1 files changed, 384 insertions, 0 deletions
diff --git a/libm/float/hypergf.c b/libm/float/hypergf.c
new file mode 100644
index 000000000..60d0eb4c5
--- /dev/null
+++ b/libm/float/hypergf.c
@@ -0,0 +1,384 @@
+/*							hypergf.c
+ *
+ *	Confluent hypergeometric function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float a, b, x, y, hypergf();
+ *
+ * y = hypergf( a, b, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Computes the confluent hypergeometric function
+ *
+ *                          1           2
+ *                       a x    a(a+1) x
+ *   F ( a,b;x )  =  1 + ---- + --------- + ...
+ *  1 1                  b 1!   b(b+1) 2!
+ *
+ * Many higher transcendental functions are special cases of
+ * this power series.
+ *
+ * As is evident from the formula, b must not be a negative
+ * integer or zero unless a is an integer with 0 >= a > b.
+ *
+ * The routine attempts both a direct summation of the series
+ * and an asymptotic expansion.  In each case error due to
+ * roundoff, cancellation, and nonconvergence is estimated.
+ * The result with smaller estimated error is returned.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Tested at random points (a, b, x), all three variables
+ * ranging from 0 to 30.
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    IEEE      0,5         10000       6.6e-7      1.3e-7
+ *    IEEE      0,30        30000       1.1e-5      6.5e-7
+ *
+ * Larger errors can be observed when b is near a negative
+ * integer or zero.  Certain combinations of arguments yield
+ * serious cancellation error in the power series summation
+ * and also are not in the region of near convergence of the
+ * asymptotic series.  An error message is printed if the
+ * self-estimated relative error is greater than 1.0e-3.
+ *
+ */
+
+/*							hyperg.c */
+
+
+/*
+Cephes Math Library Release 2.1:  November, 1988
+Copyright 1984, 1987, 1988 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+#include <math.h>
+
+extern float MAXNUMF, MACHEPF;
+
+#define fabsf(x) ( (x) < 0 ? -(x) : (x) )
+
+#ifdef ANSIC
+float expf(float);
+float hyp2f0f(float, float, float, int, float *);
+static float hy1f1af(float, float, float, float *);
+static float hy1f1pf(float, float, float, float *);
+float logf(float), gammaf(float), lgamf(float);
+#else
+float expf(), hyp2f0f();
+float logf(), gammaf(), lgamf();
+static float hy1f1pf(), hy1f1af();
+#endif
+
+float hypergf( float aa, float bb, float xx )
+{
+float a, b, x, asum, psum, acanc, pcanc, temp;
+
+
+a = aa;
+b = bb;
+x = xx;
+/* See if a Kummer transformation will help */
+temp = b - a;
+if( fabsf(temp) < 0.001 * fabsf(a) )
+	return( expf(x) * hypergf( temp, b, -x )  );
+
+psum = hy1f1pf( a, b, x, &pcanc );
+if( pcanc < 1.0e-6 )
+	goto done;
+
+
+/* try asymptotic series */
+
+asum = hy1f1af( a, b, x, &acanc );
+
+
+/* Pick the result with less estimated error */
+
+if( acanc < pcanc )
+	{
+	pcanc = acanc;
+	psum = asum;
+	}
+
+done:
+if( pcanc > 1.0e-3 )
+	mtherr( "hyperg", PLOSS );
+
+return( psum );
+}
+
+
+
+
+/* Power series summation for confluent hypergeometric function		*/
+
+
+static float hy1f1pf( float aa, float bb, float xx, float *err )
+{
+float a, b, x, n, a0, sum, t, u, temp;
+float an, bn, maxt, pcanc;
+
+a = aa;
+b = bb;
+x = xx;
+/* set up for power series summation */
+an = a;
+bn = b;
+a0 = 1.0;
+sum = 1.0;
+n = 1.0;
+t = 1.0;
+maxt = 0.0;
+
+
+while( t > MACHEPF )
+	{
+	if( bn == 0 )			/* check bn first since if both	*/
+		{
+		mtherr( "hypergf", SING );
+		return( MAXNUMF );	/* an and bn are zero it is	*/
+		}
+	if( an == 0 )			/* a singularity		*/
+		return( sum );
+	if( n > 200 )
+		goto pdone;
+	u = x * ( an / (bn * n) );
+
+	/* check for blowup */
+	temp = fabsf(u);
+	if( (temp > 1.0 ) && (maxt > (MAXNUMF/temp)) )
+		{
+		pcanc = 1.0;	/* estimate 100% error */
+		goto blowup;
+		}
+
+	a0 *= u;
+	sum += a0;
+	t = fabsf(a0);
+	if( t > maxt )
+		maxt = t;
+/*
+	if( (maxt/fabsf(sum)) > 1.0e17 )
+		{
+		pcanc = 1.0;
+		goto blowup;
+		}
+*/
+	an += 1.0;
+	bn += 1.0;
+	n += 1.0;
+	}
+
+pdone:
+
+/* estimate error due to roundoff and cancellation */
+if( sum != 0.0 )
+	maxt /= fabsf(sum);
+maxt *= MACHEPF; 	/* this way avoids multiply overflow */
+pcanc = fabsf( MACHEPF * n  +  maxt );
+
+blowup:
+
+*err = pcanc;
+
+return( sum );
+}
+
+
+/*							hy1f1a()	*/
+/* asymptotic formula for hypergeometric function:
+ *
+ *        (    -a                         
+ *  --    ( |z|                           
+ * |  (b) ( -------- 2f0( a, 1+a-b, -1/x )
+ *        (  --                           
+ *        ( |  (b-a)                      
+ *
+ *
+ *                                x    a-b                     )
+ *                               e  |x|                        )
+ *                             + -------- 2f0( b-a, 1-a, 1/x ) )
+ *                                --                           )
+ *                               |  (a)                        )
+ */
+
+static float hy1f1af( float aa, float bb, float xx, float *err )
+{
+float a, b, x, h1, h2, t, u, temp, acanc, asum, err1, err2;
+
+a = aa;
+b = bb;
+x = xx;
+if( x == 0 )
+	{
+	acanc = 1.0;
+	asum = MAXNUMF;
+	goto adone;
+	}
+temp = logf( fabsf(x) );
+t = x + temp * (a-b);
+u = -temp * a;
+
+if( b > 0 )
+	{
+	temp = lgamf(b);
+	t += temp;
+	u += temp;
+	}
+
+h1 = hyp2f0f( a, a-b+1, -1.0/x, 1, &err1 );
+
+temp = expf(u) / gammaf(b-a);
+h1 *= temp;
+err1 *= temp;
+
+h2 = hyp2f0f( b-a, 1.0-a, 1.0/x, 2, &err2 );
+
+if( a < 0 )
+	temp = expf(t) / gammaf(a);
+else
+	temp = expf( t - lgamf(a) );
+
+h2 *= temp;
+err2 *= temp;
+
+if( x < 0.0 )
+	asum = h1;
+else
+	asum = h2;
+
+acanc = fabsf(err1) + fabsf(err2);
+
+
+if( b < 0 )
+	{
+	temp = gammaf(b);
+	asum *= temp;
+	acanc *= fabsf(temp);
+	}
+
+
+if( asum != 0.0 )
+	acanc /= fabsf(asum);
+
+acanc *= 30.0;	/* fudge factor, since error of asymptotic formula
+		 * often seems this much larger than advertised */
+
+adone:
+
+
+*err = acanc;
+return( asum );
+}
+
+/*							hyp2f0()	*/
+
+float hyp2f0f(float aa, float bb, float xx, int type, float *err)
+{
+float a, b, x, a0, alast, t, tlast, maxt;
+float n, an, bn, u, sum, temp;
+
+a = aa;
+b = bb;
+x = xx;
+an = a;
+bn = b;
+a0 = 1.0;
+alast = 1.0;
+sum = 0.0;
+n = 1.0;
+t = 1.0;
+tlast = 1.0e9;
+maxt = 0.0;
+
+do
+	{
+	if( an == 0 )
+		goto pdone;
+	if( bn == 0 )
+		goto pdone;
+
+	u = an * (bn * x / n);
+
+	/* check for blowup */
+	temp = fabsf(u);
+	if( (temp > 1.0 ) && (maxt > (MAXNUMF/temp)) )
+		goto error;
+
+	a0 *= u;
+	t = fabsf(a0);
+
+	/* terminating condition for asymptotic series */
+	if( t > tlast )
+		goto ndone;
+
+	tlast = t;
+	sum += alast;	/* the sum is one term behind */
+	alast = a0;
+
+	if( n > 200 )
+		goto ndone;
+
+	an += 1.0;
+	bn += 1.0;
+	n += 1.0;
+	if( t > maxt )
+		maxt = t;
+	}
+while( t > MACHEPF );
+
+
+pdone:	/* series converged! */
+
+/* estimate error due to roundoff and cancellation */
+*err = fabsf(  MACHEPF * (n + maxt)  );
+
+alast = a0;
+goto done;
+
+ndone:	/* series did not converge */
+
+/* The following "Converging factors" are supposed to improve accuracy,
+ * but do not actually seem to accomplish very much. */
+
+n -= 1.0;
+x = 1.0/x;
+
+switch( type )	/* "type" given as subroutine argument */
+{
+case 1:
+	alast *= ( 0.5 + (0.125 + 0.25*b - 0.5*a + 0.25*x - 0.25*n)/x );
+	break;
+
+case 2:
+	alast *= 2.0/3.0 - b + 2.0*a + x - n;
+	break;
+
+default:
+	;
+}
+
+/* estimate error due to roundoff, cancellation, and nonconvergence */
+*err = MACHEPF * (n + maxt)  +  fabsf( a0 );
+
+
+done:
+sum += alast;
+return( sum );
+
+/* series blew up: */
+error:
+*err = MAXNUMF;
+mtherr( "hypergf", TLOSS );
+return( sum );
+}