mirror of
https://github.com/jart/cosmopolitan.git
synced 2025-01-31 11:37:35 +00:00
394d998315
At least in neovim, `│vi:` is not recognized as a modeline because it has no preceding whitespace. After fixing this, opening a file yields an error because `net` is not an option. (`noet`, however, is.)
219 lines
7.3 KiB
C
219 lines
7.3 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 © 2005-2020 Rich Felker, et al. │
|
||
│ │
|
||
│ Permission is hereby granted, free of charge, to any person obtaining │
|
||
│ a copy of this software and associated documentation files (the │
|
||
│ "Software"), to deal in the Software without restriction, including │
|
||
│ without limitation the rights to use, copy, modify, merge, publish, │
|
||
│ distribute, sublicense, and/or sell copies of the Software, and to │
|
||
│ permit persons to whom the Software is furnished to do so, subject to │
|
||
│ the following conditions: │
|
||
│ │
|
||
│ The above copyright notice and this permission notice shall be │
|
||
│ included in all copies or substantial portions of the Software. │
|
||
│ │
|
||
│ THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, │
|
||
│ EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF │
|
||
│ MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. │
|
||
│ IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY │
|
||
│ CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, │
|
||
│ TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE │
|
||
│ SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. │
|
||
│ │
|
||
╚─────────────────────────────────────────────────────────────────────────────*/
|
||
#include "libc/math.h"
|
||
#include "libc/tinymath/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 <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_logl.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.
|
||
*/
|
||
/*
|
||
* Natural logarithm, long double precision
|
||
*
|
||
*
|
||
* SYNOPSIS:
|
||
*
|
||
* long double x, y, logl();
|
||
*
|
||
* y = logl( x );
|
||
*
|
||
*
|
||
* DESCRIPTION:
|
||
*
|
||
* Returns the base e (2.718...) 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) = log(1+z/2) - log(1-z/2) = z + z**3 P(z)/Q(z).
|
||
*
|
||
*
|
||
* ACCURACY:
|
||
*
|
||
* Relative error:
|
||
* arithmetic domain # trials peak rms
|
||
* IEEE 0.5, 2.0 150000 8.71e-20 2.75e-20
|
||
* IEEE exp(+-10000) 100000 5.39e-20 2.34e-20
|
||
*
|
||
* In the tests over the interval exp(+-10000), the logarithms
|
||
* of the random arguments were uniformly distributed over
|
||
* [-10000, +10000].
|
||
*/
|
||
|
||
/* 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 natural logarithm of 𝑥.
|
||
*/
|
||
long double logl(long double x)
|
||
{
|
||
#ifdef __x86__
|
||
|
||
long double ln2;
|
||
asm("fldln2" : "=t"(ln2));
|
||
asm("fyl2x"
|
||
: "=t"(x)
|
||
: "0"(x), "u"(ln2)
|
||
: "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;
|
||
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;
|
||
x = 2.0*x - 1.0;
|
||
} else {
|
||
x = x - 1.0;
|
||
}
|
||
z = x*x;
|
||
y = x * (z * __polevll(x, P, 6) / __p1evll(x, Q, 6));
|
||
y = y + e * C2;
|
||
z = y - 0.5*z;
|
||
/* Note, the sum of above terms does not exceed x/4,
|
||
* so it contributes at most about 1/4 lsb to the error.
|
||
*/
|
||
z = z + x;
|
||
z = z + e * C1; /* This sum has an error of 1/2 lsb. */
|
||
return z;
|
||
|
||
#endif
|
||
}
|
||
|
||
#endif /* 80-bit floating point */
|