1 /* 2 * Copyright (c) 1985, 1993 3 * The Regents of the University of California. All rights reserved. 4 * 5 * %sccs.include.redist.c% 6 */ 7 8 #ifndef lint 9 static char sccsid[] = "@(#)sinh.c 8.1 (Berkeley) 06/04/93"; 10 #endif /* not lint */ 11 12 /* SINH(X) 13 * RETURN THE HYPERBOLIC SINE OF X 14 * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS) 15 * CODED IN C BY K.C. NG, 1/8/85; 16 * REVISED BY K.C. NG on 2/8/85, 3/7/85, 3/24/85, 4/16/85. 17 * 18 * Required system supported functions : 19 * copysign(x,y) 20 * scalb(x,N) 21 * 22 * Required kernel functions: 23 * expm1(x) ...return exp(x)-1 24 * 25 * Method : 26 * 1. reduce x to non-negative by sinh(-x) = - sinh(x). 27 * 2. 28 * 29 * expm1(x) + expm1(x)/(expm1(x)+1) 30 * 0 <= x <= lnovfl : sinh(x) := -------------------------------- 31 * 2 32 * lnovfl <= x <= lnovfl+ln2 : sinh(x) := expm1(x)/2 (avoid overflow) 33 * lnovfl+ln2 < x < INF : overflow to INF 34 * 35 * 36 * Special cases: 37 * sinh(x) is x if x is +INF, -INF, or NaN. 38 * only sinh(0)=0 is exact for finite argument. 39 * 40 * Accuracy: 41 * sinh(x) returns the exact hyperbolic sine of x nearly rounded. In 42 * a test run with 1,024,000 random arguments on a VAX, the maximum 43 * observed error was 1.93 ulps (units in the last place). 44 * 45 * Constants: 46 * The hexadecimal values are the intended ones for the following constants. 47 * The decimal values may be used, provided that the compiler will convert 48 * from decimal to binary accurately enough to produce the hexadecimal values 49 * shown. 50 */ 51 52 #include "mathimpl.h" 53 54 vc(mln2hi, 8.8029691931113054792E1 ,0f33,43b0,2bdb,c7e2, 7, .B00F33C7E22BDB) 55 vc(mln2lo,-4.9650192275318476525E-16 ,1b60,a70f,582a,279e, -50,-.8F1B60279E582A) 56 vc(lnovfl, 8.8029691931113053016E1 ,0f33,43b0,2bda,c7e2, 7, .B00F33C7E22BDA) 57 58 ic(mln2hi, 7.0978271289338397310E2, 10, 1.62E42FEFA39EF) 59 ic(mln2lo, 2.3747039373786107478E-14, -45, 1.ABC9E3B39803F) 60 ic(lnovfl, 7.0978271289338397310E2, 9, 1.62E42FEFA39EF) 61 62 #ifdef vccast 63 #define mln2hi vccast(mln2hi) 64 #define mln2lo vccast(mln2lo) 65 #define lnovfl vccast(lnovfl) 66 #endif 67 68 #if defined(vax)||defined(tahoe) 69 static max = 126 ; 70 #else /* defined(vax)||defined(tahoe) */ 71 static max = 1023 ; 72 #endif /* defined(vax)||defined(tahoe) */ 73 74 75 double sinh(x) 76 double x; 77 { 78 static const double one=1.0, half=1.0/2.0 ; 79 double t, sign; 80 #if !defined(vax)&&!defined(tahoe) 81 if(x!=x) return(x); /* x is NaN */ 82 #endif /* !defined(vax)&&!defined(tahoe) */ 83 sign=copysign(one,x); 84 x=copysign(x,one); 85 if(x<lnovfl) 86 {t=expm1(x); return(copysign((t+t/(one+t))*half,sign));} 87 88 else if(x <= lnovfl+0.7) 89 /* subtract x by ln(2^(max+1)) and return 2^max*exp(x) 90 to avoid unnecessary overflow */ 91 return(copysign(scalb(one+expm1((x-mln2hi)-mln2lo),max),sign)); 92 93 else /* sinh(+-INF) = +-INF, sinh(+-big no.) overflow to +-INF */ 94 return( expm1(x)*sign ); 95 } 96