mpq_get_d

[Paul Zimmermann]

The mpq_get_d documentation is the following:

 - Function: double mpq_get_d (mpq_t OP)
     Convert OP to a `double'.

A few more words would be helpful:

1) does the conversion depend on the machine rounding mode?
2) if yes/no, how is the conversion (mathematically) defined?

For gmp-4.1.4, the asnwer to 1) seems to be 'yes':

   for q=-1/26530884065595459276087454401792, rnd=-Inf
   mpq_get_d  gets -3.7691921517865029e-32
   for q=-1/26530884065595459276087454401792, rnd=+Inf
   mpq_get_d  gets -3.7691921517865035e-32

Unfortunately the rounding direction is the opposite to the one asked...

For 2), the conversion is not optimal. Here is an example with a rounding
precision of 53 bits, where the result of mpq_get_d is too large by 1 ulp
(but in the right direction):

   for 1/3, rnd=+Inf
   mpq_get_d  gets 3.3333333333333343e-01
   mpfr_set_q gets 3.3333333333333337e-01

and with a rounding precision of 64 bits (default on x86):

   for q=26530884065595459276087454401793/5539952800230608, rnd=+Inf
   mpq_get_d  gets 4.7890090443534240e+15
   mpfr_set_q gets 4.7890090443534250e+15

This last example gives a wrong directed rounding (not only it is not the
correct rounding, but also the wrong direction!).

Both problems can be fixed easily:

1) for negative numbers, put the sign right away (while accumulating the limbs)
2) for non-optimal results, it would be better to accumulate the limbs from
   least to most significant, and to take into account the remainder.

Paul