Data commit

Task/Legendre-prime-counting-function/CoffeeScript/legendre-prime-counting-function.coffee

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+sorenson = require('sieve').primes  # Sorenson's extensible sieve from task: Extensible Prime Generator
+
+# put in outer scope to avoid recomputing the cache
+memoPhi = {}
+primes = []
+
+isqrt = (x) -> Math.floor Math.sqrt x
+
+pi = (n) ->
+    phi = (x, a) ->
+        y = memoPhi[[x,a]]
+        return y unless y is undefined
+
+        memoPhi[[x,a]] =
+            if a is 0 then x
+            else
+                p = primes[a - 1]
+                throw "You need to generate at least #{a} primes." if p is undefined
+                phi(x, a - 1) - phi(x // p, a - 1)
+
+    if n < 2
+        0
+    else
+        a = pi isqrt n
+        phi(n, a) + a - 1
+
+maxPi = 1e9
+gen = sorenson()
+primes = while (p = gen.next().value) < isqrt maxPi then p
+
+n = 1
+for i in [0..9]
+    console.log "10^#{i}\t#{pi(n)}"
+    n *= 10