Question

I have been given the task of using java to produce a Sin table, however I seem to get some very weird results for some values of the input. I am using the below

System.out.println("| sin(" + currentPoint + ") = " + Math.sin(Math.toRadians(currentPoint)));

Where (int) currentPoint is a value in degrees (eg 90)

These are results I find weird

| sin(360) = -2.4492935982947064E-16
| sin(180) = 1.2246467991473532E-16
| sin(150) = 0.49999999999999994
| sin(120) = 0.8660254037844387

Expecting

sin(360) = 0
sin(180) = 0
sin(150) = 0.5
sin(120) = 0.866025404

Am I missing something?

Answer 1

You’re dealing with floating point numbers, looking for exact answers isn’t going to work for all values. Take a look at
What Every Computer Scientist Should Know About Floating-Point Arithmetic. You want your tests to be equivalent to your expectations within some delta. Note that the answers you’re getting are pretty close. It’s expressing values in bits that’s biting you.

From the link:

Squeezing infinitely many real numbers into a finite number of bits requires an approximate representation. Although there are infinitely many integers, in most programs the result of integer computations can be stored in 32 bits. In contrast, given any fixed number of bits, most calculations with real numbers will produce quantities that cannot be exactly represented using that many bits. Therefore the result of a floating-point calculation must often be rounded in order to fit back into its finite representation. This rounding error is the characteristic feature of floating-point computation.