Re: [Caml-list] Multiplication of matrix in C and OCaml

["Frédéric Gava" <gava@univ-paris12.fr>]

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> Because, as Jacques told you already, your C code is wrong.  "add" and
> "mult" invoke undefined behaviors of C and therefore gcc feels free to
> optimize these functions as no-ops at optimization levels 1 and above.
> That's a major speedup, for sure.  Why don't you check your code for
> correctness first before drawing conclusions on performance?

Sorry for the inconvenience and this stupid error: I am a very bad C 
programmer.

But, I do not obtain the performance of Jacques Garrigue :-( I try to 
bench a parallel matrix multiplication algorithm and test the difference 
between C+MPI and OCaml+MPI (I try to prove that OCaml is efficient 
enought for high-performance, in this community, they largely prefer 
Fortran or C...))


a) with a "polymorphic" C program (using 
"multiply_complex_generic(i,complexe_add,complexe_mult,a,b,c);")

time ./cmult 600 2 602 1
real    0m18.402s
user    0m17.333s
sys     0m0.044s

b) for a monomorphic C programs (using "multiply_complex(i,a,b,c);");

time ./cmult 600 2 602 1
real    0m5.604s
user    0m5.556s
sys     0m0.036s


c) for a polymorphic OCaml program  (using 
"ignore(multiplication_polymorphic (!i) Complex.zero Complex.add 
Complex.mul a b c);")

time ./ocamlmult 600 2 602 1

real    0m16.433s
user    0m16.125s
sys     0m0.068s

d) for a monomorphic OCaml program  (using 
"ignore(multiplication_monomorphic (!i) a b c);")

time ./ocamlmult 600 2 602 1

real    0m15.460s
user    0m15.345s
sys     0m0.072s

I win 1 second if I compile with "-inline 100". So I have not the "twice 
slower at most".

thanks,
Frédéric Gava

ps: here I have test the programs ;-)

[-- Attachment #2: mult.c --]
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/* param 1 = size of the matrices at the beginning
   param 2 = incrementation
   param 3 = size of the matrices at the end
   param 4 = number of iteration 

with 
gcc -O3 -o cmult mult.c

*/

#include <stdlib.h> 
#include <stdio.h> 
#include <math.h>

typedef struct Complexe {double re; double img;} complexe;

complexe zero;

__inline__ complexe complexe_add(complexe a, complexe b)
{
 return (complexe){a.re+b.re, a.img+b.img};
}


__inline__ complexe complexe_mult(complexe x, complexe y)
{
 return (complexe) {x.re*y.re-x.img*y.img, x.re*y.img+x.img*y.re};
}


complexe random_complexe(void)
{
 complexe c = {c.re=(double)(rand()%1000), c.img=(double)(rand()%1000)};
 return c;
}


void multiply_complex(int n, complexe *a, complexe *b, complexe *c)
{
 register int i,j,k;
 complexe tmp;

  for (i=0; i<n; i++) 
   {
    for (j=0;j<n;j++)
     {
      tmp=zero;
      for (k=0;k<n;k++) 
       tmp=complexe_add(tmp,(complexe_mult(b[k*n+j],a[i*n+k])));
      c[i*n+j]=tmp;
     }
  }
 return;
}

void multiply_complex_generic(int n, complexe (*add)(complexe x, complexe y) , complexe (*mult)(complexe x, complexe y),complexe *a, complexe *b, complexe *c)
{
 register int i,j,k;
 complexe tmp;

  for (i=0; i<n; i++) 
   {
    for (j=0;j<n;j++)
     {
      tmp=zero;
      for (k=0;k<n;k++) 
       tmp=add(tmp,(mult(b[k*n+j],a[i*n+k])));
      c[i*n+j]=tmp;
     }
  }
 return;
}


int main(int argc, char* argv[])
{
 complexe *a, *b, *c;
 int i,j,k,t1,pas,maxi,iter;

 zero.re=(double)0;
 zero.img=(double)0;
 
 i=atoi(argv[1]);
 pas=atoi(argv[2]);
 maxi=atoi(argv[3]);
 iter=atoi(argv[4]);

 srand(1000);
 while (i<maxi)
  {  
   /* initialisation des matrices */
   a=(complexe *)malloc(i*i*sizeof(complexe));
   b=(complexe *)malloc(i*i*sizeof(complexe));
   c=(complexe *)malloc(i*i*sizeof(complexe));
      
   for (j=0;j<i;j++)
    for (k=0,t1=j*i;k<i;k++)
     {
      a[t1+k]=random_complexe();
      b[t1+k]=random_complexe();
     }

  for (k=1;k<=iter;k++) 
   multiply_complex(i,a,b,c);
   /* multiply_complex_generic(i,complexe_add,complexe_mult,a,b,c); */

      

  /* suppression des vieilles matrices */
  free((complexe *)a);
  free((complexe *)b);
  free((complexe *)c);

  i=i+pas;
  }
 return 0;
}

[-- Attachment #3: mult.ml --]
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(* param 1 = size of the matrices at the beginning
   param 2 = incrementation
   param 3 = size of the matrices at the end
   param 4 = number of iteration 

ocamlopt -unsafe -o ocamlmult mult.ml

*)

let multiplication_polymorphic n zero add mul a b c =
  for i=0 to n-1 do
   for j=0 to n-1 do
    let rec loop tmp k =
     if k=n then tmp else loop (add tmp (mul b.(k*n+j) a.(i*n+k))) (k+1)
    in 
     c.(i*n+j)<-loop zero 0
   done
  done

let multiplication_monomorphic n a b c =
 let tmp=ref Complex.zero in
  for i=0 to n-1 do
   for j=0 to n-1 do
    for k=0 to n-1 do
      tmp:=Complex.add !tmp (Complex.mul b.(k*n+j) a.(i*n+k))
    done;
    c.(i*n+j)<-(!tmp)
   done
  done
(* same efficienty with the loop function *)

let random_complex n = {Complex.re=Random.float n; im=Random.float n}

let matrixRandom n = Array.init (n*n) (fun _ -> random_complex 1000.)

let _ = 
	Random.self_init();
        let i = ref (int_of_string (Sys.argv).(1))
	and pas=(int_of_string (Sys.argv).(2))
	and maxi=(int_of_string (Sys.argv).(3)) 
	and iter=(int_of_string (Sys.argv).(4)) in
	while !i<maxi do
         let a=matrixRandom (!i)
         and b=matrixRandom (!i)
         and c=Array.make ((!i)*(!i)) Complex.zero in
	  for j=1 to iter do
           (* ignore(multiplication_polymorphic (!i) Complex.zero Complex.add Complex.mul a b c); *)
	   ignore(multiplication_monomorphic (!i) a b c);
          done;
	 i:=!i+pas;
	done