MAINT: stats.randint.pmf: fix zero PMF values within the support (scipy#21353)

* TST: stats.randint: add test for surprising underflow

* MAINT: stats.randint.pmf: fix zero values within the support

Author: mdhaber

scipy/stats/_discrete_distns.py

@@ -1209,7 +1209,7 @@ def _get_support(self, low, high):
 
     def _pmf(self, k, low, high):
         # randint.pmf(k) = 1./(high - low)
-        p = np.ones_like(k) / (high - low)
+        p = np.ones_like(k) / (np.asarray(high, dtype=np.int64) - low)
         return np.where((k >= low) & (k < high), p, 0.)
 
     def _cdf(self, x, low, high):

scipy/stats/tests/test_discrete_distns.py

@@ -646,3 +646,15 @@ def test_gh20692(self):
         pmf = dist.pmf(k)
         pmf_k_int32 = dist.pmf(k_int32)
         assert_equal(pmf, pmf_k_int32)
+
+
+class TestRandInt:
+    def test_gh19759(self):
+        # test zero PMF values within the support reported by gh-19759
+        a = -354
+        max_range = abs(a)
+        all_b_1 = [a + 2 ** 31 + i for i in range(max_range)]
+        res = randint.pmf(325, a, all_b_1)
+        assert (res > 0).all()
+        ref = 1 / (np.asarray(all_b_1, dtype=np.float64) - a)
+        assert_allclose(res, ref)