158 lines
3.1 KiB
C
158 lines
3.1 KiB
C
/* $OpenBSD: s_ctan.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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/* ctan()
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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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* double complex ctan();
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* double complex z, w;
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*
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* w = ctan (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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*
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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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* ctan(z) = -i ctanh(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 5200 7.1e-17 1.6e-17
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* IEEE -10,+10 30000 7.2e-16 1.2e-16
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* Also tested by ctan * ccot = 1 and catan(ctan(z)) = z.
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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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#define MACHEP 1.1e-16
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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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/* Taylor series expansion for cosh(2y) - cos(2x) */
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static double
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_ctans(double complex z)
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{
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double f, x, x2, y, y2, rn, t;
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double d;
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x = fabs (2.0 * creal (z));
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y = fabs (2.0 * cimag(z));
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x = _redupi(x);
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x = x * x;
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y = y * y;
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x2 = 1.0;
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y2 = 1.0;
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f = 1.0;
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rn = 0.0;
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d = 0.0;
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do {
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rn += 1.0;
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f *= rn;
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rn += 1.0;
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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 += 1.0;
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f *= rn;
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rn += 1.0;
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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 (fabs(t/d) > MACHEP)
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;
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return (d);
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}
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double complex
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ctan(double complex z)
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{
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double complex w;
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double d;
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d = cos (2.0 * creal (z)) + cosh (2.0 * cimag (z));
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if (fabs(d) < 0.25)
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d = _ctans (z);
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if (d == 0.0) {
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/*mtherr ("ctan", OVERFLOW);*/
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w = MAXNUM + MAXNUM * I;
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return (w);
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}
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w = sin (2.0 * creal(z)) / d + (sinh (2.0 * cimag(z)) / d) * 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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__strong_alias(ctanl, ctan);
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#endif /* LDBL_MANT_DIG == DBL_MANT_DIG */
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