Table Lookup for tanh() versus other solutions

[martinvicanek]

Btw the same argument holds for 2-sample polyBLEP and oversampling in the context of generating band-limited saw and similar waveforms.

[mystran]

Btw the same argument holds for 2-sample polyBLEP and oversampling in the context of generating band-limited saw and similar waveforms.

Well.. yeah, except in the BLEP case it's computationally cheaper to use a longer BLEP without oversampling (or with just a little bit; I like 2x 'cos it means you get to have a wide transition which plays better with non-linearities down the line).

[Dogue]

I am curious about doing a second-order ADAA with this. F2 looks like:

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0.5x * sqrt(1+x^2) + 0.5ln|x + sqrt(1+x^2)|

Have you done second-order ADAA with this?

Frankly no, I never implemented 2nd order ADAA. The expressions grow quickly with increasing order. In my opinion, it is more efficient to stick to 1st order ADAA and increase oversampling if needed.

I've only done second-order ADAA thus far with hard clipping. Given the simplicity of this F2 (relative to, for example, the dilogarithm needed for tanh() proper), is seems this could be done fairly easily.

Using oversampling—at least with the methods I'm using—creates a ripple in the waveform, with maximum amplitude values around +/-1.3. Of course, we can just lower the output gain, although in cases of clipping or of using saturation within a feedback loop, this might be less than ideal, hence the attraction (for me) of higher-order ADAA.

[Dogue]

Just tested a second-order ADAA of this, and while I imagine the code could be optimized, it’s pretty expensive (~6x the CPU of first-order, and ~1.5x first-order tanh).

[juha_p]

Back to the topic... I've been using this reasonably fast (at least w/ GCC) tanh() approximation for many:

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float fast_tanh(float x){
   float p = 2.0f * std::pow(x, 2.0f) + 1.17f;
   return (x * p)/(std::abs(x * p) + 1.0f);
}

https://www.desmos.com/calculator/s2vjhcbuni
https://godbolt.org/z/ePbMe4a3f