1 /* 2 * Copyright (c) 1985 Regents of the University of California. 3 * All rights reserved. 4 * 5 * Redistribution and use in source and binary forms are permitted 6 * provided that the above copyright notice and this paragraph are 7 * duplicated in all such forms and that any documentation, 8 * advertising materials, and other materials related to such 9 * distribution and use acknowledge that the software was developed 10 * by the University of California, Berkeley. The name of the 11 * University may not be used to endorse or promote products derived 12 * from this software without specific prior written permission. 13 * THIS SOFTWARE IS PROVIDED ``AS IS'' AND WITHOUT ANY EXPRESS OR 14 * IMPLIED WARRANTIES, INCLUDING, WITHOUT LIMITATION, THE IMPLIED 15 * WARRANTIES OF MERCHANTIBILITY AND FITNESS FOR A PARTICULAR PURPOSE. 16 * 17 * All recipients should regard themselves as participants in an ongoing 18 * research project and hence should feel obligated to report their 19 * experiences (good or bad) with these elementary function codes, using 20 * the sendbug(8) program, to the authors. 21 */ 22 23 #ifndef lint 24 static char sccsid[] = "@(#)sinh.c 5.4 (Berkeley) 09/22/88"; 25 #endif /* not lint */ 26 27 /* SINH(X) 28 * RETURN THE HYPERBOLIC SINE OF X 29 * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS) 30 * CODED IN C BY K.C. NG, 1/8/85; 31 * REVISED BY K.C. NG on 2/8/85, 3/7/85, 3/24/85, 4/16/85. 32 * 33 * Required system supported functions : 34 * copysign(x,y) 35 * scalb(x,N) 36 * 37 * Required kernel functions: 38 * expm1(x) ...return exp(x)-1 39 * 40 * Method : 41 * 1. reduce x to non-negative by sinh(-x) = - sinh(x). 42 * 2. 43 * 44 * expm1(x) + expm1(x)/(expm1(x)+1) 45 * 0 <= x <= lnovfl : sinh(x) := -------------------------------- 46 * 2 47 * lnovfl <= x <= lnovfl+ln2 : sinh(x) := expm1(x)/2 (avoid overflow) 48 * lnovfl+ln2 < x < INF : overflow to INF 49 * 50 * 51 * Special cases: 52 * sinh(x) is x if x is +INF, -INF, or NaN. 53 * only sinh(0)=0 is exact for finite argument. 54 * 55 * Accuracy: 56 * sinh(x) returns the exact hyperbolic sine of x nearly rounded. In 57 * a test run with 1,024,000 random arguments on a VAX, the maximum 58 * observed error was 1.93 ulps (units in the last place). 59 * 60 * Constants: 61 * The hexadecimal values are the intended ones for the following constants. 62 * The decimal values may be used, provided that the compiler will convert 63 * from decimal to binary accurately enough to produce the hexadecimal values 64 * shown. 65 */ 66 67 #include "mathimpl.h" 68 69 vc(mln2hi, 8.8029691931113054792E1 ,0f33,43b0,2bdb,c7e2, 7, .B00F33C7E22BDB) 70 vc(mln2lo,-4.9650192275318476525E-16 ,1b60,a70f,582a,279e, -50,-.8F1B60279E582A) 71 vc(lnovfl, 8.8029691931113053016E1 ,0f33,43b0,2bda,c7e2, 7, .B00F33C7E22BDA) 72 73 ic(mln2hi, 7.0978271289338397310E2, 10, 1.62E42FEFA39EF) 74 ic(mln2lo, 2.3747039373786107478E-14, -45, 1.ABC9E3B39803F) 75 ic(lnovfl, 7.0978271289338397310E2, 9, 1.62E42FEFA39EF) 76 77 #ifdef vccast 78 #define mln2hi vccast(mln2hi) 79 #define mln2lo vccast(mln2lo) 80 #define lnovfl vccast(lnovfl) 81 #endif 82 83 #if defined(vax)||defined(tahoe) 84 static max = 126 ; 85 #else /* defined(vax)||defined(tahoe) */ 86 static max = 1023 ; 87 #endif /* defined(vax)||defined(tahoe) */ 88 89 90 double sinh(x) 91 double x; 92 { 93 static const double one=1.0, half=1.0/2.0 ; 94 double t, sign; 95 #if !defined(vax)&&!defined(tahoe) 96 if(x!=x) return(x); /* x is NaN */ 97 #endif /* !defined(vax)&&!defined(tahoe) */ 98 sign=copysign(one,x); 99 x=copysign(x,one); 100 if(x<lnovfl) 101 {t=expm1(x); return(copysign((t+t/(one+t))*half,sign));} 102 103 else if(x <= lnovfl+0.7) 104 /* subtract x by ln(2^(max+1)) and return 2^max*exp(x) 105 to avoid unnecessary overflow */ 106 return(copysign(scalb(one+expm1((x-mln2hi)-mln2lo),max),sign)); 107 108 else /* sinh(+-INF) = +-INF, sinh(+-big no.) overflow to +-INF */ 109 return( expm1(x)*sign ); 110 } 111