Return to tanh.c CVS log

Up to [CSRG BSD Unix] / 43BSDReno / lib / libm / common_source

Annotation of 43BSDReno/lib/libm/common_source/tanh.c, revision 1.1.1.1

1.1       root        1: /*
                      2:  * Copyright (c) 1985 Regents of the University of California.
                      3:  * All rights reserved.
                      4:  *
                      5:  * Redistribution and use in source and binary forms are permitted
                      6:  * provided that: (1) source distributions retain this entire copyright
                      7:  * notice and comment, and (2) distributions including binaries display
                      8:  * the following acknowledgement:  ``This product includes software
                      9:  * developed by the University of California, Berkeley and its contributors''
                     10:  * in the documentation or other materials provided with the distribution
                     11:  * and in all advertising materials mentioning features or use of this
                     12:  * software. Neither the name of the University nor the names of its
                     13:  * contributors may be used to endorse or promote products derived
                     14:  * from this software without specific prior written permission.
                     15:  * THIS SOFTWARE IS PROVIDED ``AS IS'' AND WITHOUT ANY EXPRESS OR
                     16:  * IMPLIED WARRANTIES, INCLUDING, WITHOUT LIMITATION, THE IMPLIED
                     17:  * WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
                     18:  *
                     19:  * All recipients should regard themselves as participants in an ongoing
                     20:  * research project and hence should feel obligated to report their
                     21:  * experiences (good or bad) with these elementary function codes, using
                     22:  * the sendbug(8) program, to the authors.
                     23:  */
                     24: 
                     25: #ifndef lint
                     26: static char sccsid[] = "@(#)tanh.c     5.4 (Berkeley) 6/1/90";
                     27: #endif /* not lint */
                     28: 
                     29: /* TANH(X)
                     30:  * RETURN THE HYPERBOLIC TANGENT OF X
                     31:  * DOUBLE PRECISION (VAX D FORMAT 56 BITS, IEEE DOUBLE 53 BITS)
                     32:  * CODED IN C BY K.C. NG, 1/8/85; 
                     33:  * REVISED BY K.C. NG on 2/8/85, 2/11/85, 3/7/85, 3/24/85.
                     34:  *
                     35:  * Required system supported functions :
                     36:  *     copysign(x,y)
                     37:  *     finite(x)
                     38:  *
                     39:  * Required kernel function:
                     40:  *     expm1(x)        ...exp(x)-1
                     41:  *
                     42:  * Method :
                     43:  *     1. reduce x to non-negative by tanh(-x) = - tanh(x).
                     44:  *     2.
                     45:  *         0      <  x <=  1.e-10 :  tanh(x) := x
                     46:  *                                               -expm1(-2x)
                     47:  *         1.e-10 <  x <=  1      :  tanh(x) := --------------
                     48:  *                                              expm1(-2x) + 2
                     49:  *                                                       2
                     50:  *         1      <= x <=  22.0   :  tanh(x) := 1 -  ---------------
                     51:  *                                                   expm1(2x) + 2
                     52:  *         22.0   <  x <= INF     :  tanh(x) := 1.
                     53:  *
                     54:  *     Note: 22 was chosen so that fl(1.0+2/(expm1(2*22)+2)) == 1.
                     55:  *
                     56:  * Special cases:
                     57:  *     tanh(NaN) is NaN;
                     58:  *     only tanh(0)=0 is exact for finite argument.
                     59:  *
                     60:  * Accuracy:
                     61:  *     tanh(x) returns the exact hyperbolic tangent of x nealy rounded.
                     62:  *     In a test run with 1,024,000 random arguments on a VAX, the maximum
                     63:  *     observed error was 2.22 ulps (units in the last place).
                     64:  */
                     65: 
                     66: double tanh(x)
                     67: double x;
                     68: {
                     69:        static double one=1.0, two=2.0, small = 1.0e-10, big = 1.0e10;
                     70:        double expm1(), t, copysign(), sign;
                     71:        int finite();
                     72: 
                     73: #if !defined(vax)&&!defined(tahoe)
                     74:        if(x!=x) return(x);     /* x is NaN */
                     75: #endif /* !defined(vax)&&!defined(tahoe) */
                     76: 
                     77:        sign=copysign(one,x);
                     78:        x=copysign(x,one);
                     79:        if(x < 22.0) 
                     80:            if( x > one )
                     81:                return(copysign(one-two/(expm1(x+x)+two),sign));
                     82:            else if ( x > small )
                     83:                {t= -expm1(-(x+x)); return(copysign(t/(two-t),sign));}
                     84:            else                /* raise the INEXACT flag for non-zero x */
                     85:                {big+x; return(copysign(x,sign));}
                     86:        else if(finite(x))
                     87:            return (sign+1.0E-37); /* raise the INEXACT flag */
                     88:        else
                     89:            return(sign);       /* x is +- INF */
                     90: }

This archive runs on limited infrastructure. Preserving old code on modern bandwidth. Automated agents are requested to crawl responsibly.