OpenLibm/src/s_ctanl.c
Ed Schouten 7e5585aaca Rename openlibm.h to openlibm_math.h.
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.
2015-01-11 23:37:01 +01:00

157 lines
3.4 KiB
C

/* $OpenBSD: s_ctanl.c,v 1.3 2011/07/20 21:02:51 martynas Exp $ */
/*
* Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>
*
* Permission to use, copy, modify, and distribute this software for any
* purpose with or without fee is hereby granted, provided that the above
* copyright notice and this permission notice appear in all copies.
*
* THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
* WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
* MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
* ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
* WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
* ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
* OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
*/
/* ctanl()
*
* Complex circular tangent
*
*
*
* SYNOPSIS:
*
* long double complex ctanl();
* long double complex z, w;
*
* w = ctanl( z );
*
*
*
* DESCRIPTION:
*
* If
* z = x + iy,
*
* then
*
* sin 2x + i sinh 2y
* w = --------------------.
* cos 2x + cosh 2y
*
* On the real axis the denominator is zero at odd multiples
* of PI/2. The denominator is evaluated by its Taylor
* series near these points.
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* DEC -10,+10 5200 7.1e-17 1.6e-17
* IEEE -10,+10 30000 7.2e-16 1.2e-16
* Also tested by ctan * ccot = 1 and catan(ctan(z)) = z.
*/
#include <float.h>
#include <openlibm_complex.h>
#include <openlibm_math.h>
#if LDBL_MANT_DIG == 64
static const long double MACHEPL= 5.42101086242752217003726400434970855712890625E-20L;
#elif LDBL_MANT_DIG == 113
static const long double MACHEPL = 9.629649721936179265279889712924636592690508e-35L;
#endif
static const long double PIL = 3.141592653589793238462643383279502884197169L;
static const long double DP1 = 3.14159265358979323829596852490908531763125L;
static const long double DP2 = 1.6667485837041756656403424829301998703007e-19L;
static const long double DP3 = 1.8830410776607851167459095484560349402753e-39L;
static long double
redupil(long double x)
{
long double t;
long i;
t = x / PIL;
if (t >= 0.0L)
t += 0.5L;
else
t -= 0.5L;
i = t; /* the multiple */
t = i;
t = ((x - t * DP1) - t * DP2) - t * DP3;
return (t);
}
static long double
ctansl(long double complex z)
{
long double f, x, x2, y, y2, rn, t;
long double d;
x = fabsl(2.0L * creall(z));
y = fabsl(2.0L * cimagl(z));
x = redupil(x);
x = x * x;
y = y * y;
x2 = 1.0L;
y2 = 1.0L;
f = 1.0L;
rn = 0.0L;
d = 0.0L;
do {
rn += 1.0L;
f *= rn;
rn += 1.0L;
f *= rn;
x2 *= x;
y2 *= y;
t = y2 + x2;
t /= f;
d += t;
rn += 1.0L;
f *= rn;
rn += 1.0L;
f *= rn;
x2 *= x;
y2 *= y;
t = y2 - x2;
t /= f;
d += t;
}
while (fabsl(t/d) > MACHEPL);
return(d);
}
long double complex
ctanl(long double complex z)
{
long double complex w;
long double d, x, y;
x = creall(z);
y = cimagl(z);
d = cosl(2.0L * x) + coshl(2.0L * y);
if (fabsl(d) < 0.25L) {
d = fabsl(d);
d = ctansl(z);
}
if (d == 0.0L) {
/*mtherr( "ctan", OVERFLOW );*/
w = LDBL_MAX + LDBL_MAX * I;
return (w);
}
w = sinl(2.0L * x) / d + (sinhl(2.0L * y) / d) * I;
return (w);
}