1 /* $NetBSD: n_cosh.c,v 1.1 1995/10/10 23:36:42 ragge 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 static char sccsid[] = "@(#)cosh.c 8.1 (Berkeley) 6/4/93"; 37 #endif /* not lint */ 38 39 /* COSH(X) 40 * RETURN THE HYPERBOLIC COSINE OF X 41 * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS) 42 * CODED IN C BY K.C. NG, 1/8/85; 43 * REVISED BY K.C. NG on 2/8/85, 2/23/85, 3/7/85, 3/29/85, 4/16/85. 44 * 45 * Required system supported functions : 46 * copysign(x,y) 47 * scalb(x,N) 48 * 49 * Required kernel function: 50 * exp(x) 51 * exp__E(x,c) ...return exp(x+c)-1-x for |x|<0.3465 52 * 53 * Method : 54 * 1. Replace x by |x|. 55 * 2. 56 * [ exp(x) - 1 ]^2 57 * 0 <= x <= 0.3465 : cosh(x) := 1 + ------------------- 58 * 2*exp(x) 59 * 60 * exp(x) + 1/exp(x) 61 * 0.3465 <= x <= 22 : cosh(x) := ------------------- 62 * 2 63 * 22 <= x <= lnovfl : cosh(x) := exp(x)/2 64 * lnovfl <= x <= lnovfl+log(2) 65 * : cosh(x) := exp(x)/2 (avoid overflow) 66 * log(2)+lnovfl < x < INF: overflow to INF 67 * 68 * Note: .3465 is a number near one half of ln2. 69 * 70 * Special cases: 71 * cosh(x) is x if x is +INF, -INF, or NaN. 72 * only cosh(0)=1 is exact for finite x. 73 * 74 * Accuracy: 75 * cosh(x) returns the exact hyperbolic cosine of x nearly rounded. 76 * In a test run with 768,000 random arguments on a VAX, the maximum 77 * observed error was 1.23 ulps (units in the last place). 78 * 79 * Constants: 80 * The hexadecimal values are the intended ones for the following constants. 81 * The decimal values may be used, provided that the compiler will convert 82 * from decimal to binary accurately enough to produce the hexadecimal values 83 * shown. 84 */ 85 86 #include "mathimpl.h" 87 88 vc(mln2hi, 8.8029691931113054792E1 ,0f33,43b0,2bdb,c7e2, 7, .B00F33C7E22BDB) 89 vc(mln2lo,-4.9650192275318476525E-16 ,1b60,a70f,582a,279e, -50,-.8F1B60279E582A) 90 vc(lnovfl, 8.8029691931113053016E1 ,0f33,43b0,2bda,c7e2, 7, .B00F33C7E22BDA) 91 92 ic(mln2hi, 7.0978271289338397310E2, 10, 1.62E42FEFA39EF) 93 ic(mln2lo, 2.3747039373786107478E-14, -45, 1.ABC9E3B39803F) 94 ic(lnovfl, 7.0978271289338397310E2, 9, 1.62E42FEFA39EF) 95 96 #ifdef vccast 97 #define mln2hi vccast(mln2hi) 98 #define mln2lo vccast(mln2lo) 99 #define lnovfl vccast(lnovfl) 100 #endif 101 102 #if defined(vax)||defined(tahoe) 103 static max = 126 ; 104 #else /* defined(vax)||defined(tahoe) */ 105 static max = 1023 ; 106 #endif /* defined(vax)||defined(tahoe) */ 107 108 double cosh(x) 109 double x; 110 { 111 static const double half=1.0/2.0, 112 one=1.0, small=1.0E-18; /* fl(1+small)==1 */ 113 double t; 114 115 #if !defined(vax)&&!defined(tahoe) 116 if(x!=x) return(x); /* x is NaN */ 117 #endif /* !defined(vax)&&!defined(tahoe) */ 118 if((x=copysign(x,one)) <= 22) 119 if(x<0.3465) 120 if(x<small) return(one+x); 121 else {t=x+__exp__E(x,0.0);x=t+t; return(one+t*t/(2.0+x)); } 122 123 else /* for x lies in [0.3465,22] */ 124 { t=exp(x); return((t+one/t)*half); } 125 126 if( lnovfl <= x && x <= (lnovfl+0.7)) 127 /* for x lies in [lnovfl, lnovfl+ln2], decrease x by ln(2^(max+1)) 128 * and return 2^max*exp(x) to avoid unnecessary overflow 129 */ 130 return(scalb(exp((x-mln2hi)-mln2lo), max)); 131 132 else 133 return(exp(x)*half); /* for large x, cosh(x)=exp(x)/2 */ 134 } 135