1 files changed, 114 insertions, 0 deletions
diff --git a/libm/float/ivf.c b/libm/float/ivf.c
new file mode 100644
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+/*							ivf.c
+ *
+ *	Modified Bessel function of noninteger order
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float v, x, y, ivf();
+ *
+ * y = ivf( 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.
+ * arithmetic   domain     # trials      peak         rms
+ *                      Relative error:
+ *    IEEE      0,15          3000      4.7e-6      5.4e-7
+ *          Absolute error (relative when function > 1)
+ *    IEEE      0,30          5000      8.5e-6      1.3e-6
+ *
+ * Accuracy is diminished if v is near a negative integer.
+ * The useful domain for relative error is limited by overflow
+ * of the single precision exponential function.
+ *
+ * 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 2.2: June, 1992
+Copyright 1984, 1987, 1988, 1992 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+
+#include <math.h>
+
+extern float MAXNUMF;
+#define fabsf(x) ( (x) < 0 ? -(x) : (x) )
+
+float hypergf(float, float, float);
+float expf(float), gammaf(float), logf(float), floorf(float);
+
+float ivf( float v, float x )
+{
+int sign;
+float t, ax;
+
+/* If v is a negative integer, invoke symmetry */
+t = floorf(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( "ivf", DOMAIN );
+		return( 0.0 );
+		}
+	if( v != 2.0 * floorf(v/2.0) )
+		sign = -1;
+	}
+
+/* Avoid logarithm singularity */
+if( x == 0.0 )
+	{
+	if( v == 0.0 )
+		return( 1.0 );
+	if( v < 0.0 )
+		{
+		mtherr( "ivf", OVERFLOW );
+		return( MAXNUMF );
+		}
+	else
+		return( 0.0 );
+	}
+
+ax = fabsf(x);
+t = v * logf( 0.5 * ax )  -  x;
+t = sign * expf(t) / gammaf( v + 1.0 );
+ax = v + 0.5;
+return( t * hypergf( ax,  2.0 * ax,  2.0 * x ) );
+}