For certain operands to mpn_div, the existing code path for
`DIG_SIZE == MPZ_DBL_DIG_SIZE / 2` had a bug in it where borrow could still
overflow in the `(x >= *n || *n - x <= borrow)` branch, ie
`borrow + x - (mpz_dbl_dig_t)*n` overflows the borrow variable. In such
cases the subsequent right-shift of borrow would not bring in the overflow
bit, leading to an error in the result. An example division that had
overflow when MPZ_DIG_SIZE = 16 is `(2 ** 48 - 1) ** 2 // (2 ** 48 - 1)`.
This is fixed in this commit by simplifying the code and handling the low
digits of borrow first, and then the upper bits (to shift down) separately.
There is no longer a distinction between `DIG_SIZE < MPZ_DBL_DIG_SIZE / 2`
and `DIG_SIZE == MPZ_DBL_DIG_SIZE / 2`.
This commit also simplifies the second part of the calculation so that
borrow does not need to be negated (instead the code just works knowing
that borrow is negative and using + instead of - in calculations involving
borrow).
Fixes#6777.
Signed-off-by: Damien George <damien@micropython.org>
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.
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.
Damien George
Damien George