alt Hacker NewsThe math looks suspicious to me, or at least how it is presented.
If, as stated, accessing one register requires ~0.3 ns and available registers sum up to ~2560 B, while accessing RAM requires ~80 ns and available RAM is ~32 GiB, then it means that memory access time is O(N^1/3) where N is the memory size.
Thus accessing the whole N bytes of memory of a certain kind (registers, or L1/L2/L3 cache, or RAM) takes N * O(N^1/3) = O(N^4/3).
One could argue that the title "Memory access is O(N^1/3)" refers to memory access time, but that contradicts the very article's body, which explains in detail "in 2x time you can access 8x as much memory" both in text and with a diagram.
Such statement would require that accessing the whole N bytes of memory of a certain kind requires O(N^1/3) time, while the measurements themselves produce a very different estimate: accessing the whole N bytes of memory of a certain kind requires O(N^4/3) time, not O(N^1/3)
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I think the article glossed over a bit about how to interpret the table and the formula. The formula is only correct if you take into account the memory hierarchy, and think of N as the working set size of an algorithm. So if your working set fits into L1 cache, then you get L1 cache latency, if your working set is very large and spills into RAM, then you get RAM latency, etc.
> "in 2x time you can access 8x as much memory"
is NOT what the article says.
The article says (in three ways!):
> if your memory is 8x bigger, it will take 2x longer to do a read or write to it.
> In a three-dimensional world, you can fit 8x as much memory within 2x the distance from you.
> Double the distance, eight times the memory.
the key worda there are a, which is a single access, and distance, which is a measure of time.
N is the amount of memory, and O() is the time to access an element of memory.
I hate big O notation. It should be O(N) = N^(1/3)
That way O is the function and it's a function of N.
The current way it's notated, O is the effectively the inverse function.
All their numbers are immediatley suspect since they admit to using ChatGPT to get their numbers. Oh, and their wonderful conclusion that something that fits fully in the CPU's caches is faster than something sitting a few hops away in main memory.
I did not interpret the article as you did, and thought it was clear throughout that the author was talking about an individual read from memory, not reading all of a given amount of memory. "Memory access, both in theory and in practice, takes O(N^⅓) time: if your memory is 8x bigger, it will take 2x longer to do a read or write to it." Emphasis on "a read or write".
I read "in 2x time you can access 8x as much memory" as "in 2x time you can access any byte in 8x as much memory", not "in 2x time you can access the entirety of 8x as much memory". Though I agree that the wording of that line is bad.
In normal big-O notation, accessing N bytes of memory is already O(N), and I think it's clear from context that the author is not claiming that you can access N bytes of memory in less time than O(N).