Enable residue-aware GPU sieve in PrimeTester
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Marek Lemańczyk committed
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@@ -1,151 +1,11 @@
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using System;
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using System.Runtime.CompilerServices;
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namespace PerfectNumbers.Core;
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public static class PrimesGenerator
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{
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public static readonly uint[] SmallPrimes;
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public static readonly ulong[] SmallPrimesPow2;
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public static readonly uint[] SmallPrimesLastOne;
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public static readonly ulong[] SmallPrimesPow2LastOne;
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public static readonly uint[] SmallPrimesLastSeven;
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public static readonly ulong[] SmallPrimesPow2LastSeven;
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static PrimesGenerator()
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{
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BuildSmallPrimes(
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out SmallPrimes,
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out SmallPrimesPow2,
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out SmallPrimesLastOne,
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out SmallPrimesPow2LastOne,
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out SmallPrimesLastSeven,
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out SmallPrimesPow2LastSeven);
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}
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private static void BuildSmallPrimes(
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out uint[] all,
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out ulong[] allPow2,
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out uint[] lastOne,
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out ulong[] lastOnePow2,
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out uint[] lastSeven,
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out ulong[] lastSevenPow2)
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{
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uint target = PerfectNumberConstants.PrimesLimit;
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int targetInt = checked((int)target);
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all = new uint[targetInt];
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allPow2 = new ulong[targetInt];
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lastOne = new uint[targetInt];
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lastOnePow2 = new ulong[targetInt];
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lastSeven = new uint[targetInt];
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lastSevenPow2 = new ulong[targetInt];
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List<uint> primes = new(targetInt * 4 / 3 + 16);
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uint candidate = 2U;
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int allCount = 0;
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int lastOneCount = 0;
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int lastSevenCount = 0;
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while (allCount < targetInt || lastOneCount < targetInt || lastSevenCount < targetInt)
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{
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bool isPrime = true;
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int primesCount = primes.Count;
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for (int i = 0; i < primesCount; i++)
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{
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uint p = primes[i];
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// TODO: Reuse a single squared local for `p` within this loop so we avoid recalculating
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// `p * p` repeatedly without storing every squared prime globally (the cache must remain
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// limited to the small-divisor tables to honor the memory constraints).
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if (p * p > candidate)
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{
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break;
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}
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// TODO: Replace this trial-division `%` with the sieve-based generator that avoids
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// per-candidate modulo work so building the small-prime tables stops dominating
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// startup time for large scans.
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if (candidate % p == 0U)
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{
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isPrime = false;
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break;
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}
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}
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if (isPrime)
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{
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primes.Add(candidate);
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if (allCount < targetInt)
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{
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// TODO: Reuse a single cached `candidateSquared` per iteration so we avoid issuing
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// three separate 64-bit multiplications when populating the pow2 arrays here and
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// in the last-one/last-seven branches below.
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all[allCount] = candidate;
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allPow2[allCount] = checked((ulong)candidate * candidate);
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allCount++;
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}
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if (candidate != 2U)
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{
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LastDigit lastDigit = GetLastDigit(candidate);
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if (lastOneCount < targetInt && IsAllowedForLastOne(candidate, lastDigit))
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{
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lastOne[lastOneCount] = candidate;
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lastOnePow2[lastOneCount] = checked((ulong)candidate * candidate);
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lastOneCount++;
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}
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if (lastSevenCount < targetInt && IsAllowedForLastSeven(candidate, lastDigit))
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{
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lastSeven[lastSevenCount] = candidate;
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lastSevenPow2[lastSevenCount] = checked((ulong)candidate * candidate);
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lastSevenCount++;
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}
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}
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}
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// TODO: Switch this increment to the Mod6 stepping table identified in the Mod6ComparisonBenchmarks
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// so we skip the composite residues without relying on per-iteration `%` checks.
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candidate = candidate == 2U ? 3U : candidate + 2U;
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}
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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private static LastDigit GetLastDigit(uint prime)
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{
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return (prime % 10U) switch
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{
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1U => LastDigit.One,
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3U => LastDigit.Three,
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5U => LastDigit.Five,
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7U => LastDigit.Seven,
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9U => LastDigit.Nine,
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_ => throw new ArgumentOutOfRangeException(nameof(prime)),
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};
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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private static bool IsAllowedForLastOne(uint prime, LastDigit lastDigit)
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{
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// TODO: Swap the `% 10` usage for ULongExtensions.Mod10 so the hot classification path
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// reuses the benchmarked residue helper instead of repeated divisions.
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return lastDigit switch
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{
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LastDigit.One or LastDigit.Three or LastDigit.Nine => true,
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LastDigit.Seven => prime == 7U,
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_ => prime == 11U,
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};
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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private static bool IsAllowedForLastSeven(uint prime, LastDigit lastDigit)
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{
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// TODO: Route this `% 10` classification through ULongExtensions.Mod10 to match the faster
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// residue helper used elsewhere in the scanner.
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return lastDigit switch
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{
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LastDigit.Three or LastDigit.Seven or LastDigit.Nine => true,
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_ => prime == 11U,
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};
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}
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public static readonly uint[] SmallPrimes = DivisorGenerator.SmallPrimes;
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public static readonly ulong[] SmallPrimesPow2 = DivisorGenerator.SmallPrimesPow2;
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public static readonly uint[] SmallPrimesLastOne = DivisorGenerator.SmallPrimesLastOne;
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public static readonly ulong[] SmallPrimesPow2LastOne = DivisorGenerator.SmallPrimesPow2LastOne;
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public static readonly uint[] SmallPrimesLastSeven = DivisorGenerator.SmallPrimesLastSeven;
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public static readonly ulong[] SmallPrimesPow2LastSeven = DivisorGenerator.SmallPrimesPow2LastSeven;
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}
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