111–120 of 167 posts
This made me realize that trigonometric functions are not deterministic across different CPU architectures, OS, and programming languages (floating point precision aside). E.g. I would assume that Math.sin(x) returns the same thing in NodeJS on Windows and Mac/M1, but it turns out it is necessarily so. https://stackoverflow.com/questions/74074312/standard-math-f...
I would use the word "consistent."
Non-determinism implies randomness.
I recently learned how Doom was ported to the SNES. It's quite impressive. The SNES hardware was nowhere near fast enough to do all the trig calculations needed for the game but cartridge based games had a trick up their sleeve: they could include actual hardware inside the cart that the game code could make use of. It was more expensive but if you expected to sell a boatload of copies, it could be worth it. However,…
Games targetting pre-Pentium PCs also used precomputed trig tables. Pentium was fast enough that it didn't matter as much. Just a few years later it was slower to read a trig precomputed table.
CORDIC is how it's usually done in hardware (and FPGAs). https://en.wikipedia.org/wiki/CORDIC
no it's not. cordic has awful convergence of 1 bit per iteration. pretty much everyone uses power series.
I recently learned how Doom was ported to the SNES. It's quite impressive. The SNES hardware was nowhere near fast enough to do all the trig calculations needed for the game but cartridge based games had a trick up their sleeve: they could include actual hardware inside the cart that the game code could make use of. It was more expensive but if you expected to sell a boatload of copies, it could be worth it. However,…
I recently learned how Doom was ported to the SNES. It's quite impressive. The SNES hardware was nowhere near fast enough to do all the trig calculations needed for the game but cartridge based games had a trick up their sleeve: they could include actual hardware inside the cart that the game code could make use of. It was more expensive but if you expected to sell a boatload of copies, it could be worth it. However,…
Games targetting pre-Pentium PCs also used precomputed trig tables. Pentium was fast enough that it didn't matter as much. Just a few years later it was slower to read a trig precomputed table.
What’s the best way to calculate it by hand? I’m brushing up my math basics (I graduated CS while dodging the math requirements) and it frustrates me that in trig I need to remember values at all. The values such as sqrt(2)/2 make sense but how hard is it to calculate sin(5 degrees) by hand?
CORDIC is how it's usually done in hardware (and FPGAs). https://en.wikipedia.org/wiki/CORDIC
CORDIC is pretty obsolete, AFAIK. Its advantage is that its hardware requirements are absolutely tiny: two (?) accumulator registers, and hardware adders and shift-ers—I think that's all. No multiplication needed, in particular. Very convenient if you're building things from discrete transistors , like the some of those earlier scientific calculators! (Also has a nice property, apparently, that CORDIC-like routines e…
Earlier quoted context omitted.
Games targetting pre-Pentium PCs also used precomputed trig tables. Pentium was fast enough that it didn't matter as much. Just a few years later it was slower to read a trig precomputed table.
Yup, I remember watching a video about how the RAM bus is the bottleneck when running Super Mario 64 on the N64. The original implementation used trig lookup tables, but the person optimized it by instead using Taylor series (I think) and some negation / shifting.
This made me realize that trigonometric functions are not deterministic across different CPU architectures, OS, and programming languages (floating point precision aside). E.g. I would assume that Math.sin(x) returns the same thing in NodeJS on Windows and Mac/M1, but it turns out it is necessarily so. https://stackoverflow.com/questions/74074312/standard-math-f...
Safer to assume that floats are never deterministic.
I wonder what the first program was that ever used a precomputed trig table.