cosmopolitan/libc/tinymath/catanl.c

/*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8   -*-│
│vi: set et ft=c ts=8 tw=8 fenc=utf-8                                       :vi│
╚──────────────────────────────────────────────────────────────────────────────╝
│                                                                              │
│ 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      │
│                                                                              │
╚─────────────────────────────────────────────────────────────────────────────*/
#include "libc/complex.h"
#include "libc/math.h"
#include "libc/tinymath/complex.internal.h"
#if !(LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024)

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

/*
 *      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().
 */

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);

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

	t = atan2l(2.0L * x, a) * 0.5L;
	w = redupil(t);

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

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

#endif /* long double is long */