pgsql: Optimise numeric multiplication for short inputs.

Optimise numeric multiplication for short inputs.

When either input has a small number of digits, and the exact product
is requested, the speed of numeric multiplication can be increased
significantly by using a faster direct multiplication algorithm. This
works by fully computing each result digit in turn, starting with the
least significant, and propagating the carry up. This save cycles by
not requiring a temporary buffer to store digit products, not making
multiple passes over the digits of the longer input, and not requiring
separate carry-propagation passes.

For now, this is used when the shorter input has 1-4 NBASE digits (up
to 13-16 decimal digits), and the longer input is of any size, which
covers a lot of common real-world cases. Also, the relative benefit
increases as the size of the longer input increases.

Possible future work would be to try extending the technique to larger
numbers of digits in the shorter input.

Joel Jacobson and Dean Rasheed.

Discussion: https://postgr.es/m/44d2ffca-d560-4919-b85a-4d07060946aa@app.fastmail.com

Branch
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master

Details
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https://git.postgresql.org/pg/commitdiff/ca481d3c9ab7bf69ff0c8d71ad3951d407f6a33c

Modified Files
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src/backend/utils/adt/numeric.c | 220 +++++++++++++++++++++++++++++++++++++++-
1 file changed, 219 insertions(+), 1 deletion(-)