# [opus] [PATCH] Optimize silk_warped_autocorrelation_FIX() for ARM NEON

Linfeng Zhang linfengz at google.com
Mon Feb 6 19:51:44 UTC 2017

```Hi Jean-Marc,

Thanks a lot for reviewing this huge assembly function!

silk_warped_autocorrelation_FIX_c()'s kernel part is
for( n = 0; n < length; n++ ) {
tmp1_QS = silk_LSHIFT32( (opus_int32)input[ n ], QS );
/* Loop over allpass sections */
for( i = 0; i < order; i++ ) {
/* Output of allpass section */
tmp2_QS = silk_SMLAWB( state_QS[ i ], state_QS[ i + 1 ] -
tmp1_QS, warping_Q16 );
state_QS[ i ]  = tmp1_QS;
corr_QC[  i ] += silk_RSHIFT64( silk_SMULL( tmp1_QS, state_QS[
0 ] ), 2 * QS - QC );
tmp1_QS = tmp2_QS;
}
state_QS[ order ] = tmp1_QS;
corr_QC[  order ] += silk_RSHIFT64( silk_SMULL( tmp1_QS, state_QS[
0 ] ), 2 * QS - QC );
}
in which corr_QC[0, 1, ..., order] is the only output.

Suppose order = 10, and each stage of the inner loop is noted by s0, s1,
..., s9. And suppose we simultaneously process 8 input in SIMD, from in0 to
in7. Let PROC(inx(sy)) denote processing input[x] at stage y.

If there is no dependency between inx(sy) and in(x+1)(sy), then we can do
this

FOR in=0 TO N WITH in+=8
FOR y=0 TO order-1 WITH y++
PROC(in0(sy) in1(sy) in2(sy) in3(sy) in4(sy) in5(sy) in6(sy) in7(sy))
END FOR
END FOR

Definitely there is no any prolog and epilog needed.

However, the critical thing is that all the states in each stage when
processing input[i] are reused by the next input[i+1]. That is input[i+1]
must wait input[i] for 1 stage, and input[i+2] must wait input[i+1] for 1
stage, etc.
Then it becomes this

FOR in=0 to N WITH in+=8
PROC(in0(s0)) /* prolog 0 */
PROC(in0(s1) in1(s0)) /* prolog 1 */
PROC(in0(s2) in1(s1) in2(s0)) /* prolog 2 */
PROC(in0(s3) in1(s2) in2(s1) in3(s0)) /* prolog 3 */
PROC(in0(s4) in1(s3) in2(s2) in3(s1) in4(s0)) /* prolog 4 */
PROC(in0(s5) in1(s4) in2(s3) in3(s2) in4(s1) in5(s0)) /* prolog 5 */
PROC(in0(s6) in1(s5) in2(s4) in3(s3) in4(s2) in5(s1) in6(s0)) /* prolog 6
*/
PROC(in0(s7) in1(s6) in2(s5) in3(s4) in4(s3) in5(s2) in6(s1) in7(s0)) /*
fully process 8 inputs */
PROC(in0(s8) in1(s7) in2(s6) in3(s5) in4(s4) in5(s3) in6(s2) in7(s1)) /*
continue */
PROC(in0(s9) in1(s8) in2(s7) in3(s6) in4(s5) in5(s4) in6(s3) in7(s2)) /*
continue */
PROC(in0(s10) in1(s9) in2(s8) in3(s7) in4(s6) in5(s5) in6(s4) in7(s3)) /*
continue */
PROC(in1(s10) in2(s9) in3(s8) in4(s7) in5(s6) in6(s5) in7(s4)) /* epilog
0 */
PROC(in2(s10) in3(s9) in4(s8) in5(s7) in6(s6) in7(s5)) /* epilog 1 */
PROC(in3(s10) in4(s9) in5(s8) in6(s7) in7(s6)) /* epilog 2 */
PROC(in4(s10) in5(s9) in6(s8) in7(s7)) /* epilog 3 */
PROC(in5(s10) in6(s9) in7(s8)) /* epilog 4 */
PROC(in6(s10) in7(s9)) /* epilog 5 */
PROC(in7(s10)) /* epilog 6 */
END FOR

And
PROC(in0(s7) in1(s6) in2(s5) in3(s4) in4(s3) in5(s2) in6(s1) in7(s0)) /*
fully process 8 inputs */
PROC(in0(s8) in1(s7) in2(s6) in3(s5) in4(s4) in5(s3) in6(s2) in7(s1)) /*
continue */
PROC(in0(s9) in1(s8) in2(s7) in3(s6) in4(s5) in5(s4) in6(s3) in7(s2)) /*
continue */
is actually the expansion of the kernel loop
FOR i=0 TO order-6 WITH i++
PROC(in0(si+7) in1(si+6) in2(si+5) in3(si+4) in4(si+3) in5(si+2)
in6(si+1) in7(si+0))
END FOR

The worst thing is that corr_QC[] is so sensitive that any extra processing
will make them wrong and propagate to the next loop (next 8 inputs).
state_QS[] is a little better but still very sensitive. For instance, if
adding PROC(in0(s11') in1(s10) in2(s9) in3(s8) in4(s7) in5(s6) in6(s5)
in7(s4)) to the kernel loop (by looping one more time) and remove epilog 0,
then all final results will be wrong.

That's why the prolog and epilog cannot be saved to the best of my
knowledge.

The assembly size of silk_warped_autocorrelation_FIX_neon() is about 2,744
bytes. Compared with the C code size (about 452 bytes), it's 2.3 KB larger.
Considering silk_warped_autocorrelation_FIX_c() is the second place CPU
heavy function in fixed-point, and our testing shows up to 7% CPU run time
saving of the total encoder with this optimization (at Complexity 8), maybe
we can take the I-cache burden even if finally we still cannot remove the
big chunk of prolog and epilog.

Thanks,
Linfeng Zhang

On Sat, Feb 4, 2017 at 4:17 PM, Jean-Marc Valin <jmvalin at jmvalin.ca> wrote:

> Hi Felicia,
>
> I've had time to work through the math in the original function and I'm
> pretty sure it's possible to vectorize this without the huge
> prologue/epilogue.
>
> For the simple case where order = vector size = N (but it should easily
> generalize to larger order), what I came up with is:
>
> initialize X, Y, M, C to vector of zeros
>
> for i=0 to N+order
>    T = [x(i), Y(0:N-2)]
>    Y = M + coeff * (Y - T)
>    M = T
>    X = [x(i), X(0:N-1)]
>    C = C + X*Y
>
> I think something similar to this (assuming I didn't mess up any
> details) should give you the correlations in vector C. Did I miss anything?
>
> Cheers,
>
>         Jean-Marc
>
>
> On 31/01/17 12:30 PM, Felicia Lim wrote:
> > Hi,
> >
> > Attached is a patch with arm neon optimizations for
> > silk_warped_autocorrelation_FIX(). Please review.
> >
> > Thanks,
> > Felicia
> >
> >
> > _______________________________________________
> > opus mailing list
> > opus at xiph.org
> > http://lists.xiph.org/mailman/listinfo/opus
> >
> _______________________________________________
> opus mailing list
> opus at xiph.org
> http://lists.xiph.org/mailman/listinfo/opus
>
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