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Merge pull request #24 from mlemanczyk/codex/modify-evenperfectbitscanner-for-residue-mode

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Report residue scan exhaustion through detailed checks
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Marek Lemańczyk authored and GitHub committed 2025-09-17 19:02:45 +02:00
2 parents b1c29ad16e 1b28584168
commit 2d024cc708
7 files changed
+465 -224
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EvenPerfectBitScanner.Tests/ProgramTests.cs
+91 -2
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@@ -142,6 +142,95 @@ public class ProgramTests
} }
} }
[Fact]
public void Divisor_mode_sets_detailedCheck_when_divisor_is_found()
{
var useDivisorField = typeof(Program).GetField("_useDivisor", BindingFlags.NonPublic | BindingFlags.Static)!;
var divisorField = typeof(Program).GetField("_divisor", BindingFlags.NonPublic | BindingFlags.Static)!;
var testerField = typeof(Program).GetField("_divisorTester", BindingFlags.NonPublic | BindingFlags.Static)!;
var candidatesField = typeof(MersenneNumberDivisorGpuTester).GetField("_divisorCandidates", BindingFlags.NonPublic | BindingFlags.Static)!;
var primeField = typeof(Program).GetField("PrimeTesters", BindingFlags.NonPublic | BindingFlags.Static)!;
var residueField = typeof(Program).GetField("PResidue", BindingFlags.NonPublic | BindingFlags.Static)!;
var forceCpuProp = typeof(GpuContextPool).GetProperty("ForceCpu");
useDivisorField.SetValue(null, true);
divisorField.SetValue(null, UInt128.Zero);
testerField.SetValue(null, new MersenneNumberDivisorGpuTester());
primeField.SetValue(null, new ThreadLocal<PrimeTester>(() => new PrimeTester(), trackAllValues: true));
residueField.SetValue(null, new ThreadLocal<ModResidueTracker>(() => new ModResidueTracker(ResidueModel.Identity, 2UL, true), trackAllValues: true));
candidatesField.SetValue(null, new (ulong, uint)[] { (23UL, 11U) });
forceCpuProp!.SetValue(null, true);
try
{
Program.IsEvenPerfectCandidate(11UL, 32UL, out bool searched, out bool detailedCheck).Should().BeFalse();
searched.Should().BeTrue();
detailedCheck.Should().BeTrue();
}
finally
{
useDivisorField.SetValue(null, false);
testerField.SetValue(null, null);
candidatesField.SetValue(null, null);
primeField.SetValue(null, null);
residueField.SetValue(null, null);
forceCpuProp!.SetValue(null, false);
}
}
[Fact]
public void Residue_mode_sets_detailedCheck_based_on_exhaustion()
{
var useDivisorField = typeof(Program).GetField("_useDivisor", BindingFlags.NonPublic | BindingFlags.Static)!;
var residueModeField = typeof(Program).GetField("_useResidueMode", BindingFlags.NonPublic | BindingFlags.Static)!;
var mersenneField = typeof(Program).GetField("MersenneTesters", BindingFlags.NonPublic | BindingFlags.Static)!;
var primeField = typeof(Program).GetField("PrimeTesters", BindingFlags.NonPublic | BindingFlags.Static)!;
var residueField = typeof(Program).GetField("PResidue", BindingFlags.NonPublic | BindingFlags.Static)!;
var forceCpuProp = typeof(GpuContextPool).GetProperty("ForceCpu");
const ulong exponent = 7UL;
useDivisorField.SetValue(null, false);
residueModeField.SetValue(null, true);
primeField.SetValue(null, new ThreadLocal<PrimeTester>(() => new PrimeTester(), trackAllValues: true));
residueField.SetValue(null, new ThreadLocal<ModResidueTracker>(() => new ModResidueTracker(ResidueModel.Identity, exponent, true), trackAllValues: true));
forceCpuProp!.SetValue(null, true);
try
{
mersenneField.SetValue(null, new ThreadLocal<MersenneNumberTester>(() => new MersenneNumberTester(
useGpuScan: false,
useGpuOrder: false,
useResidue: true,
maxK: 0UL,
residueDivisorSets: 0UL), trackAllValues: true));
Program.IsEvenPerfectCandidate(exponent, 0UL, out bool searched, out bool detailedCheck).Should().BeTrue();
searched.Should().BeTrue();
detailedCheck.Should().BeFalse();
mersenneField.SetValue(null, new ThreadLocal<MersenneNumberTester>(() => new MersenneNumberTester(
useGpuScan: false,
useGpuOrder: false,
useResidue: true,
maxK: 4UL,
residueDivisorSets: 2UL), trackAllValues: true));
Program.IsEvenPerfectCandidate(exponent, 0UL, out searched, out detailedCheck).Should().BeTrue();
searched.Should().BeTrue();
detailedCheck.Should().BeTrue();
}
finally
{
mersenneField.SetValue(null, null);
primeField.SetValue(null, null);
residueField.SetValue(null, null);
residueModeField.SetValue(null, false);
forceCpuProp!.SetValue(null, false);
useDivisorField.SetValue(null, false);
}
}
[Fact] [Fact]
public void Divisor_mode_accepts_large_search_limit() public void Divisor_mode_accepts_large_search_limit()
{ {
@@ -223,7 +312,7 @@ public class ProgramTests
var forceCpuProp = typeof(GpuContextPool).GetProperty("ForceCpu"); var forceCpuProp = typeof(GpuContextPool).GetProperty("ForceCpu");
useDivisorField.SetValue(null, false); useDivisorField.SetValue(null, false);
mersenneField.SetValue(null, new ThreadLocal<MersenneNumberTester>(() => new MersenneNumberTester(useIncremental: true, useResidue: true, maxK: 1_000UL), trackAllValues: true)); mersenneField.SetValue(null, new ThreadLocal<MersenneNumberTester>(() => new MersenneNumberTester(useIncremental: true, useResidue: true, maxK: 1_000UL, residueDivisorSets: 1UL), trackAllValues: true));
primeField.SetValue(null, new ThreadLocal<PrimeTester>(() => new PrimeTester(), trackAllValues: true)); primeField.SetValue(null, new ThreadLocal<PrimeTester>(() => new PrimeTester(), trackAllValues: true));
residueField.SetValue(null, new ThreadLocal<ModResidueTracker>(() => new ModResidueTracker(ResidueModel.Identity, 2UL, true), trackAllValues: true)); residueField.SetValue(null, new ThreadLocal<ModResidueTracker>(() => new ModResidueTracker(ResidueModel.Identity, 2UL, true), trackAllValues: true));
forceCpuProp!.SetValue(null, false); forceCpuProp!.SetValue(null, false);
@@ -232,7 +321,7 @@ public class ProgramTests
{ {
Program.IsEvenPerfectCandidate(29UL, 0UL, out bool searched, out bool detailed).Should().BeFalse(); Program.IsEvenPerfectCandidate(29UL, 0UL, out bool searched, out bool detailed).Should().BeFalse();
searched.Should().BeTrue(); searched.Should().BeTrue();
detailed.Should().BeFalse(); detailed.Should().BeTrue();
Program.IsEvenPerfectCandidate(31UL, 0UL, out searched, out detailed).Should().BeTrue(); Program.IsEvenPerfectCandidate(31UL, 0UL, out searched, out detailed).Should().BeTrue();
searched.Should().BeTrue(); searched.Should().BeTrue();
EvenPerfectBitScanner/Program.cs
+24 -22
View File
@@ -435,19 +435,20 @@ internal static class Program
// Initialize per-thread p residue tracker (Identity model) at currentP // Initialize per-thread p residue tracker (Identity model) at currentP
if (!useDivisor) if (!useDivisor)
{ {
MersenneTesters = new ThreadLocal<MersenneNumberTester>(() => MersenneTesters = new ThreadLocal<MersenneNumberTester>(() =>
{ {
var tester = new MersenneNumberTester( var tester = new MersenneNumberTester(
useIncremental: !useLucas, useIncremental: !useLucas,
useOrderCache: false, useOrderCache: false,
kernelType: kernelType, kernelType: kernelType,
useModuloWorkaround: useModuloWorkaround, useModuloWorkaround: useModuloWorkaround,
useOrder: useOrder, useOrder: useOrder,
useGpuLucas: mersenneOnGpu, useGpuLucas: mersenneOnGpu,
useGpuScan: mersenneOnGpu, useGpuScan: mersenneOnGpu,
useGpuOrder: orderOnGpu, useGpuOrder: orderOnGpu,
useResidue: useResidue, useResidue: useResidue,
maxK: residueKMax); maxK: residueKMax,
residueDivisorSets: divisorCyclesSearchLimit);
if (!useLucas) if (!useLucas)
{ {
tester.WarmUpOrders(currentP, _orderWarmupLimitOverride ?? 5_000_000UL); tester.WarmUpOrders(currentP, _orderWarmupLimitOverride ?? 5_000_000UL);
@@ -731,7 +732,7 @@ internal static class Program
Console.WriteLine(" --divisor-cycles-device=cpu|gpu device for cycles generation (default gpu)"); Console.WriteLine(" --divisor-cycles-device=cpu|gpu device for cycles generation (default gpu)");
Console.WriteLine(" --divisor-cycles-batch-size=<value> batch size for cycles generation (default 512)"); Console.WriteLine(" --divisor-cycles-batch-size=<value> batch size for cycles generation (default 512)");
Console.WriteLine(" --divisor-cycles-continue continue divisor cycles generation"); Console.WriteLine(" --divisor-cycles-continue continue divisor cycles generation");
Console.WriteLine(" --divisor-cycles-limit=<value> cycle search iterations when --mersenne=divisor"); Console.WriteLine(" --divisor-cycles-limit=<value> cycle search iterations when --mersenne=divisor or residue");
Console.WriteLine(" --use-order test primality via q order"); Console.WriteLine(" --use-order test primality via q order");
Console.WriteLine(" --workaround-mod avoid '%' operator on the GPU"); Console.WriteLine(" --workaround-mod avoid '%' operator on the GPU");
@@ -1077,15 +1078,16 @@ internal static class Program
return false; return false;
} }
searchedMersenne = true; searchedMersenne = true;
if (_useDivisor) if (_useDivisor)
{ {
return _divisorTester!.IsPrime(p, _divisor, divisorCyclesSearchLimit, out detailedCheck); return _divisorTester!.IsPrime(p, _divisor, divisorCyclesSearchLimit, out detailedCheck);
} }
detailedCheck = MersenneTesters.Value!.IsMersennePrime(p); bool mersennePrime = MersenneTesters.Value!.IsMersennePrime(p, out bool residueExhausted);
return detailedCheck; detailedCheck = residueExhausted;
} return mersennePrime;
}
// Use ModResidueTracker with a small set of primes to pre-filter composite p. // Use ModResidueTracker with a small set of primes to pre-filter composite p.
private static bool IsCompositeByResidues(ulong p) private static bool IsCompositeByResidues(ulong p)
PerfectNumbers.Core.Tests/MersenneNumberResidueCpuTesterTests.cs
+11 -1
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@@ -24,8 +24,18 @@ public class MersenneNumberResidueCpuTesterTests
private static void RunCase(MersenneNumberResidueCpuTester tester, ulong exponent, ulong maxK, bool expectedPrime) private static void RunCase(MersenneNumberResidueCpuTester tester, ulong exponent, ulong maxK, bool expectedPrime)
{ {
bool isPrime = true; bool isPrime = true;
tester.Scan(exponent, (UInt128)exponent << 1, LastDigitIsSeven(exponent), (UInt128)maxK, ref isPrime); bool exhausted = false;
tester.Scan(
exponent,
(UInt128)exponent << 1,
LastDigitIsSeven(exponent),
(UInt128)maxK,
1UL,
(UInt128)maxK,
ref isPrime,
ref exhausted);
isPrime.Should().Be(expectedPrime); isPrime.Should().Be(expectedPrime);
exhausted.Should().BeTrue();
} }
} }
PerfectNumbers.Core.Tests/MersenneNumberResidueGpuTesterTests.cs
+11 -1
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@@ -27,8 +27,18 @@ public class MersenneNumberResidueGpuTesterTests
private static void RunCase(MersenneNumberResidueGpuTester tester, ulong exponent, ulong maxK, bool expectedPrime) private static void RunCase(MersenneNumberResidueGpuTester tester, ulong exponent, ulong maxK, bool expectedPrime)
{ {
bool isPrime = true; bool isPrime = true;
tester.Scan(exponent, (UInt128)exponent << 1, LastDigitIsSeven(exponent), (UInt128)maxK, ref isPrime); bool exhausted = false;
tester.Scan(
exponent,
(UInt128)exponent << 1,
LastDigitIsSeven(exponent),
(UInt128)maxK,
1UL,
(UInt128)maxK,
ref isPrime,
ref exhausted);
isPrime.Should().Be(expectedPrime); isPrime.Should().Be(expectedPrime);
exhausted.Should().BeTrue();
} }
} }
PerfectNumbers.Core/Cpu/MersenneNumberResidueCpuTester.cs
+166 -136
View File
@@ -5,25 +5,32 @@ public class MersenneNumberResidueCpuTester
private ModResidueTracker? _mersenneResidueTracker; private ModResidueTracker? _mersenneResidueTracker;
// CPU residue variant using tracker + unrolled residue updates (no method calls in the loop). // CPU residue variant using tracker + unrolled residue updates (no method calls in the loop).
public void Scan(ulong exponent, UInt128 twoP, bool lastIsSeven, UInt128 maxK, ref bool isPrime) public void Scan(
{ ulong exponent,
// Initialize/update Mersenne residue tracker and start a merge walk for ascending q divisors UInt128 twoP,
bool lastIsSeven,
UInt128 perSetLimit,
ulong setCount,
UInt128 overallLimit,
ref bool isPrime,
ref bool divisorsExhausted)
{
if (setCount == 0UL || perSetLimit == UInt128.Zero || overallLimit == UInt128.Zero)
{
return;
}
_mersenneResidueTracker ??= new(ResidueModel.Mersenne); // Initialize/update Mersenne residue tracker and start a merge walk for ascending q divisors
// For small divisors q <= 4,000,000 use cached cycle length to fast-path checks
// and avoid per-q powmods when possible when scanning lanes.
_mersenneResidueTracker.BeginMerge(exponent);
// Start at k = 1: q0 = 2*p*1 + 1 _mersenneResidueTracker ??= new(ResidueModel.Mersenne);
UInt128 k = UInt128.One; // For small divisors q <= 4,000,000 use cached cycle length to fast-path checks
UInt128 q = twoP + UInt128.One; // and avoid per-q powmods when possible when scanning lanes.
// Current residues _mersenneResidueTracker.BeginMerge(exponent);
q.Mod10_8_5_3(out ulong r10, out ulong r8, out ulong r5, out ulong r3);
// Step residues for q += 2*p ulong step10 = (ulong)(twoP % 10UL) % 10UL;
ulong step10 = (ulong)(twoP % 10UL) % 10UL; ulong step8 = (ulong)(twoP % 8UL);
ulong step8 = (ulong)(twoP % 8UL); ulong step3 = (ulong)(twoP % 3UL);
ulong step3 = (ulong)(twoP % 3UL); ulong step5 = (ulong)(twoP % 5UL);
ulong step5 = (ulong)(twoP % 5UL);
// Allowed last-digit sets for q depending on last digit of M_p // Allowed last-digit sets for q depending on last digit of M_p
// lastIsSeven == true => allow {7,9} // lastIsSeven == true => allow {7,9}
@@ -31,139 +38,162 @@ public class MersenneNumberResidueCpuTester
int allowMask = lastIsSeven ? CpuConstants.LastSevenMask10 : CpuConstants.LastOneMask10; int allowMask = lastIsSeven ? CpuConstants.LastSevenMask10 : CpuConstants.LastOneMask10;
// Predeclare temps to avoid redeclaration overhead in the loop // Predeclare temps to avoid redeclaration overhead in the loop
UInt128 remaining; UInt128 remaining;
int i, lanes; int i, lanes;
// per-lane residues // per-lane residues
ulong r10_0, r10_1, r10_2, r10_3, r8_0, r8_1, r8_2, r8_3, r3_0, r3_1, r3_2, r3_3, r5_0, r5_1, r5_2, r5_3; ulong r10_0, r10_1, r10_2, r10_3, r8_0, r8_1, r8_2, r8_3, r3_0, r3_1, r3_2, r3_3, r5_0, r5_1, r5_2, r5_3;
// q lanes // q lanes
UInt128 twoP2 = twoP + twoP, UInt128 twoP2 = twoP + twoP,
twoP3 = twoP2 + twoP, twoP3 = twoP2 + twoP,
twoP4 = twoP3 + twoP, twoP4 = twoP3 + twoP,
qIncremental; qIncremental;
bool localIsPrime, isDivider; bool localIsPrime, isDivider;
maxK++; ModResidueTracker tracker = _mersenneResidueTracker!;
UInt128 limitInclusive = overallLimit + UInt128.One;
for (ulong setIndex = 0; setIndex < setCount && Volatile.Read(ref isPrime); setIndex++)
{
UInt128 setOffset = perSetLimit * (UInt128)setIndex;
UInt128 k = setOffset + UInt128.One;
if (k >= limitInclusive)
{
break;
}
ModResidueTracker tracker = _mersenneResidueTracker!; UInt128 setLimitExclusive = setOffset + perSetLimit + UInt128.One;
while (k < maxK && (localIsPrime = Volatile.Read(ref isPrime))) if (setLimitExclusive > limitInclusive)
{ {
remaining = maxK - k; setLimitExclusive = limitInclusive;
if (remaining == UInt128.Zero) }
{
break;
}
lanes = remaining > 4UL ? 4 : (int)remaining; UInt128 q = twoP * k + UInt128.One;
q.Mod10_8_5_3(out ulong r10, out ulong r8, out ulong r5, out ulong r3);
// Compute lane residues incrementally (avoid multiplications, minimize reductions) while (k < setLimitExclusive && (localIsPrime = Volatile.Read(ref isPrime)))
// r10 {
r10_0 = r10; remaining = setLimitExclusive - k;
r10_1 = r10_0 + step10; if (r10_1 >= 20UL) r10_1 -= 20UL; if (r10_1 >= 10UL) r10_1 -= 10UL; if (remaining == UInt128.Zero)
r10_2 = r10_1 + step10; if (r10_2 >= 20UL) r10_2 -= 20UL; if (r10_2 >= 10UL) r10_2 -= 10UL; {
r10_3 = r10_2 + step10; if (r10_3 >= 20UL) r10_3 -= 20UL; if (r10_3 >= 10UL) r10_3 -= 10UL; break;
}
// r8 lanes = remaining > 4UL ? 4 : (int)remaining;
r8_0 = r8 & 7UL; if (lanes <= 0)
r8_1 = (r8_0 + step8) & 7UL; {
r8_2 = (r8_1 + step8) & 7UL; break;
r8_3 = (r8_2 + step8) & 7UL; }
// r3 (pattern 0,1,2,0) // Compute lane residues incrementally (avoid multiplications, minimize reductions)
r3_0 = r3; if (r3_0 >= 3UL) r3_0 -= 3UL; // r10
r3_1 = r3_0 + step3; if (r3_1 >= 3UL) r3_1 -= 3UL; r10_0 = r10;
r3_2 = r3_1 + step3; if (r3_2 >= 3UL) r3_2 -= 3UL; r10_1 = r10_0 + step10; if (r10_1 >= 20UL) r10_1 -= 20UL; if (r10_1 >= 10UL) r10_1 -= 10UL;
r3_3 = r3; if (r3_3 >= 3UL) r3_3 -= 3UL; r10_2 = r10_1 + step10; if (r10_2 >= 20UL) r10_2 -= 20UL; if (r10_2 >= 10UL) r10_2 -= 10UL;
r10_3 = r10_2 + step10; if (r10_3 >= 20UL) r10_3 -= 20UL; if (r10_3 >= 10UL) r10_3 -= 10UL;
// r5 (pattern 0,1,2,3) // r8
r5_0 = r5; if (r5_0 >= 5UL) r5_0 -= 5UL; r8_0 = r8 & 7UL;
r5_1 = r5_0 + step5; if (r5_1 >= 10UL) r5_1 -= 10UL; if (r5_1 >= 5UL) r5_1 -= 5UL; r8_1 = (r8_0 + step8) & 7UL;
r5_2 = r5_1 + step5; if (r5_2 >= 10UL) r5_2 -= 10UL; if (r5_2 >= 5UL) r5_2 -= 5UL; r8_2 = (r8_1 + step8) & 7UL;
r5_3 = r5_2 + step5; if (r5_3 >= 10UL) r5_3 -= 10UL; if (r5_3 >= 5UL) r5_3 -= 5UL; r8_3 = (r8_2 + step8) & 7UL;
// lane 0 // r3 (pattern 0,1,2,0)
if (lanes >= 1 && r3_0 = r3; if (r3_0 >= 3UL) r3_0 -= 3UL;
(((allowMask >> (int)r10_0) & 1) != 0 && (r8_0 == 1UL || r8_0 == 7UL) && r3_0 != 0UL && r5_0 != 0UL)) r3_1 = r3_0 + step3; if (r3_1 >= 3UL) r3_1 -= 3UL;
{ r3_2 = r3_1 + step3; if (r3_2 >= 3UL) r3_2 -= 3UL;
// cycle-based quick check for small q r3_3 = r3; if (r3_3 >= 3UL) r3_3 -= 3UL;
if (localIsPrime && tracker.MergeOrAppend(exponent, q, out isDivider) && isDivider &&
(q <= ulong.MaxValue ? ((ulong)q).IsPrimeCandidate() : q.IsPrimeCandidate()))
{
localIsPrime = false;
}
}
// lane 1 // r5 (pattern 0,1,2,3)
qIncremental = q + twoP; r5_0 = r5; if (r5_0 >= 5UL) r5_0 -= 5UL;
if (lanes >= 2 && r5_1 = r5_0 + step5; if (r5_1 >= 10UL) r5_1 -= 10UL; if (r5_1 >= 5UL) r5_1 -= 5UL;
((allowMask >> (int)r10_1) & 1) != 0 && (r8_1 == 1UL || r8_1 == 7UL) && r3_1 != 0UL && r5_1 != 0UL && r5_2 = r5_1 + step5; if (r5_2 >= 10UL) r5_2 -= 10UL; if (r5_2 >= 5UL) r5_2 -= 5UL;
localIsPrime) r5_3 = r5_2 + step5; if (r5_3 >= 10UL) r5_3 -= 10UL; if (r5_3 >= 5UL) r5_3 -= 5UL;
{
if (localIsPrime && tracker.MergeOrAppend(exponent, qIncremental, out isDivider) && isDivider &&
(qIncremental <= ulong.MaxValue ? ((ulong)qIncremental).IsPrimeCandidate() : qIncremental.IsPrimeCandidate()))
{
localIsPrime = false;
}
}
// lane 2 // lane 0
qIncremental += twoP; if (lanes >= 1 &&
if (lanes >= 3 && (((allowMask >> (int)r10_0) & 1) != 0 && (r8_0 == 1UL || r8_0 == 7UL) && r3_0 != 0UL && r5_0 != 0UL))
((allowMask >> (int)r10_2) & 1) != 0 && (r8_2 == 1UL || r8_2 == 7UL) && r3_2 != 0UL && r5_2 != 0UL && {
localIsPrime) if (localIsPrime && tracker.MergeOrAppend(exponent, q, out isDivider) && isDivider &&
{ (q <= ulong.MaxValue ? ((ulong)q).IsPrimeCandidate() : q.IsPrimeCandidate()))
if (localIsPrime && tracker.MergeOrAppend(exponent, qIncremental, out isDivider) && isDivider && {
(qIncremental <= ulong.MaxValue ? ((ulong)qIncremental).IsPrimeCandidate() : qIncremental.IsPrimeCandidate())) localIsPrime = false;
{ }
localIsPrime = false; }
}
}
// lane 3 // lane 1
qIncremental += twoP; qIncremental = q + twoP;
if (lanes >= 4 && if (lanes >= 2 &&
((allowMask >> (int)r10_3) & 1) != 0 && (r8_3 == 1UL || r8_3 == 7UL) && r3_3 != 0UL && r5_3 != 0UL && ((allowMask >> (int)r10_1) & 1) != 0 && (r8_1 == 1UL || r8_1 == 7UL) && r3_1 != 0UL && r5_1 != 0UL &&
localIsPrime) localIsPrime)
{ {
if (localIsPrime && tracker.MergeOrAppend(exponent, qIncremental, out isDivider) && isDivider && if (localIsPrime && tracker.MergeOrAppend(exponent, qIncremental, out isDivider) && isDivider &&
(qIncremental <= ulong.MaxValue ? ((ulong)qIncremental).IsPrimeCandidate() : qIncremental.IsPrimeCandidate())) (qIncremental <= ulong.MaxValue ? ((ulong)qIncremental).IsPrimeCandidate() : qIncremental.IsPrimeCandidate()))
{ {
localIsPrime = false; localIsPrime = false;
} }
} }
if (!localIsPrime) // lane 2
{ qIncremental += twoP;
Volatile.Write(ref isPrime, false); if (lanes >= 3 &&
return; ((allowMask >> (int)r10_2) & 1) != 0 && (r8_2 == 1UL || r8_2 == 7UL) && r3_2 != 0UL && r5_2 != 0UL &&
} localIsPrime)
else if (!Volatile.Read(ref isPrime)) {
{ if (localIsPrime && tracker.MergeOrAppend(exponent, qIncremental, out isDivider) && isDivider &&
return; (qIncremental <= ulong.MaxValue ? ((ulong)qIncremental).IsPrimeCandidate() : qIncremental.IsPrimeCandidate()))
} {
localIsPrime = false;
}
}
// advance base by processed lanes // lane 3
k += (UInt128)lanes; qIncremental += twoP;
q += lanes switch if (lanes >= 4 &&
{ ((allowMask >> (int)r10_3) & 1) != 0 && (r8_3 == 1UL || r8_3 == 7UL) && r3_3 != 0UL && r5_3 != 0UL &&
0 => 0UL, localIsPrime)
1 => twoP, {
2 => twoP2, if (localIsPrime && tracker.MergeOrAppend(exponent, qIncremental, out isDivider) && isDivider &&
3 => twoP3, (qIncremental <= ulong.MaxValue ? ((ulong)qIncremental).IsPrimeCandidate() : qIncremental.IsPrimeCandidate()))
4 => twoP4, {
_ => throw new ArgumentException("Unsupproted value", nameof(twoP)) localIsPrime = false;
}; }
}
// advance residues by 'lanes' steps (consistent with base advance) if (!localIsPrime)
for (i = 0; i < lanes; i++) {
{ Volatile.Write(ref isPrime, false);
r10 += step10; if (r10 >= 20UL) r10 -= 20UL; if (r10 >= 10UL) r10 -= 10UL; divisorsExhausted = true;
r8 = (r8 + step8) & 7UL; return;
r3 += step3; if (r3 >= 3UL) r3 -= 3UL; }
r5 += step5; if (r5 >= 10UL) r5 -= 10UL; if (r5 >= 5UL) r5 -= 5UL; else if (!Volatile.Read(ref isPrime))
} {
} divisorsExhausted = true;
return;
}
return; // advance base by processed lanes
} k += (UInt128)lanes;
q += lanes switch
{
0 => 0UL,
1 => twoP,
2 => twoP2,
3 => twoP3,
4 => twoP4,
_ => throw new ArgumentException("Unsupproted value", nameof(twoP))
};
// advance residues by 'lanes' steps (consistent with base advance)
for (i = 0; i < lanes; i++)
{
r10 += step10; if (r10 >= 20UL) r10 -= 20UL; if (r10 >= 10UL) r10 -= 10UL;
r8 = (r8 + step8) & 7UL;
r3 += step3; if (r3 >= 3UL) r3 -= 3UL;
r5 += step5; if (r5 >= 10UL) r5 -= 10UL; if (r5 >= 5UL) r5 -= 5UL;
}
divisorsExhausted = true;
}
}
}
} }
PerfectNumbers.Core/Gpu/MersenneNumberResidueGpuTester.cs
+68 -42
View File
@@ -11,16 +11,28 @@ public class MersenneNumberResidueGpuTester(bool useGpuOrder)
// candidates without launching heavy kernels. Consider a device-visible constant buffer per-accelerator // candidates without launching heavy kernels. Consider a device-visible constant buffer per-accelerator
// via GpuKernelPool to avoid host round-trips. // via GpuKernelPool to avoid host round-trips.
// GPU residue variant: check 2^p % q == 1 for q = 2*p*k + 1. // GPU residue variant: check 2^p % q == 1 for q = 2*p*k + 1.
public void Scan(ulong exponent, UInt128 twoP, bool lastIsSeven, UInt128 maxK, ref bool isPrime) public void Scan(
{ ulong exponent,
var gpuLease = GpuKernelPool.GetKernel(_useGpuOrder); UInt128 twoP,
bool lastIsSeven,
UInt128 perSetLimit,
ulong setCount,
UInt128 overallLimit,
ref bool isPrime,
ref bool divisorsExhausted)
{
if (setCount == 0UL || perSetLimit == UInt128.Zero || overallLimit == UInt128.Zero)
{
return;
}
var gpuLease = GpuKernelPool.GetKernel(_useGpuOrder);
var accelerator = gpuLease.Accelerator; var accelerator = gpuLease.Accelerator;
// Ensure device has small cycles and primes tables for in-kernel lookup // Ensure device has small cycles and primes tables for in-kernel lookup
var smallCyclesView = GpuKernelPool.EnsureSmallCyclesOnDevice(accelerator); var smallCyclesView = GpuKernelPool.EnsureSmallCyclesOnDevice(accelerator);
ResiduePrimeViews primeViews = GpuKernelPool.EnsureSmallPrimesOnDevice(accelerator); ResiduePrimeViews primeViews = GpuKernelPool.EnsureSmallPrimesOnDevice(accelerator);
int batchSize = GpuConstants.ScanBatchSize; int batchSize = GpuConstants.ScanBatchSize;
UInt128 kStart = 1UL;
byte last = lastIsSeven ? (byte)1 : (byte)0; byte last = lastIsSeven ? (byte)1 : (byte)0;
var kernel = gpuLease.Pow2ModKernel; var kernel = gpuLease.Pow2ModKernel;
ulong step10 = ((exponent % 10UL) << 1) % 10UL; ulong step10 = ((exponent % 10UL) << 1) % 10UL;
@@ -31,57 +43,71 @@ public class MersenneNumberResidueGpuTester(bool useGpuOrder)
var orderBuffer = accelerator.Allocate1D<ulong>(batchSize); var orderBuffer = accelerator.Allocate1D<ulong>(batchSize);
ulong[] orderArray = ArrayPool<ulong>.Shared.Rent(batchSize); ulong[] orderArray = ArrayPool<ulong>.Shared.Rent(batchSize);
UInt128 remaining; UInt128 batchSize128 = (UInt128)batchSize;
int currentSize; UInt128 limitInclusive = overallLimit + UInt128.One;
int i;
UInt128 batchSize128 = (UInt128)batchSize, q;
Span<ulong> orders = orderArray.AsSpan(0, batchSize); Span<ulong> orders = orderArray.AsSpan(0, batchSize);
try try
{ {
while (kStart < maxK && Volatile.Read(ref isPrime)) for (ulong setIndex = 0; setIndex < setCount && Volatile.Read(ref isPrime); setIndex++)
{ {
remaining = maxK - kStart; UInt128 setOffset = perSetLimit * (UInt128)setIndex;
if (remaining > batchSize128) UInt128 setStart = setOffset + UInt128.One;
{ if (setStart >= limitInclusive)
currentSize = batchSize;
}
else
{
currentSize = (int)remaining;
orders = orderArray.AsSpan(0, currentSize);
}
q = twoP * kStart + UInt128.One;
q.Mod10_8_5_3(out ulong q0m10, out ulong q0m8, out ulong q0m5, out ulong q0m3);
var ra = new ResidueAutomatonArgs(q0m10, step10, q0m8, step8, q0m3, step3, q0m5, step5);
kernel(currentSize, exponent, twoPGpu, (GpuUInt128)kStart, last, 0UL,
ra, orderBuffer.View, smallCyclesView, primeViews.LastOne, primeViews.LastSeven, primeViews.LastOnePow2, primeViews.LastSevenPow2);
accelerator.Synchronize();
orderBuffer.View.CopyToCPU(ref MemoryMarshal.GetReference(orders), currentSize);
if (!Volatile.Read(ref isPrime))
{ {
break; break;
} }
for (i = 0; i < currentSize; i++) UInt128 setLimitExclusive = setOffset + perSetLimit + UInt128.One;
if (setLimitExclusive > limitInclusive)
{ {
if (orders[i] != 0UL) setLimitExclusive = limitInclusive;
{
Volatile.Write(ref isPrime, false);
break;
}
} }
kStart += batchSize128; UInt128 kStart = setStart;
while (kStart < setLimitExclusive && Volatile.Read(ref isPrime))
{
UInt128 remaining = setLimitExclusive - kStart;
int currentSize = remaining > batchSize128 ? batchSize : (int)remaining;
if (currentSize <= 0)
{
break;
}
orders = orderArray.AsSpan(0, currentSize);
UInt128 q = twoP * kStart + UInt128.One;
q.Mod10_8_5_3(out ulong q0m10, out ulong q0m8, out ulong q0m5, out ulong q0m3);
var ra = new ResidueAutomatonArgs(q0m10, step10, q0m8, step8, q0m3, step3, q0m5, step5);
kernel(currentSize, exponent, twoPGpu, (GpuUInt128)kStart, last, 0UL,
ra, orderBuffer.View, smallCyclesView, primeViews.LastOne, primeViews.LastSeven, primeViews.LastOnePow2, primeViews.LastSevenPow2);
accelerator.Synchronize();
orderBuffer.View.CopyToCPU(ref MemoryMarshal.GetReference(orders), currentSize);
if (!Volatile.Read(ref isPrime))
{
break;
}
for (int i = 0; i < currentSize; i++)
{
if (orders[i] != 0UL)
{
Volatile.Write(ref isPrime, false);
break;
}
}
kStart += batchSize128;
}
} }
} }
finally finally
{ {
ArrayPool<ulong>.Shared.Return(orderArray); ArrayPool<ulong>.Shared.Return(orderArray);
orderBuffer.Dispose(); orderBuffer.Dispose();
gpuLease.Dispose(); gpuLease.Dispose();
} }
}
divisorsExhausted = true;
}
} }
PerfectNumbers.Core/MersenneNumberTester.cs
+94 -20
View File
@@ -24,13 +24,15 @@ public sealed class MersenneNumberTester(
bool useGpuLucas = true, bool useGpuLucas = true,
bool useGpuScan = true, bool useGpuScan = true,
bool useGpuOrder = true, bool useGpuOrder = true,
bool useResidue = true, bool useResidue = true,
ulong maxK = 5_000_000UL) ulong maxK = 5_000_000UL,
ulong residueDivisorSets = PerfectNumberConstants.ExtraDivisorCycleSearchLimit)
{ {
private readonly bool _useResidue = useResidue; private readonly bool _useResidue = useResidue;
private readonly bool _useIncremental = useIncremental && !useResidue; private readonly bool _useIncremental = useIncremental && !useResidue;
private readonly ulong _maxK = maxK; private readonly ulong _maxK = maxK;
private readonly GpuKernelType _kernelType = kernelType; private readonly ulong _residueDivisorSetCount = residueDivisorSets;
private readonly GpuKernelType _kernelType = kernelType;
private readonly bool _useModuloWorkaround = useModuloWorkaround; private readonly bool _useModuloWorkaround = useModuloWorkaround;
private readonly bool _useGpuLucas = useGpuLucas; private readonly bool _useGpuLucas = useGpuLucas;
private readonly bool _useGpuScan = useGpuScan; // device for pow2mod/incremental scanning private readonly bool _useGpuScan = useGpuScan; // device for pow2mod/incremental scanning
@@ -42,11 +44,28 @@ public sealed class MersenneNumberTester(
private readonly MersenneNumberOrderCpuTester _orderCpuTester = new(kernelType); private readonly MersenneNumberOrderCpuTester _orderCpuTester = new(kernelType);
private readonly MersenneNumberLucasLehmerGpuTester _lucasLehmerGpuTester = new(); private readonly MersenneNumberLucasLehmerGpuTester _lucasLehmerGpuTester = new();
private readonly MersenneNumberLucasLehmerCpuTester _lucasLehmerCpuTester = new(); private readonly MersenneNumberLucasLehmerCpuTester _lucasLehmerCpuTester = new();
private readonly MersenneNumberResidueGpuTester? _residueGpuTester = useResidue ? new(useGpuOrder) : null; private readonly MersenneNumberResidueGpuTester? _residueGpuTester = useResidue ? new(useGpuOrder) : null;
private readonly MersenneNumberResidueCpuTester? _residueCpuTester = useResidue ? new() : null; private readonly MersenneNumberResidueCpuTester? _residueCpuTester = useResidue ? new() : null;
// TODO: Ensure Program passes useResidue correctly and that residue-vs-incremental-vs-LL selection respects CLI flags. // TODO: Ensure Program passes useResidue correctly and that residue-vs-incremental-vs-LL selection respects CLI flags.
// Also consider injecting a shared cycles cache (MersenneDivisorCycles.Shared) to both CPU and GPU testers. // Also consider injecting a shared cycles cache (MersenneDivisorCycles.Shared) to both CPU and GPU testers.
[MethodImpl(MethodImplOptions.AggressiveInlining)]
private static UInt128 DivideRoundUp(UInt128 value, UInt128 divisor)
{
if (divisor == UInt128.Zero)
{
return UInt128.Zero;
}
UInt128 result = value / divisor;
if (result * divisor == value)
{
return result;
}
return result + UInt128.One;
}
public void WarmUpOrders(ulong exponent, ulong limit = 5_000_000UL) public void WarmUpOrders(ulong exponent, ulong limit = 5_000_000UL)
{ {
@@ -191,27 +210,34 @@ public sealed class MersenneNumberTester(
ArrayPool<UInt128>.Shared.Return(qs); ArrayPool<UInt128>.Shared.Return(qs);
} }
public bool IsMersennePrime(ulong exponent) public bool IsMersennePrime(ulong exponent) => IsMersennePrime(exponent, out _);
public bool IsMersennePrime(ulong exponent, out bool divisorsExhausted)
{ {
divisorsExhausted = false;
// Safe early rejections using known orders for tiny primes: // Safe early rejections using known orders for tiny primes:
// 7 | M_p iff 3 | p. Avoid rejecting p == 3 where M_3 == 7 is prime. // 7 | M_p iff 3 | p. Avoid rejecting p == 3 where M_3 == 7 is prime.
if ((exponent % 3UL) == 0UL && exponent != 3UL) if ((exponent % 3UL) == 0UL && exponent != 3UL)
{ {
divisorsExhausted = true;
return false; return false;
} }
if ((exponent & 3UL) == 1UL && exponent.SharesFactorWithExponentMinusOne()) if ((exponent & 3UL) == 1UL && exponent.SharesFactorWithExponentMinusOne())
{ {
divisorsExhausted = true;
return false; return false;
} }
// Skip even exponents: for even p > 2, M_p is composite; here p is large. // Skip even exponents: for even p > 2, M_p is composite; here p is large.
if ((exponent & 1UL) == 0UL) if ((exponent & 1UL) == 0UL)
{ {
divisorsExhausted = true;
return false; return false;
} }
bool prePrime = true; bool prePrime = true;
UInt128 twoP = (UInt128)exponent << 1; // 2 * p UInt128 twoP = (UInt128)exponent << 1; // 2 * p
// UInt128 maxDivisor = new(ulong.MaxValue, ulong.MaxValue); // UInt128 maxDivisor = new(ulong.MaxValue, ulong.MaxValue);
UInt128 maxK = UInt128Numbers.Two.Pow(exponent) / 2 + 1; UInt128 maxK = UInt128Numbers.Two.Pow(exponent) / 2 + 1;
@@ -225,16 +251,60 @@ public sealed class MersenneNumberTester(
maxK = _maxK; maxK = _maxK;
} }
if (_maxK == 0UL || _residueDivisorSetCount == 0UL)
{
return prePrime;
}
UInt128 totalLimit = (UInt128)_maxK;
if (totalLimit > maxK)
{
totalLimit = maxK;
}
if (totalLimit == UInt128.Zero)
{
return true;
}
ulong requestedSets = _residueDivisorSetCount;
if (requestedSets == 0UL)
{
requestedSets = 1UL;
}
UInt128 perSetLimit = DivideRoundUp(totalLimit, (UInt128)requestedSets);
if (perSetLimit == UInt128.Zero)
{
perSetLimit = UInt128.One;
}
UInt128 setsNeeded = DivideRoundUp(totalLimit, perSetLimit);
ulong effectiveSets = requestedSets;
if (setsNeeded < (UInt128)effectiveSets)
{
effectiveSets = (ulong)setsNeeded;
}
bool scanCompleted = false;
if (_useGpuScan) if (_useGpuScan)
{ {
_residueGpuTester!.Scan(exponent, twoP, lastIsSeven, maxK, ref prePrime); _residueGpuTester!.Scan(exponent, twoP, lastIsSeven, perSetLimit, effectiveSets, totalLimit, ref prePrime, ref scanCompleted);
} }
else else
{ {
_residueCpuTester!.Scan(exponent, twoP, lastIsSeven, maxK, ref prePrime); _residueCpuTester!.Scan(exponent, twoP, lastIsSeven, perSetLimit, effectiveSets, totalLimit, ref prePrime, ref scanCompleted);
} }
return prePrime; if (!prePrime)
{
divisorsExhausted = true;
return false;
}
divisorsExhausted = scanCompleted;
return true;
} }
if (!_useIncremental) if (!_useIncremental)
@@ -253,15 +323,18 @@ public sealed class MersenneNumberTester(
_incrementalCpuTester.Scan(exponent, twoPPre, lastIsSevenPre, maxKPre, ref prePrime); _incrementalCpuTester.Scan(exponent, twoPPre, lastIsSevenPre, maxKPre, ref prePrime);
} }
if (!prePrime) if (!prePrime)
{ {
return false; divisorsExhausted = true;
} return false;
}
return _useGpuLucas bool lucasPrime = _useGpuLucas
? _lucasLehmerGpuTester.IsPrime(exponent, runOnGpu: true) ? _lucasLehmerGpuTester.IsPrime(exponent, runOnGpu: true)
: _lucasLehmerCpuTester.IsPrime(exponent); : _lucasLehmerCpuTester.IsPrime(exponent);
} divisorsExhausted = true;
return lucasPrime;
}
bool isPrime = true; bool isPrime = true;
@@ -288,6 +361,7 @@ public sealed class MersenneNumberTester(
} }
} }
divisorsExhausted = true;
return isPrime; return isPrime;
} }