0,0 → 1,94 |
/* Copyright (C) 1995 DJ Delorie, see COPYING.DJ for details */ |
/* @(#)e_cosh.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_cosh.c,v 1.5 1994/08/18 23:05:15 jtc Exp $"; |
#endif |
|
/* __ieee754_cosh(x) |
* Method : |
* mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2 |
* 1. Replace x by |x| (cosh(x) = cosh(-x)). |
* 2. |
* [ exp(x) - 1 ]^2 |
* 0 <= x <= ln2/2 : cosh(x) := 1 + ------------------- |
* 2*exp(x) |
* |
* exp(x) + 1/exp(x) |
* ln2/2 <= x <= 22 : cosh(x) := ------------------- |
* 2 |
* 22 <= x <= lnovft : cosh(x) := exp(x)/2 |
* lnovft <= x <= ln2ovft: cosh(x) := exp(x/2)/2 * exp(x/2) |
* ln2ovft < x : cosh(x) := huge*huge (overflow) |
* |
* Special cases: |
* cosh(x) is |x| if x is +INF, -INF, or NaN. |
* only cosh(0)=1 is exact for finite x. |
*/ |
|
#include "math.h" |
#include "math_private.h" |
|
#ifdef __STDC__ |
static const double one = 1.0, half=0.5, huge = 1.0e300; |
#else |
static double one = 1.0, half=0.5, huge = 1.0e300; |
#endif |
|
#ifdef __STDC__ |
double __ieee754_cosh(double x) |
#else |
double __ieee754_cosh(x) |
double x; |
#endif |
{ |
double t,w; |
int32_t ix; |
u_int32_t lx; |
|
/* High word of |x|. */ |
GET_HIGH_WORD(ix,x); |
ix &= 0x7fffffff; |
|
/* x is INF or NaN */ |
if(ix>=0x7ff00000) return x*x; |
|
/* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */ |
if(ix<0x3fd62e43) { |
t = expm1(fabs(x)); |
w = one+t; |
if (ix<0x3c800000) return w; /* cosh(tiny) = 1 */ |
return one+(t*t)/(w+w); |
} |
|
/* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */ |
if (ix < 0x40360000) { |
t = __ieee754_exp(fabs(x)); |
return half*t+half/t; |
} |
|
/* |x| in [22, log(maxdouble)] return half*exp(|x|) */ |
if (ix < 0x40862E42) return half*__ieee754_exp(fabs(x)); |
|
/* |x| in [log(maxdouble), overflowthresold] */ |
GET_LOW_WORD(lx,x); |
if (ix<0x408633CE || |
((ix==0x408633ce)&&(lx<=(u_int32_t)0x8fb9f87dU))) { |
w = __ieee754_exp(half*fabs(x)); |
t = half*w; |
return t*w; |
} |
|
/* |x| > overflowthresold, cosh(x) overflow */ |
return huge*huge; |
} |