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/* tanhf.c
*
* Hyperbolic tangent
*
*
*
* SYNOPSIS:
*
* float x, y, tanhf();
*
* y = tanhf( x );
*
*
*
* DESCRIPTION:
*
* Returns hyperbolic tangent of argument in the range MINLOG to
* MAXLOG.
*
* A polynomial approximation is used for |x| < 0.625.
* Otherwise,
*
* tanh(x) = sinh(x)/cosh(x) = 1 - 2/(exp(2x) + 1).
*
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* IEEE -2,2 100000 1.3e-7 2.6e-8
*
*/
/*
Cephes Math Library Release 2.2: June, 1992
Copyright 1984, 1987, 1989, 1992 by Stephen L. Moshier
Direct inquiries to 30 Frost Street, Cambridge, MA 02140
*/
/* Single precision hyperbolic tangent
* test interval: [-0.625, +0.625]
* trials: 10000
* peak relative error: 7.2e-8
* rms relative error: 2.6e-8
*/
#include <math.h>
extern float MAXLOGF;
float expf( float );
float tanhf( float xx )
{
float x, z;
if( xx < 0 )
x = -xx;
else
x = xx;
if( x > 0.5 * MAXLOGF )
{
if( xx > 0 )
return( 1.0 );
else
return( -1.0 );
}
if( x >= 0.625 )
{
x = expf(x+x);
z = 1.0 - 2.0/(x + 1.0);
if( xx < 0 )
z = -z;
}
else
{
z = x * x;
z =
(((( -5.70498872745E-3 * z
+ 2.06390887954E-2) * z
- 5.37397155531E-2) * z
+ 1.33314422036E-1) * z
- 3.33332819422E-1) * z * xx
+ xx;
}
return( z );
}
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