/* @(#)e_sinh.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. | |
* ==================================================== | |
*/ | |
#include <LibConfig.h> | |
#include <sys/EfiCdefs.h> | |
#if defined(LIBM_SCCS) && !defined(lint) | |
__RCSID("$NetBSD: e_sinh.c,v 1.11 2002/05/26 22:01:52 wiz Exp $"); | |
#endif | |
#include "math.h" | |
#include "math_private.h" | |
/* __ieee754_sinh(x) | |
* Method : | |
* mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2 | |
* 1. Replace x by |x| (sinh(-x) = -sinh(x)). | |
* 2. | |
* E + E/(E+1) | |
* 0 <= x <= 22 : sinh(x) := --------------, E=expm1(x) | |
* 2 | |
* | |
* 22 <= x <= lnovft : sinh(x) := exp(x)/2 | |
* lnovft <= x <= ln2ovft: sinh(x) := exp(x/2)/2 * exp(x/2) | |
* ln2ovft < x : sinh(x) := x*shuge (overflow) | |
* | |
* Special cases: | |
* sinh(x) is |x| if x is +INF, -INF, or NaN. | |
* only sinh(0)=0 is exact for finite x. | |
*/ | |
static const double one = 1.0, shuge = 1.0e307; | |
double | |
__ieee754_sinh(double x) | |
{ | |
double t,w,h; | |
int32_t ix,jx; | |
u_int32_t lx; | |
/* High word of |x|. */ | |
GET_HIGH_WORD(jx,x); | |
ix = jx&0x7fffffff; | |
/* x is INF or NaN */ | |
if(ix>=0x7ff00000) return x+x; | |
h = 0.5; | |
if (jx<0) h = -h; | |
/* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */ | |
if (ix < 0x40360000) { /* |x|<22 */ | |
if (ix<0x3e300000) /* |x|<2**-28 */ | |
if(shuge+x>one) return x;/* sinh(tiny) = tiny with inexact */ | |
t = expm1(fabs(x)); | |
if(ix<0x3ff00000) return h*(2.0*t-t*t/(t+one)); | |
return h*(t+t/(t+one)); | |
} | |
/* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */ | |
if (ix < 0x40862E42) return h*__ieee754_exp(fabs(x)); | |
/* |x| in [log(maxdouble), overflowthresold] */ | |
GET_LOW_WORD(lx,x); | |
if (ix<0x408633CE || ((ix==0x408633ce)&&(lx<=(u_int32_t)0x8fb9f87d))) { | |
w = __ieee754_exp(0.5*fabs(x)); | |
t = h*w; | |
return t*w; | |
} | |
/* |x| > overflowthresold, sinh(x) overflow */ | |
return x*shuge; | |
} |