1 /* derived from /netlib/fdlibm */ 2 3 /* @(#)e_cosh.c 1.3 95/01/18 */ 4 /* 5 * ==================================================== 6 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 7 * 8 * Developed at SunSoft, a Sun Microsystems, Inc. business. 9 * Permission to use, copy, modify, and distribute this 10 * software is freely granted, provided that this notice 11 * is preserved. 12 * ==================================================== 13 */ 14 15 /* __ieee754_cosh(x) 16 * Method : 17 * mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2 18 * 1. Replace x by |x| (cosh(x) = cosh(-x)). 19 * 2. 20 * [ exp(x) - 1 ]^2 21 * 0 <= x <= ln2/2 : cosh(x) := 1 + ------------------- 22 * 2*exp(x) 23 * 24 * exp(x) + 1/exp(x) 25 * ln2/2 <= x <= 22 : cosh(x) := ------------------- 26 * 2 27 * 22 <= x <= lnovft : cosh(x) := exp(x)/2 28 * lnovft <= x <= ln2ovft: cosh(x) := exp(x/2)/2 * exp(x/2) 29 * ln2ovft < x : cosh(x) := Huge*Huge (overflow) 30 * 31 * Special cases: 32 * cosh(x) is |x| if x is +INF, -INF, or NaN. 33 * only cosh(0)=1 is exact for finite x. 34 */ 35 36 #include "fdlibm.h" 37 38 static const double one = 1.0, half=0.5, Huge = 1.0e300; 39 40 double __ieee754_cosh(double x) 41 { 42 double t,w; 43 int ix; 44 unsigned lx; 45 46 /* High word of |x|. */ 47 ix = __HI(x); 48 ix &= 0x7fffffff; 49 50 /* x is INF or NaN */ 51 if(ix>=0x7ff00000) return x*x; 52 53 /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */ 54 if(ix<0x3fd62e43) { 55 t = expm1(fabs(x)); 56 w = one+t; 57 if (ix<0x3c800000) return w; /* cosh(tiny) = 1 */ 58 return one+(t*t)/(w+w); 59 } 60 61 /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */ 62 if (ix < 0x40360000) { 63 t = __ieee754_exp(fabs(x)); 64 return half*t+half/t; 65 } 66 67 /* |x| in [22, log(maxdouble)] return half*exp(|x|) */ 68 if (ix < 0x40862E42) return half*__ieee754_exp(fabs(x)); 69 70 /* |x| in [log(maxdouble), overflowthresold] */ 71 lx = *( (((*(unsigned*)&one)>>29)) + (unsigned*)&x); 72 if (ix<0x408633CE || 73 (ix==0x408633ce)&&(lx<=(unsigned)0x8fb9f87d)) { 74 w = __ieee754_exp(half*fabs(x)); 75 t = half*w; 76 return t*w; 77 } 78 79 /* |x| > overflowthresold, cosh(x) overflow */ 80 return Huge*Huge; 81 } 82