uClibc now has a math library. muahahahaha!

 -Erik

1 files changed, 146 insertions, 0 deletions

diff --git a/libm/ldouble/elliel.c b/libm/ldouble/elliel.c
new file mode 100644
index 000000000..851914454
--- /dev/null
+++ b/libm/ldouble/elliel.c
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+/*							elliel.c
+ *
+ *	Incomplete elliptic integral of the second kind
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double phi, m, y, elliel();
+ *
+ * y = elliel( phi, m );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Approximates the integral
+ *
+ *
+ *                phi
+ *                 -
+ *                | |
+ *                |                   2
+ * E(phi_\m)  =    |    sqrt( 1 - m sin t ) dt
+ *                |
+ *              | |    
+ *               -
+ *                0
+ *
+ * of amplitude phi and modulus m, using the arithmetic -
+ * geometric mean algorithm.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Tested at random arguments with phi in [-10, 10] and m in
+ * [0, 1].
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    IEEE     -10,10       50000       2.7e-18     2.3e-19
+ *
+ *
+ */
+
+
+/*
+Cephes Math Library Release 2.3:  November, 1995
+Copyright 1984, 1987, 1993, 1995 by Stephen L. Moshier
+*/
+
+/*	Incomplete elliptic integral of second 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 sinl ( long double );
+extern long double tanl ( long double );
+extern long double atanl ( long double );
+extern long double floorl ( long double );
+extern long double ellpel ( long double );
+extern long double ellpkl ( long double );
+long double elliel ( long double, long double );
+#else
+long double sqrtl(), fabsl(), logl(), sinl(), tanl(), atanl(), floorl();
+long double ellpel(), ellpkl(), elliel();
+#endif
+extern long double PIL, PIO2L, MACHEPL;
+
+
+long double elliel( phi, m )
+long double phi, m;
+{
+long double a, b, c, e, temp, lphi, t, E;
+int d, mod, npio2, sign;
+
+if( m == 0.0L )
+	return( phi );
+lphi = phi;
+npio2 = floorl( lphi/PIO2L );
+if( npio2 & 1 )
+	npio2 += 1;
+lphi = lphi - npio2 * PIO2L;
+if( lphi < 0.0L )
+	{
+	lphi = -lphi;
+	sign = -1;
+	}
+else
+	{
+	sign = 1;
+	}
+a = 1.0L - m;
+E = ellpel( a );
+if( a == 0.0L )
+	{
+	temp = sinl( lphi );
+	goto done;
+	}
+t = tanl( lphi );
+b = sqrtl(a);
+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);
+		temp = E + m * sinl( lphi ) * sinl( e ) - elliel( e, m );
+		goto done;
+		}
+	}
+c = sqrtl(m);
+a = 1.0L;
+d = 1;
+e = 0.0L;
+mod = 0;
+
+while( fabsl(c/a) > MACHEPL )
+	{
+	temp = b/a;
+	lphi = lphi + atanl(t*temp) + mod * PIL;
+	mod = (lphi + 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;
+	e += c * sinl(lphi);
+	}
+
+temp = E / ellpkl( 1.0L - m );
+temp *= (atanl(t) + mod * PIL)/(d * a);
+temp += e;
+
+done:
+
+if( sign < 0 )
+	temp = -temp;
+temp += npio2 * E;
+return( temp );
+}