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JuliaIntervals / IntervalArithmetic.jl

Library for validated numerics using interval arithmetic
https://juliaintervals.github.io/IntervalArithmetic.jl/
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Reinstate fast rounding with `prevfloat` and `nextfloat` #665

Closed dpsanders closed 4 months ago

dpsanders commented 4 months ago

The IEEE 758 standard for floating-point arithmetic guarantees that +, -, *, / and sqrt are faithfully rounded.

Thus directed rounding with prevfloat and nextfloat does give a guaranteed enclosure for interval arithmetic computations using those operations.

In particular this is enough for fast guaranteed enclosure of the range of polynomials.

OlivierHnt commented 4 months ago

Sounds good. Are there tests in the Julia repo on this?

dpsanders commented 4 months ago

Julia is just exposing the cpu operations, which must follow the floating point standard. But good question about tests, I don't know.