-/* 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"
+// FIXME
+
+/* asin(z) = -i log(i z + sqrt(1 - z*z)) */
+
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;
+ w = cpack(1.0 - (x - y)*(x + y), -2.0*x*y);
+ return clog(cpack(-y, x) + csqrt(w));
}