[opus] [PATCH] Optimize silk_warped_autocorrelation_FIX() for ARM NEON
Jean-Marc Valin
jmvalin at jmvalin.ca
Mon Feb 6 20:40:09 UTC 2017
Hi Linfeng,
On 06/02/17 02:51 PM, Linfeng Zhang wrote:
> 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.
That is indeed the tricky part... and the one I think you could do
slightly differently. If you approach the problem in terms of computing
chunks of the inputs N samples at a time, then indeed the approach you
are describing is the only solution. What I was proposing though is to
instead chop the "order" in chunks of N. Using your notation, you would
be doing:
PROC( in0(s0))
PROC( in0(s1) in1(s0))
PROC( in0(s2) in1(s1) in2(s0))
PROC( in0(s3) in1(s2) in2(s1) in3(s0))
PROC( in0(s4) in1(s3) in2(s2) in3(s1) in4(s0))
PROC( in0(s5) in1(s4) in2(s3) in3(s2) in4(s1) in5(s0))
PROC( in0(s6) in1(s5) in2(s4) in3(s3) in4(s2) in5(s1) in6(s0))
PROC(in0(s7) in1(s6) in2(s5) in3(s4) in4(s3) in5(s2) in6(s1) in7(s0))
PROC(in1(s7) in2(s6) in3(s5) in4(s4) in5(s3) in6(s2) in7(s1) in8(s0))
PROC(in2(s7) in3(s6) in4(s5) in5(s4) in6(s3) in7(s2) in8(s1) in9(s0))
PROC(in3(s7) in4(s6) in5(s5) in6(s4) in7(s3) in8(s2) in9(s1)in10(s0))
PROC(in4(s7) in5(s6) in6(s5) in7(s4) in8(s3) in9(s2)in10(s1)in11(s0))
...and so on until the end of the input vector
The difference is that it's now the input vector that "slides" and the
"state" values sy that remain in the same place. There's still a
prologue, but you can easily get rid of it by (implicitly) zero-padding
the in vector during the initialization phase (start with a zero vector
and real one value at a time). Getting rid of the epilogue is a little
trickier, but I think it can be done.
Cheers,
Jean-Marc
> 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
> <mailto: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
> >
> >
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> >
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