157 lines
5.8 KiB
C
157 lines
5.8 KiB
C
/*
|
|
This Software is provided under the Zope Public License (ZPL) Version 2.1.
|
|
|
|
Copyright (c) 2009, 2010 by the mingw-w64 project
|
|
|
|
See the AUTHORS file for the list of contributors to the mingw-w64 project.
|
|
|
|
This license has been certified as open source. It has also been designated
|
|
as GPL compatible by the Free Software Foundation (FSF).
|
|
|
|
Redistribution and use in source and binary forms, with or without
|
|
modification, are permitted provided that the following conditions are met:
|
|
|
|
1. Redistributions in source code must retain the accompanying copyright
|
|
notice, this list of conditions, and the following disclaimer.
|
|
2. Redistributions in binary form must reproduce the accompanying
|
|
copyright notice, this list of conditions, and the following disclaimer
|
|
in the documentation and/or other materials provided with the
|
|
distribution.
|
|
3. Names of the copyright holders must not be used to endorse or promote
|
|
products derived from this software without prior written permission
|
|
from the copyright holders.
|
|
4. The right to distribute this software or to use it for any purpose does
|
|
not give you the right to use Servicemarks (sm) or Trademarks (tm) of
|
|
the copyright holders. Use of them is covered by separate agreement
|
|
with the copyright holders.
|
|
5. If any files are modified, you must cause the modified files to carry
|
|
prominent notices stating that you changed the files and the date of
|
|
any change.
|
|
|
|
Disclaimer
|
|
|
|
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS ``AS IS'' AND ANY EXPRESSED
|
|
OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
|
|
OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO
|
|
EVENT SHALL THE COPYRIGHT HOLDERS BE LIABLE FOR ANY DIRECT, INDIRECT,
|
|
INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
|
|
LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA,
|
|
OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
|
|
LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
|
|
NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE,
|
|
EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
|
|
*/
|
|
|
|
__FLT_TYPE __complex__ __cdecl
|
|
__FLT_ABI(casinh) (__FLT_TYPE __complex__ z)
|
|
{
|
|
__complex__ __FLT_TYPE ret;
|
|
__complex__ __FLT_TYPE x;
|
|
__FLT_TYPE arz, aiz;
|
|
int r_class = fpclassify (__real__ z);
|
|
int i_class = fpclassify (__imag__ z);
|
|
|
|
if (i_class == FP_INFINITE)
|
|
{
|
|
__real__ ret = __FLT_ABI(copysign) (__FLT_HUGE_VAL, __real__ z);
|
|
__imag__ ret = (r_class == FP_NAN
|
|
? __FLT_NAN
|
|
: (__FLT_ABI(copysign) ((r_class != FP_NAN && r_class != FP_INFINITE) ? __FLT_PI_2 : __FLT_PI_4, __imag__ z)));
|
|
return ret;
|
|
}
|
|
|
|
if (r_class == FP_INFINITE)
|
|
{
|
|
__real__ ret = __real__ z;
|
|
__imag__ ret = (i_class != FP_NAN
|
|
? __FLT_ABI(copysign) (__FLT_CST(0.0), __imag__ z)
|
|
: __FLT_NAN);
|
|
return ret;
|
|
}
|
|
|
|
if (r_class == FP_NAN)
|
|
{
|
|
__real__ ret = __real__ z;
|
|
__imag__ ret = (i_class == FP_ZERO
|
|
? __FLT_ABI(copysign) (__FLT_CST(0.0), __imag__ z)
|
|
: __FLT_NAN);
|
|
return ret;
|
|
}
|
|
|
|
if (i_class == FP_NAN)
|
|
{
|
|
__real__ ret = __FLT_NAN;
|
|
__imag__ ret = __FLT_NAN;
|
|
return ret;
|
|
}
|
|
|
|
if (r_class == FP_ZERO && i_class == FP_ZERO)
|
|
return z;
|
|
|
|
/* casinh(z) = log(z + sqrt(z*z + 1)) */
|
|
|
|
/* Use symmetries to perform the calculation in the first quadrant. */
|
|
arz = __FLT_ABI(fabs) (__real__ z);
|
|
aiz = __FLT_ABI(fabs) (__imag__ z);
|
|
|
|
if (arz >= __FLT_CST(1.0)/__FLT_EPSILON
|
|
|| aiz >= __FLT_CST(1.0)/__FLT_EPSILON)
|
|
{
|
|
/* For large z, z + sqrt(z*z + 1) is approximately 2*z.
|
|
Use that approximation to avoid overflow when squaring. */
|
|
__real__ x = arz;
|
|
__imag__ x = aiz;
|
|
ret = __FLT_ABI(clog) (x);
|
|
__real__ ret += M_LN2;
|
|
}
|
|
else if (aiz < __FLT_CST(1.0) && arz <= __FLT_EPSILON)
|
|
{
|
|
/* Taylor series expansion around arz=0 for z + sqrt(z*z + 1):
|
|
c = arz + sqrt(1-aiz^2) + i*(aiz + arz*aiz / sqrt(1-aiz^2)) + O(arz^2)
|
|
Identity: clog(c) = log(|c|) + i*arg(c)
|
|
For real part of result:
|
|
|c| = 1 + arz / sqrt(1-aiz^2) + O(arz^2) (Taylor series expansion)
|
|
For imaginary part of result:
|
|
c = (arz + sqrt(1-aiz^2))/sqrt(1-aiz^2) * (sqrt(1-aiz^2) + i*aiz) + O(arz^6)
|
|
*/
|
|
__FLT_TYPE s1maiz2 = __FLT_ABI(sqrt) ((__FLT_CST(1.0)+aiz)*(__FLT_CST(1.0)-aiz));
|
|
__real__ ret = __FLT_ABI(log1p) (arz / s1maiz2);
|
|
__imag__ ret = __FLT_ABI(atan2) (aiz, s1maiz2);
|
|
}
|
|
else if (aiz < __FLT_CST(1.0) && arz*arz <= __FLT_EPSILON)
|
|
{
|
|
/* Taylor series expansion around arz=0 for z + sqrt(z*z + 1):
|
|
c = arz + sqrt(1-aiz^2) + arz^2 / (2*(1-aiz^2)^(3/2)) + i*(aiz + arz*aiz / sqrt(1-aiz^2)) + O(arz^4)
|
|
Identity: clog(c) = log(|c|) + i*arg(c)
|
|
For real part of result:
|
|
|c| = 1 + arz / sqrt(1-aiz^2) + arz^2/(2*(1-aiz^2)) + O(arz^3) (Taylor series expansion)
|
|
For imaginary part of result:
|
|
c = 1/sqrt(1-aiz^2) * ((1-aiz^2) + arz*sqrt(1-aiz^2) + arz^2/(2*(1-aiz^2)) + i*aiz*(sqrt(1-aiz^2)+arz)) + O(arz^3)
|
|
*/
|
|
__FLT_TYPE onemaiz2 = (__FLT_CST(1.0)+aiz)*(__FLT_CST(1.0)-aiz);
|
|
__FLT_TYPE s1maiz2 = __FLT_ABI(sqrt) (onemaiz2);
|
|
__FLT_TYPE arz2red = arz * arz / __FLT_CST(2.0) / s1maiz2;
|
|
__real__ ret = __FLT_ABI(log1p) ((arz + arz2red) / s1maiz2);
|
|
__imag__ ret = __FLT_ABI(atan2) (aiz * (s1maiz2 + arz),
|
|
onemaiz2 + arz*s1maiz2 + arz2red);
|
|
}
|
|
else
|
|
{
|
|
__real__ x = (arz - aiz) * (arz + aiz) + __FLT_CST(1.0);
|
|
__imag__ x = __FLT_CST(2.0) * arz * aiz;
|
|
|
|
x = __FLT_ABI(csqrt) (x);
|
|
|
|
__real__ x += arz;
|
|
__imag__ x += aiz;
|
|
|
|
ret = __FLT_ABI(clog) (x);
|
|
}
|
|
|
|
/* adjust signs for input quadrant */
|
|
__real__ ret = __FLT_ABI(copysign) (__real__ ret, __real__ z);
|
|
__imag__ ret = __FLT_ABI(copysign) (__imag__ ret, __imag__ z);
|
|
|
|
return ret;
|
|
}
|