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/double/bdtr.c | 263 +++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 263 insertions(+)
 create mode 100644 libm/double/bdtr.c

(limited to 'libm/double/bdtr.c')

diff --git a/libm/double/bdtr.c b/libm/double/bdtr.c
new file mode 100644
index 000000000..a268c7a10
--- /dev/null
+++ b/libm/double/bdtr.c
@@ -0,0 +1,263 @@
+/*							bdtr.c
+ *
+ *	Binomial distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int k, n;
+ * double p, y, bdtr();
+ *
+ * y = bdtr( 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 (a,b,p), with p between 0 and 1.
+ *
+ *               a,b                     Relative error:
+ * arithmetic  domain     # trials      peak         rms
+ *  For p between 0.001 and 1:
+ *    IEEE     0,100       100000      4.3e-15     2.6e-16
+ * See also incbet.c.
+ *
+ * ERROR MESSAGES:
+ *
+ *   message         condition      value returned
+ * bdtr domain         k < 0            0.0
+ *                     n < k
+ *                     x < 0, x > 1
+ */
+/*							bdtrc()
+ *
+ *	Complemented binomial distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int k, n;
+ * double p, y, bdtrc();
+ *
+ * y = bdtrc( 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:
+ *
+ * Tested at random points (a,b,p).
+ *
+ *               a,b                     Relative error:
+ * arithmetic  domain     # trials      peak         rms
+ *  For p between 0.001 and 1:
+ *    IEEE     0,100       100000      6.7e-15     8.2e-16
+ *  For p between 0 and .001:
+ *    IEEE     0,100       100000      1.5e-13     2.7e-15
+ *
+ * ERROR MESSAGES:
+ *
+ *   message         condition      value returned
+ * bdtrc domain      x<0, x>1, n<k       0.0
+ */
+/*							bdtri()
+ *
+ *	Inverse binomial distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int k, n;
+ * double p, y, bdtri();
+ *
+ * p = bdtr( 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:
+ *
+ * Tested at random points (a,b,p).
+ *
+ *               a,b                     Relative error:
+ * arithmetic  domain     # trials      peak         rms
+ *  For p between 0.001 and 1:
+ *    IEEE     0,100       100000      2.3e-14     6.4e-16
+ *    IEEE     0,10000     100000      6.6e-12     1.2e-13
+ *  For p between 10^-6 and 0.001:
+ *    IEEE     0,100       100000      2.0e-12     1.3e-14
+ *    IEEE     0,10000     100000      1.5e-12     3.2e-14
+ * See also incbi.c.
+ *
+ * ERROR MESSAGES:
+ *
+ *   message         condition      value returned
+ * bdtri domain     k < 0, n <= k         0.0
+ *                  x < 0, x > 1
+ */
+
+/*								bdtr() */
+
+
+/*
+Cephes Math Library Release 2.8:  June, 2000
+Copyright 1984, 1987, 1995, 2000 by Stephen L. Moshier
+*/
+
+#include <math.h>
+#ifdef ANSIPROT
+extern double incbet ( double, double, double );
+extern double incbi ( double, double, double );
+extern double pow ( double, double );
+extern double log1p ( double );
+extern double expm1 ( double );
+#else
+double incbet(), incbi(), pow(), log1p(), expm1();
+#endif
+
+double bdtrc( k, n, p )
+int k, n;
+double p;
+{
+double dk, dn;
+
+if( (p < 0.0) || (p > 1.0) )
+	goto domerr;
+if( k < 0 )
+	return( 1.0 );
+
+if( n < k )
+	{
+domerr:
+	mtherr( "bdtrc", DOMAIN );
+	return( 0.0 );
+	}
+
+if( k == n )
+	return( 0.0 );
+dn = n - k;
+if( k == 0 )
+	{
+	if( p < .01 )
+		dk = -expm1( dn * log1p(-p) );
+	else
+		dk = 1.0 - pow( 1.0-p, dn );
+	}
+else
+	{
+	dk = k + 1;
+	dk = incbet( dk, dn, p );
+	}
+return( dk );
+}
+
+
+
+double bdtr( k, n, p )
+int k, n;
+double p;
+{
+double dk, dn;
+
+if( (p < 0.0) || (p > 1.0) )
+	goto domerr;
+if( (k < 0) || (n < k) )
+	{
+domerr:
+	mtherr( "bdtr", DOMAIN );
+	return( 0.0 );
+	}
+
+if( k == n )
+	return( 1.0 );
+
+dn = n - k;
+if( k == 0 )
+	{
+	dk = pow( 1.0-p, dn );
+	}
+else
+	{
+	dk = k + 1;
+	dk = incbet( dn, dk, 1.0 - p );
+	}
+return( dk );
+}
+
+
+double bdtri( k, n, y )
+int k, n;
+double y;
+{
+double dk, dn, p;
+
+if( (y < 0.0) || (y > 1.0) )
+	goto domerr;
+if( (k < 0) || (n <= k) )
+	{
+domerr:
+	mtherr( "bdtri", DOMAIN );
+	return( 0.0 );
+	}
+
+dn = n - k;
+if( k == 0 )
+	{
+	if( y > 0.8 )
+		p = -expm1( log1p(y-1.0) / dn );
+	else
+		p = 1.0 - pow( y, 1.0/dn );
+	}
+else
+	{
+	dk = k + 1;
+	p = incbet( dn, dk, 0.5 );
+	if( p > 0.5 )
+		p = incbi( dk, dn, 1.0-y );
+	else
+		p = 1.0 - incbi( dn, dk, y );
+	}
+return( p );
+}
-- 
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