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/*-
* Copyright (c) 2005 Bruce D. Evans and Steven G. Kargl
* 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 sine of a complex argument z = x + i y.
*
* sinh(z) = sinh(x+iy)
* = sinh(x) cos(y) + i cosh(x) sin(y).
*
* Exceptional values are noted in the comments within the source code.
* These values and the return value were taken from n1124.pdf.
* The sign of the result for some exceptional values is unspecified but
* must satisfy both sinh(conj(z)) == conj(sinh(z)) and sinh(-z) == -sinh(z).
*/
#include <sys/cdefs.h>
__FBSDID("$FreeBSD$");
#include <complex.h>
#include <math.h>
#include "math_private.h"
static const double huge = 0x1p1023;
double complex
csinh(double complex z)
{
double x, y, h;
int32_t hx, hy, ix, iy, lx, ly;
x = creal(z);
y = cimag(z);
EXTRACT_WORDS(hx, lx, x);
EXTRACT_WORDS(hy, ly, y);
ix = 0x7fffffff & hx;
iy = 0x7fffffff & hy;
/* Handle the nearly-non-exceptional cases where x and y are finite. */
if (ix < 0x7ff00000 && iy < 0x7ff00000) {
if ((iy | ly) == 0)
return (CMPLX(sinh(x), y));
if (ix < 0x40360000) /* |x| < 22: normal case */
return (CMPLX(sinh(x) * cos(y), cosh(x) * sin(y)));
/* |x| >= 22, so cosh(x) ~= exp(|x|) */
if (ix < 0x40862e42) {
/* x < 710: exp(|x|) won't overflow */
h = exp(fabs(x)) * 0.5;
return (CMPLX(copysign(h, x) * cos(y), h * sin(y)));
} else if (ix < 0x4096bbaa) {
/* x < 1455: scale to avoid overflow */
z = __ldexp_cexp(CMPLX(fabs(x), y), -1);
return (CMPLX(creal(z) * copysign(1, x), cimag(z)));
} else {
/* x >= 1455: the result always overflows */
h = huge * x;
return (CMPLX(h * cos(y), h * h * sin(y)));
}
}
/*
* sinh(+-0 +- I Inf) = +-0 + I dNaN.
* The sign of 0 in the result is unspecified. Choice = same sign
* as the argument. Raise the invalid floating-point exception.
*
* sinh(+-0 +- I NaN) = +-0 + I d(NaN).
* The sign of 0 in the result is unspecified. Choice = same sign
* as the argument.
*/
if ((ix | lx) == 0) /* && iy >= 0x7ff00000 */
return (CMPLX(x, y - y));
/*
* sinh(+-Inf +- I 0) = +-Inf + I +-0.
*
* sinh(NaN +- I 0) = d(NaN) + I +-0.
*/
if ((iy | ly) == 0) /* && ix >= 0x7ff00000 */
return (CMPLX(x + x, y));
/*
* sinh(x +- I Inf) = dNaN + I dNaN.
* Raise the invalid floating-point exception for finite nonzero x.
*
* sinh(x + I NaN) = d(NaN) + I d(NaN).
* Optionally raises the invalid floating-point exception for finite
* nonzero x. Choice = don't raise (except for signaling NaNs).
*/
if (ix < 0x7ff00000) /* && iy >= 0x7ff00000 */
return (CMPLX(y - y, y - y));
/*
* sinh(+-Inf + I NaN) = +-Inf + I d(NaN).
* The sign of Inf in the result is unspecified. Choice = same sign
* as the argument.
*
* sinh(+-Inf +- I Inf) = +-Inf + I dNaN.
* The sign of Inf in the result is unspecified. Choice = same sign
* as the argument. Raise the invalid floating-point exception.
*
* sinh(+-Inf + I y) = +-Inf cos(y) + I Inf sin(y)
*/
if (ix == 0x7ff00000 && lx == 0) {
if (iy >= 0x7ff00000)
return (CMPLX(x, y - y));
return (CMPLX(x * cos(y), INFINITY * sin(y)));
}
/*
* sinh(NaN1 + I NaN2) = d(NaN1, NaN2) + I d(NaN1, NaN2).
*
* sinh(NaN +- I Inf) = d(NaN, dNaN) + I d(NaN, dNaN).
* Optionally raises the invalid floating-point exception.
* Choice = raise.
*
* sinh(NaN + I y) = d(NaN) + I d(NaN).
* Optionally raises the invalid floating-point exception for finite
* nonzero y. Choice = don't raise (except for signaling NaNs).
*/
return (CMPLX((x + x) * (y - y), (x * x) * (y - y)));
}
double complex
csin(double complex z)
{
/* csin(z) = -I * csinh(I * z) = I * conj(csinh(I * conj(z))). */
z = csinh(CMPLX(cimag(z), creal(z)));
return (CMPLX(cimag(z), creal(z)));
}
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