[PATCH, libstdc++, complex] complex multiplication algorithm improved

[Basile Starynkevitch]

On Wed, 15 Sep 2010 16:10:40 +0800
Wang Feng <wanng.fenng@gmail.com> wrote:

> Hi,
>     Complex number multiplication done with 4 multiplications, but
> this one only need 3:
> 
>              (a+ib)(c+id) = ac - bd + i( bc + ad ) -- 4 multiplies
>                                 = ac - bd + i[ ( a + b )( c + d ) - ac

Are you sure it is worth it?

I am not a processor expert, but common folklore says that floating
point addition is slower than floating point multiplication. Also, some
recent instruction sets have a multiply and add instruction, or an add
and multiply one.

Did you happen to measure the gain in CPU time for your patch on a
recent PC running Linux or some other common machine?

And there might perhaps be some rounding or precision issues (IEEE
floating point is a tricky beast in the ugly details).

Maybe your patch should depend upon the target system (for performance
or precision reasons).


But I am not a numerician, so take all this mail with a grain of salt.

Cheers.
-- 
Basile STARYNKEVITCH         http://starynkevitch.net/Basile/
email: basile<at>starynkevitch<dot>net mobile: +33 6 8501 2359
8, rue de la Faiencerie, 92340 Bourg La Reine, France
*** opinions {are only mine, sont seulement les miennes} ***