1 2 /* @(#)e_sinh.c 1.3 95/01/18 */ 3 /* 4 * ==================================================== 5 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 6 * 7 * Developed at SunSoft, a Sun Microsystems, Inc. business. 8 * Permission to use, copy, modify, and distribute this 9 * software is freely granted, provided that this notice 10 * is preserved. 11 * ==================================================== 12 */ 13 14 /* __ieee754_sinh(x) 15 * Method : 16 * mathematically ieee_sinh(x) if defined to be (ieee_exp(x)-ieee_exp(-x))/2 17 * 1. Replace x by |x| (ieee_sinh(-x) = -ieee_sinh(x)). 18 * 2. 19 * E + E/(E+1) 20 * 0 <= x <= 22 : ieee_sinh(x) := --------------, E=ieee_expm1(x) 21 * 2 22 * 23 * 22 <= x <= lnovft : ieee_sinh(x) := ieee_exp(x)/2 24 * lnovft <= x <= ln2ovft: ieee_sinh(x) := ieee_exp(x/2)/2 * ieee_exp(x/2) 25 * ln2ovft < x : ieee_sinh(x) := x*shuge (overflow) 26 * 27 * Special cases: 28 * sinh(x) is |x| if x is +INF, -INF, or NaN. 29 * only ieee_sinh(0)=0 is exact for finite x. 30 */ 31 32 #include "fdlibm.h" 33 34 #ifdef __STDC__ 35 static const double one = 1.0, shuge = 1.0e307; 36 #else 37 static double one = 1.0, shuge = 1.0e307; 38 #endif 39 40 #ifdef __STDC__ __ieee754_sinh(double x)41 double __ieee754_sinh(double x) 42 #else 43 double __ieee754_sinh(x) 44 double x; 45 #endif 46 { 47 double t,w,h; 48 int ix,jx; 49 unsigned lx; 50 51 /* High word of |x|. */ 52 jx = __HI(x); 53 ix = jx&0x7fffffff; 54 55 /* x is INF or NaN */ 56 if(ix>=0x7ff00000) return x+x; 57 58 h = 0.5; 59 if (jx<0) h = -h; 60 /* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */ 61 if (ix < 0x40360000) { /* |x|<22 */ 62 if (ix<0x3e300000) /* |x|<2**-28 */ 63 if(shuge+x>one) return x;/* ieee_sinh(tiny) = tiny with inexact */ 64 t = ieee_expm1(ieee_fabs(x)); 65 if(ix<0x3ff00000) return h*(2.0*t-t*t/(t+one)); 66 return h*(t+t/(t+one)); 67 } 68 69 /* |x| in [22, ieee_log(maxdouble)] return 0.5*ieee_exp(|x|) */ 70 if (ix < 0x40862E42) return h*__ieee754_exp(ieee_fabs(x)); 71 72 /* |x| in [log(maxdouble), overflowthresold] */ 73 lx = *( (((*(unsigned*)&one)>>29)) + (unsigned*)&x); 74 if (ix<0x408633CE || (ix==0x408633ce)&&(lx<=(unsigned)0x8fb9f87d)) { 75 w = __ieee754_exp(0.5*ieee_fabs(x)); 76 t = h*w; 77 return t*w; 78 } 79 80 /* |x| > overflowthresold, ieee_sinh(x) overflow */ 81 return x*shuge; 82 } 83