I'm not sure if I used the word "provided" in a right way in the following example:
In general, this algorithm solves Fibonacci problem with higher scores rather than the original algorithm, provided/providing reasonable values are selected for stack size and array length.
In this text I want to say that if user choose reasonable variables then it is rightly expected that the mentioned algorithm works better than the original.
Finally, please can you tell me that are "provided" and "providing" the same? which is better to use for scientific papers?