Re: A missing (?) function: exponentfp(x)

[Ilya Zakharevich <nospam-abuse@ilyaz.org>]

On Mon, Sep 16, 2024 at 09:36:37PM +0200, Loïc Grenié wrote:
> On Sat, 14 Sep, 2024 at 11:09, Ilya Zakharevich wrote:
> 
> > The function exponent(x) gives a very coarse value of log2(x).  The
> > function log(x)/log(2) gives a very fine value of log2(x) (but is
> > slow, especially if x has high precision).  But sometimes I prefer to
> > know log2(x) with an intermediate precision; in fact, any sufficiently
> > smooth monotonic function which coincides with log2 on powers of 2
> > would be enough!
> >
> > In particular, exponent(x) + mantissa12(x) - 1 would be OK.  (Here
> > mantissa12() is the (top word of) mantissa-scaled-to-[1,2].)  It
> > should be very cheap to calculate.  It may be beneficial to have two
> > flavors, returning a double, or a 1-word PARI float.
> >
> 
>  expofp(x)=my(e=exponent(x));e+(precision(x,19)>>e-1);

Yes, this does exactly what I wrote!  However, it is not very much
useful, since

  • As written, it is about 25 times slower than exponent().
  • It needs to be rewritten — slowing it yet much more, since, as you
    wrote: 

>      Works only on floating point x's.

Thanks,
Ilya