September Morn Update

Task/Extensible-prime-generator/Elixir/extensible-prime-generator.elixir

@@ -0,0 +1,63 @@
+defmodule PrimesSoEMap do
+  @typep stt :: {integer, integer, integer, Enumerable.integer, %{integer => integer}}
+
+  @spec advance(stt) :: stt
+  defp advance {n, bp, q, bps?, map} do
+    bps = if bps? === nil do Stream.drop(oddprms(), 1) else bps? end
+    nn = n + 2
+    if nn >= q do
+      inc = bp + bp
+      nbps = bps |> Stream.drop(1)
+      [nbp] = nbps |> Enum.take(1)
+      advance {nn, nbp, nbp * nbp, nbps, map |> Map.put(nn + inc, inc)}
+    else if Map.has_key?(map, nn) do
+      {inc, rmap} = Map.pop(map, nn)
+      [next] =
+        Stream.iterate(nn + inc, &(&1 + inc))
+          |> Stream.drop_while(&(Map.has_key?(rmap, &1))) |> Enum.take(1)
+      advance {nn, bp, q, bps, Map.put(rmap, next, inc)}
+    else
+      {nn, bp, q, bps, map}
+    end end
+  end
+
+  @spec oddprms() :: Enumerable.integer
+  defp oddprms do # put first base prime cull seq in Map so never empty
+    # advance base odd primes to 5 when initialized
+    init = {7, 5, 25, nil, %{9 => 6}}
+    [3, 5] # to avoid race, preseed with the first 2 elements...
+      |> Stream.concat(
+            Stream.iterate(init, &(advance &1))
+              |> Stream.map(fn {p,_,_,_,_} -> p end))
+  end
+
+  @spec primes() :: Enumerable.integer
+  def primes do
+    Stream.concat([2], oddprms())
+  end
+
+end
+
+IO.write "The first 20 primes are:\n( "
+PrimesSoEMap.primes() |> Stream.take(20) |> Enum.each(&(IO.write "#{&1} "))
+IO.puts ")"
+IO.write "The primes between 100 to 150 are:\n( "
+PrimesSoEMap.primes() |> Stream.drop_while(&(&1<100))
+  |> Stream.take_while(&(&1<150)) |> Enum.each(&(IO.write "#{&1} "))
+IO.puts ")"
+IO.write "The number of primes between 7700 and 8000 is:  "
+PrimesSoEMap.primes() |> Stream.drop_while(&(&1<7700))
+  |> Stream.take_while(&(&1<8000)) |> Enum.count |> IO.puts
+IO.write "The 10,000th prime is:  "
+PrimesSoEMap.primes() |> Stream.drop(9999)
+  |> Enum.take(1) |> List.first |>IO.puts
+IO.write "The sum of all the priems to two million is:  "
+testfunc =
+  fn () ->
+    ans =
+      PrimesSoEMap.primes() |> Stream.take_while(&(&1<=2000000))
+        |> Enum.sum() |> IO.puts
+    ans end
+:timer.tc(testfunc)
+  |> (fn {t,_} ->
+    IO.puts "This test bench took #{t} microseconds." end).()