uClibc now has a math library. muahahahaha!

 -Erik

1 files changed, 305 insertions, 0 deletions

diff --git a/libm/ldouble/incbil.c b/libm/ldouble/incbil.c
new file mode 100644
index 000000000..b7610706b
--- /dev/null
+++ b/libm/ldouble/incbil.c
@@ -0,0 +1,305 @@
+/*							incbil()
+ *
+ *      Inverse of imcomplete beta integral
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double a, b, x, y, incbil();
+ *
+ * x = incbil( a, b, y );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Given y, the function finds x such that
+ *
+ *  incbet( a, b, x ) = y.
+ *
+ * the routine performs up to 10 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    10000    1.1e-14   1.4e-16
+ */
+
+
+/*
+Cephes Math Library Release 2.3:  March, 1995
+Copyright 1984, 1995 by Stephen L. Moshier
+*/
+
+#include <math.h>
+
+extern long double MACHEPL, MAXNUML, MAXLOGL, MINLOGL;
+#ifdef ANSIPROT
+extern long double incbetl ( long double, long double, long double );
+extern long double expl ( long double );
+extern long double fabsl ( long double );
+extern long double logl ( long double );
+extern long double sqrtl ( long double );
+extern long double lgaml ( long double );
+extern long double ndtril ( long double );
+#else
+long double incbetl(), expl(), fabsl(), logl(), sqrtl(), lgaml();
+long double ndtril();
+#endif
+
+long double incbil( aa, bb, yy0 )
+long double aa, bb, yy0;
+{
+long double a, b, y0, d, y, x, x0, x1, lgm, yp, di, dithresh, yl, yh, xt;
+int i, rflg, dir, nflg;
+
+
+if( yy0 <= 0.0L )
+	return(0.0L);
+if( yy0 >= 1.0L )
+	return(1.0L);
+x0 = 0.0L;
+yl = 0.0L;
+x1 = 1.0L;
+yh = 1.0L;
+if( aa <= 1.0L || bb <= 1.0L )
+	{
+	dithresh = 1.0e-7L;
+	rflg = 0;
+	a = aa;
+	b = bb;
+	y0 = yy0;
+	x = a/(a+b);
+	y = incbetl( a, b, x );
+	nflg = 0;
+	goto ihalve;
+	}
+else
+	{
+	nflg = 0;
+	dithresh = 1.0e-4L;
+	}
+
+/* approximation to inverse function */
+
+yp = -ndtril( yy0 );
+
+if( yy0 > 0.5L )
+	{
+	rflg = 1;
+	a = bb;
+	b = aa;
+	y0 = 1.0L - yy0;
+	yp = -yp;
+	}
+else
+	{
+	rflg = 0;
+	a = aa;
+	b = bb;
+	y0 = yy0;
+	}
+
+lgm = (yp * yp - 3.0L)/6.0L;
+x = 2.0L/( 1.0L/(2.0L * a-1.0L)  +  1.0L/(2.0L * b - 1.0L) );
+d = yp * sqrtl( x + lgm ) / x
+	- ( 1.0L/(2.0L * b - 1.0L) - 1.0L/(2.0L * a - 1.0L) )
+	* (lgm + (5.0L/6.0L) - 2.0L/(3.0L * x));
+d = 2.0L * d;
+if( d < MINLOGL )
+	{
+	x = 1.0L;
+	goto under;
+	}
+x = a/( a + b * expl(d) );
+y = incbetl( a, b, x );
+yp = (y - y0)/y0;
+if( fabsl(yp) < 0.2 )
+	goto newt;
+
+/* Resort to interval halving if not close enough. */
+ihalve:
+
+dir = 0;
+di = 0.5L;
+for( i=0; i<400; i++ )
+	{
+	if( i != 0 )
+		{
+		x = x0  +  di * (x1 - x0);
+		if( x == 1.0L )
+			x = 1.0L - MACHEPL;
+		if( x == 0.0L )
+			{
+			di = 0.5;
+			x = x0  +  di * (x1 - x0);
+			if( x == 0.0 )
+				goto under;
+			}
+		y = incbetl( a, b, x );
+		yp = (x1 - x0)/(x1 + x0);
+		if( fabsl(yp) < dithresh )
+			goto newt;
+		yp = (y-y0)/y0;
+		if( fabsl(yp) < dithresh )
+			goto newt;
+		}
+	if( y < y0 )
+		{
+		x0 = x;
+		yl = y;
+		if( dir < 0 )
+			{
+			dir = 0;
+			di = 0.5L;
+			}
+		else if( dir > 3 )
+			di = 1.0L - (1.0L - di) * (1.0L - di);
+		else if( dir > 1 )
+			di = 0.5L * di + 0.5L; 
+		else
+			di = (y0 - y)/(yh - yl);
+		dir += 1;
+		if( x0 > 0.95L )
+			{
+			if( rflg == 1 )
+				{
+				rflg = 0;
+				a = aa;
+				b = bb;
+				y0 = yy0;
+				}
+			else
+				{
+				rflg = 1;
+				a = bb;
+				b = aa;
+				y0 = 1.0 - yy0;
+				}
+			x = 1.0L - x;
+			y = incbetl( a, b, x );
+			x0 = 0.0;
+			yl = 0.0;
+			x1 = 1.0;
+			yh = 1.0;
+			goto ihalve;
+			}
+		}
+	else
+		{
+		x1 = x;
+		if( rflg == 1 && x1 < MACHEPL )
+			{
+			x = 0.0L;
+			goto done;
+			}
+		yh = y;
+		if( dir > 0 )
+			{
+			dir = 0;
+			di = 0.5L;
+			}
+		else if( dir < -3 )
+			di = di * di;
+		else if( dir < -1 )
+			di = 0.5L * di;
+		else
+			di = (y - y0)/(yh - yl);
+		dir -= 1;
+		}
+	}
+mtherr( "incbil", PLOSS );
+if( x0 >= 1.0L )
+	{
+	x = 1.0L - MACHEPL;
+	goto done;
+	}
+if( x <= 0.0L )
+	{
+under:
+	mtherr( "incbil", UNDERFLOW );
+	x = 0.0L;
+	goto done;
+	}
+
+newt:
+
+if( nflg )
+	goto done;
+nflg = 1;
+lgm = lgaml(a+b) - lgaml(a) - lgaml(b);
+
+for( i=0; i<15; i++ )
+	{
+	/* Compute the function at this point. */
+	if( i != 0 )
+		y = incbetl(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 == 1.0L || x == 0.0L )
+		break;
+	/* Compute the derivative of the function at this point. */
+	d = (a - 1.0L) * logl(x) + (b - 1.0L) * logl(1.0L - x) + lgm;
+	if( d < MINLOGL )
+		goto done;
+	if( d > MAXLOGL )
+		break;
+	d = expl(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 + 0.5L * y * (x - x0);
+		if( xt <= 0.0L )
+			break;
+		}
+	if( xt >= x1 )
+		{
+		y = (x1 - x) / (x1 - x0);
+		xt = x1 - 0.5L * y * (x1 - x);
+		if( xt >= 1.0L )
+			break;
+		}
+	x = xt;
+	if( fabsl(d/x) < (128.0L * MACHEPL) )
+		goto done;
+	}
+/* Did not converge.  */
+dithresh = 256.0L * MACHEPL;
+goto ihalve;
+
+done:
+if( rflg )
+	{
+	if( x <= MACHEPL )
+		x = 1.0L - MACHEPL;
+	else
+		x = 1.0L - x;
+	}
+return( x );
+}