There are two checks that are always false so can be converted to (negated)
assertions to save code space and execution time. They are:
1. The check of the str parameter, which is required to be non-NULL as per
the original comment that it has enough space in it as calculated by
mp_int_format_size. And for all uses of this function str is indeed
non-NULL.
2. The check of the base parameter, which is already required to be between
2 and 16 (inclusive) via the assertion in mp_int_format_size.
The motivation behind this patch is to remove unreachable code in mpn_div.
This unreachable code was added some time ago in
9a21d2e070, when a loop in mpn_div was copied
and adjusted to work when mpz_dig_t was exactly half of the size of
mpz_dbl_dig_t (a common case). The loop was copied correctly but it wasn't
noticed at the time that the final part of the calculation of num-quo*den
could be optimised, and hence unreachable code was left for a case that
never occurred.
The observation for the optimisation is that the initial value of quo in
mpn_div is either exact or too large (never too small), and therefore the
subtraction of quo*den from num may subtract exactly enough or too much
(but never too little). Using this observation the part of the algorithm
that handles the borrow value can be simplified, and most importantly this
eliminates the unreachable code.
The new code has been tested with DIG_SIZE=3 and DIG_SIZE=4 by dividing all
possible combinations of non-negative integers with between 0 and 3
(inclusive) mpz digits.
Updated modbuiltin.c to add conditional support for 3-arg calls to
pow() using MICROPY_PY_BUILTINS_POW3 config parameter. Added support in
objint_mpz.c for for optimised implementation.
Previous to this patch bignum division and modulo would temporarily
modify the RHS argument to the operation (eg x/y would modify y), but on
return the RHS would be restored to its original value. This is not
allowed because arguments to binary operations are const, and in
particular might live in ROM. The modification was to normalise the arg
(and then unnormalise before returning), and this patch makes it so the
normalisation is done on the fly and the arg is now accessed as read-only.
This change doesn't increase the order complexity of the operation, and
actually reduces code size.
When DIG_SIZE=32, a uint32_t is used to store limbs, and no normalisation
is needed because the MSB is already set, then there will be left and
right shifts (in C) by 32 of a 32-bit variable, leading to undefined
behaviour. This patch fixes this bug.
This function computes (x**y)%z in an efficient way. For large arguments
this operation is otherwise not computable by doing x**y and then %z.
It's currently not used, but is added in case it's useful one day.
For these 3 bitwise operations there are now fast functions for
positive-only arguments, and general functions for arbitrary sign
arguments (the fast functions are the existing implementation).
By default the fast functions are not used (to save space) and instead
the general functions are used for all operations.
Enable MICROPY_OPT_MPZ_BITWISE to use the fast functions for positive
arguments.
msvc does not treat 1L a 64bit integer hence all occurences of shifting it left or right
result in undefined behaviour since the maximum allowed shift count for 32bit ints is 31.
Forcing the correct type explicitely, stored in MPZ_LONG_1, solves this.
Previously, mpz was restricted to using at most 15 bits in each digit,
where a digit was a uint16_t.
With this patch, mpz can use all 16 bits in the uint16_t (improvement
to mpn_div was required). This gives small inprovements in speed and
RAM usage. It also yields savings in ROM code size because all of the
digit masking operations become no-ops.
Also, mpz can now use a uint32_t as the digit type, and hence use 32
bits per digit. This will give decent improvements in mpz speed on
64-bit machines.
Test for big integer division added.
