e_sinh.c revision 2116
10Sstevel@tonic-gate/* @(#)e_sinh.c 5.1 93/09/24 */ 20Sstevel@tonic-gate/* 30Sstevel@tonic-gate * ==================================================== 40Sstevel@tonic-gate * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 50Sstevel@tonic-gate * 60Sstevel@tonic-gate * Developed at SunPro, a Sun Microsystems, Inc. business. 70Sstevel@tonic-gate * Permission to use, copy, modify, and distribute this 80Sstevel@tonic-gate * software is freely granted, provided that this notice 90Sstevel@tonic-gate * is preserved. 100Sstevel@tonic-gate * ==================================================== 110Sstevel@tonic-gate */ 120Sstevel@tonic-gate 130Sstevel@tonic-gate#ifndef lint 140Sstevel@tonic-gatestatic char rcsid[] = "$Id: e_sinh.c,v 1.5 1994/08/18 23:06:03 jtc Exp $"; 150Sstevel@tonic-gate#endif 160Sstevel@tonic-gate 170Sstevel@tonic-gate/* __ieee754_sinh(x) 180Sstevel@tonic-gate * Method : 190Sstevel@tonic-gate * mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2 200Sstevel@tonic-gate * 1. Replace x by |x| (sinh(-x) = -sinh(x)). 210Sstevel@tonic-gate * 2. 220Sstevel@tonic-gate * E + E/(E+1) 230Sstevel@tonic-gate * 0 <= x <= 22 : sinh(x) := --------------, E=expm1(x) 240Sstevel@tonic-gate * 2 250Sstevel@tonic-gate * 260Sstevel@tonic-gate * 22 <= x <= lnovft : sinh(x) := exp(x)/2 270Sstevel@tonic-gate * lnovft <= x <= ln2ovft: sinh(x) := exp(x/2)/2 * exp(x/2) 280Sstevel@tonic-gate * ln2ovft < x : sinh(x) := x*shuge (overflow) 290Sstevel@tonic-gate * 300Sstevel@tonic-gate * Special cases: 310Sstevel@tonic-gate * sinh(x) is |x| if x is +INF, -INF, or NaN. 320Sstevel@tonic-gate * only sinh(0)=0 is exact for finite x. 330Sstevel@tonic-gate */ 340Sstevel@tonic-gate 350Sstevel@tonic-gate#include "math.h" 360Sstevel@tonic-gate#include "math_private.h" 370Sstevel@tonic-gate 380Sstevel@tonic-gate#ifdef __STDC__ 390Sstevel@tonic-gatestatic const double one = 1.0, shuge = 1.0e307; 400Sstevel@tonic-gate#else 410Sstevel@tonic-gatestatic double one = 1.0, shuge = 1.0e307; 420Sstevel@tonic-gate#endif 43 44#ifdef __STDC__ 45 double __ieee754_sinh(double x) 46#else 47 double __ieee754_sinh(x) 48 double x; 49#endif 50{ 51 double t,w,h; 52 int32_t ix,jx; 53 u_int32_t lx; 54 55 /* High word of |x|. */ 56 GET_HIGH_WORD(jx,x); 57 ix = jx&0x7fffffff; 58 59 /* x is INF or NaN */ 60 if(ix>=0x7ff00000) return x+x; 61 62 h = 0.5; 63 if (jx<0) h = -h; 64 /* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */ 65 if (ix < 0x40360000) { /* |x|<22 */ 66 if (ix<0x3e300000) /* |x|<2**-28 */ 67 if(shuge+x>one) return x;/* sinh(tiny) = tiny with inexact */ 68 t = expm1(fabs(x)); 69 if(ix<0x3ff00000) return h*(2.0*t-t*t/(t+one)); 70 return h*(t+t/(t+one)); 71 } 72 73 /* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */ 74 if (ix < 0x40862E42) return h*__ieee754_exp(fabs(x)); 75 76 /* |x| in [log(maxdouble), overflowthresold] */ 77 GET_LOW_WORD(lx,x); 78 if (ix<0x408633CE || (ix==0x408633ce)&&(lx<=(u_int32_t)0x8fb9f87d)) { 79 w = __ieee754_exp(0.5*fabs(x)); 80 t = h*w; 81 return t*w; 82 } 83 84 /* |x| > overflowthresold, sinh(x) overflow */ 85 return x*shuge; 86} 87