MAINT: stats.kendalltau: avoid overflow (#18193)

scipy/stats/_stats_py.py

@@ -5820,9 +5820,10 @@ def kendalltau(x, y, initial_lexsort=None, nan_policy='propagate',
     def count_rank_tie(ranks):
         cnt = np.bincount(ranks).astype('int64', copy=False)
         cnt = cnt[cnt > 1]
-        return ((cnt * (cnt - 1) // 2).sum(),
-                (cnt * (cnt - 1.) * (cnt - 2)).sum(),
-                (cnt * (cnt - 1.) * (2*cnt + 5)).sum())
+        # Python ints to avoid overflow down the line
+        return (int((cnt * (cnt - 1) // 2).sum()),
+                int((cnt * (cnt - 1.) * (cnt - 2)).sum()),
+                int((cnt * (cnt - 1.) * (2*cnt + 5)).sum()))
 
     size = x.size
     perm = np.argsort(y)  # sort on y and convert y to dense ranks
@@ -5839,7 +5840,7 @@ def count_rank_tie(ranks):
     obs = np.r_[True, (x[1:] != x[:-1]) | (y[1:] != y[:-1]), True]
     cnt = np.diff(np.nonzero(obs)[0]).astype('int64', copy=False)
 
-    ntie = (cnt * (cnt - 1) // 2).sum()  # joint ties
+    ntie = int((cnt * (cnt - 1) // 2).sum())  # joint ties
     xtie, x0, x1 = count_rank_tie(x)     # ties in x, stats
     ytie, y0, y1 = count_rank_tie(y)     # ties in y, stats
 

scipy/stats/tests/test_stats.py

@@ -1368,6 +1368,24 @@ def test_kendalltau_dep_initial_lexsort():
         stats.kendalltau([], [], initial_lexsort=True)
 
 
+def test_kendalltau_gh18139_overflow():
+    # gh-18139 reported an overflow in `kendalltau` that appeared after
+    # SciPy 0.15.1. Check that this particular overflow does not occur.
+    # (Test would fail if warning were emitted.)
+    import random
+    random.seed(6272161)
+    classes = [1, 2, 3, 4, 5, 6, 7]
+    n_samples = 2 * 10 ** 5
+    x = random.choices(classes, k=n_samples)
+    y = random.choices(classes, k=n_samples)
+    res = stats.kendalltau(x, y)
+    # Reference value from SciPy 0.15.1
+    assert_allclose(res.statistic, 0.0011816493905730343)
+    # Reference p-value from `permutation_test` w/ n_resamples=9999 (default).
+    # Expected to be accurate to at least two digits.
+    assert_allclose(res.pvalue, 0.4894, atol=2e-3)
+
+
 class TestKendallTauAlternative:
     def test_kendalltau_alternative_asymptotic(self):
         # Test alternative parameter, asymptotic method (due to tie)