"If we are willing to give up compatibility with IEEE 754 floats
and design a number format with goals appropriate for 2016, we can
achieve several goals simultaneously: Extremely high energy efficiency
and information-per-bit, no penalty for decimal operations instead of
binary, rigorous bounds on answers without the overly pessimistic bounds
produced by interval methods, and unprecedented high speed up to some
precision. This approach extends the ideas of unum arithmetic introduced
two years ago by breaking completely from the IEEE float-type format,
resulting in fixed bit size values, fixed execution time, no exception
values or “gradual underflow” issues, no wasted bit patterns, and no
redundant representations (like “negative zero”). As an example of the
power of this format, a difficult 12-dimensional nonlinear robotic
kinematics problem that has defied solvers to date is quickly solvable
with absolute bounds. Also unlike interval methods, it becomes possible
to operate on arbitrary disconnected subsets of the real number line
with the same speed as operating on a simple bound."
http://superfri.org/superfri/article/view/94
https://news.ycombinator.com/item?id=9943589
https://github.com/LLNL/unum
https://github.com/jrmuizel/pyunum
https://github.com/JuliaComputing/Unums.jl
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