mirror of
https://github.com/jart/cosmopolitan.git
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592f6ebc20
- Write some more unit tests - memcpy() on ARM is now faster - Address the Musl complex math FIXME comments - Some libm funcs like pow() now support setting errno - Import the latest and greatest math functions from ARM - Use more accurate atan2f() and log1pf() implementations - atoi() and atol() will no longer saturate or clobber errno
140 lines
5.7 KiB
C
140 lines
5.7 KiB
C
/*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-│
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│ vi: set noet ft=c ts=8 sw=8 fenc=utf-8 :vi │
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╚──────────────────────────────────────────────────────────────────────────────╝
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│ │
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│ Musl Libc │
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│ Copyright © 2005-2014 Rich Felker, et al. │
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│ │
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│ Permission is hereby granted, free of charge, to any person obtaining │
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│ a copy of this software and associated documentation files (the │
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│ "Software"), to deal in the Software without restriction, including │
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│ without limitation the rights to use, copy, modify, merge, publish, │
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│ distribute, sublicense, and/or sell copies of the Software, and to │
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│ permit persons to whom the Software is furnished to do so, subject to │
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│ the following conditions: │
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│ │
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│ The above copyright notice and this permission notice shall be │
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│ included in all copies or substantial portions of the Software. │
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│ │
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│ THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, │
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│ EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF │
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│ MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. │
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│ IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY │
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│ CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, │
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│ TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE │
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│ SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. │
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│ │
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╚─────────────────────────────────────────────────────────────────────────────*/
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#include "libc/intrin/likely.h"
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#include "libc/math.h"
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#include "libc/tinymath/complex.internal.h"
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#include "libc/tinymath/internal.h"
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__static_yoink("musl_libc_notice");
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__static_yoink("fdlibm_notice");
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/* origin: FreeBSD /usr/src/lib/msun/src/e_log10.c */
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/*
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* ====================================================
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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*
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* Developed at SunSoft, a Sun Microsystems, Inc. business.
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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* is preserved.
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* ====================================================
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*/
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/*
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* Return the base 10 logarithm of x. See log.c for most comments.
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*
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* Reduce x to 2^k (1+f) and calculate r = log(1+f) - f + f*f/2
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* as in log.c, then combine and scale in extra precision:
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* log10(x) = (f - f*f/2 + r)/log(10) + k*log10(2)
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*/
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static const double
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ivln10hi = 4.34294481878168880939e-01, /* 0x3fdbcb7b, 0x15200000 */
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ivln10lo = 2.50829467116452752298e-11, /* 0x3dbb9438, 0xca9aadd5 */
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log10_2hi = 3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */
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log10_2lo = 3.69423907715893078616e-13, /* 0x3D59FEF3, 0x11F12B36 */
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Lg1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */
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Lg2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */
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Lg3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */
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Lg4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */
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Lg5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */
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Lg6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */
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Lg7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */
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/**
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* Calculates log₁₀𝑥.
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*/
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double log10(double x)
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{
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union {double f; uint64_t i;} u = {x};
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double_t hfsq,f,s,z,R,w,t1,t2,dk,y,hi,lo,val_hi,val_lo;
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uint32_t hx;
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int k;
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hx = u.i>>32;
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k = 0;
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if (hx < 0x00100000 || hx>>31) {
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if (u.i<<1 == 0)
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return -1/(x*x); /* log(+-0)=-inf */
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if (hx>>31)
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return (x-x)/0.0; /* log(-#) = NaN */
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/* subnormal number, scale x up */
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k -= 54;
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x *= 0x1p54;
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u.f = x;
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hx = u.i>>32;
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} else if (hx >= 0x7ff00000) {
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return x;
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} else if (hx == 0x3ff00000 && u.i<<32 == 0)
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return 0;
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/* reduce x into [sqrt(2)/2, sqrt(2)] */
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hx += 0x3ff00000 - 0x3fe6a09e;
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k += (int)(hx>>20) - 0x3ff;
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hx = (hx&0x000fffff) + 0x3fe6a09e;
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u.i = (uint64_t)hx<<32 | (u.i&0xffffffff);
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x = u.f;
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f = x - 1.0;
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hfsq = 0.5*f*f;
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s = f/(2.0+f);
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z = s*s;
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w = z*z;
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t1 = w*(Lg2+w*(Lg4+w*Lg6));
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t2 = z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7)));
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R = t2 + t1;
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/* See log2.c for details. */
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/* hi+lo = f - hfsq + s*(hfsq+R) ~ log(1+f) */
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hi = f - hfsq;
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u.f = hi;
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u.i &= (uint64_t)-1<<32;
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hi = u.f;
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lo = f - hi - hfsq + s*(hfsq+R);
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/* val_hi+val_lo ~ log10(1+f) + k*log10(2) */
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val_hi = hi*ivln10hi;
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dk = k;
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y = dk*log10_2hi;
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val_lo = dk*log10_2lo + (lo+hi)*ivln10lo + lo*ivln10hi;
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/*
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* Extra precision in for adding y is not strictly needed
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* since there is no very large cancellation near x = sqrt(2) or
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* x = 1/sqrt(2), but we do it anyway since it costs little on CPUs
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* with some parallelism and it reduces the error for many args.
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*/
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w = y + val_hi;
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val_lo += (y - w) + val_hi;
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val_hi = w;
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return val_lo + val_hi;
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}
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#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
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__weak_reference(log10, log10l);
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#endif
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