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 this notice is preserved and that due credit is given 7 * to the University of California at Berkeley. The name of the University 8 * may not be used to endorse or promote products derived from this 9 * software without specific prior written permission. This software 10 * is provided ``as is'' without express or implied warranty. 11 * 12 * All recipients should regard themselves as participants in an ongoing 13 * research project and hence should feel obligated to report their 14 * experiences (good or bad) with these elementary function codes, using 15 * the sendbug(8) program, to the authors. 16 */ 17 18 #ifndef lint 19 static char sccsid[] = "@(#)sinh.c 5.2 (Berkeley) 04/29/88"; 20 #endif /* not lint */ 21 22 /* SINH(X) 23 * RETURN THE HYPERBOLIC SINE OF X 24 * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS) 25 * CODED IN C BY K.C. NG, 1/8/85; 26 * REVISED BY K.C. NG on 2/8/85, 3/7/85, 3/24/85, 4/16/85. 27 * 28 * Required system supported functions : 29 * copysign(x,y) 30 * scalb(x,N) 31 * 32 * Required kernel functions: 33 * expm1(x) ...return exp(x)-1 34 * 35 * Method : 36 * 1. reduce x to non-negative by sinh(-x) = - sinh(x). 37 * 2. 38 * 39 * expm1(x) + expm1(x)/(expm1(x)+1) 40 * 0 <= x <= lnovfl : sinh(x) := -------------------------------- 41 * 2 42 * lnovfl <= x <= lnovfl+ln2 : sinh(x) := expm1(x)/2 (avoid overflow) 43 * lnovfl+ln2 < x < INF : overflow to INF 44 * 45 * 46 * Special cases: 47 * sinh(x) is x if x is +INF, -INF, or NaN. 48 * only sinh(0)=0 is exact for finite argument. 49 * 50 * Accuracy: 51 * sinh(x) returns the exact hyperbolic sine of x nearly rounded. In 52 * a test run with 1,024,000 random arguments on a VAX, the maximum 53 * observed error was 1.93 ulps (units in the last place). 54 * 55 * Constants: 56 * The hexadecimal values are the intended ones for the following constants. 57 * The decimal values may be used, provided that the compiler will convert 58 * from decimal to binary accurately enough to produce the hexadecimal values 59 * shown. 60 */ 61 #if defined(vax)||defined(tahoe) 62 #ifdef vax 63 #define _0x(A,B) 0x/**/A/**/B 64 #else /* vax */ 65 #define _0x(A,B) 0x/**/B/**/A 66 #endif /* vax */ 67 /* static double */ 68 /* mln2hi = 8.8029691931113054792E1 , Hex 2^ 7 * .B00F33C7E22BDB */ 69 /* mln2lo = -4.9650192275318476525E-16 , Hex 2^-50 * -.8F1B60279E582A */ 70 /* lnovfl = 8.8029691931113053016E1 ; Hex 2^ 7 * .B00F33C7E22BDA */ 71 static long mln2hix[] = { _0x(0f33,43b0), _0x(2bdb,c7e2)}; 72 static long mln2lox[] = { _0x(1b60,a70f), _0x(582a,279e)}; 73 static long lnovflx[] = { _0x(0f33,43b0), _0x(2bda,c7e2)}; 74 #define mln2hi (*(double*)mln2hix) 75 #define mln2lo (*(double*)mln2lox) 76 #define lnovfl (*(double*)lnovflx) 77 #else /* defined(vax)||defined(tahoe) */ 78 static double 79 mln2hi = 7.0978271289338397310E2 , /*Hex 2^ 10 * 1.62E42FEFA39EF */ 80 mln2lo = 2.3747039373786107478E-14 , /*Hex 2^-45 * 1.ABC9E3B39803F */ 81 lnovfl = 7.0978271289338397310E2 ; /*Hex 2^ 9 * 1.62E42FEFA39EF */ 82 #endif /* defined(vax)||defined(tahoe) */ 83 84 #if defined(vax)||defined(tahoe) 85 static max = 126 ; 86 #else /* defined(vax)||defined(tahoe) */ 87 static max = 1023 ; 88 #endif /* defined(vax)||defined(tahoe) */ 89 90 91 double sinh(x) 92 double x; 93 { 94 static double one=1.0, half=1.0/2.0 ; 95 double expm1(), t, scalb(), copysign(), sign; 96 #if !defined(vax)&&!defined(tahoe) 97 if(x!=x) return(x); /* x is NaN */ 98 #endif /* !defined(vax)&&!defined(tahoe) */ 99 sign=copysign(one,x); 100 x=copysign(x,one); 101 if(x<lnovfl) 102 {t=expm1(x); return(copysign((t+t/(one+t))*half,sign));} 103 104 else if(x <= lnovfl+0.7) 105 /* subtract x by ln(2^(max+1)) and return 2^max*exp(x) 106 to avoid unnecessary overflow */ 107 return(copysign(scalb(one+expm1((x-mln2hi)-mln2lo),max),sign)); 108 109 else /* sinh(+-INF) = +-INF, sinh(+-big no.) overflow to +-INF */ 110 return( expm1(x)*sign ); 111 } 112