Human-readable numbers are tracked by computers in a number of different ways. Nowadays we basically just do a printf or some version of it, but on a 1 megahertz platform, optimization really matters. It’s easy to think of computers as being impossibly fast, but in truth speed only ever counts relative to the efficiency of the algorithm you use. Computers are fast, but they aren’t all that fast.

One of the big tradeoffs in processor design is, fewer complex instructions that do a lot but take a lot of cycles, and processor complexity, to execute, or many simple instructions, each doing little and being relatively simple, and not needing a complex processor design to implement.

The 6502 microprocessor generally follows the latter design philosophy. It made some important tradeoffs to keep costs down. For example, it doesn’t have hardware that can multiply arbitrary numbers together. It relies on the programmer, or else a library author, to use the instructions given to code their own multiplication algorithm, if they need one. The result is going to be slower, probably, that if the chip had the circuits to do this automatically in silicon, but it reduced the cost of the chip, basically allowing more to be made, or else increasing the profits for the manufacturer.

Personally I’m a fan of just storing the score as a series of digits that match up to their positions in the character set. Gain 1,000 points? Just bump the 1000s-place up by one, and if it goes past 9, subtract 10 and bump the 10,000s place. That’s a tried-and-true system that many games use, and works well if all you ever have to do is add numbers. Comparing values, like for detecting extra life award levels, make things slightly more complex, but not by much. There’s sometimes other factors involved though, and that may explain why Super Mario Bros. uses different systems for its counters, as explained by NESHacker.

rodneylives

We link to such a variety of things here. Sometimes we post light videos where someone has Kirby do funny things. Sometimes we show explainers that explain how to do arithmetic on old processors. I presume that you’ll take from these what you want, and leave the rest to the crazy people, by definition the people who are not you. I understand.

rodneylives

He made a Youtube video detailing his most recent optimization find: getting the game’s trigonometric functions executing at their speediest. What is interesting is that the Mario 64 code already uses a couple of tricks to get sine and cosine results in a rapid manner: the game only uses 4096 discrete angles of movement direction, and contains a lookup table that covers each of those angles. But it turns out that this optimization is actually a mis-optimization, because the RAM bus hits incurred to read the values into the cache are actually more expensive than just figuring out the values in code on the N64’s hardware!

The video starts out decently comprehensible, but eventually descends into the process of figuring out sine and cosine on the fly, and the virtues of the various ways this can be done, so you can’t be faulted for bailing before the end, possibly at the moment the dreaded words “Taylor series” are mentioned. But it’s a fairly interesting watch until then!

rodneylives