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/* Return arc hyperbole sine for double value, with the imaginary part
of the result possibly adjusted for use in computing other
functions.
Copyright (C) 1997-2014 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 && ix < 1.5 && rx < 0.5)
{
if (rx < DBL_EPSILON * DBL_EPSILON)
{
double ix2m1 = (ix + 1.0) * (ix - 1.0);
double s = __ieee754_sqrt (ix2m1);
__real__ res = __log1p (2.0 * (ix2m1 + ix * s)) / 2.0;
if (adj)
__imag__ res = __ieee754_atan2 (rx, __copysign (s, __imag__ x));
else
__imag__ res = __ieee754_atan2 (s, rx);
}
else
{
double ix2m1 = (ix + 1.0) * (ix - 1.0);
double rx2 = rx * rx;
double f = rx2 * (2.0 + rx2 + 2.0 * ix * ix);
double d = __ieee754_sqrt (ix2m1 * ix2m1 + f);
double dp = d + ix2m1;
double dm = f / dp;
double r1 = __ieee754_sqrt ((dm + rx2) / 2.0);
double r2 = rx * ix / r1;
__real__ res = __log1p (rx2 + dp + 2.0 * (rx * r1 + ix * r2)) / 2.0;
if (adj)
__imag__ res = __ieee754_atan2 (rx + r1, __copysign (ix + r2,
__imag__ x));
else
__imag__ res = __ieee754_atan2 (ix + r2, rx + r1);
}
}
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 if (ix < 1.0 && rx < 0.5)
{
if (ix >= DBL_EPSILON)
{
if (rx < DBL_EPSILON * DBL_EPSILON)
{
double onemix2 = (1.0 + ix) * (1.0 - ix);
double s = __ieee754_sqrt (onemix2);
__real__ res = __log1p (2.0 * rx / s) / 2.0;
if (adj)
__imag__ res = __ieee754_atan2 (s, __imag__ x);
else
__imag__ res = __ieee754_atan2 (ix, s);
}
else
{
double onemix2 = (1.0 + ix) * (1.0 - ix);
double rx2 = rx * rx;
double f = rx2 * (2.0 + rx2 + 2.0 * ix * ix);
double d = __ieee754_sqrt (onemix2 * onemix2 + f);
double dp = d + onemix2;
double dm = f / dp;
double r1 = __ieee754_sqrt ((dp + rx2) / 2.0);
double r2 = rx * ix / r1;
__real__ res
= __log1p (rx2 + dm + 2.0 * (rx * r1 + ix * r2)) / 2.0;
if (adj)
__imag__ res = __ieee754_atan2 (rx + r1,
__copysign (ix + r2,
__imag__ x));
else
__imag__ res = __ieee754_atan2 (ix + r2, rx + r1);
}
}
else
{
double s = __ieee754_hypot (1.0, rx);
__real__ res = __log1p (2.0 * rx * (rx + s)) / 2.0;
if (adj)
__imag__ res = __ieee754_atan2 (s, __imag__ x);
else
__imag__ res = __ieee754_atan2 (ix, s);
}
if (__real__ res < DBL_MIN)
{
volatile double force_underflow = __real__ res * __real__ res;
(void) force_underflow;
}
}
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;
}
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