mardi 14 juin 2016

F# Performace: What is making this code so slow?

This F# code is an attempt to solve Project Euler problem #58:

let inc = function
| n -> n + 1
let is_prime = function
| 2 -> true
| n when n < 2 || n%2=0-> false 
| n -> 
       [3..2..(int (sqrt (float n)))] 
       |> List.tryFind (fun i -> n%i=0)
       |> Option.isNone
let spir = Seq.initInfinite (fun i -> 
    let n = i%4
    let a = 2 * (i/4 + 1)
    (a*n) + a + (a-1)*(a-1))
let rec accum se p n = 
   match se with
   | x when p*10 < n && p <> 0 -> 2*(n/4) + 1
   | x when is_prime (Seq.head x) -> accum (Seq.tail x) (inc p) (inc n)
   | x -> accum (Seq.tail x) p (inc n)
   | _ -> 0
printfn "%d" (accum spir 0 1)

I do not know the running time of this program because I refused to wait for it to finish. Instead, I wrote this code imperatively in C++:

#include "stdafx.h"
#include "math.h"
#include <iostream>

using namespace std;

int is_prime(int n)
{
    if (n % 2 == 0) return 0;
    for (int i = 3; i <= sqrt(n); i+=2)
    {
        if (n%i == 0)
        {
            return 0;
        }
    }
    return 1;
}

int spir(int i)
{
    int n = i % 4;
    int a = 2 * (i / 4 + 1);
    return (a*n) + a + ((a - 1)*(a - 1));
}

int main()
{
    int n = 1, p = 0, i = 0;
    cout << "start" << endl;
    while (p*10 >= n || p == 0)
    {
        p += is_prime(spir(i));
        n++; i++;
    }
    cout << 2*(i/4) + 1;

    return 0;
}

The above code runs in less than 2 seconds and gets the correct answer.

What is making the F# code run so slowly? Even after using some of the profiling tools mentioned in an old Stackoverflow post, I still cannot figure out what expensive operations are happening.

Edit #1

With rmunn's post, I was able to come up with a different implementation that gets the answer in a little under 30 seconds:

let inc = function
| n -> n + 1
let is_prime = function
| 2 -> true
| n when n < 2 || n%2=0-> false 
| n -> 
       [3..2..(int (sqrt (float n)))] 
       |> List.tryFind (fun i -> n%i=0)
       |> Option.isNone
let spir2 = 
    List.unfold (fun state -> 
        let p = fst state
        let i = snd state
        let n = i%4
        let a = 2 * (i/4 + 1)
        let diag = (a*n) + a + (a-1)*(a-1)
        if p*10 < (i+1) && p <> 0 then 
            printfn "%d" (2*((i+1)/4) + 1)
            None
        elif is_prime diag then
            Some(diag, (inc p, inc i))
        else Some(diag, (p, inc i))) (0, 0)

Edit #2

With FuleSnabel's informative post, his is_prime function makes the above code run in under a tenth of a second, making it faster than the C++ code:

let inc = function
| n -> n + 1
let is_prime = function
  | 1                 -> false
  | 2                 -> true
  | v when v % 2 = 0  -> false
  | v ->
    let stop = v |> float |> sqrt |> int
    let rec loop vv =
      if vv <= stop then
        if (v % vv) <> 0 then
          loop (vv + 2)
        else
          false
      else
        true
    loop 3
let spir2 = 
    List.unfold (fun state -> 
        let p = fst state
        let i = snd state
        let n = i%4
        let a = 2 * (i/4 + 1)
        let diag = (a*n) + a + (a-1)*(a-1)
        if p*10 < (i+1) && p <> 0 then 
            printfn "%d" (2*((i+1)/4) + 1)
            None
        elif i <> 3 && is_prime diag then
            Some(diag, (inc p, inc i))
        else Some(diag, (p, inc i))) (0, 0)

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