uClibc now has a math library. muahahahaha!

 -Erik

1 files changed, 313 insertions, 0 deletions

diff --git a/libm/double/incbi.c b/libm/double/incbi.c
new file mode 100644
index 000000000..817219c4a
--- /dev/null
+++ b/libm/double/incbi.c
@@ -0,0 +1,313 @@
+/*							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 );
+}