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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) 1997-2018 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 "quadmath-imp.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. */
__complex128
__quadmath_kernel_casinhq (__complex128 x, int adj)
{
__complex128 res;
__float128 rx, ix;
__complex128 y;
/* Avoid cancellation by reducing to the first quadrant. */
rx = fabsq (__real__ x);
ix = fabsq (__imag__ x);
if (rx >= 1 / FLT128_EPSILON || ix >= 1 / FLT128_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)
{
__float128 t = __real__ y;
__real__ y = copysignq (__imag__ y, __imag__ x);
__imag__ y = t;
}
res = clogq (y);
__real__ res += (__float128) M_LN2q;
}
else if (rx >= 0.5Q && ix < FLT128_EPSILON / 8)
{
__float128 s = hypotq (1, rx);
__real__ res = logq (rx + s);
if (adj)
__imag__ res = atan2q (s, __imag__ x);
else
__imag__ res = atan2q (ix, s);
}
else if (rx < FLT128_EPSILON / 8 && ix >= 1.5Q)
{
__float128 s = sqrtq ((ix + 1) * (ix - 1));
__real__ res = logq (ix + s);
if (adj)
__imag__ res = atan2q (rx, copysignq (s, __imag__ x));
else
__imag__ res = atan2q (s, rx);
}
else if (ix > 1 && ix < 1.5Q && rx < 0.5Q)
{
if (rx < FLT128_EPSILON * FLT128_EPSILON)
{
__float128 ix2m1 = (ix + 1) * (ix - 1);
__float128 s = sqrtq (ix2m1);
__real__ res = log1pq (2 * (ix2m1 + ix * s)) / 2;
if (adj)
__imag__ res = atan2q (rx, copysignq (s, __imag__ x));
else
__imag__ res = atan2q (s, rx);
}
else
{
__float128 ix2m1 = (ix + 1) * (ix - 1);
__float128 rx2 = rx * rx;
__float128 f = rx2 * (2 + rx2 + 2 * ix * ix);
__float128 d = sqrtq (ix2m1 * ix2m1 + f);
__float128 dp = d + ix2m1;
__float128 dm = f / dp;
__float128 r1 = sqrtq ((dm + rx2) / 2);
__float128 r2 = rx * ix / r1;
__real__ res = log1pq (rx2 + dp + 2 * (rx * r1 + ix * r2)) / 2;
if (adj)
__imag__ res = atan2q (rx + r1, copysignq (ix + r2, __imag__ x));
else
__imag__ res = atan2q (ix + r2, rx + r1);
}
}
else if (ix == 1 && rx < 0.5Q)
{
if (rx < FLT128_EPSILON / 8)
{
__real__ res = log1pq (2 * (rx + sqrtq (rx))) / 2;
if (adj)
__imag__ res = atan2q (sqrtq (rx), copysignq (1, __imag__ x));
else
__imag__ res = atan2q (1, sqrtq (rx));
}
else
{
__float128 d = rx * sqrtq (4 + rx * rx);
__float128 s1 = sqrtq ((d + rx * rx) / 2);
__float128 s2 = sqrtq ((d - rx * rx) / 2);
__real__ res = log1pq (rx * rx + d + 2 * (rx * s1 + s2)) / 2;
if (adj)
__imag__ res = atan2q (rx + s1, copysignq (1 + s2, __imag__ x));
else
__imag__ res = atan2q (1 + s2, rx + s1);
}
}
else if (ix < 1 && rx < 0.5Q)
{
if (ix >= FLT128_EPSILON)
{
if (rx < FLT128_EPSILON * FLT128_EPSILON)
{
__float128 onemix2 = (1 + ix) * (1 - ix);
__float128 s = sqrtq (onemix2);
__real__ res = log1pq (2 * rx / s) / 2;
if (adj)
__imag__ res = atan2q (s, __imag__ x);
else
__imag__ res = atan2q (ix, s);
}
else
{
__float128 onemix2 = (1 + ix) * (1 - ix);
__float128 rx2 = rx * rx;
__float128 f = rx2 * (2 + rx2 + 2 * ix * ix);
__float128 d = sqrtq (onemix2 * onemix2 + f);
__float128 dp = d + onemix2;
__float128 dm = f / dp;
__float128 r1 = sqrtq ((dp + rx2) / 2);
__float128 r2 = rx * ix / r1;
__real__ res = log1pq (rx2 + dm + 2 * (rx * r1 + ix * r2)) / 2;
if (adj)
__imag__ res = atan2q (rx + r1, copysignq (ix + r2,
__imag__ x));
else
__imag__ res = atan2q (ix + r2, rx + r1);
}
}
else
{
__float128 s = hypotq (1, rx);
__real__ res = log1pq (2 * rx * (rx + s)) / 2;
if (adj)
__imag__ res = atan2q (s, __imag__ x);
else
__imag__ res = atan2q (ix, s);
}
math_check_force_underflow_nonneg (__real__ res);
}
else
{
__real__ y = (rx - ix) * (rx + ix) + 1;
__imag__ y = 2 * rx * ix;
y = csqrtq (y);
__real__ y += rx;
__imag__ y += ix;
if (adj)
{
__float128 t = __real__ y;
__real__ y = copysignq (__imag__ y, __imag__ x);
__imag__ y = t;
}
res = clogq (y);
}
/* Give results the correct sign for the original argument. */
__real__ res = copysignq (__real__ res, __real__ x);
__imag__ res = copysignq (__imag__ res, (adj ? 1 : __imag__ x));
return res;
}
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