the first optimization round

2026-09-14 13:58:04 +04:00
parent cb2524980d
commit 08036a31d5
12 changed files with 1316 additions and 49 deletions
@@ -89,6 +89,38 @@ public class DoubleDoubleRepresentationTests
        (value != DoubleDouble.NaN).ShouldBeTrue();
    }

+    [Fact]
+    public void FiniteNormalizationPreservesOrderingResidualsAndZeroSigns()
+    {
+        // Exact dyadic sums, independent of the public factory. Include both
+        // magnitude orders, cancellation, subnormals, and signed zero lows.
+        double unit = Math.ScaleB(1.0, 970);
+        (double High, double Low, double ExpectedHigh, double ExpectedLow)[] cases =
+        [
+            (-0.0, 0.0, -0.0, 0.0), (-0.0, -0.0, -0.0, 0.0),
+            (0.0, -0.0, 0.0, 0.0), (1.0, -1.0, 0.0, 0.0),
+            (-1.0, 1.0, 0.0, 0.0), (double.Epsilon, -double.Epsilon, 0.0, 0.0),
+            (double.Epsilon, double.Epsilon, 2 * double.Epsilon, 0.0),
+            (0.0, double.Epsilon, double.Epsilon, 0.0),
+            (double.Epsilon, -1.0, -1.0, double.Epsilon),
+            (1.0, double.Epsilon, 1.0, double.Epsilon),
+            (double.Epsilon, 1.0, 1.0, double.Epsilon),
+            (-1.0, -double.Epsilon, -1.0, -double.Epsilon),
+            (-double.Epsilon, -1.0, -1.0, -double.Epsilon),
+            (double.MaxValue, 0.0, double.MaxValue, 0.0),
+            // MaxValue - 3*2^970 = (MaxValue - 2^971) - 2^970.
+            // An unordered TwoSum would overflow an intermediate in the reversed case.
+            (double.MaxValue, -3.0 * unit, Math.BitDecrement(double.MaxValue), -unit),
+            (-3.0 * unit, double.MaxValue, Math.BitDecrement(double.MaxValue), -unit)
+        ];
+        foreach ((double high, double low, double expectedHigh, double expectedLow) in cases)
+        {
+            DoubleDouble actual = PreciseMathHelper.NormalizeFinite(high, low);
+            BitConverter.DoubleToInt64Bits(actual.High).ShouldBe(BitConverter.DoubleToInt64Bits(expectedHigh));
+            BitConverter.DoubleToInt64Bits(actual.Low).ShouldBe(BitConverter.DoubleToInt64Bits(expectedLow));
+        }
+    }
+
    [Fact]
    public void ZeroSignsArePreservedButEqual()
    {