| /* @(#)e_cosh.c 5.1 93/09/24 */ |
| /* |
| * ==================================================== |
| * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
| * |
| * Developed at SunPro, 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 <= 40 : cosh(x) := ------------------- |
| * 2 |
| * 40 <= 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 long double one = 1.0L, half=0.5L, huge = 1.0e300L; |
| |
| long double |
| __ieee754_coshl (long double x) |
| { |
| long double t,w; |
| int64_t ix; |
| double xhi; |
| |
| /* High word of |x|. */ |
| xhi = ldbl_high (x); |
| EXTRACT_WORDS64 (ix, xhi); |
| ix &= 0x7fffffffffffffffLL; |
| |
| /* x is INF or NaN */ |
| if(ix>=0x7ff0000000000000LL) return x*x; |
| |
| /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */ |
| if(ix<0x3fd62e42fefa39efLL) { |
| t = __expm1l(fabsl(x)); |
| w = one+t; |
| if (ix<0x3c80000000000000LL) return w; /* cosh(tiny) = 1 */ |
| return one+(t*t)/(w+w); |
| } |
| |
| /* |x| in [0.5*ln2,40], return (exp(|x|)+1/exp(|x|)/2; */ |
| if (ix < 0x4044000000000000LL) { |
| t = __ieee754_expl(fabsl(x)); |
| return half*t+half/t; |
| } |
| |
| /* |x| in [40, log(maxdouble)] return half*exp(|x|) */ |
| if (ix < 0x40862e42fefa39efLL) return half*__ieee754_expl(fabsl(x)); |
| |
| /* |x| in [log(maxdouble), overflowthresold] */ |
| if (ix < 0x408633ce8fb9f87fLL) { |
| w = __ieee754_expl(half*fabsl(x)); |
| t = half*w; |
| return t*w; |
| } |
| |
| /* |x| > overflowthresold, cosh(x) overflow */ |
| return huge*huge; |
| } |
| strong_alias (__ieee754_coshl, __coshl_finite) |
