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 #include <sys/cdefs.h> 15 __FBSDID("$FreeBSD$"); 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 <float.h> 36 37 #include "math.h" 38 #include "math_private.h" 39 40 static const double one = 1.0, shuge = 1.0e307; 41 42 double 43 __ieee754_sinh(double x) 44 { 45 double t,h; 46 int32_t ix,jx; 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*__ieee754_exp(fabs(x)); 68 69 /* |x| in [log(maxdouble), overflowthresold] */ 70 if (ix<=0x408633CE) 71 return h*2.0*__ldexp_exp(fabs(x), -1); 72 73 /* |x| > overflowthresold, sinh(x) overflow */ 74 return x*shuge; 75 } 76 77 #if (LDBL_MANT_DIG == 53) 78 __weak_reference(sinh, sinhl); 79 #endif 80
