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+/* $OpenBSD: n_csin.c,v 1.1 2008/10/07 22:25:53 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.
+ */
+
+/* csin()
+ *
+ * Complex circular sine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double complex csin();
+ * double complex z, w;
+ *
+ * w = csin (z);
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * If
+ * z = x + iy,
+ *
+ * then
+ *
+ * w = sin x cosh y + i cos x sinh y.
+ *
+ * csin(z) = -i csinh(iz).
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC -10,+10 8400 5.3e-17 1.3e-17
+ * IEEE -10,+10 30000 3.8e-16 1.0e-16
+ * Also tested by csin(casin(z)) = z.
+ *
+ */
+
+#include <complex.h>
+#include <math.h>
+
+/* calculate cosh and sinh */
+
+static void
+cchsh(double x, double *c, double *s)
+{
+ double e, ei;
+
+ if (fabs(x) <= 0.5) {
+ *c = cosh(x);
+ *s = sinh(x);
+ }
+ else {
+ e = exp(x);
+ ei = 0.5/e;
+ e = 0.5 * e;
+ *s = e - ei;
+ *c = e + ei;
+ }
+}
+
+double complex
+csin(double complex z)
+{
+ double complex w;
+ double ch, sh;
+
+ cchsh( cimag (z), &ch, &sh );
+ w = sin (creal(z)) * ch + (cos (creal(z)) * sh) * I;
+ return (w);
+}