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+/* $OpenBSD: s_clog.c,v 1.1 2008/09/07 20:36:09 martynas Exp $ */
+/*
+ * Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>
+ *
+ * Permission to use, copy, modify, and distribute this software for any
+ * purpose with or without fee is hereby granted, provided that the above
+ * copyright notice and this permission notice appear in all copies.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
+ * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
+ * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
+ * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
+ * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
+ * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
+ * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
+ */
+
+/* clog.c
+ *
+ * Complex natural logarithm
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double complex clog();
+ * double complex z, w;
+ *
+ * w = clog (z);
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns complex logarithm to the base e (2.718...) of
+ * the complex argument x.
+ *
+ * If z = x + iy, r = sqrt( x**2 + y**2 ),
+ * then
+ * w = log(r) + i arctan(y/x).
+ *
+ * The arctangent ranges from -PI to +PI.
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC -10,+10 7000 8.5e-17 1.9e-17
+ * IEEE -10,+10 30000 5.0e-15 1.1e-16
+ *
+ * Larger relative error can be observed for z near 1 +i0.
+ * In IEEE arithmetic the peak absolute error is 5.2e-16, rms
+ * absolute error 1.0e-16.
+ */
+
+#include <complex.h>
+#include <math.h>
+
+double complex
+clog(double complex z)
+{
+ double complex w;
+ double p, rr;
+
+ /*rr = sqrt( z->r * z->r + z->i * z->i );*/
+ rr = cabs(z);
+ p = log(rr);
+ rr = atan2 (cimag (z), creal (z));
+ w = p + rr * I;
+ return (w);
+}