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IntervalArithmetic.jl reviews and mentions
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[Question] Interval Branch and Bound
Note that interval arithmetic is essentially an operator overloading trick where all the "primitive" operations like +, -, *, /, exp, log, etc. get redefined to work over interval arguments such that the outputs are guaranteed to enclose the true range of possible results. See here or here for the implementations of such operations. David P. Sanders, coauthor of the latter library, has many talks online about such topics which you might find useful.
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JuliaIntervals/IntervalArithmetic.jl is an open source project licensed under GNU General Public License v3.0 or later which is an OSI approved license.
The primary programming language of IntervalArithmetic.jl is Julia.
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