1/* 2 * ==================================================== 3 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 4 * 5 * Developed at SunPro, a Sun Microsystems, Inc. business. 6 * Permission to use, copy, modify, and distribute this 7 * software is freely granted, provided that this notice 8 * is preserved. 9 * ==================================================== 10 */ 11 12#if defined(LIBM_SCCS) && !defined(lint) 13static char rcsid[] = "$NetBSD: e_cosh.c,v 1.7 1995/05/10 20:44:58 jtc Exp $"; 14#endif 15 16/* __ieee754_coshl(x) 17 * Method : 18 * mathematically coshl(x) if defined to be (exp(x)+exp(-x))/2 19 * 1. Replace x by |x| (coshl(x) = coshl(-x)). 20 * 2. 21 * [ exp(x) - 1 ]^2 22 * 0 <= x <= ln2/2 : coshl(x) := 1 + ------------------- 23 * 2*exp(x) 24 * 25 * exp(x) + 1/exp(x) 26 * ln2/2 <= x <= 22 : coshl(x) := ------------------- 27 * 2 28 * 22 <= x <= lnovft : coshl(x) := expl(x)/2 29 * lnovft <= x <= ln2ovft: coshl(x) := expl(x/2)/2 * expl(x/2) 30 * ln2ovft < x : coshl(x) := huge*huge (overflow) 31 * 32 * Special cases: 33 * coshl(x) is |x| if x is +INF, -INF, or NaN. 34 * only coshl(0)=1 is exact for finite x. 35 */ 36 37#include "math.h" 38#include "math_private.h" 39 40#ifdef __STDC__ 41static const long double one = 1.0, half=0.5, huge = 1.0e4900L; 42#else 43static long double one = 1.0, half=0.5, huge = 1.0e4900L; 44#endif 45 46#ifdef __STDC__ 47 long double __ieee754_coshl(long double x) 48#else 49 long double __ieee754_coshl(x) 50 long double x; 51#endif 52{ 53 long double t,w; 54 int32_t ex; 55 u_int32_t mx,lx; 56 57 /* High word of |x|. */ 58 GET_LDOUBLE_WORDS(ex,mx,lx,x); 59 ex &= 0x7fff; 60 61 /* x is INF or NaN */ 62 if(ex==0x7fff) return x*x; 63 64 /* |x| in [0,0.5*ln2], return 1+expm1l(|x|)^2/(2*expl(|x|)) */ 65 if(ex < 0x3ffd || (ex == 0x3ffd && mx < 0xb17217f7u)) { 66 t = __expm1l(fabsl(x)); 67 w = one+t; 68 if (ex<0x3fbc) return w; /* cosh(tiny) = 1 */ 69 return one+(t*t)/(w+w); 70 } 71 72 /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */ 73 if (ex < 0x4003 || (ex == 0x4003 && mx < 0xb0000000u)) { 74 t = __ieee754_expl(fabsl(x)); 75 return half*t+half/t; 76 } 77 78 /* |x| in [22, ln(maxdouble)] return half*exp(|x|) */ 79 if (ex < 0x400c || (ex == 0x400c && mx < 0xb1700000u)) 80 return half*__ieee754_expl(fabsl(x)); 81 82 /* |x| in [log(maxdouble), log(2*maxdouble)) */ 83 if (ex == 0x400c && (mx < 0xb174ddc0u 84 || (mx == 0xb174ddc0u && lx < 0x31aec0ebu))) 85 { 86 w = __ieee754_expl(half*fabsl(x)); 87 t = half*w; 88 return t*w; 89 } 90 91 /* |x| >= log(2*maxdouble), cosh(x) overflow */ 92 return huge*huge; 93} 94