Simple question about MPFR vs. GMP

Elias P. TSIGARIDAS et at
Sun Apr 9 14:54:50 CEST 2006

Hello to all,
Even though I do not have much experience,
please allow me to express my opinion about this issue.

At the current state GMP provides operations on rationals and integers,
thus in Z and Q.
It is well known that Z \subset Q \subset R

What we actually want is to compute in R, but this is impossible
since we can not represent all the real numbers.
(Actually many things are undecidable here, but I will not go into details)
What we do is a compromise, we work with "some" real numbers, that are
represented in a very efficient representation (floating point) and that
is the work of MPFR.

Let me state an example:
If you work in mpz the sqrt(2)=1.
while when you work in mpfr  sqrt( 2) = 1.414213562...
and the digits that you get after the decimal point can be defined by
the user, with some guarantee (this is where correct rounding appears).

with best regards,


Linas Vepstas wrote:
> Hi,
> I have a rather naive question about MPFR vs. GMP that
> I could not resolve by reviewing the MPFR web page. That
> question is this:
>   Exactly HOW is MPFR better than GMP? Why, as a programmer,
>   should I care about exact rounding?
> If I'm writing a program to compute some function to 400
> decimal places, I have to do a fair bit of logic and thinking
> to make sure I actually obtained 400 bits of accuracy. A bit
> of rounding error here and there doesn't substantially change
> my eror estimates .. and so, why should I care about "exact 
> rounding"?
> --linas
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