source: azure_iot_hub/trunk/musl-1.1.18/src/complex/catan.c@ 388

/* 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;
}