extend cmath (some of the functions are dummy)

[libm] / src / cmath / catanl.c

diff --git a/src/cmath/catanl.c b/src/cmath/catanl.c
new file mode 100644 (file)
index 0000000..5ace770
--- /dev/null
+++ b/src/cmath/catanl.c
@@ -0,0 +1,126 @@
+/* origin: OpenBSD /usr/src/lib/libm/src/s_catanl.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:
+ *
+ * long double complex catanl();
+ * long double complex z, w;
+ *
+ * w = catanl( 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.
+ *
+ *
+ * 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 <complex.h>
+#include <float.h>
+#include "libm.h"
+
+#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
+long double complex catanl(long double complex z)
+{
+       return catan(z);
+}
+#else
+static const long double PIL = 3.141592653589793238462643383279502884197169L;
+static const long double DP1 = 3.14159265358979323829596852490908531763125L;
+static const long double DP2 = 1.6667485837041756656403424829301998703007e-19L;
+static const long double DP3 = 1.8830410776607851167459095484560349402753e-39L;
+
+static long double redupil(long double x)
+{
+       long double t;
+       long i;
+
+       t = x / PIL;
+       if (t >= 0.0L)
+               t += 0.5L;
+       else
+               t -= 0.5L;
+
+       i = t;  /* the multiple */
+       t = i;
+       t = ((x - t * DP1) - t * DP2) - t * DP3;
+       return t;
+}
+
+long double complex catanl(long double complex z)
+{
+       long double complex w;
+       long double a, t, x, x2, y;
+
+       x = creall(z);
+       y = cimagl(z);
+
+       if ((x == 0.0L) && (y > 1.0L))
+               goto ovrf;
+
+       x2 = x * x;
+       a = 1.0L - x2 - (y * y);
+       if (a == 0.0L)
+               goto ovrf;
+
+       t = atan2l(2.0L * x, a) * 0.5L;
+       w = redupil(t);
+
+       t = y - 1.0L;
+       a = x2 + (t * t);
+       if (a == 0.0L)
+               goto ovrf;
+
+       t = y + 1.0L;
+       a = (x2 + (t * t)) / a;
+       w = w + (0.25L * logl(a)) * I;
+       return w;
+
+ovrf:
+       // FIXME
+       w = LDBL_MAX + LDBL_MAX * I;
+       return w;
+}
+#endif