Merged revisions 77139-77140 via svnmerge from
svn+ssh://pythondev@svn.python.org/python/trunk
........
r77139 | mark.dickinson | 2009-12-30 12:12:23 +0000 (Wed, 30 Dec 2009) | 3 lines
Issue #7534: Fix handling of nans, infinities, and negative zero in **
operator, on IEEE 754 platforms. Thanks Marcos Donolo for original patch.
........
r77140 | mark.dickinson | 2009-12-30 12:22:49 +0000 (Wed, 30 Dec 2009) | 1 line
Add Marcos Donolo for work on issue 7534 patch.
........
diff --git a/Objects/floatobject.c b/Objects/floatobject.c
index b281f81..33196ff 100644
--- a/Objects/floatobject.c
+++ b/Objects/floatobject.c
@@ -671,10 +671,15 @@
return r;
}
+/* determine whether x is an odd integer or not; assumes that
+ x is not an infinity or nan. */
+#define DOUBLE_IS_ODD_INTEGER(x) (fmod(fabs(x), 2.0) == 1.0)
+
static PyObject *
float_pow(PyObject *v, PyObject *w, PyObject *z)
{
double iv, iw, ix;
+ int negate_result = 0;
if ((PyObject *)z != Py_None) {
PyErr_SetString(PyExc_TypeError, "pow() 3rd argument not "
@@ -686,20 +691,56 @@
CONVERT_TO_DOUBLE(w, iw);
/* Sort out special cases here instead of relying on pow() */
- if (iw == 0) { /* v**0 is 1, even 0**0 */
+ if (iw == 0) { /* v**0 is 1, even 0**0 */
return PyFloat_FromDouble(1.0);
}
- if (iv == 0.0) { /* 0**w is error if w<0, else 1 */
+ if (Py_IS_NAN(iv)) { /* nan**w = nan, unless w == 0 */
+ return PyFloat_FromDouble(iv);
+ }
+ if (Py_IS_NAN(iw)) { /* v**nan = nan, unless v == 1; 1**nan = 1 */
+ return PyFloat_FromDouble(iv == 1.0 ? 1.0 : iw);
+ }
+ if (Py_IS_INFINITY(iw)) {
+ /* v**inf is: 0.0 if abs(v) < 1; 1.0 if abs(v) == 1; inf if
+ * abs(v) > 1 (including case where v infinite)
+ *
+ * v**-inf is: inf if abs(v) < 1; 1.0 if abs(v) == 1; 0.0 if
+ * abs(v) > 1 (including case where v infinite)
+ */
+ iv = fabs(iv);
+ if (iv == 1.0)
+ return PyFloat_FromDouble(1.0);
+ else if ((iw > 0.0) == (iv > 1.0))
+ return PyFloat_FromDouble(fabs(iw)); /* return inf */
+ else
+ return PyFloat_FromDouble(0.0);
+ }
+ if (Py_IS_INFINITY(iv)) {
+ /* (+-inf)**w is: inf for w positive, 0 for w negative; in
+ * both cases, we need to add the appropriate sign if w is
+ * an odd integer.
+ */
+ int iw_is_odd = DOUBLE_IS_ODD_INTEGER(iw);
+ if (iw > 0.0)
+ return PyFloat_FromDouble(iw_is_odd ? iv : fabs(iv));
+ else
+ return PyFloat_FromDouble(iw_is_odd ?
+ copysign(0.0, iv) : 0.0);
+ }
+ if (iv == 0.0) { /* 0**w is: 0 for w positive, 1 for w zero
+ (already dealt with above), and an error
+ if w is negative. */
+ int iw_is_odd = DOUBLE_IS_ODD_INTEGER(iw);
if (iw < 0.0) {
PyErr_SetString(PyExc_ZeroDivisionError,
- "0.0 cannot be raised to a negative power");
+ "0.0 cannot be raised to a "
+ "negative power");
return NULL;
}
- return PyFloat_FromDouble(0.0);
+ /* use correct sign if iw is odd */
+ return PyFloat_FromDouble(iw_is_odd ? iv : 0.0);
}
- if (iv == 1.0) { /* 1**w is 1, even 1**inf and 1**nan */
- return PyFloat_FromDouble(1.0);
- }
+
if (iv < 0.0) {
/* Whether this is an error is a mess, and bumps into libm
* bugs so we have to figure it out ourselves.
@@ -710,33 +751,41 @@
*/
return PyComplex_Type.tp_as_number->nb_power(v, w, z);
}
- /* iw is an exact integer, albeit perhaps a very large one.
+ /* iw is an exact integer, albeit perhaps a very large
+ * one. Replace iv by its absolute value and remember
+ * to negate the pow result if iw is odd.
+ */
+ iv = -iv;
+ negate_result = DOUBLE_IS_ODD_INTEGER(iw);
+ }
+
+ if (iv == 1.0) { /* 1**w is 1, even 1**inf and 1**nan */
+ /* (-1) ** large_integer also ends up here. Here's an
+ * extract from the comments for the previous
+ * implementation explaining why this special case is
+ * necessary:
+ *
* -1 raised to an exact integer should never be exceptional.
* Alas, some libms (chiefly glibc as of early 2003) return
* NaN and set EDOM on pow(-1, large_int) if the int doesn't
* happen to be representable in a *C* integer. That's a
- * bug; we let that slide in math.pow() (which currently
- * reflects all platform accidents), but not for Python's **.
+ * bug.
*/
- if (iv == -1.0 && Py_IS_FINITE(iw)) {
- /* Return 1 if iw is even, -1 if iw is odd; there's
- * no guarantee that any C integral type is big
- * enough to hold iw, so we have to check this
- * indirectly.
- */
- ix = floor(iw * 0.5) * 2.0;
- return PyFloat_FromDouble(ix == iw ? 1.0 : -1.0);
- }
- /* Else iv != -1.0, and overflow or underflow are possible.
- * Unless we're to write pow() ourselves, we have to trust
- * the platform to do this correctly.
- */
+ return PyFloat_FromDouble(negate_result ? -1.0 : 1.0);
}
+
+ /* Now iv and iw are finite, iw is nonzero, and iv is
+ * positive and not equal to 1.0. We finally allow
+ * the platform pow to step in and do the rest.
+ */
errno = 0;
PyFPE_START_PROTECT("pow", return NULL)
ix = pow(iv, iw);
PyFPE_END_PROTECT(ix)
Py_ADJUST_ERANGE1(ix);
+ if (negate_result)
+ ix = -ix;
+
if (errno != 0) {
/* We don't expect any errno value other than ERANGE, but
* the range of libm bugs appears unbounded.
@@ -748,6 +797,8 @@
return PyFloat_FromDouble(ix);
}
+#undef DOUBLE_IS_ODD_INTEGER
+
static PyObject *
float_neg(PyFloatObject *v)
{