Fast Inverse Square Root — A Quake III Algorithm
Nemean3 HN recommenders · recommended in 3 months, 2021-2022
6M views · 5 years ago · explainer · evergreen
A walkthrough of the Quake III fast inverse square root, explaining where the constant 0x5f3759df comes from. It covers IEEE 754 floats, the bit hack that approximates a logarithm, and a Newton's method refinement.
HN recommends it as an approachable explanation that makes the famous algorithm finally make sense.
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4 comments from Hacker News
print("Hello World") /s But I've heard good things about the Fast Inverse Square Root Calculation algorithm in the Doom 3 source code. ▶ this video
Apparently the bit pattern of a float interpreted as an int is sorta-kinda it's own logarithm, which is why the famous fast inverse square root from quake 3 works: log(x^-½) = -½log(x) =~ -log(x) >> 1. This video is approachable and explains it pretty well: ▶ this video
> The bits of a float as an integer literal are proportional to its log2 value (plus a constant), … I watched a video[0] a while back about that. Once that coincidence(?) was explained, Q_rsqrt finally made sense. [0]: ▶ this video (~20 minutes)
Very interesting that this was posted as I literally JUST watched an even MORE interesting youtube upload about this very bit of code just last weekend. Here's the very fun video if anyone wants to take a look: ▶ this video