mirror of
https://sourceware.org/git/glibc.git
synced 2024-12-20 17:51:16 +00:00
70 lines
1.7 KiB
C
70 lines
1.7 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.
|
||
|
|
* ====================================================
|
||
|
|
*/
|
||
|
|
|
||
|
|
#if defined(LIBM_SCCS) && !defined(lint)
|
||
|
|
static char rcsid[] = "$NetBSD: e_acosh.c,v 1.9 1995/05/12 04:57:18 jtc Exp $";
|
||
|
|
#endif
|
||
|
|
|
||
|
|
/* __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"
|
||
|
|
|
||
|
|
#ifdef __STDC__
|
||
|
|
static const double
|
||
|
|
#else
|
||
|
|
static double
|
||
|
|
#endif
|
||
|
|
one = 1.0,
|
||
|
|
ln2 = 6.93147180559945286227e-01; /* 0x3FE62E42, 0xFEFA39EF */
|
||
|
|
|
||
|
|
#ifdef __STDC__
|
||
|
|
double __ieee754_acosh(double x)
|
||
|
|
#else
|
||
|
|
double __ieee754_acosh(x)
|
||
|
|
double x;
|
||
|
|
#endif
|
||
|
|
{
|
||
|
|
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+__sqrt(2.0*t+t*t));
|
||
|
|
}
|
||
|
|
}
|