/* $NetBSD: n_tanh.c,v 1.8 2024/09/07 06:17:37 andvar Exp $ */
/*
* Copyright (c) 1985, 1993
* The Regents of the University of California. All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
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* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
* 3. Neither the name of the University nor the names of its contributors
* may be used to endorse or promote products derived from this software
* without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
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*/
/* TANH(X)
* RETURN THE HYPERBOLIC TANGENT OF X
* DOUBLE PRECISION (VAX D FORMAT 56 BITS, IEEE DOUBLE 53 BITS)
* CODED IN C BY K.C. NG, 1/8/85;
* REVISED BY K.C. NG on 2/8/85, 2/11/85, 3/7/85, 3/24/85.
*
* Required system supported functions :
* copysign(x,y)
* finite(x)
*
* Required kernel function:
* expm1(x) ...exp(x)-1
*
* Method :
* 1. reduce x to non-negative by tanh(-x) = - tanh(x).
* 2.
* 0 < x <= 1.e-10 : tanh(x) := x
* -expm1(-2x)
* 1.e-10 < x <= 1 : tanh(x) := --------------
* expm1(-2x) + 2
* 2
* 1 <= x <= 22.0 : tanh(x) := 1 - ---------------
* expm1(2x) + 2
* 22.0 < x <= INF : tanh(x) := 1.
*
* Note: 22 was chosen so that fl(1.0+2/(expm1(2*22)+2)) == 1.
*
* Special cases:
* tanh(NaN) is NaN;
* only tanh(0)=0 is exact for finite argument.
*
* Accuracy:
* tanh(x) returns the exact hyperbolic tangent of x nearly rounded.
* In a test run with 1,024,000 random arguments on a VAX, the maximum
* observed error was 2.22 ulps (units in the last place).
*/
#include "mathimpl.h"
double
tanh(double x)
{
static const double one=1.0, two=2.0, small = 1.0e-10, big = 1.0e10;
double t, sign;
#if !defined(__vax__)&&!defined(tahoe)
if(x!=x) return(x); /* x is NaN */
#endif /* !defined(__vax__)&&!defined(tahoe) */
sign=copysign(one,x);
x=copysign(x,one);
if(x < 22.0)
if( x > one )
return(copysign(one-two/(expm1(x+x)+two),sign));
else if ( x > small )
{t= -expm1(-(x+x)); return(copysign(t/(two-t),sign));}
else /* raise the INEXACT flag for non-zero x */
{ t = big+x; return(copysign(x,sign));} /* ??? -ragge */
else if(finite(x))
return (sign+1.0E-37); /* raise the INEXACT flag */
else
return(sign); /* x is +- INF */
}
