initial cmath code and minor libm.h update

[libm] / src / cmath / casin.c

diff --git a/src/cmath/casin.c b/src/cmath/casin.c
new file mode 100644 (file)
index 0000000..3428457
--- /dev/null
+++ b/src/cmath/casin.c
@@ -0,0 +1,120 @@
+/* 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;
+}