Hello all,

The attached patch quite noticeably minimizes rounding errors and improves
audio quality.

I decided to drop non-SIMD variant because it would require quite a bit of
work to update for better precision. Most of the CPU cores which are
relevant nowadays have support for some kind of SIMD extension anyway.
I will also do ARMv6 SIMD version of the analysis filter after all the high
level SBC optimizations are in place.

Audio quality estimation done with tiny_psnr (lower stddev value is better):

=== before patch (4 subbands) ===

./sbc_encode_test.rb BigBuckBunny-stereo.flac
[2, 48000]
["-j -s4 -B16 -b128", "-p -j -l16 -n4 -r1584000"]
--- comparing original / sbcenc + sbcdec ---
stddev:    3.58 PSNR: 85.23 bytes:114519660/114520000

--- comparing original / sbcenc + sbc_decoder.exe ---
stddev:    1.70 PSNR: 91.71 bytes:114519660/114520000

--- comparing original / sbc_encoder.exe + sbc_decoder.exe ---
stddev:    1.44 PSNR: 93.09 bytes:114519660/114520000

--- comparing sbcenc + sbc_decoder.exe / sbc_encoder.exe + sbc_decoder.exe
stddev:    0.99 PSNR: 96.36 bytes:114519808/114519808

=== after patch (4 subbands) ===

./sbc_encode_test.rb BigBuckBunny-stereo.flac
[2, 48000]
["-j -s4 -B16 -b128", "-p -j -l16 -n4 -r1584000"]
--- comparing original / sbcenc + sbcdec ---
stddev:    3.55 PSNR: 85.31 bytes:114519660/114520000

--- comparing original / sbcenc + sbc_decoder.exe ---
stddev:    1.62 PSNR: 92.09 bytes:114519660/114520000

--- comparing original / sbc_encoder.exe + sbc_decoder.exe ---
stddev:    1.44 PSNR: 93.09 bytes:114519660/114520000

--- comparing sbcenc + sbc_decoder.exe / sbc_encoder.exe + sbc_decoder.exe
stddev:    0.77 PSNR: 98.57 bytes:114519808/114519808

=== before patch (8 subbands) ===

./sbc_encode_test.rb BigBuckBunny-stereo.flac
[2, 48000]
["-j -s8 -B16 -b255", "-p -j -l16 -n8 -r1569000"]
--- comparing original / sbcenc + sbcdec ---
stddev:    4.85 PSNR: 82.60 bytes:114519260/114520000

--- comparing original / sbcenc + sbc_decoder.exe ---
stddev:    2.07 PSNR: 89.98 bytes:114519260/114520000

--- comparing original / sbc_encoder.exe + sbc_decoder.exe ---
stddev:    1.09 PSNR: 95.56 bytes:114519260/114520000

--- comparing sbcenc + sbc_decoder.exe / sbc_encoder.exe + sbc_decoder.exe
stddev:    1.77 PSNR: 91.34 bytes:114519552/114519552

=== after patch (8 subbands) ===

./sbc_encode_test.rb BigBuckBunny-stereo.flac
[2, 48000]
["-j -s8 -B16 -b255", "-p -j -l16 -n8 -r1569000"]
--- comparing original / sbcenc + sbcdec ---
stddev:    4.55 PSNR: 83.16 bytes:114519260/114520000

--- comparing original / sbcenc + sbc_decoder.exe ---
stddev:    1.28 PSNR: 94.11 bytes:114519260/114520000

--- comparing original / sbc_encoder.exe + sbc_decoder.exe ---
stddev:    1.09 PSNR: 95.56 bytes:114519260/114520000

--- comparing sbcenc + sbc_decoder.exe / sbc_encoder.exe + sbc_decoder.exe
stddev:    0.73 PSNR: 98.96 bytes:114519552/114519552

===

So for 4 subbands encode, stddev is down from 1.70 to 1.62 (1.44 for the
reference encoder). For 8 subbands encode stddev is down from 2.07 to 1.28
(1.09 for the reference encoder).


It is very interesting to see what a more advanced PEAQ test will show.


Best regards,
Siarhei Siamashka