1 files changed, 128 insertions, 0 deletions
diff --git a/libm/float/ellpkf.c b/libm/float/ellpkf.c
new file mode 100644
index 000000000..2cc13d90a
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+++ b/libm/float/ellpkf.c
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+/*							ellpkf.c
+ *
+ *	Complete elliptic integral of the first kind
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float m1, y, ellpkf();
+ *
+ * y = ellpkf( m1 );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Approximates the integral
+ *
+ *
+ *
+ *            pi/2
+ *             -
+ *            | |
+ *            |           dt
+ * K(m)  =    |    ------------------
+ *            |                   2
+ *          | |    sqrt( 1 - m sin t )
+ *           -
+ *            0
+ *
+ * where m = 1 - m1, using the approximation
+ *
+ *     P(x)  -  log x Q(x).
+ *
+ * The argument m1 is used rather than m so that the logarithmic
+ * singularity at m = 1 will be shifted to the origin; this
+ * preserves maximum accuracy.
+ *
+ * K(0) = pi/2.
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    IEEE       0,1        30000       1.3e-7      3.4e-8
+ *
+ * ERROR MESSAGES:
+ *
+ *   message         condition      value returned
+ * ellpkf domain      x<0, x>1           0.0
+ *
+ */
+
+/*							ellpk.c */
+
+
+/*
+Cephes Math Library, Release 2.0:  April, 1987
+Copyright 1984, 1987 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+#include <math.h>
+
+static float P[] =
+{
+ 1.37982864606273237150E-4,
+ 2.28025724005875567385E-3,
+ 7.97404013220415179367E-3,
+ 9.85821379021226008714E-3,
+ 6.87489687449949877925E-3,
+ 6.18901033637687613229E-3,
+ 8.79078273952743772254E-3,
+ 1.49380448916805252718E-2,
+ 3.08851465246711995998E-2,
+ 9.65735902811690126535E-2,
+ 1.38629436111989062502E0
+};
+
+static float Q[] =
+{
+ 2.94078955048598507511E-5,
+ 9.14184723865917226571E-4,
+ 5.94058303753167793257E-3,
+ 1.54850516649762399335E-2,
+ 2.39089602715924892727E-2,
+ 3.01204715227604046988E-2,
+ 3.73774314173823228969E-2,
+ 4.88280347570998239232E-2,
+ 7.03124996963957469739E-2,
+ 1.24999999999870820058E-1,
+ 4.99999999999999999821E-1
+};
+static float C1 = 1.3862943611198906188E0; /* log(4) */
+
+extern float MACHEPF, MAXNUMF;
+
+float polevlf(float, float *, int);
+float p1evlf(float, float *, int);
+float logf(float);
+float ellpkf(float xx)
+{
+float x;
+
+x = xx;
+if( (x < 0.0) || (x > 1.0) )
+	{
+	mtherr( "ellpkf", DOMAIN );
+	return( 0.0 );
+	}
+
+if( x > MACHEPF )
+	{
+	return( polevlf(x,P,10) - logf(x) * polevlf(x,Q,10) );
+	}
+else
+	{
+	if( x == 0.0 )
+		{
+		mtherr( "ellpkf", SING );
+		return( MAXNUMF );
+		}
+	else
+		{
+		return( C1 - 0.5 * logf(x) );
+		}
+	}
+}