A student performed a thorough review of the available algorithms in the literature and constructed several coding implementations that were shown to be far more effective than previous implementations known to the supervisor for the last decade. The fundamentals of these implementations, which already existed in the literature, were complemented with a major adaptation.
The supervisor used these implementations to perform a simulation that formed one piece of key evidence for the validity of his paper. The student was not in the author list, not in the acknowledgments section and his works are not cited. In fact, the vanilla algorithm presented in the draft was insufficient to perform the required calculations.
For the sake of posing a question, let's take these claims as true and ask: - How should the student approach this matter?
A lot of questions here are left unanswered.
Are you a student? A staff programmer? Do you have a work-for-hire agreement with the university? Is it just your implementation, or is it your original synthesis of several algorithms? Is the synthesis something that is novel & not obvious and do you think it constitutes a significant intellectual contribution? Have you previously published about this synthesis and if so is that cited? How core is the use of these algorithms to the main results of the paper?
It might be reasonable to point out to your advisor how it would be helpful to your career (ability to get a great job after leaving, etc.) if your contributions are recognized in the papers that use them, at least in the acknowledgements section. It may be that for whatever reason the supervisor hasn't thought of this (or doesn't remember when writing it up close to the deadline) but may be very willing to do so.
If you are a student and the supervisor is your academic advisor, you may also ask questions/have a conversation about what authorship means in your field and what the expectations are for what contributions warrant authorship in your collaborations. Part of an academic advisor's role is to teach their students about these sorts of things.
If you don't feel comfortable with a direct conversation or with the results of one, go to your program director and see what their perspective might be.