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7e5585aaca
This is a bit more consistent with the naming of the other header files (openlibm_complex.h and openlibm_fenv.h). Re-add an openlibm.h header that includes all of the public headers as a shorthand. Fix up all of the source files to include <openlibm_math.h> instead of <openlibm.h>. While there, fix ordering of the includes.
127 lines
2.9 KiB
C
127 lines
2.9 KiB
C
/* $OpenBSD: s_catanl.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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/* catanl()
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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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* 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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*
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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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* 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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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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long double complex
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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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if ((x == 0.0L) && (y > 1.0L))
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goto ovrf;
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x2 = x * x;
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a = 1.0L - x2 - (y * y);
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if (a == 0.0L)
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goto ovrf;
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t = atan2l(2.0L * x, a) * 0.5L;
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w = redupil(t);
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t = y - 1.0L;
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a = x2 + (t * t);
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if (a == 0.0L)
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goto ovrf;
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t = y + 1.0L;
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a = (x2 + (t * t)) / a;
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w = w + (0.25L * logl(a)) * I;
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return (w);
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ovrf:
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/*mtherr( "catanl", 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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