uClibc now has a math library. muahahahaha!

 -Erik

1 files changed, 193 insertions, 0 deletions

diff --git a/libm/ldouble/igamil.c b/libm/ldouble/igamil.c
new file mode 100644
index 000000000..1abe503e9
--- /dev/null
+++ b/libm/ldouble/igamil.c
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+/*							igamil()
+ *
+ *      Inverse of complemented imcomplete gamma integral
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double a, x, y, igamil();
+ *
+ * x = igamil( a, y );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Given y, the function finds x such that
+ *
+ *  igamc( a, x ) = y.
+ *
+ * Starting with the approximate value
+ *
+ *         3
+ *  x = a t
+ *
+ *  where
+ *
+ *  t = 1 - d - ndtri(y) sqrt(d)
+ * 
+ * and
+ *
+ *  d = 1/9a,
+ *
+ * the routine performs up to 10 Newton iterations to find the
+ * root of igamc(a,x) - y = 0.
+ *
+ *
+ * ACCURACY:
+ *
+ * Tested for a ranging from 0.5 to 30 and x from 0 to 0.5.
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC       0,0.5         3400       8.8e-16     1.3e-16
+ *    IEEE      0,0.5        10000       1.1e-14     1.0e-15
+ *
+ */
+
+/*
+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 ndtril ( 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 igamcl ( long double, long double );
+#else
+long double ndtril(), expl(), fabsl(), logl(), sqrtl(), lgaml();
+long double igamcl();
+#endif
+
+long double igamil( a, y0 )
+long double a, y0;
+{
+long double x0, x1, x, yl, yh, y, d, lgm, dithresh;
+int i, dir;
+
+/* bound the solution */
+x0 = MAXNUML;
+yl = 0.0L;
+x1 = 0.0L;
+yh = 1.0L;
+dithresh = 4.0 * MACHEPL;
+
+/* approximation to inverse function */
+d = 1.0L/(9.0L*a);
+y = ( 1.0L - d - ndtril(y0) * sqrtl(d) );
+x = a * y * y * y;
+
+lgm = lgaml(a);
+
+for( i=0; i<10; i++ )
+	{
+	if( x > x0 || x < x1 )
+		goto ihalve;
+	y = igamcl(a,x);
+	if( y < yl || y > yh )
+		goto ihalve;
+	if( y < y0 )
+		{
+		x0 = x;
+		yl = y;
+		}
+	else
+		{
+		x1 = x;
+		yh = y;
+		}
+/* compute the derivative of the function at this point */
+	d = (a - 1.0L) * logl(x0) - x0 - lgm;
+	if( d < -MAXLOGL )
+		goto ihalve;
+	d = -expl(d);
+/* compute the step to the next approximation of x */
+	d = (y - y0)/d;
+	x = x - d;
+	if( i < 3 )
+		continue;
+	if( fabsl(d/x) < dithresh )
+		goto done;
+	}
+
+/* Resort to interval halving if Newton iteration did not converge. */
+ihalve:
+
+d = 0.0625L;
+if( x0 == MAXNUML )
+	{
+	if( x <= 0.0L )
+		x = 1.0L;
+	while( x0 == MAXNUML )
+		{
+		x = (1.0L + d) * x;
+		y = igamcl( a, x );
+		if( y < y0 )
+			{
+			x0 = x;
+			yl = y;
+			break;
+			}
+		d = d + d;
+		}
+	}
+d = 0.5L;
+dir = 0;
+
+for( i=0; i<400; i++ )
+	{
+	x = x1  +  d * (x0 - x1);
+	y = igamcl( a, x );
+	lgm = (x0 - x1)/(x1 + x0);
+	if( fabsl(lgm) < dithresh )
+		break;
+	lgm = (y - y0)/y0;
+	if( fabsl(lgm) < dithresh )
+		break;
+	if( x <= 0.0L )
+		break;
+	if( y > y0 )
+		{
+		x1 = x;
+		yh = y;
+		if( dir < 0 )
+			{
+			dir = 0;
+			d = 0.5L;
+			}
+		else if( dir > 1 )
+			d = 0.5L * d + 0.5L; 
+		else
+			d = (y0 - yl)/(yh - yl);
+		dir += 1;
+		}
+	else
+		{
+		x0 = x;
+		yl = y;
+		if( dir > 0 )
+			{
+			dir = 0;
+			d = 0.5L;
+			}
+		else if( dir < -1 )
+			d = 0.5L * d;
+		else
+			d = (y0 - yl)/(yh - yl);
+		dir -= 1;
+		}
+	}
+if( x == 0.0L )
+	mtherr( "igamil", UNDERFLOW );
+
+done:
+return( x );
+}