How to document an algorithm properly with sample data?

Question

I am wondering what should an algorithm documentation contain? Can't locate a proper guideline to follow. I have in mind to include

• summary of the algorithm
• description of the algorithm
• flowcharts
• pseudo codes
• sample input data set(multiple)
• output data
• unit tests
• experiments

The client requests such a documentation to: Maintain confidence in our own numbers as well as to describe our process to potential customers so they know we are taking steps to check and verify our calculations.

• How would look like such a documentation? (example PDF)
• What would you include more in this documentation?
• What I enumerated is that good, or this should be somehow documented differently?
• How would you search in Google for such documentation samples?

Answer 1

Some more points:

1. Performance analysis/benchmark with sample inputs and environments.
2. Alternates to the algorithm(if exists), really helps for new people, and for comparison analysis.
3. Examples of best and worst case scenarios/inputs.

How would look like such a documentation?
Cusotmers/Users(/Managers?) don't like PDF, they find PPTs very interesting though, at the same time business will insist on PDF. So you should have a two-level document, one in PPT just to "explain in 20 mins" and other in PDF that covers the gory details of the game.

• Talha Ahmed Khan: Also if the alternate Algos are available you must compare the efficiency of both Algos.
• Pentium10: Any samples you can show?