GCC Code Coverage Report
Directory: ./ Exec Total Coverage
File: lib/libm/src/s_ctan.c Lines: 0 41 0.0 %
Date: 2017-11-13 Branches: 0 8 0.0 %

Line Branch Exec Source
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/*	$OpenBSD: s_ctan.c,v 1.7 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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/*							ctan()
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 *
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 *	Complex circular 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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 * double complex ctan();
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 * double complex z, w;
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 *
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 * w = ctan (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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 *
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 *           sin 2x  +  i sinh 2y
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 *     w  =  --------------------.
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 *            cos 2x  +  cosh 2y
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 *
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 * On the real axis the denominator is zero at odd multiples
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 * of PI/2.  The denominator is evaluated by its Taylor
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 * series near these points.
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 *
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 * ctan(z) = -i ctanh(iz).
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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      5200       7.1e-17     1.6e-17
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 *    IEEE      -10,+10     30000       7.2e-16     1.2e-16
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 * Also tested by ctan * ccot = 1 and catan(ctan(z))  =  z.
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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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#define MACHEP 1.1e-16
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#define MAXNUM 1.0e308
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static const double DP1 = 3.14159265160560607910E0;
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static const double DP2 = 1.98418714791870343106E-9;
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static const double DP3 = 1.14423774522196636802E-17;
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static double
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_redupi(double x)
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{
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	double t;
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	long i;
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	t = x/M_PI;
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	if (t >= 0.0)
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		t += 0.5;
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	else
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		t -= 0.5;
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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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/*  Taylor series expansion for cosh(2y) - cos(2x)	*/
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static double
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_ctans(double complex z)
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{
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	double f, x, x2, y, y2, rn, t;
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	double d;
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	x = fabs (2.0 * creal (z));
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	y = fabs (2.0 * cimag(z));
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	x = _redupi(x);
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	x = x * x;
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	y = y * y;
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	x2 = 1.0;
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	y2 = 1.0;
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	f = 1.0;
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	rn = 0.0;
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	d = 0.0;
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	do {
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		rn += 1.0;
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		f *= rn;
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		rn += 1.0;
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		f *= rn;
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		x2 *= x;
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		y2 *= y;
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		t = y2 + x2;
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		t /= f;
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		d += t;
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		rn += 1.0;
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		f *= rn;
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		rn += 1.0;
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		f *= rn;
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		x2 *= x;
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		y2 *= y;
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		t = y2 - x2;
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		t /= f;
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		d += t;
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	}
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	while (fabs(t/d) > MACHEP)
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		;
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	return (d);
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}
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double complex
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ctan(double complex z)
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{
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	double complex w;
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	double d;
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	d = cos (2.0 * creal (z)) + cosh (2.0 * cimag (z));
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	if (fabs(d) < 0.25)
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		d = _ctans (z);
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	if (d == 0.0) {
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		/*mtherr ("ctan", OVERFLOW);*/
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		w = MAXNUM + MAXNUM * I;
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		return (w);
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	}
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	w = sin (2.0 * creal(z)) / d + (sinh (2.0 * cimag(z)) / d) * I;
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	return (w);
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}
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DEF_STD(ctan);
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LDBL_MAYBE_UNUSED_CLONE(ctan);