Binary output of mpf_get_str() has too many bits?
Paul.Zimmermann at loria.fr
Thu May 20 15:52:53 CEST 2010
> So what is the take home message? Is it that 'precision' number of bits are
> accurate, and that possibly a few bits beyond are as well, but not
one reason why GMP MPF class uses more bits than requested by the user is
that it uses a base 2^32 or 2^64 depending on your computer. If you want to
represent the number 1+epsilon in base 2^64, where epsilon is small, you will
realize that the most significant limb will store only one bit, that
corresponding to 1. If on the contrary you want to store 0.5+epsilon, the
most significant limb will contain 63 bits (2^63, for 0.5 with exponent -1
in base 2^64). Thus to be sure to have at least say 66 significant bits for
every number, you need at least three limbs, which will store between
129 and 192 significant bits.
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