talks in math, and buzzes like a fridge
Every finite real number, no matter how large, has a well-defined value for sin/cos. Ideally, the floating-point result returned for sin/cos would be the representable floating-point number closest to the mathematically defined result for the floating-point input. A floating-point library having this property is called correctly rounded, which is equivalent to saying the library has an error bound less than or equal to 1/2 an ulp (unit in the last place). For sin/cos, writing a correctly rounding implementation that runs at a reasonable speed is still something of a research problem so in practice platforms often use a library with a 1 ulp error bound instead, which means either of the floating-point numbers adjacent to the true result can be returned.
