uClibc now has a math library. muahahahaha!

 -Erik

1 files changed, 442 insertions, 0 deletions

diff --git a/libm/float/hyp2f1f.c b/libm/float/hyp2f1f.c
new file mode 100644
index 000000000..01fe54928
--- /dev/null
+++ b/libm/float/hyp2f1f.c
@@ -0,0 +1,442 @@
+/*							hyp2f1f.c
+ *
+ *	Gauss hypergeometric function   F
+ *	                               2 1
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float a, b, c, x, y, hyp2f1f();
+ *
+ * y = hyp2f1f( a, b, c, x );
+ *
+ *
+ * DESCRIPTION:
+ *
+ *
+ *  hyp2f1( a, b, c, x )  =   F ( a, b; c; x )
+ *                           2 1
+ *
+ *           inf.
+ *            -   a(a+1)...(a+k) b(b+1)...(b+k)   k+1
+ *   =  1 +   >   -----------------------------  x   .
+ *            -         c(c+1)...(c+k) (k+1)!
+ *          k = 0
+ *
+ *  Cases addressed are
+ *	Tests and escapes for negative integer a, b, or c
+ *	Linear transformation if c - a or c - b negative integer
+ *	Special case c = a or c = b
+ *	Linear transformation for  x near +1
+ *	Transformation for x < -0.5
+ *	Psi function expansion if x > 0.5 and c - a - b integer
+ *      Conditionally, a recurrence on c to make c-a-b > 0
+ *
+ * |x| > 1 is rejected.
+ *
+ * The parameters a, b, c are considered to be integer
+ * valued if they are within 1.0e-6 of the nearest integer.
+ *
+ * ACCURACY:
+ *
+ *                      Relative error (-1 < x < 1):
+ * arithmetic   domain     # trials      peak         rms
+ *    IEEE      0,3         30000       5.8e-4      4.3e-6
+ */
+
+/*							hyp2f1	*/
+
+
+/*
+Cephes Math Library Release 2.2:  November, 1992
+Copyright 1984, 1987, 1992 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+
+#include <math.h>
+
+#define EPS 1.0e-5
+#define EPS2 1.0e-5
+#define ETHRESH 1.0e-5
+
+extern float MAXNUMF, MACHEPF;
+
+#define fabsf(x) ( (x) < 0 ? -(x) : (x) )
+
+#ifdef ANSIC
+float powf(float, float);
+static float hys2f1f(float, float, float, float, float *);
+static float hyt2f1f(float, float, float, float, float *);
+float gammaf(float), logf(float), expf(float), psif(float);
+float floorf(float);
+#else
+float powf(), gammaf(), logf(), expf(), psif();
+float floorf();
+static float hyt2f1f(), hys2f1f();
+#endif
+
+#define roundf(x) (floorf((x)+(float )0.5))
+
+
+
+
+float hyp2f1f( float aa, float bb, float cc, float xx )
+{
+float a, b, c, x;
+float d, d1, d2, e;
+float p, q, r, s, y, ax;
+float ia, ib, ic, id, err;
+int flag, i, aid;
+
+a = aa;
+b = bb;
+c = cc;
+x = xx;
+err = 0.0;
+ax = fabsf(x);
+s = 1.0 - x;
+flag = 0;
+ia = roundf(a); /* nearest integer to a */
+ib = roundf(b);
+
+if( a <= 0 )
+	{
+	if( fabsf(a-ia) < EPS )		/* a is a negative integer */
+		flag |= 1;
+	}
+
+if( b <= 0 )
+	{
+	if( fabsf(b-ib) < EPS )		/* b is a negative integer */
+		flag |= 2;
+	}
+
+if( ax < 1.0 )
+	{
+	if( fabsf(b-c) < EPS )		/* b = c */
+		{
+		y = powf( s, -a );	/* s to the -a power */
+		goto hypdon;
+		}
+	if( fabsf(a-c) < EPS )		/* a = c */
+		{
+		y = powf( s, -b );	/* s to the -b power */
+		goto hypdon;
+		}
+	}
+
+
+
+if( c <= 0.0 )
+	{
+	ic = roundf(c); 	/* nearest integer to c */
+	if( fabsf(c-ic) < EPS )		/* c is a negative integer */
+		{
+		/* check if termination before explosion */
+		if( (flag & 1) && (ia > ic) )
+			goto hypok;
+		if( (flag & 2) && (ib > ic) )
+			goto hypok;
+		goto hypdiv;
+		}
+	}
+
+if( flag )			/* function is a polynomial */
+	goto hypok;
+
+if( ax > 1.0 )			/* series diverges	*/
+	goto hypdiv;
+
+p = c - a;
+ia = roundf(p);
+if( (ia <= 0.0) && (fabsf(p-ia) < EPS) )	/* negative int c - a */
+	flag |= 4;
+
+r = c - b;
+ib = roundf(r); /* nearest integer to r */
+if( (ib <= 0.0) && (fabsf(r-ib) < EPS) )	/* negative int c - b */
+	flag |= 8;
+
+d = c - a - b;
+id = roundf(d); /* nearest integer to d */
+q = fabsf(d-id);
+
+if( fabsf(ax-1.0) < EPS )			/* |x| == 1.0	*/
+	{
+	if( x > 0.0 )
+		{
+		if( flag & 12 ) /* negative int c-a or c-b */
+			{
+			if( d >= 0.0 )
+				goto hypf;
+			else
+				goto hypdiv;
+			}
+		if( d <= 0.0 )
+			goto hypdiv;
+		y = gammaf(c)*gammaf(d)/(gammaf(p)*gammaf(r));
+		goto hypdon;
+		}
+
+	if( d <= -1.0 )
+		goto hypdiv;
+	}
+
+/* Conditionally make d > 0 by recurrence on c
+ * AMS55 #15.2.27
+ */
+if( d < 0.0 )
+	{
+/* Try the power series first */
+	y = hyt2f1f( a, b, c, x, &err );
+	if( err < ETHRESH )
+		goto hypdon;
+/* Apply the recurrence if power series fails */
+	err = 0.0;
+	aid = 2 - id;
+	e = c + aid;
+	d2 = hyp2f1f(a,b,e,x);
+	d1 = hyp2f1f(a,b,e+1.0,x);
+	q = a + b + 1.0;
+	for( i=0; i<aid; i++ )
+		{
+		r = e - 1.0;
+		y = (e*(r-(2.0*e-q)*x)*d2 + (e-a)*(e-b)*x*d1)/(e*r*s);
+		e = r;
+		d1 = d2;
+		d2 = y;
+		}
+	goto hypdon;
+	}
+
+
+if( flag & 12 )
+	goto hypf; /* negative integer c-a or c-b */
+
+hypok:
+y = hyt2f1f( a, b, c, x, &err );
+
+hypdon:
+if( err > ETHRESH )
+	{
+	mtherr( "hyp2f1", PLOSS );
+/*	printf( "Estimated err = %.2e\n", err );*/
+	}
+return(y);
+
+/* The transformation for c-a or c-b negative integer
+ * AMS55 #15.3.3
+ */
+hypf:
+y = powf( s, d ) * hys2f1f( c-a, c-b, c, x, &err );
+goto hypdon;
+
+/* The alarm exit */
+hypdiv:
+mtherr( "hyp2f1f", OVERFLOW );
+return( MAXNUMF );
+}
+
+
+
+
+/* Apply transformations for |x| near 1
+ * then call the power series
+ */
+static float hyt2f1f( float aa, float bb, float cc, float xx, float *loss )
+{
+float a, b, c, x;
+float p, q, r, s, t, y, d, err, err1;
+float ax, id, d1, d2, e, y1;
+int i, aid;
+
+a = aa;
+b = bb;
+c = cc;
+x = xx;
+err = 0.0;
+s = 1.0 - x;
+if( x < -0.5 )
+	{
+	if( b > a )
+		y = powf( s, -a ) * hys2f1f( a, c-b, c, -x/s, &err );
+
+	else
+		y = powf( s, -b ) * hys2f1f( c-a, b, c, -x/s, &err );
+
+	goto done;
+	}
+
+
+
+d = c - a - b;
+id = roundf(d);	/* nearest integer to d */
+
+if( x > 0.8 )
+{
+
+if( fabsf(d-id) > EPS2 ) /* test for integer c-a-b */
+	{
+/* Try the power series first */
+	y = hys2f1f( a, b, c, x, &err );
+	if( err < ETHRESH )
+		goto done;
+/* If power series fails, then apply AMS55 #15.3.6 */
+	q = hys2f1f( a, b, 1.0-d, s, &err );	
+	q *= gammaf(d) /(gammaf(c-a) * gammaf(c-b));
+	r = powf(s,d) * hys2f1f( c-a, c-b, d+1.0, s, &err1 );
+	r *= gammaf(-d)/(gammaf(a) * gammaf(b));
+	y = q + r;
+
+	q = fabsf(q); /* estimate cancellation error */
+	r = fabsf(r);
+	if( q > r )
+		r = q;
+	err += err1 + (MACHEPF*r)/y;
+
+	y *= gammaf(c);
+	goto done;
+	}	
+else
+	{
+/* Psi function expansion, AMS55 #15.3.10, #15.3.11, #15.3.12 */
+	if( id >= 0.0 )
+		{
+		e = d;
+		d1 = d;
+		d2 = 0.0;
+		aid = id;
+		}
+	else
+		{
+		e = -d;
+		d1 = 0.0;
+		d2 = d;
+		aid = -id;
+		}
+
+	ax = logf(s);
+
+	/* sum for t = 0 */
+	y = psif(1.0) + psif(1.0+e) - psif(a+d1) - psif(b+d1) - ax;
+	y /= gammaf(e+1.0);
+
+	p = (a+d1) * (b+d1) * s / gammaf(e+2.0);	/* Poch for t=1 */
+	t = 1.0;
+	do
+		{
+		r = psif(1.0+t) + psif(1.0+t+e) - psif(a+t+d1)
+			- psif(b+t+d1) - ax;
+		q = p * r;
+		y += q;
+		p *= s * (a+t+d1) / (t+1.0);
+		p *= (b+t+d1) / (t+1.0+e);
+		t += 1.0;
+		}
+	while( fabsf(q/y) > EPS );
+
+
+	if( id == 0.0 )
+		{
+		y *= gammaf(c)/(gammaf(a)*gammaf(b));
+		goto psidon;
+		}
+
+	y1 = 1.0;
+
+	if( aid == 1 )
+		goto nosum;
+
+	t = 0.0;
+	p = 1.0;
+	for( i=1; i<aid; i++ )
+		{
+		r = 1.0-e+t;
+		p *= s * (a+t+d2) * (b+t+d2) / r;
+		t += 1.0;
+		p /= t;
+		y1 += p;
+		}
+
+
+nosum:
+	p = gammaf(c);
+	y1 *= gammaf(e) * p / (gammaf(a+d1) * gammaf(b+d1));
+	y *= p / (gammaf(a+d2) * gammaf(b+d2));
+	if( (aid & 1) != 0 )
+		y = -y;
+
+	q = powf( s, id );	/* s to the id power */
+	if( id > 0.0 )
+		y *= q;
+	else
+		y1 *= q;
+
+	y += y1;
+psidon:
+	goto done;
+	}
+}
+
+
+/* Use defining power series if no special cases */
+y = hys2f1f( a, b, c, x, &err );
+
+done:
+*loss = err;
+return(y);
+}
+
+
+
+
+
+/* Defining power series expansion of Gauss hypergeometric function */
+
+static float hys2f1f( float aa, float bb, float cc, float xx, float *loss )
+{
+int i;
+float a, b, c, x;
+float f, g, h, k, m, s, u, umax;
+
+
+a = aa;
+b = bb;
+c = cc;
+x = xx;
+i = 0;
+umax = 0.0;
+f = a;
+g = b;
+h = c;
+k = 0.0;
+s = 1.0;
+u = 1.0;
+
+do
+	{
+	if( fabsf(h) < EPS )
+		return( MAXNUMF );
+	m = k + 1.0;
+	u = u * ((f+k) * (g+k) * x / ((h+k) * m));
+	s += u;
+	k = fabsf(u);  /* remember largest term summed */
+	if( k > umax )
+		umax = k;
+	k = m;
+	if( ++i > 10000 ) /* should never happen */
+		{
+		*loss = 1.0;
+		return(s);
+		}
+	}
+while( fabsf(u/s) > MACHEPF );
+
+/* return estimated relative error */
+*loss = (MACHEPF*umax)/fabsf(s) + (MACHEPF*i);
+
+return(s);
+}
+
+