SepehrM - 28 days ago 12

C# Question

As a part of my BigDecimal library, I need to calculate the factorial of any given non negative integer. So I'm using .Net 4.0 's

`System.Numerics.BigInteger`

`private BigInteger Factorial(BigInteger x)`

{

BigInteger res = x;

x--;

while (x > 1)

{

res *= x;

x--;

}

return res;

}

It's working but not optimized. Now I want to use parallel computing, so here is what I've tried: (I have no experience with parallel programming)

`public BigInteger Factorial(long x)`

{

BigInteger res = 1;

ParallelLoopResult r = Parallel.For(2L, (x + 1), i =>

res *= i

);

return res;

}

The weird problem is that the above function works perfectly for small numbers like 5! but doesn't work for big numbers like 1000! and each time returns a completely different result. So I realized it's not thread safe and the problem is with the variable

`res`

And It would be nicer if I could use BigInteger instead of long for variable

`x`

Answer

You need to make sure your parallel processes do not share any state.

For example, in the case of the factorial, I would do the following:

- set a degree of parallelism (DOP) - usually the number of processors on your machine for compute-bound operations
- divide the problem into independent subsets
- process each subset in parallel
- aggregate the results obtained from the parallel processes

This is somehow a simplified Map-Reduce.

The problem consists in multiplying together a set numbers. One way to divide this set into subsets is to use `N`

parallel for loops where each start at a value `i`

(where `0 < i <= N`

) with a step of `N`

(and `N`

= `DOP`

).

Here's the code that does that:

```
/// <summary>
/// The max number of parallel tasks
/// </summary>
static readonly int DegreeOfParallelism = Environment.ProcessorCount;
public BigInteger Factorial(long x)
{
// Make as many parallel tasks as our DOP
// And make them operate on separate subsets of data
var parallelTasks =
Enumerable.Range(1, DegreeOfParallelism)
.Select(i => Task.Factory.StartNew(() => Multiply(x, i),
TaskCreationOptions.LongRunning))
.ToArray();
// after all tasks are done...
Task.WaitAll(parallelTasks);
// ... take the partial results and multiply them together
BigInteger finalResult = 1;
foreach (var partialResult in parallelTasks.Select(t => t.Result))
{
finalResult *= partialResult;
}
return finalResult;
}
/// <summary>
/// Multiplies all the integers up to upperBound, with a step equal to DOP
/// starting from a different int
/// </summary>
/// <param name="upperBoud"></param>
/// <param name="startFrom"></param>
/// <returns></returns>
public BigInteger Multiply(long upperBound, int startFrom)
{
BigInteger result = 1;
for (var i = startFrom; i <= upperBound; i += DegreeOfParallelism)
result *= i;
return result;
}
```

On my machine this computes `100000!`

in about 30 seconds and the result is what Wolfram Alpha says it should be.

After running a few more tests, I discovered something which I didn't expect: printing out the `100000!`

result to the console takes ~18 seconds (the result has `456574`

digits).

The results of the `100000!`

computation alone (without printing the number) the are:

- ~10 seconds for parallel execution
- ~16 seconds for sequential execution