mirror of
https://github.com/jart/cosmopolitan.git
synced 2025-01-31 19:43:32 +00:00
228 lines
7.6 KiB
C
228 lines
7.6 KiB
C
/*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-│
|
|
│vi: set et ft=c ts=8 tw=8 fenc=utf-8 :vi│
|
|
╚──────────────────────────────────────────────────────────────────────────────╝
|
|
│ │
|
|
│ Musl Libc │
|
|
│ Copyright © 2005-2014 Rich Felker, et al. │
|
|
│ │
|
|
│ Permission is hereby granted, free of charge, to any person obtaining │
|
|
│ a copy of this software and associated documentation files (the │
|
|
│ "Software"), to deal in the Software without restriction, including │
|
|
│ without limitation the rights to use, copy, modify, merge, publish, │
|
|
│ distribute, sublicense, and/or sell copies of the Software, and to │
|
|
│ permit persons to whom the Software is furnished to do so, subject to │
|
|
│ the following conditions: │
|
|
│ │
|
|
│ The above copyright notice and this permission notice shall be │
|
|
│ included in all copies or substantial portions of the Software. │
|
|
│ │
|
|
│ THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, │
|
|
│ EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF │
|
|
│ MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. │
|
|
│ IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY │
|
|
│ CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, │
|
|
│ TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE │
|
|
│ SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. │
|
|
│ │
|
|
╚─────────────────────────────────────────────────────────────────────────────*/
|
|
#include "libc/math.h"
|
|
#include "libc/tinymath/internal.h"
|
|
|
|
asm(".ident\t\"\\n\\n\
|
|
OpenBSD libm (MIT License)\\n\
|
|
Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>\"");
|
|
asm(".ident\t\"\\n\\n\
|
|
Musl libc (MIT License)\\n\
|
|
Copyright 2005-2014 Rich Felker, et. al.\"");
|
|
asm(".include \"libc/disclaimer.inc\"");
|
|
/* clang-format off */
|
|
|
|
/* origin: OpenBSD /usr/src/lib/libm/src/ld80/e_log10l.c */
|
|
/*
|
|
* Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>
|
|
*
|
|
* Permission to use, copy, modify, and distribute this software for any
|
|
* purpose with or without fee is hereby granted, provided that the above
|
|
* copyright notice and this permission notice appear in all copies.
|
|
*
|
|
* THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
|
|
* WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
|
|
* MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
|
|
* ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
|
|
* WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
|
|
* ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
|
|
* OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
|
|
*/
|
|
/*
|
|
* Common logarithm, long double precision
|
|
*
|
|
*
|
|
* SYNOPSIS:
|
|
*
|
|
* long double x, y, log10l();
|
|
*
|
|
* y = log10l( x );
|
|
*
|
|
*
|
|
* DESCRIPTION:
|
|
*
|
|
* Returns the base 10 logarithm of x.
|
|
*
|
|
* The argument is separated into its exponent and fractional
|
|
* parts. If the exponent is between -1 and +1, the logarithm
|
|
* of the fraction is approximated by
|
|
*
|
|
* log(1+x) = x - 0.5 x**2 + x**3 P(x)/Q(x).
|
|
*
|
|
* Otherwise, setting z = 2(x-1)/x+1),
|
|
*
|
|
* log(x) = z + z**3 P(z)/Q(z).
|
|
*
|
|
*
|
|
* ACCURACY:
|
|
*
|
|
* Relative error:
|
|
* arithmetic domain # trials peak rms
|
|
* IEEE 0.5, 2.0 30000 9.0e-20 2.6e-20
|
|
* IEEE exp(+-10000) 30000 6.0e-20 2.3e-20
|
|
*
|
|
* In the tests over the interval exp(+-10000), the logarithms
|
|
* of the random arguments were uniformly distributed over
|
|
* [-10000, +10000].
|
|
*
|
|
* ERROR MESSAGES:
|
|
*
|
|
* log singularity: x = 0; returns MINLOG
|
|
* log domain: x < 0; returns MINLOG
|
|
*/
|
|
|
|
#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
|
|
long double log10l(long double x)
|
|
{
|
|
return log10(x);
|
|
}
|
|
#elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384
|
|
/* Coefficients for log(1+x) = x - x**2/2 + x**3 P(x)/Q(x)
|
|
* 1/sqrt(2) <= x < sqrt(2)
|
|
* Theoretical peak relative error = 6.2e-22
|
|
*/
|
|
static const long double P[] = {
|
|
4.9962495940332550844739E-1L,
|
|
1.0767376367209449010438E1L,
|
|
7.7671073698359539859595E1L,
|
|
2.5620629828144409632571E2L,
|
|
4.2401812743503691187826E2L,
|
|
3.4258224542413922935104E2L,
|
|
1.0747524399916215149070E2L,
|
|
};
|
|
static const long double Q[] = {
|
|
/* 1.0000000000000000000000E0,*/
|
|
2.3479774160285863271658E1L,
|
|
1.9444210022760132894510E2L,
|
|
7.7952888181207260646090E2L,
|
|
1.6911722418503949084863E3L,
|
|
2.0307734695595183428202E3L,
|
|
1.2695660352705325274404E3L,
|
|
3.2242573199748645407652E2L,
|
|
};
|
|
|
|
/* Coefficients for log(x) = z + z^3 P(z^2)/Q(z^2),
|
|
* where z = 2(x-1)/(x+1)
|
|
* 1/sqrt(2) <= x < sqrt(2)
|
|
* Theoretical peak relative error = 6.16e-22
|
|
*/
|
|
static const long double R[4] = {
|
|
1.9757429581415468984296E-3L,
|
|
-7.1990767473014147232598E-1L,
|
|
1.0777257190312272158094E1L,
|
|
-3.5717684488096787370998E1L,
|
|
};
|
|
static const long double S[4] = {
|
|
/* 1.00000000000000000000E0L,*/
|
|
-2.6201045551331104417768E1L,
|
|
1.9361891836232102174846E2L,
|
|
-4.2861221385716144629696E2L,
|
|
};
|
|
/* log10(2) */
|
|
#define L102A 0.3125L
|
|
#define L102B -1.1470004336018804786261e-2L
|
|
/* log10(e) */
|
|
#define L10EA 0.5L
|
|
#define L10EB -6.5705518096748172348871e-2L
|
|
|
|
#define SQRTH 0.70710678118654752440L
|
|
|
|
long double log10l(long double x)
|
|
{
|
|
long double y, z;
|
|
int e;
|
|
|
|
if (isnan(x))
|
|
return x;
|
|
if(x <= 0.0) {
|
|
if(x == 0.0)
|
|
return -1.0 / (x*x);
|
|
return (x - x) / 0.0;
|
|
}
|
|
if (x == INFINITY)
|
|
return INFINITY;
|
|
/* separate mantissa from exponent */
|
|
/* Note, frexp is used so that denormal numbers
|
|
* will be handled properly.
|
|
*/
|
|
x = frexpl(x, &e);
|
|
|
|
/* logarithm using log(x) = z + z**3 P(z)/Q(z),
|
|
* where z = 2(x-1)/x+1)
|
|
*/
|
|
if (e > 2 || e < -2) {
|
|
if (x < SQRTH) { /* 2(2x-1)/(2x+1) */
|
|
e -= 1;
|
|
z = x - 0.5;
|
|
y = 0.5 * z + 0.5;
|
|
} else { /* 2 (x-1)/(x+1) */
|
|
z = x - 0.5;
|
|
z -= 0.5;
|
|
y = 0.5 * x + 0.5;
|
|
}
|
|
x = z / y;
|
|
z = x*x;
|
|
y = x * (z * __polevll(z, R, 3) / __p1evll(z, S, 3));
|
|
goto done;
|
|
}
|
|
|
|
/* logarithm using log(1+x) = x - .5x**2 + x**3 P(x)/Q(x) */
|
|
if (x < SQRTH) {
|
|
e -= 1;
|
|
x = 2.0*x - 1.0;
|
|
} else {
|
|
x = x - 1.0;
|
|
}
|
|
z = x*x;
|
|
y = x * (z * __polevll(x, P, 6) / __p1evll(x, Q, 7));
|
|
y = y - 0.5*z;
|
|
|
|
done:
|
|
/* Multiply log of fraction by log10(e)
|
|
* and base 2 exponent by log10(2).
|
|
*
|
|
* ***CAUTION***
|
|
*
|
|
* This sequence of operations is critical and it may
|
|
* be horribly defeated by some compiler optimizers.
|
|
*/
|
|
z = y * (L10EB);
|
|
z += x * (L10EB);
|
|
z += e * (L102B);
|
|
z += y * (L10EA);
|
|
z += x * (L10EA);
|
|
z += e * (L102A);
|
|
return z;
|
|
}
|
|
#elif LDBL_MANT_DIG == 113 && LDBL_MAX_EXP == 16384
|
|
// TODO: broken implementation to make things compile
|
|
long double log10l(long double x)
|
|
{
|
|
return log10(x);
|
|
}
|
|
#endif
|