Totally rework the math library, this time based on the MacOs X

math library (which is itself based on the math lib from FreeBSD).
 -Erik

1 files changed, 0 insertions, 460 deletions

diff --git a/libm/double/hyp2f1.c b/libm/double/hyp2f1.c
deleted file mode 100644
index f2e93106c..000000000
--- a/libm/double/hyp2f1.c
+++ /dev/null
@@ -1,460 +0,0 @@
-/*							hyp2f1.c
- *
- *	Gauss hypergeometric function   F
- *	                               2 1
- *
- *
- * SYNOPSIS:
- *
- * double a, b, c, x, y, hyp2f1();
- *
- * y = hyp2f1( 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-14 of the nearest integer
- * (1.0e-13 for IEEE arithmetic).
- *
- * ACCURACY:
- *
- *
- *               Relative error (-1 < x < 1):
- * arithmetic   domain     # trials      peak         rms
- *    IEEE      -1,7        230000      1.2e-11     5.2e-14
- *
- * Several special cases also tested with a, b, c in
- * the range -7 to 7.
- *
- * ERROR MESSAGES:
- *
- * A "partial loss of precision" message is printed if
- * the internally estimated relative error exceeds 1^-12.
- * A "singularity" message is printed on overflow or
- * in cases not addressed (such as x < -1).
- */
-
-/*							hyp2f1	*/
-
-
-/*
-Cephes Math Library Release 2.8:  June, 2000
-Copyright 1984, 1987, 1992, 2000 by Stephen L. Moshier
-*/
-
-
-#include <math.h>
-
-#ifdef DEC
-#define EPS 1.0e-14
-#define EPS2 1.0e-11
-#endif
-
-#ifdef IBMPC
-#define EPS 1.0e-13
-#define EPS2 1.0e-10
-#endif
-
-#ifdef MIEEE
-#define EPS 1.0e-13
-#define EPS2 1.0e-10
-#endif
-
-#ifdef UNK
-#define EPS 1.0e-13
-#define EPS2 1.0e-10
-#endif
-
-#define ETHRESH 1.0e-12
-
-#ifdef ANSIPROT
-extern double fabs ( double );
-extern double pow ( double, double );
-extern double round ( double );
-extern double gamma ( double );
-extern double log ( double );
-extern double exp ( double );
-extern double psi ( double );
-static double hyt2f1(double, double, double, double, double *);
-static double hys2f1(double, double, double, double, double *);
-double hyp2f1(double, double, double, double);
-#else
-double fabs(), pow(), round(), gamma(), log(), exp(), psi();
-static double hyt2f1();
-static double hys2f1();
-double hyp2f1();
-#endif
-extern double MAXNUM, MACHEP;
-
-double hyp2f1( a, b, c, x )
-double a, b, c, x;
-{
-double d, d1, d2, e;
-double p, q, r, s, y, ax;
-double ia, ib, ic, id, err;
-int flag, i, aid;
-
-err = 0.0;
-ax = fabs(x);
-s = 1.0 - x;
-flag = 0;
-ia = round(a); /* nearest integer to a */
-ib = round(b);
-
-if( a <= 0 )
-	{
-	if( fabs(a-ia) < EPS )		/* a is a negative integer */
-		flag |= 1;
-	}
-
-if( b <= 0 )
-	{
-	if( fabs(b-ib) < EPS )		/* b is a negative integer */
-		flag |= 2;
-	}
-
-if( ax < 1.0 )
-	{
-	if( fabs(b-c) < EPS )		/* b = c */
-		{
-		y = pow( s, -a );	/* s to the -a power */
-		goto hypdon;
-		}
-	if( fabs(a-c) < EPS )		/* a = c */
-		{
-		y = pow( s, -b );	/* s to the -b power */
-		goto hypdon;
-		}
-	}
-
-
-
-if( c <= 0.0 )
-	{
-	ic = round(c); 	/* nearest integer to c */
-	if( fabs(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 = round(p); /* nearest integer to c-a */
-if( (ia <= 0.0) && (fabs(p-ia) < EPS) )	/* negative int c - a */
-	flag |= 4;
-
-r = c - b;
-ib = round(r); /* nearest integer to c-b */
-if( (ib <= 0.0) && (fabs(r-ib) < EPS) )	/* negative int c - b */
-	flag |= 8;
-
-d = c - a - b;
-id = round(d); /* nearest integer to d */
-q = fabs(d-id);
-
-/* Thanks to Christian Burger <BURGER@DMRHRZ11.HRZ.Uni-Marburg.DE>
- * for reporting a bug here.  */
-if( fabs(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 = gamma(c)*gamma(d)/(gamma(p)*gamma(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 = hyt2f1( 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 = hyp2f1(a,b,e,x);
-	d1 = hyp2f1(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 = hyt2f1( 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 = pow( s, d ) * hys2f1( c-a, c-b, c, x, &err );
-goto hypdon;
-
-/* The alarm exit */
-hypdiv:
-mtherr( "hyp2f1", OVERFLOW );
-return( MAXNUM );
-}
-
-
-
-
-
-
-/* Apply transformations for |x| near 1
- * then call the power series
- */
-static double hyt2f1( a, b, c, x, loss )
-double a, b, c, x;
-double *loss;
-{
-double p, q, r, s, t, y, d, err, err1;
-double ax, id, d1, d2, e, y1;
-int i, aid;
-
-err = 0.0;
-s = 1.0 - x;
-if( x < -0.5 )
-	{
-	if( b > a )
-		y = pow( s, -a ) * hys2f1( a, c-b, c, -x/s, &err );
-
-	else
-		y = pow( s, -b ) * hys2f1( c-a, b, c, -x/s, &err );
-
-	goto done;
-	}
-
-d = c - a - b;
-id = round(d);	/* nearest integer to d */
-
-if( x > 0.9 )
-{
-if( fabs(d-id) > EPS ) /* test for integer c-a-b */
-	{
-/* Try the power series first */
-	y = hys2f1( a, b, c, x, &err );
-	if( err < ETHRESH )
-		goto done;
-/* If power series fails, then apply AMS55 #15.3.6 */
-	q = hys2f1( a, b, 1.0-d, s, &err );	
-	q *= gamma(d) /(gamma(c-a) * gamma(c-b));
-	r = pow(s,d) * hys2f1( c-a, c-b, d+1.0, s, &err1 );
-	r *= gamma(-d)/(gamma(a) * gamma(b));
-	y = q + r;
-
-	q = fabs(q); /* estimate cancellation error */
-	r = fabs(r);
-	if( q > r )
-		r = q;
-	err += err1 + (MACHEP*r)/y;
-
-	y *= gamma(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 = log(s);
-
-	/* sum for t = 0 */
-	y = psi(1.0) + psi(1.0+e) - psi(a+d1) - psi(b+d1) - ax;
-	y /= gamma(e+1.0);
-
-	p = (a+d1) * (b+d1) * s / gamma(e+2.0);	/* Poch for t=1 */
-	t = 1.0;
-	do
-		{
-		r = psi(1.0+t) + psi(1.0+t+e) - psi(a+t+d1)
-			- psi(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( fabs(q/y) > EPS );
-
-
-	if( id == 0.0 )
-		{
-		y *= gamma(c)/(gamma(a)*gamma(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 = gamma(c);
-	y1 *= gamma(e) * p / (gamma(a+d1) * gamma(b+d1));
-
-	y *= p / (gamma(a+d2) * gamma(b+d2));
-	if( (aid & 1) != 0 )
-		y = -y;
-
-	q = pow( 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 = hys2f1( a, b, c, x, &err );
-
-done:
-*loss = err;
-return(y);
-}
-
-
-
-
-
-/* Defining power series expansion of Gauss hypergeometric function */
-
-static double hys2f1( a, b, c, x, loss )
-double a, b, c, x;
-double *loss; /* estimates loss of significance */
-{
-double f, g, h, k, m, s, u, umax;
-int i;
-
-i = 0;
-umax = 0.0;
-f = a;
-g = b;
-h = c;
-s = 1.0;
-u = 1.0;
-k = 0.0;
-do
-	{
-	if( fabs(h) < EPS )
-		{
-		*loss = 1.0;
-		return( MAXNUM );
-		}
-	m = k + 1.0;
-	u = u * ((f+k) * (g+k) * x / ((h+k) * m));
-	s += u;
-	k = fabs(u);  /* remember largest term summed */
-	if( k > umax )
-		umax = k;
-	k = m;
-	if( ++i > 10000 ) /* should never happen */
-		{
-		*loss = 1.0;
-		return(s);
-		}
-	}
-while( fabs(u/s) > MACHEP );
-
-/* return estimated relative error */
-*loss = (MACHEP*umax)/fabs(s) + (MACHEP*i);
-
-return(s);
-}