MPFR rounding issue

Question

I've just started to work with MPFR arbitrary precision library and quite soon encounter very wierd behaviour. The main goal of using it was to improve precision of lagre argument trigs and this works extremly good in MPFR.

But then I decided to check out simple math and it was unbeleavable - even in straightforward examples with strict answers rounding errors exist and doesn't depends on used precision.

Even in the example like 1.1 * 1 the result is 1.10000000000000008881784... And this result given at insane 2000 bit precision (53 in normal double)!

Maybe it is my system's issue, but even in online MPFR similar problems exist. You can try such an example online: http://ex-cs.sist.ac.jp/~tkouya/try_mpfr.html

1 * 1.1 @ 64 bits = 1.10000000000000000002

But online version moves error further with increase of precision but in my installation - no.

My system: Ubuntu 9.10 + gmp 5.0.0.1 + mpfr 2.4.2

Answer 1

This appears to be the canonical answer to floating-point precision issues. It includes an explanation of why more bits doesn't solve the problem.

Old Answer

See question 7 of the MPFR FAQ. Anyway, there will always be some error, since many numbers are not exactly representable with binary mantissas no matter how many bits you use. See this answer to a related SO question for a good explanation.