1*37da2899SCharles.Forsyth /* derived from /netlib/fdlibm */ 2*37da2899SCharles.Forsyth 3*37da2899SCharles.Forsyth /* @(#)e_cosh.c 1.3 95/01/18 */ 4*37da2899SCharles.Forsyth /* 5*37da2899SCharles.Forsyth * ==================================================== 6*37da2899SCharles.Forsyth * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 7*37da2899SCharles.Forsyth * 8*37da2899SCharles.Forsyth * Developed at SunSoft, a Sun Microsystems, Inc. business. 9*37da2899SCharles.Forsyth * Permission to use, copy, modify, and distribute this 10*37da2899SCharles.Forsyth * software is freely granted, provided that this notice 11*37da2899SCharles.Forsyth * is preserved. 12*37da2899SCharles.Forsyth * ==================================================== 13*37da2899SCharles.Forsyth */ 14*37da2899SCharles.Forsyth 15*37da2899SCharles.Forsyth /* __ieee754_cosh(x) 16*37da2899SCharles.Forsyth * Method : 17*37da2899SCharles.Forsyth * mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2 18*37da2899SCharles.Forsyth * 1. Replace x by |x| (cosh(x) = cosh(-x)). 19*37da2899SCharles.Forsyth * 2. 20*37da2899SCharles.Forsyth * [ exp(x) - 1 ]^2 21*37da2899SCharles.Forsyth * 0 <= x <= ln2/2 : cosh(x) := 1 + ------------------- 22*37da2899SCharles.Forsyth * 2*exp(x) 23*37da2899SCharles.Forsyth * 24*37da2899SCharles.Forsyth * exp(x) + 1/exp(x) 25*37da2899SCharles.Forsyth * ln2/2 <= x <= 22 : cosh(x) := ------------------- 26*37da2899SCharles.Forsyth * 2 27*37da2899SCharles.Forsyth * 22 <= x <= lnovft : cosh(x) := exp(x)/2 28*37da2899SCharles.Forsyth * lnovft <= x <= ln2ovft: cosh(x) := exp(x/2)/2 * exp(x/2) 29*37da2899SCharles.Forsyth * ln2ovft < x : cosh(x) := Huge*Huge (overflow) 30*37da2899SCharles.Forsyth * 31*37da2899SCharles.Forsyth * Special cases: 32*37da2899SCharles.Forsyth * cosh(x) is |x| if x is +INF, -INF, or NaN. 33*37da2899SCharles.Forsyth * only cosh(0)=1 is exact for finite x. 34*37da2899SCharles.Forsyth */ 35*37da2899SCharles.Forsyth 36*37da2899SCharles.Forsyth #include "fdlibm.h" 37*37da2899SCharles.Forsyth 38*37da2899SCharles.Forsyth static const double one = 1.0, half=0.5, Huge = 1.0e300; 39*37da2899SCharles.Forsyth __ieee754_cosh(double x)40*37da2899SCharles.Forsyth double __ieee754_cosh(double x) 41*37da2899SCharles.Forsyth { 42*37da2899SCharles.Forsyth double t,w; 43*37da2899SCharles.Forsyth int ix; 44*37da2899SCharles.Forsyth unsigned lx; 45*37da2899SCharles.Forsyth 46*37da2899SCharles.Forsyth /* High word of |x|. */ 47*37da2899SCharles.Forsyth ix = __HI(x); 48*37da2899SCharles.Forsyth ix &= 0x7fffffff; 49*37da2899SCharles.Forsyth 50*37da2899SCharles.Forsyth /* x is INF or NaN */ 51*37da2899SCharles.Forsyth if(ix>=0x7ff00000) return x*x; 52*37da2899SCharles.Forsyth 53*37da2899SCharles.Forsyth /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */ 54*37da2899SCharles.Forsyth if(ix<0x3fd62e43) { 55*37da2899SCharles.Forsyth t = expm1(fabs(x)); 56*37da2899SCharles.Forsyth w = one+t; 57*37da2899SCharles.Forsyth if (ix<0x3c800000) return w; /* cosh(tiny) = 1 */ 58*37da2899SCharles.Forsyth return one+(t*t)/(w+w); 59*37da2899SCharles.Forsyth } 60*37da2899SCharles.Forsyth 61*37da2899SCharles.Forsyth /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */ 62*37da2899SCharles.Forsyth if (ix < 0x40360000) { 63*37da2899SCharles.Forsyth t = __ieee754_exp(fabs(x)); 64*37da2899SCharles.Forsyth return half*t+half/t; 65*37da2899SCharles.Forsyth } 66*37da2899SCharles.Forsyth 67*37da2899SCharles.Forsyth /* |x| in [22, log(maxdouble)] return half*exp(|x|) */ 68*37da2899SCharles.Forsyth if (ix < 0x40862E42) return half*__ieee754_exp(fabs(x)); 69*37da2899SCharles.Forsyth 70*37da2899SCharles.Forsyth /* |x| in [log(maxdouble), overflowthresold] */ 71*37da2899SCharles.Forsyth lx = *( (((*(unsigned*)&one)>>29)) + (unsigned*)&x); 72*37da2899SCharles.Forsyth if (ix<0x408633CE || 73*37da2899SCharles.Forsyth (ix==0x408633ce)&&(lx<=(unsigned)0x8fb9f87d)) { 74*37da2899SCharles.Forsyth w = __ieee754_exp(half*fabs(x)); 75*37da2899SCharles.Forsyth t = half*w; 76*37da2899SCharles.Forsyth return t*w; 77*37da2899SCharles.Forsyth } 78*37da2899SCharles.Forsyth 79*37da2899SCharles.Forsyth /* |x| > overflowthresold, cosh(x) overflow */ 80*37da2899SCharles.Forsyth return Huge*Huge; 81*37da2899SCharles.Forsyth } 82