suspect behavior when attempting to bisect an unbounded interval

I feel like this principle would be nice to have:

When i is an interval unbounded from at least one side, when α is a real number between zero and one, bisect(i, α) should not depend on α, except perhaps if α=0 or α=1 (not sure how should bisect behave for α=0 or α=1).

Does that make sense?

The principle does not hold:

julia> bisect(interval(7.0, Inf), prevfloat(0.5))
([7.0, 7.0]_dac, [7.0, ∞)_dac)

julia> bisect(interval(7.0, Inf), 0.5)
([7.0, ∞)_dac, [1.79769e+308, ∞)_dac)

Seems like α=0.5 is a branching point for bisect when the first argument is an unbounded interval. Why should 0.5 be special here?

Versions:

julia> versioninfo()
Julia Version 1.14.0-DEV.3338
Build Info:
  Official https://julialang.org release
  Commit 70fd7971038 (2026-09-23 02:23 UTC)
  GC: Built with stock GC
Platform Info:
  OS: Linux (x86_64-unknown-linux-gnu)
  CPU: 8 × AMD Ryzen 3 5300U with Radeon Graphics (znver2)
  WORD_SIZE: 64
  LLVM: libLLVM-22.1.8 (ORCJIT, znver2)
Threads: 1 default, 1 interactive, 1 GC (on 8 virtual cores)
Environment:
  JULIA_NUM_PRECOMPILE_TASKS = 2
  JULIA_PKG_PRECOMPILE_AUTO = 0

julia> using Pkg: status

julia> status("IntervalArithmetic")
Status `~/.julia/environments/v1.14/Project.toml`
  [d1acc4aa] IntervalArithmetic v1.0.12

@dpsanders

Not sure when this behavior was first introduced. Note that this is the same for mid(x, alpha).

@dpsanders @Kolaru @lbenet

I'm not sure either, but a lot is wrong here, seemingly from two different sources:

mid for half-infinite intervals is wrong when alpha is not 0.5. Note that the behavior is specified in the standard only for alpha = 0.5
High bounds prevfloat(Inf) is displayed as infinite but it shouldn't

julia> X = bareinterval(7.0, Inf)
[7.0, ∞)

julia> m = mid(X, 0.4)
7.0  # This is wrong, should be prevfloat(Inf)

julia> m2 = mid(X, 0.5) 
1.7976931348623157e308  # Correct

julia> X2 = IntervalArithmetic._unsafe_bareinterval(Float64, 7.0, m2)
[7.0, ∞) # looks wrong, should be [7.0, 1.7976931348623157e308], but it is only a display thing

julia> X2.hi
1.7976931348623157e308  # The bound is correct

the display issue above is issue #780

As discussed in today JuliaInterval call, the behavior should be for an half infinite interval X = [a, Inf):

mid(X, alpha) == prevfloat(Inf) if 0 < alpha < 1
Disallow alpha == 0 or alpha == 1

And similarly for -Inf bound.

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suspect behavior when attempting to `bisect` an unbounded interval #781

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suspect behavior when attempting to bisect an unbounded interval #781

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nsajko commented on Sep 23, 2026

OlivierHnt commented on Sep 23, 2026

Kolaru commented on Oct 5, 2026

nsajko commented on Oct 5, 2026

Kolaru commented on Oct 8, 2026

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suspect behavior when attempting to `bisect` an unbounded interval #781