First of all, this adds a function that was missing in bsemathsignal: a fast_log2 implementation. It works by using the float exponent and approximating the rest of the value using a polynomial. I found a tool that gives optimal polynomial coefficients for a given order: https://github.com/samhocevar/lolremez
Since I was at it already, I also looked at our exp2 approximations. Comparing them to what lolremez would produce, what we do is not ideal. So I also added fast_exp2. This has consistently better relative errors. So I suggest as next step replacing bse_approxN_exp2 by fast_exp2<N> everywhere, which should be as fast, but more accurate. Please review the API and let me know if this can be the canonical API for porting the old functions to.
Remarks:
bse_approxN_exp2, our new fast_exp2<N> no longer guarantees almost zero error if the argument is an integer; however I think we don't really need to preserve this propertyBse::fast_log2 better than Bse::approx_log2 because when reading code "fast" gives me an idea what the function does and why it was used instead of log2Relative exp2(x) approximation errors in interval [-1:1]:
rxprec: bse_approx2_exp2: 0.009017387
rxprec: bse_approx3_exp2: 0.0007944462
rxprec: bse_approx4_exp2: 5.568432e-05
rxprec: bse_approx5_exp2: 3.24224e-06
rxprec: bse_approx6_exp2: 1.614916e-07
rxprec: bse_approx7_exp2: 7.028907e-09
rxprec: bse_approx8_exp2: 2.716875e-10
rxprec: bse_approx9_exp2: 9.445048e-12
rxprec: fast_exp2<2, double>: 0.001724763
rxprec: fast_exp2<3, double>: 7.478144e-05
rxprec: fast_exp2<4, double>: 2.593371e-06
rxprec: fast_exp2<5, double>: 7.493647e-08
rxprec: fast_exp2<6, double>: 1.8558e-09
rxprec: fast_exp2<7, double>: 4.021119e-11
rxprec: fast_exp2<8, double>: 7.746751e-13
rxprec: fast_exp2<9, double>: 1.375958e-14
https://github.com/tim-janik/beast/pull/124
—
You are receiving this because you are subscribed to this thread.
Reply to this email directly, view it on GitHub, or mute the thread.