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92 lines
2.3 KiB
92 lines
2.3 KiB
/* origin: OpenBSD /usr/src/lib/libm/src/s_catanl.c */
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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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/*
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* Complex circular arc tangent
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*
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*
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* SYNOPSIS:
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*
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* long double complex catanl();
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* long double complex z, w;
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*
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* w = catanl( z );
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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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* 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 <complex.h>
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#include <float.h>
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#include "complex_impl.h"
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#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
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long double complex catanl(long double complex z)
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{
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return catan(z);
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}
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#else
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long double complex catanl(long double complex z)
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{
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long double complex w;
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long double a, t, x, x2, y;
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x = creall(z);
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y = cimagl(z);
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x2 = x * x;
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a = 1.0L - x2 - (y * y);
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t = atan2l(2.0L * x, a) * 0.5L;
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w = t;
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t = y - 1.0L;
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a = x2 + (t * t);
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t = y + 1.0L;
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a = (x2 + (t * t)) / a;
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w = CMPLXF(w, 0.25L * logl(a));
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return w;
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}
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#endif
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