bpo-44339: Fix math.pow corner case to comply with IEEE 754 (GH-26606)

Change the behaviour of `math.pow(0.0, -math.inf)` and `math.pow(-0.0, -math.inf)` to return positive infinity instead of raising `ValueError`. This makes `math.pow` consistent with the built-in `pow` (and the `**` operator) for this particular special case, and brings the `math.pow` special-case handling into compliance with IEEE 754.

Doc/library/math.rst

@@ -409,7 +409,7 @@ Power and logarithmic functions
 .. function:: pow(x, y)
 
    Return ``x`` raised to the power ``y``.  Exceptional cases follow
-   Annex 'F' of the C99 standard as far as possible.  In particular,
+   the IEEE 754 standard as far as possible.  In particular,
    ``pow(1.0, x)`` and ``pow(x, 0.0)`` always return ``1.0``, even
    when ``x`` is a zero or a NaN.  If both ``x`` and ``y`` are finite,
    ``x`` is negative, and ``y`` is not an integer then ``pow(x, y)``
@@ -419,6 +419,11 @@ Power and logarithmic functions
    its arguments to type :class:`float`.  Use ``**`` or the built-in
    :func:`pow` function for computing exact integer powers.
 
+   .. versionchanged:: 3.11
+      The special cases ``pow(0.0, -inf)`` and ``pow(-0.0, -inf)`` were
+      changed to return ``inf`` instead of raising :exc:`ValueError`,
+      for consistency with IEEE 754.
+
 
 .. function:: sqrt(x)
 

Doc/whatsnew/3.11.rst

@@ -96,8 +96,14 @@ string.  (Contributed by Sergey B Kirpichev in :issue:`44258`.)
 math
 ----
 
-Add :func:`math.cbrt()`: return the cube root of x.
+* Add :func:`math.cbrt`: return the cube root of x.
-(Contributed by Ajith Ramachandran in :issue:`44357`.)
+  (Contributed by Ajith Ramachandran in :issue:`44357`.)
+
+* The behaviour of two :func:`math.pow` corner cases was changed, for
+  consistency with the IEEE 754 specification. The operations
+  ``math.pow(0.0, -math.inf)`` and ``math.pow(-0.0, -math.inf)`` now return
+  ``inf``. Previously they raised :exc:`ValueError`. (Contributed by Mark
+  Dickinson in :issue:`44339`.)
 
 
 Removed

Lib/test/ieee754.txt

@@ -104,7 +104,7 @@ infinity and NaN.
 1.0
 
 The power of 0 raised to x is defined as 0, if x is positive. Negative
-values are a domain error or zero division error and NaN result in a
+finite values are a domain error or zero division error and NaN result in a
 silent NaN.
 
 >>> pow(0, 0)
@@ -112,9 +112,7 @@ silent NaN.
 >>> pow(0, INF)
 0.0
 >>> pow(0, -INF)
-Traceback (most recent call last):
+inf
-...
-ValueError: math domain error
 >>> 0 ** -1
 Traceback (most recent call last):
 ...

Lib/test/test_math.py

@@ -1230,7 +1230,7 @@ class MathTests(unittest.TestCase):
         self.assertRaises(ValueError, math.pow, 0., -2.)
         self.assertRaises(ValueError, math.pow, 0., -2.3)
         self.assertRaises(ValueError, math.pow, 0., -3.)
-        self.assertRaises(ValueError, math.pow, 0., NINF)
+        self.assertEqual(math.pow(0., NINF), INF)
         self.assertTrue(math.isnan(math.pow(0., NAN)))
 
         # pow(INF, x)
@@ -1256,7 +1256,7 @@ class MathTests(unittest.TestCase):
         self.assertRaises(ValueError, math.pow, -0., -2.)
         self.assertRaises(ValueError, math.pow, -0., -2.3)
         self.assertRaises(ValueError, math.pow, -0., -3.)
-        self.assertRaises(ValueError, math.pow, -0., NINF)
+        self.assertEqual(math.pow(-0., NINF), INF)
         self.assertTrue(math.isnan(math.pow(-0., NAN)))
 
         # pow(NINF, x)

Misc/NEWS.d/next/Library/2021-06-08-17-47-38.bpo-44339.9JwMSc.rst

@@ -0,0 +1,3 @@
+Change ``math.pow(±0.0, -math.inf)`` to return ``inf`` instead of raising
+``ValueError``. This brings the special-case handling of ``math.pow`` into
+compliance with the IEEE 754 standard.

Modules/mathmodule.c

@@ -2810,8 +2810,6 @@ math_pow_impl(PyObject *module, double x, double y)
                 r = y;
             else if (y < 0. && fabs(x) < 1.0) {
                 r = -y; /* result is +inf */
-                if (x == 0.) /* 0**-inf: divide-by-zero */
-                    errno = EDOM;
             }
             else
                 r = 0.;