158 lines
3.4 KiB
C
158 lines
3.4 KiB
C
/* $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 <float.h>
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#include <openlibm_complex.h>
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#include <openlibm_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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}
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