125 lines
2.5 KiB
C
125 lines
2.5 KiB
C
/* $OpenBSD: s_catanf.c,v 1.2 2010/07/18 18:42:26 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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/* catanf()
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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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* float complex catanf();
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* float complex z, w;
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*
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* w = catanf( 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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* IEEE -10,+10 30000 2.3e-6 5.2e-8
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*
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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 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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float complex
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catanf(float complex z)
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{
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float complex w;
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float a, t, x, x2, y;
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x = crealf(z);
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y = cimagf(z);
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if((x == 0.0f) && (y > 1.0f))
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goto ovrf;
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x2 = x * x;
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a = 1.0f - x2 - (y * y);
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if (a == 0.0f)
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goto ovrf;
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t = 0.5f * atan2f(2.0f * x, a);
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w = _redupif(t);
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t = y - 1.0f;
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a = x2 + (t * t);
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if(a == 0.0f)
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goto ovrf;
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t = y + 1.0f;
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a = (x2 + (t * t))/a;
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w = w + (0.25f * logf (a)) * I;
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return (w);
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ovrf:
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/*mtherr( "catanf", OVERFLOW );*/
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w = MAXNUMF + MAXNUMF * I;
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return (w);
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}
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