[FFmpeg-devel] Fixpoint FFT optimization, with MDCT and IMDCT wrappers for audio optimization

[Michael Niedermayer]

Hi

On Fri, Jul 27, 2007 at 09:56:34PM -0400, Marc Hoffman wrote:
> Hi,
> 
> On 7/27/07, Michael Niedermayer <michaelni at gmx.at> wrote:
> > Hi
> >
> > On Fri, Jul 27, 2007 at 05:40:14PM -0400, mmh wrote:
> > [...]
> > > +/*
> > > +  This is a fixedpoint inplace 32bit FFT which accepts 3 arguments:
> > > +
> > > +  @param X   - input signal in format 1.31
> > > +  @param W   - phase factors in 1.31 format
> > > +  @param lgN - log_2(N) where N is the size of the input data set.
> > > +
> > > +*/
> > > +void ff_fft32 (FFTContext *c, FFTComplex32 *X)
> > > +{
> > > +    FFTComplex16 *W = c->exptab16;
> > > +    int lgN    = c->nbits;
> > > +    int N      = 1<<lgN;
> > > +    int s, j, k, m, w, ws;
> > > +    int64_t wwr,wwi;
> > > +
> > > +    for (s=1; s<=lgN; s++) {
> > > +        m  = 1<<s;
> > > +        ws = 1<<(lgN-s);
> > > +        w=0;
> > > +        for (j=0; j<m/2; j++) {
> > > +            wwr=W[w].re;
> > > +            wwi=W[w].im;
> > > +            w+=ws;
> > > +            for (k=j; k<N; k+=m) {
> > > +                long tr,ti;
> > > +                int k2 = k+m/2;
> >
> > signed and /2 is slow either changed to unsiged or use >>1
> >
> Compiler should take care of this via strength reduction and to boot
> its a constant in the loop. I think m/2 is ok but will change if you
> want me too semantics are identical.

you put a lot of trust in the compiler, this is not a simple optimization
it has to proof m can not reach values where m>>1 != m/2


> 
> >
> > > +
> > > +                tr        = (X[k2].re*wwr - X[k2].im*wwi + 0x4000)>>15;
> > > +                ti        = (X[k2].re*wwi + X[k2].im*wwr + 0x4000)>>15;
> > > +
> > > +                X[k2].re  = (X[k].re - tr);
> > > +                X[k2].im  = (X[k].im - ti);
> > > +
> > > +                X[k].re   = (X[k].re + tr);
> > > +                X[k].im   = (X[k].im + ti);
> > > +            }
> > > +        }
> > > +    }
> > > +}
> >
> > what about implementing a split radix fft?
> > (http://en.wikipedia.org/wiki/Split-radix_FFT)
> 
> I'm thinking this is the begining of the whole fixedpoint thing.  My
> real goal here is to get some of this working with an audio codec and
> see what we really need to optimize.

if you agree to implement a split radix fixedpoint & float fft later
then ive no objections, otherwise i do


> 
> >
> > also several iterations have trivial (1/-1/0) w* these should not be done
> > in this generic way
> ?

these things called twiddle factors, which are represented by wwr and wwi in
your code have values like 1/-1/0, well 32768/-32768/0 as its fixedpoint
in some iterations and its very lame to do a full complex multiplication
for w being one of 1,-1,i,-i

[...]

-- 
Michael     GnuPG fingerprint: 9FF2128B147EF6730BADF133611EC787040B0FAB

No snowflake in an avalanche ever feels responsible. -- Voltaire
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