uClibc now has a math library. muahahahaha!

 -Erik

1 files changed, 220 insertions, 0 deletions

diff --git a/libm/ldouble/igaml.c b/libm/ldouble/igaml.c
new file mode 100644
index 000000000..0e59c5404
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+++ b/libm/ldouble/igaml.c
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+/*							igaml.c
+ *
+ *	Incomplete gamma integral
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double a, x, y, igaml();
+ *
+ * y = igaml( 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
+ *    DEC       0,30         4000       4.4e-15     6.3e-16
+ *    IEEE      0,30        10000       3.6e-14     5.1e-15
+ *
+ */
+/*							igamcl()
+ *
+ *	Complemented incomplete gamma integral
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double a, x, y, igamcl();
+ *
+ * y = igamcl( 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:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC       0,30         2000       2.7e-15     4.0e-16
+ *    IEEE      0,30        60000       1.4e-12     6.3e-15
+ *
+ */
+
+/*
+Cephes Math Library Release 2.3:  March, 1995
+Copyright 1985, 1995 by Stephen L. Moshier
+*/
+
+#include <math.h>
+#ifdef ANSIPROT
+extern long double lgaml ( long double );
+extern long double expl ( long double );
+extern long double logl ( long double );
+extern long double fabsl ( long double );
+extern long double gammal ( long double );
+long double igaml ( long double, long double );
+long double igamcl ( long double, long double );
+#else
+long double lgaml(), expl(), logl(), fabsl(), igaml(), gammal();
+long double igamcl();
+#endif
+
+#define BIG 9.223372036854775808e18L
+#define MAXGAML 1755.455L
+extern long double MACHEPL, MINLOGL;
+
+long double igamcl( a, x )
+long double a, x;
+{
+long double ans, c, yc, ax, y, z, r, t;
+long double pk, pkm1, pkm2, qk, qkm1, qkm2;
+
+if( (x <= 0.0L) || ( a <= 0.0L) )
+	return( 1.0L );
+
+if( (x < 1.0L) || (x < a) )
+	return( 1.0L - igaml(a,x) );
+
+ax = a * logl(x) - x - lgaml(a);
+if( ax < MINLOGL )
+	{
+	mtherr( "igamcl", UNDERFLOW );
+	return( 0.0L );
+	}
+ax = expl(ax);
+
+/* continued fraction */
+y = 1.0L - a;
+z = x + y + 1.0L;
+c = 0.0L;
+pkm2 = 1.0L;
+qkm2 = x;
+pkm1 = x + 1.0L;
+qkm1 = z * x;
+ans = pkm1/qkm1;
+
+do
+	{
+	c += 1.0L;
+	y += 1.0L;
+	z += 2.0L;
+	yc = y * c;
+	pk = pkm1 * z  -  pkm2 * yc;
+	qk = qkm1 * z  -  qkm2 * yc;
+	if( qk != 0.0L )
+		{
+		r = pk/qk;
+		t = fabsl( (ans - r)/r );
+		ans = r;
+		}
+	else
+		t = 1.0L;
+	pkm2 = pkm1;
+	pkm1 = pk;
+	qkm2 = qkm1;
+	qkm1 = qk;
+	if( fabsl(pk) > BIG )
+		{
+		pkm2 /= BIG;
+		pkm1 /= BIG;
+		qkm2 /= BIG;
+		qkm1 /= BIG;
+		}
+	}
+while( t > MACHEPL );
+
+return( ans * ax );
+}
+
+
+
+/* left tail of incomplete gamma function:
+ *
+ *          inf.      k
+ *   a  -x   -       x
+ *  x  e     >   ----------
+ *           -     -
+ *          k=0   | (a+k+1)
+ *
+ */
+
+long double igaml( a, x )
+long double a, x;
+{
+long double ans, ax, c, r;
+
+if( (x <= 0.0L) || ( a <= 0.0L) )
+	return( 0.0L );
+
+if( (x > 1.0L) && (x > a ) )
+	return( 1.0L - igamcl(a,x) );
+
+ax = a * logl(x) - x - lgaml(a);
+if( ax < MINLOGL )
+	{
+	mtherr( "igaml", UNDERFLOW );
+	return( 0.0L );
+	}
+ax = expl(ax);
+
+/* power series */
+r = a;
+c = 1.0L;
+ans = 1.0L;
+
+do
+	{
+	r += 1.0L;
+	c *= x/r;
+	ans += c;
+	}
+while( c/ans > MACHEPL );
+
+return( ans * ax/a );
+}