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      1 /*	$NetBSD: n_tanh.c,v 1.8 2024/09/07 06:17:37 andvar 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. Neither the name of the University nor the names of its contributors
     15  *    may be used to endorse or promote products derived from this software
     16  *    without specific prior written permission.
     17  *
     18  * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
     19  * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
     20  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
     21  * ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
     22  * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
     23  * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
     24  * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
     25  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
     26  * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
     27  * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
     28  * SUCH DAMAGE.
     29  */
     30 
     31 #ifndef lint
     32 #if 0
     33 static char sccsid[] = "@(#)tanh.c	8.1 (Berkeley) 6/4/93";
     34 #endif
     35 #endif /* not lint */
     36 
     37 /* TANH(X)
     38  * RETURN THE HYPERBOLIC TANGENT OF X
     39  * DOUBLE PRECISION (VAX D FORMAT 56 BITS, IEEE DOUBLE 53 BITS)
     40  * CODED IN C BY K.C. NG, 1/8/85;
     41  * REVISED BY K.C. NG on 2/8/85, 2/11/85, 3/7/85, 3/24/85.
     42  *
     43  * Required system supported functions :
     44  *	copysign(x,y)
     45  *	finite(x)
     46  *
     47  * Required kernel function:
     48  *	expm1(x)	...exp(x)-1
     49  *
     50  * Method :
     51  *	1. reduce x to non-negative by tanh(-x) = - tanh(x).
     52  *	2.
     53  *	    0      <  x <=  1.e-10 :  tanh(x) := x
     54  *					          -expm1(-2x)
     55  *	    1.e-10 <  x <=  1      :  tanh(x) := --------------
     56  *					         expm1(-2x) + 2
     57  *							  2
     58  *	    1      <= x <=  22.0   :  tanh(x) := 1 -  ---------------
     59  *						      expm1(2x) + 2
     60  *	    22.0   <  x <= INF     :  tanh(x) := 1.
     61  *
     62  *	Note: 22 was chosen so that fl(1.0+2/(expm1(2*22)+2)) == 1.
     63  *
     64  * Special cases:
     65  *	tanh(NaN) is NaN;
     66  *	only tanh(0)=0 is exact for finite argument.
     67  *
     68  * Accuracy:
     69  *	tanh(x) returns the exact hyperbolic tangent of x nearly rounded.
     70  *	In a test run with 1,024,000 random arguments on a VAX, the maximum
     71  *	observed error was 2.22 ulps (units in the last place).
     72  */
     73 
     74 #include "mathimpl.h"
     75 
     76 double
     77 tanh(double x)
     78 {
     79 	static const double one=1.0, two=2.0, small = 1.0e-10, big = 1.0e10;
     80 	double t, sign;
     81 
     82 #if !defined(__vax__)&&!defined(tahoe)
     83 	if(x!=x) return(x);	/* x is NaN */
     84 #endif	/* !defined(__vax__)&&!defined(tahoe) */
     85 
     86 	sign=copysign(one,x);
     87 	x=copysign(x,one);
     88 	if(x < 22.0)
     89 	    if( x > one )
     90 		return(copysign(one-two/(expm1(x+x)+two),sign));
     91 	    else if ( x > small )
     92 		{t= -expm1(-(x+x)); return(copysign(t/(two-t),sign));}
     93 	    else		/* raise the INEXACT flag for non-zero x */
     94 		{ t = big+x; return(copysign(x,sign));} /* ??? -ragge */
     95 	else if(finite(x))
     96 	    return (sign+1.0E-37); /* raise the INEXACT flag */
     97 	else
     98 	    return(sign);	/* x is +- INF */
     99 }
    100 
    101 float
    102 tanhf(float x)
    103 {
    104 	return tanh(x);
    105 }
    106