1 /* 2 * Copyright (c) 1985 Regents of the University of California. 3 * All rights reserved. 4 * 5 * %sccs.include.redist.c% 6 * 7 * All recipients should regard themselves as participants in an ongoing 8 * research project and hence should feel obligated to report their 9 * experiences (good or bad) with these elementary function codes, using 10 * the sendbug(8) program, to the authors. 11 */ 12 13 #ifndef lint 14 static char sccsid[] = "@(#)sinh.c 5.5 (Berkeley) 06/01/90"; 15 #endif /* not lint */ 16 17 /* SINH(X) 18 * RETURN THE HYPERBOLIC SINE OF X 19 * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS) 20 * CODED IN C BY K.C. NG, 1/8/85; 21 * REVISED BY K.C. NG on 2/8/85, 3/7/85, 3/24/85, 4/16/85. 22 * 23 * Required system supported functions : 24 * copysign(x,y) 25 * scalb(x,N) 26 * 27 * Required kernel functions: 28 * expm1(x) ...return exp(x)-1 29 * 30 * Method : 31 * 1. reduce x to non-negative by sinh(-x) = - sinh(x). 32 * 2. 33 * 34 * expm1(x) + expm1(x)/(expm1(x)+1) 35 * 0 <= x <= lnovfl : sinh(x) := -------------------------------- 36 * 2 37 * lnovfl <= x <= lnovfl+ln2 : sinh(x) := expm1(x)/2 (avoid overflow) 38 * lnovfl+ln2 < x < INF : overflow to INF 39 * 40 * 41 * Special cases: 42 * sinh(x) is x if x is +INF, -INF, or NaN. 43 * only sinh(0)=0 is exact for finite argument. 44 * 45 * Accuracy: 46 * sinh(x) returns the exact hyperbolic sine of x nearly rounded. In 47 * a test run with 1,024,000 random arguments on a VAX, the maximum 48 * observed error was 1.93 ulps (units in the last place). 49 * 50 * Constants: 51 * The hexadecimal values are the intended ones for the following constants. 52 * The decimal values may be used, provided that the compiler will convert 53 * from decimal to binary accurately enough to produce the hexadecimal values 54 * shown. 55 */ 56 57 #include "mathimpl.h" 58 59 vc(mln2hi, 8.8029691931113054792E1 ,0f33,43b0,2bdb,c7e2, 7, .B00F33C7E22BDB) 60 vc(mln2lo,-4.9650192275318476525E-16 ,1b60,a70f,582a,279e, -50,-.8F1B60279E582A) 61 vc(lnovfl, 8.8029691931113053016E1 ,0f33,43b0,2bda,c7e2, 7, .B00F33C7E22BDA) 62 63 ic(mln2hi, 7.0978271289338397310E2, 10, 1.62E42FEFA39EF) 64 ic(mln2lo, 2.3747039373786107478E-14, -45, 1.ABC9E3B39803F) 65 ic(lnovfl, 7.0978271289338397310E2, 9, 1.62E42FEFA39EF) 66 67 #ifdef vccast 68 #define mln2hi vccast(mln2hi) 69 #define mln2lo vccast(mln2lo) 70 #define lnovfl vccast(lnovfl) 71 #endif 72 73 #if defined(vax)||defined(tahoe) 74 static max = 126 ; 75 #else /* defined(vax)||defined(tahoe) */ 76 static max = 1023 ; 77 #endif /* defined(vax)||defined(tahoe) */ 78 79 80 double sinh(x) 81 double x; 82 { 83 static const double one=1.0, half=1.0/2.0 ; 84 double t, sign; 85 #if !defined(vax)&&!defined(tahoe) 86 if(x!=x) return(x); /* x is NaN */ 87 #endif /* !defined(vax)&&!defined(tahoe) */ 88 sign=copysign(one,x); 89 x=copysign(x,one); 90 if(x<lnovfl) 91 {t=expm1(x); return(copysign((t+t/(one+t))*half,sign));} 92 93 else if(x <= lnovfl+0.7) 94 /* subtract x by ln(2^(max+1)) and return 2^max*exp(x) 95 to avoid unnecessary overflow */ 96 return(copysign(scalb(one+expm1((x-mln2hi)-mln2lo),max),sign)); 97 98 else /* sinh(+-INF) = +-INF, sinh(+-big no.) overflow to +-INF */ 99 return( expm1(x)*sign ); 100 } 101