GNU Info

(gmp.info)Integer Internals

---

Next: Rational Internals Prev: Internals Up: Internals

---

Enter node , (file) or (file)node

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).