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 /* sinh(x) 14 * Method : 15 * mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2 16 * 1. Replace x by |x| (sinh(-x) = -sinh(x)). 17 * 2. 18 * E + E/(E+1) 19 * 0 <= x <= 22 : sinh(x) := --------------, E=expm1(x) 20 * 2 21 * 22 * 22 <= x <= lnovft : sinh(x) := exp(x)/2 23 * lnovft <= x <= ln2ovft: sinh(x) := exp(x/2)/2 * exp(x/2) 24 * ln2ovft < x : sinh(x) := x*shuge (overflow) 25 * 26 * Special cases: 27 * sinh(x) is |x| if x is +INF, -INF, or NaN. 28 * only sinh(0)=0 is exact for finite x. 29 */ 30 31 #include <float.h> 32 #include <math.h> 33 34 #include "math_private.h" 35 36 static const double one = 1.0, shuge = 1.0e307; 37 38 double 39 sinh(double x) 40 { 41 double t,w,h; 42 int32_t ix,jx; 43 u_int32_t lx; 44 45 /* High word of |x|. */ 46 GET_HIGH_WORD(jx,x); 47 ix = jx&0x7fffffff; 48 49 /* x is INF or NaN */ 50 if(ix>=0x7ff00000) return x+x; 51 52 h = 0.5; 53 if (jx<0) h = -h; 54 /* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */ 55 if (ix < 0x40360000) { /* |x|<22 */ 56 if (ix<0x3e300000) /* |x|<2**-28 */ 57 if(shuge+x>one) return x;/* sinh(tiny) = tiny with inexact */ 58 t = expm1(fabs(x)); 59 if(ix<0x3ff00000) return h*(2.0*t-t*t/(t+one)); 60 return h*(t+t/(t+one)); 61 } 62 63 /* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */ 64 if (ix < 0x40862E42) return h*exp(fabs(x)); 65 66 /* |x| in [log(maxdouble), overflowthresold] */ 67 GET_LOW_WORD(lx,x); 68 if (ix<0x408633CE || ((ix==0x408633ce)&&(lx<=(u_int32_t)0x8fb9f87d))) { 69 w = exp(0.5*fabs(x)); 70 t = h*w; 71 return t*w; 72 } 73 74 /* |x| > overflowthresold, sinh(x) overflow */ 75 return x*shuge; 76 } 77 78 #if LDBL_MANT_DIG == DBL_MANT_DIG 79 __strong_alias(sinhl, sinh); 80 #endif /* LDBL_MANT_DIG == DBL_MANT_DIG */ 81