zlacker

[return to "For algorithms, a little memory outweighs a lot of time"]
1. whatev+ti[view] [source] 2025-05-21 21:31:16
>>makira+(OP)
Lookup tables with precalculated things for the win!

In fact I don’t think we would need processors anymore if we were centrally storing all of the operations ever done in our processors.

Now fast retrieval is another problem for another thread.

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2. crmd+Jz[view] [source] 2025-05-22 00:23:09
>>whatev+ti
Reminds me of when I started working on storage systems as a young man and once suggested pre-computing every 4KB block once and just using pointers to the correct block as data is written, until someone pointed out that the number of unique 4KB blocks (2^32768) far exceeds the number of atoms in the universe.
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3. jodrel+DJ[view] [source] 2025-05-22 02:22:43
>>crmd+Jz
Reminds me of when I imagined brute-forcing every possible small picture as simply 256 shades of gray for each pixel x (640 x 480 = 307200 pixels) = 78 million possible pictures.

Actually I don't have any intuition for why that's wrong, except that if we catenate the rows into one long row then the picture can be considered as a number 307200 digits long in base 256, and then I see that it could represent 256^307200 possible different values. Which is a lot: https://www.wolframalpha.com/input?i=256%5E307200

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4. p1neco+CM[view] [source] 2025-05-22 03:01:10
>>jodrel+DJ
78 million is how many pixels would be in 256 different pictures with 307200 pixels each. You're only counting each pixel once for each possible value, but you actually need to count each possible value on each pixel once per possible combinations of all of the other pixels.

The number of possible pictures is indeed 256^307200, which is an unfathomably larger number than 78 million. (256 possible values for the first pixel * 256 possible values for the second pixel * 256 possi...).

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