1 /* $NetBSD: n_cosh.c,v 1.6 2002/06/15 00:10:17 matt 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. All advertising materials mentioning features or use of this software 15 * must display the following acknowledgement: 16 * This product includes software developed by the University of 17 * California, Berkeley and its contributors. 18 * 4. Neither the name of the University nor the names of its contributors 19 * may be used to endorse or promote products derived from this software 20 * without specific prior written permission. 21 * 22 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND 23 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 24 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 25 * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE 26 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 27 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 28 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 29 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 30 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 31 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 32 * SUCH DAMAGE. 33 */ 34 35 #ifndef lint 36 #if 0 37 static char sccsid[] = "@(#)cosh.c 8.1 (Berkeley) 6/4/93"; 38 #endif 39 #endif /* not lint */ 40 41 /* COSH(X) 42 * RETURN THE HYPERBOLIC COSINE OF X 43 * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS) 44 * CODED IN C BY K.C. NG, 1/8/85; 45 * REVISED BY K.C. NG on 2/8/85, 2/23/85, 3/7/85, 3/29/85, 4/16/85. 46 * 47 * Required system supported functions : 48 * copysign(x,y) 49 * scalb(x,N) 50 * 51 * Required kernel function: 52 * exp(x) 53 * exp__E(x,c) ...return exp(x+c)-1-x for |x|<0.3465 54 * 55 * Method : 56 * 1. Replace x by |x|. 57 * 2. 58 * [ exp(x) - 1 ]^2 59 * 0 <= x <= 0.3465 : cosh(x) := 1 + ------------------- 60 * 2*exp(x) 61 * 62 * exp(x) + 1/exp(x) 63 * 0.3465 <= x <= 22 : cosh(x) := ------------------- 64 * 2 65 * 22 <= x <= lnovfl : cosh(x) := exp(x)/2 66 * lnovfl <= x <= lnovfl+log(2) 67 * : cosh(x) := exp(x)/2 (avoid overflow) 68 * log(2)+lnovfl < x < INF: overflow to INF 69 * 70 * Note: .3465 is a number near one half of ln2. 71 * 72 * Special cases: 73 * cosh(x) is x if x is +INF, -INF, or NaN. 74 * only cosh(0)=1 is exact for finite x. 75 * 76 * Accuracy: 77 * cosh(x) returns the exact hyperbolic cosine of x nearly rounded. 78 * In a test run with 768,000 random arguments on a VAX, the maximum 79 * observed error was 1.23 ulps (units in the last place). 80 * 81 * Constants: 82 * The hexadecimal values are the intended ones for the following constants. 83 * The decimal values may be used, provided that the compiler will convert 84 * from decimal to binary accurately enough to produce the hexadecimal values 85 * shown. 86 */ 87 88 #define _LIBM_STATIC 89 #include "mathimpl.h" 90 91 vc(mln2hi, 8.8029691931113054792E1 ,0f33,43b0,2bdb,c7e2, 7, .B00F33C7E22BDB) 92 vc(mln2lo,-4.9650192275318476525E-16 ,1b60,a70f,582a,279e, -50,-.8F1B60279E582A) 93 vc(lnovfl, 8.8029691931113053016E1 ,0f33,43b0,2bda,c7e2, 7, .B00F33C7E22BDA) 94 95 ic(mln2hi, 7.0978271289338397310E2, 10, 1.62E42FEFA39EF) 96 ic(mln2lo, 2.3747039373786107478E-14, -45, 1.ABC9E3B39803F) 97 ic(lnovfl, 7.0978271289338397310E2, 9, 1.62E42FEFA39EF) 98 99 #ifdef vccast 100 #define mln2hi vccast(mln2hi) 101 #define mln2lo vccast(mln2lo) 102 #define lnovfl vccast(lnovfl) 103 #endif 104 105 #if defined(__vax__)||defined(tahoe) 106 #define EXPMAX 126 107 #else 108 #define EXPMAX 1023 109 #endif /* defined(__vax__)||defined(tahoe) */ 110 111 double 112 cosh(double x) 113 { 114 static const double half=1.0/2.0, 115 one=1.0, small=1.0E-18; /* fl(1+small)==1 */ 116 double t; 117 118 #if !defined(__vax__)&&!defined(tahoe) 119 if(x!=x) return(x); /* x is NaN */ 120 #endif /* !defined(__vax__)&&!defined(tahoe) */ 121 if((x=copysign(x,one)) <= 22) { 122 if(x<0.3465) { 123 if(x<small) { return(one+x); } 124 else {t=x+__exp__E(x,0.0);x=t+t; return(one+t*t/(2.0+x)); } 125 126 } else /* for x lies in [0.3465,22] */ 127 { t=exp(x); return((t+one/t)*half); } 128 } 129 130 if( lnovfl <= x && x <= (lnovfl+0.7)) 131 /* for x lies in [lnovfl, lnovfl+ln2], decrease x by ln(2^(EXPMAX+1)) 132 * and return 2^EXPMAX*exp(x) to avoid unnecessary overflow 133 */ 134 return(scalb(exp((x-mln2hi)-mln2lo), EXPMAX)); 135 136 else 137 return(exp(x)*half); /* for large x, cosh(x)=exp(x)/2 */ 138 } 139