Re: Optimize numeric multiplication for one and two base-NBASE digit multiplicands.

On Mon, 1 Jul 2024 at 20:56, Joel Jacobson <joel@compiler.org> wrote:
>
> Below is a more realistic benchmark
>
> CREATE TABLE bench_mul_var (num1 numeric, num2 numeric);
>
> INSERT INTO bench_mul_var (num1, num2)
> SELECT random(0::numeric,1e8::numeric), random(0::numeric,1e8::numeric) FROM generate_series(1,1e8);
>
> SELECT SUM(num1*num2) FROM bench_mul_var;

I had a play with this, and came up with a slightly different way of
doing it that works for var2 of any size, as long as var1 is just 1 or
2 digits.

Repeating your benchmark where both numbers have up to 2 NBASE-digits,
this new approach was slightly faster:

SELECT SUM(num1*num2) FROM bench_mul_var; -- HEAD
Time: 4762.990 ms (00:04.763)
Time: 4332.166 ms (00:04.332)
Time: 4276.211 ms (00:04.276)
Time: 4247.321 ms (00:04.247)
Time: 4166.738 ms (00:04.167)

SELECT SUM(num1*num2) FROM bench_mul_var; -- v2 patch
Time: 4398.812 ms (00:04.399)
Time: 3672.668 ms (00:03.673)
Time: 3650.227 ms (00:03.650)
Time: 3611.420 ms (00:03.611)
Time: 3534.218 ms (00:03.534)

SELECT SUM(num1*num2) FROM bench_mul_var; -- this patch
Time: 3350.596 ms (00:03.351)
Time: 3336.224 ms (00:03.336)
Time: 3335.599 ms (00:03.336)
Time: 3336.990 ms (00:03.337)
Time: 3351.453 ms (00:03.351)

(This was on an older Intel Core i9-9900K, so I'm not sure why all the
timings are faster. What compiler settings are you using?)

The approach taken in this patch only uses 32-bit integers, so in
theory it could be extended to work for var1ndigits = 3, 4, or even
more, but the code would get increasingly complex, and I ran out of
steam at 2 digits. It might be worth trying though.

Regards,
Dean