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Subject: Re: [boost] [Review Request] Multiprecision Arithmetic Library
From: Christopher Kormanyos (e_float_at_[hidden])
Date: 2012-04-06 06:57:23

>> But let's face it, my O(N^2) is very slowwww for digits. >> In your opinion, should I take a crack at this if I find a spare afternoon? > Maybe.  My understanding is that FFT doesn't become viable until the digit count grows truely huge?  Would the Karatsuba algorithm be viable sooner and help more users? > My gut feeling is that the current implementation is perfectly fine up to a few hundred (and maybe a thousand?) decimal places, which will probably take care of most use cases.... well my use cases anyway! In my previous unpublished work (mp_cpp, also using base-10^8), I tuned to the following:     static const  INT32 mp_elem_karatsuba_min = static_cast< INT32>(40);  // Approx. 280 digits.     static const  INT32 mp_elem_fft_min       = static_cast< INT32>(129); // Approx. 900 digits. I've got a recursive Karatsuba template available in my catalog already. Maybe we should try it out. The FFT mentioned above was FFTW (a sadly non-BPL wonder of mankind) so a vanilla FFT would be, maybe, 2 or 3 times slower. > So maybe examples are a higher priority for now? Yes, you are right. I just don't want to get into trouble with the community. Everyone wants to compute a million digits of pi, and they might get mad at us if boost can't do it. But you're right below. We need to stop and get a work of high quality out there to the world---maybe improving it later, like in the fall of 2012. In fact, as I told you and Paul Bristow (both of whom have helped so much in this project), I'm actually booked solid through summer. > We could also go through the current the code looking for > optimisation oportunities - for example would the inversion code be more > efficient using Halley rather than Newton iteration > (see for example Interesting... > Also multiplication and division by integer (relatively common operations?) as special cases. Fortunately, we already have this. The routines mul_unsigned_long_long() and div_unsigned_long_long() utilize O(N) linear mul/div by integer. And we support them in your interface functions eval_multiply() and eval_divide(). >> Of course, in the future we need to cooperate with FFT specialists >> who could get the speed of big-num types (with BPL licensing) >> up to state.of-the-art. But maybe we can get just a bit more >> functionality now before review and potential first distrubition. > For sure, there's always much more that can be done, it's just a case of knowing when to stop! ;-) > Cheers, John. You are right. We need to stop real soon and review what we've got. If I can contribute anything like Karatsuba or FFT relatively quickly, yet adequately reliable, I'll let you know. Best regards, Chris

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