Add TODOs for divisor metadata caching
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Marek Lemańczyk committed
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@@ -197,14 +197,17 @@ public sealed class ModResidueTracker
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}
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else
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{
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for (; i < divisors.Count; i++)
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{
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d = divisors[i];
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value = PowMod128(UInt128Numbers.Two, delta, d);
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// r' = pow2Delta*r + (pow2Delta - 1) mod d
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value = MulMod128(value, residues[i], d) + value - UInt128.One;
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if (value >= d)
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{
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for (; i < divisors.Count; i++)
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{
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d = divisors[i];
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// TODO: Replace this PowMod128 call with the upcoming eight-bit window helper once the
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// ProcessEightBitWindows scalar implementation lands so residue updates benefit from the
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// ~2× win recorded in GpuPow2ModBenchmarks for large moduli.
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value = PowMod128(UInt128Numbers.Two, delta, d);
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// r' = pow2Delta*r + (pow2Delta - 1) mod d
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value = MulMod128(value, residues[i], d) + value - UInt128.One;
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if (value >= d)
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{
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value -= d;
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}
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@@ -238,23 +241,30 @@ public sealed class ModResidueTracker
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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private UInt128 ComputeInitialResidue(UInt128 number, UInt128 divisor)
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{
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if (_model == ResidueModel.Identity)
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{
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// Fast path for 64-bit inputs
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if (number <= ulong.MaxValue && divisor <= ulong.MaxValue)
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{
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return (ulong)number % (ulong)divisor;
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}
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if (_model == ResidueModel.Identity)
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{
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// Fast path for 64-bit inputs
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if (number <= ulong.MaxValue && divisor <= ulong.MaxValue)
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{
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// TODO: Swap this modulo fallback for the shared divisor-cycle remainder helper so 64-bit
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// residues reuse cached cycles instead of recomputing `%` on every lookup.
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return (ulong)number % (ulong)divisor;
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}
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return number % divisor;
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}
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// TODO: Use the Montgomery folding helper measured faster in the Pow2Montgomery benchmarks so this
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// wide residue path avoids general `%` on UInt128 inputs.
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return number % divisor;
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}
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// residue of Mersenne number M_number = 2^number - 1 modulo divisor
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UInt128 pow = PowMod128(UInt128Numbers.Two, number, divisor);
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// residue of Mersenne number M_number = 2^number - 1 modulo divisor
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// TODO: Consult MersenneDivisorCycles.Shared (or similar caches) here so we reuse precomputed cycle lengths
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// instead of recomputing powmods for every divisor; the divisor-cycle benchmarks showed large wins once the
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// cached orders were used across scans.
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UInt128 pow = PowMod128(UInt128Numbers.Two, number, divisor);
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// q divides M_p ⇔ 2^p ≡ 1 (mod q) AND ord_q(2) | p
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if (pow != UInt128.One)
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return (pow - UInt128.One) % divisor;
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// q divides M_p ⇔ 2^p ≡ 1 (mod q) AND ord_q(2) | p
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if (pow != UInt128.One)
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return (pow - UInt128.One) % divisor;
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ulong ord = divisor.CalculateOrder();
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if (ord == 0UL || divisor % ord != UInt128.Zero)
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@@ -264,25 +274,28 @@ public sealed class ModResidueTracker
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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private static UInt128 PowMod128(UInt128 baseValue, UInt128 exponent, UInt128 modulus)
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{
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if (modulus == UInt128.One)
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{
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return UInt128.Zero;;
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}
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private static UInt128 PowMod128(UInt128 baseValue, UInt128 exponent, UInt128 modulus)
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{
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if (modulus == UInt128.One)
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{
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return UInt128.Zero;
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}
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UInt128 result = UInt128.One;
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UInt128 value = baseValue % modulus;
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UInt128 result = UInt128.One;
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UInt128 value = baseValue % modulus;
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while (exponent != UInt128.Zero)
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{
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if ((exponent & UInt128.One) != UInt128.Zero)
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{
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result = MulMod128(result, value, modulus);
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}
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while (exponent != UInt128.Zero)
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{
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if ((exponent & UInt128.One) != UInt128.Zero)
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{
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// TODO: Route this through the planned UInt128 windowed powmod so the inner MulMod adopts the
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// UInt128BuiltIn path that dominated the MulHighBenchmarks on wide operands instead of the
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// current square-and-multiply loop.
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result = MulMod128(result, value, modulus);
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}
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exponent >>= 1;
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if (exponent != UInt128.Zero)
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exponent >>= 1;
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if (exponent != UInt128.Zero)
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{
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value = MulMod128(value, value, modulus);
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}
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@@ -291,14 +304,17 @@ public sealed class ModResidueTracker
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return result;
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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private static UInt128 MulMod128(UInt128 a, UInt128 b, UInt128 modulus)
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{
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// Same approach as MulMod in MersenneNumberTester: double-and-add to avoid overflow.
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UInt128 result = UInt128.Zero;
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a %= modulus;
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private static UInt128 MulMod128(UInt128 a, UInt128 b, UInt128 modulus)
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{
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// Same approach as MulMod in MersenneNumberTester: double-and-add to avoid overflow.
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// TODO: Replace this double-and-add fallback with the UInt128 intrinsic-backed multiplier once the
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// MulHighBenchmarks-guided implementation lands; the intrinsic path measured dozens of times faster for
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// dense 128-bit workloads.
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UInt128 result = UInt128.Zero;
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a %= modulus;
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while (b != UInt128.Zero)
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{
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while (b != UInt128.Zero)
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{
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if ((b & UInt128.One) != UInt128.Zero)
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{
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result += result < modulus ? a : a - modulus;
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