1 /*
2 * Copyright (c) 1985 Regents of the University of California.
3 *
4 * Use and reproduction of this software are granted in accordance with
5 * the terms and conditions specified in the Berkeley Software License
6 * Agreement (in particular, this entails acknowledgement of the programs'
7 * source, and inclusion of this notice) with the additional understanding
8 * that all recipients should regard themselves as participants in an
9 * ongoing research project and hence should feel obligated to report
10 * their experiences (good or bad) with these elementary function codes,
11 * using "sendbug 4bsd-bugs@BERKELEY", to the authors.
12 */
13
14 #ifndef lint
15 static char sccsid[] = "@(#)tanh.c 4.3 (Berkeley) 08/21/85";
16 #endif not lint
17
18 /* TANH(X)
19 * RETURN THE HYPERBOLIC TANGENT OF X
20 * DOUBLE PRECISION (VAX D FORMAT 56 BITS, IEEE DOUBLE 53 BITS)
21 * CODED IN C BY K.C. NG, 1/8/85;
22 * REVISED BY K.C. NG on 2/8/85, 2/11/85, 3/7/85, 3/24/85.
23 *
24 * Required system supported functions :
25 * copysign(x,y)
26 * finite(x)
27 *
28 * Required kernel function:
29 * expm1(x) ...exp(x)-1
30 *
31 * Method :
32 * 1. reduce x to non-negative by tanh(-x) = - tanh(x).
33 * 2.
34 * 0 < x <= 1.e-10 : tanh(x) := x
35 * -expm1(-2x)
36 * 1.e-10 < x <= 1 : tanh(x) := --------------
37 * expm1(-2x) + 2
38 * 2
39 * 1 <= x <= 22.0 : tanh(x) := 1 - ---------------
40 * expm1(2x) + 2
41 * 22.0 < x <= INF : tanh(x) := 1.
42 *
43 * Note: 22 was chosen so that fl(1.0+2/(expm1(2*22)+2)) == 1.
44 *
45 * Special cases:
46 * tanh(NaN) is NaN;
47 * only tanh(0)=0 is exact for finite argument.
48 *
49 * Accuracy:
50 * tanh(x) returns the exact hyperbolic tangent of x nealy rounded.
51 * In a test run with 1,024,000 random arguments on a VAX, the maximum
52 * observed error was 2.22 ulps (units in the last place).
53 */
54
tanh(x)55 double tanh(x)
56 double x;
57 {
58 static double one=1.0, two=2.0, small = 1.0e-10, big = 1.0e10;
59 double expm1(), t, copysign(), sign;
60 int finite();
61
62 #ifndef VAX
63 if(x!=x) return(x); /* x is NaN */
64 #endif
65
66 sign=copysign(one,x);
67 x=copysign(x,one);
68 if(x < 22.0)
69 if( x > one )
70 return(copysign(one-two/(expm1(x+x)+two),sign));
71 else if ( x > small )
72 {t= -expm1(-(x+x)); return(copysign(t/(two-t),sign));}
73 else /* raise the INEXACT flag for non-zero x */
74 {big+x; return(copysign(x,sign));}
75 else if(finite(x))
76 return (sign+1.0E-37); /* raise the INEXACT flag */
77 else
78 return(sign); /* x is +- INF */
79 }
80