--- /dev/null
+/* origin: OpenBSD /usr/src/lib/libm/src/s_casin.c */
+/*
+ * 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.
+ */
+/*
+ * Complex circular arc sine
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double complex casin();
+ * double complex z, w;
+ *
+ * w = casin (z);
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Inverse complex sine:
+ *
+ * 2
+ * w = -i clog( iz + csqrt( 1 - z ) ).
+ *
+ * casin(z) = -i casinh(iz)
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC -10,+10 10100 2.1e-15 3.4e-16
+ * IEEE -10,+10 30000 2.2e-14 2.7e-15
+ * Larger relative error can be observed for z near zero.
+ * Also tested by csin(casin(z)) = z.
+ */
+
+#include "libm.h"
+
+double complex casin(double complex z)
+{
+ double complex w;
+ static double complex ca, ct, zz, z2;
+ double x, y;
+
+ x = creal(z);
+ y = cimag(z);
+
+ if (y == 0.0) {
+ if (fabs(x) > 1.0)
+ w = M_PI_2 + 0.0 * I;
+ else
+ w = asin(x) + 0.0 * I;
+ return w;
+ }
+
+ /* Power series expansion */
+ /*
+ b = cabs(z);
+ if( b < 0.125 ) {
+ z2.r = (x - y) * (x + y);
+ z2.i = 2.0 * x * y;
+
+ cn = 1.0;
+ n = 1.0;
+ ca.r = x;
+ ca.i = y;
+ sum.r = x;
+ sum.i = y;
+ do {
+ ct.r = z2.r * ca.r - z2.i * ca.i;
+ ct.i = z2.r * ca.i + z2.i * ca.r;
+ ca.r = ct.r;
+ ca.i = ct.i;
+
+ cn *= n;
+ n += 1.0;
+ cn /= n;
+ n += 1.0;
+ b = cn/n;
+
+ ct.r *= b;
+ ct.i *= b;
+ sum.r += ct.r;
+ sum.i += ct.i;
+ b = fabs(ct.r) + fabs(ct.i);
+ }
+ while( b > MACHEP );
+ w->r = sum.r;
+ w->i = sum.i;
+ return;
+ }
+ */
+
+ ca = x + y * I;
+ ct = ca * I;
+ /* sqrt(1 - z*z) */
+ /* cmul(&ca, &ca, &zz) */
+ /* x * x - y * y */
+ // FIXME: 1 - ()() - () I
+ zz = (x - y) * (x + y) + (2.0 * x * y) * I;
+ zz = 1.0 - creal(zz) - cimag(zz) * I;
+ z2 = csqrt(zz);
+ zz = ct + z2;
+ zz = clog(zz);
+ /* multiply by 1/i = -i */
+ // FIXME: -I
+ w = zz * (-1.0 * I);
+ return w;
+}