tpi*(j0f(x)*logf(x));
}
return u00 + tpi*logf(x);
}
/* The asymptotic expansions of pzero is
* 1 - 9/128 s^2 + 11025/98304 s^4 - ..., where s = 1/x.
* For x >= 2, We approximate pzero by
* pzero(x) = 1 + (R/S)
* where R = pR0 + pR1*s^2 + pR2*s^4 + ... + pR5*s^10
* S = 1 + pS0*s^2 + ... + pS4*s^10
* and
* | pzero(x)-1-R/S | <= 2 ** ( -60.26)
*/
static const float pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
0.0000000000e+00, /* 0x00000000 */
-7.0312500000e-02, /* 0xbd900000 */
-8.0816707611e+00, /* 0xc1014e86 */
-2.5706311035e+02, /* 0xc3808814 */
-2.4852163086e+03, /* 0xc51b5376 */
-5.2530439453e+03, /* 0xc5a4285a */
};
static const float pS8[5] = {
1.1653436279e+02, /* 0x42e91198 */
3.8337448730e+03, /* 0x456f9beb */
4.0597855469e+04, /* 0x471e95db */
1.1675296875e+05, /* 0x47e4087c */
4.7627726562e+04, /* 0x473a0bba */
};
static const float pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
-1.1412546255e-11, /* 0xad48c58a */
-7.0312492549e-02, /* 0xbd8fffff */
-4.1596107483e+00, /* 0xc0851b88 */
-6.7674766541e+01, /* 0xc287597b */
-3.3123129272e+02, /* 0xc3a59d9b */
-3.4643338013e+02, /* 0xc3ad3779 */
};
static const float pS5[5] = {
6.0753936768e+01, /* 0x42730408 */
1.0512523193e+03, /* 0x44836813 */
5.9789707031e+03, /* 0x45bad7c4 */
9.6254453125e+03, /* 0x461665c8 */
2.4060581055e+03, /* 0x451660ee */
};
static const float pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
-2.5470459075e-09, /* 0xb12f081b */
-7.0311963558e-02, /* 0xbd8fffb8 */
-2.4090321064e+00, /* 0xc01a2d95 */
-2.1965976715e+01, /* 0xc1afba52 */
-5.8079170227e+01, /* 0xc2685112 */
-3.1447946548e+01, /* 0xc1fb9565 */
};
static const float pS3[5] = {
3.5856033325e+01, /* 0x420f6c94 */
3.6151397705e+02, /* 0x43b4c1ca */
1.1936077881e+03, /* 0x44953373 */
1.1279968262e+03, /* 0x448cffe6 */
1.7358093262e+02, /* 0x432d94b8 */
};
static const float pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
-8.8753431271e-08, /* 0xb3be98b7 */
-7.0303097367e-02, /* 0xbd8ffb12 */
-1.4507384300e+00, /* 0xbfb9b1cc */
-7.6356959343e+00, /* 0xc0f4579f */
-1.1193166733e+01, /* 0xc1331736 */
-3.2336456776e+00, /* 0xc04ef40d */
};
static const float pS2[5] = {
2.2220300674e+01, /* 0x41b1c32d */
1.3620678711e+02, /* 0x430834f0 */
2.7047027588e+02, /* 0x43873c32 */
1.5387539673e+02, /* 0x4319e01a */
1.4657617569e+01, /* 0x416a859a */
};
static float pzerof(float x)
{
const float *p,*q;
float_t z,r,s;
uint32_t ix;
GET_FLOAT_WORD(ix, x);
ix &= 0x7fffffff;
if (ix >= 0x41000000){p = pR8; q = pS8;}
else if (ix >= 0x409173eb){p = pR5; q = pS5;}
else if (ix >= 0x4036d917){p = pR3; q = pS3;}
else /*ix >= 0x40000000*/ {p = pR2; q = pS2;}
z = 1.0f/(x*x);
r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
s = 1.0f+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4]))));
return 1.0f + r/s;
}
/* For x >= 8, the asymptotic expansions of qzero is
* -1/8 s + 75/1024 s^3 - ..., where s = 1/x.
* We approximate pzero by
* qzero(x) = s*(-1.25 + (R/S))
* where R = qR0 + qR1*s^2 + qR2*s^4 + ... + qR5*s^10
* S = 1 + qS0*s^2 + ... + qS5*s^12
* and
* | qzero(x)/s +1.25-R/S | <= 2 ** ( -61.22)
*/
static const float qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
0.0000000000e+00, /* 0x00000000 */
7.3242187500e-02, /* 0x3d960000 */
1.1768206596e+01, /* 0x413c4a93 */
5.5767340088e+02, /* 0x440b6b19 */
8.8591972656e+03, /* 0x460a6cca */
3.7014625000e+04, /* 0x471096a0 */
};
static const float qS8[6] = {
1.6377603149e+02, /* 0x4323c6aa */
8.0983447266e+03, /* 0x45fd12c2 */
1.4253829688e+05, /* 0x480b3293 */
8.0330925000e+05, /* 0x49441ed4 */
8.4050156250e+05, /* 0x494d3359 */
-3.4389928125e+05, /* 0xc8a7eb69 */
};
static const float qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
1.8408595828e-11, /* 0x2da1ec79 */
7.3242180049e-02, /* 0x3d95ffff */
5.8356351852e+00, /* 0x40babd86 */
1.3511157227e+02, /* 0x43071c90 */
1.0272437744e+03, /* 0x448067cd */
1.9899779053e+03, /* 0x44f8bf4b */
};
static const float qS5[6] = {
8.2776611328e+01, /* 0x42a58da0 */
2.0778142090e+03, /* 0x4501dd07 */
1.8847289062e+04, /* 0x46933e94 */
5.6751113281e+04, /* 0x475daf1d */
3.5976753906e+04, /* 0x470c88c1 */
-5.3543427734e+03, /* 0xc5a752be */
};
static const float qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
4.3774099900e-09, /* 0x3196681b */
7.3241114616e-02, /* 0x3d95ff70 */
3.3442313671e+00, /* 0x405607e3 */
4.2621845245e+01, /* 0x422a7cc5 */
1.7080809021e+02, /* 0x432acedf */
1.6673394775e+02, /* 0x4326bbe4 */
};
static const float qS3[6] = {
4.8758872986e+01, /* 0x42430916 */
7.0968920898e+02, /* 0x44316c1c */
3.7041481934e+03, /* 0x4567825f */
6.4604252930e+03, /* 0x45c9e367 */
2.5163337402e+03, /* 0x451d4557 */
-1.4924745178e+02, /* 0xc3153f59 */
};
static const float qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
1.5044444979e-07, /* 0x342189db */
7.3223426938e-02, /* 0x3d95f62a */
1.9981917143e+00, /* 0x3fffc4bf */
1.4495602608e+01, /* 0x4167edfd */
3.1666231155e+01, /* 0x41fd5471 */
1.6252708435e+01, /* 0x4182058c */
};
static const float qS2[6] = {
3.0365585327e+01, /* 0x41f2ecb8 */
2.6934811401e+02, /* 0x4386ac8f */
8.4478375244e+02, /* 0x44533229 */
8.8293585205e+02, /* 0x445cbbe5 */
2.1266638184e+02, /* 0x4354aa98 */
-5.3109550476e+00, /* 0xc0a9f358 */
};
static float qzerof(float x)
{
const float *p,*q;
float_t s,r,z;
uint32_t ix;
GET_FLOAT_WORD(ix, x);
ix &= 0x7fffffff;
if (ix >= 0x41000000){p = qR8; q = qS8;}
else if (ix >= 0x409173eb){p = qR5; q = qS5;}
else if (ix >= 0x4036d917){p = qR3; q = qS3;}
else /*ix >= 0x40000000*/ {p = qR2; q = qS2;}
z = 1.0f/(x*x);
r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
s = 1.0f+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5])))));
return (-.125f + r/s)/x;
}
| 11,831 | 348 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/lround.c | /*-*- mode:c;indent-tabs-mode:nil;c-basic-offset:2;tab-width:8;coding:utf-8 -*-â
âvi: set net ft=c ts=2 sts=2 sw=2 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ¡
â Copyright 2023 Justine Alexandra Roberts Tunney â
â â
â Permission to use, copy, modify, and/or distribute this software for â
â any purpose with or without fee is hereby granted, provided that the â
â above copyright notice and this permission notice appear in all copies. â
â â
â THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL â
â WARRANTIES WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED â
â WARRANTIES OF MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE â
â AUTHOR BE LIABLE FOR ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL â
â DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR â
â PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER â
â TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR â
â PERFORMANCE OF THIS SOFTWARE. â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
/**
* Rounds ð¥ to nearest integer, away from zero.
*/
long lround(double x) {
return round(x);
}
#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
__strong_reference(lround, lroundl);
#endif
| 2,057 | 31 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/__math_invalidl.c | /*-*- mode:c;indent-tabs-mode:nil;c-basic-offset:2;tab-width:8;coding:utf-8 -*-â
âvi: set net ft=c ts=2 sts=2 sw=2 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ¡
â Copyright 2023 Justine Alexandra Roberts Tunney â
â â
â Permission to use, copy, modify, and/or distribute this software for â
â any purpose with or without fee is hereby granted, provided that the â
â above copyright notice and this permission notice appear in all copies. â
â â
â THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL â
â WARRANTIES WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED â
â WARRANTIES OF MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE â
â AUTHOR BE LIABLE FOR ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL â
â DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR â
â PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER â
â TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR â
â PERFORMANCE OF THIS SOFTWARE. â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
#include "libc/tinymath/internal.h"
#if LDBL_MANT_DIG != DBL_MANT_DIG
long double __math_invalidl(long double x) {
return (x - x) / (x - x);
}
#endif
| 2,012 | 27 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/loglq.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Copyright (c) 2007-2013 Bruce D. Evans â
â All rights reserved. â
â â
â Redistribution and use in source and binary forms, with or without â
â modification, are permitted provided that the following conditions â
â are met: â
â 1. Redistributions of source code must retain the above copyright â
â notice unmodified, this list of conditions, and the following â
â disclaimer. â
â 2. Redistributions in binary form must reproduce the above copyright â
â notice, this list of conditions and the following disclaimer in the â
â documentation and/or other materials provided with the distribution. â
â â
â THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR â
â IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES â
â OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. â
â IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, â
â INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT â
â NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, â
â DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY â
â THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT â
â (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF â
â THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
#include "libc/tinymath/freebsd.internal.h"
#if LDBL_MANT_DIG == 113
asm(".ident\t\"\\n\\n\
FreeBSD libm (BSD-2 License)\\n\
Copyright (c) 2005-2011, Bruce D. Evans, Steven G. Kargl, David Schultz.\"");
asm(".include \"libc/disclaimer.inc\"");
// clang-format off
/**
* Implementation of the natural logarithm of x for 128-bit format.
*
* First decompose x into its base 2 representation:
*
* log(x) = log(X * 2**k), where X is in [1, 2)
* = log(X) + k * log(2).
*
* Let X = X_i + e, where X_i is the center of one of the intervals
* [-1.0/256, 1.0/256), [1.0/256, 3.0/256), .... [2.0-1.0/256, 2.0+1.0/256)
* and X is in this interval. Then
*
* log(X) = log(X_i + e)
* = log(X_i * (1 + e / X_i))
* = log(X_i) + log(1 + e / X_i).
*
* The values log(X_i) are tabulated below. Let d = e / X_i and use
*
* log(1 + d) = p(d)
*
* where p(d) = d - 0.5*d*d + ... is a special minimax polynomial of
* suitably high degree.
*
* To get sufficiently small roundoff errors, k * log(2), log(X_i), and
* sometimes (if |k| is not large) the first term in p(d) must be evaluated
* and added up in extra precision. Extra precision is not needed for the
* rest of p(d). In the worst case when k = 0 and log(X_i) is 0, the final
* error is controlled mainly by the error in the second term in p(d). The
* error in this term itself is at most 0.5 ulps from the d*d operation in
* it. The error in this term relative to the first term is thus at most
* 0.5 * |-0.5| * |d| < 1.0/1024 ulps. We aim for an accumulated error of
* at most twice this at the point of the final rounding step. Thus the
* final error should be at most 0.5 + 1.0/512 = 0.5020 ulps. Exhaustive
* testing of a float variant of this function showed a maximum final error
* of 0.5008 ulps. Non-exhaustive testing of a double variant of this
* function showed a maximum final error of 0.5078 ulps (near 1+1.0/256).
*
* We made the maximum of |d| (and thus the total relative error and the
* degree of p(d)) small by using a large number of intervals. Using
* centers of intervals instead of endpoints reduces this maximum by a
* factor of 2 for a given number of intervals. p(d) is special only
* in beginning with the Taylor coefficients 0 + 1*d, which tends to happen
* naturally. The most accurate minimax polynomial of a given degree might
* be different, but then we wouldn't want it since we would have to do
* extra work to avoid roundoff error (especially for P0*d instead of d).
*/
#ifndef NO_STRUCT_RETURN
#define STRUCT_RETURN
#endif
#if !defined(NO_UTAB) && !defined(NO_UTABL)
#define USE_UTAB
#endif
/*
* Domain [-0.005280, 0.004838], range ~[-1.1577e-37, 1.1582e-37]:
* |log(1 + d)/d - p(d)| < 2**-122.7
*/
static const long double
P2 = -0.5L,
P3 = 3.33333333333333333333333333333233795e-1L, /* 0x15555555555555555555555554d42.0p-114L */
P4 = -2.49999999999999999999999999941139296e-1L, /* -0x1ffffffffffffffffffffffdab14e.0p-115L */
P5 = 2.00000000000000000000000085468039943e-1L, /* 0x19999999999999999999a6d3567f4.0p-115L */
P6 = -1.66666666666666666666696142372698408e-1L, /* -0x15555555555555555567267a58e13.0p-115L */
P7 = 1.42857142857142857119522943477166120e-1L, /* 0x1249249249249248ed79a0ae434de.0p-115L */
P8 = -1.24999999999999994863289015033581301e-1L; /* -0x1fffffffffffffa13e91765e46140.0p-116L */
/* Double precision gives ~ 53 + log2(P9 * max(|d|)**8) ~= 120 bits. */
static const double
P9 = 1.1111111111111401e-1, /* 0x1c71c71c71c7ed.0p-56 */
P10 = -1.0000000000040135e-1, /* -0x199999999a0a92.0p-56 */
P11 = 9.0909090728136258e-2, /* 0x1745d173962111.0p-56 */
P12 = -8.3333318851855284e-2, /* -0x1555551722c7a3.0p-56 */
P13 = 7.6928634666404178e-2, /* 0x13b1985204a4ae.0p-56 */
P14 = -7.1626810078462499e-2; /* -0x12562276cdc5d0.0p-56 */
static volatile const double zero = 0;
#define INTERVALS 128
#define LOG2_INTERVALS 7
#define TSIZE (INTERVALS + 1)
#define G(i) (T[(i)].G)
#define F_hi(i) (T[(i)].F_hi)
#define F_lo(i) (T[(i)].F_lo)
#define ln2_hi F_hi(TSIZE - 1)
#define ln2_lo F_lo(TSIZE - 1)
#define E(i) (U[(i)].E)
#define H(i) (U[(i)].H)
static const struct {
float G; /* 1/(1 + i/128) rounded to 8/9 bits */
float F_hi; /* log(1 / G_i) rounded (see below) */
/* The compiler will insert 8 bytes of padding here. */
long double F_lo; /* next 113 bits for log(1 / G_i) */
} T[TSIZE] = {
/*
* ln2_hi and each F_hi(i) are rounded to a number of bits that
* makes F_hi(i) + dk*ln2_hi exact for all i and all dk.
*
* The last entry (for X just below 2) is used to define ln2_hi
* and ln2_lo, to ensure that F_hi(i) and F_lo(i) cancel exactly
* with dk*ln2_hi and dk*ln2_lo, respectively, when dk = -1.
* This is needed for accuracy when x is just below 1. (To avoid
* special cases, such x are "reduced" strangely to X just below
* 2 and dk = -1, and then the exact cancellation is needed
* because any the error from any non-exactness would be too
* large).
*
* The relevant range of dk is [-16445, 16383]. The maximum number
* of bits in F_hi(i) that works is very dependent on i but has
* a minimum of 93. We only need about 12 bits in F_hi(i) for
* it to provide enough extra precision.
*
* We round F_hi(i) to 24 bits so that it can have type float,
* mainly to minimize the size of the table. Using all 24 bits
* in a float for it automatically satisfies the above constraints.
*/
{0x800000.0p-23, 0, 0},
{0xfe0000.0p-24, 0x8080ac.0p-30, -0x14ee431dae6674afa0c4bfe16e8fd.0p-144L},
{0xfc0000.0p-24, 0x8102b3.0p-29, -0x1db29ee2d83717be918e1119642ab.0p-144L},
{0xfa0000.0p-24, 0xc24929.0p-29, 0x1191957d173697cf302cc9476f561.0p-143L},
{0xf80000.0p-24, 0x820aec.0p-28, 0x13ce8888e02e78eba9b1113bc1c18.0p-142L},
{0xf60000.0p-24, 0xa33577.0p-28, -0x17a4382ce6eb7bfa509bec8da5f22.0p-142L},
{0xf48000.0p-24, 0xbc42cb.0p-28, -0x172a21161a107674986dcdca6709c.0p-143L},
{0xf30000.0p-24, 0xd57797.0p-28, -0x1e09de07cb958897a3ea46e84abb3.0p-142L},
{0xf10000.0p-24, 0xf7518e.0p-28, 0x1ae1eec1b036c484993c549c4bf40.0p-151L},
{0xef0000.0p-24, 0x8cb9df.0p-27, -0x1d7355325d560d9e9ab3d6ebab580.0p-141L},
{0xed8000.0p-24, 0x999ec0.0p-27, -0x1f9f02d256d5037108f4ec21e48cd.0p-142L},
{0xec0000.0p-24, 0xa6988b.0p-27, -0x16fc0a9d12c17a70f7a684c596b12.0p-143L},
{0xea0000.0p-24, 0xb80698.0p-27, 0x15d581c1e8da99ded322fb08b8462.0p-141L},
{0xe80000.0p-24, 0xc99af3.0p-27, -0x1535b3ba8f150ae09996d7bb4653e.0p-143L},
{0xe70000.0p-24, 0xd273b2.0p-27, 0x163786f5251aefe0ded34c8318f52.0p-145L},
{0xe50000.0p-24, 0xe442c0.0p-27, 0x1bc4b2368e32d56699c1799a244d4.0p-144L},
{0xe38000.0p-24, 0xf1b83f.0p-27, 0x1c6090f684e6766abceccab1d7174.0p-141L},
{0xe20000.0p-24, 0xff448a.0p-27, -0x1890aa69ac9f4215f93936b709efb.0p-142L},
{0xe08000.0p-24, 0x8673f6.0p-26, 0x1b9985194b6affd511b534b72a28e.0p-140L},
{0xdf0000.0p-24, 0x8d515c.0p-26, -0x1dc08d61c6ef1d9b2ef7e68680598.0p-143L},
{0xdd8000.0p-24, 0x943a9e.0p-26, -0x1f72a2dac729b3f46662238a9425a.0p-142L},
{0xdc0000.0p-24, 0x9b2fe6.0p-26, -0x1fd4dfd3a0afb9691aed4d5e3df94.0p-140L},
{0xda8000.0p-24, 0xa2315d.0p-26, -0x11b26121629c46c186384993e1c93.0p-142L},
{0xd90000.0p-24, 0xa93f2f.0p-26, 0x1286d633e8e5697dc6a402a56fce1.0p-141L},
{0xd78000.0p-24, 0xb05988.0p-26, 0x16128eba9367707ebfa540e45350c.0p-144L},
{0xd60000.0p-24, 0xb78094.0p-26, 0x16ead577390d31ef0f4c9d43f79b2.0p-140L},
{0xd50000.0p-24, 0xbc4c6c.0p-26, 0x151131ccf7c7b75e7d900b521c48d.0p-141L},
{0xd38000.0p-24, 0xc3890a.0p-26, -0x115e2cd714bd06508aeb00d2ae3e9.0p-140L},
{0xd20000.0p-24, 0xcad2d7.0p-26, -0x1847f406ebd3af80485c2f409633c.0p-142L},
{0xd10000.0p-24, 0xcfb620.0p-26, 0x1c2259904d686581799fbce0b5f19.0p-141L},
{0xcf8000.0p-24, 0xd71653.0p-26, 0x1ece57a8d5ae54f550444ecf8b995.0p-140L},
{0xce0000.0p-24, 0xde843a.0p-26, -0x1f109d4bc4595412b5d2517aaac13.0p-141L},
{0xcd0000.0p-24, 0xe37fde.0p-26, 0x1bc03dc271a74d3a85b5b43c0e727.0p-141L},
{0xcb8000.0p-24, 0xeb050c.0p-26, -0x1bf2badc0df841a71b79dd5645b46.0p-145L},
{0xca0000.0p-24, 0xf29878.0p-26, -0x18efededd89fbe0bcfbe6d6db9f66.0p-147L},
{0xc90000.0p-24, 0xf7ad6f.0p-26, 0x1373ff977baa6911c7bafcb4d84fb.0p-141L},
{0xc80000.0p-24, 0xfcc8e3.0p-26, 0x196766f2fb328337cc050c6d83b22.0p-140L},
{0xc68000.0p-24, 0x823f30.0p-25, 0x19bd076f7c434e5fcf1a212e2a91e.0p-139L},
{0xc58000.0p-24, 0x84d52c.0p-25, -0x1a327257af0f465e5ecab5f2a6f81.0p-139L},
{0xc40000.0p-24, 0x88bc74.0p-25, 0x113f23def19c5a0fe396f40f1dda9.0p-141L},
{0xc30000.0p-24, 0x8b5ae6.0p-25, 0x1759f6e6b37de945a049a962e66c6.0p-139L},
{0xc20000.0p-24, 0x8dfccb.0p-25, 0x1ad35ca6ed5147bdb6ddcaf59c425.0p-141L},
{0xc10000.0p-24, 0x90a22b.0p-25, 0x1a1d71a87deba46bae9827221dc98.0p-139L},
{0xbf8000.0p-24, 0x94a0d8.0p-25, -0x139e5210c2b730e28aba001a9b5e0.0p-140L},
{0xbe8000.0p-24, 0x974f16.0p-25, -0x18f6ebcff3ed72e23e13431adc4a5.0p-141L},
{0xbd8000.0p-24, 0x9a00f1.0p-25, -0x1aa268be39aab7148e8d80caa10b7.0p-139L},
{0xbc8000.0p-24, 0x9cb672.0p-25, -0x14c8815839c5663663d15faed7771.0p-139L},
{0xbb0000.0p-24, 0xa0cda1.0p-25, 0x1eaf46390dbb2438273918db7df5c.0p-141L},
{0xba0000.0p-24, 0xa38c6e.0p-25, 0x138e20d831f698298adddd7f32686.0p-141L},
{0xb90000.0p-24, 0xa64f05.0p-25, -0x1e8d3c41123615b147a5d47bc208f.0p-142L},
{0xb80000.0p-24, 0xa91570.0p-25, 0x1ce28f5f3840b263acb4351104631.0p-140L},
{0xb70000.0p-24, 0xabdfbb.0p-25, -0x186e5c0a42423457e22d8c650b355.0p-139L},
{0xb60000.0p-24, 0xaeadef.0p-25, -0x14d41a0b2a08a465dc513b13f567d.0p-143L},
{0xb50000.0p-24, 0xb18018.0p-25, 0x16755892770633947ffe651e7352f.0p-139L},
{0xb40000.0p-24, 0xb45642.0p-25, -0x16395ebe59b15228bfe8798d10ff0.0p-142L},
{0xb30000.0p-24, 0xb73077.0p-25, 0x1abc65c8595f088b61a335f5b688c.0p-140L},
{0xb20000.0p-24, 0xba0ec4.0p-25, -0x1273089d3dad88e7d353e9967d548.0p-139L},
{0xb10000.0p-24, 0xbcf133.0p-25, 0x10f9f67b1f4bbf45de06ecebfaf6d.0p-139L},
{0xb00000.0p-24, 0xbfd7d2.0p-25, -0x109fab904864092b34edda19a831e.0p-140L},
{0xaf0000.0p-24, 0xc2c2ac.0p-25, -0x1124680aa43333221d8a9b475a6ba.0p-139L},
{0xae8000.0p-24, 0xc439b3.0p-25, -0x1f360cc4710fbfe24b633f4e8d84d.0p-140L},
{0xad8000.0p-24, 0xc72afd.0p-25, -0x132d91f21d89c89c45003fc5d7807.0p-140L},
{0xac8000.0p-24, 0xca20a2.0p-25, -0x16bf9b4d1f8da8002f2449e174504.0p-139L},
{0xab8000.0p-24, 0xcd1aae.0p-25, 0x19deb5ce6a6a8717d5626e16acc7d.0p-141L},
{0xaa8000.0p-24, 0xd0192f.0p-25, 0x1a29fb48f7d3ca87dabf351aa41f4.0p-139L},
{0xaa0000.0p-24, 0xd19a20.0p-25, 0x1127d3c6457f9d79f51dcc73014c9.0p-141L},
{0xa90000.0p-24, 0xd49f6a.0p-25, -0x1ba930e486a0ac42d1bf9199188e7.0p-141L},
{0xa80000.0p-24, 0xd7a94b.0p-25, -0x1b6e645f31549dd1160bcc45c7e2c.0p-139L},
{0xa70000.0p-24, 0xdab7d0.0p-25, 0x1118a425494b610665377f15625b6.0p-140L},
{0xa68000.0p-24, 0xdc40d5.0p-25, 0x1966f24d29d3a2d1b2176010478be.0p-140L},
{0xa58000.0p-24, 0xdf566d.0p-25, -0x1d8e52eb2248f0c95dd83626d7333.0p-142L},
{0xa48000.0p-24, 0xe270ce.0p-25, -0x1ee370f96e6b67ccb006a5b9890ea.0p-140L},
{0xa40000.0p-24, 0xe3ffce.0p-25, 0x1d155324911f56db28da4d629d00a.0p-140L},
{0xa30000.0p-24, 0xe72179.0p-25, -0x1fe6e2f2f867d8f4d60c713346641.0p-140L},
{0xa20000.0p-24, 0xea4812.0p-25, 0x1b7be9add7f4d3b3d406b6cbf3ce5.0p-140L},
{0xa18000.0p-24, 0xebdd3d.0p-25, 0x1b3cfb3f7511dd73692609040ccc2.0p-139L},
{0xa08000.0p-24, 0xef0b5b.0p-25, -0x1220de1f7301901b8ad85c25afd09.0p-139L},
{0xa00000.0p-24, 0xf0a451.0p-25, -0x176364c9ac81cc8a4dfb804de6867.0p-140L},
{0x9f0000.0p-24, 0xf3da16.0p-25, 0x1eed6b9aafac8d42f78d3e65d3727.0p-141L},
{0x9e8000.0p-24, 0xf576e9.0p-25, 0x1d593218675af269647b783d88999.0p-139L},
{0x9d8000.0p-24, 0xf8b47c.0p-25, -0x13e8eb7da053e063714615f7cc91d.0p-144L},
{0x9d0000.0p-24, 0xfa553f.0p-25, 0x1c063259bcade02951686d5373aec.0p-139L},
{0x9c0000.0p-24, 0xfd9ac5.0p-25, 0x1ef491085fa3c1649349630531502.0p-139L},
{0x9b8000.0p-24, 0xff3f8c.0p-25, 0x1d607a7c2b8c5320619fb9433d841.0p-139L},
{0x9a8000.0p-24, 0x814697.0p-24, -0x12ad3817004f3f0bdff99f932b273.0p-138L},
{0x9a0000.0p-24, 0x821b06.0p-24, -0x189fc53117f9e54e78103a2bc1767.0p-141L},
{0x990000.0p-24, 0x83c5f8.0p-24, 0x14cf15a048907b7d7f47ddb45c5a3.0p-139L},
{0x988000.0p-24, 0x849c7d.0p-24, 0x1cbb1d35fb82873b04a9af1dd692c.0p-138L},
{0x978000.0p-24, 0x864ba6.0p-24, 0x1128639b814f9b9770d8cb6573540.0p-138L},
{0x970000.0p-24, 0x87244c.0p-24, 0x184733853300f002e836dfd47bd41.0p-139L},
{0x968000.0p-24, 0x87fdaa.0p-24, 0x109d23aef77dd5cd7cc94306fb3ff.0p-140L},
{0x958000.0p-24, 0x89b293.0p-24, -0x1a81ef367a59de2b41eeebd550702.0p-138L},
{0x950000.0p-24, 0x8a8e20.0p-24, -0x121ad3dbb2f45275c917a30df4ac9.0p-138L},
{0x948000.0p-24, 0x8b6a6a.0p-24, -0x1cfb981628af71a89df4e6df2e93b.0p-139L},
{0x938000.0p-24, 0x8d253a.0p-24, -0x1d21730ea76cfdec367828734cae5.0p-139L},
{0x930000.0p-24, 0x8e03c2.0p-24, 0x135cc00e566f76b87333891e0dec4.0p-138L},
{0x928000.0p-24, 0x8ee30d.0p-24, -0x10fcb5df257a263e3bf446c6e3f69.0p-140L},
{0x918000.0p-24, 0x90a3ee.0p-24, -0x16e171b15433d723a4c7380a448d8.0p-139L},
{0x910000.0p-24, 0x918587.0p-24, -0x1d050da07f3236f330972da2a7a87.0p-139L},
{0x908000.0p-24, 0x9267e7.0p-24, 0x1be03669a5268d21148c6002becd3.0p-139L},
{0x8f8000.0p-24, 0x942f04.0p-24, 0x10b28e0e26c336af90e00533323ba.0p-139L},
{0x8f0000.0p-24, 0x9513c3.0p-24, 0x1a1d820da57cf2f105a89060046aa.0p-138L},
{0x8e8000.0p-24, 0x95f950.0p-24, -0x19ef8f13ae3cf162409d8ea99d4c0.0p-139L},
{0x8e0000.0p-24, 0x96dfab.0p-24, -0x109e417a6e507b9dc10dac743ad7a.0p-138L},
{0x8d0000.0p-24, 0x98aed2.0p-24, 0x10d01a2c5b0e97c4990b23d9ac1f5.0p-139L},
{0x8c8000.0p-24, 0x9997a2.0p-24, -0x1d6a50d4b61ea74540bdd2aa99a42.0p-138L},
{0x8c0000.0p-24, 0x9a8145.0p-24, 0x1b3b190b83f9527e6aba8f2d783c1.0p-138L},
{0x8b8000.0p-24, 0x9b6bbf.0p-24, 0x13a69fad7e7abe7ba81c664c107e0.0p-138L},
{0x8b0000.0p-24, 0x9c5711.0p-24, -0x11cd12316f576aad348ae79867223.0p-138L},
{0x8a8000.0p-24, 0x9d433b.0p-24, 0x1c95c444b807a246726b304ccae56.0p-139L},
{0x898000.0p-24, 0x9f1e22.0p-24, -0x1b9c224ea698c2f9b47466d6123fe.0p-139L},
{0x890000.0p-24, 0xa00ce1.0p-24, 0x125ca93186cf0f38b4619a2483399.0p-141L},
{0x888000.0p-24, 0xa0fc80.0p-24, -0x1ee38a7bc228b3597043be78eaf49.0p-139L},
{0x880000.0p-24, 0xa1ed00.0p-24, -0x1a0db876613d204147dc69a07a649.0p-138L},
{0x878000.0p-24, 0xa2de62.0p-24, 0x193224e8516c008d3602a7b41c6e8.0p-139L},
{0x870000.0p-24, 0xa3d0a9.0p-24, 0x1fa28b4d2541aca7d5844606b2421.0p-139L},
{0x868000.0p-24, 0xa4c3d6.0p-24, 0x1c1b5760fb4571acbcfb03f16daf4.0p-138L},
{0x858000.0p-24, 0xa6acea.0p-24, 0x1fed5d0f65949c0a345ad743ae1ae.0p-140L},
{0x850000.0p-24, 0xa7a2d4.0p-24, 0x1ad270c9d749362382a7688479e24.0p-140L},
{0x848000.0p-24, 0xa899ab.0p-24, 0x199ff15ce532661ea9643a3a2d378.0p-139L},
{0x840000.0p-24, 0xa99171.0p-24, 0x1a19e15ccc45d257530a682b80490.0p-139L},
{0x838000.0p-24, 0xaa8a28.0p-24, -0x121a14ec532b35ba3e1f868fd0b5e.0p-140L},
{0x830000.0p-24, 0xab83d1.0p-24, 0x1aee319980bff3303dd481779df69.0p-139L},
{0x828000.0p-24, 0xac7e6f.0p-24, -0x18ffd9e3900345a85d2d86161742e.0p-140L},
{0x820000.0p-24, 0xad7a03.0p-24, -0x1e4db102ce29f79b026b64b42caa1.0p-140L},
{0x818000.0p-24, 0xae768f.0p-24, 0x17c35c55a04a82ab19f77652d977a.0p-141L},
{0x810000.0p-24, 0xaf7415.0p-24, 0x1448324047019b48d7b98c1cf7234.0p-138L},
{0x808000.0p-24, 0xb07298.0p-24, -0x1750ee3915a197e9c7359dd94152f.0p-138L},
{0x800000.0p-24, 0xb17218.0p-24, -0x105c610ca86c3898cff81a12a17e2.0p-141L},
};
#ifdef USE_UTAB
static const struct {
float H; /* 1 + i/INTERVALS (exact) */
float E; /* H(i) * G(i) - 1 (exact) */
} U[TSIZE] = {
{0x800000.0p-23, 0},
{0x810000.0p-23, -0x800000.0p-37},
{0x820000.0p-23, -0x800000.0p-35},
{0x830000.0p-23, -0x900000.0p-34},
{0x840000.0p-23, -0x800000.0p-33},
{0x850000.0p-23, -0xc80000.0p-33},
{0x860000.0p-23, -0xa00000.0p-36},
{0x870000.0p-23, 0x940000.0p-33},
{0x880000.0p-23, 0x800000.0p-35},
{0x890000.0p-23, -0xc80000.0p-34},
{0x8a0000.0p-23, 0xe00000.0p-36},
{0x8b0000.0p-23, 0x900000.0p-33},
{0x8c0000.0p-23, -0x800000.0p-35},
{0x8d0000.0p-23, -0xe00000.0p-33},
{0x8e0000.0p-23, 0x880000.0p-33},
{0x8f0000.0p-23, -0xa80000.0p-34},
{0x900000.0p-23, -0x800000.0p-35},
{0x910000.0p-23, 0x800000.0p-37},
{0x920000.0p-23, 0x900000.0p-35},
{0x930000.0p-23, 0xd00000.0p-35},
{0x940000.0p-23, 0xe00000.0p-35},
{0x950000.0p-23, 0xc00000.0p-35},
{0x960000.0p-23, 0xe00000.0p-36},
{0x970000.0p-23, -0x800000.0p-38},
{0x980000.0p-23, -0xc00000.0p-35},
{0x990000.0p-23, -0xd00000.0p-34},
{0x9a0000.0p-23, 0x880000.0p-33},
{0x9b0000.0p-23, 0xe80000.0p-35},
{0x9c0000.0p-23, -0x800000.0p-35},
{0x9d0000.0p-23, 0xb40000.0p-33},
{0x9e0000.0p-23, 0x880000.0p-34},
{0x9f0000.0p-23, -0xe00000.0p-35},
{0xa00000.0p-23, 0x800000.0p-33},
{0xa10000.0p-23, -0x900000.0p-36},
{0xa20000.0p-23, -0xb00000.0p-33},
{0xa30000.0p-23, -0xa00000.0p-36},
{0xa40000.0p-23, 0x800000.0p-33},
{0xa50000.0p-23, -0xf80000.0p-35},
{0xa60000.0p-23, 0x880000.0p-34},
{0xa70000.0p-23, -0x900000.0p-33},
{0xa80000.0p-23, -0x800000.0p-35},
{0xa90000.0p-23, 0x900000.0p-34},
{0xaa0000.0p-23, 0xa80000.0p-33},
{0xab0000.0p-23, -0xac0000.0p-34},
{0xac0000.0p-23, -0x800000.0p-37},
{0xad0000.0p-23, 0xf80000.0p-35},
{0xae0000.0p-23, 0xf80000.0p-34},
{0xaf0000.0p-23, -0xac0000.0p-33},
{0xb00000.0p-23, -0x800000.0p-33},
{0xb10000.0p-23, -0xb80000.0p-34},
{0xb20000.0p-23, -0x800000.0p-34},
{0xb30000.0p-23, -0xb00000.0p-35},
{0xb40000.0p-23, -0x800000.0p-35},
{0xb50000.0p-23, -0xe00000.0p-36},
{0xb60000.0p-23, -0x800000.0p-35},
{0xb70000.0p-23, -0xb00000.0p-35},
{0xb80000.0p-23, -0x800000.0p-34},
{0xb90000.0p-23, -0xb80000.0p-34},
{0xba0000.0p-23, -0x800000.0p-33},
{0xbb0000.0p-23, -0xac0000.0p-33},
{0xbc0000.0p-23, 0x980000.0p-33},
{0xbd0000.0p-23, 0xbc0000.0p-34},
{0xbe0000.0p-23, 0xe00000.0p-36},
{0xbf0000.0p-23, -0xb80000.0p-35},
{0xc00000.0p-23, -0x800000.0p-33},
{0xc10000.0p-23, 0xa80000.0p-33},
{0xc20000.0p-23, 0x900000.0p-34},
{0xc30000.0p-23, -0x800000.0p-35},
{0xc40000.0p-23, -0x900000.0p-33},
{0xc50000.0p-23, 0x820000.0p-33},
{0xc60000.0p-23, 0x800000.0p-38},
{0xc70000.0p-23, -0x820000.0p-33},
{0xc80000.0p-23, 0x800000.0p-33},
{0xc90000.0p-23, -0xa00000.0p-36},
{0xca0000.0p-23, -0xb00000.0p-33},
{0xcb0000.0p-23, 0x840000.0p-34},
{0xcc0000.0p-23, -0xd00000.0p-34},
{0xcd0000.0p-23, 0x800000.0p-33},
{0xce0000.0p-23, -0xe00000.0p-35},
{0xcf0000.0p-23, 0xa60000.0p-33},
{0xd00000.0p-23, -0x800000.0p-35},
{0xd10000.0p-23, 0xb40000.0p-33},
{0xd20000.0p-23, -0x800000.0p-35},
{0xd30000.0p-23, 0xaa0000.0p-33},
{0xd40000.0p-23, -0xe00000.0p-35},
{0xd50000.0p-23, 0x880000.0p-33},
{0xd60000.0p-23, -0xd00000.0p-34},
{0xd70000.0p-23, 0x9c0000.0p-34},
{0xd80000.0p-23, -0xb00000.0p-33},
{0xd90000.0p-23, -0x800000.0p-38},
{0xda0000.0p-23, 0xa40000.0p-33},
{0xdb0000.0p-23, -0xdc0000.0p-34},
{0xdc0000.0p-23, 0xc00000.0p-35},
{0xdd0000.0p-23, 0xca0000.0p-33},
{0xde0000.0p-23, -0xb80000.0p-34},
{0xdf0000.0p-23, 0xd00000.0p-35},
{0xe00000.0p-23, 0xc00000.0p-33},
{0xe10000.0p-23, -0xf40000.0p-34},
{0xe20000.0p-23, 0x800000.0p-37},
{0xe30000.0p-23, 0x860000.0p-33},
{0xe40000.0p-23, -0xc80000.0p-33},
{0xe50000.0p-23, -0xa80000.0p-34},
{0xe60000.0p-23, 0xe00000.0p-36},
{0xe70000.0p-23, 0x880000.0p-33},
{0xe80000.0p-23, -0xe00000.0p-33},
{0xe90000.0p-23, -0xfc0000.0p-34},
{0xea0000.0p-23, -0x800000.0p-35},
{0xeb0000.0p-23, 0xe80000.0p-35},
{0xec0000.0p-23, 0x900000.0p-33},
{0xed0000.0p-23, 0xe20000.0p-33},
{0xee0000.0p-23, -0xac0000.0p-33},
{0xef0000.0p-23, -0xc80000.0p-34},
{0xf00000.0p-23, -0x800000.0p-35},
{0xf10000.0p-23, 0x800000.0p-35},
{0xf20000.0p-23, 0xb80000.0p-34},
{0xf30000.0p-23, 0x940000.0p-33},
{0xf40000.0p-23, 0xc80000.0p-33},
{0xf50000.0p-23, -0xf20000.0p-33},
{0xf60000.0p-23, -0xc80000.0p-33},
{0xf70000.0p-23, -0xa20000.0p-33},
{0xf80000.0p-23, -0x800000.0p-33},
{0xf90000.0p-23, -0xc40000.0p-34},
{0xfa0000.0p-23, -0x900000.0p-34},
{0xfb0000.0p-23, -0xc80000.0p-35},
{0xfc0000.0p-23, -0x800000.0p-35},
{0xfd0000.0p-23, -0x900000.0p-36},
{0xfe0000.0p-23, -0x800000.0p-37},
{0xff0000.0p-23, -0x800000.0p-39},
{0x800000.0p-22, 0},
};
#endif /* USE_UTAB */
#ifdef STRUCT_RETURN
#define RETURN1(rp, v) do { \
(rp)->hi = (v); \
(rp)->lo_set = 0; \
return; \
} while (0)
#define RETURN2(rp, h, l) do { \
(rp)->hi = (h); \
(rp)->lo = (l); \
(rp)->lo_set = 1; \
return; \
} while (0)
struct ld {
long double hi;
long double lo;
int lo_set;
};
#else
#define RETURN1(rp, v) RETURNF(v)
#define RETURN2(rp, h, l) RETURNI((h) + (l))
#endif
#ifdef STRUCT_RETURN
forceinline void
k_logl(long double x, struct ld *rp)
#else
long double
logl(long double x)
#endif
{
long double d, val_hi, val_lo;
double dd, dk;
uint64_t lx, llx;
int i, k;
uint16_t hx;
EXTRACT_LDBL128_WORDS(hx, lx, llx, x);
k = -16383;
#if 0 /* Hard to do efficiently. Don't do it until we support all modes. */
if (x == 1)
RETURN1(rp, 0); /* log(1) = +0 in all rounding modes */
#endif
if (hx == 0 || hx >= 0x8000) { /* zero, negative or subnormal? */
if (((hx & 0x7fff) | lx | llx) == 0)
RETURN1(rp, -1 / zero); /* log(+-0) = -Inf */
if (hx != 0)
/* log(neg or NaN) = qNaN: */
RETURN1(rp, (x - x) / zero);
x *= 0x1.0p113; /* subnormal; scale up x */
EXTRACT_LDBL128_WORDS(hx, lx, llx, x);
k = -16383 - 113;
} else if (hx >= 0x7fff)
RETURN1(rp, x + x); /* log(Inf or NaN) = Inf or qNaN */
#ifndef STRUCT_RETURN
ENTERI();
#endif
k += hx;
dk = k;
/* Scale x to be in [1, 2). */
SET_LDBL_EXPSIGN(x, 0x3fff);
/* 0 <= i <= INTERVALS: */
#define L2I (49 - LOG2_INTERVALS)
i = (lx + (1LL << (L2I - 2))) >> (L2I - 1);
/*
* -0.005280 < d < 0.004838. In particular, the infinite-
* precision |d| is <= 2**-7. Rounding of G(i) to 8 bits
* ensures that d is representable without extra precision for
* this bound on |d| (since when this calculation is expressed
* as x*G(i)-1, the multiplication needs as many extra bits as
* G(i) has and the subtraction cancels 8 bits). But for
* most i (107 cases out of 129), the infinite-precision |d|
* is <= 2**-8. G(i) is rounded to 9 bits for such i to give
* better accuracy (this works by improving the bound on |d|,
* which in turn allows rounding to 9 bits in more cases).
* This is only important when the original x is near 1 -- it
* lets us avoid using a special method to give the desired
* accuracy for such x.
*/
if (0)
d = x * G(i) - 1;
else {
#ifdef USE_UTAB
d = (x - H(i)) * G(i) + E(i);
#else
long double x_hi;
double x_lo;
/*
* Split x into x_hi + x_lo to calculate x*G(i)-1 exactly.
* G(i) has at most 9 bits, so the splitting point is not
* critical.
*/
INSERT_LDBL128_WORDS(x_hi, 0x3fff, lx,
llx & 0xffffffffff000000ULL);
x_lo = x - x_hi;
d = x_hi * G(i) - 1 + x_lo * G(i);
#endif
}
/*
* Our algorithm depends on exact cancellation of F_lo(i) and
* F_hi(i) with dk*ln_2_lo and dk*ln2_hi when k is -1 and i is
* at the end of the table. This and other technical complications
* make it difficult to avoid the double scaling in (dk*ln2) *
* log(base) for base != e without losing more accuracy and/or
* efficiency than is gained.
*/
/*
* Use double precision operations wherever possible, since
* long double operations are emulated and were very slow on
* the old sparc64 and unknown on the newer aarch64 and riscv
* machines. Also, don't try to improve parallelism by
* increasing the number of operations, since any parallelism
* on such machines is needed for the emulation. Horner's
* method is good for this, and is also good for accuracy.
* Horner's method doesn't handle the `lo' term well, either
* for efficiency or accuracy. However, for accuracy we
* evaluate d * d * P2 separately to take advantage of by P2
* being exact, and this gives a good place to sum the 'lo'
* term too.
*/
dd = (double)d;
val_lo = d * d * d * (P3 +
d * (P4 + d * (P5 + d * (P6 + d * (P7 + d * (P8 +
dd * (P9 + dd * (P10 + dd * (P11 + dd * (P12 + dd * (P13 +
dd * P14))))))))))) + (F_lo(i) + dk * ln2_lo) + d * d * P2;
val_hi = d;
#ifdef DEBUG
if (fetestexcept(FE_UNDERFLOW))
breakpoint();
#endif
_3sumF(val_hi, val_lo, F_hi(i) + dk * ln2_hi);
RETURN2(rp, val_hi, val_lo);
}
/**
* Returns log(ð·+ð¥).
*/
long double
log1pl(long double x)
{
long double d, d_hi, f_lo, val_hi, val_lo;
long double f_hi, twopminusk;
double d_lo, dd, dk;
uint64_t lx, llx;
int i, k;
int16_t ax, hx;
DOPRINT_START(&x);
EXTRACT_LDBL128_WORDS(hx, lx, llx, x);
if (hx < 0x3fff) { /* x < 1, or x neg NaN */
ax = hx & 0x7fff;
if (ax >= 0x3fff) { /* x <= -1, or x neg NaN */
if (ax == 0x3fff && (lx | llx) == 0)
RETURNP(-1 / zero); /* log1p(-1) = -Inf */
/* log1p(x < 1, or x NaN) = qNaN: */
RETURNP((x - x) / (x - x));
}
if (ax <= 0x3f8d) { /* |x| < 2**-113 */
if ((int)x == 0)
RETURNP(x); /* x with inexact if x != 0 */
}
f_hi = 1;
f_lo = x;
} else if (hx >= 0x7fff) { /* x +Inf or non-neg NaN */
RETURNP(x + x); /* log1p(Inf or NaN) = Inf or qNaN */
} else if (hx < 0x40e1) { /* 1 <= x < 2**226 */
f_hi = x;
f_lo = 1;
} else { /* 2**226 <= x < +Inf */
f_hi = x;
f_lo = 0; /* avoid underflow of the P3 term */
}
ENTERI();
x = f_hi + f_lo;
f_lo = (f_hi - x) + f_lo;
EXTRACT_LDBL128_WORDS(hx, lx, llx, x);
k = -16383;
k += hx;
dk = k;
SET_LDBL_EXPSIGN(x, 0x3fff);
twopminusk = 1;
SET_LDBL_EXPSIGN(twopminusk, 0x7ffe - (hx & 0x7fff));
f_lo *= twopminusk;
i = (lx + (1LL << (L2I - 2))) >> (L2I - 1);
/*
* x*G(i)-1 (with a reduced x) can be represented exactly, as
* above, but now we need to evaluate the polynomial on d =
* (x+f_lo)*G(i)-1 and extra precision is needed for that.
* Since x+x_lo is a hi+lo decomposition and subtracting 1
* doesn't lose too many bits, an inexact calculation for
* f_lo*G(i) is good enough.
*/
if (0)
d_hi = x * G(i) - 1;
else {
#ifdef USE_UTAB
d_hi = (x - H(i)) * G(i) + E(i);
#else
long double x_hi;
double x_lo;
INSERT_LDBL128_WORDS(x_hi, 0x3fff, lx,
llx & 0xffffffffff000000ULL);
x_lo = x - x_hi;
d_hi = x_hi * G(i) - 1 + x_lo * G(i);
#endif
}
d_lo = f_lo * G(i);
/*
* This is _2sumF(d_hi, d_lo) inlined. The condition
* (d_hi == 0 || |d_hi| >= |d_lo|) for using _2sumF() is not
* always satisifed, so it is not clear that this works, but
* it works in practice. It works even if it gives a wrong
* normalized d_lo, since |d_lo| > |d_hi| implies that i is
* nonzero and d is tiny, so the F(i) term dominates d_lo.
* In float precision:
* (By exhaustive testing, the worst case is d_hi = 0x1.bp-25.
* And if d is only a little tinier than that, we would have
* another underflow problem for the P3 term; this is also ruled
* out by exhaustive testing.)
*/
d = d_hi + d_lo;
d_lo = d_hi - d + d_lo;
d_hi = d;
dd = (double)d;
val_lo = d * d * d * (P3 +
d * (P4 + d * (P5 + d * (P6 + d * (P7 + d * (P8 +
dd * (P9 + dd * (P10 + dd * (P11 + dd * (P12 + dd * (P13 +
dd * P14))))))))))) + (F_lo(i) + dk * ln2_lo + d_lo) + d * d * P2;
val_hi = d_hi;
#ifdef DEBUG
if (fetestexcept(FE_UNDERFLOW))
breakpoint();
#endif
_3sumF(val_hi, val_lo, F_hi(i) + dk * ln2_hi);
RETURN2PI(val_hi, val_lo);
}
#ifdef STRUCT_RETURN
/**
* Returns natural logarithm of ð¥.
*/
long double
logl(long double x)
{
struct ld r;
ENTERI();
DOPRINT_START(&x);
k_logl(x, &r);
RETURNSPI(&r);
}
/*
* 29+113 bit decompositions. The bits are distributed so that the products
* of the hi terms are exact in double precision. The types are chosen so
* that the products of the hi terms are done in at least double precision,
* without any explicit conversions. More natural choices would require a
* slow long double precision multiplication.
*/
static const double
invln10_hi = 4.3429448176175356e-1, /* 0x1bcb7b15000000.0p-54 */
invln2_hi = 1.4426950402557850e0; /* 0x17154765000000.0p-52 */
static const long double
invln10_lo = 1.41498268538580090791605082294397000e-10L, /* 0x137287195355baaafad33dc323ee3.0p-145L */
invln2_lo = 6.33178418956604368501892137426645911e-10L, /* 0x15c17f0bbbe87fed0691d3e88eb57.0p-143L */
invln10_lo_plus_hi = invln10_lo + invln10_hi,
invln2_lo_plus_hi = invln2_lo + invln2_hi;
/**
* Calculates logââð¥.
*/
long double
log10l(long double x)
{
struct ld r;
long double hi, lo;
ENTERI();
DOPRINT_START(&x);
k_logl(x, &r);
if (!r.lo_set)
RETURNPI(r.hi);
_2sumF(r.hi, r.lo);
hi = (float)r.hi;
lo = r.lo + (r.hi - hi);
RETURN2PI(invln10_hi * hi,
invln10_lo_plus_hi * lo + invln10_lo * hi);
}
/**
* Calculates logâð¥.
*/
long double
log2l(long double x)
{
struct ld r;
long double hi, lo;
ENTERI();
DOPRINT_START(&x);
k_logl(x, &r);
if (!r.lo_set)
RETURNPI(r.hi);
_2sumF(r.hi, r.lo);
hi = (float)r.hi;
lo = r.lo + (r.hi - hi);
RETURN2PI(invln2_hi * hi,
invln2_lo_plus_hi * lo + invln2_lo * hi);
}
#endif /* STRUCT_RETURN */
#endif /* LDBL_MANT_DIG == 113 */
| 32,569 | 754 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/log2l.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
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â included in all copies or substantial portions of the Software. â
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â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/complex.h"
#include "libc/math.h"
#include "libc/tinymath/complex.internal.h"
#if LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384
asm(".ident\t\"\\n\\n\
OpenBSD libm (ISC License)\\n\
Copyright (c) 2008 Stephen L. Moshier <[email protected]>\"");
asm(".ident\t\"\\n\\n\
Musl libc (MIT License)\\n\
Copyright 2005-2014 Rich Felker, et. al.\"");
asm(".include \"libc/disclaimer.inc\"");
// clang-format off
/* origin: OpenBSD /usr/src/lib/libm/src/ld80/e_log2l.c */
/*
* Copyright (c) 2008 Stephen L. Moshier <[email protected]>
*
* Permission to use, copy, modify, and distribute this software for any
* purpose with or without fee is hereby granted, provided that the above
* copyright notice and this permission notice appear in all copies.
*
* THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
* WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
* MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
* ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
* WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
* ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
* OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
*/
/*
* Base 2 logarithm, long double precision
*
*
* SYNOPSIS:
*
* long double x, y, log2l();
*
* y = log2l( x );
*
*
* DESCRIPTION:
*
* Returns the base 2 logarithm of x.
*
* The argument is separated into its exponent and fractional
* parts. If the exponent is between -1 and +1, the (natural)
* logarithm of the fraction is approximated by
*
* log(1+x) = x - 0.5 x**2 + x**3 P(x)/Q(x).
*
* Otherwise, setting z = 2(x-1)/x+1),
*
* log(x) = z + z**3 P(z)/Q(z).
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* IEEE 0.5, 2.0 30000 9.8e-20 2.7e-20
* IEEE exp(+-10000) 70000 5.4e-20 2.3e-20
*
* In the tests over the interval exp(+-10000), the logarithms
* of the random arguments were uniformly distributed over
* [-10000, +10000].
*/
/* Coefficients for ln(1+x) = x - x**2/2 + x**3 P(x)/Q(x)
* 1/sqrt(2) <= x < sqrt(2)
* Theoretical peak relative error = 6.2e-22
*/
static const long double P[] = {
4.9962495940332550844739E-1L,
1.0767376367209449010438E1L,
7.7671073698359539859595E1L,
2.5620629828144409632571E2L,
4.2401812743503691187826E2L,
3.4258224542413922935104E2L,
1.0747524399916215149070E2L,
};
static const long double Q[] = {
/* 1.0000000000000000000000E0,*/
2.3479774160285863271658E1L,
1.9444210022760132894510E2L,
7.7952888181207260646090E2L,
1.6911722418503949084863E3L,
2.0307734695595183428202E3L,
1.2695660352705325274404E3L,
3.2242573199748645407652E2L,
};
/* Coefficients for log(x) = z + z^3 P(z^2)/Q(z^2),
* where z = 2(x-1)/(x+1)
* 1/sqrt(2) <= x < sqrt(2)
* Theoretical peak relative error = 6.16e-22
*/
static const long double R[4] = {
1.9757429581415468984296E-3L,
-7.1990767473014147232598E-1L,
1.0777257190312272158094E1L,
-3.5717684488096787370998E1L,
};
static const long double S[4] = {
/* 1.00000000000000000000E0L,*/
-2.6201045551331104417768E1L,
1.9361891836232102174846E2L,
-4.2861221385716144629696E2L,
};
/* log2(e) - 1 */
#define LOG2EA 4.4269504088896340735992e-1L
#define SQRTH 0.70710678118654752440L
/**
* Calculates logâð¥.
*/
long double log2l(long double x)
{
#ifdef __x86__
// asm improves performance 39ns â 21ns
// measurement made on an intel core i9
long double one;
asm("fld1" : "=t"(one));
asm("fyl2x"
: "=t"(x)
: "0"(x), "u"(one)
: "st(1)");
return x;
#else
long double y, z;
int e;
if (isnan(x))
return x;
if (x == INFINITY)
return x;
if (x <= 0.0) {
if (x == 0.0)
return -1/(x*x); /* -inf with divbyzero */
return 0/0.0f; /* nan with invalid */
}
/* separate mantissa from exponent */
/* Note, frexp is used so that denormal numbers
* will be handled properly.
*/
x = frexpl(x, &e);
/* logarithm using log(x) = z + z**3 P(z)/Q(z),
* where z = 2(x-1)/x+1)
*/
if (e > 2 || e < -2) {
if (x < SQRTH) { /* 2(2x-1)/(2x+1) */
e -= 1;
z = x - 0.5;
y = 0.5 * z + 0.5;
} else { /* 2 (x-1)/(x+1) */
z = x - 0.5;
z -= 0.5;
y = 0.5 * x + 0.5;
}
x = z / y;
z = x*x;
y = x * (z * __polevll(z, R, 3) / __p1evll(z, S, 3));
goto done;
}
/* logarithm using log(1+x) = x - .5x**2 + x**3 P(x)/Q(x) */
if (x < SQRTH) {
e -= 1;
x = 2.0*x - 1.0;
} else {
x = x - 1.0;
}
z = x*x;
y = x * (z * __polevll(x, P, 6) / __p1evll(x, Q, 7));
y = y - 0.5*z;
done:
/* Multiply log of fraction by log2(e)
* and base 2 exponent by 1
*
* ***CAUTION***
*
* This sequence of operations is critical and it may
* be horribly defeated by some compiler optimizers.
*/
z = y * LOG2EA;
z += x * LOG2EA;
z += y;
z += x;
z += e;
return z;
#endif
}
#endif /* 80-bit floating point */
| 7,593 | 230 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/ldshape.internal.h | #ifndef COSMOPOLITAN_LIBC_TINYMATH_LDSHAPE_INTERNAL_H_
#define COSMOPOLITAN_LIBC_TINYMATH_LDSHAPE_INTERNAL_H_
#include "libc/math.h"
#if !(__ASSEMBLER__ + __LINKER__ + 0)
COSMOPOLITAN_C_START_
#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
#elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384 && \
__BYTE_ORDER__ == __ORDER_LITTLE_ENDIAN__
union ldshape {
long double f;
struct {
uint64_t m;
uint16_t se;
} i;
};
#elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384 && \
__BYTE_ORDER__ == __ORDER_BIG_ENDIAN__
/* This is the m68k variant of 80-bit long double, and this definition only
* works on archs where the alignment requirement of uint64_t is <= 4. */
union ldshape {
long double f;
struct {
uint16_t se;
uint16_t pad;
uint64_t m;
} i;
};
#elif LDBL_MANT_DIG == 113 && LDBL_MAX_EXP == 16384 && \
__BYTE_ORDER__ == __ORDER_LITTLE_ENDIAN__
union ldshape {
long double f;
struct {
uint64_t lo;
uint32_t mid;
uint16_t top;
uint16_t se;
} i;
struct {
uint64_t lo;
uint64_t hi;
} i2;
};
#elif LDBL_MANT_DIG == 113 && LDBL_MAX_EXP == 16384 && \
__BYTE_ORDER__ == __ORDER_BIG_ENDIAN__
union ldshape {
long double f;
struct {
uint16_t se;
uint16_t top;
uint32_t mid;
uint64_t lo;
} i;
struct {
uint64_t hi;
uint64_t lo;
} i2;
};
#else
#error Unsupported long double representation
#endif
COSMOPOLITAN_C_END_
#endif /* !(__ASSEMBLER__ + __LINKER__ + 0) */
#endif /* COSMOPOLITAN_LIBC_TINYMATH_LDSHAPE_INTERNAL_H_ */
| 1,529 | 66 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/roundf.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
#include "libc/runtime/fenv.h"
#include "libc/tinymath/internal.h"
asm(".ident\t\"\\n\\n\
Musl libc (MIT License)\\n\
Copyright 2005-2014 Rich Felker, et. al.\"");
asm(".include \"libc/disclaimer.inc\"");
// clang-format off
#if FLT_EVAL_METHOD==0
#define EPS FLT_EPSILON
#elif FLT_EVAL_METHOD==1
#define EPS DBL_EPSILON
#elif FLT_EVAL_METHOD==2
#define EPS LDBL_EPSILON
#endif
static const float_t toint = 1/EPS;
/**
* Rounds ð¥ to nearest integer, away from zero.
*/
float roundf(float x)
{
#ifdef __aarch64__
asm("frinta\t%s0,%s1" : "=w"(x) : "w"(x));
return x;
#elif defined(__powerpc64__) && defined(_ARCH_PWR5X)
asm("frin\t%0,%1" : "=f"(x) : "f"(x));
return x;
#elif defined(__s390x__) && (defined(__HTM__) || __ARCH__ >= 9)
asm("fiebra\t%0,1,%1,4" : "=f"(x) : "f"(x));
return x;
#else
union {float f; uint32_t i;} u = {x};
int e = u.i >> 23 & 0xff;
float_t y;
if (e >= 0x7f+23)
return x;
if (u.i >> 31)
x = -x;
if (e < 0x7f-1) {
FORCE_EVAL(x + toint);
return 0*u.f;
}
y = x + toint - toint - x;
if (y > 0.5f)
y = y + x - 1;
else if (y <= -0.5f)
y = y + x + 1;
else
y = y + x;
if (u.i >> 31)
y = -y;
return y;
#endif /* __aarch64__ */
}
| 3,819 | 94 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/clogl.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/complex.h"
#include "libc/math.h"
#include "libc/tinymath/complex.internal.h"
asm(".ident\t\"\\n\\n\
Musl libc (MIT License)\\n\
Copyright 2005-2014 Rich Felker, et. al.\"");
asm(".include \"libc/disclaimer.inc\"");
// clang-format off
#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
long double complex clogl(long double complex z)
{
return clog(z);
}
#else
// FIXME
long double complex clogl(long double complex z)
{
long double r, phi;
r = cabsl(z);
phi = cargl(z);
return CMPLXL(logl(r), phi);
}
#endif
| 3,131 | 53 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/cimagl.c | /*-*- mode:c;indent-tabs-mode:nil;c-basic-offset:2;tab-width:8;coding:utf-8 -*-â
âvi: set net ft=c ts=2 sts=2 sw=2 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ¡
â Copyright 2023 Justine Alexandra Roberts Tunney â
â â
â Permission to use, copy, modify, and/or distribute this software for â
â any purpose with or without fee is hereby granted, provided that the â
â above copyright notice and this permission notice appear in all copies. â
â â
â THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL â
â WARRANTIES WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED â
â WARRANTIES OF MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE â
â AUTHOR BE LIABLE FOR ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL â
â DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR â
â PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER â
â TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR â
â PERFORMANCE OF THIS SOFTWARE. â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/complex.h"
long double(cimagl)(long double complex z) {
return cimagl(z);
}
| 1,930 | 24 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/remquol.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2020 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
#include "libc/tinymath/ldshape.internal.h"
#if !(LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024)
asm(".ident\t\"\\n\\n\
Musl libc (MIT License)\\n\
Copyright 2005-2014 Rich Felker, et. al.\"");
asm(".include \"libc/disclaimer.inc\"");
// clang-format off
/**
* Computes remainder and part of quotient.
*/
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 */
#if LDBL_MANT_DIG == 64
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;
#elif LDBL_MANT_DIG == 113
uint64_t hi, lo, xhi, xlo, yhi, ylo;
xhi = (ux.i2.hi & -1ULL>>16) | 1ULL<<48;
yhi = (uy.i2.hi & -1ULL>>16) | 1ULL<<48;
xlo = ux.i2.lo;
ylo = ux.i2.lo;
for (; ex > ey; ex--) {
hi = xhi - yhi;
lo = xlo - ylo;
if (xlo < ylo)
hi -= 1;
if (hi >> 63 == 0) {
xhi = 2*hi + (lo>>63);
xlo = 2*lo;
q++;
} else {
xhi = 2*xhi + (xlo>>63);
xlo = 2*xlo;
}
q <<= 1;
}
hi = xhi - yhi;
lo = xlo - ylo;
if (xlo < ylo)
hi -= 1;
if (hi >> 63 == 0) {
xhi = hi;
xlo = lo;
q++;
}
if ((xhi|xlo) == 0)
ex = -120;
else
for (; xhi >> 48 == 0; xhi = 2*xhi + (xlo>>63), xlo = 2*xlo, ex--);
ux.i2.hi = xhi;
ux.i2.lo = xlo;
#endif
}
/* 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;
}
#endif /* long double is long */
| 4,990 | 158 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/cacosh.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/complex.h"
#include "libc/math.h"
#include "libc/tinymath/complex.internal.h"
asm(".ident\t\"\\n\\n\
Musl libc (MIT License)\\n\
Copyright 2005-2014 Rich Felker, et. al.\"");
asm(".include \"libc/disclaimer.inc\"");
// clang-format off
/* acosh(z) = i acos(z) */
double complex cacosh(double complex z)
{
int zineg = signbit(cimag(z));
z = cacos(z);
if (zineg) return CMPLX(cimag(z), -creal(z));
else return CMPLX(-cimag(z), creal(z));
}
#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
__strong_reference(cacosh, cacoshl);
#endif
| 3,160 | 50 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/nanl.c | /*-*- mode:c;indent-tabs-mode:nil;c-basic-offset:2;tab-width:8;coding:utf-8 -*-â
âvi: set net ft=c ts=2 sts=2 sw=2 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ¡
â Copyright 2022 Justine Alexandra Roberts Tunney â
â â
â Permission to use, copy, modify, and/or distribute this software for â
â any purpose with or without fee is hereby granted, provided that the â
â above copyright notice and this permission notice appear in all copies. â
â â
â THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL â
â WARRANTIES WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED â
â WARRANTIES OF MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE â
â AUTHOR BE LIABLE FOR ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL â
â DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR â
â PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER â
â TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR â
â PERFORMANCE OF THIS SOFTWARE. â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
long double nanl(const char *s) {
return NAN;
}
| 1,910 | 24 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/nan.c | /*-*- mode:c;indent-tabs-mode:nil;c-basic-offset:2;tab-width:8;coding:utf-8 -*-â
âvi: set net ft=c ts=2 sts=2 sw=2 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ¡
â Copyright 2022 Justine Alexandra Roberts Tunney â
â â
â Permission to use, copy, modify, and/or distribute this software for â
â any purpose with or without fee is hereby granted, provided that the â
â above copyright notice and this permission notice appear in all copies. â
â â
â THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL â
â WARRANTIES WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED â
â WARRANTIES OF MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE â
â AUTHOR BE LIABLE FOR ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL â
â DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR â
â PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER â
â TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR â
â PERFORMANCE OF THIS SOFTWARE. â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
double nan(const char *s) {
return NAN;
}
| 1,904 | 24 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/nexttowardl.c | /*-*- mode:c;indent-tabs-mode:nil;c-basic-offset:2;tab-width:8;coding:utf-8 -*-â
âvi: set net ft=c ts=2 sts=2 sw=2 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ¡
â Copyright 2023 Justine Alexandra Roberts Tunney â
â â
â Permission to use, copy, modify, and/or distribute this software for â
â any purpose with or without fee is hereby granted, provided that the â
â above copyright notice and this permission notice appear in all copies. â
â â
â THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL â
â WARRANTIES WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED â
â WARRANTIES OF MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE â
â AUTHOR BE LIABLE FOR ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL â
â DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR â
â PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER â
â TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR â
â PERFORMANCE OF THIS SOFTWARE. â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
long double nexttowardl(long double x, long double y) {
return nextafterl(x, y);
}
| 1,945 | 24 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/ctanl.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/complex.h"
asm(".ident\t\"\\n\\n\
Musl libc (MIT License)\\n\
Copyright 2005-2014 Rich Felker, et. al.\"");
asm(".include \"libc/disclaimer.inc\"");
/* clang-format off */
#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
long double complex ctanl(long double complex z)
{
return ctan(z);
}
#else
long double complex ctanl(long double complex z)
{
z = ctanhl(CMPLXL(-cimagl(z), creall(z)));
return CMPLXL(cimagl(z), -creall(z));
}
#endif
| 3,058 | 48 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/copysign.c | /*-*- mode:c;indent-tabs-mode:nil;c-basic-offset:2;tab-width:8;coding:utf-8 -*-â
âvi: set net ft=c ts=2 sts=2 sw=2 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ¡
â Copyright 2023 Justine Alexandra Roberts Tunney â
â â
â Permission to use, copy, modify, and/or distribute this software for â
â any purpose with or without fee is hereby granted, provided that the â
â above copyright notice and this permission notice appear in all copies. â
â â
â THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL â
â WARRANTIES WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED â
â WARRANTIES OF MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE â
â AUTHOR BE LIABLE FOR ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL â
â DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR â
â PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER â
â TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR â
â PERFORMANCE OF THIS SOFTWARE. â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
/**
* Returns ð¥ with same sign as ð¦.
*/
double copysign(double x, double y) {
union {
double f;
uint64_t i;
} ux = {x}, uy = {y};
ux.i &= -1ULL / 2;
ux.i |= uy.i & 1ULL << 63;
return ux.f;
}
#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
__strong_reference(copysign, copysignl);
#endif
| 2,174 | 37 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/significandf.c | /*-*- mode:c;indent-tabs-mode:nil;c-basic-offset:2;tab-width:8;coding:utf-8 -*-â
âvi: set net ft=c ts=2 sts=2 sw=2 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ¡
â Copyright 2023 Justine Alexandra Roberts Tunney â
â â
â Permission to use, copy, modify, and/or distribute this software for â
â any purpose with or without fee is hereby granted, provided that the â
â above copyright notice and this permission notice appear in all copies. â
â â
â THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL â
â WARRANTIES WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED â
â WARRANTIES OF MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE â
â AUTHOR BE LIABLE FOR ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL â
â DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR â
â PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER â
â TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR â
â PERFORMANCE OF THIS SOFTWARE. â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
/**
* Return mantissa of ð¥ scaled to range [1,2).
*/
float significandf(float x) {
return scalbnf(x, -ilogbf(x));
}
| 1,983 | 27 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/poz.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:4;tab-width:4;coding:utf-8 -*-â
âvi: set et ft=c ts=4 sts=4 sw=4 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
/* clang-format off */
/*
Compute probability of measured Chi Square value.
This code was developed by Gary Perlman of the Wang
Institute (full citation below) and has been minimally
modified for use in this program.
*/
#include "libc/math.h"
/*HEADER
Module: z.c
Purpose: compute approximations to normal z distribution probabilities
Programmer: Gary Perlman
Organization: Wang Institute, Tyngsboro, MA 01879
Copyright: none
Tabstops: 4
*/
#define Z_MAX 6.0 /* maximum meaningful z value */
/*FUNCTION poz: probability of normal z value */
/*ALGORITHM
Adapted from a polynomial approximation in:
Ibbetson D, Algorithm 209
Collected Algorithms of the CACM 1963 p. 616
Note:
This routine has six digit accuracy, so it is only useful for absolute
z values < 6. For z values >= to 6.0, poz() returns 0.0.
*/
static double /*VAR returns cumulative probability from -oo to z */
poz(const double z) /*VAR normal z value */
{
double y, x, w;
if (z == 0.0) {
x = 0.0;
} else {
y = 0.5 * fabs(z);
if (y >= (Z_MAX * 0.5)) {
x = 1.0;
} else if (y < 1.0) {
w = y * y;
x = ((((((((0.000124818987 * w
-0.001075204047) * w +0.005198775019) * w
-0.019198292004) * w +0.059054035642) * w
-0.151968751364) * w +0.319152932694) * w
-0.531923007300) * w +0.797884560593) * y * 2.0;
} else {
y -= 2.0;
x = (((((((((((((-0.000045255659 * y
+0.000152529290) * y -0.000019538132) * y
-0.000676904986) * y +0.001390604284) * y
-0.000794620820) * y -0.002034254874) * y
+0.006549791214) * y -0.010557625006) * y
+0.011630447319) * y -0.009279453341) * y
+0.005353579108) * y -0.002141268741) * y
+0.000535310849) * y +0.999936657524;
}
}
return (z > 0.0 ? ((x + 1.0) * 0.5) : ((1.0 - x) * 0.5));
}
/*
Module: chisq.c
Purpose: compute approximations to chisquare distribution probabilities
Contents: pochisq()
Uses: poz() in z.c (Algorithm 209)
Programmer: Gary Perlman
Organization: Wang Institute, Tyngsboro, MA 01879
Copyright: none
Tabstops: 4
*/
#define LOG_SQRT_PI 0.5723649429247000870717135 /* log (sqrt (pi)) */
#define I_SQRT_PI 0.5641895835477562869480795 /* 1 / sqrt (pi) */
#define BIGX 20.0 /* max value to represent exp (x) */
#define ex(x) (((x) < -BIGX) ? 0.0 : exp(x))
/*FUNCTION pochisq: probability of chi square value */
/*ALGORITHM Compute probability of chi square value.
Adapted from:
Hill, I. D. and Pike, M. C. Algorithm 299
Collected Algorithms for the CACM 1967 p. 243
Updated for rounding errors based on remark in
ACM TOMS June 1985, page 185
*/
double pochisq(
const double ax, /* obtained chi-square value */
const int df /* degrees of freedom */
)
{
double x = ax;
double a, y, s;
double e, c, z;
int even; /* true if df is an even number */
y = 0.0; /* XXX: blind modification due to GCC error */
if (x <= 0.0 || df < 1) {
return 1.0;
}
a = 0.5 * x;
even = (2 * (df / 2)) == df;
if (df > 1) {
y = ex(-a);
}
s = (even ? y : (2.0 * poz(-sqrt(x))));
if (df > 2) {
x = 0.5 * (df - 1.0);
z = (even ? 1.0 : 0.5);
if (a > BIGX) {
e = (even ? 0.0 : LOG_SQRT_PI);
c = log(a);
while (z <= x) {
e = log(z) + e;
s += ex(c * z - a - e);
z += 1.0;
}
return (s);
} else {
e = (even ? 1.0 : (I_SQRT_PI / sqrt(a)));
c = 0.0;
while (z <= x) {
e = e * (a / z);
c = c + e;
z += 1.0;
}
return (c * y + s);
}
} else {
return s;
}
}
| 4,161 | 143 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/ctanf.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/complex.h"
#include "libc/math.h"
#include "libc/tinymath/complex.internal.h"
asm(".ident\t\"\\n\\n\
Musl libc (MIT License)\\n\
Copyright 2005-2014 Rich Felker, et. al.\"");
asm(".include \"libc/disclaimer.inc\"");
/* clang-format off */
float complex ctanf(float complex z)
{
z = ctanhf(CMPLXF(-cimagf(z), crealf(z)));
return CMPLXF(cimagf(z), -crealf(z));
}
| 2,984 | 45 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/fminf.c | /*-*- mode:c;indent-tabs-mode:nil;c-basic-offset:2;tab-width:8;coding:utf-8 -*-â
âvi: set net ft=c ts=2 sts=2 sw=2 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ¡
â Copyright 2020 Justine Alexandra Roberts Tunney â
â â
â Permission to use, copy, modify, and/or distribute this software for â
â any purpose with or without fee is hereby granted, provided that the â
â above copyright notice and this permission notice appear in all copies. â
â â
â THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL â
â WARRANTIES WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED â
â WARRANTIES OF MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE â
â AUTHOR BE LIABLE FOR ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL â
â DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR â
â PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER â
â TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR â
â PERFORMANCE OF THIS SOFTWARE. â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
#include "libc/tinymath/freebsd.internal.h"
/**
* Returns minimum of two floats.
*
* If one argument is NAN then the other is returned.
* This function is designed to do the right thing with
* signed zeroes.
*/
float fminf(float x, float y) {
if (isnan(x)) return y;
if (isnan(y)) return x;
if (signbit(x) != signbit(y)) {
return signbit(x) ? x : y; /* C99 Annex F.9.9.2 */
}
return x < y ? x : y;
}
| 2,280 | 37 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/cpowl.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/complex.h"
asm(".ident\t\"\\n\\n\
Musl libc (MIT License)\\n\
Copyright 2005-2014 Rich Felker, et. al.\"");
asm(".include \"libc/disclaimer.inc\"");
// clang-format off
#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
long double complex cpowl(long double complex z, long double complex c)
{
return cpow(z, c);
}
#else
long double complex cpowl(long double complex z, long double complex c)
{
return cexpl(c * clogl(z));
}
#endif
| 3,050 | 47 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/modfl.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
asm(".ident\t\"\\n\\n\
Musl libc (MIT License)\\n\
Copyright 2005-2014 Rich Felker, et. al.\"");
asm(".include \"libc/disclaimer.inc\"");
// clang-format off
#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
long double modfl(long double x, long double *iptr)
{
double d;
long double r;
r = modf(x, &d);
*iptr = d;
return r;
}
#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
static const long double toint = 1/LDBL_EPSILON;
long double modfl(long double x, long double *iptr)
{
union {
long double f;
struct {
uint64_t m;
uint16_t se;
} i;
} u = {x};
int e = (u.i.se & 0x7fff) - 0x3fff;
int s = u.i.se >> 15;
long double absx;
long double y;
/* no fractional part */
if (e >= LDBL_MANT_DIG-1) {
*iptr = x;
if (isnan(x))
return x;
return s ? -0.0 : 0.0;
}
/* no integral part*/
if (e < 0) {
*iptr = s ? -0.0 : 0.0;
return x;
}
/* raises spurious inexact */
absx = s ? -x : x;
y = absx + toint - toint - absx;
if (y == 0) {
*iptr = x;
return s ? -0.0 : 0.0;
}
if (y > 0)
y -= 1;
if (s)
y = -y;
*iptr = x + y;
return -y;
}
#else
#error "architecture unsupported"
#endif
| 3,787 | 96 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/atanf_data.c | /*-*- mode:c;indent-tabs-mode:nil;c-basic-offset:2;tab-width:8;coding:utf-8 -*-â
âvi: set net ft=c ts=2 sts=2 sw=2 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Optimized Routines â
â Copyright (c) 1999-2022, Arm Limited. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/tinymath/atanf_data.internal.h"
asm(".ident\t\"\\n\\n\
Optimized Routines (MIT License)\\n\
Copyright 2022 ARM Limited\"");
asm(".include \"libc/disclaimer.inc\"");
/* clang-format off */
/* Coefficients of polynomial P such that atan(x)~x+x*P(x^2) on [2**-128, 1.0].
*/
const struct atanf_poly_data __atanf_poly_data = {
.poly = {/* See atanf.sollya for details of how these were generated. */
-0x1.55555p-2f, 0x1.99935ep-3f, -0x1.24051ep-3f, 0x1.bd7368p-4f,
-0x1.491f0ep-4f, 0x1.93a2c0p-5f, -0x1.4c3c60p-6f, 0x1.01fd88p-8f}};
| 3,158 | 42 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/cbrt.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2020 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
asm(".ident\t\"\\n\\n\
fdlibm (fdlibm license)\\n\
Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.\"");
asm(".ident\t\"\\n\\n\
Musl libc (MIT License)\\n\
Copyright 2005-2014 Rich Felker, et. al.\"");
asm(".include \"libc/disclaimer.inc\"");
// clang-format off
/* origin: FreeBSD /usr/src/lib/msun/src/s_cbrt.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.
* ====================================================
*
* Optimized by Bruce D. Evans.
*/
static const uint32_t
B1 = 715094163, /* B1 = (1023-1023/3-0.03306235651)*2**20 */
B2 = 696219795; /* B2 = (1023-1023/3-54/3-0.03306235651)*2**20 */
/* |1/cbrt(x) - p(x)| < 2**-23.5 (~[-7.93e-8, 7.929e-8]). */
static const double
P0 = 1.87595182427177009643, /* 0x3ffe03e6, 0x0f61e692 */
P1 = -1.88497979543377169875, /* 0xbffe28e0, 0x92f02420 */
P2 = 1.621429720105354466140, /* 0x3ff9f160, 0x4a49d6c2 */
P3 = -0.758397934778766047437, /* 0xbfe844cb, 0xbee751d9 */
P4 = 0.145996192886612446982; /* 0x3fc2b000, 0xd4e4edd7 */
/**
* Returns cube root of ð¥.
*/
double cbrt(double x)
{
union {double f; uint64_t i;} u = {x};
double_t r,s,t,w;
uint32_t hx = u.i>>32 & 0x7fffffff;
if (hx >= 0x7ff00000) /* cbrt(NaN,INF) is itself */
return x+x;
/*
* Rough cbrt to 5 bits:
* cbrt(2**e*(1+m) ~= 2**(e/3)*(1+(e%3+m)/3)
* where e is integral and >= 0, m is real and in [0, 1), and "/" and
* "%" are integer division and modulus with rounding towards minus
* infinity. The RHS is always >= the LHS and has a maximum relative
* error of about 1 in 16. Adding a bias of -0.03306235651 to the
* (e%3+m)/3 term reduces the error to about 1 in 32. With the IEEE
* floating point representation, for finite positive normal values,
* ordinary integer divison of the value in bits magically gives
* almost exactly the RHS of the above provided we first subtract the
* exponent bias (1023 for doubles) and later add it back. We do the
* subtraction virtually to keep e >= 0 so that ordinary integer
* division rounds towards minus infinity; this is also efficient.
*/
if (hx < 0x00100000) { /* zero or subnormal? */
u.f = x*0x1p54;
hx = u.i>>32 & 0x7fffffff;
if (hx == 0)
return x; /* cbrt(0) is itself */
hx = hx/3 + B2;
} else
hx = hx/3 + B1;
u.i &= 1ULL<<63;
u.i |= (uint64_t)hx << 32;
t = u.f;
/*
* New cbrt to 23 bits:
* cbrt(x) = t*cbrt(x/t**3) ~= t*P(t**3/x)
* where P(r) is a polynomial of degree 4 that approximates 1/cbrt(r)
* to within 2**-23.5 when |r - 1| < 1/10. The rough approximation
* has produced t such than |t/cbrt(x) - 1| ~< 1/32, and cubing this
* gives us bounds for r = t**3/x.
*
* Try to optimize for parallel evaluation as in __tanf.c.
*/
r = (t*t)*(t/x);
t = t*((P0+r*(P1+r*P2))+((r*r)*r)*(P3+r*P4));
/*
* Round t away from zero to 23 bits (sloppily except for ensuring that
* the result is larger in magnitude than cbrt(x) but not much more than
* 2 23-bit ulps larger). With rounding towards zero, the error bound
* would be ~5/6 instead of ~4/6. With a maximum error of 2 23-bit ulps
* in the rounded t, the infinite-precision error in the Newton
* approximation barely affects third digit in the final error
* 0.667; the error in the rounded t can be up to about 3 23-bit ulps
* before the final error is larger than 0.667 ulps.
*/
u.f = t;
u.i = (u.i + 0x80000000) & 0xffffffffc0000000ULL;
t = u.f;
/* one step Newton iteration to 53 bits with error < 0.667 ulps */
s = t*t; /* t*t is exact */
r = x/s; /* error <= 0.5 ulps; |r| < |t| */
w = t+t; /* t+t is exact */
r = (r-t)/(w+r); /* r-t is exact; w+r ~= 3*t */
t = t+t*r; /* error <= 0.5 + 0.5/3 + epsilon */
return t;
}
| 6,627 | 139 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/sincos.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
#include "libc/runtime/runtime.h"
#include "libc/tinymath/feval.internal.h"
#include "libc/tinymath/kernel.internal.h"
asm(".ident\t\"\\n\\n\
fdlibm (fdlibm license)\\n\
Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.\"");
asm(".ident\t\"\\n\\n\
Musl libc (MIT License)\\n\
Copyright 2005-2014 Rich Felker, et. al.\"");
asm(".include \"libc/disclaimer.inc\"");
// clang-format off
/* origin: FreeBSD /usr/src/lib/msun/src/s_sin.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 asuint64(f) ((union{double _f; uint64_t _i;}){f})._i
#define gethighw(hi,d) (hi) = asuint64(d) >> 32
/**
* Returns sine and cosine of ð¥.
* @note should take ~10ns
*/
void sincos(double x, double *sin, double *cos)
{
double y[2], s, c;
uint32_t ix;
unsigned n;
gethighw(ix, x);
ix &= 0x7fffffff;
/* |x| ~< pi/4 */
if (ix <= 0x3fe921fb) {
/* if |x| < 2**-27 * sqrt(2) */
if (ix < 0x3e46a09e) {
/* raise inexact if x!=0 and underflow if subnormal */
feval(ix < 0x00100000 ? x/0x1p120f : x+0x1p120f);
*sin = x;
*cos = 1.0;
return;
}
*sin = __sin(x, 0.0, 0);
*cos = __cos(x, 0.0);
return;
}
/* sincos(Inf or NaN) is NaN */
if (ix >= 0x7ff00000) {
*sin = *cos = x - x;
return;
}
/* argument reduction needed */
n = __rem_pio2(x, y);
s = __sin(y[0], y[1], 1);
c = __cos(y[0], y[1]);
switch (n&3) {
case 0:
*sin = s;
*cos = c;
break;
case 1:
*sin = c;
*cos = -s;
break;
case 2:
*sin = -s;
*cos = -c;
break;
case 3:
default:
*sin = -c;
*cos = s;
break;
}
}
#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
__strong_reference(sincos, sincosl);
#endif
| 4,596 | 119 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/ctanh.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/complex.h"
#include "libc/math.h"
#include "libc/tinymath/complex.internal.h"
asm(".ident\t\"\\n\\n\
ctahnh (BSD-2 License)\\n\
Copyright (c) 2011 David Schultz <[email protected]>\"");
asm(".ident\t\"\\n\\n\
Musl libc (MIT License)\\n\
Copyright 2005-2014 Rich Felker, et. al.\"");
asm(".include \"libc/disclaimer.inc\"");
/* clang-format off */
/* origin: FreeBSD /usr/src/lib/msun/src/s_ctanh.c */
/*-
* Copyright (c) 2011 David Schultz
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* 1. Redistributions of source code must retain the above copyright
* notice unmodified, this list of conditions, and the following
* disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
*
* THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
* IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
* OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
* IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
* NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
* DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
* THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
* THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
/*
* Hyperbolic tangent of a complex argument z = x + i y.
*
* The algorithm is from:
*
* W. Kahan. Branch Cuts for Complex Elementary Functions or Much
* Ado About Nothing's Sign Bit. In The State of the Art in
* Numerical Analysis, pp. 165 ff. Iserles and Powell, eds., 1987.
*
* Method:
*
* Let t = tan(x)
* beta = 1/cos^2(y)
* s = sinh(x)
* rho = cosh(x)
*
* We have:
*
* tanh(z) = sinh(z) / cosh(z)
*
* sinh(x) cos(y) + i cosh(x) sin(y)
* = ---------------------------------
* cosh(x) cos(y) + i sinh(x) sin(y)
*
* cosh(x) sinh(x) / cos^2(y) + i tan(y)
* = -------------------------------------
* 1 + sinh^2(x) / cos^2(y)
*
* beta rho s + i t
* = ----------------
* 1 + beta s^2
*
* Modifications:
*
* I omitted the original algorithm's handling of overflow in tan(x) after
* verifying with nearpi.c that this can't happen in IEEE single or double
* precision. I also handle large x differently.
*/
double complex ctanh(double complex z)
{
double x, y;
double t, beta, s, rho, denom;
uint32_t hx, ix, lx;
x = creal(z);
y = cimag(z);
EXTRACT_WORDS(hx, lx, x);
ix = hx & 0x7fffffff;
/*
* ctanh(NaN + i 0) = NaN + i 0
*
* ctanh(NaN + i y) = NaN + i NaN for y != 0
*
* The imaginary part has the sign of x*sin(2*y), but there's no
* special effort to get this right.
*
* ctanh(+-Inf +- i Inf) = +-1 +- 0
*
* ctanh(+-Inf + i y) = +-1 + 0 sin(2y) for y finite
*
* The imaginary part of the sign is unspecified. This special
* case is only needed to avoid a spurious invalid exception when
* y is infinite.
*/
if (ix >= 0x7ff00000) {
if ((ix & 0xfffff) | lx) /* x is NaN */
return CMPLX(x, (y == 0 ? y : x * y));
SET_HIGH_WORD(x, hx - 0x40000000); /* x = copysign(1, x) */
return CMPLX(x, copysign(0, isinf(y) ? y : sin(y) * cos(y)));
}
/*
* ctanh(+-0 + i NAN) = +-0 + i NaN
* ctanh(+-0 +- i Inf) = +-0 + i NaN
* ctanh(x + i NAN) = NaN + i NaN
* ctanh(x +- i Inf) = NaN + i NaN
*/
if (!isfinite(y))
return CMPLX(x ? y - y : x, y - y);
/*
* ctanh(+-huge + i +-y) ~= +-1 +- i 2sin(2y)/exp(2x), using the
* approximation sinh^2(huge) ~= exp(2*huge) / 4.
* We use a modified formula to avoid spurious overflow.
*/
if (ix >= 0x40360000) { /* x >= 22 */
double exp_mx = exp(-fabs(x));
return CMPLX(copysign(1, x), 4 * sin(y) * cos(y) * exp_mx * exp_mx);
}
/* Kahan's algorithm */
t = tan(y);
beta = 1.0 + t * t; /* = 1 / cos^2(y) */
s = sinh(x);
rho = sqrt(1 + s * s); /* = cosh(x) */
denom = 1 + beta * s * s;
return CMPLX((beta * rho * s) / denom, t / denom);
}
| 7,139 | 170 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/round.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
#include "libc/runtime/fenv.h"
#include "libc/tinymath/internal.h"
asm(".ident\t\"\\n\\n\
Musl libc (MIT License)\\n\
Copyright 2005-2014 Rich Felker, et. al.\"");
asm(".include \"libc/disclaimer.inc\"");
// clang-format off
#if FLT_EVAL_METHOD==0 || FLT_EVAL_METHOD==1
#define EPS DBL_EPSILON
#elif FLT_EVAL_METHOD==2
#define EPS LDBL_EPSILON
#endif
static const double_t toint = 1/EPS;
/**
* Rounds ð¥ to nearest integer, away from zero.
*/
double round(double x)
{
#ifdef __aarch64__
asm("frinta\t%d0,%d1" : "=w"(x) : "w"(x));
return x;
#elif defined(__powerpc64__) && defined(_ARCH_PWR5X)
asm("frin\t%0,%1" : "=d"(x) : "d"(x));
return x;
#elif defined(__s390x__) && (defined(__HTM__) || __ARCH__ >= 9)
asm("fidbra\t%0,1,%1,4" : "=f"(x) : "f"(x));
return x;
#else
union {double f; uint64_t i;} u = {x};
int e = u.i >> 52 & 0x7ff;
double_t y;
if (e >= 0x3ff+52)
return x;
if (u.i >> 63)
x = -x;
if (e < 0x3ff-1) {
/* raise inexact if x!=0 */
FORCE_EVAL(x + toint);
return 0*u.f;
}
y = x + toint - toint - x;
if (y > 0.5)
y = y + x - 1;
else if (y <= -0.5)
y = y + x + 1;
else
y = y + x;
if (u.i >> 63)
y = -y;
return y;
#endif /* __aarch64__ */
}
#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
__strong_reference(round, roundl);
#endif
| 3,918 | 97 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/log1pl.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/complex.h"
#include "libc/math.h"
#include "libc/tinymath/complex.internal.h"
#if LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384
asm(".ident\t\"\\n\\n\
OpenBSD libm (ISC License)\\n\
Copyright (c) 2008 Stephen L. Moshier <[email protected]>\"");
asm(".ident\t\"\\n\\n\
Musl libc (MIT License)\\n\
Copyright 2005-2014 Rich Felker, et. al.\"");
asm(".include \"libc/disclaimer.inc\"");
// clang-format off
/* origin: OpenBSD /usr/src/lib/libm/src/ld80/s_log1pl.c */
/*
* Copyright (c) 2008 Stephen L. Moshier <[email protected]>
*
* Permission to use, copy, modify, and distribute this software for any
* purpose with or without fee is hereby granted, provided that the above
* copyright notice and this permission notice appear in all copies.
*
* THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
* WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
* MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
* ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
* WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
* ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
* OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
*/
/*
* Relative error logarithm
* Natural logarithm of 1+x, long double precision
*
*
* SYNOPSIS:
*
* long double x, y, log1pl();
*
* y = log1pl( x );
*
*
* DESCRIPTION:
*
* Returns the base e (2.718...) logarithm of 1+x.
*
* The argument 1+x is separated into its exponent and fractional
* parts. If the exponent is between -1 and +1, the logarithm
* of the fraction is approximated by
*
* log(1+x) = x - 0.5 x^2 + x^3 P(x)/Q(x).
*
* Otherwise, setting z = 2(x-1)/x+1),
*
* log(x) = z + z^3 P(z)/Q(z).
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* IEEE -1.0, 9.0 100000 8.2e-20 2.5e-20
*/
/* Coefficients for log(1+x) = x - x^2 / 2 + x^3 P(x)/Q(x)
* 1/sqrt(2) <= x < sqrt(2)
* Theoretical peak relative error = 2.32e-20
*/
static const long double P[] = {
4.5270000862445199635215E-5L,
4.9854102823193375972212E-1L,
6.5787325942061044846969E0L,
2.9911919328553073277375E1L,
6.0949667980987787057556E1L,
5.7112963590585538103336E1L,
2.0039553499201281259648E1L,
};
static const long double Q[] = {
/* 1.0000000000000000000000E0,*/
1.5062909083469192043167E1L,
8.3047565967967209469434E1L,
2.2176239823732856465394E2L,
3.0909872225312059774938E2L,
2.1642788614495947685003E2L,
6.0118660497603843919306E1L,
};
/* Coefficients for log(x) = z + z^3 P(z^2)/Q(z^2),
* where z = 2(x-1)/(x+1)
* 1/sqrt(2) <= x < sqrt(2)
* Theoretical peak relative error = 6.16e-22
*/
static const long double R[4] = {
1.9757429581415468984296E-3L,
-7.1990767473014147232598E-1L,
1.0777257190312272158094E1L,
-3.5717684488096787370998E1L,
};
static const long double S[4] = {
/* 1.00000000000000000000E0L,*/
-2.6201045551331104417768E1L,
1.9361891836232102174846E2L,
-4.2861221385716144629696E2L,
};
static const long double C1 = 6.9314575195312500000000E-1L;
static const long double C2 = 1.4286068203094172321215E-6L;
#define SQRTH 0.70710678118654752440L
/**
* Returns log(ð·+ð¥).
*/
long double log1pl(long double xm1)
{
long double x, y, z;
int e;
if (isnan(xm1))
return xm1;
if (xm1 == INFINITY)
return xm1;
if (xm1 == 0.0)
return xm1;
x = xm1 + 1.0;
/* Test for domain errors. */
if (x <= 0.0) {
if (x == 0.0)
return -1/(x*x); /* -inf with divbyzero */
return 0/0.0f; /* nan with invalid */
}
/* Separate mantissa from exponent.
Use frexp so that denormal numbers will be handled properly. */
x = frexpl(x, &e);
/* logarithm using log(x) = z + z^3 P(z)/Q(z),
where z = 2(x-1)/x+1) */
if (e > 2 || e < -2) {
if (x < SQRTH) { /* 2(2x-1)/(2x+1) */
e -= 1;
z = x - 0.5;
y = 0.5 * z + 0.5;
} else { /* 2 (x-1)/(x+1) */
z = x - 0.5;
z -= 0.5;
y = 0.5 * x + 0.5;
}
x = z / y;
z = x*x;
z = x * (z * __polevll(z, R, 3) / __p1evll(z, S, 3));
z = z + e * C2;
z = z + x;
z = z + e * C1;
return z;
}
/* logarithm using log(1+x) = x - .5x**2 + x**3 P(x)/Q(x) */
if (x < SQRTH) {
e -= 1;
if (e != 0)
x = 2.0 * x - 1.0;
else
x = xm1;
} else {
if (e != 0)
x = x - 1.0;
else
x = xm1;
}
z = x*x;
y = x * (z * __polevll(x, P, 6) / __p1evll(x, Q, 6));
y = y + e * C2;
z = y - 0.5 * z;
z = z + x;
z = z + e * C1;
return z;
}
#endif /* ieee80 */
| 7,174 | 209 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/cosf.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
#include "libc/tinymath/complex.internal.h"
#include "libc/tinymath/feval.internal.h"
#include "libc/tinymath/kernel.internal.h"
asm(".ident\t\"\\n\\n\
fdlibm (fdlibm license)\\n\
Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.\"");
asm(".ident\t\"\\n\\n\
Musl libc (MIT License)\\n\
Copyright 2005-2014 Rich Felker, et. al.\"");
asm(".include \"libc/disclaimer.inc\"");
/* clang-format off */
/* origin: FreeBSD /usr/src/lib/msun/src/s_cosf.c */
/*
* Conversion to float by Ian Lance Taylor, Cygnus Support, [email protected].
* Optimized by Bruce D. Evans.
*/
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/* Small multiples of pi/2 rounded to double precision. */
static const double
c1pio2 = 1*M_PI_2, /* 0x3FF921FB, 0x54442D18 */
c2pio2 = 2*M_PI_2, /* 0x400921FB, 0x54442D18 */
c3pio2 = 3*M_PI_2, /* 0x4012D97C, 0x7F3321D2 */
c4pio2 = 4*M_PI_2; /* 0x401921FB, 0x54442D18 */
/**
* Returns cosine of ð¥.
* @note should take about 5ns
*/
float cosf(float x)
{
double y;
uint32_t ix;
unsigned n, sign;
GET_FLOAT_WORD(ix, x);
sign = ix >> 31;
ix &= 0x7fffffff;
if (ix <= 0x3f490fda) { /* |x| ~<= pi/4 */
if (ix < 0x39800000) { /* |x| < 2**-12 */
/* raise inexact if x != 0 */
FORCE_EVAL(x + 0x1p120f);
return 1.0f;
}
return __cosdf(x);
}
if (ix <= 0x407b53d1) { /* |x| ~<= 5*pi/4 */
if (ix > 0x4016cbe3) /* |x| ~> 3*pi/4 */
return -__cosdf(sign ? x+c2pio2 : x-c2pio2);
else {
if (sign)
return __sindf(x + c1pio2);
else
return __sindf(c1pio2 - x);
}
}
if (ix <= 0x40e231d5) { /* |x| ~<= 9*pi/4 */
if (ix > 0x40afeddf) /* |x| ~> 7*pi/4 */
return __cosdf(sign ? x+c4pio2 : x-c4pio2);
else {
if (sign)
return __sindf(-x - c3pio2);
else
return __sindf(x - c3pio2);
}
}
/* cos(Inf or NaN) is NaN */
if (ix >= 0x7f800000)
return x-x;
/* general argument reduction needed */
n = __rem_pio2f(x,&y);
switch (n&3) {
case 0: return __cosdf(y);
case 1: return __sindf(-y);
case 2: return -__cosdf(y);
default:
return __sindf(y);
}
}
| 5,007 | 122 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/log_data.internal.h | #ifndef COSMOPOLITAN_LIBC_TINYMATH_LOG_DATA_H_
#define COSMOPOLITAN_LIBC_TINYMATH_LOG_DATA_H_
#define LOG_TABLE_BITS 7
#define LOG_POLY_ORDER 6
#define LOG_POLY1_ORDER 12
#if !(__ASSEMBLER__ + __LINKER__ + 0)
COSMOPOLITAN_C_START_
extern _Hide const struct log_data {
double ln2hi;
double ln2lo;
double poly[LOG_POLY_ORDER - 1]; /* First coefficient is 1. */
double poly1[LOG_POLY1_ORDER - 1];
struct {
double invc, logc;
} tab[1 << LOG_TABLE_BITS];
#if !__FP_FAST_FMA
struct {
double chi, clo;
} tab2[1 << LOG_TABLE_BITS];
#endif
} __log_data;
COSMOPOLITAN_C_END_
#endif /* !(__ASSEMBLER__ + __LINKER__ + 0) */
#endif /* COSMOPOLITAN_LIBC_TINYMATH_LOG_DATA_H_ */
| 695 | 29 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/erff.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2020 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
asm(".ident\t\"\\n\\n\
fdlibm (fdlibm license)\\n\
Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.\"");
asm(".ident\t\"\\n\\n\
Musl libc (MIT License)\\n\
Copyright 2005-2014 Rich Felker, et. al.\"");
asm(".include \"libc/disclaimer.inc\"");
/* clang-format off */
/* origin: FreeBSD /usr/src/lib/msun/src/s_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;
}
| 8,249 | 220 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/exp_data.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/tinymath/exp_data.internal.h"
asm(".ident\t\"\\n\\n\
Double-precision math functions (MIT License)\\n\
Copyright 2018 ARM Limited\"");
asm(".include \"libc/disclaimer.inc\"");
/* clang-format off */
/*
* Shared data between exp, exp2 and pow.
*
* Copyright (c) 2018, Arm Limited.
* SPDX-License-Identifier: MIT
*/
#define N (1 << EXP_TABLE_BITS)
const struct exp_data __exp_data = {
// N/ln2
.invln2N = 0x1.71547652b82fep0 * N,
// -ln2/N
.negln2hiN = -0x1.62e42fefa0000p-8,
.negln2loN = -0x1.cf79abc9e3b3ap-47,
// Used for rounding when !TOINT_INTRINSICS
#if EXP_USE_TOINT_NARROW
.shift = 0x1800000000.8p0,
#else
.shift = 0x1.8p52,
#endif
// exp polynomial coefficients.
.poly = {
// abs error: 1.555*2^-66
// ulp error: 0.509 (0.511 without fma)
// if |x| < ln2/256+eps
// abs error if |x| < ln2/256+0x1p-15: 1.09*2^-65
// abs error if |x| < ln2/128: 1.7145*2^-56
0x1.ffffffffffdbdp-2,
0x1.555555555543cp-3,
0x1.55555cf172b91p-5,
0x1.1111167a4d017p-7,
},
.exp2_shift = 0x1.8p52 / N,
// exp2 polynomial coefficients.
.exp2_poly = {
// abs error: 1.2195*2^-65
// ulp error: 0.507 (0.511 without fma)
// if |x| < 1/256
// abs error if |x| < 1/128: 1.9941*2^-56
0x1.62e42fefa39efp-1,
0x1.ebfbdff82c424p-3,
0x1.c6b08d70cf4b5p-5,
0x1.3b2abd24650ccp-7,
0x1.5d7e09b4e3a84p-10,
},
// 2^(k/N) ~= H[k]*(1 + T[k]) for int k in [0,N)
// tab[2*k] = asuint64(T[k])
// tab[2*k+1] = asuint64(H[k]) - (k << 52)/N
.tab = {
0x0, 0x3ff0000000000000,
0x3c9b3b4f1a88bf6e, 0x3feff63da9fb3335,
0xbc7160139cd8dc5d, 0x3fefec9a3e778061,
0xbc905e7a108766d1, 0x3fefe315e86e7f85,
0x3c8cd2523567f613, 0x3fefd9b0d3158574,
0xbc8bce8023f98efa, 0x3fefd06b29ddf6de,
0x3c60f74e61e6c861, 0x3fefc74518759bc8,
0x3c90a3e45b33d399, 0x3fefbe3ecac6f383,
0x3c979aa65d837b6d, 0x3fefb5586cf9890f,
0x3c8eb51a92fdeffc, 0x3fefac922b7247f7,
0x3c3ebe3d702f9cd1, 0x3fefa3ec32d3d1a2,
0xbc6a033489906e0b, 0x3fef9b66affed31b,
0xbc9556522a2fbd0e, 0x3fef9301d0125b51,
0xbc5080ef8c4eea55, 0x3fef8abdc06c31cc,
0xbc91c923b9d5f416, 0x3fef829aaea92de0,
0x3c80d3e3e95c55af, 0x3fef7a98c8a58e51,
0xbc801b15eaa59348, 0x3fef72b83c7d517b,
0xbc8f1ff055de323d, 0x3fef6af9388c8dea,
0x3c8b898c3f1353bf, 0x3fef635beb6fcb75,
0xbc96d99c7611eb26, 0x3fef5be084045cd4,
0x3c9aecf73e3a2f60, 0x3fef54873168b9aa,
0xbc8fe782cb86389d, 0x3fef4d5022fcd91d,
0x3c8a6f4144a6c38d, 0x3fef463b88628cd6,
0x3c807a05b0e4047d, 0x3fef3f49917ddc96,
0x3c968efde3a8a894, 0x3fef387a6e756238,
0x3c875e18f274487d, 0x3fef31ce4fb2a63f,
0x3c80472b981fe7f2, 0x3fef2b4565e27cdd,
0xbc96b87b3f71085e, 0x3fef24dfe1f56381,
0x3c82f7e16d09ab31, 0x3fef1e9df51fdee1,
0xbc3d219b1a6fbffa, 0x3fef187fd0dad990,
0x3c8b3782720c0ab4, 0x3fef1285a6e4030b,
0x3c6e149289cecb8f, 0x3fef0cafa93e2f56,
0x3c834d754db0abb6, 0x3fef06fe0a31b715,
0x3c864201e2ac744c, 0x3fef0170fc4cd831,
0x3c8fdd395dd3f84a, 0x3feefc08b26416ff,
0xbc86a3803b8e5b04, 0x3feef6c55f929ff1,
0xbc924aedcc4b5068, 0x3feef1a7373aa9cb,
0xbc9907f81b512d8e, 0x3feeecae6d05d866,
0xbc71d1e83e9436d2, 0x3feee7db34e59ff7,
0xbc991919b3ce1b15, 0x3feee32dc313a8e5,
0x3c859f48a72a4c6d, 0x3feedea64c123422,
0xbc9312607a28698a, 0x3feeda4504ac801c,
0xbc58a78f4817895b, 0x3feed60a21f72e2a,
0xbc7c2c9b67499a1b, 0x3feed1f5d950a897,
0x3c4363ed60c2ac11, 0x3feece086061892d,
0x3c9666093b0664ef, 0x3feeca41ed1d0057,
0x3c6ecce1daa10379, 0x3feec6a2b5c13cd0,
0x3c93ff8e3f0f1230, 0x3feec32af0d7d3de,
0x3c7690cebb7aafb0, 0x3feebfdad5362a27,
0x3c931dbdeb54e077, 0x3feebcb299fddd0d,
0xbc8f94340071a38e, 0x3feeb9b2769d2ca7,
0xbc87deccdc93a349, 0x3feeb6daa2cf6642,
0xbc78dec6bd0f385f, 0x3feeb42b569d4f82,
0xbc861246ec7b5cf6, 0x3feeb1a4ca5d920f,
0x3c93350518fdd78e, 0x3feeaf4736b527da,
0x3c7b98b72f8a9b05, 0x3feead12d497c7fd,
0x3c9063e1e21c5409, 0x3feeab07dd485429,
0x3c34c7855019c6ea, 0x3feea9268a5946b7,
0x3c9432e62b64c035, 0x3feea76f15ad2148,
0xbc8ce44a6199769f, 0x3feea5e1b976dc09,
0xbc8c33c53bef4da8, 0x3feea47eb03a5585,
0xbc845378892be9ae, 0x3feea34634ccc320,
0xbc93cedd78565858, 0x3feea23882552225,
0x3c5710aa807e1964, 0x3feea155d44ca973,
0xbc93b3efbf5e2228, 0x3feea09e667f3bcd,
0xbc6a12ad8734b982, 0x3feea012750bdabf,
0xbc6367efb86da9ee, 0x3fee9fb23c651a2f,
0xbc80dc3d54e08851, 0x3fee9f7df9519484,
0xbc781f647e5a3ecf, 0x3fee9f75e8ec5f74,
0xbc86ee4ac08b7db0, 0x3fee9f9a48a58174,
0xbc8619321e55e68a, 0x3fee9feb564267c9,
0x3c909ccb5e09d4d3, 0x3feea0694fde5d3f,
0xbc7b32dcb94da51d, 0x3feea11473eb0187,
0x3c94ecfd5467c06b, 0x3feea1ed0130c132,
0x3c65ebe1abd66c55, 0x3feea2f336cf4e62,
0xbc88a1c52fb3cf42, 0x3feea427543e1a12,
0xbc9369b6f13b3734, 0x3feea589994cce13,
0xbc805e843a19ff1e, 0x3feea71a4623c7ad,
0xbc94d450d872576e, 0x3feea8d99b4492ed,
0x3c90ad675b0e8a00, 0x3feeaac7d98a6699,
0x3c8db72fc1f0eab4, 0x3feeace5422aa0db,
0xbc65b6609cc5e7ff, 0x3feeaf3216b5448c,
0x3c7bf68359f35f44, 0x3feeb1ae99157736,
0xbc93091fa71e3d83, 0x3feeb45b0b91ffc6,
0xbc5da9b88b6c1e29, 0x3feeb737b0cdc5e5,
0xbc6c23f97c90b959, 0x3feeba44cbc8520f,
0xbc92434322f4f9aa, 0x3feebd829fde4e50,
0xbc85ca6cd7668e4b, 0x3feec0f170ca07ba,
0x3c71affc2b91ce27, 0x3feec49182a3f090,
0x3c6dd235e10a73bb, 0x3feec86319e32323,
0xbc87c50422622263, 0x3feecc667b5de565,
0x3c8b1c86e3e231d5, 0x3feed09bec4a2d33,
0xbc91bbd1d3bcbb15, 0x3feed503b23e255d,
0x3c90cc319cee31d2, 0x3feed99e1330b358,
0x3c8469846e735ab3, 0x3feede6b5579fdbf,
0xbc82dfcd978e9db4, 0x3feee36bbfd3f37a,
0x3c8c1a7792cb3387, 0x3feee89f995ad3ad,
0xbc907b8f4ad1d9fa, 0x3feeee07298db666,
0xbc55c3d956dcaeba, 0x3feef3a2b84f15fb,
0xbc90a40e3da6f640, 0x3feef9728de5593a,
0xbc68d6f438ad9334, 0x3feeff76f2fb5e47,
0xbc91eee26b588a35, 0x3fef05b030a1064a,
0x3c74ffd70a5fddcd, 0x3fef0c1e904bc1d2,
0xbc91bdfbfa9298ac, 0x3fef12c25bd71e09,
0x3c736eae30af0cb3, 0x3fef199bdd85529c,
0x3c8ee3325c9ffd94, 0x3fef20ab5fffd07a,
0x3c84e08fd10959ac, 0x3fef27f12e57d14b,
0x3c63cdaf384e1a67, 0x3fef2f6d9406e7b5,
0x3c676b2c6c921968, 0x3fef3720dcef9069,
0xbc808a1883ccb5d2, 0x3fef3f0b555dc3fa,
0xbc8fad5d3ffffa6f, 0x3fef472d4a07897c,
0xbc900dae3875a949, 0x3fef4f87080d89f2,
0x3c74a385a63d07a7, 0x3fef5818dcfba487,
0xbc82919e2040220f, 0x3fef60e316c98398,
0x3c8e5a50d5c192ac, 0x3fef69e603db3285,
0x3c843a59ac016b4b, 0x3fef7321f301b460,
0xbc82d52107b43e1f, 0x3fef7c97337b9b5f,
0xbc892ab93b470dc9, 0x3fef864614f5a129,
0x3c74b604603a88d3, 0x3fef902ee78b3ff6,
0x3c83c5ec519d7271, 0x3fef9a51fbc74c83,
0xbc8ff7128fd391f0, 0x3fefa4afa2a490da,
0xbc8dae98e223747d, 0x3fefaf482d8e67f1,
0x3c8ec3bc41aa2008, 0x3fefba1bee615a27,
0x3c842b94c3a9eb32, 0x3fefc52b376bba97,
0x3c8a64a931d185ee, 0x3fefd0765b6e4540,
0xbc8e37bae43be3ed, 0x3fefdbfdad9cbe14,
0x3c77893b4d91cd9d, 0x3fefe7c1819e90d8,
0x3c5305c14160cc89, 0x3feff3c22b8f71f1,
},
};
| 9,142 | 216 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/remainder.c | /*-*- mode:c;indent-tabs-mode:nil;c-basic-offset:2;tab-width:8;coding:utf-8 -*-â
âvi: set net ft=c ts=2 sts=2 sw=2 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ¡
â Copyright 2023 Justine Alexandra Roberts Tunney â
â â
â Permission to use, copy, modify, and/or distribute this software for â
â any purpose with or without fee is hereby granted, provided that the â
â above copyright notice and this permission notice appear in all copies. â
â â
â THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL â
â WARRANTIES WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED â
â WARRANTIES OF MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE â
â AUTHOR BE LIABLE FOR ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL â
â DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR â
â PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER â
â TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR â
â PERFORMANCE OF THIS SOFTWARE. â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
/**
* Returns remainder of dividing ð¥ by ð¦.
*/
double remainder(double x, double y) {
int q;
return remquo(x, y, &q);
}
__strong_reference(remainder, drem);
#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
__strong_reference(remainder, remainderl);
#endif
| 2,128 | 33 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/kexpl.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â FreeBSD lib/msun/src/s_tanhf.c â
â Converted to long double by Bruce D. Evans. â
â â
â Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. â
â â
â Developed at SunPro, a Sun Microsystems, Inc. business. â
â Permission to use, copy, modify, and distribute this â
â software is freely granted, provided that this notice â
â is preserved. â
â â
â Copyright (c) 1992-2023 The FreeBSD Project. â
â â
â Redistribution and use in source and binary forms, with or without â
â modification, are permitted provided that the following conditions â
â are met: â
â 1. Redistributions of source code must retain the above copyright â
â notice, this list of conditions and the following disclaimer. â
â 2. Redistributions in binary form must reproduce the above copyright â
â notice, this list of conditions and the following disclaimer in the â
â documentation and/or other materials provided with the distribution. â
â â
â THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND â
â ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE â
â IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE â
â ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE â
â FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL â
â DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS â
â OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) â
â HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT â
â LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY â
â OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF â
â SUCH DAMAGE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/tinymath/freebsd.internal.h"
asm(".ident\t\"\\n\\n\
FreeBSD libm (BSD-2 License)\\n\
Copyright (c) 2005-2011, Bruce D. Evans, Steven G. Kargl, David Schultz.\"");
// clang-format off
/*
* ld128 version of k_expl.h. See ../ld80/s_expl.c for most comments.
*
* See ../src/e_exp.c and ../src/k_exp.h for precision-independent comments
* about the secondary kernels.
*/
#define INTERVALS 128
#define LOG2_INTERVALS 7
static const double
/*
* ln2/INTERVALS = L1+L2 (hi+lo decomposition for multiplication). L1 must
* have at least 22 (= log2(|LDBL_MIN_EXP-extras|) + log2(INTERVALS)) lowest
* bits zero so that multiplication of it by n is exact.
*/
INV_L = 1.8466496523378731e+2, /* 0x171547652b82fe.0p-45 */
L2 = -1.0253670638894731e-29; /* -0x1.9ff0342542fc3p-97 */
static const long double
/* 0x1.62e42fefa39ef35793c768000000p-8 */
L1 = 5.41521234812457272982212595914567508e-3L;
/*
* XXX values in hex in comments have been lost (or were never present)
* from here.
*/
static const long double
/*
* Domain [-0.002708, 0.002708], range ~[-2.4021e-38, 2.4234e-38]:
* |exp(x) - p(x)| < 2**-124.9
* (0.002708 is ln2/(2*INTERVALS) rounded up a little).
*
* XXX the coeffs aren't very carefully rounded, and I get 3.6 more bits.
*/
A2 = 0.5,
A3 = 1.66666666666666666666666666651085500e-1L,
A4 = 4.16666666666666666666666666425885320e-2L,
A5 = 8.33333333333333333334522877160175842e-3L,
A6 = 1.38888888888888888889971139751596836e-3L;
static const double
A7 = 1.9841269841269470e-4, /* 0x1.a01a01a019f91p-13 */
A8 = 2.4801587301585286e-5, /* 0x1.71de3ec75a967p-19 */
A9 = 2.7557324277411235e-6, /* 0x1.71de3ec75a967p-19 */
A10 = 2.7557333722375069e-7; /* 0x1.27e505ab56259p-22 */
const struct ExplData kExplData[INTERVALS] = {
{0x1p0L, 0x0p0L},
{0x1.0163da9fb33356d84a66aep0L, 0x3.36dcdfa4003ec04c360be2404078p-92L},
{0x1.02c9a3e778060ee6f7cacap0L, 0x4.f7a29bde93d70a2cabc5cb89ba10p-92L},
{0x1.04315e86e7f84bd738f9a2p0L, 0xd.a47e6ed040bb4bfc05af6455e9b8p-96L},
{0x1.059b0d31585743ae7c548ep0L, 0xb.68ca417fe53e3495f7df4baf84a0p-92L},
{0x1.0706b29ddf6ddc6dc403a8p0L, 0x1.d87b27ed07cb8b092ac75e311753p-88L},
{0x1.0874518759bc808c35f25cp0L, 0x1.9427fa2b041b2d6829d8993a0d01p-88L},
{0x1.09e3ecac6f3834521e060cp0L, 0x5.84d6b74ba2e023da730e7fccb758p-92L},
{0x1.0b5586cf9890f6298b92b6p0L, 0x1.1842a98364291408b3ceb0a2a2bbp-88L},
{0x1.0cc922b7247f7407b705b8p0L, 0x9.3dc5e8aac564e6fe2ef1d431fd98p-92L},
{0x1.0e3ec32d3d1a2020742e4ep0L, 0x1.8af6a552ac4b358b1129e9f966a4p-88L},
{0x1.0fb66affed31af232091dcp0L, 0x1.8a1426514e0b627bda694a400a27p-88L},
{0x1.11301d0125b50a4ebbf1aep0L, 0xd.9318ceac5cc47ab166ee57427178p-92L},
{0x1.12abdc06c31cbfb92bad32p0L, 0x4.d68e2f7270bdf7cedf94eb1cb818p-92L},
{0x1.1429aaea92ddfb34101942p0L, 0x1.b2586d01844b389bea7aedd221d4p-88L},
{0x1.15a98c8a58e512480d573cp0L, 0x1.d5613bf92a2b618ee31b376c2689p-88L},
{0x1.172b83c7d517adcdf7c8c4p0L, 0x1.0eb14a792035509ff7d758693f24p-88L},
{0x1.18af9388c8de9bbbf70b9ap0L, 0x3.c2505c97c0102e5f1211941d2840p-92L},
{0x1.1a35beb6fcb753cb698f68p0L, 0x1.2d1c835a6c30724d5cfae31b84e5p-88L},
{0x1.1bbe084045cd39ab1e72b4p0L, 0x4.27e35f9acb57e473915519a1b448p-92L},
{0x1.1d4873168b9aa7805b8028p0L, 0x9.90f07a98b42206e46166cf051d70p-92L},
{0x1.1ed5022fcd91cb8819ff60p0L, 0x1.121d1e504d36c47474c9b7de6067p-88L},
{0x1.2063b88628cd63b8eeb028p0L, 0x1.50929d0fc487d21c2b84004264dep-88L},
{0x1.21f49917ddc962552fd292p0L, 0x9.4bdb4b61ea62477caa1dce823ba0p-92L},
{0x1.2387a6e75623866c1fadb0p0L, 0x1.c15cb593b0328566902df69e4de2p-88L},
{0x1.251ce4fb2a63f3582ab7dep0L, 0x9.e94811a9c8afdcf796934bc652d0p-92L},
{0x1.26b4565e27cdd257a67328p0L, 0x1.d3b249dce4e9186ddd5ff44e6b08p-92L},
{0x1.284dfe1f5638096cf15cf0p0L, 0x3.ca0967fdaa2e52d7c8106f2e262cp-92L},
{0x1.29e9df51fdee12c25d15f4p0L, 0x1.a24aa3bca890ac08d203fed80a07p-88L},
{0x1.2b87fd0dad98ffddea4652p0L, 0x1.8fcab88442fdc3cb6de4519165edp-88L},
{0x1.2d285a6e4030b40091d536p0L, 0xd.075384589c1cd1b3e4018a6b1348p-92L},
{0x1.2ecafa93e2f5611ca0f45cp0L, 0x1.523833af611bdcda253c554cf278p-88L},
{0x1.306fe0a31b7152de8d5a46p0L, 0x3.05c85edecbc27343629f502f1af2p-92L},
{0x1.32170fc4cd8313539cf1c2p0L, 0x1.008f86dde3220ae17a005b6412bep-88L},
{0x1.33c08b26416ff4c9c8610cp0L, 0x1.96696bf95d1593039539d94d662bp-88L},
{0x1.356c55f929ff0c94623476p0L, 0x3.73af38d6d8d6f9506c9bbc93cbc0p-92L},
{0x1.371a7373aa9caa7145502ep0L, 0x1.4547987e3e12516bf9c699be432fp-88L},
{0x1.38cae6d05d86585a9cb0d8p0L, 0x1.bed0c853bd30a02790931eb2e8f0p-88L},
{0x1.3a7db34e59ff6ea1bc9298p0L, 0x1.e0a1d336163fe2f852ceeb134067p-88L},
{0x1.3c32dc313a8e484001f228p0L, 0xb.58f3775e06ab66353001fae9fca0p-92L},
{0x1.3dea64c12342235b41223ep0L, 0x1.3d773fba2cb82b8244267c54443fp-92L},
{0x1.3fa4504ac801ba0bf701aap0L, 0x4.1832fb8c1c8dbdff2c49909e6c60p-92L},
{0x1.4160a21f72e29f84325b8ep0L, 0x1.3db61fb352f0540e6ba05634413ep-88L},
{0x1.431f5d950a896dc7044394p0L, 0x1.0ccec81e24b0caff7581ef4127f7p-92L},
{0x1.44e086061892d03136f408p0L, 0x1.df019fbd4f3b48709b78591d5cb5p-88L},
{0x1.46a41ed1d005772512f458p0L, 0x1.229d97df404ff21f39c1b594d3a8p-88L},
{0x1.486a2b5c13cd013c1a3b68p0L, 0x1.062f03c3dd75ce8757f780e6ec99p-88L},
{0x1.4a32af0d7d3de672d8bcf4p0L, 0x6.f9586461db1d878b1d148bd3ccb8p-92L},
{0x1.4bfdad5362a271d4397afep0L, 0xc.42e20e0363ba2e159c579f82e4b0p-92L},
{0x1.4dcb299fddd0d63b36ef1ap0L, 0x9.e0cc484b25a5566d0bd5f58ad238p-92L},
{0x1.4f9b2769d2ca6ad33d8b68p0L, 0x1.aa073ee55e028497a329a7333dbap-88L},
{0x1.516daa2cf6641c112f52c8p0L, 0x4.d822190e718226177d7608d20038p-92L},
{0x1.5342b569d4f81df0a83c48p0L, 0x1.d86a63f4e672a3e429805b049465p-88L},
{0x1.551a4ca5d920ec52ec6202p0L, 0x4.34ca672645dc6c124d6619a87574p-92L},
{0x1.56f4736b527da66ecb0046p0L, 0x1.64eb3c00f2f5ab3d801d7cc7272dp-88L},
{0x1.58d12d497c7fd252bc2b72p0L, 0x1.43bcf2ec936a970d9cc266f0072fp-88L},
{0x1.5ab07dd48542958c930150p0L, 0x1.91eb345d88d7c81280e069fbdb63p-88L},
{0x1.5c9268a5946b701c4b1b80p0L, 0x1.6986a203d84e6a4a92f179e71889p-88L},
{0x1.5e76f15ad21486e9be4c20p0L, 0x3.99766a06548a05829e853bdb2b52p-92L},
{0x1.605e1b976dc08b076f592ap0L, 0x4.86e3b34ead1b4769df867b9c89ccp-92L},
{0x1.6247eb03a5584b1f0fa06ep0L, 0x1.d2da42bb1ceaf9f732275b8aef30p-88L},
{0x1.6434634ccc31fc76f8714cp0L, 0x4.ed9a4e41000307103a18cf7a6e08p-92L},
{0x1.66238825522249127d9e28p0L, 0x1.b8f314a337f4dc0a3adf1787ff74p-88L},
{0x1.68155d44ca973081c57226p0L, 0x1.b9f32706bfe4e627d809a85dcc66p-88L},
{0x1.6a09e667f3bcc908b2fb12p0L, 0x1.66ea957d3e3adec17512775099dap-88L},
{0x1.6c012750bdabeed76a9980p0L, 0xf.4f33fdeb8b0ecd831106f57b3d00p-96L},
{0x1.6dfb23c651a2ef220e2cbep0L, 0x1.bbaa834b3f11577ceefbe6c1c411p-92L},
{0x1.6ff7df9519483cf87e1b4ep0L, 0x1.3e213bff9b702d5aa477c12523cep-88L},
{0x1.71f75e8ec5f73dd2370f2ep0L, 0xf.0acd6cb434b562d9e8a20adda648p-92L},
{0x1.73f9a48a58173bd5c9a4e6p0L, 0x8.ab1182ae217f3a7681759553e840p-92L},
{0x1.75feb564267c8bf6e9aa32p0L, 0x1.a48b27071805e61a17b954a2dad8p-88L},
{0x1.780694fde5d3f619ae0280p0L, 0x8.58b2bb2bdcf86cd08e35fb04c0f0p-92L},
{0x1.7a11473eb0186d7d51023ep0L, 0x1.6cda1f5ef42b66977960531e821bp-88L},
{0x1.7c1ed0130c1327c4933444p0L, 0x1.937562b2dc933d44fc828efd4c9cp-88L},
{0x1.7e2f336cf4e62105d02ba0p0L, 0x1.5797e170a1427f8fcdf5f3906108p-88L},
{0x1.80427543e1a11b60de6764p0L, 0x9.a354ea706b8e4d8b718a672bf7c8p-92L},
{0x1.82589994cce128acf88afap0L, 0xb.34a010f6ad65cbbac0f532d39be0p-92L},
{0x1.8471a4623c7acce52f6b96p0L, 0x1.c64095370f51f48817914dd78665p-88L},
{0x1.868d99b4492ec80e41d90ap0L, 0xc.251707484d73f136fb5779656b70p-92L},
{0x1.88ac7d98a669966530bcdep0L, 0x1.2d4e9d61283ef385de170ab20f96p-88L},
{0x1.8ace5422aa0db5ba7c55a0p0L, 0x1.92c9bb3e6ed61f2733304a346d8fp-88L},
{0x1.8cf3216b5448bef2aa1cd0p0L, 0x1.61c55d84a9848f8c453b3ca8c946p-88L},
{0x1.8f1ae991577362b982745cp0L, 0x7.2ed804efc9b4ae1458ae946099d4p-92L},
{0x1.9145b0b91ffc588a61b468p0L, 0x1.f6b70e01c2a90229a4c4309ea719p-88L},
{0x1.93737b0cdc5e4f4501c3f2p0L, 0x5.40a22d2fc4af581b63e8326efe9cp-92L},
{0x1.95a44cbc8520ee9b483694p0L, 0x1.a0fc6f7c7d61b2b3a22a0eab2cadp-88L},
{0x1.97d829fde4e4f8b9e920f8p0L, 0x1.1e8bd7edb9d7144b6f6818084cc7p-88L},
{0x1.9a0f170ca07b9ba3109b8cp0L, 0x4.6737beb19e1eada6825d3c557428p-92L},
{0x1.9c49182a3f0901c7c46b06p0L, 0x1.1f2be58ddade50c217186c90b457p-88L},
{0x1.9e86319e323231824ca78ep0L, 0x6.4c6e010f92c082bbadfaf605cfd4p-92L},
{0x1.a0c667b5de564b29ada8b8p0L, 0xc.ab349aa0422a8da7d4512edac548p-92L},
{0x1.a309bec4a2d3358c171f76p0L, 0x1.0daad547fa22c26d168ea762d854p-88L},
{0x1.a5503b23e255c8b424491cp0L, 0xa.f87bc8050a405381703ef7caff50p-92L},
{0x1.a799e1330b3586f2dfb2b0p0L, 0x1.58f1a98796ce8908ae852236ca94p-88L},
{0x1.a9e6b5579fdbf43eb243bcp0L, 0x1.ff4c4c58b571cf465caf07b4b9f5p-88L},
{0x1.ac36bbfd3f379c0db966a2p0L, 0x1.1265fc73e480712d20f8597a8e7bp-88L},
{0x1.ae89f995ad3ad5e8734d16p0L, 0x1.73205a7fbc3ae675ea440b162d6cp-88L},
{0x1.b0e07298db66590842acdep0L, 0x1.c6f6ca0e5dcae2aafffa7a0554cbp-88L},
{0x1.b33a2b84f15faf6bfd0e7ap0L, 0x1.d947c2575781dbb49b1237c87b6ep-88L},
{0x1.b59728de559398e3881110p0L, 0x1.64873c7171fefc410416be0a6525p-88L},
{0x1.b7f76f2fb5e46eaa7b081ap0L, 0xb.53c5354c8903c356e4b625aacc28p-92L},
{0x1.ba5b030a10649840cb3c6ap0L, 0xf.5b47f297203757e1cc6eadc8bad0p-92L},
{0x1.bcc1e904bc1d2247ba0f44p0L, 0x1.b3d08cd0b20287092bd59be4ad98p-88L},
{0x1.bf2c25bd71e088408d7024p0L, 0x1.18e3449fa073b356766dfb568ff4p-88L},
{0x1.c199bdd85529c2220cb12ap0L, 0x9.1ba6679444964a36661240043970p-96L},
{0x1.c40ab5fffd07a6d14df820p0L, 0xf.1828a5366fd387a7bdd54cdf7300p-92L},
{0x1.c67f12e57d14b4a2137fd2p0L, 0xf.2b301dd9e6b151a6d1f9d5d5f520p-96L},
{0x1.c8f6d9406e7b511acbc488p0L, 0x5.c442ddb55820171f319d9e5076a8p-96L},
{0x1.cb720dcef90691503cbd1ep0L, 0x9.49db761d9559ac0cb6dd3ed599e0p-92L},
{0x1.cdf0b555dc3f9c44f8958ep0L, 0x1.ac51be515f8c58bdfb6f5740a3a4p-88L},
{0x1.d072d4a07897b8d0f22f20p0L, 0x1.a158e18fbbfc625f09f4cca40874p-88L},
{0x1.d2f87080d89f18ade12398p0L, 0x9.ea2025b4c56553f5cdee4c924728p-92L},
{0x1.d5818dcfba48725da05aeap0L, 0x1.66e0dca9f589f559c0876ff23830p-88L},
{0x1.d80e316c98397bb84f9d04p0L, 0x8.805f84bec614de269900ddf98d28p-92L},
{0x1.da9e603db3285708c01a5ap0L, 0x1.6d4c97f6246f0ec614ec95c99392p-88L},
{0x1.dd321f301b4604b695de3cp0L, 0x6.30a393215299e30d4fb73503c348p-96L},
{0x1.dfc97337b9b5eb968cac38p0L, 0x1.ed291b7225a944efd5bb5524b927p-88L},
{0x1.e264614f5a128a12761fa0p0L, 0x1.7ada6467e77f73bf65e04c95e29dp-88L},
{0x1.e502ee78b3ff6273d13014p0L, 0x1.3991e8f49659e1693be17ae1d2f9p-88L},
{0x1.e7a51fbc74c834b548b282p0L, 0x1.23786758a84f4956354634a416cep-88L},
{0x1.ea4afa2a490d9858f73a18p0L, 0xf.5db301f86dea20610ceee13eb7b8p-92L},
{0x1.ecf482d8e67f08db0312fap0L, 0x1.949cef462010bb4bc4ce72a900dfp-88L},
{0x1.efa1bee615a27771fd21a8p0L, 0x1.2dac1f6dd5d229ff68e46f27e3dfp-88L},
{0x1.f252b376bba974e8696fc2p0L, 0x1.6390d4c6ad5476b5162f40e1d9a9p-88L},
{0x1.f50765b6e4540674f84b76p0L, 0x2.862baff99000dfc4352ba29b8908p-92L},
{0x1.f7bfdad9cbe138913b4bfep0L, 0x7.2bd95c5ce7280fa4d2344a3f5618p-92L},
{0x1.fa7c1819e90d82e90a7e74p0L, 0xb.263c1dc060c36f7650b4c0f233a8p-92L},
{0x1.fd3c22b8f71f10975ba4b2p0L, 0x1.2bcf3a5e12d269d8ad7c1a4a8875p-88L}
};
/*
* Kernel for expl(x). x must be finite and not tiny or huge.
* "tiny" is anything that would make us underflow (|A6*x^6| < ~LDBL_MIN).
* "huge" is anything that would make fn*L1 inexact (|x| > ~2**17*ln2).
*/
void
__k_expl(long double x, long double *hip, long double *lop, int *kp)
{
long double q, r, r1, t;
double dr, fn, r2;
int n, n2;
/* Reduce x to (k*ln2 + endpoint[n2] + r1 + r2). */
fn = rnint((double)x * INV_L);
n = irint(fn);
n2 = (unsigned)n % INTERVALS;
/* Depend on the sign bit being propagated: */
*kp = n >> LOG2_INTERVALS;
r1 = x - fn * L1;
r2 = fn * -L2;
r = r1 + r2;
/* Evaluate expl(endpoint[n2] + r1 + r2) = kExplData[n2] * expl(r1 + r2). */
dr = r;
q = r2 + r * r * (A2 + r * (A3 + r * (A4 + r * (A5 + r * (A6 +
dr * (A7 + dr * (A8 + dr * (A9 + dr * A10))))))));
t = kExplData[n2].lo + kExplData[n2].hi;
*hip = kExplData[n2].hi;
*lop = kExplData[n2].lo + t * (q + r1);
}
| 15,548 | 253 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/estrin_wrap.internal.h | #ifndef COSMOPOLITAN_LIBC_TINYMATH_ESTRIN_WRAP_INTERNAL_H_
#define COSMOPOLITAN_LIBC_TINYMATH_ESTRIN_WRAP_INTERNAL_H_
/*
* Helper macros for double-precision Estrin polynomial evaluation.
*
* Copyright (c) 2022-2023, Arm Limited.
* SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
*/
// clang-format off
#define ESTRIN_1_(x, c, i) FMA(x, c(1 + i), c(i))
#define ESTRIN_2_(x, x2, c, i) FMA(x2, c(2 + i), ESTRIN_1_(x, c, i))
#define ESTRIN_3_(x, x2, c, i) FMA(x2, ESTRIN_1_(x, c, 2 + i), ESTRIN_1_(x, c, i))
#define ESTRIN_4_(x, x2, x4, c, i) FMA(x4, c(4 + i), ESTRIN_3_(x, x2, c, i))
#define ESTRIN_5_(x, x2, x4, c, i) FMA(x4, ESTRIN_1_(x, c, 4 + i), ESTRIN_3_(x, x2, c, i))
#define ESTRIN_6_(x, x2, x4, c, i) FMA(x4, ESTRIN_2_(x, x2, c, 4 + i), ESTRIN_3_(x, x2, c, i))
#define ESTRIN_7_(x, x2, x4, c, i) FMA(x4, ESTRIN_3_(x, x2, c, 4 + i), ESTRIN_3_(x, x2, c, i))
#define ESTRIN_8_(x, x2, x4, x8, c, i) FMA(x8, c(8 + i), ESTRIN_7_(x, x2, x4, c, i))
#define ESTRIN_9_(x, x2, x4, x8, c, i) FMA(x8, ESTRIN_1_(x, c, 8 + i), ESTRIN_7_(x, x2, x4, c, i))
#define ESTRIN_10_(x, x2, x4, x8, c, i) FMA(x8, ESTRIN_2_(x, x2, c, 8 + i), ESTRIN_7_(x, x2, x4, c, i))
#define ESTRIN_11_(x, x2, x4, x8, c, i) FMA(x8, ESTRIN_3_(x, x2, c, 8 + i), ESTRIN_7_(x, x2, x4, c, i))
#define ESTRIN_12_(x, x2, x4, x8, c, i) FMA(x8, ESTRIN_4_(x, x2, x4, c, 8 + i), ESTRIN_7_(x, x2, x4, c, i))
#define ESTRIN_13_(x, x2, x4, x8, c, i) FMA(x8, ESTRIN_5_(x, x2, x4, c, 8 + i), ESTRIN_7_(x, x2, x4, c, i))
#define ESTRIN_14_(x, x2, x4, x8, c, i) FMA(x8, ESTRIN_6_(x, x2, x4, c, 8 + i), ESTRIN_7_(x, x2, x4, c, i))
#define ESTRIN_15_(x, x2, x4, x8, c, i) FMA(x8, ESTRIN_7_(x, x2, x4, c, 8 + i), ESTRIN_7_(x, x2, x4, c, i))
#define ESTRIN_16_(x, x2, x4, x8, x16, c, i) FMA(x16, c(16 + i), ESTRIN_15_(x, x2, x4, x8, c, i))
#define ESTRIN_17_(x, x2, x4, x8, x16, c, i) FMA(x16, ESTRIN_1_(x, c, 16 + i), ESTRIN_15_(x, x2, x4, x8, c, i))
#define ESTRIN_18_(x, x2, x4, x8, x16, c, i) FMA(x16, ESTRIN_2_(x, x2, c, 16 + i), ESTRIN_15_(x, x2, x4, x8, c, i))
#define ESTRIN_19_(x, x2, x4, x8, x16, c, i) FMA(x16, ESTRIN_3_(x, x2, c, 16 + i), ESTRIN_15_(x, x2, x4, x8, c, i))
#define ESTRIN_1(x, c) ESTRIN_1_(x, c, 0)
#define ESTRIN_2(x, x2, c) ESTRIN_2_(x, x2, c, 0)
#define ESTRIN_3(x, x2, c) ESTRIN_3_(x, x2, c, 0)
#define ESTRIN_4(x, x2, x4, c) ESTRIN_4_(x, x2, x4, c, 0)
#define ESTRIN_5(x, x2, x4, c) ESTRIN_5_(x, x2, x4, c, 0)
#define ESTRIN_6(x, x2, x4, c) ESTRIN_6_(x, x2, x4, c, 0)
#define ESTRIN_7(x, x2, x4, c) ESTRIN_7_(x, x2, x4, c, 0)
#define ESTRIN_8(x, x2, x4, x8, c) ESTRIN_8_(x, x2, x4, x8, c, 0)
#define ESTRIN_9(x, x2, x4, x8, c) ESTRIN_9_(x, x2, x4, x8, c, 0)
#define ESTRIN_10(x, x2, x4, x8, c) ESTRIN_10_(x, x2, x4, x8, c, 0)
#define ESTRIN_11(x, x2, x4, x8, c) ESTRIN_11_(x, x2, x4, x8, c, 0)
#define ESTRIN_12(x, x2, x4, x8, c) ESTRIN_12_(x, x2, x4, x8, c, 0)
#define ESTRIN_13(x, x2, x4, x8, c) ESTRIN_13_(x, x2, x4, x8, c, 0)
#define ESTRIN_14(x, x2, x4, x8, c) ESTRIN_14_(x, x2, x4, x8, c, 0)
#define ESTRIN_15(x, x2, x4, x8, c) ESTRIN_15_(x, x2, x4, x8, c, 0)
#define ESTRIN_16(x, x2, x4, x8, x16, c) ESTRIN_16_(x, x2, x4, x8, x16, c, 0)
#define ESTRIN_17(x, x2, x4, x8, x16, c) ESTRIN_17_(x, x2, x4, x8, x16, c, 0)
#define ESTRIN_18(x, x2, x4, x8, x16, c) ESTRIN_18_(x, x2, x4, x8, x16, c, 0)
#define ESTRIN_19(x, x2, x4, x8, x16, c) ESTRIN_19_(x, x2, x4, x8, x16, c, 0)
// clang-format on
#endif /* COSMOPOLITAN_LIBC_TINYMATH_ESTRIN_WRAP_INTERNAL_H_ */
| 4,145 | 54 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/log2f.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/intrin/likely.h"
#include "libc/math.h"
#include "libc/tinymath/complex.internal.h"
#include "libc/tinymath/internal.h"
#include "libc/tinymath/log2f_data.internal.h"
asm(".ident\t\"\\n\\n\
Double-precision math functions (MIT License)\\n\
Copyright 2018 ARM Limited\"");
asm(".include \"libc/disclaimer.inc\"");
/* clang-format off */
/*
* Single-precision log2 function.
*
* Copyright (c) 2017-2018, Arm Limited.
* SPDX-License-Identifier: MIT
*/
/*
LOG2F_TABLE_BITS = 4
LOG2F_POLY_ORDER = 4
ULP error: 0.752 (nearest rounding.)
Relative error: 1.9 * 2^-26 (before rounding.)
*/
#define N (1 << LOG2F_TABLE_BITS)
#define T __log2f_data.tab
#define A __log2f_data.poly
#define OFF 0x3f330000
/**
* Calculates logâð¥.
*/
float log2f(float x)
{
double_t z, r, r2, p, y, y0, invc, logc;
uint32_t ix, iz, top, tmp;
int k, i;
ix = asuint(x);
/* Fix sign of zero with downward rounding when x==1. */
if (WANT_ROUNDING && UNLIKELY(ix == 0x3f800000))
return 0;
if (UNLIKELY(ix - 0x00800000 >= 0x7f800000 - 0x00800000)) {
/* x < 0x1p-126 or inf or nan. */
if (ix * 2 == 0)
return __math_divzerof(1);
if (ix == 0x7f800000) /* log2(inf) == inf. */
return x;
if ((ix & 0x80000000) || ix * 2 >= 0xff000000)
return __math_invalidf(x);
/* x is subnormal, normalize it. */
ix = asuint(x * 0x1p23f);
ix -= 23 << 23;
}
/* x = 2^k z; where z is in range [OFF,2*OFF] and exact.
The range is split into N subintervals.
The ith subinterval contains z and c is near its center. */
tmp = ix - OFF;
i = (tmp >> (23 - LOG2F_TABLE_BITS)) % N;
top = tmp & 0xff800000;
iz = ix - top;
k = (int32_t)tmp >> 23; /* arithmetic shift */
invc = T[i].invc;
logc = T[i].logc;
z = (double_t)asfloat(iz);
/* log2(x) = log1p(z/c-1)/ln2 + log2(c) + k */
r = z * invc - 1;
y0 = logc + (double_t)k;
/* Pipelined polynomial evaluation to approximate log1p(r)/ln2. */
r2 = r * r;
y = A[1] * r + A[2];
y = A[0] * r2 + y;
p = A[3] * r + y0;
y = y * r2 + p;
return eval_as_float(y);
}
| 4,641 | 110 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/cosdf.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2020 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
#include "libc/tinymath/kernel.internal.h"
asm(".ident\t\"\\n\\n\
fdlibm (fdlibm license)\\n\
Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.\"");
asm(".ident\t\"\\n\\n\
Musl libc (MIT License)\\n\
Copyright 2005-2014 Rich Felker, et. al.\"");
asm(".include \"libc/disclaimer.inc\"");
/* clang-format off */
/* origin: FreeBSD /usr/src/lib/msun/src/k_cosf.c */
/*
* Conversion to float by Ian Lance Taylor, Cygnus Support, [email protected].
* Debugged and optimized by Bruce D. Evans.
*/
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/* |cos(x) - c(x)| < 2**-34.1 (~[-5.37e-11, 5.295e-11]). */
static const double
C0 = -0x1ffffffd0c5e81.0p-54, /* -0.499999997251031003120 */
C1 = 0x155553e1053a42.0p-57, /* 0.0416666233237390631894 */
C2 = -0x16c087e80f1e27.0p-62, /* -0.00138867637746099294692 */
C3 = 0x199342e0ee5069.0p-68; /* 0.0000243904487962774090654 */
noinstrument float __cosdf(double x)
{
double_t r, w, z;
/* Try to optimize for parallel evaluation as in __tandf.c. */
z = x*x;
w = z*z;
r = C2+z*C3;
return ((1.0+z*C0) + w*C1) + (w*z)*r;
}
| 4,049 | 73 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/csinhl.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/complex.h"
asm(".ident\t\"\\n\\n\
Musl libc (MIT License)\\n\
Copyright 2005-2014 Rich Felker, et. al.\"");
asm(".include \"libc/disclaimer.inc\"");
// clang-format off
//FIXME
long double complex csinhl(long double complex z)
{
return csinh(z);
}
| 2,868 | 41 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/LICENSE.fdlibm | Q29weXJpZ2h0IChDKSAxOTkzLTIwMDQgYnkgU3VuIE1pY3Jvc3lzdGVtcywgSW5jLiBBbGwgcmlnaHRzIHJlc2VydmVkLgoKRGV2ZWxvcGVkIGF0IFN1blNvZnQsIGEgU3VuIE1pY3Jvc3lzdGVtcywgSW5jLiBidXNpbmVzcy4KUGVybWlzc2lvbiB0byB1c2UsIGNvcHksIG1vZGlmeSwgYW5kIGRpc3RyaWJ1dGUgdGhpcwpzb2Z0d2FyZSBpcyBmcmVlbHkgZ3JhbnRlZCwgcHJvdmlkZWQgdGhhdCB0aGlzIG5vdGljZQppcyBwcmVzZXJ2ZWQuCg== | 336 | 1 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/fmodl.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
#include "libc/tinymath/ldshape.internal.h"
asm(".ident\t\"\\n\\n\
Musl libc (MIT License)\\n\
Copyright 2005-2014 Rich Felker, et. al.\"");
asm(".include \"libc/disclaimer.inc\"");
// clang-format off
long double fmodl(long double x, long double y) {
#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
return fmod(x, y);
#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
union ldshape ux = {x}, uy = {y};
int ex = ux.i.se & 0x7fff;
int ey = uy.i.se & 0x7fff;
int sx = ux.i.se & 0x8000;
if (y == 0 || isnan(y) || ex == 0x7fff)
return (x*y)/(x*y);
ux.i.se = ex;
uy.i.se = ey;
if (ux.f <= uy.f) {
if (ux.f == uy.f)
return 0*x;
return x;
}
/* normalize x and y */
if (!ex) {
ux.f *= 0x1p120f;
ex = ux.i.se - 120;
}
if (!ey) {
uy.f *= 0x1p120f;
ey = uy.i.se - 120;
}
/* x mod y */
#if LDBL_MANT_DIG == 64
uint64_t i, mx, my;
mx = ux.i.m;
my = uy.i.m;
for (; ex > ey; ex--) {
i = mx - my;
if (mx >= my) {
if (i == 0)
return 0*x;
mx = 2*i;
} else if (2*mx < mx) {
mx = 2*mx - my;
} else {
mx = 2*mx;
}
}
i = mx - my;
if (mx >= my) {
if (i == 0)
return 0*x;
mx = i;
}
for (; mx >> 63 == 0; mx *= 2, ex--);
ux.i.m = mx;
#elif LDBL_MANT_DIG == 113
uint64_t hi, lo, xhi, xlo, yhi, ylo;
xhi = (ux.i2.hi & -1ULL>>16) | 1ULL<<48;
yhi = (uy.i2.hi & -1ULL>>16) | 1ULL<<48;
xlo = ux.i2.lo;
ylo = uy.i2.lo;
for (; ex > ey; ex--) {
hi = xhi - yhi;
lo = xlo - ylo;
if (xlo < ylo)
hi -= 1;
if (hi >> 63 == 0) {
if ((hi|lo) == 0)
return 0*x;
xhi = 2*hi + (lo>>63);
xlo = 2*lo;
} else {
xhi = 2*xhi + (xlo>>63);
xlo = 2*xlo;
}
}
hi = xhi - yhi;
lo = xlo - ylo;
if (xlo < ylo)
hi -= 1;
if (hi >> 63 == 0) {
if ((hi|lo) == 0)
return 0*x;
xhi = hi;
xlo = lo;
}
for (; xhi >> 48 == 0; xhi = 2*xhi + (xlo>>63), xlo = 2*xlo, ex--);
ux.i2.hi = xhi;
ux.i2.lo = xlo;
#endif
/* scale result */
if (ex <= 0) {
ux.i.se = (ex+120)|sx;
ux.f *= 0x1p-120f;
} else
ux.i.se = ex|sx;
return ux.f;
#else
#error "architecture unsupported"
#endif
}
| 4,706 | 138 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/expf.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/intrin/likely.h"
#include "libc/math.h"
#include "libc/tinymath/exp2f_data.internal.h"
#include "libc/tinymath/internal.h"
asm(".ident\t\"\\n\\n\
Double-precision math functions (MIT License)\\n\
Copyright 2018 ARM Limited\"");
asm(".include \"libc/disclaimer.inc\"");
// clang-format off
/*
* Single-precision e^x function.
*
* Copyright (c) 2017-2018, Arm Limited.
* SPDX-License-Identifier: MIT
*/
/*
EXP2F_TABLE_BITS = 5
EXP2F_POLY_ORDER = 3
ULP error: 0.502 (nearest rounding.)
Relative error: 1.69 * 2^-34 in [-ln2/64, ln2/64] (before rounding.)
Wrong count: 170635 (all nearest rounding wrong results with fma.)
Non-nearest ULP error: 1 (rounded ULP error)
*/
#define N (1 << EXP2F_TABLE_BITS)
#define InvLn2N __exp2f_data.invln2_scaled
#define T __exp2f_data.tab
#define C __exp2f_data.poly_scaled
static inline uint32_t top12(float x)
{
return asuint(x) >> 20;
}
/**
* Returns ð^x.
*/
float expf(float x)
{
uint32_t abstop;
uint64_t ki, t;
double_t kd, xd, z, r, r2, y, s;
xd = (double_t)x;
abstop = top12(x) & 0x7ff;
if (UNLIKELY(abstop >= top12(88.0f))) {
/* |x| >= 88 or x is nan. */
if (asuint(x) == asuint(-INFINITY))
return 0.0f;
if (abstop >= top12(INFINITY))
return x + x;
if (x > 0x1.62e42ep6f) /* x > log(0x1p128) ~= 88.72 */
return __math_oflowf(0);
if (x < -0x1.9fe368p6f) /* x < log(0x1p-150) ~= -103.97 */
return __math_uflowf(0);
}
/* x*N/Ln2 = k + r with r in [-1/2, 1/2] and int k. */
z = InvLn2N * xd;
/* Round and convert z to int, the result is in [-150*N, 128*N] and
ideally ties-to-even rule is used, otherwise the magnitude of r
can be bigger which gives larger approximation error. */
#if TOINT_INTRINSICS
kd = roundtoint(z);
ki = converttoint(z);
#else
# define SHIFT __exp2f_data.shift
kd = eval_as_double(z + SHIFT);
ki = asuint64(kd);
kd -= SHIFT;
#endif
r = z - kd;
/* exp(x) = 2^(k/N) * 2^(r/N) ~= s * (C0*r^3 + C1*r^2 + C2*r + 1) */
t = T[ki % N];
t += ki << (52 - EXP2F_TABLE_BITS);
s = asdouble(t);
z = C[0] * r + C[1];
r2 = r * r;
y = C[2] * r + 1;
y = z * r2 + y;
y = y * s;
return eval_as_float(y);
}
| 4,744 | 117 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/csin.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/complex.h"
#include "libc/math.h"
#include "libc/tinymath/complex.internal.h"
asm(".ident\t\"\\n\\n\
Musl libc (MIT License)\\n\
Copyright 2005-2014 Rich Felker, et. al.\"");
asm(".include \"libc/disclaimer.inc\"");
/* clang-format off */
/* sin(z) = -i sinh(i z) */
double complex csin(double complex z)
{
z = csinh(CMPLX(-cimag(z), creal(z)));
return CMPLX(cimag(z), -creal(z));
}
| 3,007 | 47 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/atanf.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2020 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
#include "libc/tinymath/complex.internal.h"
asm(".ident\t\"\\n\\n\
fdlibm (fdlibm license)\\n\
Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.\"");
asm(".ident\t\"\\n\\n\
Musl libc (MIT License)\\n\
Copyright 2005-2014 Rich Felker, et. al.\"");
asm(".include \"libc/disclaimer.inc\"");
// clang-format off
/* origin: FreeBSD /usr/src/lib/msun/src/s_atanf.c */
/*
* Conversion to float by Ian Lance Taylor, Cygnus Support, [email protected].
*/
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
static const float atanhi[] = {
4.6364760399e-01, /* atan(0.5)hi 0x3eed6338 */
7.8539812565e-01, /* atan(1.0)hi 0x3f490fda */
9.8279368877e-01, /* atan(1.5)hi 0x3f7b985e */
1.5707962513e+00, /* atan(inf)hi 0x3fc90fda */
};
static const float atanlo[] = {
5.0121582440e-09, /* atan(0.5)lo 0x31ac3769 */
3.7748947079e-08, /* atan(1.0)lo 0x33222168 */
3.4473217170e-08, /* atan(1.5)lo 0x33140fb4 */
7.5497894159e-08, /* atan(inf)lo 0x33a22168 */
};
static const float aT[] = {
3.3333328366e-01,
-1.9999158382e-01,
1.4253635705e-01,
-1.0648017377e-01,
6.1687607318e-02,
};
/**
* Returns arc tangent of ð¥.
* @note should take ~12ns
*/
float atanf(float x)
{
float_t w,s1,s2,z;
uint32_t ix,sign;
int id;
GET_FLOAT_WORD(ix, x);
sign = ix>>31;
ix &= 0x7fffffff;
if (ix >= 0x4c800000) { /* if |x| >= 2**26 */
if (isnan(x))
return x;
z = atanhi[3] + 0x1p-120f;
return sign ? -z : z;
}
if (ix < 0x3ee00000) { /* |x| < 0.4375 */
if (ix < 0x39800000) { /* |x| < 2**-12 */
if (ix < 0x00800000)
/* raise underflow for subnormal x */
FORCE_EVAL(x*x);
return x;
}
id = -1;
} else {
x = fabsf(x);
if (ix < 0x3f980000) { /* |x| < 1.1875 */
if (ix < 0x3f300000) { /* 7/16 <= |x| < 11/16 */
id = 0;
x = (2.0f*x - 1.0f)/(2.0f + x);
} else { /* 11/16 <= |x| < 19/16 */
id = 1;
x = (x - 1.0f)/(x + 1.0f);
}
} else {
if (ix < 0x401c0000) { /* |x| < 2.4375 */
id = 2;
x = (x - 1.5f)/(1.0f + 1.5f*x);
} else { /* 2.4375 <= |x| < 2**26 */
id = 3;
x = -1.0f/x;
}
}
}
/* end of argument reduction */
z = x*x;
w = z*z;
/* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
s1 = z*(aT[0]+w*(aT[2]+w*aT[4]));
s2 = w*(aT[1]+w*aT[3]);
if (id < 0)
return x - x*(s1+s2);
z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
return sign ? -z : z;
}
| 5,371 | 135 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/conjl.c | /*-*- mode:c;indent-tabs-mode:nil;c-basic-offset:2;tab-width:8;coding:utf-8 -*-â
âvi: set net ft=c ts=2 sts=2 sw=2 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ¡
â Copyright 2023 Justine Alexandra Roberts Tunney â
â â
â Permission to use, copy, modify, and/or distribute this software for â
â any purpose with or without fee is hereby granted, provided that the â
â above copyright notice and this permission notice appear in all copies. â
â â
â THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL â
â WARRANTIES WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED â
â WARRANTIES OF MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE â
â AUTHOR BE LIABLE FOR ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL â
â DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR â
â PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER â
â TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR â
â PERFORMANCE OF THIS SOFTWARE. â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/complex.h"
long double complex conjl(long double complex z) {
return CMPLXL(creall(z), -cimagl(z));
}
| 1,956 | 24 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/__math_uflowf.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/tinymath/internal.h"
// clang-format off
float __math_uflowf(uint32_t sign)
{
return __math_xflowf(sign, 0x1p-95f);
}
| 2,737 | 35 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/sinhl.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â FreeBSD lib/msun/src/e_sinhl.c â
â Converted to long double by Bruce D. Evans â
â â
â Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. â
â â
â Developed at SunPro, a Sun Microsystems, Inc. business. â
â Permission to use, copy, modify, and distribute this â
â software is freely granted, provided that this notice â
â is preserved. â
â â
â Copyright (c) 1992-2023 The FreeBSD Project. â
â â
â Redistribution and use in source and binary forms, with or without â
â modification, are permitted provided that the following conditions â
â are met: â
â 1. Redistributions of source code must retain the above copyright â
â notice, this list of conditions and the following disclaimer. â
â 2. Redistributions in binary form must reproduce the above copyright â
â notice, this list of conditions and the following disclaimer in the â
â documentation and/or other materials provided with the distribution. â
â â
â THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND â
â ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE â
â IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE â
â ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE â
â FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL â
â DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS â
â OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) â
â HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT â
â LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY â
â OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF â
â SUCH DAMAGE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/intrin/likely.h"
#include "libc/math.h"
#include "libc/tinymath/freebsd.internal.h"
asm(".ident\t\"\\n\\n\
FreeBSD libm (BSD-2 License)\\n\
Copyright (c) 2005-2011, Bruce D. Evans, Steven G. Kargl, David Schultz.\"");
asm(".ident\t\"\\n\\n\
fdlibm (fdlibm license)\\n\
Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.\"");
asm(".include \"libc/disclaimer.inc\"");
// clang-format off
#if LDBL_MAX_EXP != 0x4000
/* We also require the usual expsign encoding. */
#error "Unsupported long double format"
#endif
#define BIAS (LDBL_MAX_EXP - 1)
static const long double shuge = 0x1p16383L;
#if LDBL_MANT_DIG == 64
/*
* Domain [-1, 1], range ~[-6.6749e-22, 6.6749e-22]:
* |sinh(x)/x - s(x)| < 2**-70.3
*/
static const union IEEEl2bits
S3u = LD80C(0xaaaaaaaaaaaaaaaa, -3, 1.66666666666666666658e-1L);
#define S3 S3u.e
static const double
S5 = 8.3333333333333332e-3, /* 0x11111111111111.0p-59 */
S7 = 1.9841269841270074e-4, /* 0x1a01a01a01a070.0p-65 */
S9 = 2.7557319223873889e-6, /* 0x171de3a5565fe6.0p-71 */
S11 = 2.5052108406704084e-8, /* 0x1ae6456857530f.0p-78 */
S13 = 1.6059042748655297e-10, /* 0x161245fa910697.0p-85 */
S15 = 7.6470006914396920e-13, /* 0x1ae7ce4eff2792.0p-93 */
S17 = 2.8346142308424267e-15; /* 0x19882ce789ffc6.0p-101 */
#elif LDBL_MANT_DIG == 113
/*
* Domain [-1, 1], range ~[-2.9673e-36, 2.9673e-36]:
* |sinh(x)/x - s(x)| < 2**-118.0
*/
static const long double
S3 = 1.66666666666666666666666666666666033e-1L, /* 0x1555555555555555555555555553b.0p-115L */
S5 = 8.33333333333333333333333333337643193e-3L, /* 0x111111111111111111111111180f5.0p-119L */
S7 = 1.98412698412698412698412697391263199e-4L, /* 0x1a01a01a01a01a01a01a0176aad11.0p-125L */
S9 = 2.75573192239858906525574406205464218e-6L, /* 0x171de3a556c7338faac243aaa9592.0p-131L */
S11 = 2.50521083854417187749675637460977997e-8L, /* 0x1ae64567f544e38fe59b3380d7413.0p-138L */
S13 = 1.60590438368216146368737762431552702e-10L, /* 0x16124613a86d098059c7620850fc2.0p-145L */
S15 = 7.64716373181980539786802470969096440e-13L, /* 0x1ae7f3e733b814193af09ce723043.0p-153L */
S17 = 2.81145725434775409870584280722701574e-15L; /* 0x1952c77030c36898c3fd0b6dfc562.0p-161L */
static const double
S19= 8.2206352435411005e-18, /* 0x12f49b4662b86d.0p-109 */
S21= 1.9572943931418891e-20, /* 0x171b8f2fab9628.0p-118 */
S23 = 3.8679983530666939e-23, /* 0x17617002b73afc.0p-127 */
S25 = 6.5067867911512749e-26; /* 0x1423352626048a.0p-136 */
#else
#error "Unsupported long double format"
#endif /* LDBL_MANT_DIG == 64 */
/* log(2**16385 - 0.5) rounded up: */
static const float
o_threshold = 1.13572168e4; /* 0xb174de.0p-10 */
/**
* Returns hyperbolic sine of ð¥.
*/
long double
sinhl(long double x)
{
long double hi,lo,x2,x4;
#if LDBL_MANT_DIG == 113
double dx2;
#endif
double s;
int16_t ix,jx;
GET_LDBL_EXPSIGN(jx,x);
ix = jx&0x7fff;
/* x is INF or NaN */
if(ix>=0x7fff) return x+x;
ENTERI();
s = 1;
if (jx<0) s = -1;
/* |x| < 64, return x, s(x), or accurate s*(exp(|x|)/2-1/exp(|x|)/2) */
if (ix<0x4005) { /* |x|<64 */
if (ix<BIAS-(LDBL_MANT_DIG+1)/2) /* |x|<TINY */
if(shuge+x>1) RETURNI(x); /* sinh(tiny) = tiny with inexact */
if (ix<0x3fff) { /* |x|<1 */
x2 = x*x;
#if LDBL_MANT_DIG == 64
x4 = x2*x2;
RETURNI(((S17*x2 + S15)*x4 + (S13*x2 + S11))*(x2*x*x4*x4) +
((S9*x2 + S7)*x2 + S5)*(x2*x*x2) + S3*(x2*x) + x);
#elif LDBL_MANT_DIG == 113
dx2 = x2;
RETURNI(((((((((((S25*dx2 + S23)*dx2 +
S21)*x2 + S19)*x2 +
S17)*x2 + S15)*x2 + S13)*x2 + S11)*x2 + S9)*x2 + S7)*x2 +
S5)* (x2*x*x2) +
S3*(x2*x) + x);
#endif
}
k_hexpl(fabsl(x), &hi, &lo);
RETURNI(s*(lo - 0.25/(hi + lo) + hi));
}
/* |x| in [64, o_threshold], return correctly-overflowing s*exp(|x|)/2 */
if (fabsl(x) <= o_threshold)
RETURNI(s*hexpl(fabsl(x)));
/* |x| > o_threshold, sinh(x) overflow */
return x*shuge;
}
| 7,489 | 157 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/exp10.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
asm(".ident\t\"\\n\\n\
Musl libc (MIT License)\\n\
Copyright 2005-2014 Rich Felker, et. al.\"");
asm(".include \"libc/disclaimer.inc\"");
// clang-format off
/**
* Returns 10Ë£.
*/
double exp10(double x)
{
static const double p10[] = {
1e-15, 1e-14, 1e-13, 1e-12, 1e-11, 1e-10,
1e-9, 1e-8, 1e-7, 1e-6, 1e-5, 1e-4, 1e-3, 1e-2, 1e-1,
1, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9,
1e10, 1e11, 1e12, 1e13, 1e14, 1e15
};
double n, y = modf(x, &n);
union {double f; uint64_t i;} u = {n};
/* fabs(n) < 16 without raising invalid on nan */
if ((u.i>>52 & 0x7ff) < 0x3ff+4) {
if (!y) return p10[(int)n+15];
y = exp2(3.32192809488736234787031942948939 * y);
return y * p10[(int)n+15];
}
return pow(10.0, x);
}
__strong_reference(exp10, pow10);
#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
__strong_reference(exp10, exp10l);
#endif
| 3,478 | 62 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/kernel.internal.h | #ifndef COSMOPOLITAN_LIBC_TINYMATH_KERNEL_INTERNAL_H_
#define COSMOPOLITAN_LIBC_TINYMATH_KERNEL_INTERNAL_H_
#if !(__ASSEMBLER__ + __LINKER__ + 0)
COSMOPOLITAN_C_START_
double __cos(double, double) _Hide;
double __sin(double, double, int) _Hide;
double __tan(double, double, int) _Hide;
float __cosdf(double) _Hide;
float __sindf(double) _Hide;
float __tandf(double, int) _Hide;
long double __cosl(long double, long double) _Hide;
long double __sinl(long double, long double, int) _Hide;
long double __tanl(long double, long double, int) _Hide;
int __rem_pio2(double, double *) _Hide;
int __rem_pio2l(long double, long double *) _Hide;
int __rem_pio2_large(double *, double *, int, int, int) _Hide;
int __rem_pio2f(float, double *) _Hide;
COSMOPOLITAN_C_END_
#endif /* !(__ASSEMBLER__ + __LINKER__ + 0) */
#endif /* COSMOPOLITAN_LIBC_TINYMATH_KERNEL_INTERNAL_H_ */
| 866 | 23 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/freebsd.internal.h | #ifndef COSMOPOLITAN_LIBC_TINYMATH_FREEBSD_INTERNAL_H_
#define COSMOPOLITAN_LIBC_TINYMATH_FREEBSD_INTERNAL_H_
#include "libc/assert.h"
#include "libc/complex.h"
#include "libc/math.h"
#include "libc/runtime/fenv.h"
#if !(__ASSEMBLER__ + __LINKER__ + 0)
COSMOPOLITAN_C_START_
// clang-format off
#define __CONCAT1(x,y) x ## y
#define __CONCAT(x,y) __CONCAT1(x,y)
#define __STRING(x) #x
#define __XSTRING(x) __STRING(x)
#ifdef __x86_64__
union IEEEl2bits {
long double e;
struct {
unsigned int manl :32;
unsigned int manh :32;
unsigned int exp :15;
unsigned int sign :1;
unsigned int junkl :16;
unsigned int junkh :32;
} bits;
struct {
unsigned long man :64;
unsigned int expsign :16;
unsigned long junk :48;
} xbits;
};
#define LDBL_NBIT 0x80000000
#define mask_nbit_l(u) ((u).bits.manh &= ~LDBL_NBIT)
#define LDBL_MANH_SIZE 32
#define LDBL_MANL_SIZE 32
#define LDBL_TO_ARRAY32(u, a) do { \
(a)[0] = (uint32_t)(u).bits.manl; \
(a)[1] = (uint32_t)(u).bits.manh; \
} while (0)
#elif defined(__aarch64__)
union IEEEl2bits {
long double e;
struct {
unsigned long manl :64;
unsigned long manh :48;
unsigned int exp :15;
unsigned int sign :1;
} bits;
/* TODO andrew: Check the packing here */
struct {
unsigned long manl :64;
unsigned long manh :48;
unsigned int expsign :16;
} xbits;
};
#define LDBL_NBIT 0
#define LDBL_IMPLICIT_NBIT
#define mask_nbit_l(u) ((void)0)
#define LDBL_MANH_SIZE 48
#define LDBL_MANL_SIZE 64
#define LDBL_TO_ARRAY32(u, a) do { \
(a)[0] = (uint32_t)(u).bits.manl; \
(a)[1] = (uint32_t)((u).bits.manl >> 32); \
(a)[2] = (uint32_t)(u).bits.manh; \
(a)[3] = (uint32_t)((u).bits.manh >> 32); \
} while(0)
#elif defined(__powerpc64__)
union IEEEl2bits {
long double e;
struct {
#if __BYTE_ORDER__ == __ORDER_LITTLE_ENDIAN__
unsigned int manl :32;
unsigned int manh :20;
unsigned int exp :11;
unsigned int sign :1;
#else /* _BYTE_ORDER == _LITTLE_ENDIAN */
unsigned int sign :1;
unsigned int exp :11;
unsigned int manh :20;
unsigned int manl :32;
#endif
} bits;
};
#define mask_nbit_l(u) ((void)0)
#define LDBL_IMPLICIT_NBIT
#define LDBL_NBIT 0
#define LDBL_MANH_SIZE 20
#define LDBL_MANL_SIZE 32
#define LDBL_TO_ARRAY32(u, a) do { \
(a)[0] = (uint32_t)(u).bits.manl; \
(a)[1] = (uint32_t)(u).bits.manh; \
} while(0)
#endif /* __x86_64__ */
/*
* The original fdlibm code used statements like:
* n0 = ((*(int*)&one)>>29)^1; * index of high word *
* ix0 = *(n0+(int*)&x); * high word of x *
* ix1 = *((1-n0)+(int*)&x); * low word of x *
* to dig two 32 bit words out of the 64 bit IEEE floating point
* value. That is non-ANSI, and, moreover, the gcc instruction
* scheduler gets it wrong. We instead use the following macros.
* Unlike the original code, we determine the endianness at compile
* time, not at run time; I don't see much benefit to selecting
* endianness at run time.
*/
/*
* A union which permits us to convert between a double and two 32 bit
* ints.
*/
#ifdef __arm__
#if defined(__VFP_FP__) || defined(__ARM_EABI__)
#define IEEE_WORD_ORDER __BYTE_ORDER__
#else
#define IEEE_WORD_ORDER __ORDER_BIG_ENDIAN__
#endif
#else /* __arm__ */
#define IEEE_WORD_ORDER __BYTE_ORDER__
#endif
/* A union which permits us to convert between a long double and
four 32 bit ints. */
#if IEEE_WORD_ORDER == __ORDER_BIG_ENDIAN__
typedef union
{
long double value;
struct {
uint32_t mswhi;
uint32_t mswlo;
uint32_t lswhi;
uint32_t lswlo;
} parts32;
struct {
uint64_t msw;
uint64_t lsw;
} parts64;
} ieee_quad_shape_type;
#endif
#if IEEE_WORD_ORDER == __ORDER_LITTLE_ENDIAN__
typedef union
{
long double value;
struct {
uint32_t lswlo;
uint32_t lswhi;
uint32_t mswlo;
uint32_t mswhi;
} parts32;
struct {
uint64_t lsw;
uint64_t msw;
} parts64;
} ieee_quad_shape_type;
#endif
#if IEEE_WORD_ORDER == __ORDER_BIG_ENDIAN__
typedef union
{
double value;
struct
{
uint32_t msw;
uint32_t lsw;
} parts;
struct
{
uint64_t w;
} xparts;
} ieee_double_shape_type;
#endif
#if IEEE_WORD_ORDER == __ORDER_LITTLE_ENDIAN__
typedef union
{
double value;
struct
{
uint32_t lsw;
uint32_t msw;
} parts;
struct
{
uint64_t w;
} xparts;
} ieee_double_shape_type;
#endif
/* Get two 32 bit ints from a double. */
#define EXTRACT_WORDS(ix0,ix1,d) \
do { \
ieee_double_shape_type ew_u; \
ew_u.value = (d); \
(ix0) = ew_u.parts.msw; \
(ix1) = ew_u.parts.lsw; \
} while (0)
/* Get a 64-bit int from a double. */
#define EXTRACT_WORD64(ix,d) \
do { \
ieee_double_shape_type ew_u; \
ew_u.value = (d); \
(ix) = ew_u.xparts.w; \
} while (0)
/* Get the more significant 32 bit int from a double. */
#define GET_HIGH_WORD(i,d) \
do { \
ieee_double_shape_type gh_u; \
gh_u.value = (d); \
(i) = gh_u.parts.msw; \
} while (0)
/* Get the less significant 32 bit int from a double. */
#define GET_LOW_WORD(i,d) \
do { \
ieee_double_shape_type gl_u; \
gl_u.value = (d); \
(i) = gl_u.parts.lsw; \
} while (0)
/* Set a double from two 32 bit ints. */
#define INSERT_WORDS(d,ix0,ix1) \
do { \
ieee_double_shape_type iw_u; \
iw_u.parts.msw = (ix0); \
iw_u.parts.lsw = (ix1); \
(d) = iw_u.value; \
} while (0)
/* Set a double from a 64-bit int. */
#define INSERT_WORD64(d,ix) \
do { \
ieee_double_shape_type iw_u; \
iw_u.xparts.w = (ix); \
(d) = iw_u.value; \
} while (0)
/* Set the more significant 32 bits of a double from an int. */
#define SET_HIGH_WORD(d,v) \
do { \
ieee_double_shape_type sh_u; \
sh_u.value = (d); \
sh_u.parts.msw = (v); \
(d) = sh_u.value; \
} while (0)
/* Set the less significant 32 bits of a double from an int. */
#define SET_LOW_WORD(d,v) \
do { \
ieee_double_shape_type sl_u; \
sl_u.value = (d); \
sl_u.parts.lsw = (v); \
(d) = sl_u.value; \
} while (0)
/*
* A union which permits us to convert between a float and a 32 bit
* int.
*/
typedef union
{
float value;
/* FIXME: Assumes 32 bit int. */
unsigned int word;
} ieee_float_shape_type;
/* Get a 32 bit int from a float. */
#define GET_FLOAT_WORD(i,d) \
do { \
ieee_float_shape_type gf_u; \
gf_u.value = (d); \
(i) = gf_u.word; \
} while (0)
/* Set a float from a 32 bit int. */
#define SET_FLOAT_WORD(d,i) \
do { \
ieee_float_shape_type sf_u; \
sf_u.word = (i); \
(d) = sf_u.value; \
} while (0)
/*
* Get expsign and mantissa as 16 bit and 64 bit ints from an 80 bit long
* double.
*/
#define EXTRACT_LDBL80_WORDS(ix0,ix1,d) \
do { \
union IEEEl2bits ew_u; \
ew_u.e = (d); \
(ix0) = ew_u.xbits.expsign; \
(ix1) = ew_u.xbits.man; \
} while (0)
/*
* Get expsign and mantissa as one 16 bit and two 64 bit ints from a 128 bit
* long double.
*/
#define EXTRACT_LDBL128_WORDS(ix0,ix1,ix2,d) \
do { \
union IEEEl2bits ew_u; \
ew_u.e = (d); \
(ix0) = ew_u.xbits.expsign; \
(ix1) = ew_u.xbits.manh; \
(ix2) = ew_u.xbits.manl; \
} while (0)
/* Get expsign as a 16 bit int from a long double. */
#define GET_LDBL_EXPSIGN(i,d) \
do { \
union IEEEl2bits ge_u; \
ge_u.e = (d); \
(i) = ge_u.xbits.expsign; \
} while (0)
/*
* Set an 80 bit long double from a 16 bit int expsign and a 64 bit int
* mantissa.
*/
#define INSERT_LDBL80_WORDS(d,ix0,ix1) \
do { \
union IEEEl2bits iw_u; \
iw_u.xbits.expsign = (ix0); \
iw_u.xbits.man = (ix1); \
(d) = iw_u.e; \
} while (0)
/*
* Set a 128 bit long double from a 16 bit int expsign and two 64 bit ints
* comprising the mantissa.
*/
#define INSERT_LDBL128_WORDS(d,ix0,ix1,ix2) \
do { \
union IEEEl2bits iw_u; \
iw_u.xbits.expsign = (ix0); \
iw_u.xbits.manh = (ix1); \
iw_u.xbits.manl = (ix2); \
(d) = iw_u.e; \
} while (0)
/* Set expsign of a long double from a 16 bit int. */
#define SET_LDBL_EXPSIGN(d,v) \
do { \
union IEEEl2bits se_u; \
se_u.e = (d); \
se_u.xbits.expsign = (v); \
(d) = se_u.e; \
} while (0)
#ifdef __i386__
/* Long double constants are broken on i386. */
#define LD80C(m, ex, v) { \
.xbits.man = __CONCAT(m, ULL), \
.xbits.expsign = (0x3fff + (ex)) | ((v) < 0 ? 0x8000 : 0), \
}
#else
/* The above works on non-i386 too, but we use this to check v. */
#define LD80C(m, ex, v) { .e = (v), }
#endif
#ifdef FLT_EVAL_METHOD
/*
* Attempt to get strict C99 semantics for assignment with non-C99 compilers.
*/
#if FLT_EVAL_METHOD == 0 || __GNUC__ == 0
#define STRICT_ASSIGN(type, lval, rval) ((lval) = (rval))
#else
#define STRICT_ASSIGN(type, lval, rval) do { \
volatile type __lval; \
\
if (sizeof(type) >= sizeof(long double)) \
(lval) = (rval); \
else { \
__lval = (rval); \
(lval) = __lval; \
} \
} while (0)
#endif
#endif /* FLT_EVAL_METHOD */
/* Support switching the mode to FP_PE if necessary. */
#if defined(__i386__) && !defined(NO_FPSETPREC)
#define ENTERI() ENTERIT(long double)
#define ENTERIT(returntype) \
returntype __retval; \
fp_prec_t __oprec; \
\
if ((__oprec = fpgetprec()) != FP_PE) \
fpsetprec(FP_PE)
#define RETURNI(x) do { \
__retval = (x); \
if (__oprec != FP_PE) \
fpsetprec(__oprec); \
RETURNF(__retval); \
} while (0)
#define ENTERV() \
fp_prec_t __oprec; \
\
if ((__oprec = fpgetprec()) != FP_PE) \
fpsetprec(FP_PE)
#define RETURNV() do { \
if (__oprec != FP_PE) \
fpsetprec(__oprec); \
return; \
} while (0)
#else
#define ENTERI()
#define ENTERIT(x)
#define RETURNI(x) RETURNF(x)
#define ENTERV()
#define RETURNV() return
#endif
/* Default return statement if hack*_t() is not used. */
#define RETURNF(v) return (v)
/*
* 2sum gives the same result as 2sumF without requiring |a| >= |b| or
* a == 0, but is slower.
*/
#define _2sum(a, b) do { \
__typeof(a) __s, __w; \
\
__w = (a) + (b); \
__s = __w - (a); \
(b) = ((a) - (__w - __s)) + ((b) - __s); \
(a) = __w; \
} while (0)
/*
* 2sumF algorithm.
*
* "Normalize" the terms in the infinite-precision expression a + b for
* the sum of 2 floating point values so that b is as small as possible
* relative to 'a'. (The resulting 'a' is the value of the expression in
* the same precision as 'a' and the resulting b is the rounding error.)
* |a| must be >= |b| or 0, b's type must be no larger than 'a's type, and
* exponent overflow or underflow must not occur. This uses a Theorem of
* Dekker (1971). See Knuth (1981) 4.2.2 Theorem C. The name "TwoSum"
* is apparently due to Skewchuk (1997).
*
* For this to always work, assignment of a + b to 'a' must not retain any
* extra precision in a + b. This is required by C standards but broken
* in many compilers. The brokenness cannot be worked around using
* STRICT_ASSIGN() like we do elsewhere, since the efficiency of this
* algorithm would be destroyed by non-null strict assignments. (The
* compilers are correct to be broken -- the efficiency of all floating
* point code calculations would be destroyed similarly if they forced the
* conversions.)
*
* Fortunately, a case that works well can usually be arranged by building
* any extra precision into the type of 'a' -- 'a' should have type float_t,
* double_t or long double. b's type should be no larger than 'a's type.
* Callers should use these types with scopes as large as possible, to
* reduce their own extra-precision and efficiciency problems. In
* particular, they shouldn't convert back and forth just to call here.
*/
#ifdef DEBUG
#define _2sumF(a, b) do { \
__typeof(a) __w; \
volatile __typeof(a) __ia, __ib, __r, __vw; \
\
__ia = (a); \
__ib = (b); \
assert(__ia == 0 || fabsl(__ia) >= fabsl(__ib)); \
\
__w = (a) + (b); \
(b) = ((a) - __w) + (b); \
(a) = __w; \
\
/* The next 2 assertions are weak if (a) is already long double. */ \
assert((long double)__ia + __ib == (long double)(a) + (b)); \
__vw = __ia + __ib; \
__r = __ia - __vw; \
__r += __ib; \
assert(__vw == (a) && __r == (b)); \
} while (0)
#else /* !DEBUG */
#define _2sumF(a, b) do { \
__typeof(a) __w; \
\
__w = (a) + (b); \
(b) = ((a) - __w) + (b); \
(a) = __w; \
} while (0)
#endif /* DEBUG */
/*
* Set x += c, where x is represented in extra precision as a + b.
* x must be sufficiently normalized and sufficiently larger than c,
* and the result is then sufficiently normalized.
*
* The details of ordering are that |a| must be >= |c| (so that (a, c)
* can be normalized without extra work to swap 'a' with c). The details of
* the normalization are that b must be small relative to the normalized 'a'.
* Normalization of (a, c) makes the normalized c tiny relative to the
* normalized a, so b remains small relative to 'a' in the result. However,
* b need not ever be tiny relative to 'a'. For example, b might be about
* 2**20 times smaller than 'a' to give about 20 extra bits of precision.
* That is usually enough, and adding c (which by normalization is about
* 2**53 times smaller than a) cannot change b significantly. However,
* cancellation of 'a' with c in normalization of (a, c) may reduce 'a'
* significantly relative to b. The caller must ensure that significant
* cancellation doesn't occur, either by having c of the same sign as 'a',
* or by having |c| a few percent smaller than |a|. Pre-normalization of
* (a, b) may help.
*
* This is a variant of an algorithm of Kahan (see Knuth (1981) 4.2.2
* exercise 19). We gain considerable efficiency by requiring the terms to
* be sufficiently normalized and sufficiently increasing.
*/
#define _3sumF(a, b, c) do { \
__typeof(a) __tmp; \
\
__tmp = (c); \
_2sumF(__tmp, (a)); \
(b) += (a); \
(a) = __tmp; \
} while (0)
/*
* Common routine to process the arguments to nan(), nanf(), and nanl().
*/
void _scan_nan(uint32_t *__words, int __num_words, const char *__s);
/*
* Mix 0, 1 or 2 NaNs. First add 0 to each arg. This normally just turns
* signaling NaNs into quiet NaNs by setting a quiet bit. We do this
* because we want to never return a signaling NaN, and also because we
* don't want the quiet bit to affect the result. Then mix the converted
* args using the specified operation.
*
* When one arg is NaN, the result is typically that arg quieted. When both
* args are NaNs, the result is typically the quietening of the arg whose
* mantissa is largest after quietening. When neither arg is NaN, the
* result may be NaN because it is indeterminate, or finite for subsequent
* construction of a NaN as the indeterminate 0.0L/0.0L.
*
* Technical complications: the result in bits after rounding to the final
* precision might depend on the runtime precision and/or on compiler
* optimizations, especially when different register sets are used for
* different precisions. Try to make the result not depend on at least the
* runtime precision by always doing the main mixing step in long double
* precision. Try to reduce dependencies on optimizations by adding the
* the 0's in different precisions (unless everything is in long double
* precision).
*/
#define nan_mix(x, y) (nan_mix_op((x), (y), +))
#define nan_mix_op(x, y, op) (((x) + 0.0L) op ((y) + 0))
#ifdef _COMPLEX_H
/*
* C99 specifies that complex numbers have the same representation as
* an array of two elements, where the first element is the real part
* and the second element is the imaginary part.
*/
typedef union {
float complex f;
float a[2];
} float_complex;
typedef union {
double complex f;
double a[2];
} double_complex;
typedef union {
long double complex f;
long double a[2];
} long_double_complex;
#define REALPART(z) ((z).a[0])
#define IMAGPART(z) ((z).a[1])
/*
* Inline functions that can be used to construct complex values.
*
* The C99 standard intends x+I*y to be used for this, but x+I*y is
* currently unusable in general since gcc introduces many overflow,
* underflow, sign and efficiency bugs by rewriting I*y as
* (0.0+I)*(y+0.0*I) and laboriously computing the full complex product.
* In particular, I*Inf is corrupted to NaN+I*Inf, and I*-0 is corrupted
* to -0.0+I*0.0.
*
* The C11 standard introduced the macros CMPLX(), CMPLXF() and CMPLXL()
* to construct complex values. Compilers that conform to the C99
* standard require the following functions to avoid the above issues.
*/
#ifndef CMPLXF
static __inline float complex
CMPLXF(float x, float y)
{
float_complex z;
REALPART(z) = x;
IMAGPART(z) = y;
return (z.f);
}
#endif
#ifndef CMPLX
static __inline double complex
CMPLX(double x, double y)
{
double_complex z;
REALPART(z) = x;
IMAGPART(z) = y;
return (z.f);
}
#endif
#ifndef CMPLXL
static __inline long double complex
CMPLXL(long double x, long double y)
{
long_double_complex z;
REALPART(z) = x;
IMAGPART(z) = y;
return (z.f);
}
#endif
#endif /* _COMPLEX_H */
/*
* The rnint() family rounds to the nearest integer for a restricted range
* range of args (up to about 2**MANT_DIG). We assume that the current
* rounding mode is FE_TONEAREST so that this can be done efficiently.
* Extra precision causes more problems in practice, and we only centralize
* this here to reduce those problems, and have not solved the efficiency
* problems. The exp2() family uses a more delicate version of this that
* requires extracting bits from the intermediate value, so it is not
* centralized here and should copy any solution of the efficiency problems.
*/
static inline double
rnint(double_t x)
{
/*
* This casts to double to kill any extra precision. This depends
* on the cast being applied to a double_t to avoid compiler bugs
* (this is a cleaner version of STRICT_ASSIGN()). This is
* inefficient if there actually is extra precision, but is hard
* to improve on. We use double_t in the API to minimise conversions
* for just calling here. Note that we cannot easily change the
* magic number to the one that works directly with double_t, since
* the rounding precision is variable at runtime on x86 so the
* magic number would need to be variable. Assuming that the
* rounding precision is always the default is too fragile. This
* and many other complications will move when the default is
* changed to FP_PE.
*/
return ((double)(x + 0x1.8p52) - 0x1.8p52);
}
static inline float
rnintf(float_t x)
{
/*
* As for rnint(), except we could just call that to handle the
* extra precision case, usually without losing efficiency.
*/
return ((float)(x + 0x1.8p23F) - 0x1.8p23F);
}
#ifdef LDBL_MANT_DIG
/*
* The complications for extra precision are smaller for rnintl() since it
* can safely assume that the rounding precision has been increased from
* its default to FP_PE on x86. We don't exploit that here to get small
* optimizations from limiting the rangle to double. We just need it for
* the magic number to work with long doubles. ld128 callers should use
* rnint() instead of this if possible. ld80 callers should prefer
* rnintl() since for amd64 this avoids swapping the register set, while
* for i386 it makes no difference (assuming FP_PE), and for other arches
* it makes little difference.
*/
static inline long double
rnintl(long double x)
{
return (x + __CONCAT(0x1.8p, LDBL_MANT_DIG) / 2 -
__CONCAT(0x1.8p, LDBL_MANT_DIG) / 2);
}
#endif /* LDBL_MANT_DIG */
/*
* irint() and i64rint() give the same result as casting to their integer
* return type provided their arg is a floating point integer. They can
* sometimes be more efficient because no rounding is required.
*/
#if defined(amd64) || defined(__i386__)
#define irint(x) \
(sizeof(x) == sizeof(float) && \
sizeof(float_t) == sizeof(long double) ? irintf(x) : \
sizeof(x) == sizeof(double) && \
sizeof(double_t) == sizeof(long double) ? irintd(x) : \
sizeof(x) == sizeof(long double) ? irintl(x) : (int)(x))
#else
#define irint(x) ((int)(x))
#endif
#define i64rint(x) ((int64_t)(x)) /* only needed for ld128 so not opt. */
#if defined(__i386__)
static __inline int
irintf(float x)
{
int n;
__asm("fistl %0" : "=m" (n) : "t" (x));
return (n);
}
static __inline int
irintd(double x)
{
int n;
__asm("fistl %0" : "=m" (n) : "t" (x));
return (n);
}
#endif
#if defined(__amd64__) || defined(__i386__)
static __inline int
irintl(long double x)
{
int n;
__asm("fistl %0" : "=m" (n) : "t" (x));
return (n);
}
#endif
#ifdef DEBUG
#if defined(__amd64__) || defined(__i386__)
#define breakpoint() asm("int $3")
#else
#define breakpoint() raise(SIGTRAP)
#endif
#endif
/* Write a pari script to test things externally. */
#ifdef DOPRINT
#ifndef DOPRINT_SWIZZLE
#define DOPRINT_SWIZZLE 0
#endif
#ifdef DOPRINT_LD80
#define DOPRINT_START(xp) do { \
uint64_t __lx; \
uint16_t __hx; \
\
/* Hack to give more-problematic args. */ \
EXTRACT_LDBL80_WORDS(__hx, __lx, *xp); \
__lx ^= DOPRINT_SWIZZLE; \
INSERT_LDBL80_WORDS(*xp, __hx, __lx); \
printf("x = %.21Lg; ", (long double)*xp); \
} while (0)
#define DOPRINT_END1(v) \
printf("y = %.21Lg; z = 0; show(x, y, z);\n", (long double)(v))
#define DOPRINT_END2(hi, lo) \
printf("y = %.21Lg; z = %.21Lg; show(x, y, z);\n", \
(long double)(hi), (long double)(lo))
#elif defined(DOPRINT_D64)
#define DOPRINT_START(xp) do { \
uint32_t __hx, __lx; \
\
EXTRACT_WORDS(__hx, __lx, *xp); \
__lx ^= DOPRINT_SWIZZLE; \
INSERT_WORDS(*xp, __hx, __lx); \
printf("x = %.21Lg; ", (long double)*xp); \
} while (0)
#define DOPRINT_END1(v) \
printf("y = %.21Lg; z = 0; show(x, y, z);\n", (long double)(v))
#define DOPRINT_END2(hi, lo) \
printf("y = %.21Lg; z = %.21Lg; show(x, y, z);\n", \
(long double)(hi), (long double)(lo))
#elif defined(DOPRINT_F32)
#define DOPRINT_START(xp) do { \
uint32_t __hx; \
\
GET_FLOAT_WORD(__hx, *xp); \
__hx ^= DOPRINT_SWIZZLE; \
SET_FLOAT_WORD(*xp, __hx); \
printf("x = %.21Lg; ", (long double)*xp); \
} while (0)
#define DOPRINT_END1(v) \
printf("y = %.21Lg; z = 0; show(x, y, z);\n", (long double)(v))
#define DOPRINT_END2(hi, lo) \
printf("y = %.21Lg; z = %.21Lg; show(x, y, z);\n", \
(long double)(hi), (long double)(lo))
#else /* !DOPRINT_LD80 && !DOPRINT_D64 (LD128 only) */
#ifndef DOPRINT_SWIZZLE_HIGH
#define DOPRINT_SWIZZLE_HIGH 0
#endif
#define DOPRINT_START(xp) do { \
uint64_t __lx, __llx; \
uint16_t __hx; \
\
EXTRACT_LDBL128_WORDS(__hx, __lx, __llx, *xp); \
__llx ^= DOPRINT_SWIZZLE; \
__lx ^= DOPRINT_SWIZZLE_HIGH; \
INSERT_LDBL128_WORDS(*xp, __hx, __lx, __llx); \
printf("x = %.36Lg; ", (long double)*xp); \
} while (0)
#define DOPRINT_END1(v) \
printf("y = %.36Lg; z = 0; show(x, y, z);\n", (long double)(v))
#define DOPRINT_END2(hi, lo) \
printf("y = %.36Lg; z = %.36Lg; show(x, y, z);\n", \
(long double)(hi), (long double)(lo))
#endif /* DOPRINT_LD80 */
#else /* !DOPRINT */
#define DOPRINT_START(xp)
#define DOPRINT_END1(v)
#define DOPRINT_END2(hi, lo)
#endif /* DOPRINT */
#define RETURNP(x) do { \
DOPRINT_END1(x); \
RETURNF(x); \
} while (0)
#define RETURNPI(x) do { \
DOPRINT_END1(x); \
RETURNI(x); \
} while (0)
#define RETURN2P(x, y) do { \
DOPRINT_END2((x), (y)); \
RETURNF((x) + (y)); \
} while (0)
#define RETURN2PI(x, y) do { \
DOPRINT_END2((x), (y)); \
RETURNI((x) + (y)); \
} while (0)
#define RETURNSP(rp) do { \
if (!(rp)->lo_set) \
RETURNP((rp)->hi); \
RETURN2P((rp)->hi, (rp)->lo); \
} while (0)
#define RETURNSPI(rp) do { \
if (!(rp)->lo_set) \
RETURNPI((rp)->hi); \
RETURN2PI((rp)->hi, (rp)->lo); \
} while (0)
#define SUM2P(x, y) ({ \
const __typeof (x) __x = (x); \
const __typeof (y) __y = (y); \
\
DOPRINT_END2(__x, __y); \
__x + __y; \
})
/* fdlibm kernel function */
int __kernel_rem_pio2(double*,double*,int,int,int);
/* double precision kernel functions */
#ifndef INLINE_REM_PIO2
int __ieee754_rem_pio2(double,double*);
#endif
double __kernel_sin(double,double,int);
double __kernel_cos(double,double);
double __kernel_tan(double,double,int);
double __ldexp_exp(double,int);
#ifdef _COMPLEX_H
double complex __ldexp_cexp(double complex,int);
#endif
/* float precision kernel functions */
#ifndef INLINE_REM_PIO2F
int __ieee754_rem_pio2f(float,double*);
#endif
#ifndef INLINE_KERNEL_SINDF
float __kernel_sindf(double);
#endif
#ifndef INLINE_KERNEL_COSDF
float __kernel_cosdf(double);
#endif
#ifndef INLINE_KERNEL_TANDF
float __kernel_tandf(double,int);
#endif
float __ldexp_expf(float,int);
#ifdef _COMPLEX_H
float complex __ldexp_cexpf(float complex,int);
#endif
/* long double precision kernel functions */
long double __kernel_sinl(long double, long double, int);
long double __kernel_cosl(long double, long double);
long double __kernel_tanl(long double, long double, int);
#define INTERVALS 128
#define LOG2_INTERVALS 7
#define BIAS (LDBL_MAX_EXP - 1)
struct ExplData {
/*
* hi must be rounded to at most 106 bits so that multiplication
* by r1 in expm1l() is exact, but it is rounded to 88 bits due to
* historical accidents.
*
* XXX it is wasteful to use long double for both hi and lo. ld128
* exp2l() uses only float for lo (in a very differently organized
* table; ld80 exp2l() is different again. It uses 2 doubles in a
* table organized like this one. 1 double and 1 float would
* suffice). There are different packing/locality/alignment/caching
* problems with these methods.
*
* XXX C's bad %a format makes the bits unreadable. They happen
* to all line up for the hi values 1 before the point and 88
* in 22 nybbles, but for the low values the nybbles are shifted
* randomly.
*/
long double hi;
long double lo;
};
extern const struct ExplData kExplData[INTERVALS];
void __k_expl(long double , long double *, long double *, int *) _Hide;
/*
* XXX: the rest of the functions are identical for ld80 and ld128.
* However, we should use scalbnl() for ld128, since long double
* multiplication was very slow on sparc64 and no new evaluation has
* been made for aarch64 and/or riscv.
*/
static inline void
k_hexpl(long double x, long double *hip, long double *lop)
{
float twopkm1;
int k;
__k_expl(x, hip, lop, &k);
SET_FLOAT_WORD(twopkm1, 0x3f800000 + ((k - 1) << 23));
*hip *= twopkm1;
*lop *= twopkm1;
}
static inline long double
hexpl(long double x)
{
long double hi, lo, twopkm2;
int k;
twopkm2 = 1;
__k_expl(x, &hi, &lo, &k);
SET_LDBL_EXPSIGN(twopkm2, BIAS + k - 2);
return (lo + hi) * 2 * twopkm2;
}
#ifdef _COMPLEX_H
/*
* See ../src/k_exp.c for details.
*/
static inline long double complex
__ldexp_cexpl(long double complex z, int expt)
{
long double c, exp_x, hi, lo, s;
long double x, y, scale1, scale2;
int half_expt, k;
x = creall(z);
y = cimagl(z);
__k_expl(x, &hi, &lo, &k);
exp_x = (lo + hi) * 0x1p16382L;
expt += k - 16382;
scale1 = 1;
half_expt = expt / 2;
SET_LDBL_EXPSIGN(scale1, BIAS + half_expt);
scale2 = 1;
SET_LDBL_EXPSIGN(scale2, BIAS + expt - half_expt);
sincosl(y, &s, &c);
return (CMPLXL(c * exp_x * scale1 * scale2,
s * exp_x * scale1 * scale2));
}
#endif /* _COMPLEX_H */
COSMOPOLITAN_C_END_
#endif /* !(__ASSEMBLER__ + __LINKER__ + 0) */
#endif /* COSMOPOLITAN_LIBC_TINYMATH_FREEBSD_INTERNAL_H_ */
| 27,722 | 1,041 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/tinymath.mk | #-*-mode:makefile-gmake;indent-tabs-mode:t;tab-width:8;coding:utf-8-*-â
#âââvi: set et ft=make ts=8 tw=8 fenc=utf-8 :viââââââââââââââââââââââââ
PKGS += LIBC_TINYMATH
LIBC_TINYMATH_ARTIFACTS += LIBC_TINYMATH_A
LIBC_TINYMATH = $(LIBC_TINYMATH_A_DEPS) $(LIBC_TINYMATH_A)
LIBC_TINYMATH_A = o/$(MODE)/libc/tinymath/tinymath.a
LIBC_TINYMATH_A_FILES := $(wildcard libc/tinymath/*)
LIBC_TINYMATH_A_HDRS = $(filter %.h,$(LIBC_TINYMATH_A_FILES))
LIBC_TINYMATH_A_SRCS_A = $(filter %.s,$(LIBC_TINYMATH_A_FILES))
LIBC_TINYMATH_A_SRCS_S = $(filter %.S,$(LIBC_TINYMATH_A_FILES))
LIBC_TINYMATH_A_SRCS_C = $(filter %.c,$(LIBC_TINYMATH_A_FILES))
LIBC_TINYMATH_A_SRCS = $(LIBC_TINYMATH_A_SRCS_S) $(LIBC_TINYMATH_A_SRCS_C)
LIBC_TINYMATH_A_CHECKS = $(LIBC_TINYMATH_A).pkg
LIBC_TINYMATH_A_OBJS = \
$(LIBC_TINYMATH_A_SRCS_A:%.s=o/$(MODE)/%.o) \
$(LIBC_TINYMATH_A_SRCS_S:%.S=o/$(MODE)/%.o) \
$(LIBC_TINYMATH_A_SRCS_C:%.c=o/$(MODE)/%.o)
LIBC_TINYMATH_A_CHECKS = \
$(LIBC_TINYMATH_A).pkg \
$(LIBC_TINYMATH_A_HDRS:%=o/$(MODE)/%.ok)
LIBC_TINYMATH_A_DIRECTDEPS = \
LIBC_INTRIN \
LIBC_STUBS \
LIBC_NEXGEN32E \
LIBC_SYSV \
THIRD_PARTY_COMPILER_RT
LIBC_TINYMATH_A_DEPS := \
$(call uniq,$(foreach x,$(LIBC_TINYMATH_A_DIRECTDEPS),$($(x))))
$(LIBC_TINYMATH_A): \
libc/tinymath/ \
$(LIBC_TINYMATH_A).pkg \
$(LIBC_TINYMATH_A_OBJS)
$(LIBC_TINYMATH_A).pkg: \
$(LIBC_TINYMATH_A_OBJS) \
$(foreach x,$(LIBC_TINYMATH_A_DIRECTDEPS),$($(x)_A).pkg)
o/$(MODE)/libc/tinymath/lround.o \
o/$(MODE)/libc/tinymath/lroundf.o \
o/$(MODE)/libc/tinymath/lroundl.o: private \
OVERRIDE_CFLAGS += \
-fno-builtin
o/$(MODE)/libc/tinymath/expl.o \
o/$(MODE)/libc/tinymath/loglq.o: private \
OVERRIDE_CFLAGS += \
-ffunction-sections
$(LIBC_TINYMATH_A_OBJS): private \
OVERRIDE_CFLAGS += \
-fsigned-zeros \
-ftrapping-math \
-frounding-math \
-fsignaling-nans \
-fno-reciprocal-math \
-fno-associative-math \
-fno-finite-math-only \
-fno-cx-limited-range \
-ffp-int-builtin-inexact
LIBC_TINYMATH_LIBS = $(foreach x,$(LIBC_TINYMATH_ARTIFACTS),$($(x)))
LIBC_TINYMATH_HDRS = $(foreach x,$(LIBC_TINYMATH_ARTIFACTS),$($(x)_HDRS))
LIBC_TINYMATH_SRCS = $(foreach x,$(LIBC_TINYMATH_ARTIFACTS),$($(x)_SRCS))
LIBC_TINYMATH_CHECKS = $(foreach x,$(LIBC_TINYMATH_ARTIFACTS),$($(x)_CHECKS))
LIBC_TINYMATH_OBJS = $(foreach x,$(LIBC_TINYMATH_ARTIFACTS),$($(x)_OBJS))
LIBC_TINYMATH_CHECKS = $(LIBC_TINYMATH_HDRS:%=o/$(MODE)/%.ok)
$(LIBC_TINYMATH_OBJS): $(BUILD_FILES) libc/tinymath/tinymath.mk
.PHONY: o/$(MODE)/libc/tinymath
o/$(MODE)/libc/tinymath: \
$(LIBC_TINYMATH_CHECKS) \
o/$(MODE)/libc/tinymath/tinymath.a
| 2,747 | 80 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/cosl.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/complex.h"
#include "libc/math.h"
#include "libc/tinymath/kernel.internal.h"
#include "libc/tinymath/ldshape.internal.h"
#if !(LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024)
asm(".ident\t\"\\n\\n\
Musl libc (MIT License)\\n\
Copyright 2005-2014 Rich Felker, et. al.\"");
asm(".include \"libc/disclaimer.inc\"");
// clang-format off
/**
* Returns cosine of ð¥.
*/
long double cosl(long double x)
{
union ldshape u = {x};
unsigned n;
long double y[2], hi, lo;
u.i.se &= 0x7fff;
if (u.i.se == 0x7fff)
return x - x;
x = u.f;
if (x < M_PI_4) {
if (u.i.se < 0x3fff - LDBL_MANT_DIG)
/* raise inexact if x!=0 */
return 1.0 + x;
return __cosl(x, 0);
}
n = __rem_pio2l(x, y);
hi = y[0];
lo = y[1];
switch (n & 3) {
case 0:
return __cosl(hi, lo);
case 1:
return -__sinl(hi, lo, 1);
case 2:
return -__cosl(hi, lo);
case 3:
default:
return __sinl(hi, lo, 1);
}
}
#endif /* long double is long */
| 3,544 | 76 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/hornerf.internal.h | #ifndef COSMOPOLITAN_LIBC_TINYMATH_HORNERF_INTERNAL_H_
#define COSMOPOLITAN_LIBC_TINYMATH_HORNERF_INTERNAL_H_
#include "libc/math.h"
#if !(__ASSEMBLER__ + __LINKER__ + 0)
COSMOPOLITAN_C_START_
#if WANT_VMATH
#define FMA(x, y, z) vfmaq_f32(z, x, y)
#else
#define FMA fmaf
#endif
#include "libc/tinymath/horner_wrap.internal.h"
#include "third_party/libcxx/math.h"
COSMOPOLITAN_C_END_
#endif /* !(__ASSEMBLER__ + __LINKER__ + 0) */
#endif /* COSMOPOLITAN_LIBC_TINYMATH_HORNERF_INTERNAL_H_ */
| 493 | 19 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/LICENSE.optimized-routines | MIT OR Apache-2.0 WITH LLVM-exception
=====================================
MIT License
-----------
Copyright (c) 1999-2022, Arm Limited.
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.
Apache-2.0 WITH LLVM-exception
------------------------------
Apache License
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http://www.apache.org/licenses/
TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION
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| 13,491 | 250 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/pow_data.internal.h | #ifndef COSMOPOLITAN_LIBC_TINYMATH_POW_DATA_INTERNAL_H_
#define COSMOPOLITAN_LIBC_TINYMATH_POW_DATA_INTERNAL_H_
#define POW_LOG_TABLE_BITS 7
#define POW_LOG_POLY_ORDER 8
#if !(__ASSEMBLER__ + __LINKER__ + 0)
COSMOPOLITAN_C_START_
extern _Hide const struct pow_log_data {
double ln2hi;
double ln2lo;
double poly[POW_LOG_POLY_ORDER - 1]; /* First coefficient is 1. */
/* Note: the pad field is unused, but allows slightly faster indexing. */
struct {
double invc, pad, logc, logctail;
} tab[1 << POW_LOG_TABLE_BITS];
} __pow_log_data;
COSMOPOLITAN_C_END_
#endif /* !(__ASSEMBLER__ + __LINKER__ + 0) */
#endif /* COSMOPOLITAN_LIBC_TINYMATH_POW_DATA_INTERNAL_H_ */
| 683 | 23 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/hypot.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
asm(".ident\t\"\\n\\n\
Musl libc (MIT License)\\n\
Copyright 2005-2014 Rich Felker, et. al.\"");
asm(".include \"libc/disclaimer.inc\"");
// clang-format off
#if FLT_EVAL_METHOD > 1U && LDBL_MANT_DIG == 64
#define SPLIT (0x1p32 + 1)
#else
#define SPLIT (0x1p27 + 1)
#endif
static void sq(double_t *hi, double_t *lo, double x)
{
double_t xh, xl, xc;
xc = (double_t)x*SPLIT;
xh = x - xc + xc;
xl = x - xh;
*hi = (double_t)x*x;
*lo = xh*xh - *hi + 2*xh*xl + xl*xl;
}
/**
* Returns euclidean distance.
*/
double hypot(double x, double y)
{
union {double f; uint64_t i;} ux = {x}, uy = {y}, ut;
int ex, ey;
double_t hx, lx, hy, ly, z;
/* arrange |x| >= |y| */
ux.i &= -1ULL>>1;
uy.i &= -1ULL>>1;
if (ux.i < uy.i) {
ut = ux;
ux = uy;
uy = ut;
}
/* special cases */
ex = ux.i>>52;
ey = uy.i>>52;
x = ux.f;
y = uy.f;
/* note: hypot(inf,nan) == inf */
if (ey == 0x7ff)
return y;
if (ex == 0x7ff || uy.i == 0)
return x;
/* note: hypot(x,y) ~= x + y*y/x/2 with inexact for small y/x */
/* 64 difference is enough for ld80 double_t */
if (ex - ey > 64)
return x + y;
/* precise sqrt argument in nearest rounding mode without overflow */
/* xh*xh must not overflow and xl*xl must not underflow in sq */
z = 1;
if (ex > 0x3ff+510) {
z = 0x1p700;
x *= 0x1p-700;
y *= 0x1p-700;
} else if (ey < 0x3ff-450) {
z = 0x1p-700;
x *= 0x1p700;
y *= 0x1p700;
}
sq(&hx, &lx, x);
sq(&hy, &ly, y);
return z*sqrt(ly+lx+hy+hx);
}
#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
__strong_reference(hypot, hypotl);
#endif
| 4,183 | 106 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/exp_data.internal.h | #ifndef COSMOPOLITAN_LIBC_TINYMATH_EXP_DATA_H_
#define COSMOPOLITAN_LIBC_TINYMATH_EXP_DATA_H_
#define EXP_TABLE_BITS 7
#define EXP_POLY_ORDER 5
#define EXP_USE_TOINT_NARROW 0
#define EXP2_POLY_ORDER 5
#if !(__ASSEMBLER__ + __LINKER__ + 0)
COSMOPOLITAN_C_START_
extern _Hide const struct exp_data {
double invln2N;
double shift;
double negln2hiN;
double negln2loN;
double poly[4]; /* Last four coefficients. */
double exp2_shift;
double exp2_poly[EXP2_POLY_ORDER];
uint64_t tab[2 * (1 << EXP_TABLE_BITS)];
} __exp_data;
COSMOPOLITAN_C_END_
#endif /* !(__ASSEMBLER__ + __LINKER__ + 0) */
#endif /* COSMOPOLITAN_LIBC_TINYMATH_EXP_DATA_H_ */
| 676 | 26 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/significand.c | /*-*- mode:c;indent-tabs-mode:nil;c-basic-offset:2;tab-width:8;coding:utf-8 -*-â
âvi: set net ft=c ts=2 sts=2 sw=2 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ¡
â Copyright 2023 Justine Alexandra Roberts Tunney â
â â
â Permission to use, copy, modify, and/or distribute this software for â
â any purpose with or without fee is hereby granted, provided that the â
â above copyright notice and this permission notice appear in all copies. â
â â
â THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL â
â WARRANTIES WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED â
â WARRANTIES OF MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE â
â AUTHOR BE LIABLE FOR ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL â
â DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR â
â PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER â
â TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR â
â PERFORMANCE OF THIS SOFTWARE. â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
/**
* Return mantissa of ð¥ scaled to range [1,2).
*/
double significand(double x) {
return scalbn(x, -ilogb(x));
}
#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
__strong_reference(significand, significandl);
#endif
| 2,085 | 31 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/atanf_data.internal.h | #ifndef COSMOPOLITAN_LIBC_TINYMATH_ATANF_DATA_H_
#define COSMOPOLITAN_LIBC_TINYMATH_ATANF_DATA_H_
#if !(__ASSEMBLER__ + __LINKER__ + 0)
COSMOPOLITAN_C_START_
#define ATANF_POLY_NCOEFFS 8
extern const struct atanf_poly_data {
float poly[ATANF_POLY_NCOEFFS];
} __atanf_poly_data _Hide;
COSMOPOLITAN_C_END_
#endif /* !(__ASSEMBLER__ + __LINKER__ + 0) */
#endif /* COSMOPOLITAN_LIBC_TINYMATH_ATANF_DATA_H_ */
| 409 | 14 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/truncf.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
#include "libc/tinymath/internal.h"
#include "third_party/intel/smmintrin.internal.h"
asm(".ident\t\"\\n\\n\
Musl libc (MIT License)\\n\
Copyright 2005-2014 Rich Felker, et. al.\"");
asm(".include \"libc/disclaimer.inc\"");
// clang-format off
/**
* Rounds to integer, towards zero.
*/
float truncf(float x)
{
#ifdef __aarch64__
asm("frintz\t%s0,%s1" : "=w"(x) : "w"(x));
return x;
#elif defined(__powerpc64__) && defined(_ARCH_PWR5X)
asm("friz\t%0,%1" : "=f"(x) : "f"(x));
return x;
#elif defined(__s390x__) && (defined(__HTM__) || __ARCH__ >= 9)
asm("fiebra\t%0,5,%1,4" : "=f"(x) : "f"(x));
return x;
#elif defined(__x86_64__) && defined(__SSE4_1__)
asm("roundss\t%2,%1,%0"
: "=x"(x)
: "x"(x), "i"(_MM_FROUND_TO_ZERO | _MM_FROUND_NO_EXC));
return x;
#else
union {float f; uint32_t i;} u = {x};
int e = (int)(u.i >> 23 & 0xff) - 0x7f + 9;
uint32_t m;
if (e >= 23 + 9)
return x;
if (e < 9)
e = 1;
m = -1U >> e;
if ((u.i & m) == 0)
return x;
FORCE_EVAL(x + 0x1p120f);
u.i &= ~m;
return u.f;
#endif /* __aarch64__ */
}
| 3,690 | 83 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/rempio2large.c | /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â â
â Musl Libc â
â Copyright © 2005-2014 Rich Felker, et al. â
â â
â Permission is hereby granted, free of charge, to any person obtaining â
â a copy of this software and associated documentation files (the â
â "Software"), to deal in the Software without restriction, including â
â without limitation the rights to use, copy, modify, merge, publish, â
â distribute, sublicense, and/or sell copies of the Software, and to â
â permit persons to whom the Software is furnished to do so, subject to â
â the following conditions: â
â â
â The above copyright notice and this permission notice shall be â
â included in all copies or substantial portions of the Software. â
â â
â THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, â
â EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF â
â MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. â
â IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY â
â CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, â
â TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE â
â SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. â
â â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
#include "libc/tinymath/kernel.internal.h"
asm(".ident\t\"\\n\\n\
fdlibm (fdlibm license)\\n\
Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.\"");
asm(".ident\t\"\\n\\n\
Musl libc (MIT License)\\n\
Copyright 2005-2014 Rich Felker, et. al.\"");
asm(".include \"libc/disclaimer.inc\"");
// clang-format off
/* origin: FreeBSD /usr/src/lib/msun/src/k_rem_pio2.c */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/*
* __rem_pio2_large(x,y,e0,nx,prec)
* double x[],y[]; int e0,nx,prec;
*
* __rem_pio2_large return the last three digits of N with
* y = x - N*pi/2
* so that |y| < pi/2.
*
* The method is to compute the integer (mod 8) and fraction parts of
* (2/pi)*x without doing the full multiplication. In general we
* skip the part of the product that are known to be a huge integer (
* more accurately, = 0 mod 8 ). Thus the number of operations are
* independent of the exponent of the input.
*
* (2/pi) is represented by an array of 24-bit integers in ipio2[].
*
* Input parameters:
* x[] The input value (must be positive) is broken into nx
* pieces of 24-bit integers in double precision format.
* x[i] will be the i-th 24 bit of x. The scaled exponent
* of x[0] is given in input parameter e0 (i.e., x[0]*2^e0
* match x's up to 24 bits.
*
* Example of breaking a double positive z into x[0]+x[1]+x[2]:
* e0 = ilogb(z)-23
* z = scalbn(z,-e0)
* for i = 0,1,2
* x[i] = floor(z)
* z = (z-x[i])*2**24
*
*
* y[] output result in an array of double precision numbers.
* The dimension of y[] is:
* 24-bit precision 1
* 53-bit precision 2
* 64-bit precision 2
* 113-bit precision 3
* The actual value is the sum of them. Thus for 113-bit
* precision, one may have to do something like:
*
* long double t,w,r_head, r_tail;
* t = (long double)y[2] + (long double)y[1];
* w = (long double)y[0];
* r_head = t+w;
* r_tail = w - (r_head - t);
*
* e0 The exponent of x[0]. Must be <= 16360 or you need to
* expand the ipio2 table.
*
* nx dimension of x[]
*
* prec an integer indicating the precision:
* 0 24 bits (single)
* 1 53 bits (double)
* 2 64 bits (extended)
* 3 113 bits (quad)
*
* External function:
* double scalbn(), floor();
*
*
* Here is the description of some local variables:
*
* jk jk+1 is the initial number of terms of ipio2[] needed
* in the computation. The minimum and recommended value
* for jk is 3,4,4,6 for single, double, extended, and quad.
* jk+1 must be 2 larger than you might expect so that our
* recomputation test works. (Up to 24 bits in the integer
* part (the 24 bits of it that we compute) and 23 bits in
* the fraction part may be lost to cancellation before we
* recompute.)
*
* jz local integer variable indicating the number of
* terms of ipio2[] used.
*
* jx nx - 1
*
* jv index for pointing to the suitable ipio2[] for the
* computation. In general, we want
* ( 2^e0*x[0] * ipio2[jv-1]*2^(-24jv) )/8
* is an integer. Thus
* e0-3-24*jv >= 0 or (e0-3)/24 >= jv
* Hence jv = max(0,(e0-3)/24).
*
* jp jp+1 is the number of terms in PIo2[] needed, jp = jk.
*
* q[] double array with integral value, representing the
* 24-bits chunk of the product of x and 2/pi.
*
* q0 the corresponding exponent of q[0]. Note that the
* exponent for q[i] would be q0-24*i.
*
* PIo2[] double precision array, obtained by cutting pi/2
* into 24 bits chunks.
*
* f[] ipio2[] in floating point
*
* iq[] integer array by breaking up q[] in 24-bits chunk.
*
* fq[] final product of x*(2/pi) in fq[0],..,fq[jk]
*
* ih integer. If >0 it indicates q[] is >= 0.5, hence
* it also indicates the *sign* of the result.
*
*/
/*
* Constants:
* The hexadecimal values are the intended ones for the following
* constants. The decimal values may be used, provided that the
* compiler will convert from decimal to binary accurately enough
* to produce the hexadecimal values shown.
*/
static const int init_jk[] = {3,4,4,6}; /* initial value for jk */
/*
* Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi
*
* integer array, contains the (24*i)-th to (24*i+23)-th
* bit of 2/pi after binary point. The corresponding
* floating value is
*
* ipio2[i] * 2^(-24(i+1)).
*
* NB: This table must have at least (e0-3)/24 + jk terms.
* For quad precision (e0 <= 16360, jk = 6), this is 686.
*/
static const int32_t ipio2[] = {
0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62,
0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A,
0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129,
0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41,
0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8,
0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF,
0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5,
0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08,
0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3,
0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880,
0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B,
#if LDBL_MAX_EXP > 1024
0x47C419, 0xC367CD, 0xDCE809, 0x2A8359, 0xC4768B, 0x961CA6,
0xDDAF44, 0xD15719, 0x053EA5, 0xFF0705, 0x3F7E33, 0xE832C2,
0xDE4F98, 0x327DBB, 0xC33D26, 0xEF6B1E, 0x5EF89F, 0x3A1F35,
0xCAF27F, 0x1D87F1, 0x21907C, 0x7C246A, 0xFA6ED5, 0x772D30,
0x433B15, 0xC614B5, 0x9D19C3, 0xC2C4AD, 0x414D2C, 0x5D000C,
0x467D86, 0x2D71E3, 0x9AC69B, 0x006233, 0x7CD2B4, 0x97A7B4,
0xD55537, 0xF63ED7, 0x1810A3, 0xFC764D, 0x2A9D64, 0xABD770,
0xF87C63, 0x57B07A, 0xE71517, 0x5649C0, 0xD9D63B, 0x3884A7,
0xCB2324, 0x778AD6, 0x23545A, 0xB91F00, 0x1B0AF1, 0xDFCE19,
0xFF319F, 0x6A1E66, 0x615799, 0x47FBAC, 0xD87F7E, 0xB76522,
0x89E832, 0x60BFE6, 0xCDC4EF, 0x09366C, 0xD43F5D, 0xD7DE16,
0xDE3B58, 0x929BDE, 0x2822D2, 0xE88628, 0x4D58E2, 0x32CAC6,
0x16E308, 0xCB7DE0, 0x50C017, 0xA71DF3, 0x5BE018, 0x34132E,
0x621283, 0x014883, 0x5B8EF5, 0x7FB0AD, 0xF2E91E, 0x434A48,
0xD36710, 0xD8DDAA, 0x425FAE, 0xCE616A, 0xA4280A, 0xB499D3,
0xF2A606, 0x7F775C, 0x83C2A3, 0x883C61, 0x78738A, 0x5A8CAF,
0xBDD76F, 0x63A62D, 0xCBBFF4, 0xEF818D, 0x67C126, 0x45CA55,
0x36D9CA, 0xD2A828, 0x8D61C2, 0x77C912, 0x142604, 0x9B4612,
0xC459C4, 0x44C5C8, 0x91B24D, 0xF31700, 0xAD43D4, 0xE54929,
0x10D5FD, 0xFCBE00, 0xCC941E, 0xEECE70, 0xF53E13, 0x80F1EC,
0xC3E7B3, 0x28F8C7, 0x940593, 0x3E71C1, 0xB3092E, 0xF3450B,
0x9C1288, 0x7B20AB, 0x9FB52E, 0xC29247, 0x2F327B, 0x6D550C,
0x90A772, 0x1FE76B, 0x96CB31, 0x4A1679, 0xE27941, 0x89DFF4,
0x9794E8, 0x84E6E2, 0x973199, 0x6BED88, 0x365F5F, 0x0EFDBB,
0xB49A48, 0x6CA467, 0x427271, 0x325D8D, 0xB8159F, 0x09E5BC,
0x25318D, 0x3974F7, 0x1C0530, 0x010C0D, 0x68084B, 0x58EE2C,
0x90AA47, 0x02E774, 0x24D6BD, 0xA67DF7, 0x72486E, 0xEF169F,
0xA6948E, 0xF691B4, 0x5153D1, 0xF20ACF, 0x339820, 0x7E4BF5,
0x6863B2, 0x5F3EDD, 0x035D40, 0x7F8985, 0x295255, 0xC06437,
0x10D86D, 0x324832, 0x754C5B, 0xD4714E, 0x6E5445, 0xC1090B,
0x69F52A, 0xD56614, 0x9D0727, 0x50045D, 0xDB3BB4, 0xC576EA,
0x17F987, 0x7D6B49, 0xBA271D, 0x296996, 0xACCCC6, 0x5414AD,
0x6AE290, 0x89D988, 0x50722C, 0xBEA404, 0x940777, 0x7030F3,
0x27FC00, 0xA871EA, 0x49C266, 0x3DE064, 0x83DD97, 0x973FA3,
0xFD9443, 0x8C860D, 0xDE4131, 0x9D3992, 0x8C70DD, 0xE7B717,
0x3BDF08, 0x2B3715, 0xA0805C, 0x93805A, 0x921110, 0xD8E80F,
0xAF806C, 0x4BFFDB, 0x0F9038, 0x761859, 0x15A562, 0xBBCB61,
0xB989C7, 0xBD4010, 0x04F2D2, 0x277549, 0xF6B6EB, 0xBB22DB,
0xAA140A, 0x2F2689, 0x768364, 0x333B09, 0x1A940E, 0xAA3A51,
0xC2A31D, 0xAEEDAF, 0x12265C, 0x4DC26D, 0x9C7A2D, 0x9756C0,
0x833F03, 0xF6F009, 0x8C402B, 0x99316D, 0x07B439, 0x15200C,
0x5BC3D8, 0xC492F5, 0x4BADC6, 0xA5CA4E, 0xCD37A7, 0x36A9E6,
0x9492AB, 0x6842DD, 0xDE6319, 0xEF8C76, 0x528B68, 0x37DBFC,
0xABA1AE, 0x3115DF, 0xA1AE00, 0xDAFB0C, 0x664D64, 0xB705ED,
0x306529, 0xBF5657, 0x3AFF47, 0xB9F96A, 0xF3BE75, 0xDF9328,
0x3080AB, 0xF68C66, 0x15CB04, 0x0622FA, 0x1DE4D9, 0xA4B33D,
0x8F1B57, 0x09CD36, 0xE9424E, 0xA4BE13, 0xB52333, 0x1AAAF0,
0xA8654F, 0xA5C1D2, 0x0F3F0B, 0xCD785B, 0x76F923, 0x048B7B,
0x721789, 0x53A6C6, 0xE26E6F, 0x00EBEF, 0x584A9B, 0xB7DAC4,
0xBA66AA, 0xCFCF76, 0x1D02D1, 0x2DF1B1, 0xC1998C, 0x77ADC3,
0xDA4886, 0xA05DF7, 0xF480C6, 0x2FF0AC, 0x9AECDD, 0xBC5C3F,
0x6DDED0, 0x1FC790, 0xB6DB2A, 0x3A25A3, 0x9AAF00, 0x9353AD,
0x0457B6, 0xB42D29, 0x7E804B, 0xA707DA, 0x0EAA76, 0xA1597B,
0x2A1216, 0x2DB7DC, 0xFDE5FA, 0xFEDB89, 0xFDBE89, 0x6C76E4,
0xFCA906, 0x70803E, 0x156E85, 0xFF87FD, 0x073E28, 0x336761,
0x86182A, 0xEABD4D, 0xAFE7B3, 0x6E6D8F, 0x396795, 0x5BBF31,
0x48D784, 0x16DF30, 0x432DC7, 0x356125, 0xCE70C9, 0xB8CB30,
0xFD6CBF, 0xA200A4, 0xE46C05, 0xA0DD5A, 0x476F21, 0xD21262,
0x845CB9, 0x496170, 0xE0566B, 0x015299, 0x375550, 0xB7D51E,
0xC4F133, 0x5F6E13, 0xE4305D, 0xA92E85, 0xC3B21D, 0x3632A1,
0xA4B708, 0xD4B1EA, 0x21F716, 0xE4698F, 0x77FF27, 0x80030C,
0x2D408D, 0xA0CD4F, 0x99A520, 0xD3A2B3, 0x0A5D2F, 0x42F9B4,
0xCBDA11, 0xD0BE7D, 0xC1DB9B, 0xBD17AB, 0x81A2CA, 0x5C6A08,
0x17552E, 0x550027, 0xF0147F, 0x8607E1, 0x640B14, 0x8D4196,
0xDEBE87, 0x2AFDDA, 0xB6256B, 0x34897B, 0xFEF305, 0x9EBFB9,
0x4F6A68, 0xA82A4A, 0x5AC44F, 0xBCF82D, 0x985AD7, 0x95C7F4,
0x8D4D0D, 0xA63A20, 0x5F57A4, 0xB13F14, 0x953880, 0x0120CC,
0x86DD71, 0xB6DEC9, 0xF560BF, 0x11654D, 0x6B0701, 0xACB08C,
0xD0C0B2, 0x485551, 0x0EFB1E, 0xC37295, 0x3B06A3, 0x3540C0,
0x7BDC06, 0xCC45E0, 0xFA294E, 0xC8CAD6, 0x41F3E8, 0xDE647C,
0xD8649B, 0x31BED9, 0xC397A4, 0xD45877, 0xC5E369, 0x13DAF0,
0x3C3ABA, 0x461846, 0x5F7555, 0xF5BDD2, 0xC6926E, 0x5D2EAC,
0xED440E, 0x423E1C, 0x87C461, 0xE9FD29, 0xF3D6E7, 0xCA7C22,
0x35916F, 0xC5E008, 0x8DD7FF, 0xE26A6E, 0xC6FDB0, 0xC10893,
0x745D7C, 0xB2AD6B, 0x9D6ECD, 0x7B723E, 0x6A11C6, 0xA9CFF7,
0xDF7329, 0xBAC9B5, 0x5100B7, 0x0DB2E2, 0x24BA74, 0x607DE5,
0x8AD874, 0x2C150D, 0x0C1881, 0x94667E, 0x162901, 0x767A9F,
0xBEFDFD, 0xEF4556, 0x367ED9, 0x13D9EC, 0xB9BA8B, 0xFC97C4,
0x27A831, 0xC36EF1, 0x36C594, 0x56A8D8, 0xB5A8B4, 0x0ECCCF,
0x2D8912, 0x34576F, 0x89562C, 0xE3CE99, 0xB920D6, 0xAA5E6B,
0x9C2A3E, 0xCC5F11, 0x4A0BFD, 0xFBF4E1, 0x6D3B8E, 0x2C86E2,
0x84D4E9, 0xA9B4FC, 0xD1EEEF, 0xC9352E, 0x61392F, 0x442138,
0xC8D91B, 0x0AFC81, 0x6A4AFB, 0xD81C2F, 0x84B453, 0x8C994E,
0xCC2254, 0xDC552A, 0xD6C6C0, 0x96190B, 0xB8701A, 0x649569,
0x605A26, 0xEE523F, 0x0F117F, 0x11B5F4, 0xF5CBFC, 0x2DBC34,
0xEEBC34, 0xCC5DE8, 0x605EDD, 0x9B8E67, 0xEF3392, 0xB817C9,
0x9B5861, 0xBC57E1, 0xC68351, 0x103ED8, 0x4871DD, 0xDD1C2D,
0xA118AF, 0x462C21, 0xD7F359, 0x987AD9, 0xC0549E, 0xFA864F,
0xFC0656, 0xAE79E5, 0x362289, 0x22AD38, 0xDC9367, 0xAAE855,
0x382682, 0x9BE7CA, 0xA40D51, 0xB13399, 0x0ED7A9, 0x480569,
0xF0B265, 0xA7887F, 0x974C88, 0x36D1F9, 0xB39221, 0x4A827B,
0x21CF98, 0xDC9F40, 0x5547DC, 0x3A74E1, 0x42EB67, 0xDF9DFE,
0x5FD45E, 0xA4677B, 0x7AACBA, 0xA2F655, 0x23882B, 0x55BA41,
0x086E59, 0x862A21, 0x834739, 0xE6E389, 0xD49EE5, 0x40FB49,
0xE956FF, 0xCA0F1C, 0x8A59C5, 0x2BFA94, 0xC5C1D3, 0xCFC50F,
0xAE5ADB, 0x86C547, 0x624385, 0x3B8621, 0x94792C, 0x876110,
0x7B4C2A, 0x1A2C80, 0x12BF43, 0x902688, 0x893C78, 0xE4C4A8,
0x7BDBE5, 0xC23AC4, 0xEAF426, 0x8A67F7, 0xBF920D, 0x2BA365,
0xB1933D, 0x0B7CBD, 0xDC51A4, 0x63DD27, 0xDDE169, 0x19949A,
0x9529A8, 0x28CE68, 0xB4ED09, 0x209F44, 0xCA984E, 0x638270,
0x237C7E, 0x32B90F, 0x8EF5A7, 0xE75614, 0x08F121, 0x2A9DB5,
0x4D7E6F, 0x5119A5, 0xABF9B5, 0xD6DF82, 0x61DD96, 0x023616,
0x9F3AC4, 0xA1A283, 0x6DED72, 0x7A8D39, 0xA9B882, 0x5C326B,
0x5B2746, 0xED3400, 0x7700D2, 0x55F4FC, 0x4D5901, 0x8071E0,
#endif
};
static const double PIo2[] = {
1.57079625129699707031e+00, /* 0x3FF921FB, 0x40000000 */
7.54978941586159635335e-08, /* 0x3E74442D, 0x00000000 */
5.39030252995776476554e-15, /* 0x3CF84698, 0x80000000 */
3.28200341580791294123e-22, /* 0x3B78CC51, 0x60000000 */
1.27065575308067607349e-29, /* 0x39F01B83, 0x80000000 */
1.22933308981111328932e-36, /* 0x387A2520, 0x40000000 */
2.73370053816464559624e-44, /* 0x36E38222, 0x80000000 */
2.16741683877804819444e-51, /* 0x3569F31D, 0x00000000 */
};
int __rem_pio2_large(double *x, double *y, int e0, int nx, int prec)
{
int32_t jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih;
double z,fw,f[20],fq[20],q[20];
/* initialize jk*/
jk = init_jk[prec];
jp = jk;
/* determine jx,jv,q0, note that 3>q0 */
jx = nx-1;
jv = (e0-3)/24; if(jv<0) jv=0;
q0 = e0-24*(jv+1);
/* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */
j = jv-jx; m = jx+jk;
for (i=0; i<=m; i++,j++)
f[i] = j<0 ? 0.0 : (double)ipio2[j];
/* compute q[0],q[1],...q[jk] */
for (i=0; i<=jk; i++) {
for (j=0,fw=0.0; j<=jx; j++)
fw += x[j]*f[jx+i-j];
q[i] = fw;
}
jz = jk;
recompute:
/* distill q[] into iq[] reversingly */
for (i=0,j=jz,z=q[jz]; j>0; i++,j--) {
fw = (double)(int32_t)(0x1p-24*z);
iq[i] = (int32_t)(z - 0x1p24*fw);
z = q[j-1]+fw;
}
/* compute n */
z = scalbn(z,q0); /* actual value of z */
z -= 8.0*floor(z*0.125); /* trim off integer >= 8 */
n = (int32_t)z;
z -= (double)n;
ih = 0;
if (q0 > 0) { /* need iq[jz-1] to determine n */
i = iq[jz-1]>>(24-q0); n += i;
iq[jz-1] -= i<<(24-q0);
ih = iq[jz-1]>>(23-q0);
}
else if (q0 == 0) ih = iq[jz-1]>>23;
else if (z >= 0.5) ih = 2;
if (ih > 0) { /* q > 0.5 */
n += 1; carry = 0;
for (i=0; i<jz; i++) { /* compute 1-q */
j = iq[i];
if (carry == 0) {
if (j != 0) {
carry = 1;
iq[i] = 0x1000000 - j;
}
} else
iq[i] = 0xffffff - j;
}
if (q0 > 0) { /* rare case: chance is 1 in 12 */
switch(q0) {
case 1:
iq[jz-1] &= 0x7fffff; break;
case 2:
iq[jz-1] &= 0x3fffff; break;
}
}
if (ih == 2) {
z = 1.0 - z;
if (carry != 0)
z -= scalbn(1.0,q0);
}
}
/* check if recomputation is needed */
if (z == 0.0) {
j = 0;
for (i=jz-1; i>=jk; i--) j |= iq[i];
if (j == 0) { /* need recomputation */
for (k=1; iq[jk-k]==0; k++); /* k = no. of terms needed */
for (i=jz+1; i<=jz+k; i++) { /* add q[jz+1] to q[jz+k] */
f[jx+i] = (double)ipio2[jv+i];
for (j=0,fw=0.0; j<=jx; j++)
fw += x[j]*f[jx+i-j];
q[i] = fw;
}
jz += k;
goto recompute;
}
}
/* chop off zero terms */
if (z == 0.0) {
jz -= 1;
q0 -= 24;
while (iq[jz] == 0) {
jz--;
q0 -= 24;
}
} else { /* break z into 24-bit if necessary */
z = scalbn(z,-q0);
if (z >= 0x1p24) {
fw = (double)(int32_t)(0x1p-24*z);
iq[jz] = (int32_t)(z - 0x1p24*fw);
jz += 1;
q0 += 24;
iq[jz] = (int32_t)fw;
} else
iq[jz] = (int32_t)z;
}
/* convert integer "bit" chunk to floating-point value */
fw = scalbn(1.0,q0);
for (i=jz; i>=0; i--) {
q[i] = fw*(double)iq[i];
fw *= 0x1p-24;
}
/* compute PIo2[0,...,jp]*q[jz,...,0] */
for(i=jz; i>=0; i--) {
for (fw=0.0,k=0; k<=jp && k<=jz-i; k++)
fw += PIo2[k]*q[i+k];
fq[jz-i] = fw;
}
/* compress fq[] into y[] */
switch(prec) {
case 0:
fw = 0.0;
for (i=jz; i>=0; i--)
fw += fq[i];
y[0] = ih==0 ? fw : -fw;
break;
case 1:
case 2:
fw = 0.0;
for (i=jz; i>=0; i--)
fw += fq[i];
// TODO: drop excess precision here once double_t is used
fw = (double)fw;
y[0] = ih==0 ? fw : -fw;
fw = fq[0]-fw;
for (i=1; i<=jz; i++)
fw += fq[i];
y[1] = ih==0 ? fw : -fw;
break;
case 3: /* painful */
for (i=jz; i>0; i--) {
fw = fq[i-1]+fq[i];
fq[i] += fq[i-1]-fw;
fq[i-1] = fw;
}
for (i=jz; i>1; i--) {
fw = fq[i-1]+fq[i];
fq[i] += fq[i-1]-fw;
fq[i-1] = fw;
}
for (fw=0.0,i=jz; i>=2; i--)
fw += fq[i];
if (ih==0) {
y[0] = fq[0]; y[1] = fq[1]; y[2] = fw;
} else {
y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw;
}
}
return n&7;
}
| 19,341 | 479 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/magicu.h | #ifndef COSMOPOLITAN_LIBC_TINYMATH_MAGICU_H_
#define COSMOPOLITAN_LIBC_TINYMATH_MAGICU_H_
#if !(__ASSEMBLER__ + __LINKER__ + 0)
COSMOPOLITAN_C_START_
struct magicu {
uint32_t M;
uint32_t s;
};
struct magicu __magicu_get(uint32_t);
/**
* Performs fast division using precomputed magic for constant divisor.
*
* @param x is unsigned integer that shall be divided
* @param d should be `__magicu_get(y)` if computing `x / y`
* @return result of unsigned integer division
*/
forceinline uint32_t __magicu_div(uint32_t x, struct magicu d) {
return ((((uint64_t)x * d.M) >> 32) + ((d.s & 64) ? x : 0)) >> (d.s & 63);
}
/**
* Checks if ð contains a valid initialized divisor.
*/
static inline bool __magicu_valid(struct magicu d) {
if (!d.M && !d.s) return false; /* uninitialized */
if (d.s & ~(64 | 63)) return false; /* corrupted */
return true;
}
COSMOPOLITAN_C_END_
#endif /* !(__ASSEMBLER__ + __LINKER__ + 0) */
#endif /* COSMOPOLITAN_LIBC_TINYMATH_MAGICU_H_ */
| 992 | 36 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/lrintf.c | /*-*- mode:c;indent-tabs-mode:nil;c-basic-offset:2;tab-width:8;coding:utf-8 -*-â
âvi: set net ft=c ts=2 sts=2 sw=2 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ¡
â Copyright 2023 Justine Alexandra Roberts Tunney â
â â
â Permission to use, copy, modify, and/or distribute this software for â
â any purpose with or without fee is hereby granted, provided that the â
â above copyright notice and this permission notice appear in all copies. â
â â
â THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL â
â WARRANTIES WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED â
â WARRANTIES OF MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE â
â AUTHOR BE LIABLE FOR ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL â
â DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR â
â PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER â
â TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR â
â PERFORMANCE OF THIS SOFTWARE. â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/math.h"
/**
* Rounds to integer in current rounding mode.
*
* The floating-point exception `FE_INEXACT` is raised if the result is
* different from the input.
*/
long lrintf(float x) {
long i;
#ifdef __x86_64__
asm("cvtss2si\t%1,%0" : "=r"(i) : "x"(x));
#elif defined(__aarch64__)
asm("frintx\t%s1,%s1\n\t"
"fcvtzs\t%x0,%s1"
: "=r"(i), "+w"(x));
#elif defined(__powerpc64__)
asm("fctid\t%0,%1" : "=d"(i) : "f"(x));
#else
i = rintf(x);
#endif /* __x86_64__ */
return i;
}
#if __SIZEOF_LONG__ == __SIZEOF_LONG_LONG__
__weak_reference(lrintf, llrintf);
#endif
| 2,439 | 46 | jart/cosmopolitan | false |
cosmopolitan/libc/tinymath/cabsl.c | /*-*- mode:c;indent-tabs-mode:nil;c-basic-offset:2;tab-width:8;coding:utf-8 -*-â
âvi: set net ft=c ts=2 sts=2 sw=2 fenc=utf-8 :viâ
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ¡
â Copyright 2023 Justine Alexandra Roberts Tunney â
â â
â Permission to use, copy, modify, and/or distribute this software for â
â any purpose with or without fee is hereby granted, provided that the â
â above copyright notice and this permission notice appear in all copies. â
â â
â THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL â
â WARRANTIES WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED â
â WARRANTIES OF MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE â
â AUTHOR BE LIABLE FOR ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL â
â DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR â
â PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER â
â TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR â
â PERFORMANCE OF THIS SOFTWARE. â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#include "libc/complex.h"
#include "libc/math.h"
#if !(LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024)
/**
* Returns absolute value of complex number.
*/
long double cabsl(long double complex z) {
return hypotl(creall(z), cimagl(z));
}
#endif /* long double is long */
| 2,108 | 31 | jart/cosmopolitan | false |
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