Add shift-first multiply helper and document benchmarks

PerfectNumbers.Core/HeuristicArithmetic.cs

@@ -0,0 +1,48 @@
+using System;
+using System.Runtime.CompilerServices;
+
+namespace PerfectNumbers.Core;
+
+internal static class HeuristicArithmetic
+{
+    [MethodImpl(MethodImplOptions.AggressiveInlining)]
+    public static ulong MultiplyShiftRight(ulong value, ulong multiplier, int shift)
+    {
+        if (shift < 0)
+        {
+            throw new ArgumentOutOfRangeException(nameof(shift), "Shift must be non-negative.");
+        }
+
+        UInt128 product = (UInt128)value * multiplier;
+        return (ulong)(product >> shift);
+    }
+
+    [MethodImpl(MethodImplOptions.AggressiveInlining)]
+    public static ulong MultiplyShiftRightShiftFirst(ulong value, ulong multiplier, int shift)
+    {
+        if (shift < 0)
+        {
+            throw new ArgumentOutOfRangeException(nameof(shift), "Shift must be non-negative.");
+        }
+
+        if (shift == 0)
+        {
+            return MultiplyShiftRight(value, multiplier, 0);
+        }
+
+        if (shift >= 64)
+        {
+            return 0UL;
+        }
+
+        ulong high = value >> shift;
+        ulong mask = (1UL << shift) - 1UL;
+        ulong low = value & mask;
+
+        UInt128 highContribution = (UInt128)high * multiplier;
+        UInt128 lowContribution = (UInt128)low * multiplier;
+
+        UInt128 combined = highContribution + (lowContribution >> shift);
+        return (ulong)combined;
+    }
+}