1 /* $NetBSD: n_sinh.c,v 1.1 1995/10/10 23:37:05 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[] = "@(#)sinh.c 8.1 (Berkeley) 6/4/93"; 37 #endif /* not lint */ 38 39 /* SINH(X) 40 * RETURN THE HYPERBOLIC SINE 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, 3/7/85, 3/24/85, 4/16/85. 44 * 45 * Required system supported functions : 46 * copysign(x,y) 47 * scalb(x,N) 48 * 49 * Required kernel functions: 50 * expm1(x) ...return exp(x)-1 51 * 52 * Method : 53 * 1. reduce x to non-negative by sinh(-x) = - sinh(x). 54 * 2. 55 * 56 * expm1(x) + expm1(x)/(expm1(x)+1) 57 * 0 <= x <= lnovfl : sinh(x) := -------------------------------- 58 * 2 59 * lnovfl <= x <= lnovfl+ln2 : sinh(x) := expm1(x)/2 (avoid overflow) 60 * lnovfl+ln2 < x < INF : overflow to INF 61 * 62 * 63 * Special cases: 64 * sinh(x) is x if x is +INF, -INF, or NaN. 65 * only sinh(0)=0 is exact for finite argument. 66 * 67 * Accuracy: 68 * sinh(x) returns the exact hyperbolic sine of x nearly rounded. In 69 * a test run with 1,024,000 random arguments on a VAX, the maximum 70 * observed error was 1.93 ulps (units in the last place). 71 * 72 * Constants: 73 * The hexadecimal values are the intended ones for the following constants. 74 * The decimal values may be used, provided that the compiler will convert 75 * from decimal to binary accurately enough to produce the hexadecimal values 76 * shown. 77 */ 78 79 #include "mathimpl.h" 80 81 vc(mln2hi, 8.8029691931113054792E1 ,0f33,43b0,2bdb,c7e2, 7, .B00F33C7E22BDB) 82 vc(mln2lo,-4.9650192275318476525E-16 ,1b60,a70f,582a,279e, -50,-.8F1B60279E582A) 83 vc(lnovfl, 8.8029691931113053016E1 ,0f33,43b0,2bda,c7e2, 7, .B00F33C7E22BDA) 84 85 ic(mln2hi, 7.0978271289338397310E2, 10, 1.62E42FEFA39EF) 86 ic(mln2lo, 2.3747039373786107478E-14, -45, 1.ABC9E3B39803F) 87 ic(lnovfl, 7.0978271289338397310E2, 9, 1.62E42FEFA39EF) 88 89 #ifdef vccast 90 #define mln2hi vccast(mln2hi) 91 #define mln2lo vccast(mln2lo) 92 #define lnovfl vccast(lnovfl) 93 #endif 94 95 #if defined(vax)||defined(tahoe) 96 static max = 126 ; 97 #else /* defined(vax)||defined(tahoe) */ 98 static max = 1023 ; 99 #endif /* defined(vax)||defined(tahoe) */ 100 101 102 double sinh(x) 103 double x; 104 { 105 static const double one=1.0, half=1.0/2.0 ; 106 double t, sign; 107 #if !defined(vax)&&!defined(tahoe) 108 if(x!=x) return(x); /* x is NaN */ 109 #endif /* !defined(vax)&&!defined(tahoe) */ 110 sign=copysign(one,x); 111 x=copysign(x,one); 112 if(x<lnovfl) 113 {t=expm1(x); return(copysign((t+t/(one+t))*half,sign));} 114 115 else if(x <= lnovfl+0.7) 116 /* subtract x by ln(2^(max+1)) and return 2^max*exp(x) 117 to avoid unnecessary overflow */ 118 return(copysign(scalb(one+expm1((x-mln2hi)-mln2lo),max),sign)); 119 120 else /* sinh(+-INF) = +-INF, sinh(+-big no.) overflow to +-INF */ 121 return( expm1(x)*sign ); 122 } 123