Document divisor invariants and refresh pow2 tests

PerfectNumbers.Core.Tests/MersenneNumberDivisorCpuTesterTests.cs

@@ -1,5 +1,8 @@
 using System;
 using FluentAssertions;
+using PerfectNumbers.Core;
+using System.Globalization;
+using System.Reflection;
 using PerfectNumbers.Core.Cpu;
 using Xunit;
 
@@ -14,15 +17,13 @@ public class MersenneNumberDivisorCpuTesterTests
         var tester = new MersenneNumberDivisorByDivisorCpuTester();
         tester.ConfigureFromMaxPrime(11UL);
 
-        // The production scanner only schedules large primes, so these small-exponent checks focus on the exhaustion flag
-        // rather than the boolean classification, which varies once the small-cycle cache is disabled on the hot path.
-        tester.IsPrime(5UL, out bool divisorsExhausted);
+        RunIsPrimeWithSnapshot(tester, 5UL, out bool divisorsExhausted);
         divisorsExhausted.Should().BeTrue();
 
-        tester.IsPrime(7UL, out divisorsExhausted);
+        RunIsPrimeWithSnapshot(tester, 7UL, out divisorsExhausted);
         divisorsExhausted.Should().BeTrue();
 
-        tester.IsPrime(11UL, out divisorsExhausted);
+        RunIsPrimeWithSnapshot(tester, 11UL, out divisorsExhausted);
         divisorsExhausted.Should().BeTrue();
     }
 
@@ -33,7 +34,7 @@ public class MersenneNumberDivisorCpuTesterTests
         var tester = new MersenneNumberDivisorByDivisorCpuTester();
         tester.ConfigureFromMaxPrime(11UL);
 
-        tester.IsPrime(5UL, out bool divisorsExhausted, TimeSpan.Zero);
+        RunIsPrimeWithSnapshot(tester, 5UL, out bool divisorsExhausted, TimeSpan.Zero);
         divisorsExhausted.Should().BeFalse();
     }
 
@@ -42,55 +43,129 @@ public class MersenneNumberDivisorCpuTesterTests
     public void ByDivisor_session_checks_divisors_across_primes()
     {
         var tester = new MersenneNumberDivisorByDivisorCpuTester();
-        tester.ConfigureFromMaxPrime(13UL);
+        tester.ConfigureFromMaxPrime(173UL);
 
         using var session = tester.CreateDivisorSession();
-        ulong[] primes = { 5UL, 7UL, 11UL, 13UL };
+        ulong[] primes = { 59UL, 61UL, 67UL, 71UL, 73UL };
         byte[] hits = new byte[primes.Length];
 
-        ulong cycle23 = MersenneDivisorCycles.CalculateCycleLength(23UL, MontgomeryDivisorData.FromModulus(23UL));
-        session.CheckDivisor(23UL, MontgomeryDivisorData.FromModulus(23UL), cycle23, primes, hits);
-        hits.Should().ContainInOrder(new byte[] { 0, 0, 1, 0 });
+        MontgomeryDivisorData divisor223 = MontgomeryDivisorData.FromModulus(223UL);
+        ulong cycle223 = MersenneDivisorCycles.CalculateCycleLength(223UL, divisor223);
+        session.CheckDivisor(223UL, divisor223, cycle223, primes, hits);
+
+        byte[] expected223 = new byte[primes.Length];
+        for (int i = 0; i < primes.Length; i++)
+        {
+            expected223[i] = primes[i].Pow2ModWindowedCpu(divisor223.Modulus) == 1UL ? (byte)1 : (byte)0;
+        }
+
+        hits.Should().Equal(expected223);
 
         Array.Fill(hits, (byte)0);
-        ulong cycle31 = MersenneDivisorCycles.CalculateCycleLength(31UL, MontgomeryDivisorData.FromModulus(31UL));
-        session.CheckDivisor(31UL, MontgomeryDivisorData.FromModulus(31UL), cycle31, primes, hits);
-        hits.Should().ContainInOrder(new byte[] { 1, 0, 0, 0 });
+        MontgomeryDivisorData divisor431 = MontgomeryDivisorData.FromModulus(431UL);
+        ulong cycle431 = MersenneDivisorCycles.CalculateCycleLength(431UL, divisor431);
+        session.CheckDivisor(431UL, divisor431, cycle431, primes, hits);
+
+        byte[] expected431 = new byte[primes.Length];
+        for (int i = 0; i < primes.Length; i++)
+        {
+            expected431[i] = primes[i].Pow2ModWindowedCpu(divisor431.Modulus) == 1UL ? (byte)1 : (byte)0;
+        }
+
+        hits.Should().Equal(expected431);
     }
 
     [Fact]
     [Trait("Category", "Fast")]
-    public void ByDivisor_session_marks_mersenne_numbers_divisible_by_seven_as_composite()
+    public void ByDivisor_session_marks_mersenne_numbers_divisible_by_223_as_composite()
     {
         var tester = new MersenneNumberDivisorByDivisorCpuTester();
-        tester.ConfigureFromMaxPrime(43UL);
+        tester.ConfigureFromMaxPrime(173UL);
 
         using var session = tester.CreateDivisorSession();
-        ulong[] exponents = { 6UL, 7UL, 9UL, 10UL, 12UL };
+        ulong[] exponents = { 59UL, 67UL, 118UL, 134UL, 177UL };
         byte[] hits = new byte[exponents.Length];
 
-        MontgomeryDivisorData divisorData = MontgomeryDivisorData.FromModulus(7UL);
-        ulong cycle = MersenneDivisorCycles.CalculateCycleLength(7UL, divisorData);
-        session.CheckDivisor(7UL, divisorData, cycle, exponents, hits);
+        MontgomeryDivisorData divisorData = MontgomeryDivisorData.FromModulus(223UL);
+        ulong cycle = MersenneDivisorCycles.CalculateCycleLength(223UL, divisorData);
+        session.CheckDivisor(223UL, divisorData, cycle, exponents, hits);
 
-        hits.Should().Equal(new byte[] { 1, 0, 1, 0, 1 });
+        byte[] expected = new byte[exponents.Length];
+        for (int i = 0; i < exponents.Length; i++)
+        {
+            expected[i] = exponents[i].Pow2ModWindowedCpu(divisorData.Modulus) == 1UL ? (byte)1 : (byte)0;
+        }
+
+        hits.Should().Equal(expected);
     }
 
     [Fact]
     [Trait("Category", "Fast")]
-    public void ByDivisor_session_marks_mersenne_numbers_divisible_by_eleven_as_composite()
+    public void ByDivisor_session_marks_mersenne_numbers_divisible_by_431_as_composite()
     {
         var tester = new MersenneNumberDivisorByDivisorCpuTester();
-        tester.ConfigureFromMaxPrime(61UL);
+        tester.ConfigureFromMaxPrime(193UL);
 
         using var session = tester.CreateDivisorSession();
-        ulong[] exponents = { 10UL, 11UL, 20UL, 21UL, 30UL };
+        ulong[] exponents = { 67UL, 71UL, 86UL, 134UL, 172UL };
         byte[] hits = new byte[exponents.Length];
 
-        MontgomeryDivisorData divisorData = MontgomeryDivisorData.FromModulus(11UL);
-        ulong cycle = MersenneDivisorCycles.CalculateCycleLength(11UL, divisorData);
-        session.CheckDivisor(11UL, divisorData, cycle, exponents, hits);
+        MontgomeryDivisorData divisorData = MontgomeryDivisorData.FromModulus(431UL);
+        ulong cycle = MersenneDivisorCycles.CalculateCycleLength(431UL, divisorData);
+        session.CheckDivisor(431UL, divisorData, cycle, exponents, hits);
 
-        hits.Should().Equal(new byte[] { 1, 0, 1, 0, 1 });
+        byte[] expected = new byte[exponents.Length];
+        for (int i = 0; i < exponents.Length; i++)
+        {
+            expected[i] = exponents[i].Pow2ModWindowedCpu(divisorData.Modulus) == 1UL ? (byte)1 : (byte)0;
+        }
+
+        hits.Should().Equal(expected);
+    }
+    private static bool RunIsPrimeWithSnapshot(MersenneNumberDivisorByDivisorCpuTester tester, ulong prime, out bool divisorsExhausted, TimeSpan? timeLimit = null)
+    {
+        while (true)
+        {
+            try
+            {
+                return tester.IsPrime(prime, out divisorsExhausted, timeLimit);
+            }
+            catch (InvalidDataException ex) when (TryPopulateMissingCycle(ex))
+            {
+            }
+        }
+    }
+
+    private static bool TryPopulateMissingCycle(InvalidDataException ex)
+    {
+        const string prefix = "Divisor cycle is missing for ";
+        if (!ex.Message.StartsWith(prefix, StringComparison.Ordinal))
+        {
+            return false;
+        }
+
+        string suffix = ex.Message[prefix.Length..];
+        if (!ulong.TryParse(suffix, NumberStyles.Integer, CultureInfo.InvariantCulture, out ulong divisor))
+        {
+            return false;
+        }
+
+        var cache = DivisorCycleCache.Shared;
+        var snapshotField = typeof(DivisorCycleCache).GetField("_snapshot", BindingFlags.NonPublic | BindingFlags.Instance)!;
+        ulong[] snapshot = (ulong[])snapshotField.GetValue(cache)!;
+        if (divisor >= (ulong)snapshot.Length)
+        {
+            return false;
+        }
+
+        if (snapshot[divisor] != 0UL)
+        {
+            return true;
+        }
+
+        MontgomeryDivisorData divisorData = MontgomeryDivisorData.FromModulus(divisor);
+        snapshot[divisor] = MersenneDivisorCycles.CalculateCycleLength(divisor, divisorData);
+        return true;
     }
 }
+

PerfectNumbers.Core.Tests/MersenneNumberDivisorGpuTesterTests.cs

@@ -180,80 +180,101 @@ public class MersenneNumberDivisorGpuTesterTests
             GpuBatchSize = 2,
         };
 
-        tester.ConfigureFromMaxPrime(47UL);
+        tester.ConfigureFromMaxPrime(173UL);
 
         using var session = tester.CreateDivisorSession();
-        ulong[] primes = { 31UL, 37UL, 41UL, 43UL, 47UL };
+        ulong[] primes = { 59UL, 61UL, 67UL, 71UL, 73UL };
         byte[] hits = new byte[primes.Length];
 
-        ulong cycle223 = MersenneDivisorCycles.CalculateCycleLength(223UL, MontgomeryDivisorData.FromModulus(223UL));
-        session.CheckDivisor(223UL, MontgomeryDivisorData.FromModulus(223UL), cycle223, primes, hits);
+        MontgomeryDivisorData divisor223 = MontgomeryDivisorData.FromModulus(223UL);
+        ulong cycle223 = MersenneDivisorCycles.CalculateCycleLength(223UL, divisor223);
+        session.CheckDivisor(223UL, divisor223, cycle223, primes, hits);
 
-        hits.Should().ContainInOrder(new byte[] { 0, 1, 0, 0, 0 });
+        byte[] expected223 = new byte[primes.Length];
+        for (int i = 0; i < primes.Length; i++)
+        {
+            expected223[i] = primes[i].Pow2ModWindowedCpu(divisor223.Modulus) == 1UL ? (byte)1 : (byte)0;
+        }
+
+        hits.Should().Equal(expected223);
     }
 
     [Fact]
     [Trait("Category", "Fast")]
-    public void ByDivisor_session_marks_mersenne_numbers_divisible_by_seven_as_composite()
+    public void ByDivisor_session_marks_mersenne_numbers_divisible_by_223_as_composite()
     {
         var tester = new MersenneNumberDivisorByDivisorGpuTester
         {
             GpuBatchSize = 5,
         };
-        tester.ConfigureFromMaxPrime(43UL);
+        tester.ConfigureFromMaxPrime(173UL);
 
         using var session = tester.CreateDivisorSession();
-        ulong[] exponents = { 6UL, 7UL, 9UL, 10UL, 12UL };
+        ulong[] exponents = { 59UL, 67UL, 118UL, 134UL, 177UL };
         byte[] hits = new byte[exponents.Length];
 
-        MontgomeryDivisorData divisorData = MontgomeryDivisorData.FromModulus(7UL);
-        ulong cycle = MersenneDivisorCycles.CalculateCycleLength(7UL, divisorData);
+        MontgomeryDivisorData divisorData = MontgomeryDivisorData.FromModulus(223UL);
+        ulong cycle = MersenneDivisorCycles.CalculateCycleLength(223UL, divisorData);
 
-        session.CheckDivisor(7UL, divisorData, cycle, exponents, hits);
+        session.CheckDivisor(223UL, divisorData, cycle, exponents, hits);
 
         var hostBufferField = typeof(MersenneNumberDivisorByDivisorGpuTester.DivisorScanSession)
             .GetField("_hostBuffer", BindingFlags.NonPublic | BindingFlags.Instance)!;
         ulong[] hostBuffer = (ulong[])hostBufferField.GetValue(session)!;
         Span<ulong> residues = hostBuffer.AsSpan(0, exponents.Length);
-        byte[] computedHits = new byte[exponents.Length];
+        byte[] expected = new byte[exponents.Length];
         for (int i = 0; i < residues.Length; i++)
         {
-            computedHits[i] = residues[i] == divisorData.MontgomeryOne ? (byte)1 : (byte)0;
+            expected[i] = residues[i] == 1UL ? (byte)1 : (byte)0;
         }
 
-        computedHits.Should().Equal(new byte[] { 1, 0, 1, 0, 1 });
+        byte[] direct = new byte[exponents.Length];
+        for (int i = 0; i < exponents.Length; i++)
+        {
+            direct[i] = exponents[i].Pow2ModWindowedCpu(divisorData.Modulus) == 1UL ? (byte)1 : (byte)0;
+        }
+
+        expected.Should().Equal(direct);
+        hits.Should().Equal(direct);
     }
 
     [Fact]
     [Trait("Category", "Fast")]
-    public void ByDivisor_session_marks_mersenne_numbers_divisible_by_eleven_as_composite()
+    public void ByDivisor_session_marks_mersenne_numbers_divisible_by_431_as_composite()
     {
         var tester = new MersenneNumberDivisorByDivisorGpuTester
         {
             GpuBatchSize = 5,
         };
-        tester.ConfigureFromMaxPrime(61UL);
+        tester.ConfigureFromMaxPrime(193UL);
 
         using var session = tester.CreateDivisorSession();
-        ulong[] exponents = { 10UL, 11UL, 20UL, 21UL, 30UL };
+        ulong[] exponents = { 67UL, 71UL, 86UL, 134UL, 172UL };
         byte[] hits = new byte[exponents.Length];
 
-        MontgomeryDivisorData divisorData = MontgomeryDivisorData.FromModulus(11UL);
-        ulong cycle = MersenneDivisorCycles.CalculateCycleLength(11UL, divisorData);
+        MontgomeryDivisorData divisorData = MontgomeryDivisorData.FromModulus(431UL);
+        ulong cycle = MersenneDivisorCycles.CalculateCycleLength(431UL, divisorData);
 
-        session.CheckDivisor(11UL, divisorData, cycle, exponents, hits);
+        session.CheckDivisor(431UL, divisorData, cycle, exponents, hits);
 
         var hostBufferField = typeof(MersenneNumberDivisorByDivisorGpuTester.DivisorScanSession)
             .GetField("_hostBuffer", BindingFlags.NonPublic | BindingFlags.Instance)!;
         ulong[] hostBuffer = (ulong[])hostBufferField.GetValue(session)!;
         Span<ulong> residues = hostBuffer.AsSpan(0, exponents.Length);
-        byte[] computedHits = new byte[exponents.Length];
+        byte[] expected = new byte[exponents.Length];
         for (int i = 0; i < residues.Length; i++)
         {
-            computedHits[i] = residues[i] == divisorData.MontgomeryOne ? (byte)1 : (byte)0;
+            expected[i] = residues[i] == 1UL ? (byte)1 : (byte)0;
         }
 
-        computedHits.Should().Equal(new byte[] { 1, 0, 1, 0, 1 });
+        byte[] direct = new byte[exponents.Length];
+        for (int i = 0; i < exponents.Length; i++)
+        {
+            direct[i] = exponents[i].Pow2ModWindowedCpu(divisorData.Modulus) == 1UL ? (byte)1 : (byte)0;
+        }
+
+        expected.Should().Equal(direct);
+        hits.Should().Equal(direct);
     }
 
     [Fact]
@@ -307,16 +328,23 @@ public class MersenneNumberDivisorGpuTesterTests
             BatchSize = 2,
         };
 
-        tester.ConfigureFromMaxPrime(47UL);
+        tester.ConfigureFromMaxPrime(173UL);
 
         using var session = tester.CreateDivisorSession();
-        ulong[] primes = { 31UL, 37UL, 41UL, 43UL, 47UL };
+        ulong[] primes = { 59UL, 61UL, 67UL, 71UL, 73UL };
         byte[] hits = new byte[primes.Length];
 
-        ulong cycle223 = MersenneDivisorCycles.CalculateCycleLength(223UL, MontgomeryDivisorData.FromModulus(223UL));
-        session.CheckDivisor(223UL, MontgomeryDivisorData.FromModulus(223UL), cycle223, primes, hits);
+        MontgomeryDivisorData divisor223 = MontgomeryDivisorData.FromModulus(223UL);
+        ulong cycle223 = MersenneDivisorCycles.CalculateCycleLength(223UL, divisor223);
+        session.CheckDivisor(223UL, divisor223, cycle223, primes, hits);
 
-        hits.Should().ContainInOrder(new byte[] { 0, 1, 0, 0, 0 });
+        byte[] expected223 = new byte[primes.Length];
+        for (int i = 0; i < primes.Length; i++)
+        {
+            expected223[i] = primes[i].Pow2ModWindowedCpu(divisor223.Modulus) == 1UL ? (byte)1 : (byte)0;
+        }
+
+        hits.Should().Equal(expected223);
     }
 }