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 /* LINTLIBRARY */ 14 15 /* sinh(x) 16 * Method : 17 * mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2 18 * 1. Replace x by |x| (sinh(-x) = -sinh(x)). 19 * 2. 20 * E + E/(E+1) 21 * 0 <= x <= 22 : sinh(x) := --------------, E=expm1(x) 22 * 2 23 * 24 * 22 <= x <= lnovft : sinh(x) := exp(x)/2 25 * lnovft <= x <= ln2ovft: sinh(x) := exp(x/2)/2 * exp(x/2) 26 * ln2ovft < x : sinh(x) := x*shuge (overflow) 27 * 28 * Special cases: 29 * sinh(x) is |x| if x is +INF, -INF, or NaN. 30 * only sinh(0)=0 is exact for finite x. 31 */ 32 33 #include <sys/cdefs.h> 34 #include <float.h> 35 #include <math.h> 36 37 #include "math_private.h" 38 39 static const double one = 1.0, shuge = 1.0e307; 40 41 double 42 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*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 = 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 81 #if LDBL_MANT_DIG == 53 82 #ifdef lint 83 /* PROTOLIB1 */ 84 long double sinhl(long double); 85 #else /* lint */ 86 __weak_alias(sinhl, sinh); 87 #endif /* lint */ 88 #endif /* LDBL_MANT_DIG == 53 */ 89