/*-*- 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
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ
â                                                                              â
â  Musl Libc                                                                   â
â  Copyright Â© 2005-2014 Rich Felker, et al.                                   â
â                                                                              â
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
â  "Software"), to deal in the Software without restriction, including         â
â  without limitation the rights to use, copy, modify, merge, publish,         â
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
â                                                                              â
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
â  IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY        â
â  CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,        â
â  TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE           â
â  SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.                      â
â                                                                              â
ââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââââ*/
#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_catanf.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:
 *
 * float complex catanf();
 * float complex z, w;
 *
 * w = catanf( 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
 *    IEEE      -10,+10     30000        2.3e-6      5.2e-8
 */


#define MAXNUMF 1.0e38F

static const double DP1 = 3.140625;
static const double DP2 = 9.67502593994140625E-4;
static const double DP3 = 1.509957990978376432E-7;

static float _redupif(float xx)
{
	float x, t;
	long i;

	x = xx;
	t = x/(float)M_PI;
	if (t >= 0.0f)
		t += 0.5f;
	else
		t -= 0.5f;

	i = t;  /* the multiple */
	t = i;
	t = ((x - t * DP1) - t * DP2) - t * DP3;
	return t;
}

float complex catanf(float complex z)
{
	float complex w;
	float a, t, x, x2, y;

	x = crealf(z);
	y = cimagf(z);

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

	t = 0.5f * atan2f(2.0f * x, a);
	w = _redupif(t);

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

	t = y + 1.0f;
	a = (x2 + (t * t))/a;
	w = CMPLXF(w, 0.25f * logf(a));
	return w;
}
