Trig functions lose precision at large angles

[adroitwhiz]

Expected Behavior

Since trigonometric functions are periodic, they should output the same values for angles modulo 360.

Actual Behavior

At very large angles, trigonometric functions (as implemented in the underlying JavaScript VM) accumulate rounding error.

Here's a test case. Mash the spacebar enough and the problem will manifest. Note that these angles are still less than Number.MAX_SAFE_INTEGER. I've confirmed this on Linux Chrome + Firefox and Windows Firefox.

[ecc521]

Even though the numbers are less than Number.MAX_SAFE_INTEGER, we are still encountering issues with floating point integers.

For example, try running Math.sin(360/180*Math.PI) - You will not get zero, but rather a number very close to zero (-2.4492935982947064e-16)

As you double the angle, you can see that the difference from zero is doubling. This happens because when converting from degrees to radians, we multiply by PI, an irrational number that can not be exactly represented. As the angle increases, the exponent bit of the floating point integer must be increased by 1, causing decimal precision to be halved, which eventually leads to large inaccuracies.

This issue can be remedied by taking the degrees modulo 360 before converting to radians. For example:

Old Method:

Math.sin(1509949440/180*Math.PI) //Off by about 1e-9

New Method:

Math.sin(1509949440%360/180*Math.PI) //Returns 0, the correct answer