extend cmath (some of the functions are dummy)

[libm] / src / cmath / casin.c

diff --git a/src/cmath/casin.c b/src/cmath/casin.c
index 3428457..79aff27 100644 (file)
--- a/src/cmath/casin.c
+++ b/src/cmath/casin.c
@@ -1,120 +1,16 @@
-/* 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));
 }