Improve prime algorithm

prime.roc

@@ -33,9 +33,10 @@ primesIn = \max ->
                 acc |> List.append head |> filterPrimesRec tail
 
             [_, .. as tail] -> filterPrimesRec acc tail
+    # Only take odd numbers so we only have to check half of all numbers
     [2]
     |> List.concat (List.range { start: At 3u64, end: At max, step: 2 })
-    |> \l -> filterPrimesRec [] l
+    |> \l -> filterPrimesRec (List.withCapacity (Num.toNat (Num.divTrunc max 4))) l
 
 isPrimePost = \list, n ->
     isPrimeRec = \l, limit ->
@@ -44,6 +45,7 @@ isPrimePost = \list, n ->
             [head, .. as tail] ->
                 if Num.isMultipleOf n head then
                     Bool.false
+                    # Limit check if we exceeded the squareroot
                 else if head > limit then
                     Bool.true
                 else
@@ -53,11 +55,14 @@ isPrimePost = \list, n ->
     sqrtF = Num.sqrt (Num.toF32 n)
     sqrtI = Num.floor sqrtF
 
+    # Check for an integer square root without ceiling operations to avoid linker errors
     if Num.isZero (sqrtF - Num.toF32 sqrtI) then
         Bool.false
     else
         isPrimeRec list (sqrtI + 1)
 
+### TESTING STUFF ###
+# Dumb primes for testing
 countPrimesIn : U64 -> Nat
 countPrimesIn = \limit ->
     List.range { start: At 2, end: At limit }
@@ -87,3 +92,20 @@ expect
             actual
 
     )
+
+expect
+    (
+        countPrimesIn 2
+        |> \expected ->
+            dbg expected
+
+            expected
+    )
+    == (
+        List.len (primesIn 2)
+        |> \actual ->
+            dbg actual
+
+            actual
+
+    )