412 lines
13 KiB
C#
412 lines
13 KiB
C#
using System;
|
||
using System.Buffers.Binary;
|
||
using System.Threading;
|
||
using BenchmarkDotNet.Attributes;
|
||
using BenchmarkDotNet.Jobs;
|
||
using PerfectNumbers.Core;
|
||
|
||
namespace EvenPerfectBitScanner.Benchmarks;
|
||
|
||
/// <remarks>
|
||
/// Benchmark results collected on AMD Ryzen 5 5625U (.NET 8.0, launchCount: 1, warmupCount: 1, iterationCount: 5):
|
||
/// Small sample (~1e6 random odd moduli)
|
||
/// - MontgomeryWithoutCycle: 35.41 µs (baseline)
|
||
/// - MontgomeryWithPrecomputedCycle: 25.81 µs (0.73× baseline)
|
||
/// - MontgomeryWithGpuCycleComputation: 54.09 ms (1,527× baseline, includes GPU cycle calculation)
|
||
/// Large sample (Mersenne-like moduli from 2^48-1 to 2^63-1)
|
||
/// - MontgomeryWithoutCycle: 117.33 µs (baseline)
|
||
/// - MontgomeryWithPrecomputedCycle: 9.12 µs (0.08× baseline)
|
||
/// - MontgomeryWithGpuCycleComputation: 12.91 µs (0.11× baseline)
|
||
/// </remarks>
|
||
[MemoryDiagnoser]
|
||
[SimpleJob(RuntimeMoniker.Net80, launchCount: 1, warmupCount: 1, iterationCount: 5)]
|
||
public class Pow2MontgomeryModCycleComputationBenchmarks
|
||
{
|
||
private const int SampleCount = 256;
|
||
private const ulong OneShiftedLeft63 = 1UL << 63;
|
||
private const long OneShiftedLeft60 = 1L << 60;
|
||
private readonly MontgomeryDivisorData[] _smallDivisors = new MontgomeryDivisorData[SampleCount];
|
||
private readonly MontgomeryDivisorData[] _largeDivisors = new MontgomeryDivisorData[SampleCount];
|
||
private readonly MontgomeryDivisorData[] _veryLargeDivisors = new MontgomeryDivisorData[SampleCount];
|
||
private readonly UInt128[] _wideModuli = new UInt128[SampleCount];
|
||
private readonly ulong[] _smallExponents = new ulong[SampleCount];
|
||
private readonly ulong[] _largeExponents = new ulong[SampleCount];
|
||
private readonly ulong[] _veryLargeExponents = new ulong[SampleCount];
|
||
private readonly ulong[] _smallCycles = new ulong[SampleCount];
|
||
private readonly ulong[] _largeCycles = new ulong[SampleCount];
|
||
private readonly ulong[] _veryLargeCycles = new ulong[SampleCount];
|
||
private readonly UInt128[] _wideCycles = new UInt128[SampleCount];
|
||
|
||
private readonly Random _random = new(113);
|
||
private ulong? _previousPrimeOrder;
|
||
private UInt128? _previousWidePrimeOrder;
|
||
|
||
public enum InputScale
|
||
{
|
||
Small,
|
||
Large,
|
||
VeryLarge
|
||
}
|
||
|
||
[ParamsAllValues]
|
||
public InputScale Scale { get; set; }
|
||
|
||
[GlobalSetup]
|
||
public void Setup()
|
||
{
|
||
for (int i = 0; i < SampleCount; i++)
|
||
{
|
||
#if DEBUG
|
||
Console.WriteLine($"Generating sample {i}");
|
||
#endif
|
||
ulong smallModulus = NextSmallOddModulus();
|
||
_smallDivisors[i] = CreateMontgomeryDivisorData(smallModulus);
|
||
_smallExponents[i] = NextSmallExponent();
|
||
_smallCycles[i] = CalculateCycleLengthWithHeuristics(smallModulus);
|
||
|
||
(ulong largeModulus, ulong largeCycle) = NextLargeModulusAndCycle();
|
||
_largeDivisors[i] = CreateMontgomeryDivisorData(largeModulus);
|
||
_largeExponents[i] = NextLargeExponent();
|
||
_largeCycles[i] = CalculateCycleLengthWithHeuristics(largeModulus, largeCycle);
|
||
|
||
ulong veryLargeModulus = NextVeryLargeOddModulus();
|
||
_veryLargeDivisors[i] = CreateMontgomeryDivisorData(veryLargeModulus);
|
||
_veryLargeExponents[i] = NextVeryLargeExponent();
|
||
#if DEBUG
|
||
Console.WriteLine($"Calculating cycle length {veryLargeModulus}");
|
||
#endif
|
||
_veryLargeCycles[i] = CalculateCycleLengthWithHeuristics(veryLargeModulus);
|
||
|
||
Console.WriteLine($"Generating wide sample {i}");
|
||
UInt128 wideModulus = NextWideOddModulus();
|
||
_wideModuli[i] = wideModulus;
|
||
_wideCycles[i] = CalculateCycleLengthWithHeuristics(wideModulus);
|
||
}
|
||
}
|
||
|
||
/// <summary>
|
||
/// Baseline Montgomery reduction without precomputed cycle data; measured 35.41 μs on the small sample and 117.33 μs on the
|
||
/// large set.
|
||
/// </summary>
|
||
// [Benchmark(Baseline = true)]
|
||
public ulong MontgomeryWithoutCycleCpu()
|
||
{
|
||
GetData(out ulong[] exponents, out MontgomeryDivisorData[] divisors, out _);
|
||
ulong checksum = 0UL;
|
||
|
||
for (int i = 0; i < SampleCount; i++)
|
||
{
|
||
checksum ^= exponents[i].Pow2MontgomeryModWindowedCpu(divisors[i], keepMontgomery: false);
|
||
}
|
||
|
||
return checksum;
|
||
}
|
||
|
||
/// <summary>
|
||
/// Baseline Montgomery reduction without precomputed cycle data; measured 35.41 μs on the small sample and 117.33 μs on the
|
||
/// large set.
|
||
/// </summary>
|
||
// [Benchmark(Baseline = true)]
|
||
public ulong MontgomeryWithoutCycleGpu()
|
||
{
|
||
GetData(out ulong[] exponents, out MontgomeryDivisorData[] divisors, out _);
|
||
ulong checksum = 0UL;
|
||
|
||
for (int i = 0; i < SampleCount; i++)
|
||
{
|
||
checksum ^= exponents[i].Pow2MontgomeryModWindowedGpu(divisors[i], keepMontgomery: false);
|
||
}
|
||
|
||
return checksum;
|
||
}
|
||
|
||
/// <summary>
|
||
/// Montgomery reduction with a known cycle length (cycle lookup only); 25.81 μs on the small set (0.73× baseline) and 9.12 μs
|
||
/// on the large one (0.08×).
|
||
/// </summary>
|
||
[Benchmark]
|
||
public ulong MontgomeryWithPrecomputedCycleCpu()
|
||
{
|
||
GetData(out ulong[] exponents, out MontgomeryDivisorData[] divisors, out ulong[] cycles);
|
||
ulong checksum = 0UL;
|
||
|
||
for (int i = 0; i < SampleCount; i++)
|
||
{
|
||
checksum ^= exponents[i].Pow2MontgomeryModWithCycleCpu(cycles[i], divisors[i]);
|
||
}
|
||
|
||
return checksum;
|
||
}
|
||
|
||
/// <summary>
|
||
/// Montgomery reduction with a known cycle length (cycle lookup only); 25.81 μs on the small set (0.73× baseline) and 9.12 μs
|
||
/// on the large one (0.08×).
|
||
/// </summary>
|
||
[Benchmark]
|
||
public ulong MontgomeryWithPrecomputedCycleGpu()
|
||
{
|
||
GetData(out ulong[] exponents, out MontgomeryDivisorData[] divisors, out ulong[] cycles);
|
||
ulong checksum = 0UL;
|
||
|
||
for (int i = 0; i < SampleCount; i++)
|
||
{
|
||
checksum ^= exponents[i].Pow2MontgomeryModWithCycleGpu(cycles[i], divisors[i]);
|
||
}
|
||
|
||
return checksum;
|
||
}
|
||
|
||
/// <summary>
|
||
/// Montgomery reduction with the cycle computed on the fly using the GPU helper; costs 54.09 ms on the small benchmark due to
|
||
/// cycle discovery, but drops to 12.91 μs on the large set (0.11× baseline).
|
||
/// </summary>
|
||
// [Benchmark]
|
||
public ulong MontgomeryWithGpuCycleComputationCpu()
|
||
{
|
||
GetData(out ulong[] exponents, out MontgomeryDivisorData[] divisors, out _);
|
||
ulong checksum = 0UL;
|
||
|
||
for (int i = 0; i < SampleCount; i++)
|
||
{
|
||
ulong cycle = MersenneDivisorCycles.CalculateCycleLengthGpu(divisors[i].Modulus);
|
||
checksum ^= exponents[i].Pow2MontgomeryModWithCycleCpu(cycle, divisors[i]);
|
||
}
|
||
|
||
return checksum;
|
||
}
|
||
|
||
/// <summary>
|
||
/// Montgomery reduction with the cycle computed on the fly using the GPU helper; costs 54.09 ms on the small benchmark due to
|
||
/// cycle discovery, but drops to 12.91 μs on the large set (0.11× baseline).
|
||
/// </summary>
|
||
// [Benchmark]
|
||
public ulong MontgomeryWithGpuCycleComputationGpu()
|
||
{
|
||
GetData(out ulong[] exponents, out MontgomeryDivisorData[] divisors, out _);
|
||
ulong checksum = 0UL;
|
||
|
||
for (int i = 0; i < SampleCount; i++)
|
||
{
|
||
ulong cycle = MersenneDivisorCycles.CalculateCycleLengthGpu(divisors[i].Modulus);
|
||
checksum ^= exponents[i].Pow2MontgomeryModWithCycleGpu(cycle, divisors[i]);
|
||
}
|
||
|
||
return checksum;
|
||
}
|
||
|
||
[Benchmark]
|
||
public ulong MontgomeryWithHeuristicCycleComputationCpu()
|
||
{
|
||
GetData(out ulong[] exponents, out MontgomeryDivisorData[] divisors, out _);
|
||
ulong checksum = 0UL;
|
||
|
||
for (int i = 0; i < SampleCount; i++)
|
||
{
|
||
ulong cycle = CalculateCycleLengthWithHeuristics(divisors[i].Modulus);
|
||
checksum ^= exponents[i].Pow2MontgomeryModWithCycleCpu(cycle, divisors[i]);
|
||
}
|
||
|
||
return checksum;
|
||
}
|
||
|
||
[Benchmark]
|
||
public ulong MontgomeryWithHeuristicCycleComputationGpu()
|
||
{
|
||
GetData(out ulong[] exponents, out MontgomeryDivisorData[] divisors, out _);
|
||
ulong checksum = 0UL;
|
||
|
||
for (int i = 0; i < SampleCount; i++)
|
||
{
|
||
ulong cycle = CalculateCycleLengthWithHeuristics(divisors[i].Modulus);
|
||
checksum ^= exponents[i].Pow2MontgomeryModWithCycleGpu(cycle, divisors[i]);
|
||
}
|
||
|
||
return checksum;
|
||
}
|
||
|
||
[Benchmark]
|
||
public UInt128 HeuristicWideCycleComputation()
|
||
{
|
||
UInt128 checksum = UInt128.Zero;
|
||
|
||
for (int i = 0; i < SampleCount; i++)
|
||
{
|
||
UInt128 cycle = CalculateCycleLengthWithHeuristics(_wideModuli[i]);
|
||
_wideCycles[i] = cycle;
|
||
checksum ^= cycle;
|
||
}
|
||
|
||
return checksum;
|
||
}
|
||
|
||
private void GetData(out ulong[] exponents, out MontgomeryDivisorData[] divisors, out ulong[] cycles)
|
||
{
|
||
switch (Scale)
|
||
{
|
||
case InputScale.Small:
|
||
exponents = _smallExponents;
|
||
divisors = _smallDivisors;
|
||
cycles = _smallCycles;
|
||
break;
|
||
case InputScale.Large:
|
||
exponents = _largeExponents;
|
||
divisors = _largeDivisors;
|
||
cycles = _largeCycles;
|
||
break;
|
||
case InputScale.VeryLarge:
|
||
exponents = _veryLargeExponents;
|
||
divisors = _veryLargeDivisors;
|
||
cycles = _veryLargeCycles;
|
||
break;
|
||
default:
|
||
throw new ArgumentOutOfRangeException(nameof(Scale), Scale, null);
|
||
}
|
||
}
|
||
|
||
private ulong NextSmallExponent() => (ulong)_random.NextInt64(1L, 1_000_000L);
|
||
|
||
private ulong NextLargeExponent() => (ulong)_random.NextInt64(OneShiftedLeft60, long.MaxValue);
|
||
|
||
private ulong NextVeryLargeExponent()
|
||
{
|
||
Span<byte> buffer = stackalloc byte[8];
|
||
_random.NextBytes(buffer);
|
||
ulong value = checked(BinaryPrimitives.ReadUInt64LittleEndian(buffer) | OneShiftedLeft63);
|
||
return value;
|
||
}
|
||
|
||
private ulong NextSmallOddModulus()
|
||
{
|
||
ulong value = (ulong)_random.NextInt64(3L, 1_000_000L);
|
||
return value | 1UL;
|
||
}
|
||
|
||
private (ulong modulus, ulong cycleLength) NextLargeModulusAndCycle()
|
||
{
|
||
int bitLength = _random.Next(48, 64);
|
||
ulong modulus = (1UL << bitLength) - 1UL;
|
||
return (modulus, (ulong)bitLength);
|
||
}
|
||
|
||
private ulong NextVeryLargeOddModulus()
|
||
{
|
||
Span<byte> buffer = stackalloc byte[8];
|
||
_random.NextBytes(buffer);
|
||
ulong value = BinaryPrimitives.ReadUInt64LittleEndian(buffer) | OneShiftedLeft63 | 1UL;
|
||
return value;
|
||
}
|
||
|
||
private UInt128 NextWideOddModulus()
|
||
{
|
||
Span<byte> buffer = stackalloc byte[16];
|
||
_random.NextBytes(buffer);
|
||
ulong low = BinaryPrimitives.ReadUInt64LittleEndian(buffer);
|
||
Span<byte> highSlice = buffer.Slice(8, 8);
|
||
ulong high = BinaryPrimitives.ReadUInt64LittleEndian(highSlice) | (1UL << 63);
|
||
UInt128 value = ((UInt128)high << 64) | low;
|
||
return value | UInt128.One;
|
||
}
|
||
|
||
private static MontgomeryDivisorData CreateMontgomeryDivisorData(ulong modulus)
|
||
{
|
||
if (modulus <= 1UL || (modulus & 1UL) == 0UL)
|
||
{
|
||
return new MontgomeryDivisorData(modulus, 0UL, 0UL, 0UL, 0UL);
|
||
}
|
||
|
||
ulong nPrime = ComputeMontgomeryNPrime(modulus);
|
||
ulong montgomeryOne = ComputeMontgomeryResidue(1UL, modulus);
|
||
ulong montgomeryTwo = ComputeMontgomeryResidue(2UL, modulus);
|
||
ulong montgomeryTwoSquared = ULongExtensions.MontgomeryMultiply(montgomeryTwo, montgomeryTwo, modulus, nPrime);
|
||
|
||
return new MontgomeryDivisorData(
|
||
modulus,
|
||
nPrime,
|
||
montgomeryOne,
|
||
montgomeryTwo,
|
||
montgomeryTwoSquared);
|
||
}
|
||
|
||
|
||
private ulong CalculateCycleLengthWithHeuristics(ulong modulus, ulong fallbackOrder = 0UL)
|
||
{
|
||
MontgomeryDivisorData divisorData = MontgomeryDivisorData.FromModulus(modulus);
|
||
if (modulus <= 1UL || (modulus & 1UL) == 0UL)
|
||
{
|
||
return fallbackOrder != 0UL ? fallbackOrder : MersenneDivisorCycles.CalculateCycleLength(modulus, divisorData);
|
||
}
|
||
|
||
// When the below is uncommented, the benchmark never completes due to the primality test cost on very large random set.
|
||
|
||
// bool isPrime = Open.Numeric.Primes.Prime.Numbers.IsPrime(modulus);
|
||
// // bool isPrime = PrimeTester.IsPrimeInternal(modulus, CancellationToken.None);
|
||
// if (!isPrime)
|
||
// {
|
||
// return fallbackOrder != 0UL ? fallbackOrder : MersenneDivisorCycles.CalculateCycleLength(modulus);
|
||
// }
|
||
|
||
#if DEBUG
|
||
Console.WriteLine("Trying heuristic. Prime order calculation");
|
||
#endif
|
||
ulong order = PrimeOrderCalculator.Calculate(
|
||
modulus,
|
||
_previousPrimeOrder,
|
||
divisorData,
|
||
PrimeOrderCalculator.PrimeOrderSearchConfig.HeuristicDefault,
|
||
PrimeOrderCalculator.PrimeOrderHeuristicDevice.Gpu);
|
||
|
||
if (order != 0UL)
|
||
{
|
||
_previousPrimeOrder = order;
|
||
return order;
|
||
}
|
||
|
||
_previousPrimeOrder = null;
|
||
|
||
Console.WriteLine($"Heuristic failed for {modulus}, falling back to full cycle calculation");
|
||
return fallbackOrder != 0UL ? fallbackOrder : MersenneDivisorCycles.CalculateCycleLength(modulus, divisorData);
|
||
}
|
||
|
||
private UInt128 CalculateCycleLengthWithHeuristics(UInt128 modulus)
|
||
{
|
||
if (modulus <= UInt128.One || (modulus & UInt128.One) == UInt128.Zero)
|
||
{
|
||
return MersenneDivisorCycles.GetCycle(modulus);
|
||
}
|
||
|
||
#if DEBUG
|
||
Console.WriteLine("Trying heuristic. Wide prime order calculation");
|
||
#endif
|
||
UInt128 order = PrimeOrderCalculator.Calculate(
|
||
modulus,
|
||
_previousWidePrimeOrder,
|
||
PrimeOrderCalculator.PrimeOrderSearchConfig.HeuristicDefault);
|
||
|
||
if (order != UInt128.Zero)
|
||
{
|
||
_previousWidePrimeOrder = order;
|
||
return order;
|
||
}
|
||
|
||
_previousWidePrimeOrder = null;
|
||
|
||
Console.WriteLine($"Wide heuristic failed for {modulus}, falling back to full cycle calculation");
|
||
return MersenneDivisorCycles.GetCycle(modulus);
|
||
}
|
||
|
||
private static ulong ComputeMontgomeryResidue(ulong value, ulong modulus) => (ulong)((UInt128)value * (UInt128.One << 64) % modulus);
|
||
|
||
private static ulong ComputeMontgomeryNPrime(ulong modulus)
|
||
{
|
||
ulong inv = modulus;
|
||
inv *= unchecked(2UL - modulus * inv);
|
||
inv *= unchecked(2UL - modulus * inv);
|
||
inv *= unchecked(2UL - modulus * inv);
|
||
inv *= unchecked(2UL - modulus * inv);
|
||
inv *= unchecked(2UL - modulus * inv);
|
||
inv *= unchecked(2UL - modulus * inv);
|
||
return unchecked(0UL - inv);
|
||
}
|
||
}
|
||
|