What does 40x mean?

 So you created your algorithm, tested and you got least say a 40x improvement ( like i did :).  What does this mean? How much more data you can process in the same amount of time?

 The answer of this questions is related with the complexity of your algorithm. Least say you have a O(n^2) edit distance algorithm and you can compare 2 string of length 1000 in about 1 second using your CPU and 40 times faster using your GPU, the question is what is the length of the string that you can process in 1 second using your CPU?

 The answer to this question it turns our to be rather simple:

more precisely 6324. So basically you will be able to process strings 6 times bigger in the same amount of time.

 How i calculated this? i will let you figure it out :). As a help you can use the following speed gain table.

Algorithm complexity	Speed gain ( D = speedup factor )