Optimize BitOps

[Joy-less]

Since this library is about micro-optimizations, I decided to dive into BitOps.

Firstly, one of the methods (CeilingPowerOfTwo) now has a corresponding BitOperations method (RoundUpToPowerOf2) which internally does the same thing as the NETSTANDARD version with optimizations depending on hardware.

Secondly, I replaced the while loop in another method with some code copy-pasted from the internal implementation of BitOperations.PopCount. I assume the C# team knows best here.

Here are some benchmarks. The BitCount optimizations are much more performant in NETSTANDARD, whereas the CeilingPowerOfTwo optimizations are the same performance but simpler source code-wise.

Method	Mean	Error	StdDev
CeilingPowerOfTwo_uint_NET_Old	25.39 us	0.062 us	0.055 us
CeilingPowerOfTwo_uint_NET_New	25.30 us	0.065 us	0.061 us
CeilingPowerOfTwo_ulong_NET_Old	25.30 us	0.041 us	0.036 us
CeilingPowerOfTwo_ulong_NET_New	25.32 us	0.042 us	0.039 us
BitCount_NETSTANDARD_uint_Old	152.31 us	0.235 us	0.184 us
BitCount_NETSTANDARD_uint_New	25.32 us	0.068 us	0.064 us
BitCount_NETSTANDARD_ulong_Old	152.46 us	0.461 us	0.431 us
BitCount_NETSTANDARD_ulong_New	25.31 us	0.067 us	0.063 us

Benchmark code

using System.Numerics;
using BenchmarkDotNet.Attributes;
using BenchmarkDotNet.Running;

namespace ConsoleApp1;

internal class Program {
    static void Main() {
        BenchmarkSwitcher.FromAssembly(typeof(Program).Assembly).Run();
    }
}

public class Benchmarks {
    private const int Iterations = 100_000;

    [Benchmark]
    public void CeilingPowerOfTwo_uint_NET_Old() {
        for (int Counter = 0; Counter < Iterations; Counter++) {
            BitOperationMethods.CeilingPowerOfTwo_uint_NET_Old(100);
        }
    }
    [Benchmark]
    public void CeilingPowerOfTwo_uint_NET_New() {
        for (int Counter = 0; Counter < Iterations; Counter++) {
            BitOperationMethods.CeilingPowerOfTwo_uint_NET_New(100);
        }
    }
    [Benchmark]
    public void CeilingPowerOfTwo_ulong_NET_Old() {
        for (int Counter = 0; Counter < Iterations; Counter++) {
            BitOperationMethods.CeilingPowerOfTwo_ulong_NET_Old(100);
        }
    }
    [Benchmark]
    public void CeilingPowerOfTwo_ulong_NET_New() {
        for (int Counter = 0; Counter < Iterations; Counter++) {
            BitOperationMethods.CeilingPowerOfTwo_ulong_NET_New(100);
        }
    }
    [Benchmark]
    public void BitCount_NETSTANDARD_uint_Old() {
        for (int Counter = 0; Counter < Iterations; Counter++) {
            BitOperationMethods.BitCount_NETSTANDARD_uint_Old(100);
        }
    }
    [Benchmark]
    public void BitCount_NETSTANDARD_uint_New() {
        for (int Counter = 0; Counter < Iterations; Counter++) {
            BitOperationMethods.BitCount_NETSTANDARD_uint_New(100);
        }
    }
    [Benchmark]
    public void BitCount_NETSTANDARD_ulong_Old() {
        for (int Counter = 0; Counter < Iterations; Counter++) {
            BitOperationMethods.BitCount_NETSTANDARD_ulong_Old(100);
        }
    }
    [Benchmark]
    public void BitCount_NETSTANDARD_ulong_New() {
        for (int Counter = 0; Counter < Iterations; Counter++) {
            BitOperationMethods.BitCount_NETSTANDARD_ulong_New(100);
        }
    }
}

public static class BitOperationMethods {
    public static uint CeilingPowerOfTwo_uint_NET_Old(uint x) {
        return 1u << -BitOperations.LeadingZeroCount(x - 1);
    }
    public static uint CeilingPowerOfTwo_uint_NET_New(uint x) {
        return BitOperations.RoundUpToPowerOf2(x);
    }
    public static ulong CeilingPowerOfTwo_ulong_NET_Old(ulong x) {
        return 1ul << -BitOperations.LeadingZeroCount(x - 1);
    }
    public static ulong CeilingPowerOfTwo_ulong_NET_New(ulong x) {
        return BitOperations.RoundUpToPowerOf2(x);
    }
    public static int BitCount_NETSTANDARD_uint_Old(uint x) {
        var count = 0;
        while (x != 0)
        {
            count++;
            x &= x - 1; //walking through all the bits which are set to one
        }

        return count;
    }
    public static int BitCount_NETSTANDARD_uint_New(uint x) {
        const uint c1 = 0x_55555555u;
        const uint c2 = 0x_33333333u;
        const uint c3 = 0x_0F0F0F0Fu;
        const uint c4 = 0x_01010101u;

        x -= (x >> 1) & c1;
        x = (x & c2) + ((x >> 2) & c2);
        x = (((x + (x >> 4)) & c3) * c4) >> 24;

        return (int)x;
    }
    public static int BitCount_NETSTANDARD_ulong_Old(ulong x) {
        var count = 0;
        while (x != 0) {
            count++;
            x &= x - 1; //walking through all the bits which are set to one
        }

        return count;
    }
    public static int BitCount_NETSTANDARD_ulong_New(ulong x) {
        const ulong c1 = 0x_55555555_55555555ul;
        const ulong c2 = 0x_33333333_33333333ul;
        const ulong c3 = 0x_0F0F0F0F_0F0F0F0Ful;
        const ulong c4 = 0x_01010101_01010101ul;

        x -= (x >> 1) & c1;
        x = (x & c2) + ((x >> 2) & c2);
        x = (((x + (x >> 4)) & c3) * c4) >> 56;

        return (int)x;
    }
}

[Joy-less]

This is failing because it relies on #662.