Hi...
Recently a problem was discovered with the function pow().
It is possible to let it's computation run into an infinite loop,
when using mingw-w64-crt!
I took a *DEEP* look into it:
This - fortunately - only happens with a special case:
x^-2147483648
This is (in hexadecimal) 0x80000000.
pow() detects that the exponent is an integer and diverts execution
to powi() which is specialized to integer exponents.
As x^-y is mathematically handled as 1/(x^y) powi() tries to
invert y (the exponent) by executing
y = -y;
and continues to do computation as having a positive exponent.
But, 0x80000000 cannot be inverted. The result is again 0x80000000.
Afterwards powi() shifts y by one bit to the right as long as y is > 0.
This can never be 0. After 31 shifts y is 0xffffffff => Endless loop.
I created 2 patches to solve this problem. The patches have undergone
an intensive test during the last weekend.
One to powi.def.h and one to pow.def.h.
powi.def.h patch:
=================
It simply catches the case when powi() is called
with this very special exponent and returns 0 as result.
pow.def.h patch:
================
pow() calls powi() in case y is an integer and INT_MIN <= y <= INT_MAX.
My patch changes to call powi() only if INT_MIN < y <= INT_MAX.
When y = -2147483648 (INT_MIN) now it uses floating point implementation
now which produces the correct result but has a
slight speed impact for THIS exponent.
Well the pow() patch itself is sufficient to solve the problem.
I created the additional powi() patch just for the case powi() is
once called directly without pow() in front to prevent an endless
loop.
Furthermore I have removed duplicate including of errno.h in both files.
I hope this can easily be applied.
Greetings from OneVision,
Roland
--- mingw-w64-crt/math/pow.def.h.orig 2013-01-02 15:40:35.000000000 +0100
+++ mingw-w64-crt/math/pow.def.h 2014-03-24 11:30:45.726875500 +0100
@@ -71,7 +71,7 @@
#include <limits.h>
#include <fenv.h>
#include <math.h>
-#include <errno.h>
+
#define FE_ROUNDING_MASK \
(FE_TONEAREST | FE_DOWNWARD | FE_UPWARD | FE_TOWARDZERO)
@@ -204,7 +204,7 @@
return rslt;
}
}
- else if ((d <= (__FLT_TYPE) INT_MAX && d >= (__FLT_TYPE) INT_MIN))
+ 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)));
--- mingw-w64-crt/math/powi.def.h.orig 2012-01-18 22:30:59.000000000 +0100
+++ mingw-w64-crt/math/powi.def.h 2014-03-21 10:38:37.746213800 +0100
@@ -66,7 +66,6 @@
#include <limits.h>
#include <fenv.h>
#include <math.h>
-#include <errno.h>
__FLT_TYPE __cdecl
__FLT_ABI(__powi) (__FLT_TYPE x, int y);
@@ -125,6 +124,11 @@
if (y < 0)
{
+ /* corner case y == -2147483648 (0x80000000)
+ this is not negateable => return 0 */
+ if (y == -2147483648)
+ return __FLT_CST (0.0);
+
d = __FLT_CST(1.0) / d;
y = -y;
}
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