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Annotation of 43BSDTahoe/usr.lib/libm/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 the above copyright notice and this paragraph are
                      7:  * duplicated in all such forms and that any documentation,
                      8:  * advertising materials, and other materials related to such
                      9:  * distribution and use acknowledge that the software was developed
                     10:  * by the University of California, Berkeley.  The name of the
                     11:  * University may not be used to endorse or promote products derived
                     12:  * from this software without specific prior written permission.
                     13:  * THIS SOFTWARE IS PROVIDED ``AS IS'' AND WITHOUT ANY EXPRESS OR
                     14:  * IMPLIED WARRANTIES, INCLUDING, WITHOUT LIMITATION, THE IMPLIED
                     15:  * WARRANTIES OF MERCHANTIBILITY AND FITNESS FOR A PARTICULAR PURPOSE.
                     16:  *
                     17:  * All recipients should regard themselves as participants in an ongoing
                     18:  * research project and hence should feel obligated to report their
                     19:  * experiences (good or bad) with these elementary function codes, using
                     20:  * the sendbug(8) program, to the authors.
                     21:  */
                     22: 
                     23: #ifndef lint
                     24: static char sccsid[] = "@(#)tanh.c     5.3 (Berkeley) 6/30/88";
                     25: #endif /* not lint */
                     26: 
                     27: /* TANH(X)
                     28:  * RETURN THE HYPERBOLIC TANGENT OF X
                     29:  * DOUBLE PRECISION (VAX D FORMAT 56 BITS, IEEE DOUBLE 53 BITS)
                     30:  * CODED IN C BY K.C. NG, 1/8/85; 
                     31:  * REVISED BY K.C. NG on 2/8/85, 2/11/85, 3/7/85, 3/24/85.
                     32:  *
                     33:  * Required system supported functions :
                     34:  *     copysign(x,y)
                     35:  *     finite(x)
                     36:  *
                     37:  * Required kernel function:
                     38:  *     expm1(x)        ...exp(x)-1
                     39:  *
                     40:  * Method :
                     41:  *     1. reduce x to non-negative by tanh(-x) = - tanh(x).
                     42:  *     2.
                     43:  *         0      <  x <=  1.e-10 :  tanh(x) := x
                     44:  *                                               -expm1(-2x)
                     45:  *         1.e-10 <  x <=  1      :  tanh(x) := --------------
                     46:  *                                              expm1(-2x) + 2
                     47:  *                                                       2
                     48:  *         1      <= x <=  22.0   :  tanh(x) := 1 -  ---------------
                     49:  *                                                   expm1(2x) + 2
                     50:  *         22.0   <  x <= INF     :  tanh(x) := 1.
                     51:  *
                     52:  *     Note: 22 was chosen so that fl(1.0+2/(expm1(2*22)+2)) == 1.
                     53:  *
                     54:  * Special cases:
                     55:  *     tanh(NaN) is NaN;
                     56:  *     only tanh(0)=0 is exact for finite argument.
                     57:  *
                     58:  * Accuracy:
                     59:  *     tanh(x) returns the exact hyperbolic tangent of x nealy rounded.
                     60:  *     In a test run with 1,024,000 random arguments on a VAX, the maximum
                     61:  *     observed error was 2.22 ulps (units in the last place).
                     62:  */
                     63: 
                     64: double tanh(x)
                     65: double x;
                     66: {
                     67:        static double one=1.0, two=2.0, small = 1.0e-10, big = 1.0e10;
                     68:        double expm1(), t, copysign(), sign;
                     69:        int finite();
                     70: 
                     71: #if !defined(vax)&&!defined(tahoe)
                     72:        if(x!=x) return(x);     /* x is NaN */
                     73: #endif /* !defined(vax)&&!defined(tahoe) */
                     74: 
                     75:        sign=copysign(one,x);
                     76:        x=copysign(x,one);
                     77:        if(x < 22.0) 
                     78:            if( x > one )
                     79:                return(copysign(one-two/(expm1(x+x)+two),sign));
                     80:            else if ( x > small )
                     81:                {t= -expm1(-(x+x)); return(copysign(t/(two-t),sign));}
                     82:            else                /* raise the INEXACT flag for non-zero x */
                     83:                {big+x; return(copysign(x,sign));}
                     84:        else if(finite(x))
                     85:            return (sign+1.0E-37); /* raise the INEXACT flag */
                     86:        else
                     87:            return(sign);       /* x is +- INF */
                     88: }

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