| |
| /* @(#)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. |
| * ==================================================== |
| */ |
| |
| #include <sys/cdefs.h> |
| __FBSDID("$FreeBSD$"); |
| |
| /* __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 "math.h" |
| #include "math_private.h" |
| |
| static const double one = 1.0, half=0.5, huge = 1.0e300; |
| |
| double |
| __ieee754_cosh(double x) |
| { |
| double t,w; |
| int32_t ix; |
| |
| /* High word of |x|. */ |
| GET_HIGH_WORD(ix,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] */ |
| if (ix<=0x408633CE) |
| return __ldexp_exp(fabs(x), -1); |
| |
| /* |x| > overflowthresold, cosh(x) overflow */ |
| return huge*huge; |
| } |
