216 lines
7.8 KiB
C
216 lines
7.8 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.
|
|
*/
|
|
|
|
/* IEEE 754 - Elementary Functions - Special Cases
|
|
* pow(+/-0, oo) is +0
|
|
* pow(+/-0, -oo) is +oo
|
|
* pow (x, +/-0) is 1 for any x (even a zero, quiet NaN, or infinity)
|
|
* pow (+1, y) is 1 for any y (even a quiet NaN)
|
|
* pow (+/-0, y) is +/-oo and signals the divideByZero exception for y an odd integer < 0
|
|
* pow (+/-0, y) is +oo and signals the divideByZero exception for finite y < 0 and not an odd integer
|
|
* pow (+/-0, y) is +/-0 for finite y > 0 an odd integer
|
|
* pow (+/-0, y) is +0 for finite y > 0 and not an odd integer
|
|
* pow (-1, +/-oo) is 1 with no exception
|
|
pow( -inf, y) = +0 for y<0 and not an odd integer
|
|
pow( -inf, y) = -inf for y an odd integer > 0
|
|
pow( -inf, y) = +inf for y>0 and not an odd integer
|
|
pow (+/-inf, y) is +/-0 with no exception for y an odd integer < 0
|
|
pow (+/-inf, -inf) is +0 with no exception
|
|
pow (+/-inf, +inf) is +inf with no exception
|
|
pow (+/-inf, y) is +0 with no exception for finite y < 0 and not an odd integer
|
|
pow (+/-inf, y) is +/-inf with no exception for finite y > 0 an odd integer
|
|
pow (+/-inf, y) is +inf with no exception for finite y > 0 and not an odd integer
|
|
pow (x, y) signals the invalid operation exception for finite x < 0 and finite non-integer y.
|
|
|
|
For x /= 0: lim y->oo (1/x)^y results as: for |x| < 1 that sgn(x)*0 and for |x| > 0 that sgn(x)*Infinity
|
|
|
|
*/
|
|
#include "complex_internal.h"
|
|
#include <errno.h>
|
|
#include <limits.h>
|
|
#include <fenv.h>
|
|
#include <math.h>
|
|
#include <errno.h>
|
|
#define FE_ROUNDING_MASK \
|
|
(FE_TONEAREST | FE_DOWNWARD | FE_UPWARD | FE_TOWARDZERO)
|
|
|
|
static __FLT_TYPE
|
|
internal_modf (__FLT_TYPE value, __FLT_TYPE *iptr)
|
|
{
|
|
__FLT_TYPE int_part = (__FLT_TYPE) 0.0;
|
|
/* truncate */
|
|
/* truncate */
|
|
#ifdef __x86_64__
|
|
asm ("pushq %%rax\n\tsubq $8, %%rsp\n"
|
|
"fnstcw 4(%%rsp)\n"
|
|
"movzwl 4(%%rsp), %%eax\n"
|
|
"orb $12, %%ah\n"
|
|
"movw %%ax, (%%rsp)\n"
|
|
"fldcw (%%rsp)\n"
|
|
"frndint\n"
|
|
"fldcw 4(%%rsp)\n"
|
|
"addq $8, %%rsp\npopq %%rax" : "=t" (int_part) : "0" (value)); /* round */
|
|
#else
|
|
asm ("push %%eax\n\tsubl $8, %%esp\n"
|
|
"fnstcw 4(%%esp)\n"
|
|
"movzwl 4(%%esp), %%eax\n"
|
|
"orb $12, %%ah\n"
|
|
"movw %%ax, (%%esp)\n"
|
|
"fldcw (%%esp)\n"
|
|
"frndint\n"
|
|
"fldcw 4(%%esp)\n"
|
|
"addl $8, %%esp\n\tpop %%eax\n" : "=t" (int_part) : "0" (value)); /* round */
|
|
#endif
|
|
if (iptr)
|
|
*iptr = int_part;
|
|
return (isinf (value) ? (__FLT_TYPE) 0.0 : value - int_part);
|
|
}
|
|
|
|
__FLT_TYPE __cdecl __FLT_ABI(__powi) (__FLT_TYPE x, int n);
|
|
|
|
__FLT_TYPE __cdecl
|
|
__FLT_ABI(pow) (__FLT_TYPE x, __FLT_TYPE y)
|
|
{
|
|
int x_class = fpclassify (x);
|
|
int y_class = fpclassify (y);
|
|
long odd_y = 0;
|
|
__FLT_TYPE d, rslt;
|
|
|
|
if (y_class == FP_ZERO || x == __FLT_CST(1.0))
|
|
return __FLT_CST(1.0);
|
|
else if (x_class == FP_NAN || y_class == FP_NAN)
|
|
{
|
|
rslt = (signbit(x) ? -__FLT_NAN : __FLT_NAN);
|
|
errno = EDOM;
|
|
return rslt;
|
|
}
|
|
else if (x_class == FP_ZERO)
|
|
{
|
|
if (y_class == FP_INFINITE)
|
|
return (signbit(y) ? __FLT_HUGE_VAL : __FLT_CST(0.0));
|
|
|
|
if (signbit(x) && internal_modf (y, &d) != 0.0)
|
|
{
|
|
return signbit (y) ? (1.0 / -x) : __FLT_CST (0.0);
|
|
/*errno = EDOM;
|
|
return -__FLT_NAN; */
|
|
}
|
|
odd_y = (internal_modf (__FLT_ABI (ldexp) (y, -1), &d) != 0.0) ? 1 : 0;
|
|
if (!signbit(y))
|
|
{
|
|
if (!odd_y || !signbit (x))
|
|
return __FLT_CST (0.0);
|
|
return -__FLT_CST(0.0);
|
|
}
|
|
|
|
if (!odd_y || !signbit (x))
|
|
return __FLT_HUGE_VAL;
|
|
return (signbit(x) ? -__FLT_HUGE_VAL : __FLT_HUGE_VAL);
|
|
}
|
|
else if (y_class == FP_INFINITE)
|
|
{
|
|
__FLT_TYPE a_x;
|
|
|
|
if (x_class == FP_INFINITE)
|
|
return (signbit (y) ? __FLT_CST (0.0) : __FLT_HUGE_VAL);
|
|
a_x = (signbit (x) ? -x : x);
|
|
if (a_x == 1.0)
|
|
return __FLT_CST (1.0);
|
|
if (a_x > 1.0)
|
|
return (signbit (y) == 0 ? __FLT_HUGE_VAL : __FLT_CST (0.0));
|
|
return (!signbit (y) ? __FLT_CST (0.0) : __FLT_HUGE_VAL);
|
|
}
|
|
else if (x_class == FP_INFINITE)
|
|
{
|
|
/* pow (x, y) signals the invalid operation exception for finite x < 0 and finite non-integer y. */
|
|
if (signbit(x) && internal_modf (y, &d) != 0.0)
|
|
{
|
|
return signbit(y) ? 1.0 / -x : -x;
|
|
/*errno = EDOM;
|
|
return -__FLT_NAN;*/
|
|
}
|
|
odd_y = (internal_modf (__FLT_ABI (ldexp) (y, -1), &d) != 0.0) ? 1 : 0;
|
|
/* pow( -inf, y) = +0 for y<0 and not an odd integer, */
|
|
if (signbit(x) && signbit(y) && !odd_y)
|
|
return __FLT_CST(0.0);
|
|
/* pow( -inf, y) = -inf for y an odd integer > 0. */
|
|
if (signbit(x) && !signbit(y) && odd_y)
|
|
return -__FLT_HUGE_VAL;
|
|
/* pow( -inf, y) = +inf for y>0 and not an odd integer. */
|
|
if (signbit(x) && !signbit(y) && !odd_y)
|
|
return __FLT_HUGE_VAL;
|
|
/* pow (+/-inf, y) is +/-0 with no exception for y an odd integer < 0. */
|
|
if (signbit(y))
|
|
{
|
|
/* pow (+/-inf, y) is +0 with no exception for finite y < 0 and not an odd integer. */
|
|
return (odd_y && signbit(x) ? -__FLT_CST(0.0) : __FLT_CST(0.0));
|
|
}
|
|
/* pow (+/-inf, y) is +/-inf with no exception for finite y > 0 an odd integer. */
|
|
/* pow (+/-inf, y) is +inf with no exception for finite y > 0 and not an odd integer. */
|
|
return (odd_y && signbit(x) ? -__FLT_HUGE_VAL : __FLT_HUGE_VAL);
|
|
}
|
|
|
|
if (internal_modf (y, &d) != 0.0)
|
|
{
|
|
if (signbit (x))
|
|
{
|
|
errno = EDOM;
|
|
return -__FLT_NAN;
|
|
}
|
|
if (y == __FLT_CST(0.5))
|
|
{
|
|
asm ("fsqrt" : "=t" (rslt) : "0" (x));
|
|
return rslt;
|
|
}
|
|
}
|
|
else if ((d <= (__FLT_TYPE) INT_MAX && d >= (__FLT_TYPE) INT_MIN))
|
|
return __FLT_ABI (__powi) (x, (int) y);
|
|
/* As exp already checks for minlog and maxlog no further checks are necessary. */
|
|
rslt = (__FLT_TYPE) exp2l ((long double) y * log2l ((long double) __FLT_ABI(fabs) (x)));
|
|
|
|
if (signbit (x) && internal_modf (__FLT_ABI (ldexp) (y, -1), &d) != 0.0)
|
|
rslt = -rslt;
|
|
return rslt;
|
|
}
|