This profiling program shows that on a 64 bit machine, binary search on a int64 list is faster than binary searching on a in32 list.

HashVsBinarySearch.cs

using System;
using System.Collections;
using System.Collections.Generic;
using System.Diagnostics;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using MathNet.Numerics.Statistics;

namespace HashVsBinarySearch
{
    /// <summary>
    /// This profiling program shows that on a 64 bit machine, binary search on a int64 list is faster than binary searching on a in32 list.
    /// In fact, the 64 bit binary search is so fast that it even slightly outperforms hashset lookup. Although not a common sense, as I performed
    /// CPU sampling based profiling, HashSet.Contains() takes quite a portion of the samples, GetHashCode only takes a 0.2% of HashSet.Contains().
    /// So I guess it's the implementation of HashSet.Contains() makes it slow.
    /// 
    /// But the point is - 64 bit binary search on 64 bit machine is really fast! (32bit binary search is slower than 32bit hashset lookup)
    /// 
    ///     intHashSet
    ///     Count: 2000000, nQueries: 10000000
    ///     Elapsed: 00:00:01.5116004, Found rate: 0.0009278
    ///     
    ///     longHashSet
    ///     Count: 2000000, nQueries: 10000000
    ///     Elapsed: 00:00:02.0519113, Found rate: 0
    ///     
    ///     intList
    ///     Count: 2000000, nQueries: 10000000
    ///     Elapsed: 00:00:03.0172173, Found rate: 0.0009281
    ///     
    ///     longList
    ///     Count: 2000000, nQueries: 10000000
    ///     Elapsed: 00:00:01.1434541, Found rate: 0
    ///     
    /// </summary>
    public class Program
    {
        const int count = 2000000;
        const int nQueries = 10000000;
        const long magic = 0x1234123412341234L;
        const int magicInt = 0x12341234;

        static void Main(string[] args)
        {
            //Main_Profile(args);

            if (args[0].ToLower() == "list") Main_HashSetRAM<List<long>, long>(args.Skip(1).ToArray(), (seed, size) => GenLongSet(seed, size).OrderBy(x => x).ToList());
            else if (args[0].ToLower() == "hashset") Main_HashSetRAM<HashSet<long>, long>(args.Skip(1).ToArray(), (seed, size) => GenLongSet(seed, size));
        }

        public static void Main_HashSetRAM<T, TElement>(string[] args, Func<Random, int, T> genSet) where T : IEnumerable<TElement>
        {
            Random seed = new Random();
            int size = int.Parse(args[0]);
            GC.Collect();
            var ram = GC.GetTotalMemory(true);

            var set = genSet(seed, size);

            GC.Collect();
            var ram2 = GC.GetTotalMemory(true);

            Console.WriteLine($"{ram2 -ram}");

            Console.WriteLine($"set size: {set.Count()}");
        }

        public static void Main_Profile(string[] args)
        {
            Random seed = new Random();

            HashSet<int> intHashSet = GenIntSet(seed);
            List<int> intList = intHashSet.OrderBy(x=>x).ToList();
            HashSet<long> longHashSet = GenLongSet(seed);
            List<long> longList = longHashSet.OrderBy(x => x).ToList();


            Console.WriteLine(longList.First(x => x > 0));
            long prev = long.MinValue;
            foreach (var item in longList)
            {
                if (item < prev) throw new InvalidOperationException();
                prev = item;
            }


            //Func<long> genLong = () => RandLong(seed);
            //Func<int> genInt = () => seed.Next(int.MinValue, int.MaxValue);
            Func<long> genLong = () => seed.Next();
            Func<int> genInt = () => seed.Next();
            //Func<long> genLong = () => magic; // query a number that's not in the set
            //Func<int> genInt = () => magicInt;

            Console.WriteLine("intHashSet");
            Profile<HashSet<int>, int>(seed, intHashSet, nQueries, (set, x) => ((HashSet<int>)set).Contains(x), genInt);

            Console.WriteLine("longHashSet");
            Profile<HashSet<long>, long>(seed, longHashSet, nQueries, (set, x) => ((HashSet<long>)set).Contains(x), genLong);

            Console.WriteLine("intList");
            //Profile<List<int>, int>(seed, intList, nQueries, (list, x) => BinarySearch(list, x) >= 0, genInt);
            Profile<List<int>, int>(seed, intList, nQueries, (list, x) => list.BinarySearch(x) >= 0, genInt); 

            Console.WriteLine("longList");
            //Profile<List<long>, long>(seed, longList, nQueries, (list, x) => BinarySearch(list,x) >= 0, genLong);
            Profile<List<long>, long>(seed, longList, nQueries, (list, x) => list.BinarySearch(x) >= 0, genLong);

            // make sure GC isn't kick in to impact performance
            Console.WriteLine($"{intHashSet.Count} {intList.Count} {longHashSet.Count} {longList.Count}");
        }

        public static void Profile<T, TElement>(Random seed, T set, int nQueries, Func<T, TElement, bool> query, Func<TElement> genSample) where T : IEnumerable<TElement>
        {
            int count = set.Count();
            Console.WriteLine($"Count: {count}, nQueries: {nQueries}");

            var sw = new Stopwatch();
            sw.Restart();
            int found = 0;
            for (int i = 0; i < nQueries; i++)
            {
                var res = query(set, genSample());
                if (res) found++;
            }
            sw.Stop();

            Console.WriteLine($"Elapsed: {sw.Elapsed}, Found rate: {found / (double)nQueries}");
        }

        public static HashSet<int> GenIntSet(Random seed)
        {

            HashSet<int> set = new HashSet<int>();

            for (int i = 0; i < count; i++)
            {
                while (true)
                {
                    int x = seed.Next(int.MinValue, int.MaxValue);
                    if (x == magicInt) continue;  // don't add magic number
                    if (set.Add(x))
                    {
                        break;
                    }
                }
            }

            Console.WriteLine("Set size: {0}", set.Count);
            return set;
        }

        public static HashSet<long> GenLongSet(Random seed, int count = -1)
        {
            if (count < 0) count = Program.count;
            HashSet<long> set = new HashSet<long>();

            for (int i = 0; i < count; i++)
            {
                while (true)
                {
                    long x = RandLong(seed);
                    if (x == magic) continue; // don't add magic number
                    if (set.Add(x))
                    {
                        break;
                    }
                }
            }

            //Console.WriteLine("Set size: {0}", set.Count);
            return set;
        }

        public static long RandLong(Random seed)
        {
            //return seed.Next();
            //int x = seed.Next();
            //return ((long)((x << 1) ^ x) << 32) | (uint)x;

            //int x = seed.Next();
            //return ((long)(x * 6367) << 32) | (uint)x;

            byte[] buf = new byte[8];
            seed.NextBytes(buf);
            return BitConverter.ToInt64(buf, 0);
        }

        private static int BinarySearch<T>(List<T> array, T value) where T : IComparable<T>
        {
            int index = 0;
            int length = array.Count;
            int lo = index;
            int hi = index + length - 1;
            while (lo <= hi)
            {
                int i = lo + ((hi - lo) >> 1);
                int order;
                if (array[i] == null)
                {
                    order = (value == null) ? 0 : -1;
                }
                else
                {
                    order = array[i].CompareTo(value);
                }

                if (order == 0)
                {
                    return i;
                }

                if (order < 0)
                {
                    lo = i + 1;
                }
                else
                {
                    hi = i - 1;
                }
            }

            return ~lo;
        }
    }
}

plot.fsx

#load "./packages/FsLab/FsLab.fsx"

open FSharp.Charting
open MathNet.Numerics.Statistics
open MathNet.Numerics.Statistics.Statistics

let hashfile = @"C:\Users\Desktop\HashValues.txt"

open System.IO
let  readLines (transform) (file:string) =
    let rec reads (stream: StreamReader) (transform) =
        seq {
            match stream.ReadLine() with
            | null -> ()
            | line -> 
                yield transform line
                yield! reads stream transform
        }
    
    use stream = new StreamReader(new FileStream(file, FileMode.Open))
    reads stream transform |> Array.ofSeq

let data = readLines int64 hashfile
let hashes = data |> Array.map (fun x -> x.GetHashCode())

(** This is quite uniformly distributed *)
let hist = Histogram(hashes |> Array.map float, 200)

let chart_hist =
    [0 .. hist.BucketCount-1]
    |> List.map (fun i -> i, hist.[i].Count)
    |> Chart.Column

printfn "hashes in range: [%f, %f]. Int.min=%d Int.max=%d" hist.LowerBound hist.UpperBound System.Int32.MinValue System.Int32.MaxValue