mirror of
https://sourceware.org/git/glibc.git
synced 2024-12-25 20:21:07 +00:00
70 lines
1.8 KiB
C
70 lines
1.8 KiB
C
/* @(#)e_acosh.c 5.1 93/09/24 */
|
|
/*
|
|
* ====================================================
|
|
* 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.
|
|
* ====================================================
|
|
*/
|
|
|
|
/* __ieee754_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 <math.h>
|
|
#include <math_private.h>
|
|
|
|
static const double
|
|
one = 1.0,
|
|
ln2 = 6.93147180559945286227e-01; /* 0x3FE62E42, 0xFEFA39EF */
|
|
|
|
double
|
|
__ieee754_acosh (double x)
|
|
{
|
|
double t;
|
|
int32_t hx;
|
|
u_int32_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;
|
|
}
|
|
else
|
|
return __ieee754_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 __ieee754_log (2.0 * x - one / (x + __ieee754_sqrt (t - one)));
|
|
}
|
|
else /* 1<x<2 */
|
|
{
|
|
t = x - one;
|
|
return __log1p (t + __ieee754_sqrt (2.0 * t + t * t));
|
|
}
|
|
}
|
|
strong_alias (__ieee754_acosh, __acosh_finite)
|