Using math.info to treat 0 denominators for IFDRational

Tests/test_file_tiff_metadata.py

@@ -302,7 +302,10 @@ def test_tagtype_on_zero_denominator(
 
     with Image.open(out) as reloaded:
         assert isinstance(reloaded, TiffImagePlugin.TiffImageFile)
-        assert math.isnan(reloaded.tag_v2[37380])
+        if expected == TiffTags.RATIONAL:
+            assert reloaded.tag_v2[37380] == math.inf
+        elif TiffTags.SIGNED_RATIONAL:
+            assert reloaded.tag_v2[37380] == -math.inf
 
 
 def test_undefined_zero(tmp_path: Path) -> None:

Tests/test_tiff_ifdrational.py

@@ -1,6 +1,7 @@
 from __future__ import annotations
 
 from fractions import Fraction
+import math
 from pathlib import Path
 
 import pytest
@@ -80,8 +81,14 @@ def test_ifd_rational_save(
     "numerator, denominator, expected_result",
     [
         (1, 1, 1.0),
-        (1, 0, float("nan")),
+        (1, 0, math.inf),
+        (-1, 0, -math.inf),
+        (0, 0, float("nan")),
     ],
 )
 def test_float_cast(numerator, denominator, expected_result):
-    float(IFDRational(numerator, denominator)) == expected_result
+    value = float(IFDRational(numerator, denominator))
+    if math.isnan(expected_result):
+        assert value
+    else:
+        assert value == expected_result

src/PIL/TiffImagePlugin.py

@@ -372,7 +372,12 @@ class IFDRational(Rational):
             self._denominator = denominator
 
         if denominator == 0:
+            if value == 0:
                 self._val = float("nan")
+            elif value > 0:
+                self._val = math.inf
+            else:
+                self._val = -math.inf
         elif denominator == 1:
             self._val = Fraction(value)
         elif int(value) == value:
@@ -691,7 +696,7 @@ class ImageFileDirectory_v2(_IFDv2Base):
                 if all(isinstance(v, IFDRational) for v in values):
                     for v in values:
                         assert isinstance(v, IFDRational)
-                        if v < 0 or (math.isnan(v) and float(v.numerator) < 0):
+                        if v < 0:
                             self.tagtype[tag] = TiffTags.SIGNED_RATIONAL
                             break
                     else: