1 /* @(#)e_cosh.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 #ifndef lint 14 static char rcsid[] = "$Id: e_cosh.c,v 1.3 1994/02/18 02:24:59 jtc Exp $"; 15 #endif 16 17 /* __ieee754_cosh(x) 18 * Method : 19 * mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2 20 * 1. Replace x by |x| (cosh(x) = cosh(-x)). 21 * 2. 22 * [ exp(x) - 1 ]^2 23 * 0 <= x <= ln2/2 : cosh(x) := 1 + ------------------- 24 * 2*exp(x) 25 * 26 * exp(x) + 1/exp(x) 27 * ln2/2 <= x <= 22 : cosh(x) := ------------------- 28 * 2 29 * 22 <= x <= lnovft : cosh(x) := exp(x)/2 30 * lnovft <= x <= ln2ovft: cosh(x) := exp(x/2)/2 * exp(x/2) 31 * ln2ovft < x : cosh(x) := huge*huge (overflow) 32 * 33 * Special cases: 34 * cosh(x) is |x| if x is +INF, -INF, or NaN. 35 * only cosh(0)=1 is exact for finite x. 36 */ 37 38 #include <math.h> 39 40 #ifdef __STDC__ 41 static const double one = 1.0, half=0.5, huge = 1.0e300; 42 #else 43 static double one = 1.0, half=0.5, huge = 1.0e300; 44 #endif 45 46 #ifdef __STDC__ 47 double __ieee754_cosh(double x) 48 #else 49 double __ieee754_cosh(x) 50 double x; 51 #endif 52 { 53 double t,w; 54 int ix; 55 unsigned lx; 56 57 /* High word of |x|. */ 58 ix = *( (((*(int*)&one)>>29)^1) + (int*)&x); 59 ix &= 0x7fffffff; 60 61 /* x is INF or NaN */ 62 if(ix>=0x7ff00000) return x*x; 63 64 /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */ 65 if(ix<0x3fd62e43) { 66 t = expm1(fabs(x)); 67 w = one+t; 68 if (ix<0x3c800000) return w; /* cosh(tiny) = 1 */ 69 return one+(t*t)/(w+w); 70 } 71 72 /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */ 73 if (ix < 0x40360000) { 74 t = __ieee754_exp(fabs(x)); 75 return half*t+half/t; 76 } 77 78 /* |x| in [22, log(maxdouble)] return half*exp(|x|) */ 79 if (ix < 0x40862E42) return half*__ieee754_exp(fabs(x)); 80 81 /* |x| in [log(maxdouble), overflowthresold] */ 82 lx = *( (((*(unsigned*)&one)>>29)) + (unsigned*)&x); 83 if (ix<0x408633CE || 84 (ix==0x408633ce)&&(lx<=(unsigned)0x8fb9f87d)) { 85 w = __ieee754_exp(half*fabs(x)); 86 t = half*w; 87 return t*w; 88 } 89 90 /* |x| > overflowthresold, cosh(x) overflow */ 91 return huge*huge; 92 } 93