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Annotation of 43BSD/usr.lib/libm/tanh.c, revision 1.1

1.1     ! root        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) 8/21/85";
        !            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: 
        !            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: }

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