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Annotation of 43BSD/usr.lib/libm/atanh.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[] = "@(#)atanh.c    1.2 (Berkeley) 8/21/85";
        !            16: #endif not lint
        !            17: 
        !            18: /* ATANH(X)
        !            19:  * RETURN THE HYPERBOLIC ARC 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 2/7/85, 3/7/85, 8/18/85.
        !            23:  *
        !            24:  * Required kernel function:
        !            25:  *     log1p(x)        ...return log(1+x)
        !            26:  *
        !            27:  * Method :
        !            28:  *     Return 
        !            29:  *                          1              2x                          x
        !            30:  *             atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
        !            31:  *                          2             1 - x                      1 - x
        !            32:  *
        !            33:  * Special cases:
        !            34:  *     atanh(x) is NaN if |x| > 1 with signal;
        !            35:  *     atanh(NaN) is that NaN with no signal;
        !            36:  *     atanh(+-1) is +-INF with signal.
        !            37:  *
        !            38:  * Accuracy:
        !            39:  *     atanh(x) returns the exact hyperbolic arc tangent of x nearly rounded.
        !            40:  *     In a test run with 512,000 random arguments on a VAX, the maximum
        !            41:  *     observed error was 1.87 ulps (units in the last place) at
        !            42:  *     x= -3.8962076028810414000e-03.
        !            43:  */
        !            44: #ifdef VAX
        !            45: #include <errno.h>
        !            46: #endif
        !            47: 
        !            48: double atanh(x)
        !            49: double x;
        !            50: {
        !            51:        double copysign(),log1p(),z;
        !            52:        z = copysign(0.5,x);
        !            53:        x = copysign(x,1.0);
        !            54: #ifdef VAX
        !            55:        if (x == 1.0) {
        !            56:            extern double infnan();
        !            57:            return(copysign(1.0,z)*infnan(ERANGE));     /* sign(x)*INF */
        !            58:        }
        !            59: #endif
        !            60:        x = x/(1.0-x);
        !            61:        return( z*log1p(x+x) );
        !            62: }

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