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Windowed Pow2Mod implemented and integrated across repository.

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Marek Lemańczyk committed 2025-10-03 19:37:15 +02:00
1 parent 56e3a7695f
commit 941b51ebcf
12 files changed
+666 -246
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PerfectNumbers.Core/Gpu/GpuUInt128.cs
+69 -129
View File
@@ -1,3 +1,4 @@
using System;
using System.Numerics;
using System.Runtime.CompilerServices;
@@ -15,6 +16,10 @@ public struct GpuUInt128 : IComparable<GpuUInt128>, IEquatable<GpuUInt128>
private const ulong NativeModuloChunkMask = (1UL << NativeModuloChunkBits) - 1UL;
private static readonly ulong[] NativeModuloBitMasks = CreateNativeModuloBitMasks();
private const int Pow2WindowSizeBits = 8;
private const int Pow2WindowOddPowerCount = 1 << (Pow2WindowSizeBits - 1);
private const int Pow2WindowMaxExponent = (1 << Pow2WindowSizeBits) - 1;
public static readonly GpuUInt128 Zero = new();
public static readonly GpuUInt128 One = new(1UL);
@@ -256,122 +261,24 @@ public struct GpuUInt128 : IComparable<GpuUInt128>, IEquatable<GpuUInt128>
return Zero;
}
// TODO: Replace this single-bit ladder with the ProcessEightBitWindows strategy measured
// in GpuPow2ModBenchmarks once the GPU kernels can share the windowed helper. The windowed
// version held 21.5 µs for 33-bit moduli versus 51.0 µs here when scanning large divisors.
GpuUInt128 result = Zero;
ulong i = 0UL;
while (i < exponent)
GpuUInt128 pow = Pow2Mod(exponent, modulus);
if (pow.IsZero)
{
// result = (result * 2) % modulus
result += result;
if (result.CompareTo(modulus) >= 0)
{
result -= modulus;
}
// result = (result + 1) % modulus
result += One;
if (result.CompareTo(modulus) >= 0)
{
result -= modulus;
}
i++;
pow = modulus;
}
return result;
pow.Sub(One);
return pow;
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static void Pow2Minus1ModBatch(GpuUInt128 modulus, ReadOnlySpan<ulong> exponents, Span<GpuUInt128> results)
{
GpuUInt128 r0 = Zero, r1 = Zero, r2 = Zero, r3 = Zero, r4 = Zero, r5 = Zero, r6 = Zero, r7 = Zero;
ulong e0 = 0UL, e1 = 0UL, e2 = 0UL, e3 = 0UL, e4 = 0UL, e5 = 0UL, e6 = 0UL, e7 = 0UL;
bool a0 = false, a1 = false, a2 = false, a3 = false, a4 = false, a5 = false, a6 = false, a7 = false;
// TODO: Mirror the eight-bit window batching once the scalar helper above switches; the
// current bit-serial loop lags by ~3× on 8k–33-bit moduli compared to the windowed path.
int len = exponents.Length;
if (len > 0) { e0 = exponents[0]; a0 = true; }
if (len > 1) { e1 = exponents[1]; a1 = true; }
if (len > 2) { e2 = exponents[2]; a2 = true; }
if (len > 3) { e3 = exponents[3]; a3 = true; }
if (len > 4) { e4 = exponents[4]; a4 = true; }
if (len > 5) { e5 = exponents[5]; a5 = true; }
if (len > 6) { e6 = exponents[6]; a6 = true; }
if (len > 7) { e7 = exponents[7]; a7 = true; }
ulong max = 0UL;
if (a0 && e0 > max) max = e0;
if (a1 && e1 > max) max = e1;
if (a2 && e2 > max) max = e2;
if (a3 && e3 > max) max = e3;
if (a4 && e4 > max) max = e4;
if (a5 && e5 > max) max = e5;
if (a6 && e6 > max) max = e6;
if (a7 && e7 > max) max = e7;
for (ulong i = 0UL; i < max; i++)
int count = exponents.Length;
for (int i = 0; i < count; i++)
{
if (a0)
{
r0 += r0; if (r0.CompareTo(modulus) >= 0) r0 -= modulus;
r0 += One; if (r0.CompareTo(modulus) >= 0) r0 -= modulus;
if (i + 1UL == e0) a0 = false;
}
if (a1)
{
r1 += r1; if (r1.CompareTo(modulus) >= 0) r1 -= modulus;
r1 += One; if (r1.CompareTo(modulus) >= 0) r1 -= modulus;
if (i + 1UL == e1) a1 = false;
}
if (a2)
{
r2 += r2; if (r2.CompareTo(modulus) >= 0) r2 -= modulus;
r2 += One; if (r2.CompareTo(modulus) >= 0) r2 -= modulus;
if (i + 1UL == e2) a2 = false;
}
if (a3)
{
r3 += r3; if (r3.CompareTo(modulus) >= 0) r3 -= modulus;
r3 += One; if (r3.CompareTo(modulus) >= 0) r3 -= modulus;
if (i + 1UL == e3) a3 = false;
}
if (a4)
{
r4 += r4; if (r4.CompareTo(modulus) >= 0) r4 -= modulus;
r4 += One; if (r4.CompareTo(modulus) >= 0) r4 -= modulus;
if (i + 1UL == e4) a4 = false;
}
if (a5)
{
r5 += r5; if (r5.CompareTo(modulus) >= 0) r5 -= modulus;
r5 += One; if (r5.CompareTo(modulus) >= 0) r5 -= modulus;
if (i + 1UL == e5) a5 = false;
}
if (a6)
{
r6 += r6; if (r6.CompareTo(modulus) >= 0) r6 -= modulus;
r6 += One; if (r6.CompareTo(modulus) >= 0) r6 -= modulus;
if (i + 1UL == e6) a6 = false;
}
if (a7)
{
r7 += r7; if (r7.CompareTo(modulus) >= 0) r7 -= modulus;
r7 += One; if (r7.CompareTo(modulus) >= 0) r7 -= modulus;
if (i + 1UL == e7) a7 = false;
}
results[i] = Pow2Minus1Mod(exponents[i], modulus);
}
if (len > 0) results[0] = r0;
if (len > 1) results[1] = r1;
if (len > 2) results[2] = r2;
if (len > 3) results[3] = r3;
if (len > 4) results[4] = r4;
if (len > 5) results[5] = r5;
if (len > 6) results[6] = r6;
if (len > 7) results[7] = r7;
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
@@ -483,7 +390,6 @@ public struct GpuUInt128 : IComparable<GpuUInt128>, IEquatable<GpuUInt128>
}
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static GpuUInt128 Pow2Mod(ulong exponent, GpuUInt128 modulus)
{
@@ -492,36 +398,71 @@ public struct GpuUInt128 : IComparable<GpuUInt128>, IEquatable<GpuUInt128>
return new();
}
const int WindowSizeBits = 8;
const ulong WindowMask = (1UL << WindowSizeBits) - 1UL;
GpuUInt128 result = new(1UL);
GpuUInt128 baseVal = new(2UL);
ulong e = exponent;
while (e != 0UL)
if (exponent == 0UL)
{
int remainingBits = BitOperations.Log2(e) + 1;
int bitsToProcess = remainingBits >= WindowSizeBits ? WindowSizeBits : remainingBits;
ulong chunk = e & (WindowMask >> (WindowSizeBits - bitsToProcess));
return new GpuUInt128(1UL);
}
for (int bitIndex = 0; bitIndex < bitsToProcess; bitIndex++)
Span<GpuUInt128> oddPowers = stackalloc GpuUInt128[Pow2WindowOddPowerCount];
GpuUInt128 power = new GpuUInt128(1UL);
int oddIndex = 0;
for (int bit = 1; bit <= Pow2WindowMaxExponent; bit++)
{
power += power;
if (power.CompareTo(modulus) >= 0)
{
if ((chunk & 1UL) != 0UL)
{
result.MulMod(baseVal, modulus);
}
baseVal.MulMod(baseVal, modulus);
chunk >>= 1;
power.Sub(modulus);
}
e >>= bitsToProcess;
if ((bit & 1) != 0)
{
oddPowers[oddIndex++] = power;
}
}
GpuUInt128 result = new GpuUInt128(1UL);
int bitLength = BitOperations.Log2(exponent) + 1;
int index = bitLength - 1;
while (index >= 0)
{
if (((exponent >> index) & 1UL) == 0UL)
{
result.SquareMod(modulus);
index--;
continue;
}
int windowStart = index - Pow2WindowSizeBits + 1;
if (windowStart < 0)
{
windowStart = 0;
}
while (((exponent >> windowStart) & 1UL) == 0UL)
{
windowStart++;
}
int windowBitCount = index - windowStart + 1;
for (int square = 0; square < windowBitCount; square++)
{
result.SquareMod(modulus);
}
ulong mask = (1UL << windowBitCount) - 1UL;
ulong windowValue = (exponent >> windowStart) & mask;
int tableIndex = (int)((windowValue - 1UL) >> 1);
GpuUInt128 factor = oddPowers[tableIndex];
result.MulMod(factor, modulus);
index = windowStart - 1;
}
return result;
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static int TrailingZeroCount(GpuUInt128 value)
{
@@ -1258,7 +1199,6 @@ public struct GpuUInt128 : IComparable<GpuUInt128>, IEquatable<GpuUInt128>
p3 = hHH + c2;
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
private static ulong MulMod64(ulong a, ulong b, ulong modulus)
{
PerfectNumbers.Core/Gpu/MersenneNumberDivisorByDivisorGpuTester.cs
+14 -6
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@@ -1,6 +1,7 @@
using System;
using System.Buffers;
using System.Collections.Concurrent;
using System.Collections.Generic;
using System.Runtime.CompilerServices;
using System.Runtime.InteropServices;
using System.Numerics;
@@ -371,7 +372,7 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
}
ulong exponent = exponents[index];
hits[index] = exponent.Pow2MontgomeryMod(divisor) == 1UL ? (byte)1 : (byte)0; // TODO: Replace Pow2MontgomeryMod with the ProcessEightBitWindows helper once available so GPU by-divisor scans reuse the benchmarked fast pow2 ladder.
hits[index] = exponent.Pow2MontgomeryModWindowed(divisor, keepMontgomery: false) == 1UL ? (byte)1 : (byte)0;
}
public sealed class DivisorScanSession : IMersenneNumberDivisorByDivisorTester.IDivisorScanSession
@@ -384,6 +385,7 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
private MemoryBuffer1D<ulong, Stride1D.Dense> _resultsBuffer;
private ulong[] _hostBuffer;
private int[]? _positionBuffer;
private Dictionary<ulong, MersenneDivisorCycles.FactorCacheEntry>? _factorCache;
private int _capacity;
private bool _disposed;
@@ -403,6 +405,7 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
internal void Reset()
{
_disposed = false;
_factorCache?.Clear();
}
public void CheckDivisor(ulong divisor, ulong divisorCycle, ReadOnlySpan<ulong> primes, Span<byte> hits)
@@ -428,11 +431,15 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
if (divisorCycle == 0UL)
{
divisorCycle = DivisorCycleCache.Shared.GetCycleLength(divisor);
if (divisorCycle == 0UL)
Dictionary<ulong, MersenneDivisorCycles.FactorCacheEntry> cache = _factorCache ??= new Dictionary<ulong, MersenneDivisorCycles.FactorCacheEntry>(16);
if (!MersenneDivisorCycles.TryCalculateCycleLengthForExponent(divisor, primes[0], cache, out divisorCycle) || divisorCycle == 0UL)
{
hits.Clear();
return;
divisorCycle = DivisorCycleCache.Shared.GetCycleLength(divisor);
if (divisorCycle == 0UL)
{
hits.Clear();
return;
}
}
}
@@ -569,6 +576,7 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
}
_disposed = true;
_factorCache?.Clear();
_owner._sessionPool.Add(this);
}
}
@@ -584,7 +592,7 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
ulong exponent = exponents[index];
results[index] = exponent.Pow2MontgomeryModMontgomery(divisor); // TODO: Swap this Montgomery-domain pow2 with the windowed helper slated to replace the slower ladder in Pow2Minus1Mod benchmarks.
results[index] = exponent.Pow2MontgomeryModWindowed(divisor, keepMontgomery: true);
}
public ulong DivisorLimit