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/ldouble/ellpjl.c | 164 ++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 164 insertions(+)
 create mode 100644 libm/ldouble/ellpjl.c

(limited to 'libm/ldouble/ellpjl.c')

diff --git a/libm/ldouble/ellpjl.c b/libm/ldouble/ellpjl.c
new file mode 100644
index 000000000..bb57fe6a1
--- /dev/null
+++ b/libm/ldouble/ellpjl.c
@@ -0,0 +1,164 @@
+/*							ellpjl.c
+ *
+ *	Jacobian Elliptic Functions
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double u, m, sn, cn, dn, phi;
+ * int ellpjl();
+ *
+ * ellpjl( u, m, _&sn, _&cn, _&dn, _&phi );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ *
+ * Evaluates the Jacobian elliptic functions sn(u|m), cn(u|m),
+ * and dn(u|m) of parameter m between 0 and 1, and real
+ * argument u.
+ *
+ * These functions are periodic, with quarter-period on the
+ * real axis equal to the complete elliptic integral
+ * ellpk(1.0-m).
+ *
+ * Relation to incomplete elliptic integral:
+ * If u = ellik(phi,m), then sn(u|m) = sin(phi),
+ * and cn(u|m) = cos(phi).  Phi is called the amplitude of u.
+ *
+ * Computation is by means of the arithmetic-geometric mean
+ * algorithm, except when m is within 1e-12 of 0 or 1.  In the
+ * latter case with m close to 1, the approximation applies
+ * only for phi < pi/2.
+ *
+ * ACCURACY:
+ *
+ * Tested at random points with u between 0 and 10, m between
+ * 0 and 1.
+ *
+ *            Absolute error (* = relative error):
+ * arithmetic   function   # trials      peak         rms
+ *    IEEE      sn          10000       1.7e-18     2.3e-19
+ *    IEEE      cn          20000       1.6e-18     2.2e-19
+ *    IEEE      dn          10000       4.7e-15     2.7e-17
+ *    IEEE      phi         10000       4.0e-19*    6.6e-20*
+ *
+ * Accuracy deteriorates when u is large.
+ *
+ */
+
+/*
+Cephes Math Library Release 2.3:  November, 1995
+Copyright 1984, 1987, 1995 by Stephen L. Moshier
+*/
+
+#include <math.h>
+#ifdef ANSIPROT
+extern long double sqrtl ( long double );
+extern long double fabsl ( long double );
+extern long double sinl ( long double );
+extern long double cosl ( long double );
+extern long double asinl ( long double );
+extern long double tanhl ( long double );
+extern long double sinhl ( long double );
+extern long double coshl ( long double );
+extern long double atanl ( long double );
+extern long double expl ( long double );
+#else
+long double sqrtl(), fabsl(), sinl(), cosl(), asinl(), tanhl();
+long double sinhl(), coshl(), atanl(), expl();
+#endif
+extern long double PIO2L, MACHEPL;
+
+int ellpjl( u, m, sn, cn, dn, ph )
+long double u, m;
+long double *sn, *cn, *dn, *ph;
+{
+long double ai, b, phi, t, twon;
+long double a[9], c[9];
+int i;
+
+
+/* Check for special cases */
+
+if( m < 0.0L || m > 1.0L )
+	{
+	mtherr( "ellpjl", DOMAIN );
+	*sn = 0.0L;
+	*cn = 0.0L;
+	*ph = 0.0L;
+	*dn = 0.0L;
+	return(-1);
+	}
+if( m < 1.0e-12L )
+	{
+	t = sinl(u);
+	b = cosl(u);
+	ai = 0.25L * m * (u - t*b);
+	*sn = t - ai*b;
+	*cn = b + ai*t;
+	*ph = u - ai;
+	*dn = 1.0L - 0.5L*m*t*t;
+	return(0);
+	}
+
+if( m >= 0.999999999999L )
+	{
+	ai = 0.25L * (1.0L-m);
+	b = coshl(u);
+	t = tanhl(u);
+	phi = 1.0L/b;
+	twon = b * sinhl(u);
+	*sn = t + ai * (twon - u)/(b*b);
+	*ph = 2.0L*atanl(expl(u)) - PIO2L + ai*(twon - u)/b;
+	ai *= t * phi;
+	*cn = phi - ai * (twon - u);
+	*dn = phi + ai * (twon + u);
+	return(0);
+	}
+
+
+/*	A. G. M. scale		*/
+a[0] = 1.0L;
+b = sqrtl(1.0L - m);
+c[0] = sqrtl(m);
+twon = 1.0L;
+i = 0;
+
+while( fabsl(c[i]/a[i]) > MACHEPL )
+	{
+	if( i > 7 )
+		{
+		mtherr( "ellpjl", OVERFLOW );
+		goto done;
+		}
+	ai = a[i];
+	++i;
+	c[i] = 0.5L * ( ai - b );
+	t = sqrtl( ai * b );
+	a[i] = 0.5L * ( ai + b );
+	b = t;
+	twon *= 2.0L;
+	}
+
+done:
+
+/* backward recurrence */
+phi = twon * a[i] * u;
+do
+	{
+	t = c[i] * sinl(phi) / a[i];
+	b = phi;
+	phi = 0.5L * (asinl(t) + phi);
+	}
+while( --i );
+
+*sn = sinl(phi);
+t = cosl(phi);
+*cn = t;
+*dn = t/cosl(phi-b);
+*ph = phi;
+return(0);
+}
-- 
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