this post was submitted on 21 Dec 2023
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Programming
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Just try it and decide for yourself. Make the computer do the math. I've done tons of angle stuff with quaternions in code and what the fuck even is a quaternion. What even is a matrix or imaginary number. Computer doesn't care that I don't know and just does what I tell it to. Results may not be what I hoped for sometimes but I can usually figure out what I did wrong after seeing the differences in the result.
"seeing the differences in the result"
This just means that you are testing against a very narrow output. It's actually pretty common to run across tests that don't even check for the likely failure cases, because the developer(s) don't actually understand the algorithm.
A common example is prime factorisation, most nontrivial factorisation algorithms (Pollard rho, elliptic curves), don't guarantee producing a prime factor they simply tend to produce them because they prioritize small factors. Programmers see that their function produces primes for the one or 2 test cases (out of say 2^64) and assume that it works. It generally does, but when it doesn't you get incorrect results (often undetectably) which poisons all the rest of your calculations.