Implementation for strictly negative divisors for mod

Author: petvana

src/intervals/functions.jl

@@ -378,8 +378,13 @@ end
 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."
+    @assert y != zero(y) """mod(x::Interval, y::Real) 
+is currently implemented only for a strictly positive or negative divisor y."""
     division = x / y
     fl = floor(division)
-    fl.lo < fl.hi ? Interval(zero(y), y) : y * (division - fl)
+    if !isthin(fl)
+        return y > zero(y) ? Interval(zero(y), y) : Interval(y, zero(y))
+    else
+        return y * (division - fl)
+    end
 end

test/interval_tests/numeric.jl

@@ -446,20 +446,30 @@ end
     @test mod(x, 2) == mod(x, 2.0) ⪆ x
     @test mod(x, 2.5) ⪆ x
     @test mod(x, 0.5) == 0..0.5
+    @test mod(x, -1) == mod(x, -1.0) == -1..0
+    @test mod(x, -2) == mod(x, -2.0) ⪆ -2+x
+    @test mod(x, -2.5) ⪆ -2.5+x
+    @test mod(x, -0.5) == -0.5..0
 
     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
+    @test mod(x, -1) == mod(x, -1.0) ⪆ x
+    @test mod(x, -2) == mod(x, -2.0) ⪆ x
+    @test mod(x, -2.5) ⪆ x
+    @test mod(x, -0.5) == -0.5..0
 
     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
-
-    @test_throws AssertionError mod(x, -1)
+    @test mod(x, -1) == mod(x, -1.0) == -1..0
+    @test mod(x, -2) == mod(x, -2.0) == -2..0
+    @test mod(x, -2.5) == -2.5..0
+    @test mod(x, -0.5) == -0.5..0
 
     # TODO - implement mod for two intervals
     @test_throws TypeError mod(1..2, 1.4..1.5)