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
sinh(x)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