342 lines
10 KiB
C#
342 lines
10 KiB
C#
using System.Numerics;
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using System.Runtime.CompilerServices;
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namespace PerfectNumbers.Core;
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public static class UInt128Extensions
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{
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static UInt128 BinaryGcd(this UInt128 u, UInt128 v)
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{
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// TODO: Replace this hand-rolled binary GCD with the shared subtract-free ladder from
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// GpuUInt128BinaryGcdBenchmarks so wide operands reuse the optimized helper instead of
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// repeating the slower shift/subtract loop on both CPU and GPU paths.
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UInt128 zero = UInt128.Zero;
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if (u == zero)
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{
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return v;
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}
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if (v == zero)
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{
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return u;
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}
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int shift = CountTrailingZeros(u | v);
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u >>= CountTrailingZeros(u);
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do
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{
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v >>= CountTrailingZeros(v);
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if (u > v)
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{
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(u, v) = (v, u);
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}
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v -= u;
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}
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while (v != zero);
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return u << shift;
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}
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public static ulong CalculateOrder(this UInt128 q)
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{
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if (q <= UInt128Numbers.Two)
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{
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return 0UL;
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}
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UInt128 one = UInt128.One;
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UInt128 phi = q - one;
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if (phi > ulong.MaxValue)
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{
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throw new NotImplementedException("Such big values are not yet supported");
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}
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ulong order = (ulong)phi;
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uint[] smallPrimes = PrimesGenerator.SmallPrimes;
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ulong[] smallPrimesPow2 = PrimesGenerator.SmallPrimesPow2;
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int i = 0, primesLength = smallPrimes.Length;
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UInt128 cycle = MersenneDivisorCycles.GetCycle(q);
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// TODO: If the cache lacks this cycle, immediately schedule the configured device
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// (GPU by default) to compute it on the fly and skip inserting it into the cache so
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// wide-order factoring can still leverage cycle stepping without breaching the
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// memory cap or introducing extra synchronization.
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ulong prime, temp;
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for (; i < primesLength; i++)
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{
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if (smallPrimesPow2[i] > order)
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{
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break;
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}
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prime = smallPrimes[i];
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while (order % prime == 0UL)
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{
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temp = order / prime;
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// TODO: Switch this divisor-order powmod to the ProcessEightBitWindows helper so the
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// cycle factoring loop benefits from the faster windowed pow2 ladder measured in CPU benchmarks.
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if (temp.PowModWithCycle(q, cycle) == one)
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{
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order = temp;
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}
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else
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{
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break;
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}
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}
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}
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return order;
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static int CountTrailingZeros(this UInt128 value)
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{
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ulong valuePart = (ulong)value;
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if (valuePart != 0UL)
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{
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return BitOperations.TrailingZeroCount(valuePart);
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}
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return 64 + BitOperations.TrailingZeroCount((ulong)(value >> 64));
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static bool IsPrimeCandidate(this UInt128 n)
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{
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UInt128 p, zero = UInt128.Zero;
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uint[] smallPrimes = PrimesGenerator.SmallPrimes;
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ulong[] smallPrimesPow2 = PrimesGenerator.SmallPrimesPow2;
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ulong i, smallPrimesCount = (ulong)smallPrimes.Length;
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for (i = 0UL; i < smallPrimesCount; i++)
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{
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if (smallPrimesPow2[i] > n)
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{
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break;
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}
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p = smallPrimes[i];
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// TODO: Replace this direct `%` test with the shared divisor-cycle filter once the
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// UInt128 path is wired into the cached cycle tables so wide candidates skip the slow
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// modulo checks during primality pre-filtering.
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if (n % p == zero)
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{
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return n == p;
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}
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}
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return true;
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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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// TODO: Fold these reductions into the multiply-high trick captured in Mod3BenchmarkResults so
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// the UInt128 modulo helpers avoid `%` altogether and align with the faster CPU/GPU residue filters.
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ulong remainder = ((ulong)value) % 3UL + ((ulong)(value >> 64)) % 3UL;
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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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// TODO: Replace the `% 5` operations with the precomputed multiply-high constants from the Mod5
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// benchmarks so the UInt128 path matches the 64-bit helpers without extra modulo instructions.
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ulong remainder = (((ulong)value) % 5UL) + (((ulong)(value >> 64)) % 5UL);
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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 Mod6(this UInt128 value) => ((value.Mod3() << 1) | ((ulong)value & 1UL)) switch
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{
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0UL => 0UL,
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1UL => 3UL,
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2UL => 4UL,
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3UL => 1UL,
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4UL => 2UL,
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_ => 5UL,
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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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// TODO: Inline the lookup-based Mod7 reducer validated in the residue benchmarks so this helper
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// stops relying on `% 7` in hot loops and mirrors the optimized CPU cycle filters.
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ulong low = (ulong)value % 7UL;
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ulong high = (ulong)(value >> 64) % 7UL;
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ulong remainder = low + (high * 2UL);
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if (remainder >= 7UL)
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{
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remainder -= 7UL;
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if (remainder >= 7UL)
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{
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remainder -= 7UL;
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}
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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 Mod8(this UInt128 value) => (ulong)value & 7UL;
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static ulong Mod10(this UInt128 value128)
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{
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// Split and fold under mod 10: 2^64 ≡ 6 (mod 10)
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// TODO: Precompute the 2^64 ≡ 6 folding constants once so this path stops recomputing `% 10`
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// on each half and instead uses the span-based lookup captured in Mod10BenchmarkResults.
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ulong low = (ulong)value128;
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ulong high = (ulong)(value128 >> 64);
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return ((low % 10UL) + ((high % 10UL) * 6UL)) % 10UL;
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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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byte current;
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uint byteSum = 0U;
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mod8 = (ulong)value & 7UL;
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UInt128 zero = UInt128.Zero;
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do
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{
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current = (byte)value;
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byteSum += current;
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value >>= 8;
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}
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while (value != zero);
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mod5 = byteSum.Mod5();
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// TODO: Collapse this Mod10 switch into the shared lookup table from the CLI benchmarks so we
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// avoid the nested switch expressions once the pooled residue tables become available.
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mod10 = (mod8 & 1UL) == 0UL
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? mod5 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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: mod5 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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mod3 = byteSum % 3U;
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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) % 11UL) + (((ulong)(value >> 64)) % 11UL) * 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 ModPow(this UInt128 value, UInt128 exponent, UInt128 modulus)
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{
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UInt128 zero = UInt128.Zero;
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UInt128 one = UInt128.One;
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UInt128 result = UInt128.One;
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value %= modulus;
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while (exponent != zero)
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{
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if ((exponent & one) != zero)
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{
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result = MulMod(result, value, modulus);
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}
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value = MulMod(value, value, modulus);
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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 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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ulong bHigh = (ulong)(b >> 64);
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ulong low = aLow * bLow;
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// Keep the high-word accumulation in locals so the JIT does not rebuild the
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// expression tree around the shift. Mirroring the MulHigh layout lets RyuJIT
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// keep the intermediate sum in registers instead of reloading the partial
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// product from the stack.
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ulong high = aLow.MulHigh(bLow);
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high += aLow * bHigh;
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return ((UInt128)high << 64) | low;
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static UInt128 MulMod(this UInt128 a, UInt128 b, UInt128 modulus)
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{
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UInt128 one = UInt128.One,
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result = UInt128.Zero,
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zero = UInt128.Zero;
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while (b != zero)
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{
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if ((b & one) != zero)
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{
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result += a;
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if (result >= modulus)
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{
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result -= modulus;
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}
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}
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a <<= 1;
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if (a >= modulus)
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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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return result;
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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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while (exponent != 0UL)
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{
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if ((exponent & 1UL) != 0UL)
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{
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result *= value;
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}
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value *= value;
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exponent >>= 1;
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}
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return result;
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}
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}
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