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+/*-
+ * 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.
+ */
+
+/* cpow
+ *
+ * Complex power function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double complex cpow();
+ * double complex a, z, w;
+ *
+ * w = cpow (a, z);
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Raises complex A to the complex Zth power.
+ * Definition is per AMS55 # 4.2.8,
+ * analytically equivalent to cpow(a,z) = cexp(z clog(a)).
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -10,+10 30000 9.4e-15 1.5e-15
+ *
+ */
+
+#include <complex.h>
+#include <float.h>
+#include <math.h>
+#include "math_private.h"
+
+double complex
+cpow(double complex a, double complex z)
+{
+ double complex w;
+ double x, y, r, theta, absa, arga;
+
+ x = creal (z);
+ y = cimag (z);
+ absa = cabs (a);
+ if (absa == 0.0) {
+ if (x == 0 && y == 0)
+ return (CMPLX(1., 0.));
+ else
+ return (CMPLX(0., 0.));
+ }
+ arga = carg (a);
+ r = pow (absa, x);
+ theta = x * arga;
+ if (y != 0.0) {
+ r = r * exp (-y * arga);
+ theta = theta + y * log (absa);
+ }
+ w = CMPLX(r * cos (theta), r * sin (theta));
+ return (w);
+}