e_sinh.c revision 50476
12116Sjkh/* @(#)e_sinh.c 5.1 93/09/24 */ 22116Sjkh/* 32116Sjkh * ==================================================== 42116Sjkh * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 52116Sjkh * 62116Sjkh * Developed at SunPro, a Sun Microsystems, Inc. business. 72116Sjkh * Permission to use, copy, modify, and distribute this 88870Srgrimes * software is freely granted, provided that this notice 92116Sjkh * is preserved. 102116Sjkh * ==================================================== 112116Sjkh */ 122116Sjkh 132116Sjkh#ifndef lint 1450476Speterstatic char rcsid[] = "$FreeBSD: head/lib/msun/src/e_sinh.c 50476 1999-08-28 00:22:10Z peter $"; 152116Sjkh#endif 162116Sjkh 172116Sjkh/* __ieee754_sinh(x) 188870Srgrimes * Method : 192116Sjkh * mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2 208870Srgrimes * 1. Replace x by |x| (sinh(-x) = -sinh(x)). 218870Srgrimes * 2. 222116Sjkh * E + E/(E+1) 232116Sjkh * 0 <= x <= 22 : sinh(x) := --------------, E=expm1(x) 242116Sjkh * 2 252116Sjkh * 268870Srgrimes * 22 <= x <= lnovft : sinh(x) := exp(x)/2 272116Sjkh * lnovft <= x <= ln2ovft: sinh(x) := exp(x/2)/2 * exp(x/2) 282116Sjkh * ln2ovft < x : sinh(x) := x*shuge (overflow) 292116Sjkh * 302116Sjkh * Special cases: 312116Sjkh * sinh(x) is |x| if x is +INF, -INF, or NaN. 322116Sjkh * only sinh(0)=0 is exact for finite x. 332116Sjkh */ 342116Sjkh 352116Sjkh#include "math.h" 362116Sjkh#include "math_private.h" 372116Sjkh 382116Sjkh#ifdef __STDC__ 392116Sjkhstatic const double one = 1.0, shuge = 1.0e307; 402116Sjkh#else 412116Sjkhstatic double one = 1.0, shuge = 1.0e307; 422116Sjkh#endif 432116Sjkh 442116Sjkh#ifdef __STDC__ 452116Sjkh double __ieee754_sinh(double x) 462116Sjkh#else 472116Sjkh double __ieee754_sinh(x) 482116Sjkh double x; 492116Sjkh#endif 508870Srgrimes{ 512116Sjkh double t,w,h; 522116Sjkh int32_t ix,jx; 532116Sjkh u_int32_t lx; 542116Sjkh 552116Sjkh /* High word of |x|. */ 562116Sjkh GET_HIGH_WORD(jx,x); 572116Sjkh ix = jx&0x7fffffff; 582116Sjkh 592116Sjkh /* x is INF or NaN */ 608870Srgrimes if(ix>=0x7ff00000) return x+x; 612116Sjkh 622116Sjkh h = 0.5; 632116Sjkh if (jx<0) h = -h; 642116Sjkh /* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */ 652116Sjkh if (ix < 0x40360000) { /* |x|<22 */ 662116Sjkh if (ix<0x3e300000) /* |x|<2**-28 */ 672116Sjkh if(shuge+x>one) return x;/* sinh(tiny) = tiny with inexact */ 682116Sjkh t = expm1(fabs(x)); 692116Sjkh if(ix<0x3ff00000) return h*(2.0*t-t*t/(t+one)); 702116Sjkh return h*(t+t/(t+one)); 712116Sjkh } 722116Sjkh 732116Sjkh /* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */ 742116Sjkh if (ix < 0x40862E42) return h*__ieee754_exp(fabs(x)); 752116Sjkh 762116Sjkh /* |x| in [log(maxdouble), overflowthresold] */ 772116Sjkh GET_LOW_WORD(lx,x); 7817141Sjkh if (ix<0x408633CE || ((ix==0x408633ce)&&(lx<=(u_int32_t)0x8fb9f87d))) { 792116Sjkh w = __ieee754_exp(0.5*fabs(x)); 802116Sjkh t = h*w; 812116Sjkh return t*w; 822116Sjkh } 832116Sjkh 842116Sjkh /* |x| > overflowthresold, sinh(x) overflow */ 852116Sjkh return x*shuge; 862116Sjkh} 87