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

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

2 files changed, 216 insertions, 2 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):