gh-150318: Fix quantiles(method='exclusive') returning unsorted cut points for duplicate floats

When all data points are identical floats, the interpolation formula in the exclusive branch can produce results off by 1 ULP due to floating point rounding. Hence, adjacent cut points differ and the returned list violates the non-decreasing rule.

This short-circuits the interpolation, returning the data value directly instead.

Author: edvilme

Lib/statistics.py

@@ -1217,7 +1217,13 @@ def quantiles(data, *, n=4, method='exclusive'):
             j = i * m // n                               # rescale i to m/n
             j = 1 if j < 1 else ld-1 if j > ld-1 else j  # clamp to 1 .. ld-1
             delta = i*m - j*n                            # exact integer math
-            interpolated = (data[j - 1] * (n - delta) + data[j] * delta) / n
+            # When the endpoints are equal or delta is zero, avoid
+            # the interpolation formula which can be off by 1 ULP
+            # due to floating-point rounding
+            if (data[j - 1] == data[j]) or not delta:
+                interpolated = data[j - 1]
+            else:
+                interpolated = (data[j - 1] * (n - delta) + data[j] * delta) / n
             result.append(interpolated)
         return result
 

Lib/test/test_statistics.py

@@ -2652,6 +2652,24 @@ def test_equal_inputs(self):
             self.assertEqual(quantiles(data, method='inclusive'),
                             [10.0, 10.0, 10.0])
 
+    def test_monotonic_with_duplicate_floats(self):
+        quantiles = statistics.quantiles
+        for x in (3.141592653589793,  # irrational-ish
+                  1/3,                # repeating binary fraction
+                  0.1,                # non-exact decimal
+                  2.0,                # exact power of two
+                  1e300,              # large magnitude
+                  1e-300,             # small magnitude
+                  float.fromhex('0x1.fffffffffffffp+1023'),  # near max float
+                  sys.float_info.min, # smallest normal
+                  ):
+            for n in range(2, 20):
+                result = quantiles([x, x], n=n, method='exclusive')
+                self.assertEqual(result, sorted(result),
+                                 msg=f'x={x}, n={n}')
+                self.assertTrue(all(v == x for v in result),
+                                msg=f'x={x}, n={n}')
+
     def test_equal_sized_groups(self):
         quantiles = statistics.quantiles
         total = 10_000