initial cmath code and minor libm.h update

[libm] / src / cmath / catan.c

diff --git a/src/cmath/catan.c b/src/cmath/catan.c
new file mode 100644 (file)
index 0000000..39ce6cf
--- /dev/null
+++ b/src/cmath/catan.c
@@ -0,0 +1,119 @@
+/* origin: OpenBSD /usr/src/lib/libm/src/s_catan.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 tangent
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double complex catan();
+ * double complex z, w;
+ *
+ * w = catan (z);
+ *
+ *
+ * DESCRIPTION:
+ *
+ * If
+ *     z = x + iy,
+ *
+ * then
+ *          1       (    2x     )
+ * Re w  =  - arctan(-----------)  +  k PI
+ *          2       (     2    2)
+ *                  (1 - x  - y )
+ *
+ *               ( 2         2)
+ *          1    (x  +  (y+1) )
+ * Im w  =  - log(------------)
+ *          4    ( 2         2)
+ *               (x  +  (y-1) )
+ *
+ * Where k is an arbitrary integer.
+ *
+ * catan(z) = -i catanh(iz).
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC       -10,+10      5900       1.3e-16     7.8e-18
+ *    IEEE      -10,+10     30000       2.3e-15     8.5e-17
+ * The check catan( ctan(z) )  =  z, with |x| and |y| < PI/2,
+ * had peak relative error 1.5e-16, rms relative error
+ * 2.9e-17.  See also clog().
+ */
+
+#include "libm.h"
+
+#define MAXNUM 1.0e308
+
+static const double DP1 = 3.14159265160560607910E0;
+static const double DP2 = 1.98418714791870343106E-9;
+static const double DP3 = 1.14423774522196636802E-17;
+
+static double _redupi(double x)
+{
+       double t;
+       long i;
+
+       t = x/M_PI;
+       if (t >= 0.0)
+               t += 0.5;
+       else
+               t -= 0.5;
+
+       i = t;  /* the multiple */
+       t = i;
+       t = ((x - t * DP1) - t * DP2) - t * DP3;
+       return t;
+}
+
+double complex catan(double complex z)
+{
+       double complex w;
+       double a, t, x, x2, y;
+
+       x = creal(z);
+       y = cimag(z);
+
+       if (x == 0.0 && y > 1.0)
+               goto ovrf;
+
+       x2 = x * x;
+       a = 1.0 - x2 - (y * y);
+       if (a == 0.0)
+               goto ovrf;
+
+       t = 0.5 * atan2(2.0 * x, a);
+       w = _redupi(t);
+
+       t = y - 1.0;
+       a = x2 + (t * t);
+       if (a == 0.0)
+               goto ovrf;
+
+       t = y + 1.0;
+       a = (x2 + t * t)/a;
+       w = w + (0.25 * log(a)) * I;
+       return w;
+
+ovrf:
+       // FIXME
+       w = MAXNUM + MAXNUM * I;
+       return w;
+}