ocaml and int64

Ludovic Coquelle
 Jon Harrop
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Date:   (:) 
From:  Jon Harrop <jon@f...> 
Subject:  Re: [Camllist] ocaml and int64 
On Wednesday 02 April 2008 01:54:54 Ludovic Coquelle wrote: > Hi, > > I wrote a direct translation of a simple algo from F# to ocaml. > (details can be found here: > http://khigia.wordpress.com/2008/03/30/ocamlvsfforbigintegersurprisin >gperformancetest/ ) > > The compile F# program (12s) is much faster than Ocaml (30s), probably > because the algo do integer arithmetic with Int64 module (thanks to David > for this info). > > Have someone here face this kind of problem (optimizing a code doing > arithmetic on big integer)? > Any advice to improve the Ocaml code (without changing the algo)? Get a 64bit machine. ;) There are some performance pitfalls in your code (which takes 21s on my machine): . OCaml makes no attempt to optimize integer div and mod so avoid these at all costs. In this case, use bitwise ANDs and shifts. . Int64 is boxed by default and your use of recursion is likely to worsen this effect. Optimizing for these, the following code takes only 4.6s, which is 4.6x faster than your original: let int = Int64.to_int let int64 = Int64.of_int let ( +: ) = Int64.add let ( : ) = Int64.sub let ( *: ) = Int64.mul let ( >>> ) = Int64.shift_right let rec seq_length x n = match x with  0L > n +: 1L  1L > seq_length 0L (n +: 1L)  x when int x land 1 = 0 > seq_length (x >>> 1) (n +: 1L)  _ > seq_length (3L *: x +: 1L) (n +: 1L) let rec loop i imax n = let n' = seq_length i 0L in let imax, n = if n' > n then (i, n') else (imax, n) in if i < 1000000L then loop (i +: 1L) imax n else imax let _ = print_string (Int64.to_string (loop 1L 0L 0L)) Using 63bit ints on a 64bit machine, the time drops to only 2s: let rec seq_length x n = match x with  0 > n + 1  1 > seq_length 0 (n + 1)  x when x land 1 = 0 > seq_length (x lsr 1) (n + 1)  _ > seq_length (3*x + 1) (n + 1) let rec loop i imax n = let n' = seq_length i 0 in let imax, n = if n' > n then (i, n') else (imax, n) in if i < 1000000 then loop (i+1) imax n else imax let _ = print_string (string_of_int (loop 1 0 0)) As you have allured to, algorithmic optimizations buy you even more. The following implementation is several times faster again, taking only 0.6s to complete: let int = Int64.to_int let int64 = Int64.of_int let ( +: ) = Int64.add let ( : ) = Int64.sub let ( *: ) = Int64.mul let rec inside a n = if n<=1L then 0 else if a.(int n)>0 then a.(int n) else let p = if int n land 1 = 0 then inside a (Int64.shift_right n 1) else let n = 3L *: n +: 1L in if n < int64(Array.length a) then inside a n else outside a n in a.(int n) < 1 + p; 1 + p and outside a n = let n = if int n land 1 = 0 then Int64.shift_right n 1 else 3L *: n +: 1L in 1 + if n < int64(Array.length a) then inside a n else outside a n let euler14 n = let a = Array.create (n+1) 0 in let longest_n = ref 0 and longest_len = ref 0 in for n=1 to n do let len = inside a (int64 n) in if len > !longest_len then begin longest_n := n; longest_len := len end done; !longest_n, !longest_len let () = let n, len = euler14 1000000 in Printf.printf "%d: %d\n%!" n len Converting this to use native ints on my 64bit machine the time drops to only 0.2s, which is over 100x faster than your original! However, this benchmark really plays to F#'s strengths and you will probably never beat F# here. My best F# is 3x faster than anything I can write in OCaml, not least because it is trivial to parallelize efficiently but also because F# and .NET automate many relevant optimizations. HTH.  Dr Jon D Harrop, Flying Frog Consultancy Ltd. http://www.ffconsultancy.com/products/?e