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/* asinhf.c
*
* Inverse hyperbolic sine
*
*
*
* SYNOPSIS:
*
* float x, y, asinhf();
*
* y = asinhf( x );
*
*
*
* DESCRIPTION:
*
* Returns inverse hyperbolic sine of argument.
*
* If |x| < 0.5, the function is approximated by a rational
* form x + x**3 P(x)/Q(x). Otherwise,
*
* asinh(x) = log( x + sqrt(1 + x*x) ).
*
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* IEEE -3,3 100000 2.4e-7 4.1e-8
*
*/
/* asinh.c */
/*
Cephes Math Library Release 2.2: June, 1992
Copyright 1984, 1987, 1988, 1992 by Stephen L. Moshier
Direct inquiries to 30 Frost Street, Cambridge, MA 02140
*/
/* Single precision inverse hyperbolic sine
* test interval: [-0.5, +0.5]
* trials: 10000
* peak relative error: 8.8e-8
* rms relative error: 3.2e-8
*/
#include <math.h>
extern float LOGE2F;
float logf( float );
float sqrtf( float );
float asinhf( float xx )
{
float x, z;
if( xx < 0 )
x = -xx;
else
x = xx;
if( x > 1500.0 )
{
z = logf(x) + LOGE2F;
goto done;
}
z = x * x;
if( x < 0.5 )
{
z =
((( 2.0122003309E-2 * z
- 4.2699340972E-2) * z
+ 7.4847586088E-2) * z
- 1.6666288134E-1) * z * x
+ x;
}
else
{
z = sqrtf( z + 1.0 );
z = logf( x + z );
}
done:
if( xx < 0 )
z = -z;
return( z );
}
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