query: nearest integer divide

[Jason Moxham]

On Monday 24 Mar 2003 10:59 am, Torbjorn Granlund wrote:
> [Let's try again.  Last reply had some typos that made it hard to
> understand.]
>
> keith.briggs@bt.com writes:
>
>   1. mpz_ui_pow_ui(temp,2,p-1);
>       mpz_add(y,x,temp);
>       mpz_tdiv_q_2exp(y,y,p);
>
> It would save a lot of time to perform that mpz_ui_pow_ui with
> mpz_mul_2exp instead.  That would bring time down from O(M(2^p)) to
> O(2^p), where M(n) is the time for multiplying two n-bit numbers.
>
> (If your x is computed for the sole purpose of getting this
> nearest integer, you might be able to save a great amount of time
> by not computing the full precision of x, and instead just some
> upper part of it.)


Assuming the x is needed only for getting this nearest integer I have found 
the papers below to be useful 


On computing short products , Thom Mulders , Technical Report No 276
Department of Computer Science ETH Zurich , Nov 1997
www.inf.ethz.ch/research/publications/data/tech-reports/2xx/276.ps

Efficient Multiprecision Floating point Multiplication with exact rounding ,
Werner Krandick , Jeremy R Johnson 
ftp://ftp.risc.uni-linz.ac.at/pub/techreports/1993/93-74.ps.gz 

Detecting Perfect Powers in essentially linear time , Daniel J Bernstein
http://cr.yp.to/papers.html