1/* 2 * Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved. 3 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. 4 * 5 * This code is free software; you can redistribute it and/or modify it 6 * under the terms of the GNU General Public License version 2 only, as 7 * published by the Free Software Foundation. Oracle designates this 8 * particular file as subject to the "Classpath" exception as provided 9 * by Oracle in the LICENSE file that accompanied this code. 10 * 11 * This code is distributed in the hope that it will be useful, but WITHOUT 12 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or 13 * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License 14 * version 2 for more details (a copy is included in the LICENSE file that 15 * accompanied this code). 16 * 17 * You should have received a copy of the GNU General Public License version 18 * 2 along with this work; if not, write to the Free Software Foundation, 19 * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. 20 * 21 * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA 22 * or visit www.oracle.com if you need additional information or have any 23 * questions. 24 */ 25 26/* __ieee754_cosh(x) 27 * Method : 28 * mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2 29 * 1. Replace x by |x| (cosh(x) = cosh(-x)). 30 * 2. 31 * [ exp(x) - 1 ]^2 32 * 0 <= x <= ln2/2 : cosh(x) := 1 + ------------------- 33 * 2*exp(x) 34 * 35 * exp(x) + 1/exp(x) 36 * ln2/2 <= x <= 22 : cosh(x) := ------------------- 37 * 2 38 * 22 <= x <= lnovft : cosh(x) := exp(x)/2 39 * lnovft <= x <= ln2ovft: cosh(x) := exp(x/2)/2 * exp(x/2) 40 * ln2ovft < x : cosh(x) := huge*huge (overflow) 41 * 42 * Special cases: 43 * cosh(x) is |x| if x is +INF, -INF, or NaN. 44 * only cosh(0)=1 is exact for finite x. 45 */ 46 47#include "fdlibm.h" 48 49#ifdef __STDC__ 50static const double one = 1.0, half=0.5, huge = 1.0e300; 51#else 52static double one = 1.0, half=0.5, huge = 1.0e300; 53#endif 54 55#ifdef __STDC__ 56 double __ieee754_cosh(double x) 57#else 58 double __ieee754_cosh(x) 59 double x; 60#endif 61{ 62 double t,w; 63 int ix; 64 unsigned lx; 65 66 /* High word of |x|. */ 67 ix = __HI(x); 68 ix &= 0x7fffffff; 69 70 /* x is INF or NaN */ 71 if(ix>=0x7ff00000) return x*x; 72 73 /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */ 74 if(ix<0x3fd62e43) { 75 t = expm1(fabs(x)); 76 w = one+t; 77 if (ix<0x3c800000) return w; /* cosh(tiny) = 1 */ 78 return one+(t*t)/(w+w); 79 } 80 81 /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */ 82 if (ix < 0x40360000) { 83 t = __ieee754_exp(fabs(x)); 84 return half*t+half/t; 85 } 86 87 /* |x| in [22, log(maxdouble)] return half*exp(|x|) */ 88 if (ix < 0x40862E42) return half*__ieee754_exp(fabs(x)); 89 90 /* |x| in [log(maxdouble), overflowthresold] */ 91 lx = *( (((*(unsigned*)&one)>>29)) + (unsigned*)&x); 92 if (ix<0x408633CE || 93 ((ix==0x408633ce)&&(lx<=(unsigned)0x8fb9f87d))) { 94 w = __ieee754_exp(half*fabs(x)); 95 t = half*w; 96 return t*w; 97 } 98 99 /* |x| > overflowthresold, cosh(x) overflow */ 100 return huge*huge; 101} 102