Couple of things:

• Whether your program has bug is not a fixed or constant truth, but rather a conclusion made based on the way of observation. If our way of observation is black box testing, obviously we will say that your program has no bug as far as we tested. But if part of our observation is a code review, someone may quickly realize that you are not implementing the algorithm, regardless whether the algorithm is correct, your program has a bug. Or someone might realize that the algorithm is faulty, thus regardless of your implementation, your program is faulty.

• Secondly, to say that the algorithm or the implementation is/are faulty is meaningless, unless such claim is supported by facts. If the only fact is your seemingly successful testing, no suggestion can be made that the implementation or algorithm is/are faulty. There might be some hidden truth, but you cannot claim it until it is proved so. For example, we can make that conclusion if there is a correct implementation of the faulty algorithm, or vice versa, and subsequently fail the testing, and lead to the realization of such truth.

  On the other hand, human understanding of the natural or so called truth is never complete, thus it can only be considered as true under a complex set of assumptions, or to be more straight "always faulty", but as time goes, you are getting more and more close to the never reaching truth, and sometime you could even go backwards. In the world of computer science, all programs with a certain level (this level can be easily exceeded, much easier than you thought) of complexity are buggy, and it is just a timing issue for you to find the next bug in a perfect program.