Simplified version of mod(x::Interval, y::Real) #525

petvana · 2022-05-24T18:18:52Z

This PR cherry-picks mod(x::Interval, y::Real) from #178 because it seems to be the most useful case (at least for me), and also easiest to implement.

Cc: @dpsanders @lbenet

fixes #129

petvana · 2022-05-24T18:41:35Z

Btw, I've also found that mod can be tighter for two intervals than in #178 because I believe mod(1..1, 0.9..1.1) == 0..1.

julia> using IntervalArithmetic

julia> function mod178(X::Interval, a::Interval)
           division = X / a
           fl = floor(division)

           if fl.lo < fl.hi
               return 0..(a.hi)
           end

           return (division - fl) * a
       end
mod178 (generic function with 1 method)

julia> mod178(1..1, 0.9..1.1)
[0, 1.10001]

julia> maximum(mod(1, x) for x in 0.9:0.01:1.1)
1.0

codecov-commenter · 2022-05-24T18:59:41Z

Codecov Report

Patch coverage: 100.00% and project coverage change: +0.59 🎉

Comparison is base (f8a5b5e) 90.36% compared to head (7bef23e) 90.96%.

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Additional details and impacted files

@@            Coverage Diff             @@
##           master     #525      +/-   ##
==========================================
+ Coverage   90.36%   90.96%   +0.59%     
==========================================
  Files          25       25              
  Lines        1796     1837      +41     
==========================================
+ Hits         1623     1671      +48     
+ Misses        173      166       -7

Impacted Files	Coverage Δ
src/IntervalArithmetic.jl	`100.00% <ø> (ø)`
src/intervals/functions.jl	`96.27% <100.00%> (+0.18%)`	⬆️

... and 6 files with indirect coverage changes

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src/intervals/functions.jl

Co-authored-by: lucaferranti <49938764+lucaferranti@users.noreply.github.com>

lbenet

Thanks a lot for addressing #129.

In general the pull-request LGTM! I left some suggestions, which I think are easy to implement.

src/intervals/functions.jl

lbenet · 2022-05-25T21:27:35Z

src/intervals/functions.jl

+Calculate `x mod y` where `x` is an interval and `y` is a positive divisor.
+"""
+function mod(x::Interval, y::Real)
+    @assert y > zero(y) "modulo is currently implemented only for a positive divisor."


Is it possible to extend this to have strictly negative y? I understand that having 0 ∈ y complicates things....

Updated for strictly negative divisor. Hope its correct.

The implementation seems to me correct if we have y::AbstractFloat (perhaps also including Rationals, but let me forget about them now), which corresponds to the tests.

However, if y::Interval (and we have Interval <: Real) then there this function throws errors: e.g., try mod(1..2, 1..2), which I think should return Interval(0.0, 2.0). In this case things are subtle, because y != zero(y) is true for [-1, 1], but that interval is not strictly positive or negative. Also, Interval(zero(y), y) causes the error mentioned above. I guess this is the reason that mod has two methods in #178.

My suggestion is either restrict y::AbstractFloat, or include a new method where y::Interval.

This is my mistake. My intention was to constrain y NOT to be Interval. I've not realized 1..3 isa Real -> true. However, If I constraint it to y::AbstractFloat it does not accept integers for example because 1 isa AbstractFloat -> false, right?

you could do Union{AbstractFloat, Integer} to accept both integers and floats but no intervals (similar to add rationals and irrationals).

Can the method be generalized to the case of y interval?

actually forget about the union, a better suggestion would be to define

mod(x::Real, y::Interval) = throw(ArgumentError("mod not defined for second argument interval")) mod(x::Interval, y::Interval) = throw(ArgumentError("mod not defined for second argument interval"))

mod can indeed be generalized for y::Interval. It's tricky with respect of having zero within the interval, which is part of the reason I was suggesting to have either a strictly positive or negative y. Actually, a motivating example would be to have y::Irrational, or actually any (mathematical) real number which is not exactly representable as a Float64. Note that #178 includes such an implementation, though it does not include the restriction of strictly positive/negative intervals. The subtleties related to zero at the end are related to the division: y appears in the denominator.

I unresolved this conversation, so it is easy to track the discussion...

fwiw in octave

>> mod(infsup(-3, 2), infsup(-1, 0.5)) ans = [-1, +0.5] >> mod(infsup(-3, 2), infsup(0, 0)) ans = [Empty] >> mod(infsup(-3, 2), infsup(0, 3)) ans = [0, 3] >> mod(infsup(-3, 2), infsup(1, 3)) ans = [0, 3] >> mod(infsup(-3, 2), infsup(-3, 2)) ans = [-3, +2]

test/interval_tests/numeric.jl

lucaferranti · 2022-05-27T07:31:24Z

src/intervals/functions.jl

+Calculate `x::Interval mod y::Real`, limited by `y != 0`.
+"""
+function mod(x::Interval, y::Real)
+    @assert y != zero(y) """mod(x::Interval, y::Real) 


an alternative would be to return an empty interval, I think this would be more conformant with the IEEE standard behavior, e.g.

julia> sqrt(-1.. -1) ∅ julia> log(-2.. -1) ∅

Or we can define mod(a..b, 0) == 0..0 ⊇ ∅ as Wolfram says
https://www.wolframalpha.com/input?i=limit+x-%3E0%2B+mod%281%2C+x%29

Consequently, for 0 ∈ y, we can define smth like mod(x,y) = union(mod(x,(y.lo..y.lo/3)), mod(x, (y.hi/3)..(y.hi))) because the maximum value needs to by in (y.hi/2)..(y.hi)

I propose to solve this in some future PR, and move the discussion to #129, to keep track once this PR merged.

Or we can define mod(a..b, 0) == 0..0 ⊇ ∅ as Wolfram says https://www.wolframalpha.com/input?i=limit+x-%3E0%2B+mod%281%2C+x%29

Julia (and Wolfram) return NaN (undefined) for mod(3.2, 0.0), which makes sense due to the division in the algorithm.

Consequently, for 0 ∈ y, we can define smth like mod(x,y) = union(mod(x,(y.lo..y.lo/3)), mod(x, (y.hi/3)..(y.hi))) because the maximum value needs to by in (y.hi/2)..(y.hi)

This idea is interesting, and reminds me a little bit what we have for extended_div. That certainly should be addressed in another PR. Yet, I think for (mathematical) reals, mod(x,y) is a number in the interval [0,y] for y>0, or [y, 0] if y<0, isn't it?

From the range of mod(x,y) for real y, then for a strictly positive interval y, we should return [0, sup(y)], or if it is strictly negative [inf(y), 0]. If 0 ∈ y, we should return the hull of these intervals.

I think my last comment corresponds to these results... Or not?

…c.jl into simplified-mod

Kolaru · 2023-07-03T22:34:08Z

Sorry for the extended delay.

Since all tests are passing and all discussions are passing, I am merging. Thanks a lot for your contribution !

commit 1c0522f Merge: 4c239d5 ee93bd4 Author: Benoît Richard <kolaru@hotmail.com> Date: Sun Jul 23 23:13:48 2023 +0200 Merge pull request #569 from vaerksted/master fix typos commit ee93bd4 Author: spaette <spaette@gmx.com> Date: Sat Jul 22 12:11:01 2023 -0500 typos commit 4c239d5 Author: Benoît Richard <kolaru@hotmail.com> Date: Tue Jul 4 00:35:20 2023 +0200 Bump version commit 249040d Merge: 4404658 7bef23e Author: Benoît Richard <kolaru@hotmail.com> Date: Tue Jul 4 00:34:13 2023 +0200 Merge pull request #525 from petvana/simplified-mod Simplified version of mod(x::Interval, y::Real) commit 4404658 Author: Benoît Richard <kolaru@hotmail.com> Date: Wed Jun 14 14:03:14 2023 +0200 Bump version for release commit 7bef23e Author: Petr Vana <petvana@centrum.cz> Date: Fri May 27 11:11:53 2022 +0200 Cleanup commit f9f4733 Author: Petr Vana <petvana@centrum.cz> Date: Fri May 27 11:10:05 2022 +0200 Throw ArgumentError for Interval divisor for mod commit 6fdc809 Merge: 439723f d2603d6 Author: Petr Vana <petvana@centrum.cz> Date: Fri May 27 11:01:43 2022 +0200 Merge branch 'simplified-mod' of github.com:petvana/IntervalArithmetic.jl into simplified-mod commit 439723f Author: Petr Vana <petvana@centrum.cz> Date: Fri May 27 11:01:27 2022 +0200 Disable divisor for mod to be an interval commit d2603d6 Author: Petr Vana <vanapet1@fel.cvut.cz> Date: Thu May 26 11:34:04 2022 +0200 Update docs commit 45abc46 Author: Petr Vana <vanapet1@fel.cvut.cz> Date: Thu May 26 11:30:14 2022 +0200 Implementation for strictly negative divisors for mod commit ff47910 Author: Petr Vana <vanapet1@fel.cvut.cz> Date: Thu May 26 11:11:35 2022 +0200 Add todo for mod with between two intervals commit ea00b23 Author: Petr Vana <petvana@centrum.cz> Date: Wed May 25 19:59:30 2022 +0200 Imrpove test coverage + use zero() commit b56f4be Author: Petr Vana <vanapet1@fel.cvut.cz> Date: Wed May 25 13:44:24 2022 +0200 Use ⊇ operator commit d23df89 Author: Petr Vana <petvana@centrum.cz> Date: Tue May 24 21:13:53 2022 +0200 Update src/intervals/functions.jl Co-authored-by: lucaferranti <49938764+lucaferranti@users.noreply.github.com> commit 153d749 Author: Petr Vana <petvana@centrum.cz> Date: Tue May 24 20:27:51 2022 +0200 Improve testing commit fea1b34 Author: Petr Vana <petvana@centrum.cz> Date: Tue May 24 20:10:05 2022 +0200 Introduce simplified version of mod

Introduce simplified version of mod

fea1b34

petvana changed the title ~~Introduce simplified version of mod~~ Smplified version of mod(x::Interval, y::Real) May 24, 2022

Improve testing

153d749

petvana changed the title ~~Smplified version of mod(x::Interval, y::Real)~~ Simplified version of mod(x::Interval, y::Real) May 24, 2022

lucaferranti reviewed May 24, 2022

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petvana and others added 3 commits May 24, 2022 21:13

Update src/intervals/functions.jl

d23df89

Co-authored-by: lucaferranti <49938764+lucaferranti@users.noreply.github.com>

Use ⊇ operator

b56f4be

Imrpove test coverage + use zero()

ea00b23

lbenet reviewed May 25, 2022

View reviewed changes

petvana added 3 commits May 26, 2022 11:11

Add todo for mod with between two intervals

ff47910

Implementation for strictly negative divisors for mod

45abc46

Update docs

d2603d6

lucaferranti reviewed May 27, 2022

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petvana added 4 commits May 27, 2022 11:01

Disable divisor for mod to be an interval

439723f

Merge branch 'simplified-mod' of github.com:petvana/IntervalArithmeti…

6fdc809

…c.jl into simplified-mod

Throw ArgumentError for Interval divisor for mod

f9f4733

Cleanup

7bef23e

lbenet mentioned this pull request May 27, 2022

Docs: how to handle branching? #524

Open

Datseris mentioned this pull request Jun 30, 2023

What to do with mod? #129

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Kolaru closed this Jul 3, 2023

Kolaru reopened this Jul 3, 2023

Kolaru merged commit 249040d into JuliaIntervals:master Jul 3, 2023
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Simplified version of mod(x::Interval, y::Real) #525

Simplified version of mod(x::Interval, y::Real) #525

petvana commented May 24, 2022 •

edited by lucaferranti

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Kolaru commented Jul 3, 2023

Simplified version of mod(x::Interval, y::Real) #525

Simplified version of mod(x::Interval, y::Real) #525

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petvana commented May 24, 2022 • edited by lucaferranti

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Kolaru commented Jul 3, 2023

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