1/* $NetBSD: n_cosh.c,v 1.8 2008/03/20 16:41:26 mhitch Exp $ */ 2/* 3 * Copyright (c) 1985, 1993 4 * The Regents of the University of California. All rights reserved. 5 * 6 * Redistribution and use in source and binary forms, with or without 7 * modification, are permitted provided that the following conditions 8 * are met: 9 * 1. Redistributions of source code must retain the above copyright 10 * notice, this list of conditions and the following disclaimer. 11 * 2. Redistributions in binary form must reproduce the above copyright 12 * notice, this list of conditions and the following disclaimer in the 13 * documentation and/or other materials provided with the distribution. 14 * 3. Neither the name of the University nor the names of its contributors 15 * may be used to endorse or promote products derived from this software 16 * without specific prior written permission. 17 * 18 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND 19 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 20 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 21 * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE 22 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 23 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 24 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 25 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 26 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 27 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 28 * SUCH DAMAGE. 29 */ 30 31#ifndef lint 32#if 0 33static char sccsid[] = "@(#)cosh.c 8.1 (Berkeley) 6/4/93"; 34#endif 35#endif /* not lint */ 36 37/* COSH(X) 38 * RETURN THE HYPERBOLIC COSINE OF X 39 * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS) 40 * CODED IN C BY K.C. NG, 1/8/85; 41 * REVISED BY K.C. NG on 2/8/85, 2/23/85, 3/7/85, 3/29/85, 4/16/85. 42 * 43 * Required system supported functions : 44 * copysign(x,y) 45 * scalb(x,N) 46 * 47 * Required kernel function: 48 * exp(x) 49 * exp__E(x,c) ...return exp(x+c)-1-x for |x|<0.3465 50 * 51 * Method : 52 * 1. Replace x by |x|. 53 * 2. 54 * [ exp(x) - 1 ]^2 55 * 0 <= x <= 0.3465 : cosh(x) := 1 + ------------------- 56 * 2*exp(x) 57 * 58 * exp(x) + 1/exp(x) 59 * 0.3465 <= x <= 22 : cosh(x) := ------------------- 60 * 2 61 * 22 <= x <= lnovfl : cosh(x) := exp(x)/2 62 * lnovfl <= x <= lnovfl+log(2) 63 * : cosh(x) := exp(x)/2 (avoid overflow) 64 * log(2)+lnovfl < x < INF: overflow to INF 65 * 66 * Note: .3465 is a number near one half of ln2. 67 * 68 * Special cases: 69 * cosh(x) is x if x is +INF, -INF, or NaN. 70 * only cosh(0)=1 is exact for finite x. 71 * 72 * Accuracy: 73 * cosh(x) returns the exact hyperbolic cosine of x nearly rounded. 74 * In a test run with 768,000 random arguments on a VAX, the maximum 75 * observed error was 1.23 ulps (units in the last place). 76 * 77 * Constants: 78 * The hexadecimal values are the intended ones for the following constants. 79 * The decimal values may be used, provided that the compiler will convert 80 * from decimal to binary accurately enough to produce the hexadecimal values 81 * shown. 82 */ 83 84#define _LIBM_STATIC 85#include "../src/namespace.h" 86#include "mathimpl.h" 87 88#ifdef __weak_alias 89__weak_alias(cosh, _cosh); 90__weak_alias(_coshl, _cosh); 91__weak_alias(coshf, _coshf); 92#endif 93 94vc(mln2hi, 8.8029691931113054792E1 ,0f33,43b0,2bdb,c7e2, 7, .B00F33C7E22BDB) 95vc(mln2lo,-4.9650192275318476525E-16 ,1b60,a70f,582a,279e, -50,-.8F1B60279E582A) 96vc(lnovfl, 8.8029691931113053016E1 ,0f33,43b0,2bda,c7e2, 7, .B00F33C7E22BDA) 97 98ic(mln2hi, 7.0978271289338397310E2, 10, 1.62E42FEFA39EF) 99ic(mln2lo, 2.3747039373786107478E-14, -45, 1.ABC9E3B39803F) 100ic(lnovfl, 7.0978271289338397310E2, 9, 1.62E42FEFA39EF) 101 102#ifdef vccast 103#define mln2hi vccast(mln2hi) 104#define mln2lo vccast(mln2lo) 105#define lnovfl vccast(lnovfl) 106#endif 107 108#if defined(__vax__)||defined(tahoe) 109#define EXPMAX 126 110#else 111#define EXPMAX 1023 112#endif /* defined(__vax__)||defined(tahoe) */ 113 114double 115cosh(double x) 116{ 117 static const double half=1.0/2.0, 118 one=1.0, small=1.0E-18; /* fl(1+small)==1 */ 119 double t; 120 121#if !defined(__vax__)&&!defined(tahoe) 122 if(x!=x) return(x); /* x is NaN */ 123#endif /* !defined(__vax__)&&!defined(tahoe) */ 124 if((x=copysign(x,one)) <= 22) { 125 if(x<0.3465) { 126 if(x<small) { return(one+x); } 127 else {t=x+__exp__E(x,0.0);x=t+t; return(one+t*t/(2.0+x)); } 128 129 } else /* for x lies in [0.3465,22] */ 130 { t=exp(x); return((t+one/t)*half); } 131 } 132 133 if( lnovfl <= x && x <= (lnovfl+0.7)) 134 /* for x lies in [lnovfl, lnovfl+ln2], decrease x by ln(2^(EXPMAX+1)) 135 * and return 2^EXPMAX*exp(x) to avoid unnecessary overflow 136 */ 137 return(scalb(exp((x-mln2hi)-mln2lo), EXPMAX)); 138 139 else 140 return(exp(x)*half); /* for large x, cosh(x)=exp(x)/2 */ 141} 142 143float 144coshf(float x) 145{ 146 return(cosh((double)x)); 147} 148