You shouldn't use a word that can carry a precise mathematical meaning in a sentence that literally uses mathematical notation in order to speak precisely and then expect readers not to interpret the word in the precise mathematical way.
You should if you expect your readers to be normal humans who understand obvious context, and not pedantic HN readers who understand obvious context but delight in nit-picking it anyway.
Who the fuck do you think is the intended audience for an article about an algorithm in `git bundle create`? I spent approximately two minutes of my life trying to figure out where the O(n^2) algorithm was being invoked in such a way that it influenced an exponential.
Exponential was bolded in the same sentence as a big-O. 50/50 troll/author oversight.
Algorithmic? Big-O? Polynomially? Linear improvement? O(n^2) to O(n)? Or if you want to be less mathematically precise: enormous improvement?
Using exponential in this way in any context is a faux pas, because it's highly ambiguous, and requires context for clarification. But in this situation the context clearly resolved to the mathematically accurate definition, except it was used in the other way.
Quadratically doesn't have the same punch because it is actually exponentially less than exponentially. So doing it for extra punch (as opposed to not knowing the correct word) in a technical context would just be lying. It'd be like a paper saying they had a result with p less than one in a trillion for "extra punch" when they actually had p=0.1.
If you just mean "a lot" in a non-technical sense, there are plenty of words available. enormously. immensely. tremendously. remarkably. incredibly. vastly.
I understood every word, phrase, and sentence you wrote. But I did not understand your point. Still, I got the meaning of your words, so presumably you're satisfied.
>Ultimately, we traced the issue to a 15-year-old Git function with O(N²) complexity and fixed it with an algorithmic change, reducing backup times exponentially.
No, not in the exact same sentence as a big-O. That's either author error, or an intentional troll. Either way it's egg on their faces.
The algorithm complexity went down in the function they patched (6x improvement in their benchmark), but in the context of how they benefited with how they were using the algorithm the impact was much larger (improved to taking 1% of the time), which is plausibly exponential (and figuring out the actual complexity is neither relevant nor an economic use of time).
> figuring out the actual complexity is neither relevant nor an economic use of time
The fix was replacing a nested loop with a map. Figuring out that this goes from O(n^2) to O(n) (modulo details like bucket count) is immediate if you know what the words mean and understand enough to identify the problem and make the fix in the first place.
That is not true unless n^C / e^n = log(n) where C is some constant, which it is not. The difference between log(n) and some polynomial is logarithmic, not exponential.
But if you happen to have n=2^c, then an algorithm with logarithmic complexity only needs c time. Thats why this is usually referred to as exponential speedup in complexity theory, just like from O(2^n) to O(n). More concretely if the first algorithm needs 1024 seconds, the second one will need only 10 seconds in both cases, so I think it makes sense.
The man, or llm, used the mathematically imprecise definition of exponential in a sentence with a big-O notation. I don't think he's going to be writing entire arguments formally.
I interpreted that as n->log(n) since log and exp are inverses.
Also because I've often heard tha the quantum Fourier transform is an exponential speedup over the discrete Fourier transform, and there the scaling goes n^2->nlogn.
I'm not the OP you're responding to, but to be fair, in a sentence about big-O perf characteristics, which includes the word "algorithms", using "exponentially" in a colloquial non-technical sense is an absolutely terrible word choice.
I disagree. Misuse of the word "exponential" is a major pet peeve of mine. It's a particular case of the much more common "use mathematically precise phrasing to sound careful/precise" that you often find in less than honest writing.
Here they are actually using it to refer to growth functions (which is rare for this error) and being honest (which is also rare IMO) but it's still wrong. They should have written about quadratic or quadratic vs linear.
Regardless sloppy language leads to sloppy thought.