From 1077fa4d772832f77a677ce7fb7c2d513b959e3f Mon Sep 17 00:00:00 2001
From: Eric Andersen <andersen@codepoet.org>
Date: Thu, 10 May 2001 00:40:28 +0000
Subject: uClibc now has a math library.  muahahahaha!  -Erik

---
 libm/ldouble/bdtrl.c | 260 +++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 260 insertions(+)
 create mode 100644 libm/ldouble/bdtrl.c

(limited to 'libm/ldouble/bdtrl.c')

diff --git a/libm/ldouble/bdtrl.c b/libm/ldouble/bdtrl.c
new file mode 100644
index 000000000..aca9577d1
--- /dev/null
+++ b/libm/ldouble/bdtrl.c
@@ -0,0 +1,260 @@
+/*							bdtrl.c
+ *
+ *	Binomial distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int k, n;
+ * long double p, y, bdtrl();
+ *
+ * y = bdtrl( k, n, p );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the sum of the terms 0 through k of the Binomial
+ * probability density:
+ *
+ *   k
+ *   --  ( n )   j      n-j
+ *   >   (   )  p  (1-p)
+ *   --  ( j )
+ *  j=0
+ *
+ * The terms are not summed directly; instead the incomplete
+ * beta integral is employed, according to the formula
+ *
+ * y = bdtr( k, n, p ) = incbet( n-k, k+1, 1-p ).
+ *
+ * The arguments must be positive, with p ranging from 0 to 1.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Tested at random points (k,n,p) with a and b between 0
+ * and 10000 and p between 0 and 1.
+ *    Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    IEEE      0,10000      3000       1.6e-14     2.2e-15
+ *
+ * ERROR MESSAGES:
+ *
+ *   message         condition      value returned
+ * bdtrl domain        k < 0            0.0
+ *                     n < k
+ *                     x < 0, x > 1
+ *
+ */
+/*							bdtrcl()
+ *
+ *	Complemented binomial distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int k, n;
+ * long double p, y, bdtrcl();
+ *
+ * y = bdtrcl( k, n, p );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the sum of the terms k+1 through n of the Binomial
+ * probability density:
+ *
+ *   n
+ *   --  ( n )   j      n-j
+ *   >   (   )  p  (1-p)
+ *   --  ( j )
+ *  j=k+1
+ *
+ * The terms are not summed directly; instead the incomplete
+ * beta integral is employed, according to the formula
+ *
+ * y = bdtrc( k, n, p ) = incbet( k+1, n-k, p ).
+ *
+ * The arguments must be positive, with p ranging from 0 to 1.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * See incbet.c.
+ *
+ * ERROR MESSAGES:
+ *
+ *   message         condition      value returned
+ * bdtrcl domain     x<0, x>1, n<k       0.0
+ */
+/*							bdtril()
+ *
+ *	Inverse binomial distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int k, n;
+ * long double p, y, bdtril();
+ *
+ * p = bdtril( k, n, y );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Finds the event probability p such that the sum of the
+ * terms 0 through k of the Binomial probability density
+ * is equal to the given cumulative probability y.
+ *
+ * This is accomplished using the inverse beta integral
+ * function and the relation
+ *
+ * 1 - p = incbi( n-k, k+1, y ).
+ *
+ * ACCURACY:
+ *
+ * See incbi.c.
+ * Tested at random k, n between 1 and 10000.  The "domain" refers to p:
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    IEEE       0,1        3500       2.0e-15     8.2e-17
+ *
+ * ERROR MESSAGES:
+ *
+ *   message         condition      value returned
+ * bdtril domain     k < 0, n <= k         0.0
+ *                  x < 0, x > 1
+ */
+
+/*								bdtr() */
+
+
+/*
+Cephes Math Library Release 2.3:  March, 1995
+Copyright 1984, 1995 by Stephen L. Moshier
+*/
+
+#include <math.h>
+#ifdef ANSIPROT
+extern long double incbetl ( long double, long double, long double );
+extern long double incbil ( long double, long double, long double );
+extern long double powl ( long double, long double );
+extern long double expm1l ( long double );
+extern long double log1pl ( long double );
+#else
+long double incbetl(), incbil(), powl(), expm1l(), log1pl();
+#endif
+
+long double bdtrcl( k, n, p )
+int k, n;
+long double p;
+{
+long double dk, dn;
+
+if( (p < 0.0L) || (p > 1.0L) )
+	goto domerr;
+if( k < 0 )
+	return( 1.0L );
+
+if( n < k )
+	{
+domerr:
+	mtherr( "bdtrcl", DOMAIN );
+	return( 0.0L );
+	}
+
+if( k == n )
+	return( 0.0L );
+dn = n - k;
+if( k == 0 )
+	{
+	if( p < .01L )
+		dk = -expm1l( dn * log1pl(-p) );
+	else
+		dk = 1.0L - powl( 1.0L-p, dn );
+	}
+else
+	{
+	dk = k + 1;
+	dk = incbetl( dk, dn, p );
+	}
+return( dk );
+}
+
+
+
+long double bdtrl( k, n, p )
+int k, n;
+long double p;
+{
+long double dk, dn, q;
+
+if( (p < 0.0L) || (p > 1.0L) )
+	goto domerr;
+if( (k < 0) || (n < k) )
+	{
+domerr:
+	mtherr( "bdtrl", DOMAIN );
+	return( 0.0L );
+	}
+
+if( k == n )
+	return( 1.0L );
+
+q = 1.0L - p;
+dn = n - k;
+if( k == 0 )
+	{
+	dk = powl( q, dn );
+	}
+else
+	{
+	dk = k + 1;
+	dk = incbetl( dn, dk, q );
+	}
+return( dk );
+}
+
+
+long double bdtril( k, n, y )
+int k, n;
+long double y;
+{
+long double dk, dn, p;
+
+if( (y < 0.0L) || (y > 1.0L) )
+	goto domerr;
+if( (k < 0) || (n <= k) )
+	{
+domerr:
+	mtherr( "bdtril", DOMAIN );
+	return( 0.0L );
+	}
+
+dn = n - k;
+if( k == 0 )
+	{
+	if( y > 0.8L )
+		p = -expm1l( log1pl(y-1.0L) / dn );
+	else
+		p = 1.0L - powl( y, 1.0L/dn );
+	}
+else
+	{
+	dk = k + 1;
+	p = incbetl( dn, dk, y );
+	if( p > 0.5 )
+		p = incbil( dk, dn, 1.0L-y );
+	else
+		p = 1.0 - incbil( dn, dk, y );
+	}
+return( p );
+}
-- 
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