Avoid underflow in exponential wait threshold

releasenotes/notes/fix-exponential-multiplier-underflow-4fd1d6d6b9c8e2a1.yaml

@@ -0,0 +1,5 @@
+---
+fixes:
+  - |
+    Prevent ``wait_exponential`` from raising ``ValueError`` when dividing the
+    configured maximum wait by a large multiplier underflows to zero.

tenacity/wait.py

@@ -208,7 +208,9 @@ def __call__(self, retry_state: "RetryCallState") -> float:
             and self.max > 0
             and self.exp_base > 1
             and math.isfinite(self.max)
-            and exponent > math.log(self.max / self.multiplier, self.exp_base)
+            and exponent
+            > math.log(self.max, self.exp_base)
+            - math.log(self.multiplier, self.exp_base)
         ):
             return max(max(0, self.min), self.max)
         try:

tests/test_tenacity.py

@@ -367,6 +367,10 @@ def __pow__(self, exponent: float, modulo: int | None = None) -> float:
         r = Retrying(wait=tenacity.wait_exponential(max=40, exp_base=ExplodingPower(2)))
         self.assertEqual(r.wait(make_retry_state(50, 0)), 40)
 
+    def test_exponential_caps_when_max_multiplier_ratio_underflows(self) -> None:
+        r = Retrying(wait=tenacity.wait_exponential(multiplier=1e300, max=1e-100))
+        self.assertEqual(r.wait(make_retry_state(1, 0)), 1e-100)
+
     def test_exponential_with_min_wait(self) -> None:
         r = Retrying(wait=tenacity.wait_exponential(min=20))
         self.assertEqual(r.wait(make_retry_state(1, 0)), 20)