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33 * @(#)tanh.c 8.1 (Berkeley) 6/4/93
37 * RETURN THE HYPERBOLIC TANGENT OF X
38 * DOUBLE PRECISION (VAX D FORMAT 56 BITS, IEEE DOUBLE 53 BITS)
39 * CODED IN C BY K.C. NG, 1/8/85;
40 * REVISED BY K.C. NG on 2/8/85, 2/11/85, 3/7/85, 3/24/85.
42 * Required system supported functions :
46 * Required kernel function:
47 * expm1(x) ...exp(x)-1
50 * 1. reduce x to non-negative by tanh(-x) = - tanh(x).
52 * 0 < x <= 1.e-10 : tanh(x) := x
54 * 1.e-10 < x <= 1 : tanh(x) := --------------
57 * 1 <= x <= 22.0 : tanh(x) := 1 - ---------------
59 * 22.0 < x <= INF : tanh(x) := 1.
61 * Note: 22 was chosen so that fl(1.0+2/(expm1(2*22)+2)) == 1.
65 * only tanh(0)=0 is exact for finite argument.
68 * tanh(x) returns the exact hyperbolic tangent of x nealy rounded.
69 * In a test run with 1,024,000 random arguments on a VAX, the maximum
70 * observed error was 2.22 ulps (units in the last place).
76 static double one=1.0, two=2.0, small = 1.0e-10, big = 1.0e10;
77 double expm1(), t, copysign(), sign;
80 #if !defined(vax)&&!defined(tahoe)
81 if(x!=x) return(x); /* x is NaN */
82 #endif /* !defined(vax)&&!defined(tahoe) */
88 return(copysign(one-two/(expm1(x+x)+two),sign));
90 {t= -expm1(-(x+x)); return(copysign(t/(two-t),sign));}
91 else /* raise the INEXACT flag for non-zero x */
92 {big+x; return(copysign(x,sign));}
94 return (sign+1.0E-37); /* raise the INEXACT flag */
96 return(sign); /* x is +- INF */