Add precalculated values of sin/cos for speeding up FFT

[AlexandrGraschenkov]

The code works in the same way as before, except that we don't spend time on sin/cos calculations. This is a real bottleneck for FFT calculations.

System info:

Apple M1 Pro, Mac OS Ventura 13.3
n_threads = 4 / 10 | AVX = 0 | AVX2 = 0 | AVX512 = 0 | FMA = 0 | NEON = 1 | ARM_FMA = 1 | F16C = 0 | FP16_VA = 1 | WASM_SIMD = 0 | BLAS = 1 | SSE3 = 0 | VSX = 0 | COREML = 0 | OPENVINO = 0 |

Testing base.en model on: ./main -f samples/a13.wav

Version	mel time
Original	55.17 ms
Cos/sin table	19.15 ms

Testing base.en model on: ./main -f samples/diffusion2023-07-03.wav

Version	mel time
Original	2142.07 ms
Cos/sin table	734.42 ms

[bobqianic]

@AlexandrGraschenkov If you have some free time, could you do me a favor and test how much of an improvement there would be if the optimization in #1148 is combined with your optimization? This is because I've set it to skip FFT calculations and output the results directly when the FFT input is all zeros during the calculation of log Mel. If you have more time, please help me see how much the quality of speech-to-text has improved. Thank you!

[ggerganov]

This is because I've set it to skip FFT calculations and output the results directly when the FFT input is all zeros during the calculation of log Mel.

How often do you observe this to be the case? I would guess it never happens for normal audio

[bobqianic]

This is because I've set it to skip FFT calculations and output the results directly when the FFT input is all zeros during the calculation of log Mel.

How often do you observe this to be the case? I would guess it never happens for normal audio

After the log Mel correction, we should have 30 seconds of zeros, equating to 480,000 samples or approximately 2,998 frames. The presence of these zeros is due to the zero padding added to the end of the sample before performing calculations. With each FFT taking an estimated 25 microseconds, we anticipate a time saving of 75ms. Additionally, by removing the if statement from the loop, we can reduce the number of branch predictions.

[ggerganov]

Ok, makes sense. This change won't interfere with your changes and it is OK to merge, correct?

I'm slowly working my way through the oldest PRs and will soon reach your changes.

[bobqianic]

Ok, makes sense. This change won't interfere with your changes and it is OK to merge, correct?

I'm slowly working my way through the oldest PRs and will soon reach your changes.

No, in this PR we should switch from sin and cos to sinf and cosf. Once that's done, everything should be fine.