1 files changed, 124 insertions, 0 deletions
diff --git a/libm/float/jnf.c b/libm/float/jnf.c
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+/*							jnf.c
+ *
+ *	Bessel function of integer order
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int n;
+ * float x, y, jnf();
+ *
+ * y = jnf( n, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns Bessel function of order n, where n is a
+ * (possibly negative) integer.
+ *
+ * The ratio of jn(x) to j0(x) is computed by backward
+ * recurrence.  First the ratio jn/jn-1 is found by a
+ * continued fraction expansion.  Then the recurrence
+ * relating successive orders is applied until j0 or j1 is
+ * reached.
+ *
+ * If n = 0 or 1 the routine for j0 or j1 is called
+ * directly.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Absolute error:
+ * arithmetic   range      # trials      peak         rms
+ *    IEEE      0, 15       30000       3.6e-7      3.6e-8
+ *
+ *
+ * Not suitable for large n or x. Use jvf() instead.
+ *
+ */
+
+/*							jn.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>
+
+extern float MACHEPF;
+
+float j0f(float), j1f(float);
+
+float jnf( int n, float xx )
+{
+float x, pkm2, pkm1, pk, xk, r, ans, xinv, sign;
+int k;
+
+x = xx;
+sign = 1.0;
+if( n < 0 )
+	{
+	n = -n;
+	if( (n & 1) != 0 )	/* -1**n */
+		sign = -1.0;
+	}
+
+if( n == 0 )
+	return( sign * j0f(x) );
+if( n == 1 )
+	return( sign * j1f(x) );
+if( n == 2 )
+	return( sign * (2.0 * j1f(x) / x  -  j0f(x)) );
+
+/*
+if( x < MACHEPF )
+	return( 0.0 );
+*/
+
+/* continued fraction */
+k = 24;
+pk = 2 * (n + k);
+ans = pk;
+xk = x * x;
+
+do
+	{
+	pk -= 2.0;
+	ans = pk - (xk/ans);
+	}
+while( --k > 0 );
+/*ans = x/ans;*/
+
+/* backward recurrence */
+
+pk = 1.0;
+/*pkm1 = 1.0/ans;*/
+xinv = 1.0/x;
+pkm1 = ans * xinv;
+k = n-1;
+r = (float )(2 * k);
+
+do
+	{
+	pkm2 = (pkm1 * r  -  pk * x) * xinv;
+	pk = pkm1;
+	pkm1 = pkm2;
+	r -= 2.0;
+	}
+while( --k > 0 );
+
+r = pk;
+if( r < 0 )
+	r = -r;
+ans = pkm1;
+if( ans < 0 )
+	ans = -ans;
+
+if( r > ans )  /* if( fabs(pk) > fabs(pkm1) ) */
+	ans = sign * j1f(x)/pk;
+else
+	ans = sign * j0f(x)/pkm1;
+return( ans );
+}