#! /usr/bin/gawk -f
# Last edited on 2012-08-02 19:56:05 by stolfilocal

# Finds best base image size for pyramid.

BEGIN { 
  if (nx == "") { arg_error(("must define {nx}")); }
  if (ny == "") { arg_error(("must define {ny}")); }

  # Best combination found so far:
  kbest = 0; fbest = 0; sxbest = 0; sybest = 0;
  for (x = 1; x <= 10; x++)
    { for (y = 1; y <= 10; y++)
        { if (((x % 2) != 0) || ((y % 2) != 0))
            { # The smallest image size is {sx,sy}: 
              sx = 5*x; sy = 5*y;
              if ((sx <= nx) && (sy <= ny))
                { # Find base image size {bx,by}
                  bx = sx; by = sy; k = 1;
                  while (1)
                    { tx = 7*bx/5; ty = 7*by/5;
                      if ((tx > nx) || (ty > ny)) { break; }
                      bx = tx; by = ty; k++;
                      tx = 10*bx/7; ty = 10*by/7;
                      if ((tx > nx) || (ty > ny)) { break; }
                      bx = tx; by = ty; k++;
                    }
                  
                  fx = bx/nx; fy = by/ny; f = fx*fy;
                  if ((k > kbest) || ((k == kbest) && (f > fbest)))
                  { sxbest = sx; sybest = sy; kbest = k; fbest = f; }
                  printf "%3d %3d  %3d  %6d %6d  %8.6f %8.6f %8.6f\n", sx,sy,k,bx,by,fx,fy,f;
                }
            }
        }
    }
  printf "best:\n";
  printf "%3d %3d  %3d  %8.6f\n", sxbest,sybest,kbest,fbest;
}

function arg_error(msg)
{ printf "** %s\n", msg > "/dev/stderr"; 
  exit(1);
}