| /* |
| * ==================================================== |
| * 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. |
| * ==================================================== |
| */ |
| |
| #if defined(LIBM_SCCS) && !defined(lint) |
| static char rcsid[] = "$NetBSD: e_cosh.c,v 1.7 1995/05/10 20:44:58 jtc Exp $"; |
| #endif |
| |
| /* __ieee754_coshl(x) |
| * Method : |
| * mathematically coshl(x) if defined to be (exp(x)+exp(-x))/2 |
| * 1. Replace x by |x| (coshl(x) = coshl(-x)). |
| * 2. |
| * [ exp(x) - 1 ]^2 |
| * 0 <= x <= ln2/2 : coshl(x) := 1 + ------------------- |
| * 2*exp(x) |
| * |
| * exp(x) + 1/exp(x) |
| * ln2/2 <= x <= 22 : coshl(x) := ------------------- |
| * 2 |
| * 22 <= x <= lnovft : coshl(x) := expl(x)/2 |
| * lnovft <= x <= ln2ovft: coshl(x) := expl(x/2)/2 * expl(x/2) |
| * ln2ovft < x : coshl(x) := huge*huge (overflow) |
| * |
| * Special cases: |
| * coshl(x) is |x| if x is +INF, -INF, or NaN. |
| * only coshl(0)=1 is exact for finite x. |
| */ |
| |
| #include "math.h" |
| #include "math_private.h" |
| |
| #ifdef __STDC__ |
| static const long double one = 1.0, half=0.5, huge = 1.0e4900L; |
| #else |
| static long double one = 1.0, half=0.5, huge = 1.0e4900L; |
| #endif |
| |
| #ifdef __STDC__ |
| long double __ieee754_coshl(long double x) |
| #else |
| long double __ieee754_coshl(x) |
| long double x; |
| #endif |
| { |
| long double t,w; |
| int32_t ex; |
| u_int32_t mx,lx; |
| |
| /* High word of |x|. */ |
| GET_LDOUBLE_WORDS(ex,mx,lx,x); |
| ex &= 0x7fff; |
| |
| /* x is INF or NaN */ |
| if(ex==0x7fff) return x*x; |
| |
| /* |x| in [0,0.5*ln2], return 1+expm1l(|x|)^2/(2*expl(|x|)) */ |
| if(ex < 0x3ffd || (ex == 0x3ffd && mx < 0xb17217f7u)) { |
| t = __expm1l(fabsl(x)); |
| w = one+t; |
| if (ex<0x3fbc) 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 (ex < 0x4003 || (ex == 0x4003 && mx < 0xb0000000u)) { |
| t = __ieee754_expl(fabsl(x)); |
| return half*t+half/t; |
| } |
| |
| /* |x| in [22, ln(maxdouble)] return half*exp(|x|) */ |
| if (ex < 0x400c || (ex == 0x400c && mx < 0xb1700000u)) |
| return half*__ieee754_expl(fabsl(x)); |
| |
| /* |x| in [log(maxdouble), log(2*maxdouble)) */ |
| if (ex == 0x400c && (mx < 0xb174ddc0u |
| || (mx == 0xb174ddc0u && lx < 0x31aec0ebu))) |
| { |
| w = __ieee754_expl(half*fabsl(x)); |
| t = half*w; |
| return t*w; |
| } |
| |
| /* |x| >= log(2*maxdouble), cosh(x) overflow */ |
| return huge*huge; |
| } |