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Annotation of 43BSD/usr.lib/libm/atanh.c, revision 1.1.1.1

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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