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/* i0f.c
*
* Modified Bessel function of order zero
*
*
*
* SYNOPSIS:
*
* float x, y, i0();
*
* y = i0f( x );
*
*
*
* DESCRIPTION:
*
* Returns modified Bessel function of order zero of the
* argument.
*
* The function is defined as i0(x) = j0( ix ).
*
* The range is partitioned into the two intervals [0,8] and
* (8, infinity). Chebyshev polynomial expansions are employed
* in each interval.
*
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* IEEE 0,30 100000 4.0e-7 7.9e-8
*
*/
/* i0ef.c
*
* Modified Bessel function of order zero,
* exponentially scaled
*
*
*
* SYNOPSIS:
*
* float x, y, i0ef();
*
* y = i0ef( x );
*
*
*
* DESCRIPTION:
*
* Returns exponentially scaled modified Bessel function
* of order zero of the argument.
*
* The function is defined as i0e(x) = exp(-|x|) j0( ix ).
*
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* IEEE 0,30 100000 3.7e-7 7.0e-8
* See i0f().
*
*/
/* i0.c */
/*
Cephes Math Library Release 2.2: June, 1992
Copyright 1984, 1987, 1992 by Stephen L. Moshier
Direct inquiries to 30 Frost Street, Cambridge, MA 02140
*/
#include <math.h>
/* Chebyshev coefficients for exp(-x) I0(x)
* in the interval [0,8].
*
* lim(x->0){ exp(-x) I0(x) } = 1.
*/
static float A[] =
{
-1.30002500998624804212E-8f,
6.04699502254191894932E-8f,
-2.67079385394061173391E-7f,
1.11738753912010371815E-6f,
-4.41673835845875056359E-6f,
1.64484480707288970893E-5f,
-5.75419501008210370398E-5f,
1.88502885095841655729E-4f,
-5.76375574538582365885E-4f,
1.63947561694133579842E-3f,
-4.32430999505057594430E-3f,
1.05464603945949983183E-2f,
-2.37374148058994688156E-2f,
4.93052842396707084878E-2f,
-9.49010970480476444210E-2f,
1.71620901522208775349E-1f,
-3.04682672343198398683E-1f,
6.76795274409476084995E-1f
};
/* Chebyshev coefficients for exp(-x) sqrt(x) I0(x)
* in the inverted interval [8,infinity].
*
* lim(x->inf){ exp(-x) sqrt(x) I0(x) } = 1/sqrt(2pi).
*/
static float B[] =
{
3.39623202570838634515E-9f,
2.26666899049817806459E-8f,
2.04891858946906374183E-7f,
2.89137052083475648297E-6f,
6.88975834691682398426E-5f,
3.36911647825569408990E-3f,
8.04490411014108831608E-1f
};
float chbevlf(float, float *, int), expf(float), sqrtf(float);
float i0f( float x )
{
float y;
if( x < 0 )
x = -x;
if( x <= 8.0f )
{
y = 0.5f*x - 2.0f;
return( expf(x) * chbevlf( y, A, 18 ) );
}
return( expf(x) * chbevlf( 32.0f/x - 2.0f, B, 7 ) / sqrtf(x) );
}
float chbevlf(float, float *, int), expf(float), sqrtf(float);
float i0ef( float x )
{
float y;
if( x < 0 )
x = -x;
if( x <= 8.0f )
{
y = 0.5f*x - 2.0f;
return( chbevlf( y, A, 18 ) );
}
return( chbevlf( 32.0f/x - 2.0f, B, 7 ) / sqrtf(x) );
}
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