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/* Return arc hyperbole sine for float value, with the imaginary part
of the result possibly adjusted for use in computing other
functions.
Copyright (C) 1997-2015 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__ float
__kernel_casinhf (__complex__ float x, int adj)
{
__complex__ float res;
float rx, ix;
__complex__ float y;
/* Avoid cancellation by reducing to the first quadrant. */
rx = fabsf (__real__ x);
ix = fabsf (__imag__ x);
if (rx >= 1.0f / FLT_EPSILON || ix >= 1.0f / FLT_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 = __copysignf (__imag__ y, __imag__ x);
__imag__ y = t;
}
res = __clogf (y);
__real__ res += (float) M_LN2;
}
else if (rx >= 0.5f && ix < FLT_EPSILON / 8.0f)
{
float s = __ieee754_hypotf (1.0f, rx);
__real__ res = __ieee754_logf (rx + s);
if (adj)
__imag__ res = __ieee754_atan2f (s, __imag__ x);
else
__imag__ res = __ieee754_atan2f (ix, s);
}
else if (rx < FLT_EPSILON / 8.0f && ix >= 1.5f)
{
float s = __ieee754_sqrtf ((ix + 1.0f) * (ix - 1.0f));
__real__ res = __ieee754_logf (ix + s);
if (adj)
__imag__ res = __ieee754_atan2f (rx, __copysignf (s, __imag__ x));
else
__imag__ res = __ieee754_atan2f (s, rx);
}
else if (ix > 1.0f && ix < 1.5f && rx < 0.5f)
{
if (rx < FLT_EPSILON * FLT_EPSILON)
{
float ix2m1 = (ix + 1.0f) * (ix - 1.0f);
float s = __ieee754_sqrtf (ix2m1);
__real__ res = __log1pf (2.0f * (ix2m1 + ix * s)) / 2.0f;
if (adj)
__imag__ res = __ieee754_atan2f (rx, __copysignf (s, __imag__ x));
else
__imag__ res = __ieee754_atan2f (s, rx);
}
else
{
float ix2m1 = (ix + 1.0f) * (ix - 1.0f);
float rx2 = rx * rx;
float f = rx2 * (2.0f + rx2 + 2.0f * ix * ix);
float d = __ieee754_sqrtf (ix2m1 * ix2m1 + f);
float dp = d + ix2m1;
float dm = f / dp;
float r1 = __ieee754_sqrtf ((dm + rx2) / 2.0f);
float r2 = rx * ix / r1;
__real__ res
= __log1pf (rx2 + dp + 2.0f * (rx * r1 + ix * r2)) / 2.0f;
if (adj)
__imag__ res = __ieee754_atan2f (rx + r1, __copysignf (ix + r2,
__imag__ x));
else
__imag__ res = __ieee754_atan2f (ix + r2, rx + r1);
}
}
else if (ix == 1.0f && rx < 0.5f)
{
if (rx < FLT_EPSILON / 8.0f)
{
__real__ res = __log1pf (2.0f * (rx + __ieee754_sqrtf (rx))) / 2.0f;
if (adj)
__imag__ res = __ieee754_atan2f (__ieee754_sqrtf (rx),
__copysignf (1.0f, __imag__ x));
else
__imag__ res = __ieee754_atan2f (1.0f, __ieee754_sqrtf (rx));
}
else
{
float d = rx * __ieee754_sqrtf (4.0f + rx * rx);
float s1 = __ieee754_sqrtf ((d + rx * rx) / 2.0f);
float s2 = __ieee754_sqrtf ((d - rx * rx) / 2.0f);
__real__ res = __log1pf (rx * rx + d + 2.0f * (rx * s1 + s2)) / 2.0f;
if (adj)
__imag__ res = __ieee754_atan2f (rx + s1,
__copysignf (1.0f + s2,
__imag__ x));
else
__imag__ res = __ieee754_atan2f (1.0f + s2, rx + s1);
}
}
else if (ix < 1.0f && rx < 0.5f)
{
if (ix >= FLT_EPSILON)
{
if (rx < FLT_EPSILON * FLT_EPSILON)
{
float onemix2 = (1.0f + ix) * (1.0f - ix);
float s = __ieee754_sqrtf (onemix2);
__real__ res = __log1pf (2.0f * rx / s) / 2.0f;
if (adj)
__imag__ res = __ieee754_atan2f (s, __imag__ x);
else
__imag__ res = __ieee754_atan2f (ix, s);
}
else
{
float onemix2 = (1.0f + ix) * (1.0f - ix);
float rx2 = rx * rx;
float f = rx2 * (2.0f + rx2 + 2.0f * ix * ix);
float d = __ieee754_sqrtf (onemix2 * onemix2 + f);
float dp = d + onemix2;
float dm = f / dp;
float r1 = __ieee754_sqrtf ((dp + rx2) / 2.0f);
float r2 = rx * ix / r1;
__real__ res
= __log1pf (rx2 + dm + 2.0f * (rx * r1 + ix * r2)) / 2.0f;
if (adj)
__imag__ res = __ieee754_atan2f (rx + r1,
__copysignf (ix + r2,
__imag__ x));
else
__imag__ res = __ieee754_atan2f (ix + r2, rx + r1);
}
}
else
{
float s = __ieee754_hypotf (1.0f, rx);
__real__ res = __log1pf (2.0f * rx * (rx + s)) / 2.0f;
if (adj)
__imag__ res = __ieee754_atan2f (s, __imag__ x);
else
__imag__ res = __ieee754_atan2f (ix, s);
}
if (__real__ res < FLT_MIN)
{
volatile float force_underflow = __real__ res * __real__ res;
(void) force_underflow;
}
}
else
{
__real__ y = (rx - ix) * (rx + ix) + 1.0f;
__imag__ y = 2.0f * rx * ix;
y = __csqrtf (y);
__real__ y += rx;
__imag__ y += ix;
if (adj)
{
float t = __real__ y;
__real__ y = __copysignf (__imag__ y, __imag__ x);
__imag__ y = t;
}
res = __clogf (y);
}
/* Give results the correct sign for the original argument. */
__real__ res = __copysignf (__real__ res, __real__ x);
__imag__ res = __copysignf (__imag__ res, (adj ? 1.0f : __imag__ x));
return res;
}
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