Develop Reference

Molecular MC simulation is not equilibrating

Suppose, a polymer has N monomers in its chain. I want to simulate its movement using the bead-spring model. However, there was no periodic boundary condition applied. Coz, points were generated such that they never cross the boundary.
So, I wrote the following program.
Polymer chain simulation with Monte Carlo method
I am using 1 million steps. The energy is not fluctuating as expected. After several thousand steps the curve goes totally flat.
The X-axis is steps. Y-axis is total energy.
Can anyone check the source code and tell me what I should change?
N.B. I am especially concerned with the function that calculates the total energy of the polymer.
Probably, the algorithm is incorrect.
public double GetTotalPotential()
{
double totalBeadPotential = 0.0;
double totalSpringPotential = 0.0;
// calculate total bead-energy
for (int i = 0; i < beadsList.Count; i++)
{
Bead item_i = beadsList[i];
Bead item_i_plus_1 = null;
try
{
item_i_plus_1 = beadsList[i + 1];
if (i != beadsList.Count - 1)
{
// calculate total spring energy.
totalSpringPotential += item_i.GetHarmonicPotential(item_i_plus_1);
}
}
catch { }
for (int j = 0; j < beadsList.Count; j++)
{
if (i != j)
{
Bead item_j = beadsList[j];
totalBeadPotential += item_i.GetPairPotential(item_j);
//Console.Write(totalBeadPotential + "\n");
//Thread.Sleep(100);
}
}
}
return totalBeadPotential + totalSpringPotential;
}

Problem of this application is that simulations (Simulation.SimulateMotion) are run in separate thread in parallel to the draw timer (SimulationGuiForm.timer1_Tick) and share the same state (polymerChain) without any sync/signaling, so some mutations of polymerChain are skipped completely (not drawn) and when the simulation is finished (far before the finish of the drawing) the timer1_Tick will redraw the same polymerChain. You can easily check that by adding counter to Simulation and increasing it in the SimulateMotion:
public class Simulation
{
public static int Simulations = 0; // counter
public static void SimulateMotion(PolymerChain polymerChain, int iterations)
{
Random random = new Random();
for (int i = 0; i < iterations; i++)
{
Simulations++; // bump the counter
// rest of the code
// ...
And checking it in timer1_Tick:
private void timer1_Tick(object sender, EventArgs e)
{
// ...
// previous code
if (Simulation.Simulations == totalIterations)
{
// breakpoint or Console.Writeline() ...
// will be hit as soon as "the curve goes totally flat"
}
DrawZGraph();
}
You need to rewrite your application in such way that SimulateMotion either stores iterations in some collection which is consumed by timer1_Tick (basically implementing producer-consumer pattern, for example you can try using BlockingCollection, like I do in the pull request) or performs it's actions only when the current state is rendered.

What is the fastest way to do Array Table Lookup with an Integer Index?

I have a video processing application that moves a lot of data.
To speed things up, I have made a lookup table, as many calculations in essence only need to be calculated one time and can be reused.
However I'm at the point where all the lookups now takes 30% of the processing time. I'm wondering if it might be slow RAM.. However, I would still like to try to optimize it some more.
Currently I have the following:
public readonly int[] largeArray = new int[3000*2000];
public readonly int[] lookUp = new int[width*height];
I then perform a lookup with a pointer p (which is equivalent to width * y + x) to fetch the result.
int[] newResults = new int[width*height];
int p = 0;
for (int y = 0; y < height; y++) {
for (int x = 0; x < width; x++, p++) {
newResults[p] = largeArray[lookUp[p]];
}
}
Note that I cannot do an entire array copy to optimize. Also, the application is heavily multithreaded.
Some progress was in shortening the function stack, so no getters but a straight retrieval from a readonly array.
I've tried converting to ushort as well, but it seemed to be slower (as I understand it's due to word size).
Would an IntPtr be faster? How would I go about that?
Attached below is a screenshot of time distribution:

It looks like what you're doing here is effectively a "gather". Modern CPUs have dedicated instructions for this, in particular VPGATHER** . This is exposed in .NET Core 3, and should work something like below, which is the single loop scenario (you can probably work from here to get the double-loop version);
results first:
AVX enabled: False; slow loop from 0
e7ad04457529f201558c8a53f639fed30d3a880f75e613afe203e80a7317d0cb
for 524288 loops: 1524ms
AVX enabled: True; slow loop from 1024
e7ad04457529f201558c8a53f639fed30d3a880f75e613afe203e80a7317d0cb
for 524288 loops: 667ms
code:
using System;
using System.Diagnostics;
using System.Runtime.InteropServices;
using System.Runtime.Intrinsics;
using System.Runtime.Intrinsics.X86;
static class P
{
static int Gather(int[] source, int[] index, int[] results, bool avx)
{ // normally you wouldn't have avx as a parameter; that is just so
// I can turn it off and on for the test; likewise the "int" return
// here is so I can monitor (in the test) how much we did in the "old"
// loop, vs AVX2; in real code this would be void return
int y = 0;
if (Avx2.IsSupported && avx)
{
var iv = MemoryMarshal.Cast<int, Vector256<int>>(index);
var rv = MemoryMarshal.Cast<int, Vector256<int>>(results);
unsafe
{
fixed (int* sPtr = source)
{
// note: here I'm assuming we are trying to fill "results" in
// a single outer loop; for a double-loop, you'll probably need
// to slice the spans
for (int i = 0; i < rv.Length; i++)
{
rv[i] = Avx2.GatherVector256(sPtr, iv[i], 4);
}
}
}
// move past everything we've processed via SIMD
y += rv.Length * Vector256<int>.Count;
}
// now do anything left, which includes anything not aligned to 256 bits,
// plus the "no AVX2" scenario
int result = y;
int end = results.Length; // hoist, since this is not the JIT recognized pattern
for (; y < end; y++)
{
results[y] = source[index[y]];
}
return result;
}
static void Main()
{
// invent some random data
var rand = new Random(12345);
int size = 1024 * 512;
int[] data = new int[size];
for (int i = 0; i < data.Length; i++)
data[i] = rand.Next(255);
// build a fake index
int[] index = new int[1024];
for (int i = 0; i < index.Length; i++)
index[i] = rand.Next(size);
int[] results = new int[1024];
void GatherLocal(bool avx)
{
// prove that we're getting the same data
Array.Clear(results, 0, results.Length);
int from = Gather(data, index, results, avx);
Console.WriteLine($"AVX enabled: {avx}; slow loop from {from}");
for (int i = 0; i < 32; i++)
{
Console.Write(results[i].ToString("x2"));
}
Console.WriteLine();
const int TimeLoop = 1024 * 512;
var watch = Stopwatch.StartNew();
for (int i = 0; i < TimeLoop; i++)
Gather(data, index, results, avx);
watch.Stop();
Console.WriteLine($"for {TimeLoop} loops: {watch.ElapsedMilliseconds}ms");
Console.WriteLine();
}
GatherLocal(false);
if (Avx2.IsSupported) GatherLocal(true);
}
}

RAM is already one of the fastest things possible. The only memory faster is the CPU caches. So it will be Memory Bound, but that is still plenty fast.
Of course at the given sizes, this array is 6 Million entries in size. That will likely not fit in any cache. And will take forever to itterate over. It does not mater what the speed is, this is simply too much data.
As a general rule, video processing is done on the GPU nowadays. GPU's are literally desinged to operate on giant arrays. Because that is what the Image you are seeing right now is - a giant array.
If you have to keep it on the GPU side, maybe caching or Lazy Initilisation would help? Chances are that you do not truly need every value. You only need to common values. Take a examples from dicerolling: If you roll 2 6-sided dice, every result from 2-12 is possible. But the result 7 happens 6 out of 36 casess. The 2 and 12 only 1 out of 36 cases each. So having the 7 stored is a lot more beneficial then the 2 and 12.

Code sample that shows casting to uint is more efficient than range check

So I am looking at this question and the general consensus is that uint cast version is more efficient than range check with 0. Since the code is also in MS's implementation of List I assume it is a real optimization. However I have failed to produce a code sample that results in better performance for the uint version. I have tried different tests and there is something missing or some other part of my code is dwarfing the time for the checks. My last attempt looks like this:
class TestType
{
public TestType(int size)
{
MaxSize = size;
Random rand = new Random(100);
for (int i = 0; i < MaxIterations; i++)
{
indexes[i] = rand.Next(0, MaxSize);
}
}
public const int MaxIterations = 10000000;
private int MaxSize;
private int[] indexes = new int[MaxIterations];
public void Test()
{
var timer = new Stopwatch();
int inRange = 0;
int outOfRange = 0;
timer.Start();
for (int i = 0; i < MaxIterations; i++)
{
int x = indexes[i];
if (x < 0 || x > MaxSize)
{
throw new Exception();
}
inRange += indexes[x];
}
timer.Stop();
Console.WriteLine("Comparision 1: " + inRange + "/" + outOfRange + ", elapsed: " + timer.ElapsedMilliseconds + "ms");
inRange = 0;
outOfRange = 0;
timer.Reset();
timer.Start();
for (int i = 0; i < MaxIterations; i++)
{
int x = indexes[i];
if ((uint)x > (uint)MaxSize)
{
throw new Exception();
}
inRange += indexes[x];
}
timer.Stop();
Console.WriteLine("Comparision 2: " + inRange + "/" + outOfRange + ", elapsed: " + timer.ElapsedMilliseconds + "ms");
}
}
class Program
{
static void Main()
{
TestType t = new TestType(TestType.MaxIterations);
t.Test();
TestType t2 = new TestType(TestType.MaxIterations);
t2.Test();
TestType t3 = new TestType(TestType.MaxIterations);
t3.Test();
}
}
The code is a bit of a mess because I tried many things to make uint check perform faster like moving the compared variable into a field of a class, generating random index access and so on but in every case the result seems to be the same for both versions. So is this change applicable on modern x86 processors and can someone demonstrate it somehow?
Note that I am not asking for someone to fix my sample or explain what is wrong with it. I just want to see the case where the optimization does work.

if (x < 0 || x > MaxSize)
The comparison is performed by the CMP processor instruction (Compare). You'll want to take a look at Agner Fog's instruction tables document (PDF), it list the cost of instructions. Find your processor back in the list, then locate the CMP instruction.
For mine, Haswell, CMP takes 1 cycle of latency and 0.25 cycles of throughput.
A fractional cost like that could use an explanation, Haswell has 4 integer execution units that can execute instructions at the same time. When a program contains enough integer operations, like CMP, without an interdependency then they can all execute at the same time. In effect making the program 4 times faster. You don't always manage to keep all 4 of them busy at the same time with your code, it is actually pretty rare. But you do keep 2 of them busy in this case. Or in other words, two comparisons take just as long as single one, 1 cycle.
There are other factors at play that make the execution time identical. One thing helps is that the processor can predict the branch very well, it can speculatively execute x > MaxSize in spite of the short-circuit evaluation. And it will in fact end up using the result since the branch is never taken.
And the true bottleneck in this code is the array indexing, accessing memory is one of the slowest thing the processor can do. So the "fast" version of the code isn't faster even though it provides more opportunity to allow the processor to concurrently execute instructions. It isn't much of an opportunity today anyway, a processor has too many execution units to keep busy. Otherwise the feature that makes HyperThreading work. In both cases the processor bogs down at the same rate.
On my machine, I have to write code that occupies more than 4 engines to make it slower. Silly code like this:
if (x < 0 || x > MaxSize || x > 10000000 || x > 20000000 || x > 3000000) {
outOfRange++;
}
else {
inRange++;
}
Using 5 compares, now I can a difference, 61 vs 47 msec. Or in other words, this is a way to count the number of integer engines in the processor. Hehe :)
So this is a micro-optimization that probably used to pay off a decade ago. It doesn't anymore. Scratch it off your list of things to worry about :)

I would suggest attempting code which does not throw an exception when the index is out of range. Exceptions are incredibly expensive and can completely throw off your bench results.
The code below does a timed-average bench for 1,000 iterations of 1,000,000 results.
using System;
using System.Diagnostics;
namespace BenchTest
{
class Program
{
const int LoopCount = 1000000;
const int AverageCount = 1000;
static void Main(string[] args)
{
Console.WriteLine("Starting Benchmark");
RunTest();
Console.WriteLine("Finished Benchmark");
Console.Write("Press any key to exit...");
Console.ReadKey();
}
static void RunTest()
{
int cursorRow = Console.CursorTop; int cursorCol = Console.CursorLeft;
long totalTime1 = 0; long totalTime2 = 0;
long invalidOperationCount1 = 0; long invalidOperationCount2 = 0;
for (int i = 0; i < AverageCount; i++)
{
Console.SetCursorPosition(cursorCol, cursorRow);
Console.WriteLine("Running iteration: {0}/{1}", i + 1, AverageCount);
int[] indexArgs = RandomFill(LoopCount, int.MinValue, int.MaxValue);
int[] sizeArgs = RandomFill(LoopCount, 0, int.MaxValue);
totalTime1 += RunLoop(TestMethod1, indexArgs, sizeArgs, ref invalidOperationCount1);
totalTime2 += RunLoop(TestMethod2, indexArgs, sizeArgs, ref invalidOperationCount2);
}
PrintResult("Test 1", TimeSpan.FromTicks(totalTime1 / AverageCount), invalidOperationCount1);
PrintResult("Test 2", TimeSpan.FromTicks(totalTime2 / AverageCount), invalidOperationCount2);
}
static void PrintResult(string testName, TimeSpan averageTime, long invalidOperationCount)
{
Console.WriteLine(testName);
Console.WriteLine(" Average Time: {0}", averageTime);
Console.WriteLine(" Invalid Operations: {0} ({1})", invalidOperationCount, (invalidOperationCount / (double)(AverageCount * LoopCount)).ToString("P3"));
}
static long RunLoop(Func<int, int, int> testMethod, int[] indexArgs, int[] sizeArgs, ref long invalidOperationCount)
{
Stopwatch sw = new Stopwatch();
Console.Write("Running {0} sub-iterations", LoopCount);
sw.Start();
long startTickCount = sw.ElapsedTicks;
for (int i = 0; i < LoopCount; i++)
{
invalidOperationCount += testMethod(indexArgs[i], sizeArgs[i]);
}
sw.Stop();
long stopTickCount = sw.ElapsedTicks;
long elapsedTickCount = stopTickCount - startTickCount;
Console.WriteLine(" - Time Taken: {0}", new TimeSpan(elapsedTickCount));
return elapsedTickCount;
}
static int[] RandomFill(int size, int minValue, int maxValue)
{
int[] randomArray = new int[size];
Random rng = new Random();
for (int i = 0; i < size; i++)
{
randomArray[i] = rng.Next(minValue, maxValue);
}
return randomArray;
}
static int TestMethod1(int index, int size)
{
return (index < 0 || index >= size) ? 1 : 0;
}
static int TestMethod2(int index, int size)
{
return ((uint)(index) >= (uint)(size)) ? 1 : 0;
}
}
}

You aren't comparing like with like.
The code you were talking about not only saved one branch by using the optimisation, but also 4 bytes of CIL in a small method.
In a small method 4 bytes can be the difference in being inlined and not being inlined.
And if the method calling that method is also written to be small, then that can mean two (or more) method calls are jitted as one piece of inline code.
And maybe some of it is then, because it is inline and available for analysis by the jitter, optimised further again.
The real difference is not between index < 0 || index >= _size and (uint)index >= (uint)_size, but between code that has repeated efforts to minimise the method body size and code that does not. Look for example at how another method is used to throw the exception if necessary, further shaving off a couple of bytes of CIL.
(And no, that's not to say that I think all methods should be written like that, but there certainly can be performance differences when one does).

Difference in declaring variable as a array index and "0"?

I'm new to c# so be ready for some dumb questions.
My current task is to find a score from an array where the highest/lowest scores have been taken away, and if the highest/lowest occur more than once (ONLY if they occur more than once), one of them can be added:
eg. int[] scores = [4, 8, 6, 4, 8, 5] therefore the final addition will be 4+8+6+5 = 23.
Another condition of the task is that LINQ cannot be used, as well as any of the System.Array methods. (you can see by my previously ask questions that has been a bit of a pain for me, since I solved this with LINQ in less than 5 minutes).
So here is the problem: I have working code the solves the problem but the task requires multiple methods/functions, so I cannot receive full marks if I have only 3 methods (including main). I have been trying to restructure the program but with all sorts of issues. Here is my code (just so I can explain it better):
using System;
using System.Collections.Generic;
//using System.Linq;
using System.Text;
using System.Threading.Tasks;
namespace Scoring {
class Program {
static int highOccurrence = 0;
static int lowOccurrence = 0;
//static int high; <------
//static int low; <------
static void Main(string[] args) {
int[] scores = { 4, 8, 6, 4, 8, 5 };
findScore(scores);
ExitProgram();
}
static int findOccurrence(int[] scores, int low, int high) { //find the number of times a high/low occurs
for (int i = 0; i < scores.Length; i++) {
if (low == scores[i]) {
lowOccurrence++;
//record number of time slow occurs
}
if (high == scores[i]) {
highOccurrence++;
//record number of times high occurs }
}
return highOccurrence;
}
static int findScore(int[] scores) { //calculates score, needs to be restructured
int[] arrofNormal = new int[scores.Length];
//int low = scores[0]; <----This is where the issue is
//int high = scores[0]; <----- ^^^^^
int total = 0;
for (int i = 0; i < scores.Length; i++) {
if (low > scores[i]) {
low = scores[i];
} //record lowest value
if (high < scores[i]) {
high = scores[i];
//record highest value
}
}
for (int x = 0; x < scores.Length; x++) {
if (scores[x] != low && scores[x] != high) {
arrofNormal[x] = scores[x];
//provides the total of the scores (not including the high and the low)
}
total += arrofNormal[x];
}
findOccurrence(scores, low, high);
if (highOccurrence > 1) { //if there is more than 1 high (or 1 low) it is added once into the total
total += high;
if (lowOccurrence > 1) {
total += low;
}
}
Console.WriteLine("Sum = " + total);
return total; //remove not all code paths return.. error
}
static void ExitProgram() {
Console.Write("\n\nPress any key to exit program: ");
Console.ReadKey();
}//end ExitProgram
}
}
I have placed arrows in the code above to show where my issue is. If I try to declare "high" and "low" as global variables, my final answer is always a few numbers off, buy if I leave the variables declared as "high = scores[0]" etc, I will get the right answer.
What I want ideally is to have separate methods for each step of the calculation, so right now I have method for finding the number of times a specific value shows up in the array. The next I would like to do is finding the highest/lowest value in the array, one method would do the final calculation, and the final one would write the results into the console window. The last two parts (finding the high/low and final calculation) are currently in the find score method.
Any help would be greatly appreciated. Thanks.

How can I make my function run as fast as "Contains" on an ArrayList?

I can't figure out a discrepancy between the time it takes for the Contains method to find an element in an ArrayList and the time it takes for a small function that I wrote to do the same thing. The documentation states that Contains performs a linear search, so it's supposed to be in O(n) and not any other faster method. However, while the exact values may not be relevant, the Contains method returns in 00:00:00.1087087 seconds while my function takes 00:00:00.1876165. It might not be much, but this difference becomes more evident when dealing with even larger arrays. What am I missing and how should I write my function to match Contains's performances?
I'm using C# on .NET 3.5.
public partial class Window1 : Window
{
public bool DoesContain(ArrayList list, object element)
{
for (int i = 0; i < list.Count; i++)
if (list[i].Equals(element)) return true;
return false;
}
public Window1()
{
InitializeComponent();
ArrayList list = new ArrayList();
for (int i = 0; i < 10000000; i++) list.Add("zzz " + i);
Stopwatch sw = new Stopwatch();
sw.Start();
//Console.Out.WriteLine(list.Contains("zzz 9000000") + " " + sw.Elapsed);
Console.Out.WriteLine(DoesContain(list, "zzz 9000000") + " " + sw.Elapsed);
}
}
EDIT:
Okay, now, lads, look:
public partial class Window1 : Window
{
public bool DoesContain(ArrayList list, object element)
{
int count = list.Count;
for (int i = count - 1; i >= 0; i--)
if (element.Equals(list[i])) return true;
return false;
}
public bool DoesContain1(ArrayList list, object element)
{
int count = list.Count;
for (int i = 0; i < count; i++)
if (element.Equals(list[i])) return true;
return false;
}
public Window1()
{
InitializeComponent();
ArrayList list = new ArrayList();
for (int i = 0; i < 10000000; i++) list.Add("zzz " + i);
Stopwatch sw = new Stopwatch();
long total = 0;
int nr = 100;
for (int i = 0; i < nr; i++)
{
sw.Reset();
sw.Start();
DoesContain(list,"zzz");
total += sw.ElapsedMilliseconds;
}
Console.Out.WriteLine(total / nr);
total = 0;
for (int i = 0; i < nr; i++)
{
sw.Reset();
sw.Start();
DoesContain1(list, "zzz");
total += sw.ElapsedMilliseconds;
}
Console.Out.WriteLine(total / nr);
total = 0;
for (int i = 0; i < nr; i++)
{
sw.Reset();
sw.Start();
list.Contains("zzz");
total += sw.ElapsedMilliseconds;
}
Console.Out.WriteLine(total / nr);
}
}
I made an average of 100 running times for two versions of my function(forward and backward loop) and for the default Contains function. The times I've got are 136 and
133 milliseconds for my functions and a distant winner of 87 for the Contains version. Well now, if before you could argue that the data was scarce and I based my conclusions on a first, isolated run, what do you say about this test? Not does only on average Contains perform better, but it achieves consistently better results in each run. So, is there some kind of disadvantage in here for 3rd party functions, or what?

First, you're not running it many times and comparing averages.
Second, your method isn't being jitted until it actually runs. So the just in time compile time is added into its execution time.
A true test would run each multiple times and average the results (any number of things could cause one or the other to be slower for run X out of a total of Y), and your assemblies should be pre-jitted using ngen.exe.

As you're using .NET 3.5, why are you using ArrayList to start with, rather than List<string>?
A few things to try:
You could see whether using foreach instead of a for loop helps
You could cache the count:
public bool DoesContain(ArrayList list, object element)
{
int count = list.Count;
for (int i = 0; i < count; i++)
{
if (list[i].Equals(element))
{
return true;
}
return false;
}
}
You could reverse the comparison:
if (element.Equals(list[i]))
While I don't expect any of these to make a significant (positive) difference, they're the next things I'd try.
Do you need to do this containment test more than once? If so, you might want to build a HashSet<T> and use that repeatedly.

I'm not sure if you're allowed to post Reflector code, but if you open the method using Reflector, you can see that's it's essentially the same (there are some optimizations for null values, but your test harness doesn't include nulls).
The only difference that I can see is that calling list[i] does bounds checking on i whereas the Contains method does not.

Using the code below I was able to get the following timings relatively consitently (within a few ms):
1: 190ms DoesContainRev
2: 198ms DoesContainRev1
3: 188ms DoesContainFwd
4: 203ms DoesContainFwd1
5: 199ms Contains
Several things to notice here.
This is run with release compiled code from the commandline. Many people make the mistake of benchmarking code inside the Visual Studio debugging environment, not to say anyone here did but something to be careful of.
The list[i].Equals(element) appears to be just a bit slower than element.Equals(list[i]).
using System;
using System.Diagnostics;
using System.Collections;
namespace ArrayListBenchmark
{
class Program
{
static void Main(string[] args)
{
Stopwatch sw = new Stopwatch();
const int arrayCount = 10000000;
ArrayList list = new ArrayList(arrayCount);
for (int i = 0; i < arrayCount; i++) list.Add("zzz " + i);
sw.Start();
DoesContainRev(list, "zzz");
sw.Stop();
Console.WriteLine(String.Format("1: {0}", sw.ElapsedMilliseconds));
sw.Reset();
sw.Start();
DoesContainRev1(list, "zzz");
sw.Stop();
Console.WriteLine(String.Format("2: {0}", sw.ElapsedMilliseconds));
sw.Reset();
sw.Start();
DoesContainFwd(list, "zzz");
sw.Stop();
Console.WriteLine(String.Format("3: {0}", sw.ElapsedMilliseconds));
sw.Reset();
sw.Start();
DoesContainFwd1(list, "zzz");
sw.Stop();
Console.WriteLine(String.Format("4: {0}", sw.ElapsedMilliseconds));
sw.Reset();
sw.Start();
list.Contains("zzz");
sw.Stop();
Console.WriteLine(String.Format("5: {0}", sw.ElapsedMilliseconds));
sw.Reset();
Console.ReadKey();
}
public static bool DoesContainRev(ArrayList list, object element)
{
int count = list.Count;
for (int i = count - 1; i >= 0; i--)
if (element.Equals(list[i])) return true;
return false;
}
public static bool DoesContainFwd(ArrayList list, object element)
{
int count = list.Count;
for (int i = 0; i < count; i++)
if (element.Equals(list[i])) return true;
return false;
}
public static bool DoesContainRev1(ArrayList list, object element)
{
int count = list.Count;
for (int i = count - 1; i >= 0; i--)
if (list[i].Equals(element)) return true;
return false;
}
public static bool DoesContainFwd1(ArrayList list, object element)
{
int count = list.Count;
for (int i = 0; i < count; i++)
if (list[i].Equals(element)) return true;
return false;
}
}
}

With a really good optimizer there should not be difference at all, because the semantics seems to be the same. However the existing optimizer can optimize your function not so good as the hardcoded Contains is optimized. Some of the points for optimization:
comparing to a property each time can be slower than counting downwards and comparing against 0
function call itself has its performance penalty
using iterators instead of explicit indexing can be faster (foreach loop instead of plain for)

First, if you are using types you know ahead of time, I'd suggest using generics. So List instead of ArrayList. Underneath the hood, ArrayList.Contains actually does a bit more than what you are doing. The following is from reflector:
public virtual bool Contains(object item)
{
if (item == null)
{
for (int j = 0; j < this._size; j++)
{
if (this._items[j] == null)
{
return true;
}
}
return false;
}
for (int i = 0; i < this._size; i++)
{
if ((this._items[i] != null) && this._items[i].Equals(item))
{
return true;
}
}
return false;
}
Notice that it forks itself on being passed a null value for item. However, since all the values in your example are not null, the additional check on null at the beginning and in the second loop should in theory take longer.
Are you positive you are dealing with fully compiled code? I.e., when your code runs the first time it gets JIT compiled where as the framework is obviously already compiled.

After your Edit, I copied the code and made a few improvements to it.
The difference was not reproducable, it turns out to be a measuring/rounding issue.
To see that, change your runs to this form:
sw.Reset();
sw.Start();
for (int i = 0; i < nr; i++)
{
DoesContain(list,"zzz");
}
total += sw.ElapsedMilliseconds;
Console.WriteLine(total / nr);
I just moved some lines. The JIT issue was insignificant with this numbr of repetitions.

My guess would be that ArrayList is written in C++ and could be taking advantage of some micro-optimizations (note: this is a guess).
For instance, in C++ you can use pointer arithmetic (specifically incrementing a pointer to iterate an array) to be faster than using an index.

using an array structure, you can't search faster than O(n) whithout any additional information.
if you know that the array is sorted, then you can use binary search algorithm and spent only o(log(n))
otherwise you should use a set.

Revised after reading comments:
It does not use some Hash-alogorithm to enable fast lookup.

Use SortedList<TKey,TValue>, Dictionary<TKey, TValue> or System.Collections.ObjectModel.KeyedCollection<TKey, TValue> for fast access based on a key.
var list = new List<myObject>(); // Search is sequential
var dictionary = new Dictionary<myObject, myObject>(); // key based lookup, but no sequential lookup, Contains fast
var sortedList = new SortedList<myObject, myObject>(); // key based and sequential lookup, Contains fast
KeyedCollection<TKey, TValue> is also fast and allows indexed lookup, however, it needs to be inherited as it is abstract. Therefore, you need a specific collection. However, with the following you can create a generic KeyedCollection.
public class GenericKeyedCollection<TKey, TValue> : KeyedCollection<TKey, TValue> {
public GenericKeyedCollection(Func<TValue, TKey> keyExtractor) {
this.keyExtractor = keyExtractor;
}
private Func<TValue, TKey> keyExtractor;
protected override TKey GetKeyForItem(TValue value) {
return this.keyExtractor(value);
}
}
The advantage of using the KeyedCollection is that the Add method does not require that a key is specified.