GCC Code Coverage Report
Directory: ./ Exec Total Coverage
File: lib/libm/src/s_catanl.c Lines: 0 24 0.0 %
Date: 2017-11-13 Branches: 0 8 0.0 %

Line Branch Exec Source
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/*	$OpenBSD: s_catanl.c,v 1.4 2016/09/12 19:47:02 guenther Exp $	*/
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/*
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 * Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>
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 *
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 * Permission to use, copy, modify, and distribute this software for any
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 * purpose with or without fee is hereby granted, provided that the above
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 * copyright notice and this permission notice appear in all copies.
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 *
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 * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
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 * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
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 * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
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 * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
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 * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
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 * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
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 * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
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 */
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/*							catanl()
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 *
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 *	Complex circular arc tangent
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 *
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 *
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 *
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 * SYNOPSIS:
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 *
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 * long double complex catanl();
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 * long double complex z, w;
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 *
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 * w = catanl( z );
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 *
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 *
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 *
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 * DESCRIPTION:
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 *
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 * If
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 *     z = x + iy,
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 *
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 * then
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 *          1       (    2x     )
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 * Re w  =  - arctan(-----------)  +  k PI
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 *          2       (     2    2)
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 *                  (1 - x  - y )
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 *
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 *               ( 2         2)
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 *          1    (x  +  (y+1) )
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 * Im w  =  - log(------------)
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 *          4    ( 2         2)
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 *               (x  +  (y-1) )
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 *
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 * Where k is an arbitrary integer.
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 *
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 *
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 *
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 * ACCURACY:
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 *
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 *                      Relative error:
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 * arithmetic   domain     # trials      peak         rms
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 *    DEC       -10,+10      5900       1.3e-16     7.8e-18
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 *    IEEE      -10,+10     30000       2.3e-15     8.5e-17
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 * The check catan( ctan(z) )  =  z, with |x| and |y| < PI/2,
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 * had peak relative error 1.5e-16, rms relative error
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 * 2.9e-17.  See also clog().
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 */
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#include <complex.h>
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#include <float.h>
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#include <math.h>
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static const long double PIL = 3.141592653589793238462643383279502884197169L;
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static const long double DP1 = 3.14159265358979323829596852490908531763125L;
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static const long double DP2 = 1.6667485837041756656403424829301998703007e-19L;
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static const long double DP3 = 1.8830410776607851167459095484560349402753e-39L;
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static long double
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redupil(long double x)
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{
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	long double t;
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	long i;
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	t = x / PIL;
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	if (t >= 0.0L)
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		t += 0.5L;
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	else
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		t -= 0.5L;
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	i = t;	/* the multiple */
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	t = i;
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	t = ((x - t * DP1) - t * DP2) - t * DP3;
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	return (t);
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}
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long double complex
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catanl(long double complex z)
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{
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	long double complex w;
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	long double a, t, x, x2, y;
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	x = creall(z);
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	y = cimagl(z);
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	if ((x == 0.0L) && (y > 1.0L))
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		goto ovrf;
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	x2 = x * x;
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	a = 1.0L - x2 - (y * y);
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	if (a == 0.0L)
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		goto ovrf;
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	t = atan2l(2.0L * x, a) * 0.5L;
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	w = redupil(t);
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	t = y - 1.0L;
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	a = x2 + (t * t);
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	if (a == 0.0L)
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		goto ovrf;
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	t = y + 1.0L;
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	a = (x2 + (t * t)) / a;
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	w = w + (0.25L * logl(a)) * I;
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	return (w);
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ovrf:
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	/*mtherr( "catanl", OVERFLOW );*/
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	w = LDBL_MAX + LDBL_MAX * I;
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	return (w);
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}
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DEF_STD(catanl);