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-rw-r--r--libm/double/iv.c116
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diff --git a/libm/double/iv.c b/libm/double/iv.c
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-/* 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 ) );
-}