Add heuristic prime sieves for cached divisor sequences

PerfectNumbers.Core/HeuristicPrimeSieves.cs

@@ -0,0 +1,209 @@
+using System;
+
+namespace PerfectNumbers.Core;
+
+public static class HeuristicPrimeSieves
+{
+    private const int SieveLength = PerfectNumberConstants.MaxQForDivisorCycles;
+    private const int Wheel210 = 210;
+
+    private static readonly int[] GroupAConstants = [3, 7, 11, 13];
+    private static readonly int[] GroupAIncrementPattern = [20, 10];
+
+    private static readonly ushort[] GroupBResiduesEnding1 = [1, 11, 31, 41, 61, 71, 101, 121, 131, 151, 181, 191];
+    private static readonly ushort[] GroupBResiduesEnding3 = [13, 23, 43, 53, 73, 83, 103, 113, 143, 163, 173, 193];
+    private static readonly ushort[] GroupBResiduesEnding7 = [17, 37, 47, 67, 97, 107, 127, 137, 157, 167, 187, 197];
+    private static readonly ushort[] GroupBResiduesEnding9 = [19, 29, 59, 79, 89, 109, 139, 149, 169, 179, 199, 209];
+
+    private static int[]? s_groupADivisors;
+    private static ulong[]? s_groupADivisorSquares;
+
+    private static int[]? s_groupBDivisorsEnding1;
+    private static ulong[]? s_groupBDivisorSquaresEnding1;
+
+    private static int[]? s_groupBDivisorsEnding3;
+    private static ulong[]? s_groupBDivisorSquaresEnding3;
+
+    private static int[]? s_groupBDivisorsEnding7;
+    private static ulong[]? s_groupBDivisorSquaresEnding7;
+
+    private static int[]? s_groupBDivisorsEnding9;
+    private static ulong[]? s_groupBDivisorSquaresEnding9;
+
+    private static readonly object InitLock = new();
+
+    public static ReadOnlySpan<int> GroupADivisors
+    {
+        get
+        {
+            EnsureGroupAInitialized();
+            return s_groupADivisors!;
+        }
+    }
+
+    public static ReadOnlySpan<ulong> GroupADivisorSquares
+    {
+        get
+        {
+            EnsureGroupAInitialized();
+            return s_groupADivisorSquares!;
+        }
+    }
+
+    public static ReadOnlySpan<int> GroupBDivisorsEnding1
+    {
+        get
+        {
+            EnsureGroupBInitialized(ref s_groupBDivisorsEnding1, ref s_groupBDivisorSquaresEnding1, GroupBResiduesEnding1);
+            return s_groupBDivisorsEnding1!;
+        }
+    }
+
+    public static ReadOnlySpan<ulong> GroupBDivisorSquaresEnding1
+    {
+        get
+        {
+            EnsureGroupBInitialized(ref s_groupBDivisorsEnding1, ref s_groupBDivisorSquaresEnding1, GroupBResiduesEnding1);
+            return s_groupBDivisorSquaresEnding1!;
+        }
+    }
+
+    public static ReadOnlySpan<int> GroupBDivisorsEnding3
+    {
+        get
+        {
+            EnsureGroupBInitialized(ref s_groupBDivisorsEnding3, ref s_groupBDivisorSquaresEnding3, GroupBResiduesEnding3);
+            return s_groupBDivisorsEnding3!;
+        }
+    }
+
+    public static ReadOnlySpan<ulong> GroupBDivisorSquaresEnding3
+    {
+        get
+        {
+            EnsureGroupBInitialized(ref s_groupBDivisorsEnding3, ref s_groupBDivisorSquaresEnding3, GroupBResiduesEnding3);
+            return s_groupBDivisorSquaresEnding3!;
+        }
+    }
+
+    public static ReadOnlySpan<int> GroupBDivisorsEnding7
+    {
+        get
+        {
+            EnsureGroupBInitialized(ref s_groupBDivisorsEnding7, ref s_groupBDivisorSquaresEnding7, GroupBResiduesEnding7);
+            return s_groupBDivisorsEnding7!;
+        }
+    }
+
+    public static ReadOnlySpan<ulong> GroupBDivisorSquaresEnding7
+    {
+        get
+        {
+            EnsureGroupBInitialized(ref s_groupBDivisorsEnding7, ref s_groupBDivisorSquaresEnding7, GroupBResiduesEnding7);
+            return s_groupBDivisorSquaresEnding7!;
+        }
+    }
+
+    public static ReadOnlySpan<int> GroupBDivisorsEnding9
+    {
+        get
+        {
+            EnsureGroupBInitialized(ref s_groupBDivisorsEnding9, ref s_groupBDivisorSquaresEnding9, GroupBResiduesEnding9);
+            return s_groupBDivisorsEnding9!;
+        }
+    }
+
+    public static ReadOnlySpan<ulong> GroupBDivisorSquaresEnding9
+    {
+        get
+        {
+            EnsureGroupBInitialized(ref s_groupBDivisorsEnding9, ref s_groupBDivisorSquaresEnding9, GroupBResiduesEnding9);
+            return s_groupBDivisorSquaresEnding9!;
+        }
+    }
+
+    private static void EnsureGroupAInitialized()
+    {
+        if (s_groupADivisors is not null)
+        {
+            return;
+        }
+
+        lock (InitLock)
+        {
+            if (s_groupADivisors is not null)
+            {
+                return;
+            }
+
+            var divisors = new int[SieveLength];
+            var squares = new ulong[SieveLength];
+
+            int index = 0;
+            for (; index < GroupAConstants.Length && index < divisors.Length; index++)
+            {
+                int value = GroupAConstants[index];
+                divisors[index] = value;
+                squares[index] = (ulong)value * (ulong)value;
+            }
+
+            int candidate = 23;
+            int incrementIndex = 0;
+            while (index < divisors.Length)
+            {
+                divisors[index] = candidate;
+                squares[index] = (ulong)candidate * (ulong)candidate;
+
+                candidate += GroupAIncrementPattern[incrementIndex];
+                incrementIndex ^= 1;
+                index++;
+            }
+
+            s_groupADivisors = divisors;
+            s_groupADivisorSquares = squares;
+        }
+    }
+
+    private static void EnsureGroupBInitialized(ref int[]? divisorsField, ref ulong[]? squaresField, ReadOnlySpan<ushort> residues)
+    {
+        if (divisorsField is not null)
+        {
+            return;
+        }
+
+        lock (InitLock)
+        {
+            if (divisorsField is not null)
+            {
+                return;
+            }
+
+            var divisors = new int[SieveLength];
+            var squares = new ulong[SieveLength];
+
+            int index = 0;
+            ulong baseValue = 0UL;
+
+            while (index < divisors.Length)
+            {
+                for (int i = 0; i < residues.Length && index < divisors.Length; i++)
+                {
+                    ulong candidate = baseValue + residues[i];
+                    if (candidate <= 13UL)
+                    {
+                        continue;
+                    }
+
+                    divisors[index] = (int)candidate;
+                    squares[index] = candidate * candidate;
+                    index++;
+                }
+
+                baseValue += (ulong)Wheel210;
+            }
+
+            divisorsField = divisors;
+            squaresField = squares;
+        }
+    }
+}