MOD bug? Or something else?

Seems to be a bug in MOD. The values inside the range from 0 to 1 that should result in MOD of 0 (or 0 to machine precision) for the example below (i.e., 0.4 and 0.8) are no where near 0.

>> [-2:.2:2;mod(-2:.2:2,.4)]'

ans =

   -2.0000         0
   -1.8000    0.2000
   -1.6000         0
   -1.4000    0.2000
   -1.2000         0
   -1.0000    0.2000
   -0.8000    0.0000
   -0.6000    0.2000
   -0.4000    0.0000
   -0.2000    0.2000
         0         0
    0.2000    0.2000
    0.4000    0.4000
    0.6000    0.2000
    0.8000    0.4000
    1.0000    0.2000
    1.2000         0
    1.4000    0.2000
    1.6000         0
    1.8000    0.2000
    2.0000         0

I am running R2011a on UNIX... anyone else encounter this problem?

Answer 1

[Matt Fig]

Floating point arithmetic.... Look closely at the numbers.

x = [-2:.2:2];
fprintf('%16.16f\n',x)

You can read more about it here.

[Dr. Seis]

Yep... I was thinking this had nothing to do with floating point stuff. But if the value was very close to 0.4 (i.e., 0.4 +/- epsilon), the behavior of MOD would be very different if it was +epsilon versus -epsilon.

mod(0.39999999999,0.4) = 0.39999999999

vs.

mod(0.40000000001,0.4) = 0.00000000001

Looks like I will need to overload MOD

Answer 2

[Dr. Seis]

This overloaded MOD function seems to overcome my issue:

function answer = mod(X,Y)
  tol = 1e7;
  X = round(X*tol)/tol;
  Y = round(Y*tol)/tol;
  answer = builtin('mod',X,Y);
end

*Note: I am dealing with numbers with less than 7 significant digits