# Final Results (Kind of)

The wiki page has now been updated with the final set of results for small pattern sizes. I’ve upped the number of repeats for each test from 3 to 7, so everything’s taking a little longer, but I’ll set up some new tests for larger pattern sizes to run over the weekend. Fortunately, I’ve now modified the test harness to output a data file with which I can plot a graph with gnuplot nice and quickly. Not quite sure why I wasn’t doing that before to be honest. This also has the bonus of producing SVG output.

The latest set of results include real-to-real transforms, the $O(n \log m)$ algorithm with a minimum sub-string size, a variation where no wild cards are allowed in the text and combinations of the above. To summarize some results:

• All methods seem to be performing better wrt to the naive approach. I can only assume this is relation to improvements in the compiler after I updated earlier in the week.
• The absolute best seems to be a combination of the above (using every trick in the book you might say): we use the $O(n \log m)$ algorithm, with a minimum sub-string size, disallowing wild-cards in the text, and use the real-to-real transform. This beats the naive method on all but the first sample point at $m=32$.
• Forcing a minimum size has completely gotten rid of the erratic behaviour for small $m$
• If we allow wild cards in the text, the $O(n \log n)$ and $O(n \log m)$ versions become faster than the naive approach when $m$ is greater than approximately 300 and 80 respectively.
• These results seem to hold fairly well for different $n$ — i’m currently running a test with $n=2^{21}=2097152$ which should verify that.
• FLINT is the exception to the consistency rule — it gets noticeably worse wrt to the naive method as $m$ increases (ranging from being faster for $m > 600$ to $m > 900$ so far)

There’s plenty of graphs on the wiki page here, as well as updated results. The FFT page has also been updated.

So, still to do:

• Produce final results for large m
• Put the library of methods together so it’s a bit more usable and upload it to the wiki
• Maybe give some consideration to memory usage