I have to take back a couple things. The Julia docs are clearer than I thought about the BigFloat type: it's fixed-sized but arbitrarily large, with size resettable by a function call. Second,
julia> eps(BigFloat) 1.727233711018888925077270372560079914223200072887256277004740694033718360632485e-77 so an 1e-77 error in sin(BigFloat(pi)) is just what you'd expect. I'll have to read up on how many bits the type gets by default, how many are in the mantissa, how many in the exponent, and why the string rep gives three more digits than epsilon. And I think I understand your motivation for the double-double type, if not the Float125 and Float127 names. Tom, thanks for the pointer to Unum --it looks very interesting. John On Saturday, October 17, 2015 at 4:56:20 PM UTC-4, Jeffrey Sarnoff wrote: > > I have re-implemented a number of them. The better double-double libraries > are very good +,-,*,^, exp, slightly less so with /; I found some trig lsbs > to be wiggly. > > I mapped triple-double basics and quad-double algorithms into a triplet > cooperative, used internally to assure the manifold smoothness. > > On Saturday, October 17, 2015 at 4:41:44 PM UTC-4, Jeffrey Sarnoff wrote: >> >> I have been -- this has taken up much of the past month. The better >> double-double libraries are very good +,-,*,^, exp, slightly less so with >> /; I found some trig lsbs to be wiggly. >> >> I hand down-converted some quad-double algorithms and routines to be >> triple-double work-alikes. I use them internally to obtain an exported type >> that is numerically smoother. >> >> >> On Saturday, October 17, 2015 at 4:12:44 PM UTC-4, Steven G. Johnson >> wrote: >>> >>> >>> >>> On Saturday, October 17, 2015 at 9:39:54 AM UTC-4, Jeffrey Sarnoff wrote: >>>> >>>> I am working on routines for a double-double-like floating point type. >>>>> >>>>> >>> There are plenty of such libraries already existing as free/open-source >>> software. Why not crib from them? >>> >>
