Extract divisor validator and rename legacy CPU prime helper

EvenPerfectBitScanner.Benchmarks/PrimeTesterBenchmarks.cs

@@ -105,7 +105,7 @@ public class PrimeTesterBenchmarks
 
         for (int i = 0; i < values.Length; i++)
         {
-            if (PrimeTester.IsPrimeCp(values[i], cancellationToken))
+            if (PrimeTester.IsPrimeCpu(values[i], cancellationToken))
             {
                 primeCount++;
             }

PerfectNumbers.Core/DivisorGenerator.cs

@@ -0,0 +1,38 @@
+using System.Runtime.CompilerServices;
+
+namespace PerfectNumbers.Core;
+
+internal static class DivisorGenerator
+{
+    private const ushort DecimalMaskWhenLastIsSeven = (1 << 3) | (1 << 7) | (1 << 9);
+    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)
+    {
+        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;
+    }
+}

PerfectNumbers.Core/Gpu/MersenneNumberDivisorByDivisorGpuTester.cs

@@ -263,7 +263,7 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
             {
                 ulong candidate = (ulong)nextDivisor128;
 
-                if (CandidatePassesHeuristics(localRemainder10, localRemainder8, localRemainder3, localRemainder5, localRemainder7, localRemainder11, lastDigit))
+                if (DivisorGenerator.IsValidDivisor(localRemainder10, localRemainder8, localRemainder3, localRemainder5, localRemainder7, localRemainder11, lastDigit))
                 {
                     filteredStorage[filteredCount++] = candidate;
                 }
@@ -378,38 +378,6 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
         return computedCycle;
     }
 
-    [MethodImpl(MethodImplOptions.AggressiveInlining)]
-    private static bool CandidatePassesHeuristics(
-        byte remainder10,
-        byte remainder8,
-        byte remainder3,
-        byte remainder5,
-        byte remainder7,
-        byte remainder11,
-        LastDigit lastDigit)
-    {
-        const ushort DecimalMaskWhenLastIsSeven = (1 << 3) | (1 << 7) | (1 << 9);
-        const ushort DecimalMaskOtherwise = (1 << 1) | (1 << 3) | (1 << 9);
-
-        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;
-    }
-
     [MethodImpl(MethodImplOptions.AggressiveInlining)]
     private static byte AddMod(byte value, byte delta, byte modulus)
     {

PerfectNumbers.Core/MersenneDivisorCycles.cs

@@ -394,9 +394,9 @@ public class MersenneDivisorCycles
             return true;
         }
 
-        // TODO: Benchmark PrimeTester.IsPrimeCp against Open.Numeric.Primes on the EvenPerfectBitScanner workloads to confirm the faster option for wide composites.
+        // TODO: Benchmark PrimeTester.IsPrimeCpu against Open.Numeric.Primes on the EvenPerfectBitScanner workloads to confirm the faster option for wide composites.
         // if (HeuristicPrimeTester.Exclusive.IsPrimeCpu(remaining, CancellationToken.None))
-        if (PrimeTester.IsPrimeCp(remaining, CancellationToken.None))
+        if (PrimeTester.IsPrimeCpu(remaining, CancellationToken.None))
         {
             AddFactor(counts, remaining);
             return true;
@@ -929,7 +929,7 @@ public class MersenneDivisorCycles
         }
 
         // if (!skipPrimeOrderHeuristic && HeuristicPrimeTester.Exclusive.IsPrimeCpu(divisor, CancellationToken.None))
-        if (!skipPrimeOrderHeuristic && PrimeTester.IsPrimeCp(divisor, CancellationToken.None))
+        if (!skipPrimeOrderHeuristic && PrimeTester.IsPrimeCpu(divisor, CancellationToken.None))
         {
             ulong computedOrder = PrimeOrderCalculator.Calculate(
                     divisor,

PerfectNumbers.Core/MersennePrimeFactorTester.cs

@@ -26,7 +26,7 @@ public static class MersennePrimeFactorTester
         }
 
         // if (!HeuristicPrimeTester.Exclusive.IsPrimeCpu(q, ct))
-        if (!PrimeTester.IsPrimeCp(q, ct))
+        if (!PrimeTester.IsPrimeCpu(q, ct))
         {
             return false;
         }
@@ -235,7 +235,7 @@ public static class MersennePrimeFactorTester
             }
 
             // if (HeuristicPrimeTester.Exclusive.IsPrimeCpu(m, ct))
-            if (PrimeTester.IsPrimeCp(m, ct))
+            if (PrimeTester.IsPrimeCpu(m, ct))
             {
                 dict[m] = 1;
                 continue;

PerfectNumbers.Core/PrimeOrderCalculator.Cpu.cs

@@ -516,7 +516,7 @@ internal static partial class PrimeOrderCalculator
 					return false;
 				}
 
-				// if (!PrimeTester.IsPrimeCp(orderFactors.Cofactor, CancellationToken.None))
+				// if (!PrimeTester.IsPrimeCpu(orderFactors.Cofactor, CancellationToken.None))
 				if (!orderFactors.CofactorIsPrime)
 				{
 					return false;
@@ -1123,8 +1123,8 @@ internal static partial class PrimeOrderCalculator
 					// }
 
 					// bool isPrime = primeTester.HeuristicIsPrimeGpu(composite);
-					// bool isPrime = PrimeTester.IsPrimeCp(composite, CancellationToken.None);
+					// bool isPrime = PrimeTester.IsPrimeCpu(composite, CancellationToken.None);
-					bool isPrime = PrimeTester.IsPrimeCp(composite, CancellationToken.None);
+					bool isPrime = PrimeTester.IsPrimeCpu(composite, CancellationToken.None);
 					// bool isPrime = Open.Numeric.Primes.Prime.Numbers.IsPrime(composite);
 
 					if (isPrime)
@@ -1186,8 +1186,8 @@ internal static partial class PrimeOrderCalculator
 			if (!entry.HasKnownPrimality)
 			{
 				// bool isPrime = primeTester.HeuristicIsPrimeGpu(composite);
-				// bool isPrime = PrimeTester.IsPrimeCp(composite, CancellationToken.None);
+				// bool isPrime = PrimeTester.IsPrimeCpu(composite, CancellationToken.None);
-				bool isPrime = PrimeTester.IsPrimeCp(composite, CancellationToken.None);
+				bool isPrime = PrimeTester.IsPrimeCpu(composite, CancellationToken.None);
 				// bool isPrime = Open.Numeric.Primes.Prime.Numbers.IsPrime(composite);
 				
 				entry = entry.WithPrimality(isPrime);
@@ -1219,8 +1219,8 @@ internal static partial class PrimeOrderCalculator
 		else
 		{
 			// cofactorIsPrime = primeTester.HeuristicIsPrimeGpu(cofactor);
-			// cofactorIsPrime = PrimeTester.IsPrimeCp(cofactor, CancellationToken.None);
+			// cofactorIsPrime = PrimeTester.IsPrimeCpu(cofactor, CancellationToken.None);
-			cofactorIsPrime = PrimeTester.IsPrimeCp(cofactor, CancellationToken.None);
+			cofactorIsPrime = PrimeTester.IsPrimeCpu(cofactor, CancellationToken.None);
 			// cofactorIsPrime = Open.Numeric.Primes.Prime.Numbers.IsPrime(cofactor);
 		}
 
@@ -1752,8 +1752,8 @@ internal static partial class PrimeOrderCalculator
 		PrimeTester primeTester = PrimeTester.Exclusive;
 
 		// bool isPrime = primeTester.HeuristicIsPrimeGpu(value);
-		// bool isPrime = PrimeTester.IsPrimeCp(value, CancellationToken.None);
+		// bool isPrime = PrimeTester.IsPrimeCpu(value, CancellationToken.None);
-		bool isPrime = PrimeTester.IsPrimeCp(value, CancellationToken.None);
+		bool isPrime = PrimeTester.IsPrimeCpu(value, CancellationToken.None);
 		// bool isPrime = Open.Numeric.Primes.Prime.Numbers.IsPrime(value);
 		if (!knownComposite && isPrime)
 		{
@@ -1765,8 +1765,8 @@ internal static partial class PrimeOrderCalculator
 		ulong quotient = value / factor;
 
 		// isPrime = primeTester.HeuristicIsPrimeGpu(factor);
-		// isPrime = PrimeTester.IsPrimeCp(factor, CancellationToken.None);
+		// isPrime = PrimeTester.IsPrimeCpu(factor, CancellationToken.None);
-		isPrime = PrimeTester.IsPrimeCp(factor, CancellationToken.None);
+		isPrime = PrimeTester.IsPrimeCpu(factor, CancellationToken.None);
 		// isPrime = Open.Numeric.Primes.Prime.Numbers.IsPrime(factor);
 		if (isPrime)
 		{
@@ -1797,8 +1797,8 @@ internal static partial class PrimeOrderCalculator
 		else
 		{
 			// isPrime = primeTester.HeuristicIsPrimeGpu(quotient);
-			// isPrime = PrimeTester.IsPrimeCp(quotient, CancellationToken.None);
+			// isPrime = PrimeTester.IsPrimeCpu(quotient, CancellationToken.None);
-			isPrime = PrimeTester.IsPrimeCp(quotient, CancellationToken.None);
+			isPrime = PrimeTester.IsPrimeCpu(quotient, CancellationToken.None);
 			// isPrime = Open.Numeric.Primes.Prime.Numbers.IsPrime(quotient);
 		}
 

PerfectNumbers.Core/PrimeOrderCalculator.Shared.cs

@@ -956,7 +956,7 @@ internal static partial class PrimeOrderCalculator
         if (value <= ulong.MaxValue)
         {
             // return HeuristicPrimeTester.Exclusive.IsPrimeCpu((ulong)value, CancellationToken.None);
-            return PrimeTester.IsPrimeCp((ulong)value, CancellationToken.None);
+            return PrimeTester.IsPrimeCpu((ulong)value, CancellationToken.None);
         }
 
         if ((value & UInt128.One) == UInt128.Zero)

PerfectNumbers.Core/PrimeTester.cs

@@ -93,10 +93,10 @@ public sealed class PrimeTester
         bool gpuReportedPrime = !forceCpu && !belowGpuRange && outFlags[0] != 0;
         bool requiresCpuFallback = forceCpu || belowGpuRange || !gpuReportedPrime;
 
-        return requiresCpuFallback ? IsPrimeCp(n, ct) : true;
+        return requiresCpuFallback ? IsPrimeCpu(n, ct) : true;
     }
 
-    public static bool IsPrimeCp(ulong n, CancellationToken ct)
+    public static bool IsPrimeCpu(ulong n, CancellationToken ct)
     {
         // Preserve the legacy entry point for callers that bypass the thread-local caches.
         return Exclusive.IsPrime(n, ct);

docs/HeuristicIsPrimePlan.md

@@ -64,12 +64,12 @@ public bool IsPrimeGpu(ulong n, CancellationToken ct)
     bool gpuReportedPrime = !forceCpu && !belowGpuRange && outFlags[0] != 0;
     bool requiresCpuFallback = forceCpu || belowGpuRange || !gpuReportedPrime;
 
-    return requiresCpuFallback ? IsPrimeCp(n, ct) : true;
+    return requiresCpuFallback ? IsPrimeCpu(n, ct) : true;
 }
 ```
 
 ```csharp
-internal static bool IsPrimeCp(ulong n, CancellationToken ct)
+internal static bool IsPrimeCpu(ulong n, CancellationToken ct)
 {
     bool isTwo = n == 2UL;
     bool isOdd = (n & 1UL) != 0UL;
@@ -113,7 +113,7 @@ internal static bool IsPrimeCp(ulong n, CancellationToken ct)
 
 The plan incorporates the updated divisor-class heuristics (Groups A/B, wheels, residue priorities) and connects them to both CPU and GPU execution, including every by-divisor integration point. Items already completed are marked with `[done]`.
 
-1. [done] **Snapshot current implementations** – preserve `IsPrimeGpu` and `IsPrimeCp` as references for regression comparisons and migration checkpoints (see Section 2).
+1. [done] **Snapshot current implementations** – preserve `IsPrimeGpu` and `IsPrimeCpu` as references for regression comparisons and migration checkpoints (see Section 2).
 2. [done] **Introduce placeholder heuristic entry points** – add `IsPrimeCpu` and `IsPrimeGpu` by copying the current internal and GPU methods so subsequent commits can iterate without disrupting legacy behavior.
 3. [done] **Design shared heuristic scaffolding**
    * [done] Added `HeuristicPrimeSieves` to precompute 4M-entry Group A/B divisor tables so heuristic prime checks reuse cached sequences without regenerating wheel steps at runtime; the enumerator remains available for residue-driven consumers.
@@ -140,7 +140,7 @@ The plan incorporates the updated divisor-class heuristics (Groups A/B, wheels,
    * [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.
-   * [done] Maintain legacy paths for benchmarking via `PrimeTester.IsPrimeCp`, `PrimeTester.Exclusive.IsPrimeGpu`, and the explicit `HeuristicPrimeTester` entry points so benchmark harnesses can compare behaviours without runtime switches.
+   * [done] Maintain legacy paths for benchmarking via `PrimeTester.IsPrimeCpu`, `PrimeTester.Exclusive.IsPrimeGpu`, and the explicit `HeuristicPrimeTester` entry points so benchmark harnesses can compare behaviours without runtime switches.
 10. **Validation and benchmarking**
     * Create targeted unit tests covering boundary cases for Group A/B transitions, wheel enumerations, residue deltas, and the stop-on-hit behaviour.
     * Expand GPU test harnesses to assert equivalence between CPU/GPU heuristics on sampled composite and prime inputs and to verify the residue-stream contract with by-divisor sessions.

docs/HeuristicIsPrimeSpecification.md

@@ -62,7 +62,7 @@ No other endings are allowed or reordered.
 ## Default Prime Tester Entry Points
 
 * `PrimeTester.IsPrime` and `PrimeTester.IsPrimeGpu` continue to run the legacy trial-division and GPU sieve paths. Use `HeuristicPrimeTester` when the heuristic CPU/GPU flow is required.
-* `HeuristicPrimeTester` always executes the heuristic CPU/GPU implementations; opt into the legacy paths by calling `PrimeTester.IsPrimeCp` or `PrimeTester.Exclusive.IsPrimeGpu` directly.
+* `HeuristicPrimeTester` always executes the heuristic CPU/GPU implementations; opt into the legacy paths by calling `PrimeTester.IsPrimeCpu` or `PrimeTester.Exclusive.IsPrimeGpu` directly.
 * Benchmark harnesses can compare behaviours by calling the legacy helpers on `PrimeTester` alongside the heuristic equivalents on `HeuristicPrimeTester`.
 
 ## Integration with the By-Divisor Pipeline

todo_list.txt

@@ -18,7 +18,7 @@ Divisor Cycle Cache & Generation
 - PerfectNumbers.Core/UInt128Extensions.cs:372: If the cache lacks this cycle, immediately schedule the configured device (GPU by default) to compute it on the fly and skip inserting it into the cache so wide-order factoring can still leverage cycle stepping without breaching the memory cap or introducing extra synchronization.
 
 Primality & Order Screening
-- PerfectNumbers.Core/MersenneDivisorCycles.cs:477: Benchmark PrimeTester.IsPrimeCp against Open.Numeric.Primes on the EvenPerfectBitScanner workloads to confirm the faster option for wide composites.
+- PerfectNumbers.Core/MersenneDivisorCycles.cs:477: Benchmark PrimeTester.IsPrimeCpu against Open.Numeric.Primes on the EvenPerfectBitScanner workloads to confirm the faster option for wide composites.
 - PerfectNumbers.Core/ULongExtensions.cs:119: When the shared cycle snapshot cannot serve this divisor, trigger an on-demand GPU computation (respecting the configured device) without promoting the result into the cache so the order calculator still benefits from cycle stepping while keeping the single-block memory plan intact.
 - PerfectNumbers.Core/ULongExtensions.cs:132: Replace this `%` driven factor peeling with the divisor-cycle aware factoring helper so large orders reuse the cached remainders highlighted in the latest divisor-cycle benchmarks instead of recomputing slow modulo checks.
 - PerfectNumbers.Core/ULongExtensions.cs:279: Swap this modulo check for the shared small-prime cycle filter once the divisor-cycle cache is mandatory, matching the PrimeTester improvements noted in the CPU sieve benchmarks.