Re: exp is faster the second time round

[Karim Belabas <Karim.Belabas@math.u-bordeaux1.fr>]

* Karim Belabas [2012-10-22 22:31]:
> * Dirk Laurie [2012-10-22 22:19]:
> > With \p 1000000, it takes about a minute to compute exp
> > on my laptop.  Immediate afterwards, it takes about 30 seconds.
> > 
> > Obviously some constants are being memoized.  Which
> > constants are these?
> 
> log(2)     
> 
> Since exp(x - k log(2)) = x / 2^k, argument reduction allows us to
> assume that |x| <= log(2)/2

And Pi as well. In this range, we compute exp() via log() + Newton,
and compute log itself via an AGM that requires Pi  
[ Pi / 2AGM(1, 4/Q) ~ log Q for large Q ]].

    K.B.
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