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I have an inputStream that I want to use to compute a hash and save the file to disk. I would like to know how to do that efficiently. Should I use some task to do that concurrently, should I duplicate the stream pass to two streams, one for the the saveFile method and one for thecomputeHash method, or should I do something else?

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What about using a hash algorithms that operate on a block level? You can add the block to the hash (using the TransformBlock) and subsequently write the block to the file foreach block in the stream.

Untested rough shot:

using System.IO;
using System.Security.Cryptography;

...

public byte[] HashedFileWrite(string filename, Stream input)
{
    var hash_algorithm = MD5.Create();

    using(var file = File.OpenWrite(filename))
    {
        byte[] buffer = new byte[4096];
        int read = 0;

        while ((read = input.Read(buffer, 0, buffer.Length)) > 0)
        {
            hash_algorithm.TransformBlock(buffer, 0, read, null, 0);
            file.Write(buffer, 0, read);
        }

        hash_algorithm.TransformFinalBlock(buffer, 0, read);
    }

    return hash_algorithm.Hash;
}

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