If you just want to experiment without having to sort out scaling, performance, portability, etc. you can use an arbitrary precision arithmetic library. Then there are no denormals or under/overflows.
E On Wed, Apr 12, 2023 at 6:16 AM Julien Brulé <[email protected]> wrote: > hi all, > thank you for the highlight on the subject. subsidiary question you know > your hardware and your algorithm do you use any high precision libraries > in an realtime environment ? > best, > j > > On 12/04/2023 05:25, brianw wrote: > > On Apr 11, 2023, at 3:27 AM, STEFFAN DIEDRICHSEN wrote: > >> - Stefan Stenzel proposed to gain up the input by some hundred dBs and > gain down the output accordingly to push out the likelihood of an > underflow, which leads to ahen interesting compander scheme. > > > > I'm philosophising here, but I don't think it's accurate to call this > option a "compander," because there's no compression of expansion. > > > > The fact that floating point signal samples are normalized to the range > of -1.0 to +1.0 is basically arbitrary. It seems like one of those > decisions made for human convenience, and not mathematical optimization. > > > > Even with this standard, there's a conversion required before the DAC to > convert floating point to fixed point (I'm going to ignore floating point > DAC chips). In other words, there's already a gain in and out for the > ADC-to-sample-to-DAC flow, so changing the specifics is nothing like > companding. > > > > Given the natural range of IEEE floats, it might make sense to dispense > with the normal -1.0 to +1.0 assumption and use something larger. One might > merely need to consider the maximum number of channels that need to be > mixed together, and not bother with any more headroom than would be needed. > > > > Of course, all the software would have to be rewritten if the -1.0 to > +1.0 standard were abandoned. However, that's not too far fetched because > we already have DSP systems that are entirely proprietary at the sample > level (the digital audio I/O, ADC and DAC are operating with 24-bit fixed > point, and thus remain compatible no matter what the internal floating > point normalization is used). > > > > Thanks to Stefan Stenzel for bringing something to my attention that I > hadn't stopped to consider: The natural range of floating point, and how > digital audio signals might best fit within that range. > > > > Brian Willoughby >
