diff options
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 ) ); +} |