342 lines
12 KiB
C#
342 lines
12 KiB
C#
using System;
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using System.Buffers.Binary;
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using System.Threading;
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using BenchmarkDotNet.Attributes;
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using BenchmarkDotNet.Jobs;
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using PerfectNumbers.Core;
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namespace EvenPerfectBitScanner.Benchmarks;
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/// <remarks>
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/// Benchmark results collected on AMD Ryzen 5 5625U (.NET 8.0, launchCount: 1, warmupCount: 1, iterationCount: 5):
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/// Small sample (~1e6 random odd moduli)
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/// - MontgomeryWithoutCycle: 35.41 µs (baseline)
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/// - MontgomeryWithPrecomputedCycle: 25.81 µs (0.73× baseline)
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/// - MontgomeryWithGpuCycleComputation: 54.09 ms (1,527× baseline, includes GPU cycle calculation)
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/// Large sample (Mersenne-like moduli from 2^48-1 to 2^63-1)
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/// - MontgomeryWithoutCycle: 117.33 µs (baseline)
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/// - MontgomeryWithPrecomputedCycle: 9.12 µs (0.08× baseline)
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/// - MontgomeryWithGpuCycleComputation: 12.91 µs (0.11× baseline)
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/// </remarks>
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[MemoryDiagnoser]
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[SimpleJob(RuntimeMoniker.Net80, launchCount: 1, warmupCount: 1, iterationCount: 5)]
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public class Pow2MontgomeryModCycleComputationBenchmarks
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{
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private const int SampleCount = 256;
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private const ulong OneShiftedLeft63 = 1UL << 63;
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private const long OneShiftedLeft60 = 1L << 60;
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private readonly MontgomeryDivisorData[] _smallDivisors = new MontgomeryDivisorData[SampleCount];
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private readonly MontgomeryDivisorData[] _largeDivisors = new MontgomeryDivisorData[SampleCount];
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private readonly MontgomeryDivisorData[] _veryLargeDivisors = new MontgomeryDivisorData[SampleCount];
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private readonly UInt128[] _wideModuli = new UInt128[SampleCount];
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private readonly ulong[] _smallExponents = new ulong[SampleCount];
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private readonly ulong[] _largeExponents = new ulong[SampleCount];
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private readonly ulong[] _veryLargeExponents = new ulong[SampleCount];
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private readonly ulong[] _smallCycles = new ulong[SampleCount];
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private readonly ulong[] _largeCycles = new ulong[SampleCount];
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private readonly ulong[] _veryLargeCycles = new ulong[SampleCount];
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private readonly UInt128[] _wideCycles = new UInt128[SampleCount];
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private readonly Random _random = new(113);
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private ulong? _previousPrimeOrder;
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private UInt128? _previousWidePrimeOrder;
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public enum InputScale
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{
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Small,
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Large,
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VeryLarge
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}
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[ParamsAllValues]
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public InputScale Scale { get; set; }
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[GlobalSetup]
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public void Setup()
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{
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for (int i = 0; i < SampleCount; i++)
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{
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#if DEBUG
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Console.WriteLine($"Generating sample {i}");
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#endif
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ulong smallModulus = NextSmallOddModulus();
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_smallDivisors[i] = CreateMontgomeryDivisorData(smallModulus);
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_smallExponents[i] = NextSmallExponent();
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_smallCycles[i] = CalculateCycleLengthWithHeuristics(smallModulus);
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(ulong largeModulus, ulong largeCycle) = NextLargeModulusAndCycle();
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_largeDivisors[i] = CreateMontgomeryDivisorData(largeModulus);
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_largeExponents[i] = NextLargeExponent();
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_largeCycles[i] = CalculateCycleLengthWithHeuristics(largeModulus, largeCycle);
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ulong veryLargeModulus = NextVeryLargeOddModulus();
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_veryLargeDivisors[i] = CreateMontgomeryDivisorData(veryLargeModulus);
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_veryLargeExponents[i] = NextVeryLargeExponent();
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#if DEBUG
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Console.WriteLine($"Calculating cycle length {veryLargeModulus}");
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#endif
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_veryLargeCycles[i] = CalculateCycleLengthWithHeuristics(veryLargeModulus);
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Console.WriteLine($"Generating wide sample {i}");
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UInt128 wideModulus = NextWideOddModulus();
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_wideModuli[i] = wideModulus;
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_wideCycles[i] = CalculateCycleLengthWithHeuristics(wideModulus);
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}
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}
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/// <summary>
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/// Baseline Montgomery reduction without precomputed cycle data; measured 35.41 μs on the small sample and 117.33 μs on the
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/// large set.
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/// </summary>
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// [Benchmark(Baseline = true)]
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public ulong MontgomeryWithoutCycle()
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{
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GetData(out ulong[] exponents, out MontgomeryDivisorData[] divisors, out _);
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ulong checksum = 0UL;
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for (int i = 0; i < SampleCount; i++)
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{
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checksum ^= exponents[i].Pow2MontgomeryModWindowed(divisors[i], keepMontgomery: false);
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}
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return checksum;
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}
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/// <summary>
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/// Montgomery reduction with a known cycle length (cycle lookup only); 25.81 μs on the small set (0.73× baseline) and 9.12 μs
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/// on the large one (0.08×).
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/// </summary>
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[Benchmark]
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public ulong MontgomeryWithPrecomputedCycle()
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{
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GetData(out ulong[] exponents, out MontgomeryDivisorData[] divisors, out ulong[] cycles);
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ulong checksum = 0UL;
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for (int i = 0; i < SampleCount; i++)
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{
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checksum ^= exponents[i].Pow2MontgomeryModWithCycle(cycles[i], divisors[i]);
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}
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return checksum;
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}
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/// <summary>
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/// Montgomery reduction with the cycle computed on the fly using the GPU helper; costs 54.09 ms on the small benchmark due to
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/// cycle discovery, but drops to 12.91 μs on the large set (0.11× baseline).
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/// </summary>
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// [Benchmark]
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public ulong MontgomeryWithGpuCycleComputation()
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{
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GetData(out ulong[] exponents, out MontgomeryDivisorData[] divisors, out _);
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ulong checksum = 0UL;
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for (int i = 0; i < SampleCount; i++)
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{
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ulong cycle = MersenneDivisorCycles.CalculateCycleLengthGpu(divisors[i].Modulus);
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checksum ^= exponents[i].Pow2MontgomeryModWithCycle(cycle, divisors[i]);
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}
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return checksum;
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}
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[Benchmark]
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public ulong MontgomeryWithHeuristicCycleComputation()
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{
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GetData(out ulong[] exponents, out MontgomeryDivisorData[] divisors, out _);
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ulong checksum = 0UL;
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for (int i = 0; i < SampleCount; i++)
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{
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ulong cycle = CalculateCycleLengthWithHeuristics(divisors[i].Modulus);
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checksum ^= exponents[i].Pow2MontgomeryModWithCycle(cycle, divisors[i]);
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}
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return checksum;
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}
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[Benchmark]
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public UInt128 HeuristicWideCycleComputation()
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{
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UInt128 checksum = UInt128.Zero;
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for (int i = 0; i < SampleCount; i++)
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{
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UInt128 cycle = CalculateCycleLengthWithHeuristics(_wideModuli[i]);
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_wideCycles[i] = cycle;
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checksum ^= cycle;
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}
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return checksum;
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}
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private void GetData(out ulong[] exponents, out MontgomeryDivisorData[] divisors, out ulong[] cycles)
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{
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switch (Scale)
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{
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case InputScale.Small:
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exponents = _smallExponents;
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divisors = _smallDivisors;
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cycles = _smallCycles;
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break;
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case InputScale.Large:
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exponents = _largeExponents;
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divisors = _largeDivisors;
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cycles = _largeCycles;
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break;
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case InputScale.VeryLarge:
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exponents = _veryLargeExponents;
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divisors = _veryLargeDivisors;
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cycles = _veryLargeCycles;
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break;
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default:
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throw new ArgumentOutOfRangeException(nameof(Scale), Scale, null);
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}
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}
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private ulong NextSmallExponent() => (ulong)_random.NextInt64(1L, 1_000_000L);
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private ulong NextLargeExponent() => (ulong)_random.NextInt64(OneShiftedLeft60, long.MaxValue);
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private ulong NextVeryLargeExponent()
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{
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Span<byte> buffer = stackalloc byte[8];
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_random.NextBytes(buffer);
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ulong value = checked(BinaryPrimitives.ReadUInt64LittleEndian(buffer) | OneShiftedLeft63);
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return value;
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}
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private ulong NextSmallOddModulus()
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{
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ulong value = (ulong)_random.NextInt64(3L, 1_000_000L);
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return value | 1UL;
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}
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private (ulong modulus, ulong cycleLength) NextLargeModulusAndCycle()
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{
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int bitLength = _random.Next(48, 64);
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ulong modulus = (1UL << bitLength) - 1UL;
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return (modulus, (ulong)bitLength);
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}
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private ulong NextVeryLargeOddModulus()
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{
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Span<byte> buffer = stackalloc byte[8];
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_random.NextBytes(buffer);
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ulong value = BinaryPrimitives.ReadUInt64LittleEndian(buffer) | OneShiftedLeft63 | 1UL;
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return value;
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}
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private UInt128 NextWideOddModulus()
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{
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Span<byte> buffer = stackalloc byte[16];
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_random.NextBytes(buffer);
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ulong low = BinaryPrimitives.ReadUInt64LittleEndian(buffer);
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Span<byte> highSlice = buffer.Slice(8, 8);
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ulong high = BinaryPrimitives.ReadUInt64LittleEndian(highSlice) | (1UL << 63);
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UInt128 value = ((UInt128)high << 64) | low;
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return value | UInt128.One;
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}
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private static MontgomeryDivisorData CreateMontgomeryDivisorData(ulong modulus)
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{
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if (modulus <= 1UL || (modulus & 1UL) == 0UL)
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{
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return new MontgomeryDivisorData(modulus, 0UL, 0UL, 0UL, 0UL);
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}
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ulong nPrime = ComputeMontgomeryNPrime(modulus);
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ulong montgomeryOne = ComputeMontgomeryResidue(1UL, modulus);
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ulong montgomeryTwo = ComputeMontgomeryResidue(2UL, modulus);
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ulong montgomeryTwoSquared = ULongExtensions.MontgomeryMultiply(montgomeryTwo, montgomeryTwo, modulus, nPrime);
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return new MontgomeryDivisorData(
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modulus,
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nPrime,
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montgomeryOne,
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montgomeryTwo,
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montgomeryTwoSquared);
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}
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private ulong CalculateCycleLengthWithHeuristics(ulong modulus, ulong fallbackOrder = 0UL)
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{
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MontgomeryDivisorData divisorData = MontgomeryDivisorData.FromModulus(modulus);
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if (modulus <= 1UL || (modulus & 1UL) == 0UL)
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{
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return fallbackOrder != 0UL ? fallbackOrder : MersenneDivisorCycles.CalculateCycleLength(modulus, divisorData);
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}
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// When the below is uncommented, the benchmark never completes due to the primality test cost on very large random set.
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// bool isPrime = Open.Numeric.Primes.Prime.Numbers.IsPrime(modulus);
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// // bool isPrime = PrimeTester.IsPrimeInternal(modulus, CancellationToken.None);
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// if (!isPrime)
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// {
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// return fallbackOrder != 0UL ? fallbackOrder : MersenneDivisorCycles.CalculateCycleLength(modulus);
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// }
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#if DEBUG
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Console.WriteLine("Trying heuristic. Prime order calculation");
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#endif
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PrimeOrderCalculator.PrimeOrderResult orderResult = PrimeOrderCalculator.Calculate(
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modulus,
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_previousPrimeOrder,
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divisorData,
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PrimeOrderCalculator.PrimeOrderSearchConfig.HeuristicDefault);
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if (orderResult.Order != 0UL)
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{
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_previousPrimeOrder = orderResult.Order;
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return orderResult.Order;
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}
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_previousPrimeOrder = null;
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Console.WriteLine($"Heuristic failed for {modulus}, falling back to full cycle calculation");
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return fallbackOrder != 0UL ? fallbackOrder : MersenneDivisorCycles.CalculateCycleLength(modulus, divisorData);
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}
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private UInt128 CalculateCycleLengthWithHeuristics(UInt128 modulus)
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{
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if (modulus <= UInt128.One || (modulus & UInt128.One) == UInt128.Zero)
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{
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return MersenneDivisorCycles.GetCycle(modulus);
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}
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#if DEBUG
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Console.WriteLine("Trying heuristic. Wide prime order calculation");
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#endif
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PrimeOrderCalculator.PrimeOrderResultWide orderResult = PrimeOrderCalculator.Calculate(
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modulus,
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_previousWidePrimeOrder,
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PrimeOrderCalculator.PrimeOrderSearchConfig.HeuristicDefault);
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if (orderResult.Order != UInt128.Zero)
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{
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_previousWidePrimeOrder = orderResult.Order;
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return orderResult.Order;
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}
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_previousWidePrimeOrder = null;
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Console.WriteLine($"Wide heuristic failed for {modulus}, falling back to full cycle calculation");
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return MersenneDivisorCycles.GetCycle(modulus);
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}
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private static ulong ComputeMontgomeryResidue(ulong value, ulong modulus) => (ulong)((UInt128)value * (UInt128.One << 64) % modulus);
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private static ulong ComputeMontgomeryNPrime(ulong modulus)
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{
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ulong inv = modulus;
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inv *= unchecked(2UL - modulus * inv);
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inv *= unchecked(2UL - modulus * inv);
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inv *= unchecked(2UL - modulus * inv);
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inv *= unchecked(2UL - modulus * inv);
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inv *= unchecked(2UL - modulus * inv);
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inv *= unchecked(2UL - modulus * inv);
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return unchecked(0UL - inv);
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}
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}
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