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/* Return arc hyperbolic sine for a complex float type, with the
imaginary part of the result possibly adjusted for use in
computing other functions.
Copyright (C) 1997-2020 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
<https://www.gnu.org/licenses/>. */
#include <complex.h>
#include <math.h>
#include <math_private.h>
#include <math-underflow.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. */
CFLOAT
M_DECL_FUNC (__kernel_casinh) (CFLOAT x, int adj)
{
CFLOAT res;
FLOAT rx, ix;
CFLOAT y;
/* Avoid cancellation by reducing to the first quadrant. */
rx = M_FABS (__real__ x);
ix = M_FABS (__imag__ x);
if (rx >= 1 / M_EPSILON || ix >= 1 / M_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)
{
FLOAT t = __real__ y;
__real__ y = M_COPYSIGN (__imag__ y, __imag__ x);
__imag__ y = t;
}
res = M_SUF (__clog) (y);
__real__ res += (FLOAT) M_MLIT (M_LN2);
}
else if (rx >= M_LIT (0.5) && ix < M_EPSILON / 8)
{
FLOAT s = M_HYPOT (1, rx);
__real__ res = M_LOG (rx + s);
if (adj)
__imag__ res = M_ATAN2 (s, __imag__ x);
else
__imag__ res = M_ATAN2 (ix, s);
}
else if (rx < M_EPSILON / 8 && ix >= M_LIT (1.5))
{
FLOAT s = M_SQRT ((ix + 1) * (ix - 1));
__real__ res = M_LOG (ix + s);
if (adj)
__imag__ res = M_ATAN2 (rx, M_COPYSIGN (s, __imag__ x));
else
__imag__ res = M_ATAN2 (s, rx);
}
else if (ix > 1 && ix < M_LIT (1.5) && rx < M_LIT (0.5))
{
if (rx < M_EPSILON * M_EPSILON)
{
FLOAT ix2m1 = (ix + 1) * (ix - 1);
FLOAT s = M_SQRT (ix2m1);
__real__ res = M_LOG1P (2 * (ix2m1 + ix * s)) / 2;
if (adj)
__imag__ res = M_ATAN2 (rx, M_COPYSIGN (s, __imag__ x));
else
__imag__ res = M_ATAN2 (s, rx);
}
else
{
FLOAT ix2m1 = (ix + 1) * (ix - 1);
FLOAT rx2 = rx * rx;
FLOAT f = rx2 * (2 + rx2 + 2 * ix * ix);
FLOAT d = M_SQRT (ix2m1 * ix2m1 + f);
FLOAT dp = d + ix2m1;
FLOAT dm = f / dp;
FLOAT r1 = M_SQRT ((dm + rx2) / 2);
FLOAT r2 = rx * ix / r1;
__real__ res = M_LOG1P (rx2 + dp + 2 * (rx * r1 + ix * r2)) / 2;
if (adj)
__imag__ res = M_ATAN2 (rx + r1, M_COPYSIGN (ix + r2, __imag__ x));
else
__imag__ res = M_ATAN2 (ix + r2, rx + r1);
}
}
else if (ix == 1 && rx < M_LIT (0.5))
{
if (rx < M_EPSILON / 8)
{
__real__ res = M_LOG1P (2 * (rx + M_SQRT (rx))) / 2;
if (adj)
__imag__ res = M_ATAN2 (M_SQRT (rx), M_COPYSIGN (1, __imag__ x));
else
__imag__ res = M_ATAN2 (1, M_SQRT (rx));
}
else
{
FLOAT d = rx * M_SQRT (4 + rx * rx);
FLOAT s1 = M_SQRT ((d + rx * rx) / 2);
FLOAT s2 = M_SQRT ((d - rx * rx) / 2);
__real__ res = M_LOG1P (rx * rx + d + 2 * (rx * s1 + s2)) / 2;
if (adj)
__imag__ res = M_ATAN2 (rx + s1, M_COPYSIGN (1 + s2, __imag__ x));
else
__imag__ res = M_ATAN2 (1 + s2, rx + s1);
}
}
else if (ix < 1 && rx < M_LIT (0.5))
{
if (ix >= M_EPSILON)
{
if (rx < M_EPSILON * M_EPSILON)
{
FLOAT onemix2 = (1 + ix) * (1 - ix);
FLOAT s = M_SQRT (onemix2);
__real__ res = M_LOG1P (2 * rx / s) / 2;
if (adj)
__imag__ res = M_ATAN2 (s, __imag__ x);
else
__imag__ res = M_ATAN2 (ix, s);
}
else
{
FLOAT onemix2 = (1 + ix) * (1 - ix);
FLOAT rx2 = rx * rx;
FLOAT f = rx2 * (2 + rx2 + 2 * ix * ix);
FLOAT d = M_SQRT (onemix2 * onemix2 + f);
FLOAT dp = d + onemix2;
FLOAT dm = f / dp;
FLOAT r1 = M_SQRT ((dp + rx2) / 2);
FLOAT r2 = rx * ix / r1;
__real__ res = M_LOG1P (rx2 + dm + 2 * (rx * r1 + ix * r2)) / 2;
if (adj)
__imag__ res = M_ATAN2 (rx + r1, M_COPYSIGN (ix + r2,
__imag__ x));
else
__imag__ res = M_ATAN2 (ix + r2, rx + r1);
}
}
else
{
FLOAT s = M_HYPOT (1, rx);
__real__ res = M_LOG1P (2 * rx * (rx + s)) / 2;
if (adj)
__imag__ res = M_ATAN2 (s, __imag__ x);
else
__imag__ res = M_ATAN2 (ix, s);
}
math_check_force_underflow_nonneg (__real__ res);
}
else
{
__real__ y = (rx - ix) * (rx + ix) + 1;
__imag__ y = 2 * rx * ix;
y = M_SUF (__csqrt) (y);
__real__ y += rx;
__imag__ y += ix;
if (adj)
{
FLOAT t = __real__ y;
__real__ y = M_COPYSIGN (__imag__ y, __imag__ x);
__imag__ y = t;
}
res = M_SUF (__clog) (y);
}
/* Give results the correct sign for the original argument. */
__real__ res = M_COPYSIGN (__real__ res, __real__ x);
__imag__ res = M_COPYSIGN (__imag__ res, (adj ? 1 : __imag__ x));
return res;
}
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