Issue #7534: Fix handling of nans, infinities, and negative zero in **

operator, on IEEE 754 platforms.  Thanks Marcos Donolo for original patch.

4 files changed, 294 insertions, 25 deletions

diff --git a/Lib/test/ieee754.txt b/Lib/test/ieee754.txt
index 5a41c8f..89bb0c5 100644
--- a/Lib/test/ieee754.txt
+++ b/Lib/test/ieee754.txt
@@ -72,7 +72,7 @@ False
 >>> NAN >= 0
 False
 
-All operations involving a NaN return a NaN except for the power of *0* and *1*.
+All operations involving a NaN return a NaN except for nan**0 and 1**nan.
 >>> 1 + NAN
 nan
 >>> 1 * NAN
@@ -81,8 +81,10 @@ nan
 nan
 >>> 1 ** NAN
 1.0
+>>> NAN ** 0
+1.0
 >>> 0 ** NAN
-0.0
+nan
 >>> (1.0 + FI.epsilon) * NAN
 nan
 
diff --git a/Lib/test/test_float.py b/Lib/test/test_float.py
index 564f24f..ddaf7bd 100644
--- a/Lib/test/test_float.py
+++ b/Lib/test/test_float.py
@@ -12,6 +12,11 @@ import sys
 INF = float("inf")
 NAN = float("nan")
 
+# decorator for skipping tests on non-IEEE 754 platforms
+requires_IEEE_754 = unittest.skipUnless(
+    float.__getformat__("double").startswith("IEEE"),
+    "test requires IEEE 754 doubles")
+
 #locate file with float format test values
 test_dir = os.path.dirname(__file__) or os.curdir
 format_testfile = os.path.join(test_dir, 'formatfloat_testcases.txt')
@@ -142,6 +147,213 @@ class GeneralFloatCases(unittest.TestCase):
         self.assertRaises(OverflowError, float('-inf').as_integer_ratio)
         self.assertRaises(ValueError, float('nan').as_integer_ratio)
 
+    def assertEqualAndEqualSign(self, a, b):
+        # fail unless a == b and a and b have the same sign bit;
+        # the only difference from assertEqual is that this test
+        # distingishes -0.0 and 0.0.
+        self.assertEqual((a, copysign(1.0, a)), (b, copysign(1.0, b)))
+
+    @requires_IEEE_754
+    def test_float_pow(self):
+        # test builtin pow and ** operator for IEEE 754 special cases.
+        # Special cases taken from section F.9.4.4 of the C99 specification
+
+        for pow_op in pow, operator.pow:
+            # x**NAN is NAN for any x except 1
+            self.assertTrue(isnan(pow_op(-INF, NAN)))
+            self.assertTrue(isnan(pow_op(-2.0, NAN)))
+            self.assertTrue(isnan(pow_op(-1.0, NAN)))
+            self.assertTrue(isnan(pow_op(-0.5, NAN)))
+            self.assertTrue(isnan(pow_op(-0.0, NAN)))
+            self.assertTrue(isnan(pow_op(0.0, NAN)))
+            self.assertTrue(isnan(pow_op(0.5, NAN)))
+            self.assertTrue(isnan(pow_op(2.0, NAN)))
+            self.assertTrue(isnan(pow_op(INF, NAN)))
+            self.assertTrue(isnan(pow_op(NAN, NAN)))
+
+            # NAN**y is NAN for any y except +-0
+            self.assertTrue(isnan(pow_op(NAN, -INF)))
+            self.assertTrue(isnan(pow_op(NAN, -2.0)))
+            self.assertTrue(isnan(pow_op(NAN, -1.0)))
+            self.assertTrue(isnan(pow_op(NAN, -0.5)))
+            self.assertTrue(isnan(pow_op(NAN, 0.5)))
+            self.assertTrue(isnan(pow_op(NAN, 1.0)))
+            self.assertTrue(isnan(pow_op(NAN, 2.0)))
+            self.assertTrue(isnan(pow_op(NAN, INF)))
+
+            # (+-0)**y raises ZeroDivisionError for y a negative odd integer
+            self.assertRaises(ZeroDivisionError, pow_op, -0.0, -1.0)
+            self.assertRaises(ZeroDivisionError, pow_op, 0.0, -1.0)
+
+            # (+-0)**y raises ZeroDivisionError for y finite and negative
+            # but not an odd integer
+            self.assertRaises(ZeroDivisionError, pow_op, -0.0, -2.0)
+            self.assertRaises(ZeroDivisionError, pow_op, -0.0, -0.5)
+            self.assertRaises(ZeroDivisionError, pow_op, 0.0, -2.0)
+            self.assertRaises(ZeroDivisionError, pow_op, 0.0, -0.5)
+
+            # (+-0)**y is +-0 for y a positive odd integer
+            self.assertEqualAndEqualSign(pow_op(-0.0, 1.0), -0.0)
+            self.assertEqualAndEqualSign(pow_op(0.0, 1.0), 0.0)
+
+            # (+-0)**y is 0 for y finite and positive but not an odd integer
+            self.assertEqualAndEqualSign(pow_op(-0.0, 0.5), 0.0)
+            self.assertEqualAndEqualSign(pow_op(-0.0, 2.0), 0.0)
+            self.assertEqualAndEqualSign(pow_op(0.0, 0.5), 0.0)
+            self.assertEqualAndEqualSign(pow_op(0.0, 2.0), 0.0)
+
+            # (-1)**+-inf is 1
+            self.assertEqualAndEqualSign(pow_op(-1.0, -INF), 1.0)
+            self.assertEqualAndEqualSign(pow_op(-1.0, INF), 1.0)
+
+            # 1**y is 1 for any y, even if y is an infinity or nan
+            self.assertEqualAndEqualSign(pow_op(1.0, -INF), 1.0)
+            self.assertEqualAndEqualSign(pow_op(1.0, -2.0), 1.0)
+            self.assertEqualAndEqualSign(pow_op(1.0, -1.0), 1.0)
+            self.assertEqualAndEqualSign(pow_op(1.0, -0.5), 1.0)
+            self.assertEqualAndEqualSign(pow_op(1.0, -0.0), 1.0)
+            self.assertEqualAndEqualSign(pow_op(1.0, 0.0), 1.0)
+            self.assertEqualAndEqualSign(pow_op(1.0, 0.5), 1.0)
+            self.assertEqualAndEqualSign(pow_op(1.0, 1.0), 1.0)
+            self.assertEqualAndEqualSign(pow_op(1.0, 2.0), 1.0)
+            self.assertEqualAndEqualSign(pow_op(1.0, INF), 1.0)
+            self.assertEqualAndEqualSign(pow_op(1.0, NAN), 1.0)
+
+            # x**+-0 is 1 for any x, even if x is a zero, infinity, or nan
+            self.assertEqualAndEqualSign(pow_op(-INF, 0.0), 1.0)
+            self.assertEqualAndEqualSign(pow_op(-2.0, 0.0), 1.0)
+            self.assertEqualAndEqualSign(pow_op(-1.0, 0.0), 1.0)
+            self.assertEqualAndEqualSign(pow_op(-0.5, 0.0), 1.0)
+            self.assertEqualAndEqualSign(pow_op(-0.0, 0.0), 1.0)
+            self.assertEqualAndEqualSign(pow_op(0.0, 0.0), 1.0)
+            self.assertEqualAndEqualSign(pow_op(0.5, 0.0), 1.0)
+            self.assertEqualAndEqualSign(pow_op(1.0, 0.0), 1.0)
+            self.assertEqualAndEqualSign(pow_op(2.0, 0.0), 1.0)
+            self.assertEqualAndEqualSign(pow_op(INF, 0.0), 1.0)
+            self.assertEqualAndEqualSign(pow_op(NAN, 0.0), 1.0)
+            self.assertEqualAndEqualSign(pow_op(-INF, -0.0), 1.0)
+            self.assertEqualAndEqualSign(pow_op(-2.0, -0.0), 1.0)
+            self.assertEqualAndEqualSign(pow_op(-1.0, -0.0), 1.0)
+            self.assertEqualAndEqualSign(pow_op(-0.5, -0.0), 1.0)
+            self.assertEqualAndEqualSign(pow_op(-0.0, -0.0), 1.0)
+            self.assertEqualAndEqualSign(pow_op(0.0, -0.0), 1.0)
+            self.assertEqualAndEqualSign(pow_op(0.5, -0.0), 1.0)
+            self.assertEqualAndEqualSign(pow_op(1.0, -0.0), 1.0)
+            self.assertEqualAndEqualSign(pow_op(2.0, -0.0), 1.0)
+            self.assertEqualAndEqualSign(pow_op(INF, -0.0), 1.0)
+            self.assertEqualAndEqualSign(pow_op(NAN, -0.0), 1.0)
+
+            # x**y raises ValueError for finite negative x and non-integral y
+            self.assertRaises(ValueError, pow_op, -2.0, -0.5)
+            self.assertRaises(ValueError, pow_op, -2.0, 0.5)
+            self.assertRaises(ValueError, pow_op, -1.0, -0.5)
+            self.assertRaises(ValueError, pow_op, -1.0, 0.5)
+            self.assertRaises(ValueError, pow_op, -0.5, -0.5)
+            self.assertRaises(ValueError, pow_op, -0.5, 0.5)
+
+            # x**-INF is INF for abs(x) < 1
+            self.assertEqualAndEqualSign(pow_op(-0.5, -INF), INF)
+            self.assertEqualAndEqualSign(pow_op(-0.0, -INF), INF)
+            self.assertEqualAndEqualSign(pow_op(0.0, -INF), INF)
+            self.assertEqualAndEqualSign(pow_op(0.5, -INF), INF)
+
+            # x**-INF is 0 for abs(x) > 1
+            self.assertEqualAndEqualSign(pow_op(-INF, -INF), 0.0)
+            self.assertEqualAndEqualSign(pow_op(-2.0, -INF), 0.0)
+            self.assertEqualAndEqualSign(pow_op(2.0, -INF), 0.0)
+            self.assertEqualAndEqualSign(pow_op(INF, -INF), 0.0)
+
+            # x**INF is 0 for abs(x) < 1
+            self.assertEqualAndEqualSign(pow_op(-0.5, INF), 0.0)
+            self.assertEqualAndEqualSign(pow_op(-0.0, INF), 0.0)
+            self.assertEqualAndEqualSign(pow_op(0.0, INF), 0.0)
+            self.assertEqualAndEqualSign(pow_op(0.5, INF), 0.0)
+
+            # x**INF is INF for abs(x) > 1
+            self.assertEqualAndEqualSign(pow_op(-INF, INF), INF)
+            self.assertEqualAndEqualSign(pow_op(-2.0, INF), INF)
+            self.assertEqualAndEqualSign(pow_op(2.0, INF), INF)
+            self.assertEqualAndEqualSign(pow_op(INF, INF), INF)
+
+            # (-INF)**y is -0.0 for y a negative odd integer
+            self.assertEqualAndEqualSign(pow_op(-INF, -1.0), -0.0)
+
+            # (-INF)**y is 0.0 for y negative but not an odd integer
+            self.assertEqualAndEqualSign(pow_op(-INF, -0.5), 0.0)
+            self.assertEqualAndEqualSign(pow_op(-INF, -2.0), 0.0)
+
+            # (-INF)**y is -INF for y a positive odd integer
+            self.assertEqualAndEqualSign(pow_op(-INF, 1.0), -INF)
+
+            # (-INF)**y is INF for y positive but not an odd integer
+            self.assertEqualAndEqualSign(pow_op(-INF, 0.5), INF)
+            self.assertEqualAndEqualSign(pow_op(-INF, 2.0), INF)
+
+            # INF**y is INF for y positive
+            self.assertEqualAndEqualSign(pow_op(INF, 0.5), INF)
+            self.assertEqualAndEqualSign(pow_op(INF, 1.0), INF)
+            self.assertEqualAndEqualSign(pow_op(INF, 2.0), INF)
+
+            # INF**y is 0.0 for y negative
+            self.assertEqualAndEqualSign(pow_op(INF, -2.0), 0.0)
+            self.assertEqualAndEqualSign(pow_op(INF, -1.0), 0.0)
+            self.assertEqualAndEqualSign(pow_op(INF, -0.5), 0.0)
+
+            # basic checks not covered by the special cases above
+            self.assertEqualAndEqualSign(pow_op(-2.0, -2.0), 0.25)
+            self.assertEqualAndEqualSign(pow_op(-2.0, -1.0), -0.5)
+            self.assertEqualAndEqualSign(pow_op(-2.0, -0.0), 1.0)
+            self.assertEqualAndEqualSign(pow_op(-2.0, 0.0), 1.0)
+            self.assertEqualAndEqualSign(pow_op(-2.0, 1.0), -2.0)
+            self.assertEqualAndEqualSign(pow_op(-2.0, 2.0), 4.0)
+            self.assertEqualAndEqualSign(pow_op(-1.0, -2.0), 1.0)
+            self.assertEqualAndEqualSign(pow_op(-1.0, -1.0), -1.0)
+            self.assertEqualAndEqualSign(pow_op(-1.0, -0.0), 1.0)
+            self.assertEqualAndEqualSign(pow_op(-1.0, 0.0), 1.0)
+            self.assertEqualAndEqualSign(pow_op(-1.0, 1.0), -1.0)
+            self.assertEqualAndEqualSign(pow_op(-1.0, 2.0), 1.0)
+            self.assertEqualAndEqualSign(pow_op(2.0, -2.0), 0.25)
+            self.assertEqualAndEqualSign(pow_op(2.0, -1.0), 0.5)
+            self.assertEqualAndEqualSign(pow_op(2.0, -0.0), 1.0)
+            self.assertEqualAndEqualSign(pow_op(2.0, 0.0), 1.0)
+            self.assertEqualAndEqualSign(pow_op(2.0, 1.0), 2.0)
+            self.assertEqualAndEqualSign(pow_op(2.0, 2.0), 4.0)
+
+            # 1 ** large and -1 ** large; some libms apparently
+            # have problems with these
+            self.assertEqualAndEqualSign(pow_op(1.0, -1e100), 1.0)
+            self.assertEqualAndEqualSign(pow_op(1.0, 1e100), 1.0)
+            self.assertEqualAndEqualSign(pow_op(-1.0, -1e100), 1.0)
+            self.assertEqualAndEqualSign(pow_op(-1.0, 1e100), 1.0)
+
+            # check sign for results that underflow to 0
+            self.assertEqualAndEqualSign(pow_op(-2.0, -2000.0), 0.0)
+            self.assertRaises(ValueError, pow_op, -2.0, -2000.5)
+            self.assertEqualAndEqualSign(pow_op(-2.0, -2001.0), -0.0)
+            self.assertEqualAndEqualSign(pow_op(2.0, -2000.0), 0.0)
+            self.assertEqualAndEqualSign(pow_op(2.0, -2000.5), 0.0)
+            self.assertEqualAndEqualSign(pow_op(2.0, -2001.0), 0.0)
+            self.assertEqualAndEqualSign(pow_op(-0.5, 2000.0), 0.0)
+            self.assertRaises(ValueError, pow_op, -0.5, 2000.5)
+            self.assertEqualAndEqualSign(pow_op(-0.5, 2001.0), -0.0)
+            self.assertEqualAndEqualSign(pow_op(0.5, 2000.0), 0.0)
+            self.assertEqualAndEqualSign(pow_op(0.5, 2000.5), 0.0)
+            self.assertEqualAndEqualSign(pow_op(0.5, 2001.0), 0.0)
+
+            # check we don't raise an exception for subnormal results,
+            # and validate signs.  Tests currently disabled, since
+            # they fail on systems where a subnormal result from pow
+            # is flushed to zero (e.g. Debian/ia64.)
+            #self.assertTrue(0.0 < pow_op(0.5, 1048) < 1e-315)
+            #self.assertTrue(0.0 < pow_op(-0.5, 1048) < 1e-315)
+            #self.assertTrue(0.0 < pow_op(0.5, 1047) < 1e-315)
+            #self.assertTrue(0.0 > pow_op(-0.5, 1047) > -1e-315)
+            #self.assertTrue(0.0 < pow_op(2.0, -1048) < 1e-315)
+            #self.assertTrue(0.0 < pow_op(-2.0, -1048) < 1e-315)
+            #self.assertTrue(0.0 < pow_op(2.0, -1047) < 1e-315)
+            #self.assertTrue(0.0 > pow_op(-2.0, -1047) > -1e-315)
+
+
 class FormatFunctionsTestCase(unittest.TestCase):
 
     def setUp(self):
diff --git a/Misc/NEWS b/Misc/NEWS
index 627ba07..3098505 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -12,6 +12,10 @@ What's New in Python 2.7 alpha 2?
 Core and Builtins
 -----------------
 
+- Issue #7534: Fix handling of IEEE specials (infinities, nans,
+  negative zero) in ** operator.  The behaviour now conforms to that
+  described in C99 Annex F.
+
 - Issue #7579: the msvcrt module now has docstrings for all its functions.
 
 - Issue #7413: Passing '\0' as the separator to datetime.datetime.isoformat()
diff --git a/Objects/floatobject.c b/Objects/floatobject.c
index 01e5825..d93d9f9 100644
--- a/Objects/floatobject.c
+++ b/Objects/floatobject.c
@@ -791,10 +791,15 @@ float_floor_div(PyObject *v, PyObject *w)
 	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 "
@@ -806,20 +811,56 @@ float_pow(PyObject *v, PyObject *w, PyObject *z)
 	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);
-	}
-	if (iv == 1.0) { /* 1**w is 1, even 1**inf and 1**nan */
-		return PyFloat_FromDouble(1.0);
+		/* use correct sign if iw is odd */
+		return PyFloat_FromDouble(iw_is_odd ? iv : 0.0);
 	}
+
 	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.
@@ -829,33 +870,41 @@ float_pow(PyObject *v, PyObject *w, PyObject *z)
 				"cannot be raised to a fractional power");
 			return NULL;
 		}
-		/* 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 **.
-		 */
-		 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.
+		 * bug.
 		 */
+		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.
@@ -867,6 +916,8 @@ float_pow(PyObject *v, PyObject *w, PyObject *z)
 	return PyFloat_FromDouble(ix);
 }
 
+#undef DOUBLE_IS_ODD_INTEGER
+
 static PyObject *
 float_neg(PyFloatObject *v)
 {