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 /* sinhl(x) 14 * Method : 15 * mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2 16 * 1. Replace x by |x| (sinhl(-x) = -sinhl(x)). 17 * 2. 18 * E + E/(E+1) 19 * 0 <= x <= 25 : sinhl(x) := --------------, E=expm1l(x) 20 * 2 21 * 22 * 25 <= x <= lnovft : sinhl(x) := expl(x)/2 23 * lnovft <= x <= ln2ovft: sinhl(x) := expl(x/2)/2 * expl(x/2) 24 * ln2ovft < x : sinhl(x) := x*shuge (overflow) 25 * 26 * Special cases: 27 * sinhl(x) is |x| if x is +INF, -INF, or NaN. 28 * only sinhl(0)=0 is exact for finite x. 29 */ 30 31 #include <math.h> 32 33 #include "math_private.h" 34 35 static const long double one = 1.0, shuge = 1.0e4931L; 36 37 long double 38 sinhl(long double x) 39 { 40 long double t,w,h; 41 u_int32_t jx,ix,i0,i1; 42 43 /* Words of |x|. */ 44 GET_LDOUBLE_WORDS(jx,i0,i1,x); 45 ix = jx&0x7fff; 46 47 /* x is INF or NaN */ 48 if(ix==0x7fff) return x+x; 49 50 h = 0.5; 51 if (jx & 0x8000) h = -h; 52 /* |x| in [0,25], return sign(x)*0.5*(E+E/(E+1))) */ 53 if (ix < 0x4003 || (ix == 0x4003 && i0 <= 0xc8000000)) { /* |x|<25 */ 54 if (ix<0x3fdf) /* |x|<2**-32 */ 55 if(shuge+x>one) return x;/* sinh(tiny) = tiny with inexact */ 56 t = expm1l(fabsl(x)); 57 if(ix<0x3fff) return h*(2.0*t-t*t/(t+one)); 58 return h*(t+t/(t+one)); 59 } 60 61 /* |x| in [25, log(maxdouble)] return 0.5*exp(|x|) */ 62 if (ix < 0x400c || (ix == 0x400c && i0 < 0xb17217f7)) 63 return h*expl(fabsl(x)); 64 65 /* |x| in [log(maxdouble), overflowthreshold] */ 66 if (ix<0x400c || (ix == 0x400c && (i0 < 0xb174ddc0 67 || (i0 == 0xb174ddc0 68 && i1 <= 0x31aec0ea)))) { 69 w = expl(0.5*fabsl(x)); 70 t = h*w; 71 return t*w; 72 } 73 74 /* |x| > overflowthreshold, sinhl(x) overflow */ 75 return x*shuge; 76 } 77