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first commit of the new libm!

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thanks to the hard work of Szabolcs Nagy (nsz), identifying the best
(from correctness and license standpoint) implementations from freebsd
and openbsd and cleaning them up! musl should now fully support c99
float and long double math functions, and has near-complete complex
math support. tgmath should also work (fully on gcc-compatible
compilers, and mostly on any c99 compiler).

based largely on commit 0376d44a890fea261506f1fc63833e7a686dca19 from
nsz's libm git repo, with some additions (dummy versions of a few
missing long double complex functions, etc.) by me.

various cleanups still need to be made, including re-adding (if
they're correct) some asm functions that were dropped.
This commit is contained in:
Rich Felker
2012-03-13 01:17:53 -04:00
parent d46cf2e14c
commit b69f695ace
378 changed files with 20552 additions and 7743 deletions
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55
src/math/acosh.c Normal file
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/* origin: FreeBSD /usr/src/lib/msun/src/e_acosh.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.
* ====================================================
*
*/
/* acosh(x)
* Method :
* Based on
* acosh(x) = log [ x + sqrt(x*x-1) ]
* we have
* acosh(x) := log(x)+ln2, if x is large; else
* acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else
* acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1.
*
* Special cases:
* acosh(x) is NaN with signal if x<1.
* acosh(NaN) is NaN without signal.
*/
#include "libm.h"
static const double
one = 1.0,
ln2 = 6.93147180559945286227e-01; /* 0x3FE62E42, 0xFEFA39EF */
double acosh(double x)
{
double t;
int32_t hx;
uint32_t lx;
EXTRACT_WORDS(hx, lx, x);
if (hx < 0x3ff00000) { /* x < 1 */
return (x-x)/(x-x);
} else if (hx >= 0x41b00000) { /* x > 2**28 */
if (hx >= 0x7ff00000) /* x is inf of NaN */
return x+x;
return log(x) + ln2; /* acosh(huge) = log(2x) */
} else if ((hx-0x3ff00000 | lx) == 0) {
return 0.0; /* acosh(1) = 0 */
} else if (hx > 0x40000000) { /* 2**28 > x > 2 */
t = x*x;
return log(2.0*x - one/(x+sqrt(t-one)));
} else { /* 1 < x < 2 */
t = x-one;
return log1p(t + sqrt(2.0*t+t*t));
}
}