Add extended_div() (#111)

* Add extended_div()

* Fix bug

* Implement using / and return tuple

* Fix test case

Author: eeshan9815

src/IntervalArithmetic.jl

@@ -44,7 +44,7 @@ export
     RoundTiesToEven, RoundTiesToAway,
     cancelminus, cancelplus, isunbounded,
     .., @I_str, ±,
-    pow,
+    pow, extended_div,
     setformat, @format
 
 export

src/intervals/arithmetic.jl

@@ -193,6 +193,23 @@ function /(a::Interval{T}, b::Interval{T}) where T<:Real
     end
 end
 
+function extended_div(a::Interval{T}, b::Interval{T}) where T<:Real
+
+    S = typeof(a.lo / b.lo)
+    if 0 < b.hi && 0 > b.lo && 0 ∉ a
+        if a.hi < 0
+            return (Interval(-Inf, a.hi / b.hi), Interval(a.hi / b.lo, Inf))
+
+        elseif a.lo > 0
+            return (Interval(-Inf, a.lo / b.lo), Interval(a.lo / b.hi, Inf))
+
+        end
+
+    else
+        return (a / b, emptyinterval(S))
+    end
+end
+
 //(a::Interval, b::Interval) = a / b    # to deal with rationals
 
 

test/interval_tests/numeric.jl

@@ -34,6 +34,19 @@ setprecision(Interval, Float64)
     @test Interval(0.0, 1.0)/Interval(0.0,1.0) == Interval(0.0, Inf)
     @test Interval(-1.0, 1.0)/Interval(0.0,1.0) == entireinterval(c)
     @test Interval(-1.0, 1.0)/Interval(-1.0,1.0) == entireinterval(c)
+
+    @test extended_div(interval(-30.0,-15.0), interval(-5.0,-3.0)) == (interval(3.0, 10.0), emptyinterval(c))
+    @test extended_div(@interval(-30,-15) , @interval(-5,-3)) == (interval(3.0, 10.0), emptyinterval(c))
+    @test extended_div(1.0..2.0, 0.1..1.0) == (interval(1, 20.000000000000004), emptyinterval(c))
+    @test extended_div(a, c) == (interval(2.4999999999999998e-02, 4.4e+00), emptyinterval(c))
+    @test extended_div(c, interval(4.0)) == (interval(6.25e-02, 1e+00), emptyinterval(c))
+    @test extended_div(c, zero(c)) == (emptyinterval(c), emptyinterval(c))
+    @test extended_div(interval( 0.0, 1.0), interval(0.0,1.0)) == (interval(0.0, Inf), emptyinterval(c))
+    @test extended_div(interval(-1.0, 1.0), interval(0.0,1.0)) == (entireinterval(c), emptyinterval(c))
+    @test extended_div(interval(-1.0, 1.0), interval(-1.0,1.0)) == (entireinterval(c), emptyinterval(c))
+    @test extended_div(interval(1.0, 2.0), interval(-4.0, 4.0)) == ((-∞.. -0.25), (0.25..∞))
+    @test extended_div(interval(-2.0, -1.0), interval(-2.0, 4.0)) == ((-∞.. -0.25), (0.5..∞))
+
     a = @interval(1.e-20)
     @test a == Interval(1.0e-20, 1.0000000000000001e-20)
     @test diam(a) == eps(1.e-20)