MiniZinc int out of range

Question

I am trying to create a function in MiniZinc that can determine the distance between a line and a point. I want the function to only use integers. My idea is as follows: In the case the point is not perpendicular to the line, the closest point should be chosen. If the point is perpendicular to the line, I want to approximate the point and then calculate the distance to the approximated point.

However when I am implementing this, I keep getting errors like below with Gecode and other solvers:

Error: The literal '-8004400200000' of the type int is out of range (-2147483646..2147483646) in line no. 13
Error: syntax error, unexpected FZ_DOTDOT in line no. 13
=====ERROR=====

Why does it say the int is out of range when they are nowhere near the maximum integer value?

My code:

var 0..100: u;
var 0..100: v;
var 0..100: w;
var 0..100: x;
var 0..100: y;
var 0..100: z;

var 0..20000: a = distancePointLine(u, v, w, x, y, z);

function var 0..20000: distancePointLine(var 0..100: x, var 0..100: y, var 0..100: x1, var 0..100: y1, var 0..100: x2, var 0..100: y2) =
  let {
  var -200..200: dot = (x-x1) * (x2-x1) + (y-y1) * (y2-y1);
  var -2000..2000: dot10 = ((x-x1) * (x2-x1) + (y-y1) * (y2-y1)) * 10;
  var -20000..20000: len = (x2-x1) * (x2-x1) + (y2-y1) * (y2-y1);
  var 0..2000: param = if len == 0 then -1 else dot div len endif;
  var 0..10: onLine = if param != 0 then 1 else dot10 div len endif;
  var 0..100: xLine = if param < 0 then x1 elseif param >= 1 then x2 else pointLine(x1,x2,onLine) endif;
  var 0..100: yLine = if param < 0 then y1 elseif param >= 1 then y2 else pointLine(y1,y2,onLine) endif;
  var 0..20000: distance = (x-xLine) * (x - xLine) + (y-yLine) * (y-yLine);
  } in distance;
  
function var 0..100: pointLine(var int: x1, var int: x2, var 0..10: segment) = 
  let {
    var 0..100: point = 10 * x1 + segment * (x1-x2) div 10;
  } in point;
  
solve maximize a;

output [
         "Res: \(a) ",
         ];
    ```

Answer 1

The error indicates that some calculated value (-8004400200000) is outside the possible supported domain of a variable (which is in the range -2147483646..2147483646 for Gecode). And the reason for that is the unlimited (and large) domains in distancePointLine were most variables are defined as var int, e.g. dot, dot10, len; and distance has a very large domain.

To fix the error for this specific problem, you can restrict the domain of the variable a, e.g.

var 0..10000: a = distancePointLine(7, 6, w, x, 100, 100);   

Gecode then generate this solution:

Res: 8649 
----------
==========

However, some solvers (e.g. Chuffed) still has problem even with this: it throws Cannot handle non-sign-fixed vars.

A better approach would be to restrict the domains of the variables in the function distancePointLine, if possible.