Re: mpz_sizeinbase

[Kevin Ryde]

"Winfried Dreckmann" <address@hidden> writes:
> 
> I have a problem with the source code for "mpz_sizeinbase" in gmp 3.1.1.
> If the base is not a power of 2 it calculates its result by the
> following expression:
> 
>  return (size_t) (totbits * __mp_bases[base].chars_per_bit_exactly) + 1;
> 
> Here "totbits" is the number of significant bits and
> "__mp_bases[base].chars_per_bit_exactly" an approximation of the
> logarithm of 2 in the given base. Due to limited precision there is no
> garantuee that this result is actually greater than the true
> mathematical logarithm. As a consequence is may happen for very, very
> large numbers that the result is 1 too small. (The manual states that
> the result is exact or 1 too big.)

Well, there should be 53 bits of precision on that log, which should
be enough.

> Using the gmp approximation:
> 
> 198096465 * 0.3010299956639811 = 59632977.99999998373681149999

I'm unable to reproduce that on a ppc604e (or an i386), I get ...78 as
expected.  Is the compiler giving the right value for chars_per_bit?

    printf ("%A\n", __mp_bases[10].chars_per_bit_exactly);

should print 0X1.34413509F79FFP-2 by my reckoning.


But your point is taken though, it'd be better not to depend on
floating point for this.  A fixed point integer approximation would
make it easier to guarantee the results, and would also hopefully make
it possible to address the problem with 64-bit mpf exponents noted in
doc/tasks.html.