Here's a nice post by Fredrik Johannson about ball arithmetic in general and how he implements it in Arb:
http://fredrikj.net/blog/2013/10/tradeoffs-in-ball-arithmetic/ On Tue, Dec 29, 2015 at 11:30 PM, Jeffrey Sarnoff <[email protected] > wrote: > > FloatHigher.jl <https://github.com/J-Sarnoff/FloatHigher.jl> > > > Accurate high precision floating point math computed quickly. > Fredrik Johannson's Arb, included with Nemo.jl, does the work. > > The type[s] that this module exports is user selectable, > one or more of { Float128, Float256, Float512, Float1024 }. > Float128 is the type if none is selected overtly (see README). > > + Accurate, faster than BigFloat, not BigFloat > + Basic arithmetic, exp, log, most [arc][hyp]trig > - Other ops and Float64 functions are not exposed > - Requires all of Nemo to use a smaller part of it > >
