0,0 → 1,70 |
/* Copyright (C) 1994 DJ Delorie, see COPYING.DJ for details */ |
/* @(#)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[] = "$Id: e_acosh.c,v 1.6 1994/08/18 23:04:54 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+sqrt(t-one))); |
} else { /* 1<x<2 */ |
t = x-one; |
return log1p(t+sqrt(2.0*t+t*t)); |
} |
} |