ref: 53aac62a54ebbcc1781c0000d3e2384ed038c7bb
dir: /libmath/fdlibm/e_cosh.c/
/* derived from /netlib/fdlibm */ /* @(#)e_cosh.c 1.3 95/01/18 */ /* * ==================================================== * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. * * Developed at SunSoft, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this * software is freely granted, provided that this notice * is preserved. * ==================================================== */ /* __ieee754_cosh(x) * Method : * mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2 * 1. Replace x by |x| (cosh(x) = cosh(-x)). * 2. * [ exp(x) - 1 ]^2 * 0 <= x <= ln2/2 : cosh(x) := 1 + ------------------- * 2*exp(x) * * exp(x) + 1/exp(x) * ln2/2 <= x <= 22 : cosh(x) := ------------------- * 2 * 22 <= x <= lnovft : cosh(x) := exp(x)/2 * lnovft <= x <= ln2ovft: cosh(x) := exp(x/2)/2 * exp(x/2) * ln2ovft < x : cosh(x) := Huge*Huge (overflow) * * Special cases: * cosh(x) is |x| if x is +INF, -INF, or NaN. * only cosh(0)=1 is exact for finite x. */ #include "fdlibm.h" static const double one = 1.0, half=0.5, Huge = 1.0e300; double __ieee754_cosh(double x) { double t,w; int ix; unsigned lx; /* High word of |x|. */ ix = __HI(x); ix &= 0x7fffffff; /* x is INF or NaN */ if(ix>=0x7ff00000) return x*x; /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */ if(ix<0x3fd62e43) { t = expm1(fabs(x)); w = one+t; if (ix<0x3c800000) return w; /* cosh(tiny) = 1 */ return one+(t*t)/(w+w); } /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */ if (ix < 0x40360000) { t = __ieee754_exp(fabs(x)); return half*t+half/t; } /* |x| in [22, log(maxdouble)] return half*exp(|x|) */ if (ix < 0x40862E42) return half*__ieee754_exp(fabs(x)); /* |x| in [log(maxdouble), overflowthresold] */ lx = *( (((*(unsigned*)&one)>>29)) + (unsigned*)&x); if (ix<0x408633CE || (ix==0x408633ce)&&(lx<=(unsigned)0x8fb9f87d)) { w = __ieee754_exp(half*fabs(x)); t = half*w; return t*w; } /* |x| > overflowthresold, cosh(x) overflow */ return Huge*Huge; }