

There are (too) many proof files for log-de. 

Those with "acc" in the filename concern the accurate step (double-double-extended computation).

The others concern the quick phase (double-extended computation, with Estrin polynomial evaluation).

The most interesting files are the latter. There are three files:
  log-de-index1N-E0N.gappa covers all the table index values, except 0.
  log-de-index0-E1N.gappa covers the index 0 and all the exponents, except 0.
  log-de-index0-E0.gappa covers the case where both the index and the exponent are zero.
 
The hints given to Gappa need to be different in the three
cases. Basically, as soon as either the exponent or the index is
different from zero, Gappa computes the relative error by dividing an
absolute error by the max value of the function, which is sufficiently
large. In these cases, Estrin evaluation is just as easy as Horner to
handle.  However, in the case where both index and exponent are zero
(this correspond to the interval where the logarithm goes through
zero) we have to compute directly the relative error of the Estrin
evaluation. 

The same holds for log-de-acc, but without the Estrin bravery.

Note that some of these files forget the case z=0. It is easy the prove by
hand that the Estrin evaluation, in this case, returns logir+E*log2 (with
roundings on logir, log2, the + and the *), which is accurate enough.
