/*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8   -*-â
âvi: set et ft=c ts=8 tw=8 fenc=utf-8                                       :viâ
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â                                                                              â
â  Musl Libc                                                                   â
â  Copyright Â© 2005-2014 Rich Felker, et al.                                   â
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â  Permission is hereby granted, free of charge, to any person obtaining       â
â  a copy of this software and associated documentation files (the             â
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â  distribute, sublicense, and/or sell copies of the Software, and to          â
â  permit persons to whom the Software is furnished to do so, subject to       â
â  the following conditions:                                                   â
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â  The above copyright notice and this permission notice shall be              â
â  included in all copies or substantial portions of the Software.             â
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â  THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,             â
â  EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF          â
â  MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.      â
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#include "libc/complex.h"
#include "libc/math.h"
#include "libc/tinymath/complex.internal.h"

asm(".ident\t\"\\n\\n\
OpenBSD libm (ISC License)\\n\
Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>\"");
asm(".ident\t\"\\n\\n\
Musl libc (MIT License)\\n\
Copyright 2005-2014 Rich Felker, et. al.\"");
asm(".include \"libc/disclaimer.inc\"");
// clang-format off


/* 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().
 */


#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);

	x2 = x * x;
	a = 1.0 - x2 - (y * y);

	t = 0.5 * atan2(2.0 * x, a);
	w = _redupi(t);

	t = y - 1.0;
	a = x2 + (t * t);

	t = y + 1.0;
	a = (x2 + t * t)/a;
	w = CMPLX(w, 0.25 * log(a));
	return w;
}

#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
__strong_reference(catan, catanl);
#endif
