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, 313 deletions

diff --git a/libm/double/incbi.c b/libm/double/incbi.c
deleted file mode 100644
index 817219c4a..000000000
--- a/libm/double/incbi.c
+++ /dev/null
@@ -1,313 +0,0 @@
-/*							incbi()
- *
- *      Inverse of imcomplete beta integral
- *
- *
- *
- * SYNOPSIS:
- *
- * double a, b, x, y, incbi();
- *
- * x = incbi( a, b, y );
- *
- *
- *
- * DESCRIPTION:
- *
- * Given y, the function finds x such that
- *
- *  incbet( a, b, x ) = y .
- *
- * The routine performs interval halving or Newton iterations to find the
- * root of incbet(a,b,x) - y = 0.
- *
- *
- * ACCURACY:
- *
- *                      Relative error:
- *                x     a,b
- * arithmetic   domain  domain  # trials    peak       rms
- *    IEEE      0,1    .5,10000   50000    5.8e-12   1.3e-13
- *    IEEE      0,1   .25,100    100000    1.8e-13   3.9e-15
- *    IEEE      0,1     0,5       50000    1.1e-12   5.5e-15
- *    VAX       0,1    .5,100     25000    3.5e-14   1.1e-15
- * With a and b constrained to half-integer or integer values:
- *    IEEE      0,1    .5,10000   50000    5.8e-12   1.1e-13
- *    IEEE      0,1    .5,100    100000    1.7e-14   7.9e-16
- * With a = .5, b constrained to half-integer or integer values:
- *    IEEE      0,1    .5,10000   10000    8.3e-11   1.0e-11
- */
-
-
-/*
-Cephes Math Library Release 2.8:  June, 2000
-Copyright 1984, 1996, 2000 by Stephen L. Moshier
-*/
-
-#include <math.h>
-
-extern double MACHEP, MAXNUM, MAXLOG, MINLOG;
-#ifdef ANSIPROT
-extern double ndtri ( double );
-extern double exp ( double );
-extern double fabs ( double );
-extern double log ( double );
-extern double sqrt ( double );
-extern double lgam ( double );
-extern double incbet ( double, double, double );
-#else
-double ndtri(), exp(), fabs(), log(), sqrt(), lgam(), incbet();
-#endif
-
-double incbi( aa, bb, yy0 )
-double aa, bb, yy0;
-{
-double a, b, y0, d, y, x, x0, x1, lgm, yp, di, dithresh, yl, yh, xt;
-int i, rflg, dir, nflg;
-
-
-i = 0;
-if( yy0 <= 0 )
-	return(0.0);
-if( yy0 >= 1.0 )
-	return(1.0);
-x0 = 0.0;
-yl = 0.0;
-x1 = 1.0;
-yh = 1.0;
-nflg = 0;
-
-if( aa <= 1.0 || bb <= 1.0 )
-	{
-	dithresh = 1.0e-6;
-	rflg = 0;
-	a = aa;
-	b = bb;
-	y0 = yy0;
-	x = a/(a+b);
-	y = incbet( a, b, x );
-	goto ihalve;
-	}
-else
-	{
-	dithresh = 1.0e-4;
-	}
-/* approximation to inverse function */
-
-yp = -ndtri(yy0);
-
-if( yy0 > 0.5 )
-	{
-	rflg = 1;
-	a = bb;
-	b = aa;
-	y0 = 1.0 - yy0;
-	yp = -yp;
-	}
-else
-	{
-	rflg = 0;
-	a = aa;
-	b = bb;
-	y0 = yy0;
-	}
-
-lgm = (yp * yp - 3.0)/6.0;
-x = 2.0/( 1.0/(2.0*a-1.0)  +  1.0/(2.0*b-1.0) );
-d = yp * sqrt( x + lgm ) / x
-	- ( 1.0/(2.0*b-1.0) - 1.0/(2.0*a-1.0) )
-	* (lgm + 5.0/6.0 - 2.0/(3.0*x));
-d = 2.0 * d;
-if( d < MINLOG )
-	{
-	x = 1.0;
-	goto under;
-	}
-x = a/( a + b * exp(d) );
-y = incbet( a, b, x );
-yp = (y - y0)/y0;
-if( fabs(yp) < 0.2 )
-	goto newt;
-
-/* Resort to interval halving if not close enough. */
-ihalve:
-
-dir = 0;
-di = 0.5;
-for( i=0; i<100; i++ )
-	{
-	if( i != 0 )
-		{
-		x = x0  +  di * (x1 - x0);
-		if( x == 1.0 )
-			x = 1.0 - MACHEP;
-		if( x == 0.0 )
-			{
-			di = 0.5;
-			x = x0  +  di * (x1 - x0);
-			if( x == 0.0 )
-				goto under;
-			}
-		y = incbet( a, b, x );
-		yp = (x1 - x0)/(x1 + x0);
-		if( fabs(yp) < dithresh )
-			goto newt;
-		yp = (y-y0)/y0;
-		if( fabs(yp) < dithresh )
-			goto newt;
-		}
-	if( y < y0 )
-		{
-		x0 = x;
-		yl = y;
-		if( dir < 0 )
-			{
-			dir = 0;
-			di = 0.5;
-			}
-		else if( dir > 3 )
-			di = 1.0 - (1.0 - di) * (1.0 - di);
-		else if( dir > 1 )
-			di = 0.5 * di + 0.5; 
-		else
-			di = (y0 - y)/(yh - yl);
-		dir += 1;
-		if( x0 > 0.75 )
-			{
-			if( rflg == 1 )
-				{
-				rflg = 0;
-				a = aa;
-				b = bb;
-				y0 = yy0;
-				}
-			else
-				{
-				rflg = 1;
-				a = bb;
-				b = aa;
-				y0 = 1.0 - yy0;
-				}
-			x = 1.0 - x;
-			y = incbet( a, b, x );
-			x0 = 0.0;
-			yl = 0.0;
-			x1 = 1.0;
-			yh = 1.0;
-			goto ihalve;
-			}
-		}
-	else
-		{
-		x1 = x;
-		if( rflg == 1 && x1 < MACHEP )
-			{
-			x = 0.0;
-			goto done;
-			}
-		yh = y;
-		if( dir > 0 )
-			{
-			dir = 0;
-			di = 0.5;
-			}
-		else if( dir < -3 )
-			di = di * di;
-		else if( dir < -1 )
-			di = 0.5 * di;
-		else
-			di = (y - y0)/(yh - yl);
-		dir -= 1;
-		}
-	}
-mtherr( "incbi", PLOSS );
-if( x0 >= 1.0 )
-	{
-	x = 1.0 - MACHEP;
-	goto done;
-	}
-if( x <= 0.0 )
-	{
-under:
-	mtherr( "incbi", UNDERFLOW );
-	x = 0.0;
-	goto done;
-	}
-
-newt:
-
-if( nflg )
-	goto done;
-nflg = 1;
-lgm = lgam(a+b) - lgam(a) - lgam(b);
-
-for( i=0; i<8; i++ )
-	{
-	/* Compute the function at this point. */
-	if( i != 0 )
-		y = incbet(a,b,x);
-	if( y < yl )
-		{
-		x = x0;
-		y = yl;
-		}
-	else if( y > yh )
-		{
-		x = x1;
-		y = yh;
-		}
-	else if( y < y0 )
-		{
-		x0 = x;
-		yl = y;
-		}
-	else
-		{
-		x1 = x;
-		yh = y;
-		}
-	if( x == 1.0 || x == 0.0 )
-		break;
-	/* Compute the derivative of the function at this point. */
-	d = (a - 1.0) * log(x) + (b - 1.0) * log(1.0-x) + lgm;
-	if( d < MINLOG )
-		goto done;
-	if( d > MAXLOG )
-		break;
-	d = exp(d);
-	/* Compute the step to the next approximation of x. */
-	d = (y - y0)/d;
-	xt = x - d;
-	if( xt <= x0 )
-		{
-		y = (x - x0) / (x1 - x0);
-		xt = x0 + 0.5 * y * (x - x0);
-		if( xt <= 0.0 )
-			break;
-		}
-	if( xt >= x1 )
-		{
-		y = (x1 - x) / (x1 - x0);
-		xt = x1 - 0.5 * y * (x1 - x);
-		if( xt >= 1.0 )
-			break;
-		}
-	x = xt;
-	if( fabs(d/x) < 128.0 * MACHEP )
-		goto done;
-	}
-/* Did not converge.  */
-dithresh = 256.0 * MACHEP;
-goto ihalve;
-
-done:
-
-if( rflg )
-	{
-	if( x <= MACHEP )
-		x = 1.0 - MACHEP;
-	else
-		x = 1.0 - x;
-	}
-return( x );
-}