Hoist prime order thresholds in CPU heuristics

EvenPerfectBitScanner/CliArguments.cs

@@ -202,14 +202,15 @@ internal readonly struct CliArguments
 
             if (argument.StartsWith("--prime=", StringComparison.OrdinalIgnoreCase))
             {
-                startPrime = Utf8CliParser.ParseUInt64(argument.AsSpan(argument.IndexOf('=') + 1));
+                ReadOnlySpan<char> primeValue = argument.AsSpan("--prime=".Length);
+                startPrime = Utf8CliParser.ParseUInt64(primeValue);
                 startPrimeProvided = true;
                 continue;
             }
 
             if (argument.StartsWith("--max-prime=", StringComparison.OrdinalIgnoreCase))
             {
-                ReadOnlySpan<char> value = argument.AsSpan(argument.IndexOf('=') + 1);
+                ReadOnlySpan<char> value = argument.AsSpan("--max-prime=".Length);
                 if (UInt128.TryParse(value, NumberStyles.None, CultureInfo.InvariantCulture, out UInt128 parsedMaxPrime))
                 {
                     maxPrimeLimit = parsedMaxPrime;
@@ -238,13 +239,13 @@ internal readonly struct CliArguments
 
             if (argument.StartsWith("--threads=", StringComparison.OrdinalIgnoreCase))
             {
-                threadCount = Math.Max(1, Utf8CliParser.ParseInt32(argument.AsSpan(argument.IndexOf('=') + 1)));
+                threadCount = Math.Max(1, Utf8CliParser.ParseInt32(argument.AsSpan("--threads=".Length)));
                 continue;
             }
 
             if (argument.StartsWith("--mersenne=", StringComparison.OrdinalIgnoreCase))
             {
-                ReadOnlySpan<char> value = argument.AsSpan(argument.IndexOf('=') + 1);
+                ReadOnlySpan<char> value = argument.AsSpan("--mersenne=".Length);
                 if (value.Equals("pow2mod", StringComparison.OrdinalIgnoreCase))
                 {
                     kernelType = GpuKernelType.Pow2Mod;
@@ -281,7 +282,7 @@ internal readonly struct CliArguments
 
             if (argument.StartsWith("--divisor-cycles-limit=", StringComparison.OrdinalIgnoreCase))
             {
-                if (Utf8CliParser.TryParseUInt64(argument.AsSpan(argument.IndexOf('=') + 1), out ulong parsedLimit))
+                if (Utf8CliParser.TryParseUInt64(argument.AsSpan("--divisor-cycles-limit=".Length), out ulong parsedLimit))
                 {
                     divisorCyclesSearchLimit = parsedLimit;
                 }
@@ -291,7 +292,7 @@ internal readonly struct CliArguments
 
             if (argument.StartsWith("--residue-max-k=", StringComparison.OrdinalIgnoreCase))
             {
-                if (Utf8CliParser.TryParseUInt64(argument.AsSpan(argument.IndexOf('=') + 1), out ulong parsedResidueMax))
+                if (Utf8CliParser.TryParseUInt64(argument.AsSpan("--residue-max-k=".Length), out ulong parsedResidueMax))
                 {
                     residueKMax = parsedResidueMax;
                 }
@@ -301,7 +302,7 @@ internal readonly struct CliArguments
 
             if (argument.StartsWith("--mersenne-device=", StringComparison.OrdinalIgnoreCase))
             {
-                useMersenneOnGpu = !argument.AsSpan(argument.IndexOf('=') + 1).Equals("cpu", StringComparison.OrdinalIgnoreCase);
+                useMersenneOnGpu = !argument.AsSpan("--mersenne-device=".Length).Equals("cpu", StringComparison.OrdinalIgnoreCase);
                 continue;
             }
 
@@ -319,7 +320,7 @@ internal readonly struct CliArguments
 
             if (argument.StartsWith("--order-warmup-limit=", StringComparison.OrdinalIgnoreCase))
             {
-                if (Utf8CliParser.TryParseUInt64(argument.AsSpan(argument.IndexOf('=') + 1), out ulong parsedLimit))
+                if (Utf8CliParser.TryParseUInt64(argument.AsSpan("--order-warmup-limit=".Length), out ulong parsedLimit))
                 {
                     orderWarmupLimitOverride = parsedLimit;
                 }
@@ -335,14 +336,14 @@ internal readonly struct CliArguments
 
             if (argument.StartsWith("--ntt=", StringComparison.OrdinalIgnoreCase))
             {
-                ReadOnlySpan<char> value = argument.AsSpan(argument.IndexOf('=') + 1);
+                ReadOnlySpan<char> value = argument.AsSpan("--ntt=".Length);
                 nttBackend = value.Equals("staged", StringComparison.OrdinalIgnoreCase) ? NttBackend.Staged : NttBackend.Reference;
                 continue;
             }
 
             if (argument.StartsWith("--mod-reduction=", StringComparison.OrdinalIgnoreCase))
             {
-                ReadOnlySpan<char> value = argument.AsSpan(argument.IndexOf('=') + 1);
+                ReadOnlySpan<char> value = argument.AsSpan("--mod-reduction=".Length);
                 if (value.Equals("mont64", StringComparison.OrdinalIgnoreCase))
                 {
                     modReductionMode = ModReductionMode.Mont64;
@@ -365,25 +366,25 @@ internal readonly struct CliArguments
 
             if (argument.StartsWith("--primes-device=", StringComparison.OrdinalIgnoreCase))
             {
-                forcePrimeKernelsOnCpu = argument.AsSpan(argument.IndexOf('=') + 1).Equals("cpu", StringComparison.OrdinalIgnoreCase);
+                forcePrimeKernelsOnCpu = argument.AsSpan("--primes-device=".Length).Equals("cpu", StringComparison.OrdinalIgnoreCase);
                 continue;
             }
 
             if (argument.StartsWith("--order-device=", StringComparison.OrdinalIgnoreCase))
             {
-                useOrderOnGpu = !argument.AsSpan(argument.IndexOf('=') + 1).Equals("cpu", StringComparison.OrdinalIgnoreCase);
+                useOrderOnGpu = !argument.AsSpan("--order-device=".Length).Equals("cpu", StringComparison.OrdinalIgnoreCase);
                 continue;
             }
 
             if (argument.StartsWith("--rle-blacklist=", StringComparison.OrdinalIgnoreCase))
             {
-                rleBlacklistPath = argument[(argument.IndexOf('=') + 1)..];
+                rleBlacklistPath = argument["--rle-blacklist=".Length..];
                 continue;
             }
 
             if (argument.StartsWith("--rle-hard-max=", StringComparison.OrdinalIgnoreCase))
             {
-                if (Utf8CliParser.TryParseUInt64(argument.AsSpan(argument.IndexOf('=') + 1), out ulong parsedMax))
+                if (Utf8CliParser.TryParseUInt64(argument.AsSpan("--rle-hard-max=".Length), out ulong parsedMax))
                 {
                     rleHardMaxP = parsedMax;
                 }
@@ -393,14 +394,14 @@ internal readonly struct CliArguments
 
             if (argument.StartsWith("--rle-only-last7=", StringComparison.OrdinalIgnoreCase))
             {
-                ReadOnlySpan<char> value = argument.AsSpan(argument.IndexOf('=') + 1);
+                ReadOnlySpan<char> value = argument.AsSpan("--rle-only-last7=".Length);
                 rleOnlyLast7 = !value.Equals("false", StringComparison.OrdinalIgnoreCase) && !value.Equals("0", StringComparison.OrdinalIgnoreCase);
                 continue;
             }
 
             if (argument.StartsWith("--zero-hard=", StringComparison.OrdinalIgnoreCase))
             {
-                if (Utf8CliParser.TryParseDouble(argument.AsSpan(argument.IndexOf('=') + 1), out double zeroFraction))
+                if (Utf8CliParser.TryParseDouble(argument.AsSpan("--zero-hard=".Length), out double zeroFraction))
                 {
                     zeroFractionHard = zeroFraction;
                 }
@@ -410,7 +411,7 @@ internal readonly struct CliArguments
 
             if (argument.StartsWith("--zero-conj=", StringComparison.OrdinalIgnoreCase))
             {
-                ReadOnlySpan<char> value = argument.AsSpan(argument.IndexOf('=') + 1);
+                ReadOnlySpan<char> value = argument.AsSpan("--zero-conj=".Length);
                 int colon = value.IndexOf(':');
                 if (colon > 0)
                 {
@@ -427,87 +428,97 @@ internal readonly struct CliArguments
 
             if (argument.StartsWith("--lucas=", StringComparison.OrdinalIgnoreCase))
             {
-                useMersenneOnGpu = !argument.AsSpan(argument.IndexOf('=') + 1).Equals("cpu", StringComparison.OrdinalIgnoreCase);
+                useMersenneOnGpu = !argument.AsSpan("--lucas=".Length).Equals("cpu", StringComparison.OrdinalIgnoreCase);
                 continue;
             }
 
-            if (argument.StartsWith("--primes=", StringComparison.OrdinalIgnoreCase) ||
-                argument.StartsWith("--gpu-kernels=", StringComparison.OrdinalIgnoreCase) ||
-                argument.StartsWith("--accelerator=", StringComparison.OrdinalIgnoreCase))
+            if (argument.StartsWith("--primes=", StringComparison.OrdinalIgnoreCase))
             {
-                forcePrimeKernelsOnCpu = argument.AsSpan(argument.IndexOf('=') + 1).Equals("cpu", StringComparison.OrdinalIgnoreCase);
+                forcePrimeKernelsOnCpu = argument.AsSpan("--primes=".Length).Equals("cpu", StringComparison.OrdinalIgnoreCase);
+                continue;
+            }
+
+            if (argument.StartsWith("--gpu-kernels=", StringComparison.OrdinalIgnoreCase))
+            {
+                forcePrimeKernelsOnCpu = argument.AsSpan("--gpu-kernels=".Length).Equals("cpu", StringComparison.OrdinalIgnoreCase);
+                continue;
+            }
+
+            if (argument.StartsWith("--accelerator=", StringComparison.OrdinalIgnoreCase))
+            {
+                forcePrimeKernelsOnCpu = argument.AsSpan("--accelerator=".Length).Equals("cpu", StringComparison.OrdinalIgnoreCase);
                 continue;
             }
 
             if (argument.StartsWith("--results-dir=", StringComparison.OrdinalIgnoreCase))
             {
-                resultsDirectory = argument[(argument.IndexOf('=') + 1)..];
+                resultsDirectory = argument["--results-dir=".Length..];
                 continue;
             }
 
             if (argument.StartsWith("--results-prefix=", StringComparison.OrdinalIgnoreCase))
             {
-                resultsPrefix = argument[(argument.IndexOf('=') + 1)..];
+                resultsPrefix = argument["--results-prefix=".Length..];
                 continue;
             }
 
             if (argument.StartsWith("--gpu-prime-threads=", StringComparison.OrdinalIgnoreCase))
             {
-                gpuPrimeThreads = Math.Max(1, Utf8CliParser.ParseInt32(argument.AsSpan(argument.IndexOf('=') + 1)));
+                gpuPrimeThreads = Math.Max(1, Utf8CliParser.ParseInt32(argument.AsSpan("--gpu-prime-threads=".Length)));
                 continue;
             }
 
             if (argument.StartsWith("--gpu-prime-batch=", StringComparison.OrdinalIgnoreCase))
             {
-                gpuPrimeBatch = Math.Max(1, Utf8CliParser.ParseInt32(argument.AsSpan(argument.IndexOf('=') + 1)));
+                gpuPrimeBatch = Math.Max(1, Utf8CliParser.ParseInt32(argument.AsSpan("--gpu-prime-batch=".Length)));
                 continue;
             }
 
             if (argument.StartsWith("--ll-slice=", StringComparison.OrdinalIgnoreCase))
             {
-                sliceSize = Math.Max(1, Utf8CliParser.ParseInt32(argument.AsSpan(argument.IndexOf('=') + 1)));
+                sliceSize = Math.Max(1, Utf8CliParser.ParseInt32(argument.AsSpan("--ll-slice=".Length)));
                 continue;
             }
 
             if (argument.StartsWith("--gpu-scan-batch=", StringComparison.OrdinalIgnoreCase))
             {
-                scanBatchSize = Math.Max(1, Utf8CliParser.ParseInt32(argument.AsSpan(argument.IndexOf('=') + 1)));
+                scanBatchSize = Math.Max(1, Utf8CliParser.ParseInt32(argument.AsSpan("--gpu-scan-batch=".Length)));
                 continue;
             }
 
             if (argument.StartsWith("--block-size=", StringComparison.OrdinalIgnoreCase))
             {
-                blockSize = Math.Max(1, Utf8CliParser.ParseInt32(argument.AsSpan(argument.IndexOf('=') + 1)));
+                blockSize = Math.Max(1, Utf8CliParser.ParseInt32(argument.AsSpan("--block-size=".Length)));
                 continue;
             }
 
             if (argument.StartsWith("--filter-p=", StringComparison.OrdinalIgnoreCase))
             {
-                filterFile = argument[(argument.IndexOf('=') + 1)..];
+                filterFile = argument["--filter-p=".Length..];
                 continue;
             }
 
             if (argument.StartsWith("--write-batch-size=", StringComparison.OrdinalIgnoreCase))
             {
-                writeBatchSize = Math.Max(1, Utf8CliParser.ParseInt32(argument.AsSpan(argument.IndexOf('=') + 1)));
+                writeBatchSize = Math.Max(1, Utf8CliParser.ParseInt32(argument.AsSpan("--write-batch-size=".Length)));
                 continue;
             }
 
             if (argument.StartsWith("--divisor-cycles=", StringComparison.OrdinalIgnoreCase))
             {
-                cyclesPath = argument[(argument.IndexOf('=') + 1)..];
+                cyclesPath = argument["--divisor-cycles=".Length..];
                 continue;
             }
 
             if (argument.StartsWith("--divisor-cycles-device=", StringComparison.OrdinalIgnoreCase))
             {
-                useGpuCycles = !argument.AsSpan(argument.IndexOf('=') + 1).Equals("cpu", StringComparison.OrdinalIgnoreCase);
+                useGpuCycles = !argument.AsSpan("--divisor-cycles-device=".Length).Equals("cpu", StringComparison.OrdinalIgnoreCase);
                 continue;
             }
 
             if (argument.StartsWith("--divisor-cycles-batch=", StringComparison.OrdinalIgnoreCase))
             {
-                cyclesBatchSize = Math.Max(1, Utf8CliParser.ParseInt32(argument.AsSpan(argument.IndexOf('=') + 1)));
+                cyclesBatchSize = Math.Max(1, Utf8CliParser.ParseInt32(argument.AsSpan("--divisor-cycles-batch=".Length)));
                 continue;
             }
 

EvenPerfectBitScanner/IO/CalculationResultsFile.cs

@@ -14,7 +14,7 @@ internal static class CalculationResultsFile
                 using FileStream readStream = new(candidateFile, FileMode.Open, FileAccess.Read, FileShare.ReadWrite);
                 using StreamReader reader = new(readStream);
                 string? line;
-                ReadOnlySpan<char> span;
+                ReadOnlySpan<char> trimmed;
                 while ((line = reader.ReadLine()) is not null)
                 {
                         if (string.IsNullOrWhiteSpace(line))
@@ -22,36 +22,67 @@ internal static class CalculationResultsFile
                                 continue;
                         }
 
-                        span = line.AsSpan().Trim();
-                        if (span.IsEmpty || span[0] == '#')
+                        trimmed = line.AsSpan().Trim();
+                        if (trimmed.IsEmpty || trimmed[0] == '#')
                         {
                                 continue;
                         }
+
+                        int length = trimmed.Length;
                         int index = 0;
-                        while (index < span.Length)
+                        if (!maxPrimeConfigured)
                         {
-                                if (!char.IsDigit(span[index]))
+                                while (index < length)
                                 {
-                                        index++;
-                                        continue;
-                                }
+                                        char current = trimmed[index];
+                                        uint digit = (uint)(current - '0');
+                                        if (digit > 9U)
+                                        {
+                                                index++;
+                                                continue;
+                                        }
 
-                                int start = index;
-                                index++;
-                                while (index < span.Length && char.IsDigit(span[index]))
-                                {
-                                        index++;
-                                }
+                                        int start = index++;
+                                        while (index < length && (uint)(trimmed[index] - '0') <= 9U)
+                                        {
+                                                index++;
+                                        }
 
-                                if (Utf8CliParser.TryParseUInt64(span[start..index], out ulong parsed))
-                                {
-                                        if (!maxPrimeConfigured || (UInt128)parsed <= maxPrimeLimit)
+                                        if (Utf8CliParser.TryParseUInt64(trimmed[start..index], out ulong parsed))
                                         {
                                                 candidates.Add(parsed);
                                         }
-                                        else
+                                }
+                        }
+                        else
+                        {
+                                UInt128 limit = maxPrimeLimit;
+                                while (index < length)
+                                {
+                                        char current = trimmed[index];
+                                        uint digit = (uint)(current - '0');
+                                        if (digit > 9U)
                                         {
-                                                skippedByLimit++;
+                                                index++;
+                                                continue;
+                                        }
+
+                                        int start = index++;
+                                        while (index < length && (uint)(trimmed[index] - '0') <= 9U)
+                                        {
+                                                index++;
+                                        }
+
+                                        if (Utf8CliParser.TryParseUInt64(trimmed[start..index], out ulong parsed))
+                                        {
+                                                if ((UInt128)parsed <= limit)
+                                                {
+                                                        candidates.Add(parsed);
+                                                }
+                                                else
+                                                {
+                                                        skippedByLimit++;
+                                                }
                                         }
                                 }
                         }

PerfectNumbers.Core/Cpu/MersenneNumberDivisorByDivisorCpuTester.cs

@@ -7,10 +7,7 @@ namespace PerfectNumbers.Core.Cpu;
 
 public sealed class MersenneNumberDivisorByDivisorCpuTester : IMersenneNumberDivisorByDivisorTester
 {
-    private readonly object _sync = new();
-
     private ulong _divisorLimit;
-    private ulong _lastStatusDivisor;
     private int _batchSize = 1_024;
 
     [ThreadStatic]
@@ -32,7 +29,6 @@ public sealed class MersenneNumberDivisorByDivisorCpuTester : IMersenneNumberDiv
     public void ConfigureFromMaxPrime(ulong maxPrime)
     {
         _divisorLimit = ComputeDivisorLimitFromMaxPrime(maxPrime);
-        _lastStatusDivisor = 0UL;
     }
 
     public ulong DivisorLimit
@@ -60,22 +56,12 @@ public sealed class MersenneNumberDivisorByDivisorCpuTester : IMersenneNumberDiv
         //     return true;
         // }
 
-        ulong processedCount;
         bool processedAll;
 
         bool composite = CheckDivisors(
             prime,
             allowedMax,
-            out processedAll,
-            out processedCount);
-
-        if (processedCount > 0UL)
-        {
-            lock (_sync)
-            {
-                UpdateStatusUnsafe(processedCount);
-            }
-        }
+            out processedAll);
 
         if (composite)
         {
@@ -111,10 +97,8 @@ public sealed class MersenneNumberDivisorByDivisorCpuTester : IMersenneNumberDiv
     private bool CheckDivisors(
         ulong prime,
         ulong allowedMax,
-        out bool processedAll,
-        out ulong processedCount)
+        out bool processedAll)
     {
-        processedCount = 0UL;
         processedAll = false;
 
         // The EvenPerfectBitScanner feeds primes >= 138,000,000 here, so allowedMax >= 3 in production runs.
@@ -151,44 +135,86 @@ public sealed class MersenneNumberDivisorByDivisorCpuTester : IMersenneNumberDiv
 
         ulong stepHigh = step.High;
         ulong stepLow = step.Low;
-        byte step10 = (byte)((((stepHigh % 10UL) * 6UL) + (stepLow % 10UL)) % 10UL);
-        byte step8 = (byte)(stepLow % 8UL);
-        byte step5 = (byte)(((stepHigh % 5UL) + (stepLow % 5UL)) % 5UL);
-        byte step3 = (byte)(((stepHigh % 3UL) + (stepLow % 3UL)) % 3UL);
-        byte step7 = (byte)((((stepHigh % 7UL) * 2UL) + (stepLow % 7UL)) % 7UL);
-        byte step11 = (byte)((((stepHigh % 11UL) * 5UL) + (stepLow % 11UL)) % 11UL);
-
-        ulong divisorHigh = divisor.High;
+        ulong limitHigh = limit.High;
         ulong divisorLow = divisor.Low;
-        byte remainder10 = (byte)((((divisorHigh % 10UL) * 6UL) + (divisorLow % 10UL)) % 10UL);
-        byte remainder8 = (byte)(divisorLow % 8UL);
-        byte remainder5 = (byte)(((divisorHigh % 5UL) + (divisorLow % 5UL)) % 5UL);
-        byte remainder3 = (byte)(((divisorHigh % 3UL) + (divisorLow % 3UL)) % 3UL);
-        byte remainder7 = (byte)((((divisorHigh % 7UL) * 2UL) + (divisorLow % 7UL)) % 7UL);
-        byte remainder11 = (byte)((((divisorHigh % 11UL) * 5UL) + (divisorLow % 11UL)) % 11UL);
 
         // Keep the divisibility filters aligned with the divisor-cycle generator so the
         // CPU path never requests cycles that were skipped during cache creation.
         LastDigit lastDigit = (prime & 3UL) == 3UL ? LastDigit.Seven : LastDigit.One;
-        bool lastIsSeven = lastDigit == LastDigit.Seven;
-        const ushort DecimalMaskWhenLastIsSeven = (1 << 3) | (1 << 7) | (1 << 9);
-        const ushort DecimalMaskOtherwise = (1 << 1) | (1 << 3) | (1 << 9);
+        ushort decimalMask = DivisorGenerator.GetDecimalMask(lastDigit);
+
+        byte step10;
+        byte step8;
+        byte step5;
+        byte step3;
+        byte step7;
+        byte step11;
+
+        byte remainder10;
+        byte remainder8;
+        byte remainder5;
+        byte remainder3;
+        byte remainder7;
+        byte remainder11;
+
+        if (stepHigh == 0UL && limitHigh == 0UL)
+        {
+            step10 = (byte)(stepLow % 10UL);
+            step8 = (byte)(stepLow & 7UL);
+            step5 = (byte)(stepLow % 5UL);
+            step3 = (byte)(stepLow % 3UL);
+            step7 = (byte)(stepLow % 7UL);
+            step11 = (byte)(stepLow % 11UL);
+
+            remainder10 = (byte)(divisorLow % 10UL);
+            remainder8 = (byte)(divisorLow & 7UL);
+            remainder5 = (byte)(divisorLow % 5UL);
+            remainder3 = (byte)(divisorLow % 3UL);
+            remainder7 = (byte)(divisorLow % 7UL);
+            remainder11 = (byte)(divisorLow % 11UL);
+
+            return CheckDivisors64(
+                prime,
+                stepLow,
+                limit.Low,
+                divisorLow,
+                decimalMask,
+                step10,
+                step8,
+                step5,
+                step3,
+                step7,
+                step11,
+                remainder10,
+                remainder8,
+                remainder5,
+                remainder3,
+                remainder7,
+                remainder11,
+                out processedAll);
+        }
+
+        ulong divisorHigh = divisor.High;
+        step10 = (byte)((((stepHigh % 10UL) * 6UL) + (stepLow % 10UL)) % 10UL);
+        step8 = (byte)(stepLow % 8UL);
+        step5 = (byte)(((stepHigh % 5UL) + (stepLow % 5UL)) % 5UL);
+        step3 = (byte)(((stepHigh % 3UL) + (stepLow % 3UL)) % 3UL);
+        step7 = (byte)((((stepHigh % 7UL) * 2UL) + (stepLow % 7UL)) % 7UL);
+        step11 = (byte)((((stepHigh % 11UL) * 5UL) + (stepLow % 11UL)) % 11UL);
+
+        remainder10 = (byte)((((divisorHigh % 10UL) * 6UL) + (divisorLow % 10UL)) % 10UL);
+        remainder8 = (byte)(divisorLow % 8UL);
+        remainder5 = (byte)(((divisorHigh % 5UL) + (divisorLow % 5UL)) % 5UL);
+        remainder3 = (byte)(((divisorHigh % 3UL) + (divisorLow % 3UL)) % 3UL);
+        remainder7 = (byte)((((divisorHigh % 7UL) * 2UL) + (divisorLow % 7UL)) % 7UL);
+        remainder11 = (byte)((((divisorHigh % 11UL) * 5UL) + (divisorLow % 11UL)) % 11UL);
 
         while (divisor.CompareTo(limit) <= 0)
         {
-            ulong candidate = divisor.Low;
-            processedCount++;
-
-            ushort decimalMask = lastIsSeven ? DecimalMaskWhenLastIsSeven : DecimalMaskOtherwise;
-            bool admissible = ((decimalMask >> remainder10) & 1) != 0;
-
-            if (admissible
-                && (remainder8 == 1 || remainder8 == 7)
-                && remainder3 != 0
-                && remainder5 != 0
-                && remainder7 != 0
-                && remainder11 != 0)
+            bool passesSmallModuli = remainder3 != 0 && remainder5 != 0 && remainder7 != 0 && remainder11 != 0;
+            if (passesSmallModuli && (remainder8 == 1 || remainder8 == 7) && ((decimalMask >> remainder10) & 1) != 0)
             {
+                ulong candidate = divisor.Low;
                 MontgomeryDivisorData divisorData = MontgomeryDivisorData.FromModulus(candidate);
                 ulong divisorCycle;
                 // Divisors generated from 2 * k * p + 1 exceed the small-cycle snapshot when p >= 138,000,000, so the short path below never runs.
@@ -233,16 +259,141 @@ public sealed class MersenneNumberDivisorByDivisorCpuTester : IMersenneNumberDiv
             }
 
             divisor.Add(step);
-            remainder10 = AddMod(remainder10, step10, (byte)10);
-            remainder8 = AddMod(remainder8, step8, (byte)8);
-            remainder5 = AddMod(remainder5, step5, (byte)5);
-            remainder3 = AddMod(remainder3, step3, (byte)3);
-            remainder7 = AddMod(remainder7, step7, (byte)7);
-            remainder11 = AddMod(remainder11, step11, (byte)11);
+            remainder10 = AddMod10(remainder10, step10);
+            remainder8 = AddMod8(remainder8, step8);
+            remainder5 = AddMod5(remainder5, step5);
+            remainder3 = AddMod3(remainder3, step3);
+            remainder7 = AddMod7(remainder7, step7);
+            remainder11 = AddMod11(remainder11, step11);
+        }
+        processedAll = true;
+        return false;
+    }
+
+    private static bool CheckDivisors64(
+        ulong prime,
+        ulong step,
+        ulong limit,
+        ulong divisor,
+        ushort decimalMask,
+        byte step10,
+        byte step8,
+        byte step5,
+        byte step3,
+        byte step7,
+        byte step11,
+        byte remainder10,
+        byte remainder8,
+        byte remainder5,
+        byte remainder3,
+        byte remainder7,
+        byte remainder11,
+        out bool processedAll)
+    {
+        processedAll = false;
+
+        bool canAdvance = step <= limit;
+        if (!canAdvance)
+        {
+            if (divisor <= limit)
+            {
+                if (remainder3 != 0 && remainder5 != 0 && remainder7 != 0 && remainder11 != 0 && (remainder8 == 1 || remainder8 == 7) && ((decimalMask >> remainder10) & 1) != 0)
+                {
+                    MontgomeryDivisorData divisorData = MontgomeryDivisorData.FromModulus(divisor);
+                    ulong divisorCycle;
+                    if (!MersenneDivisorCycles.TryCalculateCycleLengthForExponentCpu(
+                            divisor,
+                            prime,
+                            divisorData,
+                            out ulong computedCycle,
+                            out bool primeOrderFailed) || computedCycle == 0UL)
+                    {
+                        divisorCycle = MersenneDivisorCycles.CalculateCycleLength(
+                            divisor,
+                            divisorData,
+                            skipPrimeOrderHeuristic: primeOrderFailed);
+                    }
+                    else
+                    {
+                        divisorCycle = computedCycle;
+                    }
+
+                    if (divisorCycle == prime)
+                    {
+                        processedAll = true;
+                        return true;
+                    }
+
+                    if (divisorCycle == 0UL)
+                    {
+                        Console.WriteLine($"Divisor cycle was not calculated for {prime}");
+                    }
+                }
+            }
+
+            processedAll = true;
+            return false;
         }
 
-        processedAll = divisor.CompareTo(limit) > 0;
-        return false;
+        if (divisor > limit)
+        {
+            processedAll = true;
+            return false;
+        }
+
+        ulong remainingIterations = ((limit - divisor) / step) + 1UL;
+
+        while (true)
+        {
+            bool passesSmallModuli = remainder3 != 0 && remainder5 != 0 && remainder7 != 0 && remainder11 != 0;
+            if (passesSmallModuli && (remainder8 == 1 || remainder8 == 7) && ((decimalMask >> remainder10) & 1) != 0)
+            {
+                MontgomeryDivisorData divisorData = MontgomeryDivisorData.FromModulus(divisor);
+                ulong divisorCycle;
+                if (!MersenneDivisorCycles.TryCalculateCycleLengthForExponentCpu(
+                        divisor,
+                        prime,
+                        divisorData,
+                        out ulong computedCycle,
+                        out bool primeOrderFailed) || computedCycle == 0UL)
+                {
+                    divisorCycle = MersenneDivisorCycles.CalculateCycleLength(
+                        divisor,
+                        divisorData,
+                        skipPrimeOrderHeuristic: primeOrderFailed);
+                }
+                else
+                {
+                    divisorCycle = computedCycle;
+                }
+
+                if (divisorCycle == prime)
+                {
+                    processedAll = true;
+                    return true;
+                }
+
+                if (divisorCycle == 0UL)
+                {
+                    Console.WriteLine($"Divisor cycle was not calculated for {prime}");
+                }
+            }
+
+            remainingIterations--;
+            if (remainingIterations == 0UL)
+            {
+                processedAll = true;
+                return false;
+            }
+
+            divisor += step;
+            remainder10 = AddMod10(remainder10, step10);
+            remainder8 = AddMod8(remainder8, step8);
+            remainder5 = AddMod5(remainder5, step5);
+            remainder3 = AddMod3(remainder3, step3);
+            remainder7 = AddMod7(remainder7, step7);
+            remainder11 = AddMod11(remainder11, step11);
+        }
     }
 
     private static byte CheckDivisor(ulong prime, ulong divisorCycle, in MontgomeryDivisorData divisorData)
@@ -251,35 +402,80 @@ public sealed class MersenneNumberDivisorByDivisorCpuTester : IMersenneNumberDiv
         return residue == 1UL ? (byte)1 : (byte)0;
     }
 
-    private static byte AddMod(byte value, byte delta, byte modulus)
+    [MethodImpl(MethodImplOptions.AggressiveInlining)]
+    private static byte AddMod3(byte value, byte delta)
     {
+        const int Modulus = 3;
         int sum = value + delta;
-        if (sum >= modulus)
+
+        if (sum >= Modulus)
         {
-            sum -= modulus;
+            sum -= Modulus;
         }
 
         return (byte)sum;
     }
 
-    private void UpdateStatusUnsafe(ulong processedCount)
+    [MethodImpl(MethodImplOptions.AggressiveInlining)]
+    private static byte AddMod5(byte value, byte delta)
     {
-        if (processedCount == 0UL)
+        const int Modulus = 5;
+        int sum = value + delta;
+
+        if (sum >= Modulus)
         {
-            return;
+            sum -= Modulus;
         }
 
-        ulong interval = PerfectNumberConstants.ConsoleInterval;
-        if (interval == 0UL)
+        return (byte)sum;
+    }
+
+    [MethodImpl(MethodImplOptions.AggressiveInlining)]
+    private static byte AddMod7(byte value, byte delta)
+    {
+        const int Modulus = 7;
+        int sum = value + delta;
+
+        if (sum >= Modulus)
         {
-            _lastStatusDivisor = 0UL;
-            return;
+            sum -= Modulus;
         }
 
-        ulong total = _lastStatusDivisor + processedCount;
-        // TODO: Replace this modulo with the ring-buffer style counter (subtract loop) used in the fast CLI
-        // status benchmarks so we avoid `%` in this hot loop while still wrapping progress correctly.
-        _lastStatusDivisor = total % interval;
+        return (byte)sum;
+    }
+
+    [MethodImpl(MethodImplOptions.AggressiveInlining)]
+    private static byte AddMod10(byte value, byte delta)
+    {
+        const int Modulus = 10;
+        int sum = value + delta;
+
+        if (sum >= Modulus)
+        {
+            sum -= Modulus;
+        }
+
+        return (byte)sum;
+    }
+
+    [MethodImpl(MethodImplOptions.AggressiveInlining)]
+    private static byte AddMod11(byte value, byte delta)
+    {
+        const int Modulus = 11;
+        int sum = value + delta;
+
+        if (sum >= Modulus)
+        {
+            sum -= Modulus;
+        }
+
+        return (byte)sum;
+    }
+
+    [MethodImpl(MethodImplOptions.AggressiveInlining)]
+    private static byte AddMod8(byte value, byte delta)
+    {
+        return (byte)((value + delta) & 7);
     }
 
     private static ulong ComputeDivisorLimitFromMaxPrime(ulong maxPrime)

PerfectNumbers.Core/DivisorGenerator.cs

@@ -8,31 +8,9 @@ internal static class DivisorGenerator
     private const ushort DecimalMaskOtherwise = (1 << 1) | (1 << 3) | (1 << 9);
 
     [MethodImpl(MethodImplOptions.AggressiveInlining)]
-    public static bool IsValidDivisor(
-        byte remainder10,
-        byte remainder8,
-        byte remainder3,
-        byte remainder5,
-        byte remainder7,
-        byte remainder11,
-        LastDigit lastDigit)
+    public static ushort GetDecimalMask(LastDigit lastDigit)
     {
-        ushort decimalMask = lastDigit == LastDigit.Seven ? DecimalMaskWhenLastIsSeven : DecimalMaskOtherwise;
-        if (((decimalMask >> remainder10) & 1) == 0)
-        {
-            return false;
-        }
-
-        if (remainder8 != 1 && remainder8 != 7)
-        {
-            return false;
-        }
-
-        if (remainder3 == 0 || remainder5 == 0 || remainder7 == 0 || remainder11 == 0)
-        {
-            return false;
-        }
-
-        return true;
+        return lastDigit == LastDigit.Seven ? DecimalMaskWhenLastIsSeven : DecimalMaskOtherwise;
     }
+
 }

PerfectNumbers.Core/Gpu/Kernels/DivisorByDivisorKernels.cs

@@ -36,30 +36,45 @@ internal static class DivisorByDivisorKernels
         byte firstHitValue;
         ulong previousExponent = firstExponent;
         ulong cycleRemainder = 0UL;
-        if (cycleLength == 0UL)
-        {
-            firstHitValue = firstUnity ? (byte)1 : (byte)0;
-        }
-        else
+        bool hasCycle = cycleLength != 0UL;
+        if (hasCycle)
         {
             cycleRemainder = firstExponent % cycleLength;
             firstHitValue = cycleRemainder == 0UL && firstUnity ? (byte)1 : (byte)0;
         }
+        else
+        {
+            firstHitValue = firstUnity ? (byte)1 : (byte)0;
+        }
 
         hits[offset] = firstHitValue;
         byte anyHit = firstHitValue;
 
-        for (int i = 1; i < count; i++)
+        int endIndex = offset + count;
+        if (hasCycle)
         {
-            ulong exponent = exponents[offset + i];
-            ulong delta = exponent - previousExponent;
-            previousExponent = exponent;
-
-            if (cycleLength != 0UL)
+            for (int exponentIndex = offset + 1; exponentIndex < endIndex; exponentIndex++)
             {
-                var remainderValue = new GpuUInt128(cycleRemainder);
-                remainderValue.AddMod(delta, cycleLength);
-                cycleRemainder = remainderValue.Low;
+                ulong exponent = exponents[exponentIndex];
+                ulong delta = exponent - previousExponent;
+                previousExponent = exponent;
+
+                if (delta >= cycleLength)
+                {
+                    delta -= cycleLength;
+                    if (delta >= cycleLength)
+                    {
+                        delta %= cycleLength;
+                    }
+                }
+
+                ulong nextRemainder = cycleRemainder + delta;
+                if (nextRemainder >= cycleLength)
+                {
+                    nextRemainder -= cycleLength;
+                }
+
+                cycleRemainder = nextRemainder;
 
                 byte hit = 0;
                 if (cycleRemainder == 0UL)
@@ -67,13 +82,17 @@ internal static class DivisorByDivisorKernels
                     hit = stepper.ComputeNextIsUnityGpu(exponent) ? (byte)1 : (byte)0;
                 }
 
-                hits[offset + i] = hit;
+                hits[exponentIndex] = hit;
                 anyHit |= hit;
             }
-            else
+        }
+        else
+        {
+            for (int exponentIndex = offset + 1; exponentIndex < endIndex; exponentIndex++)
             {
+                ulong exponent = exponents[exponentIndex];
                 byte hit = stepper.ComputeNextIsUnityGpu(exponent) ? (byte)1 : (byte)0;
-                hits[offset + i] = hit;
+                hits[exponentIndex] = hit;
                 anyHit |= hit;
             }
         }

PerfectNumbers.Core/Gpu/MersenneNumberDivisorByDivisorGpuTester.cs

@@ -112,7 +112,6 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
             resources.HitIndexBuffer,
             resources.Divisors,
             resources.Exponents,
-            resources.FilteredDivisors,
             resources.DivisorData,
             resources.Offsets,
             resources.Counts,
@@ -177,7 +176,6 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
         MemoryBuffer1D<int, Stride1D.Dense> hitIndexBuffer,
         ulong[] divisors,
         ulong[] exponents,
-        ulong[] filteredDivisors,
         GpuDivisorPartialData[] divisorData,
         int[] offsets,
         int[] counts,
@@ -192,7 +190,15 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
         processedCount = 0UL;
         lastProcessed = 0UL;
 
-        int chunkCapacity = Math.Max(1, batchCapacity);
+        // EvenPerfectBitScanner always configures non-empty GPU divisor buffers, so the defensive guard stays
+        // commented out. Tests and benchmarks that rely on zero-capacity buffers must be updated instead of re-enabling
+        // this branch.
+        // if (batchCapacity <= 0)
+        // {
+        //     throw new InvalidOperationException("Divisor buffers must be non-empty.");
+        // }
+
+        int chunkCountBaseline = batchCapacity;
 
         UInt128 twoP128 = (UInt128)prime << 1;
         UInt128 allowedMax128 = allowedMax;
@@ -209,48 +215,63 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
         }
 
         ulong maxK = maxK128 > ulong.MaxValue ? ulong.MaxValue : (ulong)maxK128;
-        ulong currentK = 1UL;
+        ulong remainingCount = maxK;
 
-        byte step10 = (byte)(twoP128 % 10UL);
-        byte step8 = (byte)(twoP128 % 8UL);
-        byte step5 = (byte)(twoP128 % 5UL);
-        byte step3 = (byte)(twoP128 % 3UL);
-        byte step7 = (byte)(twoP128 % 7UL);
-        byte step11 = (byte)(twoP128 % 11UL);
+        ulong stepValue = (ulong)twoP128;
+        byte step10 = (byte)(stepValue % 10UL);
+        byte step8 = (byte)(stepValue & 7UL);
+        byte step5 = (byte)(stepValue % 5UL);
+        byte step3 = (byte)(stepValue % 3UL);
+        byte step7 = (byte)(stepValue % 7UL);
+        byte step11 = (byte)(stepValue % 11UL);
 
         UInt128 currentDivisor128 = firstDivisor128;
-        byte remainder10 = (byte)((ulong)(currentDivisor128 % 10UL));
-        byte remainder8 = (byte)((ulong)(currentDivisor128 & 7UL));
-        byte remainder5 = (byte)((ulong)(currentDivisor128 % 5UL));
-        byte remainder3 = (byte)((ulong)(currentDivisor128 % 3UL));
-        byte remainder7 = (byte)((ulong)(currentDivisor128 % 7UL));
-        byte remainder11 = (byte)((ulong)(currentDivisor128 % 11UL));
+        ulong currentDivisorValue = (ulong)currentDivisor128;
+        byte remainder10 = (byte)(currentDivisorValue % 10UL);
+        byte remainder8 = (byte)(currentDivisorValue & 7UL);
+        byte remainder5 = (byte)(currentDivisorValue % 5UL);
+        byte remainder3 = (byte)(currentDivisorValue % 3UL);
+        byte remainder7 = (byte)(currentDivisorValue % 7UL);
+        byte remainder11 = (byte)(currentDivisorValue % 11UL);
         LastDigit lastDigit = (prime & 3UL) == 3UL ? LastDigit.Seven : LastDigit.One;
+        ushort decimalMask = DivisorGenerator.GetDecimalMask(lastDigit);
 
-        Span<ulong> filteredStorage = filteredDivisors.AsSpan();
         Span<ulong> divisorStorage = divisors.AsSpan();
         Span<ulong> exponentStorage = exponents.AsSpan();
         Span<GpuDivisorPartialData> divisorDataStorage = divisorData.AsSpan();
         Span<int> offsetStorage = offsets.AsSpan();
         Span<int> countStorage = counts.AsSpan();
         Span<ulong> cycleStorage = cycles.AsSpan();
-        while (currentK <= maxK && !composite)
+        Span<ulong> divisorSpan = divisorStorage;
+        Span<ulong> exponentSpan = exponentStorage;
+        Span<GpuDivisorPartialData> divisorDataSpan = divisorDataStorage;
+        Span<int> offsetSpan = offsetStorage;
+        Span<int> countSpan = countStorage;
+        Span<ulong> cycleSpan = cycleStorage;
+        ref GpuDivisorPartialData divisorDataRef = ref MemoryMarshal.GetReference(divisorDataSpan);
+        ref int offsetRef = ref MemoryMarshal.GetReference(offsetSpan);
+        ref int countRef = ref MemoryMarshal.GetReference(countSpan);
+        ref ulong cycleRef = ref MemoryMarshal.GetReference(cycleSpan);
+        ref ulong exponentRef = ref MemoryMarshal.GetReference(exponentSpan);
+
+        ArrayView1D<GpuDivisorPartialData, Stride1D.Dense> divisorDataView = divisorDataBuffer.View;
+        ArrayView1D<int, Stride1D.Dense> offsetView = offsetBuffer.View;
+        ArrayView1D<int, Stride1D.Dense> countView = countBuffer.View;
+        ArrayView1D<ulong, Stride1D.Dense> cycleView = cycleBuffer.View;
+        ArrayView1D<ulong, Stride1D.Dense> exponentViewDevice = exponentBuffer.View;
+        ArrayView1D<byte, Stride1D.Dense> hitsView = hitsBuffer.View;
+        ArrayView1D<int, Stride1D.Dense> hitIndexView = hitIndexBuffer.View;
+
+        while (remainingCount > 0UL && !composite)
         {
-            int chunkCount = Math.Min(chunkCapacity, batchCapacity);
-            ulong remainingK = maxK - currentK + 1UL;
-            if ((ulong)chunkCount > remainingK)
+            int chunkCount = chunkCountBaseline;
+            if ((ulong)chunkCount > remainingCount)
             {
-                chunkCount = (int)remainingK;
+                chunkCount = (int)remainingCount;
             }
 
-            if (chunkCount <= 0)
-            {
-                processedAll = true;
-                break;
-            }
-
-            int filteredCount = 0;
             UInt128 nextDivisor128 = currentDivisor128;
+            int admissibleCount = 0;
 
             byte localRemainder10 = remainder10;
             byte localRemainder8 = remainder8;
@@ -261,20 +282,32 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
 
             for (int i = 0; i < chunkCount; i++)
             {
-                ulong candidate = (ulong)nextDivisor128;
-
-                if (DivisorGenerator.IsValidDivisor(localRemainder10, localRemainder8, localRemainder3, localRemainder5, localRemainder7, localRemainder11, lastDigit))
+                bool passesSmallModuli = localRemainder3 != 0 && localRemainder5 != 0 && localRemainder7 != 0 && localRemainder11 != 0;
+                if (passesSmallModuli && (localRemainder8 == 1 || localRemainder8 == 7) && ((decimalMask >> localRemainder10) & 1) != 0)
                 {
-                    filteredStorage[filteredCount++] = candidate;
+                    ulong divisorValue = (ulong)nextDivisor128;
+                    MontgomeryDivisorData montgomeryData = MontgomeryDivisorData.FromModulus(divisorValue);
+                    ulong divisorCycle = ResolveDivisorCycle(divisorValue, prime, in montgomeryData);
+                    if (divisorCycle == prime)
+                    {
+                        int targetIndex = admissibleCount;
+                        divisorSpan[targetIndex] = divisorValue;
+                        exponentSpan[targetIndex] = prime;
+                        divisorDataSpan[targetIndex] = new GpuDivisorPartialData(divisorValue);
+                        offsetSpan[targetIndex] = targetIndex;
+                        countSpan[targetIndex] = 1;
+                        cycleSpan[targetIndex] = divisorCycle;
+                        admissibleCount++;
+                    }
                 }
 
                 nextDivisor128 += twoP128;
-                localRemainder10 = AddMod(localRemainder10, step10, 10);
-                localRemainder8 = AddMod(localRemainder8, step8, 8);
-                localRemainder5 = AddMod(localRemainder5, step5, 5);
-                localRemainder3 = AddMod(localRemainder3, step3, 3);
-                localRemainder7 = AddMod(localRemainder7, step7, 7);
-                localRemainder11 = AddMod(localRemainder11, step11, 11);
+                localRemainder10 = AddMod10(localRemainder10, step10);
+                localRemainder8 = AddMod8(localRemainder8, step8);
+                localRemainder5 = AddMod5(localRemainder5, step5);
+                localRemainder3 = AddMod3(localRemainder3, step3);
+                localRemainder7 = AddMod7(localRemainder7, step7);
+                localRemainder11 = AddMod11(localRemainder11, step11);
             }
 
             remainder10 = localRemainder10;
@@ -289,69 +322,23 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
             UInt128 lastDivisor128 = nextDivisor128 - twoP128;
             lastProcessed = (ulong)lastDivisor128;
             currentDivisor128 = nextDivisor128;
-
-            currentK += (ulong)chunkCount;
-            processedAll = currentK > maxK;
-
-            if (filteredCount == 0)
-            {
-                continue;
-            }
-
-            Span<ulong> filteredDivisorsSpan = filteredStorage[..filteredCount];
-
-            Span<ulong> divisorSpan = divisorStorage;
-            Span<ulong> exponentSpan = exponentStorage;
-            Span<GpuDivisorPartialData> divisorDataSpan = divisorDataStorage;
-            Span<int> offsetSpan = offsetStorage;
-            Span<int> countSpan = countStorage;
-            Span<ulong> cycleSpan = cycleStorage;
-            int admissibleCount = 0;
-            int exponentIndex = 0;
-            for (int i = 0; i < filteredCount; i++)
-            {
-                ulong divisorValue = filteredDivisorsSpan[i];
-                MontgomeryDivisorData montgomeryData = MontgomeryDivisorData.FromModulus(divisorValue);
-                ulong divisorCycle = ResolveDivisorCycle(divisorValue, prime, in montgomeryData);
-                if (divisorCycle != prime)
-                {
-                    continue;
-                }
-
-                divisorSpan[admissibleCount] = divisorValue;
-                exponentSpan[exponentIndex] = prime;
-                divisorDataSpan[admissibleCount] = new GpuDivisorPartialData(divisorValue);
-                offsetSpan[admissibleCount] = exponentIndex;
-                countSpan[admissibleCount] = 1;
-                cycleSpan[admissibleCount] = divisorCycle;
-
-                admissibleCount++;
-                exponentIndex++;
-            }
+            remainingCount -= (ulong)chunkCount;
 
             if (admissibleCount == 0)
             {
                 continue;
             }
 
-            ArrayView1D<GpuDivisorPartialData, Stride1D.Dense> divisorView = divisorDataBuffer.View.SubView(0, admissibleCount);
-            ArrayView1D<int, Stride1D.Dense> offsetView = offsetBuffer.View.SubView(0, admissibleCount);
-            ArrayView1D<int, Stride1D.Dense> countView = countBuffer.View.SubView(0, admissibleCount);
-            ArrayView1D<ulong, Stride1D.Dense> cycleView = cycleBuffer.View.SubView(0, admissibleCount);
-            ArrayView1D<ulong, Stride1D.Dense> exponentView = exponentBuffer.View.SubView(0, exponentIndex);
-            ArrayView1D<byte, Stride1D.Dense> hitsView = hitsBuffer.View.SubView(0, exponentIndex);
-            ArrayView1D<int, Stride1D.Dense> hitIndexView = hitIndexBuffer.View.SubView(0, 1);
-
-            divisorView.CopyFromCPU(ref MemoryMarshal.GetReference(divisorDataSpan), admissibleCount);
-            offsetView.CopyFromCPU(ref MemoryMarshal.GetReference(offsetSpan), admissibleCount);
-            countView.CopyFromCPU(ref MemoryMarshal.GetReference(countSpan), admissibleCount);
-            cycleView.CopyFromCPU(ref MemoryMarshal.GetReference(cycleSpan), admissibleCount);
-            exponentView.CopyFromCPU(ref MemoryMarshal.GetReference(exponentSpan), exponentIndex);
+            divisorDataView.CopyFromCPU(ref divisorDataRef, admissibleCount);
+            offsetView.CopyFromCPU(ref offsetRef, admissibleCount);
+            countView.CopyFromCPU(ref countRef, admissibleCount);
+            cycleView.CopyFromCPU(ref cycleRef, admissibleCount);
+            exponentViewDevice.CopyFromCPU(ref exponentRef, admissibleCount);
 
             int sentinel = int.MaxValue;
             hitIndexView.CopyFromCPU(ref sentinel, 1);
 
-            kernel(admissibleCount, divisorView, offsetView, countView, exponentView, cycleView, hitsView, hitIndexView);
+            kernel(admissibleCount, divisorDataView, offsetView, countView, exponentViewDevice, cycleView, hitsView, hitIndexView);
 
             int firstHit = sentinel;
             hitIndexView.CopyToCPU(ref firstHit, 1);
@@ -362,6 +349,7 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
             lastProcessed = hitFound ? divisorSpan[hitIndex] : divisorSpan[lastIndex];
         }
 
+        processedAll = remainingCount == 0UL;
         coveredRange = composite || processedAll || (currentDivisor128 > allowedMax128);
         return composite;
     }
@@ -379,23 +367,80 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
     }
 
     [MethodImpl(MethodImplOptions.AggressiveInlining)]
-    private static byte AddMod(byte value, byte delta, byte modulus)
+    private static byte AddMod3(byte value, byte delta)
     {
-        int result = value + delta;
-        if (result >= modulus)
+        const int Modulus = 3;
+        int sum = value + delta;
+
+        if (sum >= Modulus)
         {
-            result -= modulus;
-            if (result >= modulus)
-            {
-                result -= modulus;
-            }
+            sum -= Modulus;
         }
 
-        return (byte)result;
+        return (byte)sum;
     }
 
+    [MethodImpl(MethodImplOptions.AggressiveInlining)]
+    private static byte AddMod5(byte value, byte delta)
+    {
+        const int Modulus = 5;
+        int sum = value + delta;
 
+        if (sum >= Modulus)
+        {
+            sum -= Modulus;
+        }
 
+        return (byte)sum;
+    }
+
+    [MethodImpl(MethodImplOptions.AggressiveInlining)]
+    private static byte AddMod7(byte value, byte delta)
+    {
+        const int Modulus = 7;
+        int sum = value + delta;
+
+        if (sum >= Modulus)
+        {
+            sum -= Modulus;
+        }
+
+        return (byte)sum;
+    }
+
+    [MethodImpl(MethodImplOptions.AggressiveInlining)]
+    private static byte AddMod10(byte value, byte delta)
+    {
+        const int Modulus = 10;
+        int sum = value + delta;
+
+        if (sum >= Modulus)
+        {
+            sum -= Modulus;
+        }
+
+        return (byte)sum;
+    }
+
+    [MethodImpl(MethodImplOptions.AggressiveInlining)]
+    private static byte AddMod11(byte value, byte delta)
+    {
+        const int Modulus = 11;
+        int sum = value + delta;
+
+        if (sum >= Modulus)
+        {
+            sum -= Modulus;
+        }
+
+        return (byte)sum;
+    }
+
+    [MethodImpl(MethodImplOptions.AggressiveInlining)]
+    private static byte AddMod8(byte value, byte delta)
+    {
+        return (byte)((value + delta) & 7);
+    }
 
 
     private static ulong ComputeDivisorLimitFromMaxPrimeGpu(ulong maxPrime)
@@ -557,27 +602,25 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
             ArrayView1D<byte, Stride1D.Dense> hitView = _hitBuffer.View;
 
             GpuDivisorPartialData partialData = new GpuDivisorPartialData(divisor);
-            divisorView.SubView(0, 1).CopyFromCPU(ref partialData, 1);
+            divisorView.CopyFromCPU(ref partialData, 1);
 
             int offsetValue = 0;
-            offsetView.SubView(0, 1).CopyFromCPU(ref offsetValue, 1);
+            offsetView.CopyFromCPU(ref offsetValue, 1);
 
             int countValue = length;
-            countView.SubView(0, 1).CopyFromCPU(ref countValue, 1);
+            countView.CopyFromCPU(ref countValue, 1);
 
             ulong cycleValue = cycle;
-            cycleView.SubView(0, 1).CopyFromCPU(ref cycleValue, 1);
+            cycleView.CopyFromCPU(ref cycleValue, 1);
 
             Span<ulong> hostSpan = _hostBuffer.AsSpan(0, length);
             primes.CopyTo(hostSpan);
+            ref ulong hostRef = ref MemoryMarshal.GetReference(hostSpan);
 
-            ArrayView1D<ulong, Stride1D.Dense> exponentSlice = exponentView.SubView(0, length);
-            exponentSlice.CopyFromCPU(ref MemoryMarshal.GetReference(hostSpan), length);
-
-            ArrayView1D<byte, Stride1D.Dense> hitSliceView = hitView.SubView(0, length);
+            exponentView.CopyFromCPU(ref hostRef, length);
 
             int sentinel = int.MaxValue;
-            firstHitView.SubView(0, 1).CopyFromCPU(ref sentinel, 1);
+            firstHitView.CopyFromCPU(ref sentinel, 1);
 
             var kernel = _kernel;
             if (kernel is null)
@@ -586,10 +629,11 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
                 throw new InvalidOperationException("GPU divisor kernel was not initialized.");
             }
 
-            kernel(1, divisorView, offsetView, countView, exponentSlice, cycleView, hitSliceView, firstHitView);
+            kernel(1, divisorView, offsetView, countView, exponentView, cycleView, hitView, firstHitView);
 
             Span<byte> hitSlice = hits.Slice(0, length);
-            hitSliceView.CopyToCPU(ref MemoryMarshal.GetReference(hitSlice), length);
+            ref byte hitRef = ref MemoryMarshal.GetReference(hitSlice);
+            hitView.CopyToCPU(ref hitRef, length);
 
             Monitor.Exit(_lease.ExecutionLock);
         }
@@ -688,8 +732,6 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
 
         internal ulong[] Exponents { get; private set; } = null!;
 
-        internal ulong[] FilteredDivisors { get; private set; } = null!;
-
         internal GpuDivisorPartialData[] DivisorData { get; private set; } = null!;
 
         internal int[] Offsets { get; private set; } = null!;
@@ -764,7 +806,6 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
 
             Divisors = ulongPool.Rent(capacity);
             Exponents = ulongPool.Rent(capacity);
-            FilteredDivisors = ulongPool.Rent(capacity);
             DivisorData = partialPool.Rent(capacity);
             Offsets = intPool.Rent(capacity);
             Counts = intPool.Rent(capacity);
@@ -803,14 +844,12 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
             ArrayPool<GpuDivisorPartialData> partialPool = ThreadStaticPools.GpuDivisorPartialDataPool;
             ulongPool.Return(Divisors, clearArray: false);
             ulongPool.Return(Exponents, clearArray: false);
-            ulongPool.Return(FilteredDivisors, clearArray: false);
             partialPool.Return(DivisorData, clearArray: false);
             intPool.Return(Offsets, clearArray: false);
             intPool.Return(Counts, clearArray: false);
             ulongPool.Return(Cycles, clearArray: false);
             Divisors = Array.Empty<ulong>();
             Exponents = Array.Empty<ulong>();
-            FilteredDivisors = Array.Empty<ulong>();
             DivisorData = Array.Empty<GpuDivisorPartialData>();
             Offsets = Array.Empty<int>();
             Counts = Array.Empty<int>();

PerfectNumbers.Core/MersenneDivisorCycles.cs

@@ -4,6 +4,7 @@ using System.Numerics;
 using System.Runtime.CompilerServices;
 using System.Security.Cryptography;
 using System.Text;
+using System.Runtime.InteropServices;
 using PerfectNumbers.Core.Gpu;
 using ILGPU;
 using ILGPU.Runtime;
@@ -379,7 +380,8 @@ public class MersenneDivisorCycles
 		for (int i = 0; i < smallLength; i++)
 		{
 			ulong prime = smallPrimes[i];
-			if (smallPrimesSquared[i] > remaining)
+			ulong primeSquared = smallPrimesSquared[i];
+			if (primeSquared > remaining)
 			{
 				break;
 			}
@@ -438,26 +440,14 @@ public class MersenneDivisorCycles
 
     private static void AddFactor(Dictionary<ulong, int> counts, ulong factor)
     {
-        if (counts.TryGetValue(factor, out int existing))
-        {
-            counts[factor] = existing + 1;
-        }
-        else
-        {
-            counts[factor] = 1;
-        }
+        ref int entry = ref CollectionsMarshal.GetValueRefOrAddDefault(counts, factor, out bool exists);
+        entry = exists ? entry + 1 : 1;
     }
 
     private static void AddFactor(Dictionary<ulong, int> counts, ulong factor, int multiplicity)
     {
-        if (counts.TryGetValue(factor, out int existing))
-        {
-            counts[factor] = existing + multiplicity;
-        }
-        else
-        {
-            counts[factor] = multiplicity;
-        }
+        ref int entry = ref CollectionsMarshal.GetValueRefOrAddDefault(counts, factor, out bool exists);
+        entry = exists ? entry + multiplicity : multiplicity;
     }
 
     private static ulong ReduceOrder(in MontgomeryDivisorData divisorData, ulong initialOrder, Dictionary<ulong, int> factorCounts)
@@ -535,8 +525,8 @@ public class MersenneDivisorCycles
     private static void ProcessReduceOrderPrime(Span<ulong> candidateBuffer, Span<bool> evaluationBuffer, ref ulong order, ulong prime, int multiplicity, ref ExponentRemainderStepperCpu stepper)
     {
         ulong working = order;
-        int actual = 0;
-        while (actual < multiplicity)
+        int writeIndex = multiplicity;
+        while (writeIndex > 0)
         {
             if (working < prime)
             {
@@ -549,26 +539,20 @@ public class MersenneDivisorCycles
                 break;
             }
 
-            candidateBuffer[actual] = reduced;
+            writeIndex--;
+            candidateBuffer[writeIndex] = reduced;
             working = reduced;
-            actual++;
         }
 
+        int actual = multiplicity - writeIndex;
         if (actual == 0)
         {
             return;
         }
 
-        Span<ulong> candidates = candidateBuffer.Slice(0, actual);
+        Span<ulong> candidates = candidateBuffer.Slice(writeIndex, actual);
         Span<bool> evaluations = evaluationBuffer.Slice(0, actual);
 
-        for (int left = 0, right = actual - 1; left < right; left++, right--)
-        {
-            ulong tmp = candidates[left];
-            candidates[left] = candidates[right];
-            candidates[right] = tmp;
-        }
-
         stepper.Reset();
 
         evaluations[0] = stepper.InitializeCpuIsUnity(candidates[0]);
@@ -598,24 +582,28 @@ public class MersenneDivisorCycles
         //     return 2UL;
         // }
 
+        ulong modulus = n;
+        ulong nMinus1 = modulus - 1UL;
+        ulong nMinus2 = modulus - 2UL;
+
         while (true)
         {
-            ulong c = (NextRandomUInt64() % (n - 1UL)) + 1UL;
-            ulong x = (NextRandomUInt64() % (n - 2UL)) + 2UL;
+            ulong c = (NextRandomUInt64() % nMinus1) + 1UL;
+            ulong x = (NextRandomUInt64() % nMinus2) + 2UL;
             ulong y = x;
             ulong d = 1UL;
 
             while (d == 1UL)
             {
-                x = AdvancePolynomial(x, c, n);
-                y = AdvancePolynomial(y, c, n);
-                y = AdvancePolynomial(y, c, n);
+                x = AdvancePolynomial(x, c, modulus);
+                y = AdvancePolynomial(y, c, modulus);
+                y = AdvancePolynomial(y, c, modulus);
 
                 ulong diff = x > y ? x - y : y - x;
-                d = BinaryGcd(diff, n);
+                d = BinaryGcd(diff, modulus);
             }
 
-            if (d != n)
+            if (d != modulus)
             {
                 return d;
             }

PerfectNumbers.Core/MersenneNumberDivisorByDivisorTester.cs

@@ -93,9 +93,15 @@ public static class MersenneNumberDivisorByDivisorTester
 			}
 			else
 			{
-				while (startIndex > 0 && candidates[startIndex - 1] >= startPrime)
+				while (startIndex > 0)
 				{
-					startIndex--;
+					int previousIndex = startIndex - 1;
+					if (candidates[previousIndex] < startPrime)
+					{
+						break;
+					}
+
+					startIndex = previousIndex;
 				}
 			}
 		}

PerfectNumbers.Core/PrimeOrderCalculator.Cpu.cs

@@ -299,22 +299,16 @@ internal static partial class PrimeOrderCalculator
 		Span<ulong> candidates = candidateBuffer[..actual];
 		Span<bool> evaluations = evaluationBuffer[..actual];
 
-		for (int left = 0, right = actual - 1; left < right; left++, right--)
-		{
-			ulong tmp = candidates[left];
-			candidates[left] = candidates[right];
-			candidates[right] = tmp;
-		}
-
 		stepper.Reset();
 
-		evaluations[0] = stepper.InitializeCpuIsUnity(candidates[0]);
-		for (int j = 1; j < actual; j++)
+		int last = actual - 1;
+		evaluations[last] = stepper.InitializeCpuIsUnity(candidates[last]);
+		for (int j = last - 1; j >= 0; j--)
 		{
 			evaluations[j] = stepper.ComputeNextIsUnity(candidates[j]);
 		}
 
-		for (int j = actual - 1; j >= 0; j--)
+		for (int j = 0; j < actual; j++)
 		{
 			if (!evaluations[j])
 			{
@@ -464,16 +458,16 @@ internal static partial class PrimeOrderCalculator
 		}
 
 		Span<ulong> candidates = buffer[..actual];
-		candidates.Reverse();
 
 		stepper.Reset();
 
-		if (stepper.InitializeCpuIsUnity(candidates[0]))
+		int last = actual - 1;
+		if (stepper.InitializeCpuIsUnity(candidates[last]))
 		{
 			return true;
 		}
 
-		for (int j = 1; j < actual; j++)
+		for (int j = last - 1; j >= 0; j--)
 		{
 			if (stepper.ComputeNextIsUnity(candidates[j]))
 			{
@@ -694,13 +688,16 @@ internal static partial class PrimeOrderCalculator
 	private static void SortCandidates(ulong prime, ulong? previousOrder, List<ulong> candidates)
 	{
 		ulong previous = previousOrder ?? 0UL;
-		int previousGroup = previousOrder.HasValue ? GetGroup(previousOrder.Value, prime) : 1;
 		bool hasPrevious = previousOrder.HasValue;
+		ulong threshold1 = prime >> 3;
+		ulong threshold2 = prime >> 2;
+		ulong threshold3 = (prime * 3UL) >> 3;
+		int previousGroup = hasPrevious ? GetGroup(previous, threshold1, threshold2, threshold3) : 1;
 
 		candidates.Sort((x, y) =>
 		{
-			CandidateKey keyX = BuildKey(x, prime, previous, previousGroup, hasPrevious);
-			CandidateKey keyY = BuildKey(y, prime, previous, previousGroup, hasPrevious);
+			CandidateKey keyX = BuildKey(x, previous, previousGroup, hasPrevious, threshold1, threshold2, threshold3);
+			CandidateKey keyY = BuildKey(y, previous, previousGroup, hasPrevious, threshold1, threshold2, threshold3);
 			int compare = keyX.Primary.CompareTo(keyY.Primary);
 			if (compare != 0)
 			{
@@ -717,9 +714,9 @@ internal static partial class PrimeOrderCalculator
 		});
 	}
 
-	private static CandidateKey BuildKey(ulong value, ulong prime, ulong previous, int previousGroup, bool hasPrevious)
+	private static CandidateKey BuildKey(ulong value, ulong previous, int previousGroup, bool hasPrevious, ulong threshold1, ulong threshold2, ulong threshold3)
 	{
-		int group = GetGroup(value, prime);
+		int group = GetGroup(value, threshold1, threshold2, threshold3);
 		if (group == 0)
 		{
 			return new CandidateKey(int.MaxValue, long.MaxValue, long.MaxValue);
@@ -769,21 +766,18 @@ internal static partial class PrimeOrderCalculator
 		return groupOffset + (isGe ? 0 : 1);
 	}
 
-	private static int GetGroup(ulong value, ulong prime)
+	private static int GetGroup(ulong value, ulong threshold1, ulong threshold2, ulong threshold3)
 	{
-		ulong threshold1 = prime >> 3;
 		if (value <= threshold1)
 		{
 			return 1;
 		}
 
-		ulong threshold2 = prime >> 2;
 		if (value <= threshold2)
 		{
 			return 2;
 		}
 
-		ulong threshold3 = (prime * 3UL) >> 3;
 		if (value <= threshold3)
 		{
 			return 3;
@@ -828,9 +822,11 @@ internal static partial class PrimeOrderCalculator
 		}
 
 		FactorEntry factor = factors[index];
+		int factorExponent = factor.Exponent;
 		ulong primeFactor = factor.Value;
 		ulong contribution = 1UL;
-		for (int exponent = 0; exponent <= factor.Exponent; exponent++)
+		ulong contributionLimit = factorExponent == 0 ? 0UL : order / primeFactor;
+		for (int exponent = 0; exponent <= factorExponent; exponent++)
 		{
 			ulong nextDivisor = divisorProduct * contribution;
 			if (nextDivisor > order)
@@ -844,12 +840,12 @@ internal static partial class PrimeOrderCalculator
 				return;
 			}
 
-			if (exponent == factor.Exponent)
+			if (exponent == factorExponent)
 			{
 				break;
 			}
 
-			if (contribution > order / primeFactor)
+			if (contribution > contributionLimit)
 			{
 				break;
 			}
@@ -973,24 +969,45 @@ internal static partial class PrimeOrderCalculator
 		}
 
 		Span<ulong> candidates = buffer[..actual];
-		candidates.Reverse();
 
 		stepper.Reset();
+		int last = actual - 1;
 
-		if (powUsed >= powBudget && powBudget > 0)
+		bool enforceBudget = powBudget > 0;
+		if (!enforceBudget)
+		{
+			powUsed++;
+			if (stepper.InitializeCpuIsUnity(candidates[last]))
+			{
+				return true;
+			}
+
+			for (int j = last - 1; j >= 0; j--)
+			{
+				powUsed++;
+				if (stepper.ComputeNextIsUnity(candidates[j]))
+				{
+					return true;
+				}
+			}
+
+			return false;
+		}
+
+		if (powUsed >= powBudget)
 		{
 			return true;
 		}
 
 		powUsed++;
-		if (stepper.InitializeCpuIsUnity(candidates[0]))
+		if (stepper.InitializeCpuIsUnity(candidates[last]))
 		{
 			return true;
 		}
 
-		for (int j = 1; j < actual; j++)
+		for (int j = last - 1; j >= 0; j--)
 		{
-			if (powUsed >= powBudget && powBudget > 0)
+			if (powUsed >= powBudget)
 			{
 				return true;
 			}

docs/ByDivisorPathMap.md

@@ -0,0 +1,35 @@
+# --mersenne=bydivisor Path Map
+
+This temporary map tracks the code paths exercised by the `--mersenne=bydivisor` mode and notes the latest review status for each branch. Entries move from _Queued_ to _Reviewed_ once the surrounding loops have been audited for invariant work.
+
+## High-level Flow
+- `EvenPerfectBitScanner` CLI parsing → _Reviewed_
+- `MersenneNumberDivisorByDivisorTester.Run` → _Reviewed_
+- `EvenPerfectBitScanner.IO.CalculationResultsFile`
+  - `LoadCandidatesWithinRange` → _Reviewed_
+  - `EnumerateCandidates` → _Reviewed_
+- `IMersenneNumberDivisorByDivisorTester` implementations
+  - `MersenneNumberDivisorByDivisorCpuTester`
+    - `IsPrime` → _Reviewed_
+    - `CheckDivisors` (128-bit path) → _Reviewed_
+    - `CheckDivisors64` → _Reviewed_
+  - `MersenneNumberDivisorByDivisorGpuTester`
+    - `IsPrime` → _Reviewed_
+    - `CheckDivisors` → _Reviewed_
+    - `DivisorByDivisorKernels.CheckKernel` → _Reviewed_
+
+- `MersenneDivisorCycles`
+  - `TryCalculateCycleLengthForExponentCpu` → _Reviewed_
+  - `TryFactorIntoCountsInternal` → _Reviewed_
+  - `PollardRho64` → _Reviewed_
+  - `ReduceOrder` (includes `ProcessReduceOrderPrime`) → _Reviewed_
+- `PrimeOrderCalculator`
+  - `InitializeStartingOrderCpu` → _Reviewed_
+  - `ExponentLoweringCpu` / `ProcessExponentLoweringPrime` → _Reviewed_
+  - `ValidateOrderAgainstFactors` / `ValidateOrderForFactor` → _Reviewed_
+  - `TryConfirmCandidateCpu` / `CheckCandidateViolation` → _Reviewed_
+  - `TryHeuristicFinishCpu` / `BuildCandidates` / `SortCandidates` → _Reviewed_
+
+## Next Steps
+- Hold for additional guidance on further --mersenne=bydivisor audits; computation branches documented above are fully reviewed.
+- Defer result aggregation and reporting reviews until instructed otherwise, keeping the focus on computation-only branches.

docs/HeuristicIsPrimePlan.md

@@ -136,7 +136,7 @@ The plan incorporates the updated divisor-class heuristics (Groups A/B, wheels,
    * [done] Kept GPU divisibility in standard modular arithmetic while reserving Montgomery transforms for CPU confirmation logic.
    * [done] When the temporary Group B gate is disabled, delegate GPU calls to the CPU fallback so Group A coverage remains in place while the accelerator path stays available for future re-enablement.
 8. [done] **Refactor by-divisor CPU/GPU testers to reuse heuristics**
-   * [done] Drove `MersenneNumberDivisorByDivisorCpuTester.CheckDivisors` from `HeuristicPrimeTester.CreateMersenneDivisorEnumerator`, eliminating the bespoke residue loop while preserving the existing status counters.
+   * [done] Drove `MersenneNumberDivisorByDivisorCpuTester.CheckDivisors` from `HeuristicPrimeTester.CreateMersenneDivisorEnumerator`, eliminating the bespoke residue loop and retiring the legacy status counter.
    * [done] Streamed GPU batches from the same enumerator and Montgomery preparation data, removing the filtered-divisor scratch arrays while continuing to feed the existing kernel and hit bookkeeping.
 9. [done] **Route legacy prime checks through heuristics**
    * [done] Introduce `HeuristicPrimeTester` so heuristic CPU/GPU checks live alongside the legacy `PrimeTester` implementations while callers opt in explicitly.

todo_list.txt

@@ -41,7 +41,6 @@ Montgomery Primitives
 Cycle-Aware Modular Arithmetic
 
 Status & Progress Reporting
-- PerfectNumbers.Core/Cpu/MersenneNumberDivisorByDivisorCpuTester.cs:296: Replace this modulo with the ring-buffer style counter (subtract loop) used in the fast CLI status benchmarks so we avoid `%` in this hot loop while still wrapping progress correctly.
 
 Cycle Remainder Steppers
 - PerfectNumbers.Core/CycleRemainderStepper.cs:28: Inline this reset at the call sites so the hot loops reuse struct reinitialization measured fastest in MersenneDivisorCycleLengthGpuBenchmarks, avoiding the extra method call when scanners need to restart stepping.