Talk:CalmoSoft primes: Difference between revisions
→Sequence length: Discovered what was making {2, 3, 5} wheel slower.
(→Sequence length: Commented.) |
(→Sequence length: Discovered what was making {2, 3, 5} wheel slower.) |
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===Raku incorrect (now fixed) ===
I'm getting
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:What would make a difference is to speed up the sieving. The C++ entry is using ''primesieve'' which, amongst other tricks, uses all available cores to maximize speed. Unfortunately, Wren is single threaded and so this technique is not available to the CLI version though, in an embedded application, one could write a function to utilize this library from a C/C++ host which Wren could then call. --[[User:PureFox|PureFox]] ([[User talk:PureFox|talk]]) 13:23, 10 April 2023 (UTC)
::Of course the real key to performance is ''not'' summing all 12.5e14 consecutive subsequences and testing every single one of those for primality, which would take quite some time no matter how good your compiler or how many cores you had. --[[User:Petelomax|Petelomax]] ([[User talk:Petelomax|talk]]) 01:55, 12 April 2023 (UTC)
:::An area I've been investigating is how best to check if the candidate sequence sums are prime or not which is quite slow in Wren for the larger sums. My 'Int.isPrime' routine uses an implicit {2, 3} basis for wheel factorization which, curiously, seems optimal for Wren - if I try to use {2, 3, 5} as in the C++ example - it's slightly slower.
::::Just as a matter of interest, it turned out that what was making the {2, 3, 5} basis wheel slightly slower than {2, 3} in Wren was the cost of accessing the wheel increments via a list. If I don't use a list, then it's 25% quicker! --[[User:PureFox|PureFox]] ([[User talk:PureFox|talk]]) 10:04, 27 April 2023 (UTC)
:::However, what does help is to use the Miller-Rabin test instead which brings the overall time down from 4.3 to 3.5 seconds. Unfortunately, you can't use this for checking primality generally as it's much slower than wheel-based factorization if you're checking a block of numbers which are mostly non-prime. I checked the first 1 million integers for primeness and Miller-Rabin took about 30 times as long. It's best used therefore for checking isolated large numbers as we have for this task. --[[User:PureFox|PureFox]] ([[User talk:PureFox|talk]]) 11:06, 12 April 2023 (UTC)
::::I've just realized that the above test was unfair because there's no need to use the full 'witness' array for smaller numbers. Using the table in [https://oeis.org/A014233 A014233] means that Miller-Rabin takes about 8.5 as long as wheel factorization to check the first million integers and the multiple falls to around 7.1 for the first three million numbers. --[[User:PureFox|PureFox]] ([[User talk:PureFox|talk]]) 16:03, 12 April 2023 (UTC)
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