Fast Inverse Square Root

The cluster centers on the Quake III fast inverse square root algorithm and related performance hacks for computing square roots, reciprocals, and trigonometric functions using techniques like CORDIC, Chebyshev approximations, Newton-Raphson, and lookup tables.

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Keywords

SQRTPS CPU FP DIY V1 ROM ULP FMA uwplse.org DIVPS square root square inverse root floating point floating multiplication fast multiply rows

Sample Comments

bla3 Dec 9, 2021 View on HN

Recent post on the same topic that gets the same information across with fewer words: https://kristerw.github.io/2021/10/19/fast-math/

speedgoose Apr 28, 2022 View on HN

Do we have another example than the famous quake fast square root function?

enriquto Jul 7, 2021 View on HN

Fast inverse square root is an ultra-fancy hack for a very particular processor. Apollo's trigonometric functions are the most natural optimal approximation that could be done.

ficklepickle Dec 21, 2020 View on HN

How do you compute the reciprocal without division? A precomputed lookup table?

EliRivers Jun 5, 2017 View on HN

Fast inverse square root as seen in Quake (as mentioned in other comments)https://en.wikipedia.org/wiki/Fast_inverse_square_root#Overv...

bee_rider Nov 30, 2023 View on HN

I tried 1/sqrt(9x-6) from .7 to 1e308, and got as one alternativesqrt(-.16666…)It did correctly mark this as 0% accurate, but I’m kinda curious as to where it came from.It does have a 1.1x speedup apparently. None of the other (more accurate) options provide a speedup. Maybe there aren’t any value options that provide a speedup, but the tool allows increasingly reduced accuracy (down to zero) until it finds a speedup?

fegu Oct 31, 2022 View on HN

The doom square root trick. Reducing an expensive function to almost nothing with low error. Many writeups on the web far better than I could give.

jacobolus Apr 12, 2017 View on HN

Nitpick: inverse square root is not a transcendental function.

pclmulqdq Apr 18, 2025 View on HN

Oof this is bad. If you're going to ask people to approximate, use a Chebyshev approximation please. You will do sin(x) faster than this and more accurately.

LarsDu88 Nov 1, 2022 View on HN

Fast inverse square root. Commonly attributed to john carmack, it actually predates his application of it by several years