Data update

Task/Legendre-prime-counting-function/FreeBASIC/legendre-prime-counting-function.basic

@@ -1,24 +1,45 @@
-Function isPrime(n As Uinteger) As Boolean
-    Dim As Uinteger i
-    For i = 2 To Sqr(n)
-        If n Mod i = 0 Then Return False
-    Next i
-    Return True
+Sub primeSieve(limit As Uinteger, primes() As Uinteger)
+    Dim As Uinteger i, j
+    Dim As Uinteger sieve(limit)
+
+    For i = 2 To limit
+        sieve(i) = 1
+    Next
+
+    For i = 2 To limit
+        If sieve(i) Then
+            Redim Preserve primes(Ubound(primes) + 1)
+            primes(Ubound(primes)) = i
+            For j = i * i To limit Step i
+                sieve(j) = 0
+            Next
+        End If
+    Next
+End Sub
+
+Function phi(x As Uinteger, a As Uinteger, primes() As Uinteger) As Uinteger
+    If a <= 1 Then Return Iif(a < 1, x, x - (x \ 2))
+
+    Dim As Uinteger pa = primes(a - 1)
+    If x <= pa Then Return 1
+
+    Return phi(x, a - 1, primes()) - phi(x \ pa, a - 1, primes())
 End Function
 
-Dim As Uinteger n, i, j, count
-Dim Shared As Ulongint primes(1e8)
-n = 1
+Function pi(n As Uinteger) As Uinteger
+    If n < 3 Then Return Iif(n < 2, 0, 1)
+
+    Dim As Uinteger primes()
+    primeSieve(Int(Sqr(n)), primes())
+
+    Dim As Uinteger a = Ubound(primes) + 1
+    Return phi(n, a, primes()) + a - 1
+End Function
+
+Dim As Uinteger i, n = 1
 For i = 0 To 9
-    count = 0
-    For j = 2 To n
-        If isPrime(j) Then
-            count += 1
-            primes(count) = j
-        End If
-    Next j
-    Print "10^"; i; "  "; count
+    Print "10^" & i & "  " & pi(n)
     n *= 10
-Next i
+Next
 
 Sleep