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Annotation of 43BSD/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:  * 
                      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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