long double in arguments and return value

[yanovich]

Great job done, first of all!

I would like to suggest an improvement. If k is close to 1.0, elliptic functions become difficult to calculate. It seems that K(k) is limited to ~70 in practice. Having 128bit floating point values will allow far greater values of K(k).

[Dsplib]

Thanks! Need to research 64 and 128 bits influence to the elliptic functions calculation accuracy. I have compared elliptic IIR filters which was calculated in "double" and I have close accuracy corrssponds to Matlab, Python and Octave realization.

[rat-and-catcher]

Its an issue. The Hi-Q (extremely low transition width) IIR elliptic coefficients (filter order 19-20) looks inexactly. The gcc __float128 looks good for the case; but GNU MPFR looks just more good (is 500+dB real? :). Btw, it seems, that Matlab, Python and Octave uses double 64-bit float by default, so the result looks same.