1 files changed, 105 insertions, 0 deletions
diff --git a/libm/float/ellpef.c b/libm/float/ellpef.c
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+/*							ellpef.c
+ *
+ *	Complete elliptic integral of the second kind
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float m1, y, ellpef();
+ *
+ * y = ellpef( m1 );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Approximates the integral
+ *
+ *
+ *            pi/2
+ *             -
+ *            | |                 2
+ * E(m)  =    |    sqrt( 1 - m sin t ) dt
+ *          | |    
+ *           -
+ *            0
+ *
+ * Where m = 1 - m1, using the approximation
+ *
+ *      P(x)  -  x log x Q(x).
+ *
+ * Though there are no singularities, the argument m1 is used
+ * rather than m for compatibility with ellpk().
+ *
+ * E(1) = 1; E(0) = pi/2.
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    IEEE       0, 1       30000       1.1e-7      3.9e-8
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ *   message         condition      value returned
+ * ellpef domain     x<0, x>1            0.0
+ *
+ */
+
+/*							ellpe.c		*/
+
+/* Elliptic integral of second kind */
+
+/*
+Cephes Math Library, Release 2.1:  February, 1989
+Copyright 1984, 1987, 1989 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+#include <math.h>
+
+
+static float P[] = {
+  1.53552577301013293365E-4,
+  2.50888492163602060990E-3,
+  8.68786816565889628429E-3,
+  1.07350949056076193403E-2,
+  7.77395492516787092951E-3,
+  7.58395289413514708519E-3,
+  1.15688436810574127319E-2,
+  2.18317996015557253103E-2,
+  5.68051945617860553470E-2,
+  4.43147180560990850618E-1,
+  1.00000000000000000299E0
+};
+static float Q[] = {
+  3.27954898576485872656E-5,
+  1.00962792679356715133E-3,
+  6.50609489976927491433E-3,
+  1.68862163993311317300E-2,
+  2.61769742454493659583E-2,
+  3.34833904888224918614E-2,
+  4.27180926518931511717E-2,
+  5.85936634471101055642E-2,
+  9.37499997197644278445E-2,
+  2.49999999999888314361E-1
+};
+
+float polevlf(float, float *, int), logf(float);
+float ellpef( float xx)
+{
+float x;
+
+x = xx;
+if( (x <= 0.0) || (x > 1.0) )
+	{
+	if( x == 0.0 )
+		return( 1.0 );
+	mtherr( "ellpef", DOMAIN );
+	return( 0.0 );
+	}
+return( polevlf(x,P,10) - logf(x) * (x * polevlf(x,Q,9)) );
+}