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Diffstat (limited to 'libm/double/iv.c')
| -rw-r--r-- | libm/double/iv.c | 116 | 
1 files changed, 116 insertions, 0 deletions
| diff --git a/libm/double/iv.c b/libm/double/iv.c new file mode 100644 index 000000000..ec0e96244 --- /dev/null +++ b/libm/double/iv.c @@ -0,0 +1,116 @@ +/*							iv.c + * + *	Modified Bessel function of noninteger order + * + * + * + * SYNOPSIS: + * + * double v, x, y, iv(); + * + * y = iv( v, x ); + * + * + * + * DESCRIPTION: + * + * Returns modified Bessel function of order v of the + * argument.  If x is negative, v must be integer valued. + * + * The function is defined as Iv(x) = Jv( ix ).  It is + * here computed in terms of the confluent hypergeometric + * function, according to the formula + * + *              v  -x + * Iv(x) = (x/2)  e   hyperg( v+0.5, 2v+1, 2x ) / gamma(v+1) + * + * If v is a negative integer, then v is replaced by -v. + * + * + * ACCURACY: + * + * Tested at random points (v, x), with v between 0 and + * 30, x between 0 and 28. + *                      Relative error: + * arithmetic   domain     # trials      peak         rms + *    DEC       0,30          2000      3.1e-15     5.4e-16 + *    IEEE      0,30         10000      1.7e-14     2.7e-15 + * + * Accuracy is diminished if v is near a negative integer. + * + * See also hyperg.c. + * + */ +/*							iv.c	*/ +/*	Modified Bessel function of noninteger order		*/ +/* If x < 0, then v must be an integer. */ + + +/* +Cephes Math Library Release 2.8:  June, 2000 +Copyright 1984, 1987, 1988, 2000 by Stephen L. Moshier +*/ + + +#include <math.h> +#ifdef ANSIPROT +extern double hyperg ( double, double, double ); +extern double exp ( double ); +extern double gamma ( double ); +extern double log ( double ); +extern double fabs ( double ); +extern double floor ( double ); +#else +double hyperg(), exp(), gamma(), log(), fabs(), floor(); +#endif +extern double MACHEP, MAXNUM; + +double iv( v, x ) +double v, x; +{ +int sign; +double t, ax; + +/* If v is a negative integer, invoke symmetry */ +t = floor(v); +if( v < 0.0 ) +	{ +	if( t == v ) +		{ +		v = -v;	/* symmetry */ +		t = -t; +		} +	} +/* If x is negative, require v to be an integer */ +sign = 1; +if( x < 0.0 ) +	{ +	if( t != v ) +		{ +		mtherr( "iv", DOMAIN ); +		return( 0.0 ); +		} +	if( v != 2.0 * floor(v/2.0) ) +		sign = -1; +	} + +/* Avoid logarithm singularity */ +if( x == 0.0 ) +	{ +	if( v == 0.0 ) +		return( 1.0 ); +	if( v < 0.0 ) +		{ +		mtherr( "iv", OVERFLOW ); +		return( MAXNUM ); +		} +	else +		return( 0.0 ); +	} + +ax = fabs(x); +t = v * log( 0.5 * ax )  -  x; +t = sign * exp(t) / gamma( v + 1.0 ); +ax = v + 0.5; +return( t * hyperg( ax,  2.0 * ax,  2.0 * x ) ); +} | 
