Improve on the original prime to beat the sieve alorithm

prime-sieve.roc

@@ -1,31 +1,43 @@
 app "prime2"
     packages { pf: "https://github.com/roc-lang/basic-cli/releases/download/0.7.1/Icc3xJoIixF3hCcfXrDwLCu4wQHtNdPyoJkEbkgIElA.tar.br" }
-    imports [pf.Stdout, pf.Task]
+    imports [pf.Stdout, pf.Task, pf.Arg]
     provides [main] to pf
 
 main : Task.Task {} I32
 main =
+    max <- Task.await parseArg
     numStrings =
-        primesIn 50_000_000
+        primesIn max
         |> List.map Num.toStr
         |> Str.joinWith "\n"
 
     Stdout.line "$(numStrings)"
 
+parseArg =
+    args <- Task.await (Arg.list)
+    arg =
+        args
+        |> List.get 1
+        |> Result.withDefault "50_000_000"
+        |> Str.toU64
+    when arg is
+        Ok a -> a |> Task.ok
+        Err InvalidNumStr -> crash "Passed argument is not a numberr"
+
 primesIn : U64 -> List U64
 primesIn = \n ->
     numbers = List.concat [2] (List.range { start: At 3u64, end: At n, step: 2 })
-    primeSieve numbers
+    primeSieve numbers n
 
-primeSieve : List U64 -> List U64
-primeSieve = \l ->
+primeSieve : List U64, U64 -> List U64
+primeSieve = \l, max ->
     when l is
         [] -> []
         [a] -> [a]
-        [head, .., tail] if (Num.powInt head 2) > tail -> l
+        [head, ..] if (Num.powInt head 2) > max -> l
         [head, .. as tail] ->
             filteredList = List.dropIf tail (\e -> Num.isMultipleOf e head)
-            List.concat [head] (primeSieve filteredList)
+            List.concat [head] (primeSieve filteredList max)
 
 countPrimesIn : U64 -> Nat
 countPrimesIn = \limit ->
@@ -40,7 +52,6 @@ countPrimesIn = \limit ->
                 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

prime.roc

@@ -1,73 +1,62 @@
 app "prime"
     packages { pf: "https://github.com/roc-lang/basic-cli/releases/download/0.7.1/Icc3xJoIixF3hCcfXrDwLCu4wQHtNdPyoJkEbkgIElA.tar.br" }
-    imports [pf.Stdout, pf.Task]
+    imports [pf.Stdout, pf.Task, pf.Arg]
     provides [main] to pf
 
 main : Task.Task {} I32
 main =
+    max <- Task.await parseArg
     numStrings =
-        primesIn 50_000_000
+        primesIn max
         |> 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
+parseArg =
+    args <- Task.await (Arg.list)
+    arg =
+        args
+        |> List.get 1
+        |> Result.withDefault "50_000_000"
+        |> Str.toU64
+    when arg is
+        Ok a -> a |> Task.ok
+        Err InvalidNumStr -> crash "Passed argument is not a numberr"
 
-PrimeResult : [No U64, Yes U64, Maybe U64]
+primesIn : U64 -> List U64
+primesIn = \max ->
+    filterPrimesRec = \acc, l ->
+        when l is
+            [] -> acc
+            [head, .. as tail] if isPrimePost acc head ->
+                acc |> List.append head |> filterPrimesRec tail
 
-primeWalk : List U64, PrimeResult -> List U64
-primeWalk = \l, n ->
-    when n is
-        Yes n2 ->
-            List.append l n2
+            [_, .. as tail] -> filterPrimesRec acc tail
+    [2]
+    |> List.concat (List.range { start: At 3u64, end: At max, step: 2 })
+    |> \l -> filterPrimesRec [] l
 
-        Maybe n2 ->
-            if isPrimePost l n2 then
-                List.append l n2
-            else
-                l
+isPrimePost = \list, n ->
+    isPrimeRec = \l, limit ->
+        when l is
+            [_] -> Bool.true
+            [head, .. as tail] ->
+                if Num.isMultipleOf n head then
+                    Bool.false
+                else if head > limit then
+                    Bool.true
+                else
+                    isPrimeRec tail limit
 
-        No _ -> l
+            [] -> Bool.true
+    sqrtF = Num.sqrt (Num.toF32 n)
+    sqrtI = Num.floor sqrtF
 
-isPrimePre : U64 -> PrimeResult
-isPrimePre = \n ->
-    if n < 2 then
-        No n
-    else if n < 4 then
-        Yes n
-    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
+    if Num.isZero (sqrtF - Num.toF32 sqrtI) then
+        Bool.false
     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.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.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 -> Num.isMultipleOf n p
-    |> Bool.not
+        isPrimeRec list (sqrtI + 1)
 
 countPrimesIn : U64 -> Nat
 countPrimesIn = \limit ->
@@ -75,14 +64,26 @@ countPrimesIn = \limit ->
     |> List.countIf \n ->
         if n < 4 then
             Bool.true
-        else if n % 2 == 0 then
+        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
+            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
+
+expect
+    (
+        countPrimesIn 1000000
+        |> \expected ->
+            dbg expected
+
+            expected
+    )
+    == (
+        List.len (primesIn 1000000)
+        |> \actual ->
+            dbg actual
 
-            res
+            actual
 
-expect countPrimesIn 10000 == List.len (primesIn 10000)
+    )