Trigonometric Rounding errors

[NoteToSelf]

I've been trying to create a rotational operator using the rotational matrix R (2x2 matrix).

The elements of this matrix consist of trigonometrical functions, cos and sin from the cmath library, which take the angle in radians as their argument.

Problem is, when I try to input a multiple of pi (taken as acos(1.)) close to a known value, there is a significant rounding error.

For example; cos( pi / 2 ) = cos (90 deg) should equal 0; but the value returned is 6.12323e-17. Which is very close...but not quite right (because the value for Pi is not exact).

I've tried adding a check:

	double A = cos(DEG), B = sin(DEG);
	if (A < -0.9999999){A = ceil(A);}
	if (B < -0.9999999){B = ceil(B);}
	if (A > -0.0000001 && A < 0.0000001){A = 0.;}
	if (B > -0.0000001 && B < 0.0000001){B = 0.;}
	if (A > 0.9999999){A = floor(A);}
	if (B > 0.9999999){B = floor(B);}
	cout << "A" << A << endl;
	cout << "B" << B << ",\t-B" << -B << endl;	
	

These I think should round to the nearest key value; but A still returns the value 6.12323e-17 for cos( pi / 2) after this. Surely it should fall into the middle case for A?

[hamsterman]

When doing floating point arithmetics, errors are something you have to live with. Is there really something wrong with an error of 6*10^-17 ? I really doubt that..

[NoteToSelf]

Managed to fit a rounding method in in the end.
The reason I wanted to round it up is because I thought it might have been the cause of an error later in the function, but it's looking more like a reference mistake (a value of the order e+66 is returned where a 1 is expected).

So while 6*10-17 is pretty much 0 for this application, and should work, a matrix of
/ 0 1 \
\ -1 0 /
is a lot easier for me to process than:
/ 6.12323*10-17 1 \
\ -1 6.12323*10-17 /

EDIT: Found and fixed the problem causing the e+66 error - rounding is just to clean up the output coordinates, which should be simple enough now using the above code segment
(reason it wasn't working before was I was editing a different class to the one I was testing /facepalm)

[anonymous23323124]

Surely you have to process an arbitrary matrix. How does it make it easier if in one particular case the matrix becomes <<0, 1>, <-1, 0>>?

[NoteToSelf]

I mistakenly thought a non-zero result would skew a different part of my code.

This rotation works for a number of polygons, but one of the classes (rectangle) has a check to ensure that it is a rectangle (dot product for each pair of consecutive sides, should = 0).

My fear was that after a rotation, because of the non-zero component it would fail the check and not acknowledge that the final result was still a rectangle. This is incorrect though, as the error is consistent for each of the sides.
In fact; including the correction would have messed up the check more than leaving it be.

[anonymous23323124]

If you are concerned about equality checks failing due to error, you could do something like this. Replace:
if (double_variable == 0) // etc
with

const double tolerance = <choose some tolerance>;
// etc
if (fabs(double_variable) < tolerance) // etc 

It's not great, but it would work.

[NoteToSelf]

Looks like it would work - but given the other features yet to be fixed I think I'll just explain where the error comes from in the comments and documentation.

Thanks everyone!