gmp_printf bug?

[Vincent Lefevre]

On 2011-08-10 12:18:53 +0200, Niels Möller wrote:
> Vincent Lefevre <vincent at vinc17.net> writes:
> > I've attached a small program I've written that shows how this can
> > be done. It uses double-precision arithmetic, but of course, the
> > same algorithm works in fixed point (so that mpz can be used). With
> > the included parameters, it can compute log2(x) with x between 1 and
> > 2^64 at least.
> 
> Hmm, it starts by computing a table using log1p, with the value
> log_2(1+2^k) for various positive and negative integer k. Do I
> understand that correctly?

Yes, the table would be hardcoded in the source (just like other
fixed tables). AFAIK, the only drawbacks are:
  * The precision cannot be extended dynamically (unless you have
    some other function to compute the logarithm).
  * The range of the input is limited to some interval (though you
    can also do basic range reduction if needed).

Is this important in the case of gmp_printf?

> Then, the method seems suitable for computing log_2 at run time, but not
> so suitable in the bootstrap context where we want to tabulate certain
> logarithms, without relying on other tables, (or on floating point
> operations).

I'm not sure what you mean here. But perhaps I've answered a part of
this above.

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