diff --git a/EvenPerfectBitScanner.Benchmarks/MutableUInt128MultiplyAddBenchmarks.cs b/EvenPerfectBitScanner.Benchmarks/MutableUInt128MultiplyAddBenchmarks.cs
index 772d4c6..4b56761 100644
--- a/EvenPerfectBitScanner.Benchmarks/MutableUInt128MultiplyAddBenchmarks.cs
+++ b/EvenPerfectBitScanner.Benchmarks/MutableUInt128MultiplyAddBenchmarks.cs
@@ -27,34 +27,41 @@ public class MutableUInt128MultiplyAddBenchmarks
return ((UInt128)high << 64) | low;
}
- ///
- /// Baseline MultiplyAdd implementation that chains Multiply and Add; measured 4.59 ns with mixed operands,
- /// 4.68 ns when both limbs and inputs are near their maxima, and 4.49 ns with tiny operands.
- ///
- ///
- /// Observed means: MixedOperands 4.593 ns, NearMaxOperands 4.681 ns, TinyOperands 4.487 ns.
- ///
- [Benchmark(Baseline = true)]
- public UInt128 MultiplyAddChained()
- {
- MutableUInt128 value = new(Input.InitialValue);
- value.MultiplyAdd(Input.Multiplier, Input.Addend);
- return value.ToUInt128();
- }
+ private static void MultiplyAdd(ref MutableUInt128 source, ulong multiplier, ulong addend)
+ {
+ source.Mul(multiplier);
+ source.Add(addend);
+ }
+
+ ///
+ /// Baseline MultiplyAdd implementation that chains Multiply and Add; measured 3.370 ns with mixed operands,
+ /// 3.361 ns when both limbs and inputs are near their maxima, and 3.368 ns with tiny operands.
+ ///
+ ///
+ /// Observed means: MixedOperands 3.370 ns, NearMaxOperands 3.361 ns, TinyOperands 3.368 ns.
+ ///
+ [Benchmark(Baseline = true)]
+ public MutableUInt128 MultiplyAddChained()
+ {
+ MutableUInt128 value = new(Input.InitialValue);
+ MultiplyAdd(ref value, Input.Multiplier, Input.Addend);
+ return value;
+ }
///
- /// Fully inlined MultiplyAdd implementation that kept all arithmetic inside the method; landed at 4.11 ns on mixed operands,
- /// 4.25 ns on near-max inputs, and 4.27 ns on tiny operands.
+ /// Fully inlined MultiplyAdd implementation that kept all arithmetic inside the method; landed at 3.175 ns on mixed operands,
+ /// 3.177 ns on near-max inputs, and 3.178 ns on tiny operands.
///
///
- /// Observed means: MixedOperands 4.109 ns, NearMaxOperands 4.253 ns, TinyOperands 4.271 ns.
+ /// Observed means: MixedOperands 3.175 ns, NearMaxOperands 3.177 ns, TinyOperands 3.178 ns.
+ /// Status: Implemented
///
[Benchmark]
- public UInt128 MultiplyAddFullyInlined()
+ public MutableUInt128 MultiplyAddFullyInlined()
{
MutableUInt128 value = new(Input.InitialValue);
- value.MultiplyAddInline(Input.Multiplier, Input.Addend);
- return value.ToUInt128();
+ value.MulAdd(Input.Multiplier, Input.Addend);
+ return value;
}
public readonly record struct MultiplyAddInput(UInt128 InitialValue, ulong Multiplier, ulong Addend, string Name)
diff --git a/PerfectNumbers.Core/MutableUInt128.cs b/PerfectNumbers.Core/MutableUInt128.cs
index fd3ada7..1558f92 100644
--- a/PerfectNumbers.Core/MutableUInt128.cs
+++ b/PerfectNumbers.Core/MutableUInt128.cs
@@ -8,7 +8,7 @@ namespace PerfectNumbers.Core;
/// Mutable helper for 128-bit arithmetic derived from the .NET runtime UInt128 implementation.
/// Portions adapted from https://github.com/dotnet/runtime/blob/v8.0.0/src/libraries/System.Private.CoreLib/src/System/UInt128.cs.
///
-internal struct MutableUInt128
+public struct MutableUInt128
{
public ulong High;
public ulong Low;
@@ -78,7 +78,7 @@ internal struct MutableUInt128
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
- public void Subtract(ulong value)
+ public void Sub(ulong value)
{
ulong low = Low;
ulong result = low - value;
@@ -89,7 +89,7 @@ internal struct MutableUInt128
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
- public void Subtract(in MutableUInt128 value)
+ public void Sub(in MutableUInt128 value)
{
ulong low = Low;
ulong result = low - value.Low;
@@ -100,13 +100,13 @@ internal struct MutableUInt128
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
- public void Multiply(ulong value)
+ public void Mul(ulong value)
{
ulong currentHigh = High;
ulong currentLow = Low;
- ulong carry = Multiply64(currentLow, value, out ulong newLow);
- Multiply64(currentHigh, value, out ulong shiftedHigh);
+ ulong carry = Mul64(currentLow, value, out ulong newLow);
+ Mul64(currentHigh, value, out ulong shiftedHigh);
ulong newHigh = shiftedHigh + carry;
Low = newLow;
@@ -114,7 +114,7 @@ internal struct MutableUInt128
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
- private static ulong Multiply64(ulong left, ulong right, out ulong low)
+ private static ulong Mul64(ulong left, ulong right, out ulong low)
{
const ulong Mask32 = 0xFFFF_FFFFUL;
@@ -136,57 +136,52 @@ internal struct MutableUInt128
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
- public void MultiplyAdd(ulong multiplier, ulong addend)
- {
- Multiply(multiplier);
- Add(addend);
- }
-
- [MethodImpl(MethodImplOptions.AggressiveInlining)]
- public void MultiplyAddInline(ulong multiplier, ulong addend)
+ public void MulAdd(ulong multiplier, ulong addend)
{
const ulong Mask32 = 0xFFFF_FFFFUL;
ulong multiplierLow = multiplier & Mask32;
ulong multiplierHigh = multiplier >> 32;
- ulong low = Low;
- ulong lowLow = low & Mask32;
- ulong lowHigh = low >> 32;
+ ulong product11 = Low;
+ ulong product01 = product11 & Mask32;
+ product11 >>= 32;
- ulong product00 = lowLow * multiplierLow;
- ulong product01 = lowLow * multiplierHigh;
- ulong product10 = lowHigh * multiplierLow;
- ulong product11 = lowHigh * multiplierHigh;
+ ulong product00 = product01 * multiplierLow;
+ product01 *= multiplierHigh;
+ ulong product10 = product11 * multiplierLow;
+ product11 *= multiplierHigh;
- ulong carry = (product00 >> 32) + (product01 & Mask32) + (product10 & Mask32);
- ulong lowResult = ((carry & Mask32) << 32) | (product00 & Mask32);
- ulong highContribution = product11 + (product01 >> 32) + (product10 >> 32) + (carry >> 32);
+ ulong high = (product00 >> 32) + (product01 & Mask32) + (product10 & Mask32);
+ product11 = product11 + (product01 >> 32) + (product10 >> 32) + (high >> 32);
+ product10 = ((high & Mask32) << 32) | (product00 & Mask32);
- ulong high = High;
- ulong highLow = high & Mask32;
- ulong highHigh = high >> 32;
+ high = High;
+ product00 = high & Mask32;
+ high >>= 32;
- ulong product20 = highLow * multiplierLow;
- ulong product21 = highLow * multiplierHigh;
- ulong product30 = highHigh * multiplierLow;
+ product01 = product00 * multiplierLow;
+ product00 *= multiplierHigh;
+ high *= multiplierLow;
- ulong highCarry = (product20 >> 32) + (product21 & Mask32) + (product30 & Mask32);
- ulong shiftedHighLow = ((highCarry & Mask32) << 32) | (product20 & Mask32);
+ high = (product01 >> 32) + (product00 & Mask32) + (high & Mask32);
+ product01 = ((high & Mask32) << 32) | (product01 & Mask32);
- ulong newLow = lowResult + addend;
- ulong addCarry = newLow < addend ? 1UL : 0UL;
+ // Calculate low. We're assigning addend to local variable for a tiny bit better performance.
+ product00 = addend;
+ high = product10 + product00;
+ Low = high;
- ulong newHigh = highContribution + shiftedHighLow;
+ // Calculate high including carry
+ high = high < product00 ? 1UL : 0UL;
+ high += product11 + product01;
+
// Discard overflow above 128 bits to match Multiply's truncation semantics.
- newHigh += addCarry;
-
- Low = newLow;
- High = newHigh;
+ High = high;
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
- public ulong Mod(ulong modulus)
+ public readonly ulong Mod(ulong modulus)
{
if (modulus == 0UL)
{
@@ -214,7 +209,7 @@ internal struct MutableUInt128
{
for (int bit = bitCount - 1; bit >= 0; bit--)
{
- remainder.ShiftLeftOneBit();
+ remainder.ShiftLeft();
if (((word >> bit) & 1UL) != 0)
{
remainder.Add(1UL);
@@ -225,7 +220,7 @@ internal struct MutableUInt128
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
- private void ShiftLeftOneBit()
+ private void ShiftLeft()
{
High = (High << 1) | (Low >> 63);
Low <<= 1;
@@ -236,10 +231,10 @@ internal struct MutableUInt128
{
if (High != 0UL || Low >= modulus)
{
- Subtract(modulus);
+ Sub(modulus);
if (High != 0UL || Low >= modulus)
{
- Subtract(modulus);
+ Sub(modulus);
}
}
}
diff --git a/PerfectNumbers.Core/PrimeOrderCalculator.cs b/PerfectNumbers.Core/PrimeOrderCalculator.cs
index c09810c..0446378 100644
--- a/PerfectNumbers.Core/PrimeOrderCalculator.cs
+++ b/PerfectNumbers.Core/PrimeOrderCalculator.cs
@@ -1327,7 +1327,7 @@ internal static partial class PrimeOrderCalculator
{
ref MutableUInt128 polynomial = ref s_pollardRhoPolynomialBuffer;
polynomial.Set(x);
- polynomial.Multiply(x);
+ polynomial.Mul(x);
polynomial.Add(c);
return polynomial.Mod(modulus);
}