(gmp.info.gz) Integer Internals

 
 Integer Internals
 =================
 
 `mpz_t' variables represent integers using sign and magnitude, in space
 dynamically allocated and reallocated.  The fields are as follows.
 
 `_mp_size'
      The number of limbs, or the negative of that when representing a
      negative integer.  Zero is represented by `_mp_size' set to zero,
      in which case the `_mp_d' data is unused.
 
 `_mp_d'
      A pointer to an array of limbs which is the magnitude.  These are
      stored "little endian" as per the `mpn' functions, so `_mp_d[0]'
      is the least significant limb and `_mp_d[ABS(_mp_size)-1]' is the
      most significant.  Whenever `_mp_size' is non-zero, the most
      significant limb is non-zero.
 
      Currently there's always at least one limb allocated, so for
      instance `mpz_set_ui' never needs to reallocate, and `mpz_get_ui'
      can fetch `_mp_d[0]' unconditionally (though its value is then
      only wanted if `_mp_size' is non-zero).
 
 `_mp_alloc'
      `_mp_alloc' is the number of limbs currently allocated at `_mp_d',
      and naturally `_mp_alloc >= ABS(_mp_size)'.  When an `mpz' routine
      is about to (or might be about to) increase `_mp_size', it checks
      `_mp_alloc' to see whether there's enough space, and reallocates
      if not.  `MPZ_REALLOC' is generally used for this.
 
    The various bitwise logical functions like `mpz_and' behave as if
 negative values were twos complement.  But sign and magnitude is always
 used internally, and necessary adjustments are made during the
 calculations.  Sometimes this isn't pretty, but sign and magnitude are
 best for other routines.
 
    Some internal temporary variables are setup with `MPZ_TMP_INIT' and
 these have `_mp_d' space obtained from `TMP_ALLOC' rather than the
 memory allocation functions.  Care is taken to ensure that these are
 big enough that no reallocation is necessary (since it would have
 unpredictable consequences).
 
    `_mp_size' and `_mp_alloc' are `int', although `mp_size_t' is
 usually a `long'.  This is done to make the fields just 32 bits on some
 64 bits systems, thereby saving a few bytes of data space but still
 providing plenty of range.
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