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

src/IntervalArithmetic.jl

@@ -24,6 +24,7 @@ import Base:
     in, zero, one, eps, typemin, typemax, abs, abs2, real, min, max,
     sqrt, exp, log, sin, cos, tan, cot, inv, cbrt, csc, hypot, sec,
     exp2, exp10, log2, log10,
+    mod,
     asin, acos, atan,
     sinh, cosh, tanh, coth, csch, sech, asinh, acosh, atanh, sinpi, cospi,
     union, intersect, isempty,

src/intervals/functions.jl

@@ -373,3 +373,13 @@ function nthroot(a::Interval{T}, n::Integer) where T
     b = nthroot(bigequiv(a), n)
     return convert(Interval{T}, b)
 end
+
+"""
+Calculate `x mod y` where `x` is an interval and `y` is a positive divisor.
+"""
+function mod(x::Interval, y::Real)
+    @assert y > 0 "modulo is currently implemented only for a positive divisor."
+    division = x / y
+    fl = floor(division)
+    fl.lo < fl.hi ? 0..y : y * (division - fl)
+end

test/interval_tests/numeric.jl

@@ -434,3 +434,28 @@ end
     @test nthroot(Interval{BigFloat}(-81, -16), -4) == ∅
     @test nthroot(Interval{BigFloat}(-81, -16), 1) == Interval{BigFloat}(-81, -16)
 end
+
+# approximation used for testing (not to rely on ≈ for intervals)
+# ⪆(x, y) = (x ≈ y) && (y ⊆ x)
+⪆(x::Interval, y::Interval) = x.lo ≈ y.lo && x.hi ≈ y.hi && y ⊆ x
+
+@testset "`mod`" begin
+    r = 0.0625
+    x = r..(1+r)
+    @test mod(x, 1) == mod(x, 1.0) == 0..1
+    @test mod(x, 2) == mod(x, 2.0) ⪆ x
+    @test mod(x, 2.5) ⪆ x
+    @test mod(x, 0.5) == 0..0.5
+
+    x = (-1+r) .. -r
+    @test mod(x, 1) == mod(x, 1.0) ⪆ 1+x
+    @test mod(x, 2) == mod(x, 2.0) ⪆ 2+x
+    @test mod(x, 2.5) ⪆ 2.5+x
+    @test mod(x, 0.5) == 0..0.5
+
+    x = -r .. 1-r
+    @test mod(x, 1) == mod(x, 1.0) == 0..1
+    @test mod(x, 2) == mod(x, 2.0) == 0..2
+    @test mod(x, 2.5) == 0..2.5
+    @test mod(x, 0.5) == 0..0.5
+end