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 33 static 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(coshf, _coshf); 91 #endif 92 93 vc(mln2hi, 8.8029691931113054792E1 ,0f33,43b0,2bdb,c7e2, 7, .B00F33C7E22BDB) 94 vc(mln2lo,-4.9650192275318476525E-16 ,1b60,a70f,582a,279e, -50,-.8F1B60279E582A) 95 vc(lnovfl, 8.8029691931113053016E1 ,0f33,43b0,2bda,c7e2, 7, .B00F33C7E22BDA) 96 97 ic(mln2hi, 7.0978271289338397310E2, 10, 1.62E42FEFA39EF) 98 ic(mln2lo, 2.3747039373786107478E-14, -45, 1.ABC9E3B39803F) 99 ic(lnovfl, 7.0978271289338397310E2, 9, 1.62E42FEFA39EF) 100 101 #ifdef vccast 102 #define mln2hi vccast(mln2hi) 103 #define mln2lo vccast(mln2lo) 104 #define lnovfl vccast(lnovfl) 105 #endif 106 107 #if defined(__vax__)||defined(tahoe) 108 #define EXPMAX 126 109 #else 110 #define EXPMAX 1023 111 #endif /* defined(__vax__)||defined(tahoe) */ 112 113 double 114 cosh(double x) 115 { 116 static const double half=1.0/2.0, 117 one=1.0, small=1.0E-18; /* fl(1+small)==1 */ 118 double t; 119 120 #if !defined(__vax__)&&!defined(tahoe) 121 if(x!=x) return(x); /* x is NaN */ 122 #endif /* !defined(__vax__)&&!defined(tahoe) */ 123 if((x=copysign(x,one)) <= 22) { 124 if(x<0.3465) { 125 if(x<small) { return(one+x); } 126 else {t=x+__exp__E(x,0.0);x=t+t; return(one+t*t/(2.0+x)); } 127 128 } else /* for x lies in [0.3465,22] */ 129 { t=exp(x); return((t+one/t)*half); } 130 } 131 132 if( lnovfl <= x && x <= (lnovfl+0.7)) 133 /* for x lies in [lnovfl, lnovfl+ln2], decrease x by ln(2^(EXPMAX+1)) 134 * and return 2^EXPMAX*exp(x) to avoid unnecessary overflow 135 */ 136 return(scalb(exp((x-mln2hi)-mln2lo), EXPMAX)); 137 138 else 139 return(exp(x)*half); /* for large x, cosh(x)=exp(x)/2 */ 140 } 141 142 float 143 coshf(float x) 144 { 145 return(cosh((double)x)); 146 } 147