134 lines
2.9 KiB
C
134 lines
2.9 KiB
C
/* $OpenBSD: s_catan.c,v 1.6 2013/07/03 04:46:36 espie 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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/* catan()
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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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* double complex catan();
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* double complex z, w;
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*
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* w = catan (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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* catan(z) = -i catanh(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 5900 1.3e-16 7.8e-18
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* IEEE -10,+10 30000 2.3e-15 8.5e-17
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* The check catan( ctan(z) ) = z, with |x| and |y| < PI/2,
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* had peak relative error 1.5e-16, rms relative error
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* 2.9e-17. See also clog().
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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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#include "math_private.h"
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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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double complex
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catan(double complex z)
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{
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double complex w;
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double a, t, x, x2, y;
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x = creal (z);
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y = cimag (z);
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if ((x == 0.0) && (y > 1.0))
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goto ovrf;
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x2 = x * x;
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a = 1.0 - x2 - (y * y);
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if (a == 0.0)
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goto ovrf;
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t = 0.5 * atan2 (2.0 * x, a);
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w = _redupi (t);
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t = y - 1.0;
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a = x2 + (t * t);
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if (a == 0.0)
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goto ovrf;
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t = y + 1.0;
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a = (x2 + (t * t))/a;
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w = w + (0.25 * log (a)) * I;
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return (w);
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ovrf:
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/*mtherr ("catan", OVERFLOW);*/
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w = MAXNUM + MAXNUM * I;
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return (w);
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}
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#if LDBL_MANT_DIG == DBL_MANT_DIG
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openlibm_strong_reference(catan, catanl);
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#endif /* LDBL_MANT_DIG == DBL_MANT_DIG */
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