mpz_t variables represent integers using sign and magnitude, in space
dynamically allocated and reallocated. The fields are as follows.
_mp_sizeThe 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 undefined.
_mp_dA 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 readable limb, so for instance
mpz_get_ui can fetch _mp_d[0] unconditionally (though its value
is undefined if _mp_size is zero).
_mp_alloc_mp_alloc is the number of limbs currently allocated at _mp_d,
and normally _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.
mpz_t variables initialised with the mpz_roinit_n function or
the MPZ_ROINIT_N macro have _mp_alloc = 0 but can have a
non-zero _mp_size. They can only be used as read-only constants. See
Special Functions for details.
The various bitwise logical functions like mpz_and behave as if
negative values were two’s 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 set up 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.