Something interesting is I've seen this mythologized as evidenced of the "cracked engineer" theory, wherein random engineers will accidentally stumble upon incredibly complex discoveries in the course of their day to day work and expect no fanfare for this, besting the scientists and researchers who take the traditional route but aren't spurred by necessity. People, like xkcd, purported this was either Carmack or some random employee who figured it out in a few hours when stuck on a problem then waltzed onto the next one. In truth, as noted in the document, it has a history that goes back decades in academia, this was simply the most notable time it was implemented.
I think it speaks to an issue I see in the software engineering world where people assume that collaboration is for low-IQ people and all great innovation comes from some super-genius working on their own for long enough, and isn't required to share how they arrived at their findings. I'm sure the mythology of this algorithm is propelled somewhat by the enigmatic character of writing "what the fuck" next to adding the constant, implying a mystical element to its utility that was arrived at without needing to clarify it in some long boring research paper.
But that is what happened [1]. The article, which is probably the most definitive investigation to date, has Greg Walsh claim they invented the fast inverse square root while working at Ardent, which Wikipedia claims was founded in 1985 [2], to meet product performance benchmarks.
The Green Hills Software C compiler had a fast square root algorithm of similar form:
(x >> 1) + {magic constant}
dating between 1983-1985 if I recall correctly. Also implemented to maximize floating point performance benchmarks, and again not drawn from academia. If my recollection is correct, that is one of the earliest known examples of the general technique and predates even the official IEEE 754 floating point specification which was not formally ratified until 1985 (but the standard was in development since 1977 and already de facto adopted by the time it was formally ratified).
> where people assume that collaboration is for low-IQ people
I've also seen a phenomenon where developers believe their code is so valuable and amazing that they don't share it; it's really ordinary code but useful to novices nonetheless. Some communities I participated in when I was younger (e.g. PS3 jailbreak scene) were very protective of their code for no reason. Executables were obfuscated, nothing was open source, and developers were very hostile or intentionally trolled you when asking questions about their software.
I've met some people like this before, and I think this phenomenon has a lot to do with having one's identity closely bound to the code. Any criticism of the code is interpreted as a personal attack. Conversely, the attitude of "I'm so awesome therefore my code must be super important and really important to protect".
I've also seen the reverse - perhaps more. People need advice but don't want to share their code because they are embarrassed by it. They wrote it thinking "no one will ever see this".
By contrast I sell code, so I know it'll be seen by lots of people, so I tend to spend time making sure style is consistent, things are well named, and so on. But equally, to me, it's just code. Feel free to comment on it - there's always room for improvement.
I think the xkcd comic was more about academia vs product engineering in for profit entities. If anything, it is the collaborative effort of many people working on a product with deadlines that ends up with some of them coming up with really interesting solutions just due to the number of people looking. The lack of sharing between companies does increase the incidence of the outsider effect, at the massive cost of reinventing basic knowledge over and over. The only reason breakthroughs still happen despite that is just the large number of people trying random stuff that probably won't work motivated by unrealistic deadlines. They don't know it probably won't work though...
The point seems more to me that in engineering, breakthroughs worthy of academic repute aren't given much fanfare, though probably a bit of an exaggeration. It's hard to tell to what extent his comics reflect actual sentiments or rather an artifice of some abstraction taken to an absurd level.
I think it speaks to an issue I see in the software engineering world where people assume that collaboration is for low-IQ people and all great innovation comes from some super-genius working on their own for long enough, and isn't required to share how they arrived at their findings. I'm sure the mythology of this algorithm is propelled somewhat by the enigmatic character of writing "what the fuck" next to adding the constant, implying a mystical element to its utility that was arrived at without needing to clarify it in some long boring research paper.