Was messing around with C and found this quirk. How does this function work so quickly? How is it implemented?
In: Mathematics
Be aware that at least the Intel x86 architecture has an FSINCOS instruction. The ELI5 of that is that the CPU does the hard work in a single operation, meaning the C function isn’t doing anything interesting. FSINCOS is faster than running both FSIN and FCOS.
Of course the CPU isn’t magic and must be doing similar things internally to what a C function would be doing, although more efficiently. There is some commonality in computing the sine and cosine which both CPU instructions of C functions can take advantage of. The details depend on how they’re implemented.
Most implementations use a Taylor series expansion (cos = 1 – x^2 /2! + x^4 /4! – x^6 /6! …, sin = x – x^3 /3! + x^5 /5! – …) or lookup table. Cos and Sin are the same, just pi/2 out of phase, so you only need to do it once.
The ELI5 answer is because sin and cos have the same values just 90 degrees out of phase. Just look at a graph of sin and a graph of cos to see what I mean.
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