uClibc now has a math library. muahahahaha!

 -Erik

1 files changed, 210 insertions, 0 deletions

diff --git a/libm/double/igam.c b/libm/double/igam.c
new file mode 100644
index 000000000..a1d0bab36
--- /dev/null
+++ b/libm/double/igam.c
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+/*							igam.c
+ *
+ *	Incomplete gamma integral
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double a, x, y, igam();
+ *
+ * y = igam( a, x );
+ *
+ * DESCRIPTION:
+ *
+ * The function is defined by
+ *
+ *                           x
+ *                            -
+ *                   1       | |  -t  a-1
+ *  igam(a,x)  =   -----     |   e   t   dt.
+ *                  -      | |
+ *                 | (a)    -
+ *                           0
+ *
+ *
+ * In this implementation both arguments must be positive.
+ * The integral is evaluated by either a power series or
+ * continued fraction expansion, depending on the relative
+ * values of a and x.
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    IEEE      0,30       200000       3.6e-14     2.9e-15
+ *    IEEE      0,100      300000       9.9e-14     1.5e-14
+ */
+/*							igamc()
+ *
+ *	Complemented incomplete gamma integral
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double a, x, y, igamc();
+ *
+ * y = igamc( a, x );
+ *
+ * DESCRIPTION:
+ *
+ * The function is defined by
+ *
+ *
+ *  igamc(a,x)   =   1 - igam(a,x)
+ *
+ *                            inf.
+ *                              -
+ *                     1       | |  -t  a-1
+ *               =   -----     |   e   t   dt.
+ *                    -      | |
+ *                   | (a)    -
+ *                             x
+ *
+ *
+ * In this implementation both arguments must be positive.
+ * The integral is evaluated by either a power series or
+ * continued fraction expansion, depending on the relative
+ * values of a and x.
+ *
+ * ACCURACY:
+ *
+ * Tested at random a, x.
+ *                a         x                      Relative error:
+ * arithmetic   domain   domain     # trials      peak         rms
+ *    IEEE     0.5,100   0,100      200000       1.9e-14     1.7e-15
+ *    IEEE     0.01,0.5  0,100      200000       1.4e-13     1.6e-15
+ */
+
+/*
+Cephes Math Library Release 2.8:  June, 2000
+Copyright 1985, 1987, 2000 by Stephen L. Moshier
+*/
+
+#include <math.h>
+#ifdef ANSIPROT
+extern double lgam ( double );
+extern double exp ( double );
+extern double log ( double );
+extern double fabs ( double );
+extern double igam ( double, double );
+extern double igamc ( double, double );
+#else
+double lgam(), exp(), log(), fabs(), igam(), igamc();
+#endif
+
+extern double MACHEP, MAXLOG;
+static double big = 4.503599627370496e15;
+static double biginv =  2.22044604925031308085e-16;
+
+double igamc( a, x )
+double a, x;
+{
+double ans, ax, c, yc, r, t, y, z;
+double pk, pkm1, pkm2, qk, qkm1, qkm2;
+
+if( (x <= 0) || ( a <= 0) )
+	return( 1.0 );
+
+if( (x < 1.0) || (x < a) )
+	return( 1.0 - igam(a,x) );
+
+ax = a * log(x) - x - lgam(a);
+if( ax < -MAXLOG )
+	{
+	mtherr( "igamc", UNDERFLOW );
+	return( 0.0 );
+	}
+ax = exp(ax);
+
+/* continued fraction */
+y = 1.0 - a;
+z = x + y + 1.0;
+c = 0.0;
+pkm2 = 1.0;
+qkm2 = x;
+pkm1 = x + 1.0;
+qkm1 = z * x;
+ans = pkm1/qkm1;
+
+do
+	{
+	c += 1.0;
+	y += 1.0;
+	z += 2.0;
+	yc = y * c;
+	pk = pkm1 * z  -  pkm2 * yc;
+	qk = qkm1 * z  -  qkm2 * yc;
+	if( qk != 0 )
+		{
+		r = pk/qk;
+		t = fabs( (ans - r)/r );
+		ans = r;
+		}
+	else
+		t = 1.0;
+	pkm2 = pkm1;
+	pkm1 = pk;
+	qkm2 = qkm1;
+	qkm1 = qk;
+	if( fabs(pk) > big )
+		{
+		pkm2 *= biginv;
+		pkm1 *= biginv;
+		qkm2 *= biginv;
+		qkm1 *= biginv;
+		}
+	}
+while( t > MACHEP );
+
+return( ans * ax );
+}
+
+
+
+/* left tail of incomplete gamma function:
+ *
+ *          inf.      k
+ *   a  -x   -       x
+ *  x  e     >   ----------
+ *           -     -
+ *          k=0   | (a+k+1)
+ *
+ */
+
+double igam( a, x )
+double a, x;
+{
+double ans, ax, c, r;
+
+if( (x <= 0) || ( a <= 0) )
+	return( 0.0 );
+
+if( (x > 1.0) && (x > a ) )
+	return( 1.0 - igamc(a,x) );
+
+/* Compute  x**a * exp(-x) / gamma(a)  */
+ax = a * log(x) - x - lgam(a);
+if( ax < -MAXLOG )
+	{
+	mtherr( "igam", UNDERFLOW );
+	return( 0.0 );
+	}
+ax = exp(ax);
+
+/* power series */
+r = a;
+c = 1.0;
+ans = 1.0;
+
+do
+	{
+	r += 1.0;
+	c *= x/r;
+	ans += c;
+	}
+while( c/ans > MACHEP );
+
+return( ans * ax/a );
+}