usr/src/lib/libm/common_source/tanh.c

/*
 * Copyright (c) 1985 Regents of the University of California.
 * All rights reserved.
 *
 * %sccs.include.redist.c%
 */

#ifndef lint
static char sccsid[] = "@(#)tanh.c      5.5 (Berkeley) %G%";
#endif /* not lint */

/* TANH(X)
 * RETURN THE HYPERBOLIC TANGENT OF X
 * DOUBLE PRECISION (VAX D FORMAT 56 BITS, IEEE DOUBLE 53 BITS)
 * CODED IN C BY K.C. NG, 1/8/85;
 * REVISED BY K.C. NG on 2/8/85, 2/11/85, 3/7/85, 3/24/85.
 *
 * Required system supported functions :
 *      copysign(x,y)
 *      finite(x)
 *
 * Required kernel function:
 *      expm1(x)        ...exp(x)-1
 *
 * Method :
 *      1. reduce x to non-negative by tanh(-x) = - tanh(x).
 *      2.
 *          0      <  x <=  1.e-10 :  tanh(x) := x
 *                                                -expm1(-2x)
 *          1.e-10 <  x <=  1      :  tanh(x) := --------------
 *                                               expm1(-2x) + 2
 *                                                        2
 *          1      <= x <=  22.0   :  tanh(x) := 1 -  ---------------
 *                                                    expm1(2x) + 2
 *          22.0   <  x <= INF     :  tanh(x) := 1.
 *
 *      Note: 22 was chosen so that fl(1.0+2/(expm1(2*22)+2)) == 1.
 *
 * Special cases:
 *      tanh(NaN) is NaN;
 *      only tanh(0)=0 is exact for finite argument.
 *
 * Accuracy:
 *      tanh(x) returns the exact hyperbolic tangent of x nealy rounded.
 *      In a test run with 1,024,000 random arguments on a VAX, the maximum
 *      observed error was 2.22 ulps (units in the last place).
 */

double tanh(x)
double x;
{
        static double one=1.0, two=2.0, small = 1.0e-10, big = 1.0e10;
        double expm1(), t, copysign(), sign;
        int finite();

#if !defined(vax)&&!defined(tahoe)
        if(x!=x) return(x);     /* x is NaN */
#endif  /* !defined(vax)&&!defined(tahoe) */

        sign=copysign(one,x);
        x=copysign(x,one);
        if(x < 22.0)
            if( x > one )
                return(copysign(one-two/(expm1(x+x)+two),sign));
            else if ( x > small )
                {t= -expm1(-(x+x)); return(copysign(t/(two-t),sign));}
            else                /* raise the INEXACT flag for non-zero x */
                {big+x; return(copysign(x,sign));}
        else if(finite(x))
            return (sign+1.0E-37); /* raise the INEXACT flag */
        else
            return(sign);       /* x is +- INF */
}