[benchmark] Round quantile idx to nearest or even

Explicitly use round-half-to-even rounding algorithm to match the behavior of numpy's quantile(interpolation='nearest') and quantile estimate type R-3, SAS-2. See:
https://en.wikipedia.org/wiki/Quantile#Estimating_quantiles_from_a_sample

Author: palimondo

benchmark/scripts/compare_perf_tests.py

@@ -34,6 +34,7 @@ class `ReportFormatter` creates the test comparison report in specified format.
 import sys
 from bisect import bisect, bisect_left, bisect_right
 from collections import namedtuple
+from decimal import Decimal, ROUND_HALF_EVEN
 from math import sqrt
 
 
@@ -141,24 +142,32 @@ def max(self):
         """Maximum sampled value."""
         return self.samples[-1].runtime
 
-    def _quantile_index(self, q, i):
-        """Return index of the element nearest to the i-th q-quantile."""
-        return int(round((self.count - 1) / float(q) * float(i)))
+    def quantile(self, q):
+        """Return runtime of a sample nearest to the quantile.
+
+        Explicitly uses round-half-to-even rounding algorithm to match the
+        behavior of numpy's quantile(interpolation='nearest') and quantile
+        estimate type R-3, SAS-2. See:
+        https://en.wikipedia.org/wiki/Quantile#Estimating_quantiles_from_a_sample
+        """
+        index = int(Decimal((self.count - 1) * Decimal(q))
+                    .quantize(0, ROUND_HALF_EVEN))
+        return self.samples[index].runtime
 
     @property
     def median(self):
         """Median sampled value."""
-        return self.samples[self._quantile_index(2, 1)].runtime
+        return self.quantile(0.5)
 
     @property
     def q1(self):
         """First Quartile (25th Percentile)."""
-        return self.samples[self._quantile_index(4, 1)].runtime
+        return self.quantile(0.25)
 
     @property
     def q3(self):
         """Third Quartile (75th Percentile)."""
-        return self.samples[self._quantile_index(4, 3)].runtime
+        return self.quantile(0.75)
 
     @property
     def iqr(self):

benchmark/scripts/test_compare_perf_tests.py

@@ -75,10 +75,10 @@ def test_computes_five_number_summary(self):
             self.samples, (1000, 1000, 1000, 1000, 1000))
         self.samples.add(Sample(2, 1, 1100))
         self.assertEqualFiveNumberSummary(
-            self.samples, (1000, 1000, 1100, 1100, 1100))
+            self.samples, (1000, 1000, 1000, 1100, 1100))
         self.samples.add(Sample(3, 1, 1050))
         self.assertEqualFiveNumberSummary(
-            self.samples, (1000, 1050, 1050, 1100, 1100))
+            self.samples, (1000, 1000, 1050, 1100, 1100))
         self.samples.add(Sample(4, 1, 1025))
         self.assertEqualFiveNumberSummary(
             self.samples, (1000, 1025, 1050, 1050, 1100))

benchmark/utils/DriverUtils.swift

@@ -32,8 +32,14 @@ struct BenchResults {
   }
 
   /// Return sample at index nearest to the `quantile`.
+  ///
+  /// Explicitly uses round-half-to-even rounding algorithm to match the
+  /// behavior of numpy's quantile(interpolation='nearest') and quantile
+  /// estimate type R-3, SAS-2. See:
+  /// https://en.wikipedia.org/wiki/Quantile#Estimating_quantiles_from_a_sample
   subscript(_ quantile: Double) -> T {
-    let index = Int((Double(samples.count - 1) * quantile).rounded())
+    let index = Int(
+      (Double(samples.count - 1) * quantile).rounded(.toNearestOrEven))
     return samples[index]
   }