149 lines
2.8 KiB
C
149 lines
2.8 KiB
C
/* $OpenBSD: s_ctanf.c,v 1.2 2011/07/20 19:28:33 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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/* ctanf()
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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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* void ctanf();
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* cmplxf z, w;
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*
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* ctanf( &z, &w );
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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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* IEEE -10,+10 30000 3.3e-7 5.1e-8
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*/
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#include <openlibm_complex.h>
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#include <openlibm_math.h>
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#define MACHEPF 3.0e-8
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#define MAXNUMF 1.0e38f
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static const double DP1 = 3.140625;
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static const double DP2 = 9.67502593994140625E-4;
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static const double DP3 = 1.509957990978376432E-7;
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static float
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_redupif(float xx)
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{
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float x, t;
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long i;
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x = xx;
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t = x/(float)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 float
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_ctansf(float complex z)
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{
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float f, x, x2, y, y2, rn, t, d;
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x = fabsf(2.0f * crealf(z));
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y = fabsf(2.0f * cimagf(z));
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x = _redupif(x);
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x = x * x;
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y = y * y;
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x2 = 1.0f;
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y2 = 1.0f;
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f = 1.0f;
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rn = 0.0f;
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d = 0.0f;
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do {
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rn += 1.0f;
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f *= rn;
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rn += 1.0f;
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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 += 1.0f;
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f *= rn;
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rn += 1.0f;
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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 (fabsf(t/d) > MACHEPF)
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;
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return(d);
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}
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float complex
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ctanf(float complex z)
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{
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float complex w;
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float d;
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d = cosf( 2.0f * crealf(z) ) + coshf( 2.0f * cimagf(z) );
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if(fabsf(d) < 0.25f)
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d = _ctansf(z);
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if (d == 0.0f) {
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/*mtherr( "ctanf", OVERFLOW );*/
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w = MAXNUMF + MAXNUMF * I;
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return (w);
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}
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w = sinf (2.0f * crealf(z)) / d + (sinhf (2.0f * cimagf(z)) / d) * I;
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return (w);
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}
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