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 #ifndef lint 14 static char rcsid[] = "$FreeBSD$"; 15 #endif 16 17 /* __ieee754_sinh(x) 18 * Method : 19 * mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2 20 * 1. Replace x by |x| (sinh(-x) = -sinh(x)). 21 * 2. 22 * E + E/(E+1) 23 * 0 <= x <= 22 : sinh(x) := --------------, E=expm1(x) 24 * 2 25 * 26 * 22 <= x <= lnovft : sinh(x) := exp(x)/2 27 * lnovft <= x <= ln2ovft: sinh(x) := exp(x/2)/2 * exp(x/2) 28 * ln2ovft < x : sinh(x) := x*shuge (overflow) 29 * 30 * Special cases: 31 * sinh(x) is |x| if x is +INF, -INF, or NaN. 32 * only sinh(0)=0 is exact for finite x. 33 */ 34 35 #include "math.h" 36 #include "math_private.h" 37 38 #ifdef __STDC__ 39 static const double one = 1.0, shuge = 1.0e307; 40 #else 41 static double one = 1.0, shuge = 1.0e307; 42 #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