Modulo operators replaced with steppers, where possible.

PerfectNumbers.Core/BidirectionalCycleRemainderStepper.cs

@@ -0,0 +1,62 @@
+using System.Runtime.CompilerServices;
+
+namespace PerfectNumbers.Core;
+
+public struct BidirectionalCycleRemainderStepper(ulong modulus)
+{
+	private readonly ulong _modulus = modulus;
+	private ulong _previous = 0UL;
+	private ulong _remainder = 0UL;
+
+	public readonly ulong Modulus
+	{
+		[MethodImpl(MethodImplOptions.AggressiveInlining)]
+		get
+		{
+			return _modulus;
+		}
+	}
+
+	[MethodImpl(MethodImplOptions.AggressiveInlining)]
+	public void Initialize(ulong value)
+	{
+		_remainder = value.ReduceCycleRemainder(_modulus);
+		_previous = value;
+	}
+
+	[MethodImpl(MethodImplOptions.AggressiveInlining)]
+	public ulong Step(ulong value)
+	{
+		long delta = unchecked((long)value - (long)_previous);
+		_previous = value;
+		if (delta == 0)
+		{
+			return _remainder;
+		}
+
+		if (delta > 0)
+		{
+			ulong step = ((ulong)delta).ReduceCycleRemainder(_modulus);
+			ulong sum = _remainder + step;
+			if (sum >= _modulus)
+			{
+				sum -= _modulus;
+			}
+
+			_remainder = sum;
+			return _remainder;
+		}
+
+		ulong backward = ((ulong)-delta).ReduceCycleRemainder(_modulus);
+		if (backward > _remainder)
+		{
+			ulong diff = backward - _remainder;
+			ulong wrap = diff.ReduceCycleRemainder(_modulus);
+			_remainder = wrap == 0 ? 0UL : _modulus - wrap;
+			return _remainder;
+		}
+
+		_remainder -= backward;
+		return _remainder;
+	}
+}