Add optimized modulo helpers for unsigned integers
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Marek Lemańczyk committed
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@@ -24,10 +24,7 @@ public class MersenneNumberResidueGpuTester(bool useGpuOrder)
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UInt128 kStart = 1UL;
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byte last = lastIsSeven ? (byte)1 : (byte)0;
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var kernel = gpuLease.Pow2ModKernel;
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ulong step10 = (exponent.Mod10() << 1).Mod10();
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ulong step8 = ((exponent & 7UL) << 1) & 7UL;
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ulong step3 = ((exponent % 3UL) << 1) % 3UL;
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ulong step5 = ((exponent % 5UL) << 1) % 5UL;
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exponent.Mod10_8_5_3Steps(out ulong step10, out ulong step8, out ulong step5, out ulong step3);
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GpuUInt128 twoPGpu = (GpuUInt128)twoP;
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var orderBuffer = accelerator.Allocate1D<ulong>(batchSize);
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@@ -203,48 +203,73 @@ public static class UInt128Extensions
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static ulong Mod10(this UInt128 value)
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{
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UInt128 zero = UInt128.Zero;
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if (value == zero)
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return 0UL;
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public static ulong Mod10(this UInt128 value)
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{
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UInt128 zero = UInt128.Zero;
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if (value == zero)
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return 0UL;
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ulong result = (ulong)value;
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UInt128 high = value >> 64;
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ulong result = (ulong)value;
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UInt128 high = value >> 64;
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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).Mod10();
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high >>= 64;
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}
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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).Mod10();
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high >>= 64;
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}
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return result.Mod10();
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}
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return result.Mod10();
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static ulong Mod8(this UInt128 value) => (ulong)value & 7UL;
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static ulong Mod3(this UInt128 value)
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{
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// 2^64 ≡ 1 (mod 3)
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ulong rem = ((ulong)value % 3UL) + ((ulong)(value >> 64) % 3UL);
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return rem >= 3UL ? rem - 3UL : rem;
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static ulong Mod8(this UInt128 value) => (ulong)value & 7UL;
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static ulong Mod5(this UInt128 value)
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{
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// 2^64 ≡ 1 (mod 5)
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ulong rem = ((ulong)value % 5UL) + ((ulong)(value >> 64) % 5UL);
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return rem >= 5UL ? rem - 5UL : rem;
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static ulong Mod3(this UInt128 value)
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{
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ulong remainder = ((ulong)value).Mod3() + ((ulong)(value >> 64)).Mod3();
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return remainder >= 3UL ? remainder - 3UL : remainder;
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static ulong Mod5(this UInt128 value)
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{
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ulong remainder = ((ulong)value).Mod5() + ((ulong)(value >> 64)).Mod5();
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return remainder >= 5UL ? remainder - 5UL : remainder;
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static ulong Mod7(this UInt128 value)
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{
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ulong remainder = ((ulong)value).Mod7() + ((ulong)(value >> 64)).Mod7() * 2UL;
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while (remainder >= 7UL)
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{
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remainder -= 7UL;
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}
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return remainder;
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static ulong Mod11(this UInt128 value)
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{
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ulong remainder = ((ulong)value).Mod11() + ((ulong)(value >> 64)).Mod11() * 5UL;
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while (remainder >= 11UL)
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{
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remainder -= 11UL;
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}
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return remainder;
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static ulong Mod128(this UInt128 value) => (ulong)value & 127UL;
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static UInt128 Mul64(this UInt128 a, UInt128 b)
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{
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static UInt128 Mul64(this UInt128 a, UInt128 b)
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{
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ulong aLow = (ulong)a;
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ulong bLow = (ulong)b;
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return ((UInt128)(aLow * (ulong)(b >> 64) + aLow.MulHigh(bLow)) << 64) | (aLow * bLow);
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@@ -0,0 +1,61 @@
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using System.Runtime.CompilerServices;
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namespace PerfectNumbers.Core;
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public static class UIntExtensions
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{
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static uint Mod3(this uint value) => PerfectNumbersMath.FastRemainder3(value);
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static uint Mod5(this uint value) => PerfectNumbersMath.FastRemainder5(value);
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static uint Mod7(this uint value)
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{
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uint remainder = 0U;
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uint temp = value;
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while (temp != 0U)
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{
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remainder += temp & 7U;
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temp >>= 3;
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if (remainder >= 7U)
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{
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remainder -= 7U;
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}
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}
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return remainder >= 7U ? remainder - 7U : remainder;
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static uint Mod8(this uint value) => value & 7U;
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static uint Mod10(this uint value)
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{
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uint quotient = (uint)(((ulong)value * 0xCCCCCCCDUL) >> 35);
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return value - quotient * 10U;
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static uint Mod11(this uint value)
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{
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uint remainder = 0U;
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uint temp = value;
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while (temp != 0U)
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{
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remainder += temp & 1023U;
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temp >>= 10;
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remainder -= 11U * (remainder / 11U);
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}
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return remainder;
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static uint Mod128(this uint value) => value & 127U;
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}
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@@ -58,51 +58,62 @@ public static class ULongExtensions
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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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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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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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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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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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public static bool IsPrimeCandidate(this ulong n)
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{
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int i = 0;
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ulong p;
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static void Mod10_8_5_3Steps(this ulong value, out ulong step10, out ulong step8, out ulong step5, out ulong step3)
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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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step10 = (mod10 << 1).Mod10();
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step8 = ((mod8 << 1) & 7UL);
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step5 = (mod5 << 1).Mod5();
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step3 = (mod3 << 1).Mod3();
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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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int i = 0;
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ulong p;
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uint[] smallPrimes = PrimesGenerator.SmallPrimes;
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ulong[] smallPrimesPow2 = PrimesGenerator.SmallPrimesPow2;
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int len = smallPrimes.Length;
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@@ -123,12 +134,70 @@ public static class ULongExtensions
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return true;
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static ulong Mod10(this ulong value)
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{
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ulong quotient = (ulong)(((UInt128)value * 0xCCCCCCCCCCCCCCCDUL) >> 67);
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return value - quotient * 10UL;
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static ulong Mod10(this ulong value)
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{
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ulong quotient = (ulong)(((UInt128)value * 0xCCCCCCCCCCCCCCCDUL) >> 67);
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return value - quotient * 10UL;
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static ulong Mod8(this ulong value) => value & 7UL;
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static ulong Mod3(this ulong value)
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{
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uint sum = (uint)(value & 0xFFFFUL);
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sum += (uint)((value >> 16) & 0xFFFFUL);
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sum += (uint)((value >> 32) & 0xFFFFUL);
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sum += (uint)((value >> 48) & 0xFFFFUL);
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return PerfectNumbersMath.FastRemainder3(sum);
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static ulong Mod5(this ulong value)
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{
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uint sum = (uint)(value & 0xFFFFUL);
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sum += (uint)((value >> 16) & 0xFFFFUL);
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sum += (uint)((value >> 32) & 0xFFFFUL);
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sum += (uint)((value >> 48) & 0xFFFFUL);
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return PerfectNumbersMath.FastRemainder5(sum);
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static ulong Mod7(this ulong value)
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{
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uint low = (uint)value;
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uint high = (uint)(value >> 32);
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ulong remainder = low.Mod7() + (ulong)high.Mod7() * 4UL;
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while (remainder >= 7UL)
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{
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remainder -= 7UL;
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}
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return remainder;
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static ulong Mod11(this ulong value)
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{
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uint low = (uint)value;
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uint high = (uint)(value >> 32);
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ulong remainder = low.Mod11() + (ulong)high.Mod11() * 4UL;
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while (remainder >= 11UL)
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{
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remainder -= 11UL;
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}
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return remainder;
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static ulong Mod128(this ulong value) => value & 127UL;
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static UInt128 Mul64(this ulong a, ulong b) => ((UInt128)a.MulHigh(b) << 64) | (UInt128)(a * b);
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