Some of these might work

justfile

@@ -3,7 +3,7 @@ set shell := ["nu", "-c"]
 default:
 	print "Select a command"
 
-dev target +FLAGS="": (build target FLAGS)
+dev target +FLAGS="--dev": (build target FLAGS)
 	if ('out/{{target}}' | path exists) { out/{{target}} } else { ^$"out/('{{target}}' | str replace -r '\.roc$' '')" }
 
 build target +FLAGS="--optimize": init

prime-bin-search.roc

@@ -0,0 +1,122 @@
+app "prime-bin-search"
+    packages { pf: "https://github.com/roc-lang/basic-cli/releases/download/0.7.1/Icc3xJoIixF3hCcfXrDwLCu4wQHtNdPyoJkEbkgIElA.tar.br" }
+    imports [pf.Stdout, pf.Task]
+    provides [main] to pf
+
+main : Task.Task {} I32
+main =
+    numStrings =
+        primesIn 500_000
+        |> List.map Num.toStr
+        |> Str.joinWith "\n"
+
+    Stdout.line "$(numStrings)"
+
+primesIn : U64 -> List U64
+primesIn = \n ->
+    numbers = List.range { start: At 2u64, end: At n }
+    List.walk numbers numbers primeWalk
+
+primeWalk : List U64, U64 -> List U64
+primeWalk = \l, n ->
+    if l |> binarySearchContains n then
+        if n > 1 then
+            l
+            |> List.dropIf \e ->
+                e > n && Num.isMultipleOf e n
+        else
+            l
+    else
+        l
+
+binarySearchContains : List U64, U64 -> Bool where a implements Eq
+binarySearchContains = \l, a ->
+    len = List.len l
+
+    if Num.isZero len then
+        Bool.false
+    else
+        half = Num.shiftRightBy len 1
+        binarySearchContainsRec l a half half
+
+binarySearchContainsRec : List U64, U64, Nat, Nat -> Bool where a implements Eq
+binarySearchContainsRec = \l, n, mid, step ->
+    if step <= 1 then
+        sublist = List.sublist l { start: (mid - (Num.min step mid)), len: (step * 2 + 1) }
+
+        when sublist is
+            [] -> Bool.false
+            [a] -> n == a
+            [a, b] -> n == a || n == b
+            [a, b, c] -> n == a || n == b || n == c
+            _ -> crash "This shoulnd't have happened"
+    else
+        element = List.get l mid |> Result.withDefault 0
+
+        when Num.compare n element is
+            EQ -> Bool.true
+            ne ->
+                newStep = Num.divCeil step 2
+                len = l |> List.len
+
+                when ne is
+                    GT if mid >= len -> Bool.false
+                    GT -> binarySearchContainsRec l n (mid + newStep) newStep
+                    LT if mid < newStep -> binarySearchContainsRec l n 0 newStep
+                    LT -> binarySearchContainsRec l n (mid - newStep) newStep
+                    _ -> crash "This shoulnd't have happened"
+
+orderedContains : List (Num a), Num a -> Bool where a implements Eq
+orderedContains = \l, a ->
+    when l |> List.findFirst \e -> e >= a is
+        Err NotFound -> Bool.false
+        Ok f -> f == a
+
+expect orderedContains [0, 1, 2, 3, 4, 5, 6] 5 == Bool.true
+expect binarySearchContains [0, 1, 2, 3, 4, 5, 6] 5 == Bool.true
+expect binarySearchContains [0, 1, 3, 4, 5, 6] 2 == Bool.false
+expect binarySearchContains [0, 1, 3, 4, 5, 6] 7 == Bool.false
+expect binarySearchContains [] 7 == Bool.false
+expect binarySearchContains [2] 2 == Bool.true
+expect binarySearchContains [1, 2, 3] 3 == Bool.true
+expect binarySearchContains [1, 2, 3] 1 == Bool.true
+expect binarySearchContains [1, 2, 3, 4, 5, 6] 0 == Bool.false
+
+expect binarySearchContains (List.range { start: At 0, end: At 100000 }) 4 == Bool.true
+expect binarySearchContains (List.range { start: At 0, end: At 100000 } |> List.dropIf Num.isEven) 4 == Bool.false
+expect binarySearchContains (List.range { start: At 0, end: At 100000 } |> List.dropIf Num.isOdd) 97 == Bool.false
+expect binarySearchContains (List.range { start: At 0, end: At 100000 }) 99998 == Bool.true
+expect binarySearchContains (List.range { start: At 0, end: At 100000 }) 100001 == Bool.false
+
+countPrimesIn : U64 -> Nat
+countPrimesIn = \limit ->
+    List.range { start: At 2, end: At limit }
+    |> List.countIf \n ->
+        if n < 4 then
+            Bool.true
+        else if n % 2 == 0 then
+            Bool.false
+        else
+            res =
+                List.range { start: At 3, end: At (Num.ceiling (Num.sqrt (Num.toF64 n))), step: 2 }
+                |> List.any \a -> Num.isMultipleOf n a
+                |> Bool.not
+
+            res
+
+expect
+    (
+        countPrimesIn 100000
+        |> \expected ->
+            dbg expected
+
+            expected
+    )
+    == (
+        List.len (primesIn 100000)
+        |> \actual ->
+            dbg actual
+
+            actual
+
+    )

prime-sieve.roc

@@ -0,0 +1,61 @@
+app "prime2"
+    packages { pf: "https://github.com/roc-lang/basic-cli/releases/download/0.7.1/Icc3xJoIixF3hCcfXrDwLCu4wQHtNdPyoJkEbkgIElA.tar.br" }
+    imports [pf.Stdout, pf.Task]
+    provides [main] to pf
+
+main : Task.Task {} I32
+main =
+    numStrings =
+        primesIn 50_000_000
+        |> List.map Num.toStr
+        |> Str.joinWith "\n"
+
+    Stdout.line "$(numStrings)"
+
+primesIn : U64 -> List U64
+primesIn = \n ->
+    numbers = List.concat [2] (List.range { start: At 3u64, end: At n, step: 2 })
+    primeSieve numbers
+
+primeSieve : List U64 -> List U64
+primeSieve = \l ->
+    when l is
+        [] -> []
+        [a] -> [a]
+        [head, .., tail] if (Num.powInt head 2) > tail -> l
+        [head, .. as tail] ->
+            filteredList = List.dropIf tail (\e -> Num.isMultipleOf e head)
+            List.concat [head] (primeSieve filteredList)
+
+countPrimesIn : U64 -> Nat
+countPrimesIn = \limit ->
+    List.range { start: At 2, end: At limit }
+    |> List.countIf \n ->
+        if n < 4 then
+            Bool.true
+        else if Num.isEven n then
+            Bool.false
+        else
+            res =
+                List.range { start: At 3, end: At (Num.ceiling (Num.sqrt (Num.toF64 n))), step: 2 }
+                |> List.any \a -> Num.isMultipleOf n a
+                |> Bool.not
+
+            res
+
+expect
+    (
+        countPrimesIn 100000
+        |> \expected ->
+            dbg expected
+
+            expected
+    )
+    == (
+        List.len (primesIn 100000)
+        |> \actual ->
+            dbg actual
+
+            actual
+
+    )

prime.roc

@@ -6,14 +6,18 @@ app "prime"
 main : Task.Task {} I32
 main =
     numStrings =
-        List.range { start: At 0u64, end: At 1_000_000u64 }
-        |> List.map \e -> isPrimePre e
-        |> List.walk [] primeWalk
+        primesIn 50_000_000
         |> List.map Num.toStr
         |> Str.joinWith "\n"
 
     Stdout.line "$(numStrings)"
 
+primesIn : U64 -> List U64
+primesIn = \n ->
+    List.range { start: At 0u64, end: At n }
+    |> List.map \e -> isPrimePre e
+    |> List.walk [] primeWalk
+
 PrimeResult : [No U64, Yes U64, Maybe U64]
 
 primeWalk : List U64, PrimeResult -> List U64
@@ -36,23 +40,49 @@ isPrimePre = \n ->
         No n
     else if n < 4 then
         Yes n
-    else if (firstPrimes |> List.any \p -> n > p && n % p == 0) then
+    else if Num.isEven n then
+        No n
+    else if
+        (
+            firstPrimes
+            |> List.dropIf \p -> n < p
+            |> List.any \p -> Num.isMultipleOf n p
+        )
+    then
         No n
     else
         Maybe n
 
+firstPrimes =
+    [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]
+
 isPrimePost : List U64, U64 -> Bool
 isPrimePost = \l, n ->
-    nFloat = Num.toF64 n
+    nFloat = Num.toF32 n
     valLimit = Num.ceiling (Num.sqrt nFloat)
     # approximate the number of primes < sqrt(n) to limit the range we have to check with a 25% error tolerance
-    valLimitF = Num.toF64 valLimit
+    valLimitF = Num.toF32 valLimit
     limit = Num.ceiling (valLimitF * 1.25 / (Num.log valLimitF))
     l
     |> List.sublist { start: 0, len: limit }
     |> List.dropIf \p -> p > valLimit
-    |> List.any \p -> n % p == 0
+    |> List.any \p -> Num.isMultipleOf n p
     |> Bool.not
 
-firstPrimes =
-    [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]
+countPrimesIn : U64 -> Nat
+countPrimesIn = \limit ->
+    List.range { start: At 2, end: At limit }
+    |> List.countIf \n ->
+        if n < 4 then
+            Bool.true
+        else if n % 2 == 0 then
+            Bool.false
+        else
+            res =
+                List.range { start: At 3, end: At (Num.ceiling (Num.sqrt (Num.toF64 n))), step: 2 }
+                |> List.any \a -> Num.isMultipleOf n a
+                |> Bool.not
+
+            res
+
+expect countPrimesIn 10000 == List.len (primesIn 10000)

prime2.roc

@@ -0,0 +1,93 @@
+app "prime2"
+    packages { pf: "https://github.com/roc-lang/basic-cli/releases/download/0.7.1/Icc3xJoIixF3hCcfXrDwLCu4wQHtNdPyoJkEbkgIElA.tar.br" }
+    imports [pf.Stdout, pf.Task]
+    provides [main] to pf
+
+main : Task.Task {} I32
+main =
+    numStrings =
+        primesIn 50_000_000
+        |> List.map Num.toStr
+        |> Str.joinWith "\n"
+
+    Stdout.line "$(numStrings)"
+
+primesIn : U64 -> List U64
+primesIn = \n ->
+    List.range { start: At 0, end: At n }
+    |> List.map Yes
+    |> primeSieve 0 n
+    |> List.keepIf isYes
+    |> List.map extractValueUnsafe
+
+PrimeResult : [No, Yes U64]
+
+primeSieve : List PrimeResult, U64, U64 -> List PrimeResult U64
+primeSieve = \l, idx, max ->
+    len = List.len l
+    when nextPrime l idx is
+        Ok p if (Num.powInt p 2) > max -> l
+        Ok p ->
+            setNo l (List.range { start: At (Num.toNat (p * 2)), step: Num.toNat p, end: At len })
+            |> primeSieve (idx + 1) max
+
+        Err _ -> l
+
+isYes : PrimeResult -> Bool
+isYes = \r ->
+    when r is
+        No -> Bool.false
+        Yes _ -> Bool.true
+
+setNo : List PrimeResult, List Nat -> List PrimeResult U64
+setNo = \l, idxs ->
+    when idxs is
+        [] -> l
+        [idx] -> l |> List.set idx No
+        [head, .. as tail] -> l |> List.set head No |> setNo tail
+
+nextPrime : List PrimeResult, U64 -> Result U64 [NotFound]
+nextPrime = \l, startIdx ->
+    l
+    |> List.dropFirst (Num.toNat (startIdx + 1))
+    |> List.findFirst isYes
+    |> Result.map extractValueUnsafe
+
+extractValueUnsafe : PrimeResult -> U64
+extractValueUnsafe = \res ->
+    when res is
+        Yes n -> n
+        No -> crash "No value found"
+
+countPrimesIn : U64 -> Nat
+countPrimesIn = \limit ->
+    List.range { start: At 2, end: At limit }
+    |> List.countIf \n ->
+        if n < 4 then
+            Bool.true
+        else if Num.isEven n then
+            Bool.false
+        else
+            res =
+                List.range { start: At 3, end: At (Num.ceiling (Num.sqrt (Num.toF64 n))), step: 2 }
+                |> List.any \a -> Num.isMultipleOf n a
+                |> Bool.not
+
+            res
+
+expect
+    (
+        countPrimesIn 100000
+        |> \expected ->
+            dbg expected
+
+            expected
+    )
+    == (
+        List.len (primesIn 100000)
+        |> \actual ->
+            dbg actual
+
+            actual
+
+    )