sin, cos, tan and rounding error

Question

I\'m doing some trigonometry calculations in C/C++ and am running into problems with rounding errors. For example, on my Linux system:

#include 

        

Answer 1

An IEEE double stores 52 bits of mantissa, with the "implicit leading one" forming a 53 bit number. An error in the bottom bit of a result therefore makes up about 1/2^53 of the scale of the numbers. Your output is of the same order as 1.0, so that comes out to just about exactly one part in 10^16 (because 53*log(2)/log(10) == 15.9).

So yes. This is about the limit of the precision you can expect. I'm not sure what the ULP technique you're using is, but I suspect you're applying it wrong.