Round error using if statement. Two things don't equal each other

Ok this is the problem I am having.

I have an M-File containing the following...

>> x = sin(pi/6)
>> y = cos(pi/6)
>> mytan = x/y;
>> if mytan == tan (pi/6)
          disp('equal')
      else
          disp('not equal')
      end

......

When I run it, I want to get 'equal' to display but I keep getting 'not equal'

I know x = .5000 or .500000000000000 using format long

and y = .8660 or .866025403784439 using format long.

now mytan = x/y

comes out to be .5774 or 0.577350269189626 using format long

and tan(pi/6) is .5774 or 0.577350269189626 using format long

I should be getting the "equal to display"

however I am not.

Im pretty sure this is due to round off error, so how should I change my if statement to get the equal message to display.

Thank You

Answer 1

[Fangjun Jiang]

You are right about floating point rounding error. You can use eps

x = sin(pi/6)
y = cos(pi/6)
mytan = x/y;
if abs(mytan-tan(pi/6))<eps
  disp('equal')
else
  disp('not equal')
end

[Walter Roberson]

Fangjun, did you happen to reformat the question to get the >> to look right? I'm chasing an obscure formatting bug that was there earlier and now is gone!

[Fangjun Jiang]

Yes, I did the re-formating. But I didn't pay particular attention. What type of problem did you have before?

[Walter Roberson]

The original text with the >> lines was visually correct, and appeared to have 2 spaces at the beginning of every line, and showed up as formatted in the preview, but in the actual message display it showed up as if it was unformatted. I have encountered exactly the same situation once before and was hoping to preserve it so Mathworks could look at the binary of the file. Oh well. Next time.

Answer 2

[Walter Roberson]

This is a known and unavoidable issue in any finite-precision computer, no matter what the base of arithmetic (decimal, binary, hex, whatever) that it uses. For more information, please read this FAQ

Answer 3

[Derrick]

Thank you Fangjun this worked for me. I was aware of eps and abs() i just didnt think to put them in like that. Thanks again.