1 files changed, 148 insertions, 0 deletions
diff --git a/libm/ldouble/ellikl.c b/libm/ldouble/ellikl.c
new file mode 100644
index 000000000..4eeffe0f5
--- /dev/null
+++ b/libm/ldouble/ellikl.c
@@ -0,0 +1,148 @@
+/*							ellikl.c
+ *
+ *	Incomplete elliptic integral of the first kind
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double phi, m, y, ellikl();
+ *
+ * y = ellikl( phi, m );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Approximates the integral
+ *
+ *
+ *
+ *                phi
+ *                 -
+ *                | |
+ *                |           dt
+ * F(phi_\m)  =    |    ------------------
+ *                |                   2
+ *              | |    sqrt( 1 - m sin t )
+ *               -
+ *                0
+ *
+ * of amplitude phi and modulus m, using the arithmetic -
+ * geometric mean algorithm.
+ *
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Tested at random points with m in [0, 1] and phi as indicated.
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    IEEE     -10,10        30000      3.6e-18     4.1e-19
+ *
+ *
+ */
+
+
+/*
+Cephes Math Library Release 2.3:  November, 1995
+Copyright 1984, 1987, 1995 by Stephen L. Moshier
+*/
+
+/*	Incomplete elliptic integral of first kind	*/
+
+#include <math.h>
+#ifdef ANSIPROT
+extern long double sqrtl ( long double );
+extern long double fabsl ( long double );
+extern long double logl ( long double );
+extern long double tanl ( long double );
+extern long double atanl ( long double );
+extern long double floorl ( long double );
+extern long double ellpkl ( long double );
+long double ellikl ( long double, long double );
+#else
+long double sqrtl(), fabsl(), logl(), tanl(), atanl(), floorl(), ellpkl();
+long double ellikl();
+#endif
+extern long double PIL, PIO2L, MACHEPL, MAXNUML;
+
+long double ellikl( phi, m )
+long double phi, m;
+{
+long double a, b, c, e, temp, t, K;
+int d, mod, sign, npio2;
+
+if( m == 0.0L )
+	return( phi );
+a = 1.0L - m;
+if( a == 0.0L )
+	{
+	if( fabsl(phi) >= PIO2L )
+		{
+		mtherr( "ellikl", SING );
+		return( MAXNUML );
+		}
+	return(  logl(  tanl( 0.5L*(PIO2L + phi) )  )   );
+	}
+npio2 = floorl( phi/PIO2L );
+if( npio2 & 1 )
+	npio2 += 1;
+if( npio2 )
+	{
+	K = ellpkl( a );
+	phi = phi - npio2 * PIO2L;
+	}
+else
+	K = 0.0L;
+if( phi < 0.0L )
+	{
+	phi = -phi;
+	sign = -1;
+	}
+else
+	sign = 0;
+b = sqrtl(a);
+t = tanl( phi );
+if( fabsl(t) > 10.0L )
+	{
+	/* Transform the amplitude */
+	e = 1.0L/(b*t);
+	/* ... but avoid multiple recursions.  */
+	if( fabsl(e) < 10.0L )
+		{
+		e = atanl(e);
+		if( npio2 == 0 )
+			K = ellpkl( a );
+		temp = K - ellikl( e, m );
+		goto done;
+		}
+	}
+a = 1.0L;
+c = sqrtl(m);
+d = 1;
+mod = 0;
+
+while( fabsl(c/a) > MACHEPL )
+	{
+	temp = b/a;
+	phi = phi + atanl(t*temp) + mod * PIL;
+	mod = (phi + PIO2L)/PIL;
+	t = t * ( 1.0L + temp )/( 1.0L - temp * t * t );
+	c = 0.5L * ( a - b );
+	temp = sqrtl( a * b );
+	a = 0.5L * ( a + b );
+	b = temp;
+	d += d;
+	}
+
+temp = (atanl(t) + mod * PIL)/(d * a);
+
+done:
+if( sign < 0 )
+	temp = -temp;
+temp += npio2 * K;
+return( temp );
+}