Benchmarks extended. Small optimizations.
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Marek Lemańczyk committed
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@@ -24,13 +24,12 @@ public class ResidueComputationBenchmarks
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[Benchmark]
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public (ulong Step10, ulong Step8, ulong Step3, ulong Step5) ModMethodModulo()
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{
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UInt128 exponent128 = Exponent;
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exponent128.Mod10_8_5_3(out ulong mod10, out ulong mod8, out ulong mod5, out ulong mod3);
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ulong step10 = (mod10 << 1) % 10UL;
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ulong step8 = (mod8 << 1) & 7UL;
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ulong step3 = (mod3 << 1) % 3UL;
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ulong step5 = (mod5 << 1) % 5UL;
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return (step10, step8, step3, step5);
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Exponent.Mod10_8_5_3(out ulong mod10, out ulong mod8, out ulong mod5, out ulong mod3);
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mod10 = (mod10 << 1) % 10UL;
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mod8 = (mod8 << 1) & 7UL;
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mod3 = (mod3 << 1) % 3UL;
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mod5 = (mod5 << 1) % 5UL;
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return (mod10, mod8, mod3, mod5);
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}
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}
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@@ -0,0 +1,55 @@
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using System.Numerics;
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using BenchmarkDotNet.Attributes;
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using PerfectNumbers.Core;
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namespace EvenPerfectBitScanner.Benchmarks;
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[MemoryDiagnoser]
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public class UInt128ExtensionsBenchmarks
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{
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[Params(3UL, 8191UL, 131071UL, 2147483647UL)]
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public ulong Value { get; set; }
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[Benchmark(Baseline = true)]
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public (ulong Mod10, ulong Mod8, ulong Mod3, ulong Mod5) LegacyModulo()
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{
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ulong mod10, mod8, mod3, mod5;
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UInt128 zero = UInt128.Zero;
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if (Value == zero)
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{
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mod3 = 0UL;
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mod5 = 0UL;
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mod8 = 0UL;
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mod10 = 0UL;
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return (mod10, mod8, mod3, mod5);
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}
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UInt128 high = Value >> 64;
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ulong result = Value;
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mod8 = result & 7UL;
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// 2^64 ≡ 1 (mod 3)
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ulong modRem = (result % 3UL) + ((ulong)high % 3UL);
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mod3 = modRem >= 3UL ? modRem - 3UL : modRem;
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// 2^64 ≡ 1 (mod 5)
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modRem = (result % 5UL) + ((ulong)high % 5UL);
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mod5 = modRem >= 5UL ? modRem - 5UL : modRem;
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while (high != zero)
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{
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// 2^64 ≡ 6 (mod 10)
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result = (result + (ulong)high * 6UL) % 10UL;
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high >>= 64;
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}
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mod10 = result % 10UL;
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return (mod10, mod8, mod3, mod5);
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}
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[Benchmark]
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public (ulong Mod10, ulong Mod8, ulong Mod3, ulong Mod5) ModMethodModulo()
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{
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Value.Mod10_8_5_3(out ulong mod10, out ulong mod8, out ulong mod5, out ulong mod3);
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return (mod10, mod8, mod3, mod5);
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}
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}
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@@ -0,0 +1,21 @@
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using System.Runtime.CompilerServices;
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namespace PerfectNumbers.Core;
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public static class PerfectNumbersMath
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{
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static uint FastRemainder3(uint value)
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{
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uint quotient = (uint)(((ulong)value * 0xAAAAAAABUL) >> 33);
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return value - quotient * 3U;
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static uint FastRemainder5(uint value)
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{
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uint quotient = (uint)(((ulong)value * 0xCCCCCCCDUL) >> 34);
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return value - quotient * 5U;
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}
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}
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@@ -120,87 +120,73 @@ public static class UInt128Extensions
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return true;
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static void Mod10_8_5_3(this UInt128 value, out ulong mod10, out ulong mod8, out ulong mod5, out ulong mod3)
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{
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UInt128 temp = value;
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uint byteSum = 0U;
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static void Mod10_8_5_3(this UInt128 value, out ulong mod10, out ulong mod8, out ulong mod5, out ulong mod3)
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{
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UInt128 temp = value;
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uint byteSum = 0U;
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do
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{
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byteSum += (uint)(byte)temp;
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temp >>= 8;
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}
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while (temp != UInt128.Zero);
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do
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{
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byteSum += (byte)temp;
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temp >>= 8;
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}
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while (temp != UInt128.Zero);
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mod8 = (ulong)value & 7UL;
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mod8 = (ulong)value & 7UL;
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uint mod5Value = FastRemainder5(byteSum);
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uint mod3Value = FastRemainder3(byteSum);
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uint mod5Value = PerfectNumbersMath.FastRemainder5(byteSum);
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uint mod3Value = PerfectNumbersMath.FastRemainder3(byteSum);
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ulong parity = mod8 & 1UL;
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mod10 = parity == 0UL
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? mod5Value switch
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{
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0U => 0UL,
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1U => 6UL,
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2U => 2UL,
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3U => 8UL,
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_ => 4UL,
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}
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: mod5Value switch
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{
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0U => 5UL,
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1U => 1UL,
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2U => 7UL,
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3U => 3UL,
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_ => 9UL,
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};
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ulong parity = mod8 & 1UL;
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mod10 = parity == 0UL
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? mod5Value switch
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{
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0U => 0UL,
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1U => 6UL,
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2U => 2UL,
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3U => 8UL,
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_ => 4UL,
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}
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: mod5Value switch
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{
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0U => 5UL,
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1U => 1UL,
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2U => 7UL,
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3U => 3UL,
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_ => 9UL,
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};
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mod5 = mod5Value;
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mod3 = mod3Value;
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}
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mod5 = mod5Value;
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mod3 = mod3Value;
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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private static uint FastRemainder3(uint value)
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{
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uint quotient = (uint)(((ulong)value * 0xAAAAAAABUL) >> 33);
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return value - quotient * 3U;
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static UInt128 Pow(this UInt128 value, ulong exponent)
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{
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UInt128 result = UInt128.One;
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UInt128 baseValue = value;
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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private static uint FastRemainder5(uint value)
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{
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uint quotient = (uint)(((ulong)value * 0xCCCCCCCDUL) >> 34);
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return value - quotient * 5U;
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}
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while (exponent != 0UL)
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{
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if ((exponent & 1UL) != 0UL)
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{
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result *= baseValue;
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static UInt128 Pow(this UInt128 value, ulong exponent)
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{
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UInt128 result = UInt128.One;
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UInt128 baseValue = value;
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baseValue *= baseValue;
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exponent >>= 1;
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}
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while (exponent != 0UL)
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{
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if ((exponent & 1UL) != 0UL)
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{
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result *= baseValue;
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}
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return result;
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}
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baseValue *= baseValue;
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exponent >>= 1;
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}
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return result;
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static UInt128 ModPow(this UInt128 value, UInt128 exponent, UInt128 modulus)
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{
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UInt128 result, one = result = UInt128.One,
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zero = UInt128.Zero,
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baseValue = value % modulus;
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static UInt128 ModPow(this UInt128 value, UInt128 exponent, UInt128 modulus)
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{
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UInt128 result, one = result = UInt128.One,
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zero = UInt128.Zero,
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baseValue = value % modulus;
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while (exponent != zero)
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{
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@@ -284,7 +270,7 @@ public static class UInt128Extensions
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{
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a -= modulus;
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}
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b >>= 1;
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}
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@@ -57,6 +57,47 @@ public static class ULongExtensions
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return q;
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static void Mod10_8_5_3(this ulong value, out ulong mod10, out ulong mod8, out ulong mod5, out ulong mod3)
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{
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ulong temp = value;
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uint byteSum = 0U;
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do
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{
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byteSum += (byte)temp;
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temp >>= 8;
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}
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while (temp != 0UL);
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mod8 = value & 7UL;
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uint mod5Value = PerfectNumbersMath.FastRemainder5(byteSum);
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uint mod3Value = PerfectNumbersMath.FastRemainder3(byteSum);
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ulong parity = mod8 & 1UL;
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mod10 = parity == 0UL
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? mod5Value switch
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{
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0U => 0UL,
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1U => 6UL,
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2U => 2UL,
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3U => 8UL,
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_ => 4UL,
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}
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: mod5Value switch
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{
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0U => 5UL,
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1U => 1UL,
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2U => 7UL,
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3U => 3UL,
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_ => 9UL,
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};
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mod5 = mod5Value;
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mod3 = mod3Value;
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static bool IsPrimeCandidate(this ulong n)
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{
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