mirror of
https://sourceware.org/git/glibc.git
synced 2024-11-22 13:00:06 +00:00
131 lines
3.7 KiB
C
131 lines
3.7 KiB
C
/* Return arc hyperbole sine for double value, with the imaginary part
|
|
of the result possibly adjusted for use in computing other
|
|
functions.
|
|
Copyright (C) 1997-2013 Free Software Foundation, Inc.
|
|
This file is part of the GNU C Library.
|
|
|
|
The GNU C Library is free software; you can redistribute it and/or
|
|
modify it under the terms of the GNU Lesser General Public
|
|
License as published by the Free Software Foundation; either
|
|
version 2.1 of the License, or (at your option) any later version.
|
|
|
|
The GNU C Library is distributed in the hope that it will be useful,
|
|
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
|
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
|
|
Lesser General Public License for more details.
|
|
|
|
You should have received a copy of the GNU Lesser General Public
|
|
License along with the GNU C Library; if not, see
|
|
<http://www.gnu.org/licenses/>. */
|
|
|
|
#include <complex.h>
|
|
#include <math.h>
|
|
#include <math_private.h>
|
|
#include <float.h>
|
|
|
|
/* Return the complex inverse hyperbolic sine of finite nonzero Z,
|
|
with the imaginary part of the result subtracted from pi/2 if ADJ
|
|
is nonzero. */
|
|
|
|
__complex__ double
|
|
__kernel_casinh (__complex__ double x, int adj)
|
|
{
|
|
__complex__ double res;
|
|
double rx, ix;
|
|
__complex__ double y;
|
|
|
|
/* Avoid cancellation by reducing to the first quadrant. */
|
|
rx = fabs (__real__ x);
|
|
ix = fabs (__imag__ x);
|
|
|
|
if (rx >= 1.0 / DBL_EPSILON || ix >= 1.0 / DBL_EPSILON)
|
|
{
|
|
/* For large x in the first quadrant, x + csqrt (1 + x * x)
|
|
is sufficiently close to 2 * x to make no significant
|
|
difference to the result; avoid possible overflow from
|
|
the squaring and addition. */
|
|
__real__ y = rx;
|
|
__imag__ y = ix;
|
|
|
|
if (adj)
|
|
{
|
|
double t = __real__ y;
|
|
__real__ y = __copysign (__imag__ y, __imag__ x);
|
|
__imag__ y = t;
|
|
}
|
|
|
|
res = __clog (y);
|
|
__real__ res += M_LN2;
|
|
}
|
|
else if (rx >= 0.5 && ix < DBL_EPSILON / 8.0)
|
|
{
|
|
double s = __ieee754_hypot (1.0, rx);
|
|
|
|
__real__ res = __ieee754_log (rx + s);
|
|
if (adj)
|
|
__imag__ res = __ieee754_atan2 (s, __imag__ x);
|
|
else
|
|
__imag__ res = __ieee754_atan2 (ix, s);
|
|
}
|
|
else if (rx < DBL_EPSILON / 8.0 && ix >= 1.5)
|
|
{
|
|
double s = __ieee754_sqrt ((ix + 1.0) * (ix - 1.0));
|
|
|
|
__real__ res = __ieee754_log (ix + s);
|
|
if (adj)
|
|
__imag__ res = __ieee754_atan2 (rx, __copysign (s, __imag__ x));
|
|
else
|
|
__imag__ res = __ieee754_atan2 (s, rx);
|
|
}
|
|
else if (ix == 1.0 && rx < 0.5)
|
|
{
|
|
if (rx < DBL_EPSILON / 8.0)
|
|
{
|
|
__real__ res = __log1p (2.0 * (rx + __ieee754_sqrt (rx))) / 2.0;
|
|
if (adj)
|
|
__imag__ res = __ieee754_atan2 (__ieee754_sqrt (rx),
|
|
__copysign (1.0, __imag__ x));
|
|
else
|
|
__imag__ res = __ieee754_atan2 (1.0, __ieee754_sqrt (rx));
|
|
}
|
|
else
|
|
{
|
|
double d = rx * __ieee754_sqrt (4.0 + rx * rx);
|
|
double s1 = __ieee754_sqrt ((d + rx * rx) / 2.0);
|
|
double s2 = __ieee754_sqrt ((d - rx * rx) / 2.0);
|
|
|
|
__real__ res = __log1p (rx * rx + d + 2.0 * (rx * s1 + s2)) / 2.0;
|
|
if (adj)
|
|
__imag__ res = __ieee754_atan2 (rx + s1, __copysign (1.0 + s2,
|
|
__imag__ x));
|
|
else
|
|
__imag__ res = __ieee754_atan2 (1.0 + s2, rx + s1);
|
|
}
|
|
}
|
|
else
|
|
{
|
|
__real__ y = (rx - ix) * (rx + ix) + 1.0;
|
|
__imag__ y = 2.0 * rx * ix;
|
|
|
|
y = __csqrt (y);
|
|
|
|
__real__ y += rx;
|
|
__imag__ y += ix;
|
|
|
|
if (adj)
|
|
{
|
|
double t = __real__ y;
|
|
__real__ y = copysign (__imag__ y, __imag__ x);
|
|
__imag__ y = t;
|
|
}
|
|
|
|
res = __clog (y);
|
|
}
|
|
|
|
/* Give results the correct sign for the original argument. */
|
|
__real__ res = __copysign (__real__ res, __real__ x);
|
|
__imag__ res = __copysign (__imag__ res, (adj ? 1.0 : __imag__ x));
|
|
|
|
return res;
|
|
}
|