Paul.Zimmermann at inria.fr
Tue Jul 19 12:21:58 UTC 2016
in my current effort of optimizing MPFR for small precisions (1-2 limbs),
I am currently reviewing mpn_sqrtrem1() and mpn_sqrtrem2(), since we need
such functions to speed up mpfr_sqrt.
In mpn_sqrtrem1, I wonder what the 0x30000 constant is used for. By exhaustive
search on all possible values of a1 (there are only 3/4*2^33) on a 64-bit computer,
the maximal error on the 16-bit approximation x0 is the same without this constant,
more precisely -0.000023 <= x0/2^32 - (a0/2^64)^(-1/2) <= 0.
The worst error is even smaller (in absolute value) without the 0x30000 constant,
since with - 0x30000 it is attained for a1=2248147012 (error -0.0000231867), and
without 0x30000 it is attained for a1=2248147013 (error -0.0000231863).
Also "make check" passes without the 0x30000 constant. If the 0x30000 constant is
really needed, it would be nice to add an example that breaks make check if we
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