GCC Code Coverage Report
Directory: ./ Exec Total Coverage
File: lib/libm/src/s_ctanl.c Lines: 0 43 0.0 %
Date: 2017-11-13 Branches: 0 8 0.0 %

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/*	$OpenBSD: s_ctanl.c,v 1.3 2011/07/20 21:02:51 martynas 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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/*							ctanl()
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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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 * long double complex ctanl();
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 * long double complex z, w;
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 *
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 * w = ctanl( 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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 *
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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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#if	LDBL_MANT_DIG == 64
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static const long double MACHEPL= 5.42101086242752217003726400434970855712890625E-20L;
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#elif	LDBL_MANT_DIG == 113
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static const long double MACHEPL = 9.629649721936179265279889712924636592690508e-35L;
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#endif
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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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static long double
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ctansl(long double complex z)
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{
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	long double f, x, x2, y, y2, rn, t;
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	long double d;
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	x = fabsl(2.0L * creall(z));
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	y = fabsl(2.0L * cimagl(z));
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	x = redupil(x);
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	x = x * x;
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	y = y * y;
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	x2 = 1.0L;
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	y2 = 1.0L;
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	f = 1.0L;
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	rn = 0.0L;
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	d = 0.0L;
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	do {
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		rn += 1.0L;
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		f *= rn;
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		rn += 1.0L;
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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 += 1.0L;
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		f *= rn;
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		rn += 1.0L;
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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 (fabsl(t/d) > MACHEPL);
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	return(d);
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}
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long double complex
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ctanl(long double complex z)
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{
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	long double complex w;
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	long double d, x, y;
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	x = creall(z);
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	y = cimagl(z);
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	d = cosl(2.0L * x) + coshl(2.0L * y);
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	if (fabsl(d) < 0.25L) {
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		d = fabsl(d);
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		d = ctansl(z);
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	}
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	if (d == 0.0L) {
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		/*mtherr( "ctan", 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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	w = sinl(2.0L * x) / d + (sinhl(2.0L * y) / d) * I;
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	return (w);
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}