mirror of
https://git.planet-casio.com/Lephenixnoir/OpenLibm.git
synced 2025-01-01 06:23:39 +01:00
144 lines
4.3 KiB
C
144 lines
4.3 KiB
C
/*-
|
|
* Copyright (c) 2011 David Schultz
|
|
* All rights reserved.
|
|
*
|
|
* Redistribution and use in source and binary forms, with or without
|
|
* modification, are permitted provided that the following conditions
|
|
* are met:
|
|
* 1. Redistributions of source code must retain the above copyright
|
|
* notice unmodified, this list of conditions, and the following
|
|
* disclaimer.
|
|
* 2. Redistributions in binary form must reproduce the above copyright
|
|
* notice, this list of conditions and the following disclaimer in the
|
|
* documentation and/or other materials provided with the distribution.
|
|
*
|
|
* THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
|
|
* IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
|
|
* OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
|
|
* IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
|
|
* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
|
|
* NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
|
|
* DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
|
|
* THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
|
|
* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
|
|
* THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
|
|
*/
|
|
|
|
/*
|
|
* Hyperbolic tangent of a complex argument z = x + i y.
|
|
*
|
|
* The algorithm is from:
|
|
*
|
|
* W. Kahan. Branch Cuts for Complex Elementary Functions or Much
|
|
* Ado About Nothing's Sign Bit. In The State of the Art in
|
|
* Numerical Analysis, pp. 165 ff. Iserles and Powell, eds., 1987.
|
|
*
|
|
* Method:
|
|
*
|
|
* Let t = tan(x)
|
|
* beta = 1/cos^2(y)
|
|
* s = sinh(x)
|
|
* rho = cosh(x)
|
|
*
|
|
* We have:
|
|
*
|
|
* tanh(z) = sinh(z) / cosh(z)
|
|
*
|
|
* sinh(x) cos(y) + i cosh(x) sin(y)
|
|
* = ---------------------------------
|
|
* cosh(x) cos(y) + i sinh(x) sin(y)
|
|
*
|
|
* cosh(x) sinh(x) / cos^2(y) + i tan(y)
|
|
* = -------------------------------------
|
|
* 1 + sinh^2(x) / cos^2(y)
|
|
*
|
|
* beta rho s + i t
|
|
* = ----------------
|
|
* 1 + beta s^2
|
|
*
|
|
* Modifications:
|
|
*
|
|
* I omitted the original algorithm's handling of overflow in tan(x) after
|
|
* verifying with nearpi.c that this can't happen in IEEE single or double
|
|
* precision. I also handle large x differently.
|
|
*/
|
|
|
|
#include "cdefs-compat.h"
|
|
//__FBSDID("$FreeBSD: src/lib/msun/src/s_ctanh.c,v 1.2 2011/10/21 06:30:16 das Exp $");
|
|
|
|
#include <openlibm_complex.h>
|
|
#include <openlibm_math.h>
|
|
|
|
#include "math_private.h"
|
|
|
|
OLM_DLLEXPORT double complex
|
|
ctanh(double complex z)
|
|
{
|
|
double x, y;
|
|
double t, beta, s, rho, denom;
|
|
u_int32_t hx, ix, lx;
|
|
|
|
x = creal(z);
|
|
y = cimag(z);
|
|
|
|
EXTRACT_WORDS(hx, lx, x);
|
|
ix = hx & 0x7fffffff;
|
|
|
|
/*
|
|
* ctanh(NaN + i 0) = NaN + i 0
|
|
*
|
|
* ctanh(NaN + i y) = NaN + i NaN for y != 0
|
|
*
|
|
* The imaginary part has the sign of x*sin(2*y), but there's no
|
|
* special effort to get this right.
|
|
*
|
|
* ctanh(+-Inf +- i Inf) = +-1 +- 0
|
|
*
|
|
* ctanh(+-Inf + i y) = +-1 + 0 sin(2y) for y finite
|
|
*
|
|
* The imaginary part of the sign is unspecified. This special
|
|
* case is only needed to avoid a spurious invalid exception when
|
|
* y is infinite.
|
|
*/
|
|
if (ix >= 0x7ff00000) {
|
|
if ((ix & 0xfffff) | lx) /* x is NaN */
|
|
return (CMPLX(x, (y == 0 ? y : x * y)));
|
|
SET_HIGH_WORD(x, hx - 0x40000000); /* x = copysign(1, x) */
|
|
return (CMPLX(x, copysign(0, isinf(y) ? y : sin(y) * cos(y))));
|
|
}
|
|
|
|
/*
|
|
* ctanh(x + i NAN) = NaN + i NaN
|
|
* ctanh(x +- i Inf) = NaN + i NaN
|
|
*/
|
|
if (!isfinite(y))
|
|
return (CMPLX(y - y, y - y));
|
|
|
|
/*
|
|
* ctanh(+-huge + i +-y) ~= +-1 +- i 2sin(2y)/exp(2x), using the
|
|
* approximation sinh^2(huge) ~= exp(2*huge) / 4.
|
|
* We use a modified formula to avoid spurious overflow.
|
|
*/
|
|
if (ix >= 0x40360000) { /* x >= 22 */
|
|
double exp_mx = exp(-fabs(x));
|
|
return (CMPLX(copysign(1, x),
|
|
4 * sin(y) * cos(y) * exp_mx * exp_mx));
|
|
}
|
|
|
|
/* Kahan's algorithm */
|
|
t = tan(y);
|
|
beta = 1.0 + t * t; /* = 1 / cos^2(y) */
|
|
s = sinh(x);
|
|
rho = sqrt(1 + s * s); /* = cosh(x) */
|
|
denom = 1 + beta * s * s;
|
|
return (CMPLX((beta * rho * s) / denom, t / denom));
|
|
}
|
|
|
|
OLM_DLLEXPORT double complex
|
|
ctan(double complex z)
|
|
{
|
|
|
|
/* ctan(z) = -I * ctanh(I * z) */
|
|
z = ctanh(CMPLX(-cimag(z), creal(z)));
|
|
return (CMPLX(cimag(z), -creal(z)));
|
|
}
|