Optimise target gain computation in parametric binauralizer.

Description

The function getDirectPartGains in the parametric binauralizer has been one of the most significant complexity contributors within. This is due to the function being called quite many times per frame as the gain coefficients are required for each frequency bin (60), each subframe (4), each direction (2), and coherence rendering (3). Thus, it can be called up to 60*4*2*3 = 1440 times for each frame (2dir 512 kbps MASA).

However, in many cases, the direction data (azi & ele) is provided on frequency bands which means that there is a lot of data duplication. Furthermore, real analysed data often may have neighbouring bands pointing to the same direction. Although the HRTF is frequency dependent, it is possible to reduce complexity a lot by employing cache approach to solving of 3rd order SHD response which is required for obtaining the gains.

Another optimization is also possible by including the azi & ele rotation function into the cached value. This is because new head orientation is provided for each subframe and is not frequency dependent, and thus it is possible to reuse the rotated azi & ele as long as the input azi & ele have not changed.

One more trivial optimization is to disable call to azi & ele rotation if head-tracking is not active. This seems to have been left into the code.

These optimisations are BE. In practice, there can be a minor complexity increase if the input azi & ele are always completely different due to storing to cache the new values. However, this is offset by having even one cache hit within one frame as the complexity decrease is so significant in that case.

Complexity analysis

Zero RAM impact as cache is stored in stack and is not on the highest stack path (in practice, stores 6 * (2*int16 + 16*float))
Minor increase in renderer PROM (was something like +100 earlier but analysed version did not provide renderer PROM)

WMOPS compared against main at 21a710dc

2dir MASA 512 kbps -> BIN (no head-track)

       min     max     avg     
ref  143.329 149.788 147.745     
opt  129.852 133.336 131.296     
diff -13.477 -16.452 -16.449

2dir MASA 512 kbps -> BIN (head-track)

       min     max     avg     
ref  145.550 152.007 149.965     
opt  135.221 139.559 137.495     
diff -10.329 -12.448 -12.470

MASA 48 kbps -> BIN (no head-track)

       min     max     avg     
ref  109.099 125.702 118.370     
opt  100.760 114.290 107.060     
diff  -8.339 -11.412 -11.310

MASA 48 kbps -> BIN (head-track)

       min     max     avg     
ref  111.319 127.921 120.589     
opt  103.217 116.907 109.648     
diff  -8.102 -11.014 -10.941

MC 7.1+4 96 kbps -> BIN (no head-track)

       min     max     avg     
ref  132.409 165.895 150.045     
opt  124.582 150.386 137.842     
diff  -7.827 -15.509 -12.203

MC 7.1+4 96 kbps -> BIN (head-track)

       min     max     avg     
ref  134.629 168.115 152.264     
opt  126.956 152.955 140.354     
diff  -7.673 -15.160 -11.910

HOA3 80 kbps -> BIN (no head-track)

       min     max     avg     
ref  124.859 165.918 132.328     
opt  121.713 163.541 131.325     
diff  -3.146  -2.377  -1.003

HOA3 80 kbps -> BIN (head-track)

       min     max     avg     
ref  127.365 168.137 134.862     
opt  124.966 166.609 135.400     
diff  -2.399  -1.528  +0.538

ParamISM 4 obj 32 kbps -> BIN (no head-track)

       min    max     avg     
ref  90.441 122.542 109.355     
opt  82.855 114.522 101.960
diff -7.586  -8.020  -7.395

ParamISM 4 obj 32 kbps -> BIN (head-track)

       min    max     avg     
ref  92.638 124.752 111.573     
opt  85.278 116.789 104.550     
diff -7.360  -7.963  -7.023

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