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89 lines
2.3 KiB
Plaintext
89 lines
2.3 KiB
Plaintext
app "prime"
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packages { pf: "https://github.com/roc-lang/basic-cli/releases/download/0.7.1/Icc3xJoIixF3hCcfXrDwLCu4wQHtNdPyoJkEbkgIElA.tar.br" }
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imports [pf.Stdout, pf.Task]
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provides [main] to pf
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main : Task.Task {} I32
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main =
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numStrings =
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primesIn 50_000_000
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|> List.map Num.toStr
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|> Str.joinWith "\n"
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Stdout.line "$(numStrings)"
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primesIn : U64 -> List U64
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primesIn = \n ->
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List.range { start: At 0u64, end: At n }
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|> List.map \e -> isPrimePre e
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|> List.walk [] primeWalk
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PrimeResult : [No U64, Yes U64, Maybe U64]
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primeWalk : List U64, PrimeResult -> List U64
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primeWalk = \l, n ->
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when n is
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Yes n2 ->
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List.append l n2
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Maybe n2 ->
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if isPrimePost l n2 then
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List.append l n2
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else
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l
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No _ -> l
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isPrimePre : U64 -> PrimeResult
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isPrimePre = \n ->
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if n < 2 then
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No n
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else if n < 4 then
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Yes n
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else if Num.isEven n then
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No n
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else if
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(
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firstPrimes
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|> List.dropIf \p -> n < p
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|> List.any \p -> Num.isMultipleOf n p
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)
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then
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No n
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else
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Maybe n
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firstPrimes =
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[2, 3, 5, 7, 9, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 51, 67, 71, 73, 79, 83, 89, 97]
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isPrimePost : List U64, U64 -> Bool
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isPrimePost = \l, n ->
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nFloat = Num.toF32 n
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valLimit = Num.ceiling (Num.sqrt nFloat)
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# approximate the number of primes < sqrt(n) to limit the range we have to check with a 25% error tolerance
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valLimitF = Num.toF32 valLimit
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limit = Num.ceiling (valLimitF * 1.25 / (Num.log valLimitF))
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l
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|> List.sublist { start: 0, len: limit }
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|> List.dropIf \p -> p > valLimit
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|> List.any \p -> Num.isMultipleOf n p
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|> Bool.not
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countPrimesIn : U64 -> Nat
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countPrimesIn = \limit ->
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List.range { start: At 2, end: At limit }
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|> List.countIf \n ->
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if n < 4 then
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Bool.true
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else if n % 2 == 0 then
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Bool.false
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else
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res =
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List.range { start: At 3, end: At (Num.ceiling (Num.sqrt (Num.toF64 n))), step: 2 }
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|> List.any \a -> Num.isMultipleOf n a
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|> Bool.not
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res
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expect countPrimesIn 10000 == List.len (primesIn 10000)
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