1 /* @(#)e_sinh.c 5.1 93/09/24 */ 2 /* 3 * ==================================================== 4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 5 * 6 * Developed at SunPro, a Sun Microsystems, Inc. business. 7 * Permission to use, copy, modify, and distribute this 8 * software is freely granted, provided that this notice 9 * is preserved. 10 * ==================================================== 11 */ 12 13 #include <sys/cdefs.h> 14 #if defined(LIBM_SCCS) && !defined(lint) 15 __RCSID("$NetBSD: e_sinh.c,v 1.11 2002/05/26 22:01:52 wiz Exp $"); 16 #endif 17 18 /* __ieee754_sinh(x) 19 * Method : 20 * mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2 21 * 1. Replace x by |x| (sinh(-x) = -sinh(x)). 22 * 2. 23 * E + E/(E+1) 24 * 0 <= x <= 22 : sinh(x) := --------------, E=expm1(x) 25 * 2 26 * 27 * 22 <= x <= lnovft : sinh(x) := exp(x)/2 28 * lnovft <= x <= ln2ovft: sinh(x) := exp(x/2)/2 * exp(x/2) 29 * ln2ovft < x : sinh(x) := x*shuge (overflow) 30 * 31 * Special cases: 32 * sinh(x) is |x| if x is +INF, -INF, or NaN. 33 * only sinh(0)=0 is exact for finite x. 34 */ 35 36 #include "math.h" 37 #include "math_private.h" 38 39 static const double one = 1.0, shuge = 1.0e307; 40 41 double 42 __ieee754_sinh(double x) 43 { 44 double t,w,h; 45 int32_t ix,jx; 46 u_int32_t lx; 47 48 /* High word of |x|. */ 49 GET_HIGH_WORD(jx,x); 50 ix = jx&0x7fffffff; 51 52 /* x is INF or NaN */ 53 if(ix>=0x7ff00000) return x+x; 54 55 h = 0.5; 56 if (jx<0) h = -h; 57 /* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */ 58 if (ix < 0x40360000) { /* |x|<22 */ 59 if (ix<0x3e300000) /* |x|<2**-28 */ 60 if(shuge+x>one) return x;/* sinh(tiny) = tiny with inexact */ 61 t = expm1(fabs(x)); 62 if(ix<0x3ff00000) return h*(2.0*t-t*t/(t+one)); 63 return h*(t+t/(t+one)); 64 } 65 66 /* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */ 67 if (ix < 0x40862E42) return h*__ieee754_exp(fabs(x)); 68 69 /* |x| in [log(maxdouble), overflowthresold] */ 70 GET_LOW_WORD(lx,x); 71 if (ix<0x408633CE || ((ix==0x408633ce)&&(lx<=(u_int32_t)0x8fb9f87d))) { 72 w = __ieee754_exp(0.5*fabs(x)); 73 t = h*w; 74 return t*w; 75 } 76 77 /* |x| > overflowthresold, sinh(x) overflow */ 78 return x*shuge; 79 } 80