Bit flip only function?

[Torbjörn Granlund]

Viktor Kletzhändler <vkletzhaendler at swissonline.ch> writes:

  That would mean, mpz_com assumes that all numbers are signed two's
  complement representations. Therefore it silently adds a sign bit to
  any positive argument, and calculates the two's complement for any
  negative argument.
  
  This is ok. However, that would also mean that mpz_com can't take
  unsigned arguments, i.e. a bit string without embedded sign, for
  example (unsigned int) 175. Or am I missing something again?
  
Don't think in "types", think maths.  The number 175 can be represented
by mpz (sic!).  If you negate it, you'll get -175, if you apply ~ (alias
mpz_com) you'll get -176.  It is completely well-defined, and will not
be affected by some host word sizes or the sizes of this or that type of
your C compiler.  (You might notice that - and ~ applied to "unsigned"
integral types in C will yield different values depending on the word
size; except for that quirk they are well-defined.)

>From your reasoning I suspect that you shouldn't be using GMP at all, or
at least not the mpz functions.  Handling "bit strings" is easy enough
to do with a few discrete C functions.  But if your bit strings are very
large, you may get some benefit from using mpn_ logic functions; you
might be relieved to know that they handle any number of 'words' (aka
limbs) without mpz's implied infinite left extensions of ones or zeros.


Torbjörn
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