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n_tanh.c revision 1.3 
      1 /*	$NetBSD: n_tanh.c,v 1.3 1998/10/20 02:26:13 matt Exp $	*/
      2 /*
      3  * Copyright (c) 1985, 1993
      4  *	The Regents of the University of California.  All rights reserved.
      5  *
      6  * Redistribution and use in source and binary forms, with or without
      7  * modification, are permitted provided that the following conditions
      8  * are met:
      9  * 1. Redistributions of source code must retain the above copyright
     10  *    notice, this list of conditions and the following disclaimer.
     11  * 2. Redistributions in binary form must reproduce the above copyright
     12  *    notice, this list of conditions and the following disclaimer in the
     13  *    documentation and/or other materials provided with the distribution.
     14  * 3. All advertising materials mentioning features or use of this software
     15  *    must display the following acknowledgement:
     16  *	This product includes software developed by the University of
     17  *	California, Berkeley and its contributors.
     18  * 4. Neither the name of the University nor the names of its contributors
     19  *    may be used to endorse or promote products derived from this software
     20  *    without specific prior written permission.
     21  *
     22  * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
     23  * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
     24  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
     25  * ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
     26  * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
     27  * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
     28  * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
     29  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
     30  * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
     31  * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
     32  * SUCH DAMAGE.
     33  */
     34 
     35 #ifndef lint
     36 #if 0
     37 static char sccsid[] = "@(#)tanh.c	8.1 (Berkeley) 6/4/93";
     38 #endif
     39 #endif /* not lint */
     40 
     41 /* TANH(X)
     42  * RETURN THE HYPERBOLIC TANGENT OF X
     43  * DOUBLE PRECISION (VAX D FORMAT 56 BITS, IEEE DOUBLE 53 BITS)
     44  * CODED IN C BY K.C. NG, 1/8/85;
     45  * REVISED BY K.C. NG on 2/8/85, 2/11/85, 3/7/85, 3/24/85.
     46  *
     47  * Required system supported functions :
     48  *	copysign(x,y)
     49  *	finite(x)
     50  *
     51  * Required kernel function:
     52  *	expm1(x)	...exp(x)-1
     53  *
     54  * Method :
     55  *	1. reduce x to non-negative by tanh(-x) = - tanh(x).
     56  *	2.
     57  *	    0      <  x <=  1.e-10 :  tanh(x) := x
     58  *					          -expm1(-2x)
     59  *	    1.e-10 <  x <=  1      :  tanh(x) := --------------
     60  *					         expm1(-2x) + 2
     61  *							  2
     62  *	    1      <= x <=  22.0   :  tanh(x) := 1 -  ---------------
     63  *						      expm1(2x) + 2
     64  *	    22.0   <  x <= INF     :  tanh(x) := 1.
     65  *
     66  *	Note: 22 was chosen so that fl(1.0+2/(expm1(2*22)+2)) == 1.
     67  *
     68  * Special cases:
     69  *	tanh(NaN) is NaN;
     70  *	only tanh(0)=0 is exact for finite argument.
     71  *
     72  * Accuracy:
     73  *	tanh(x) returns the exact hyperbolic tangent of x nealy rounded.
     74  *	In a test run with 1,024,000 random arguments on a VAX, the maximum
     75  *	observed error was 2.22 ulps (units in the last place).
     76  */
     77 
     78 #include "mathimpl.h"
     79 
     80 double tanh(x)
     81 double x;
     82 {
     83 	static double one=1.0, two=2.0, small = 1.0e-10, big = 1.0e10;
     84 	double t, sign;
     85 
     86 #if !defined(__vax__)&&!defined(tahoe)
     87 	if(x!=x) return(x);	/* x is NaN */
     88 #endif	/* !defined(__vax__)&&!defined(tahoe) */
     89 
     90 	sign=copysign(one,x);
     91 	x=copysign(x,one);
     92 	if(x < 22.0)
     93 	    if( x > one )
     94 		return(copysign(one-two/(expm1(x+x)+two),sign));
     95 	    else if ( x > small )
     96 		{t= -expm1(-(x+x)); return(copysign(t/(two-t),sign));}
     97 	    else		/* raise the INEXACT flag for non-zero x */
     98 		{ t = big+x; return(copysign(x,sign));} /* ??? -ragge */
     99 	else if(finite(x))
    100 	    return (sign+1.0E-37); /* raise the INEXACT flag */
    101 	else
    102 	    return(sign);	/* x is +- INF */
    103 }
    104