Data commit

Task/Legendre-prime-counting-function/11l/legendre-prime-counting-function.11l

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+F primes_up_to_limit(Int limit)
+   [Int] r
+   I limit >= 2
+      r.append(2)
+
+   V isprime = [1B] * ((limit - 1) I/ 2)
+   V sieveend = Int(sqrt(limit))
+   L(i) 0 .< isprime.len
+      I isprime[i]
+         Int p = i * 2 + 3
+         r.append(p)
+         I i <= sieveend
+            L(j) ((p * p - 3) >> 1 .< isprime.len).step(p)
+               isprime[j] = 0B
+   R r
+
+V p = primes_up_to_limit(Int(sqrt(1'000'000'000)))
+
+F phi(x, =a)
+   F phi_cached(x, a)
+      [(Int, Int) = Int] :cache
+      I (x, a) C :cache
+         R :cache[(x, a)]
+      V r = phi(x, a)
+      :cache[(x, a)] = r
+      R r
+
+   V res = 0
+   L
+      I a == 0 | x == 0
+         R x + res
+
+      a--
+      res -= phi_cached(x I/ :p[a], a)
+
+F legpi(n)
+   I n < 2
+      R 0
+
+   V a = legpi(Int(sqrt(n)))
+   R phi(n, a) + a - 1
+
+L(e) 10
+   print(‘10^’e‘ ’legpi(10 ^ e))