Add function abs2 (#101)

* Add function abs2

* Add tests for abs2

Author: eeshan9815

src/IntervalArithmetic.jl

@@ -12,7 +12,7 @@ using AdjacentFloats
 import Base:
     +, -, *, /, //, fma,
     <, >, ==, !=, ⊆, ^, <=,
-    in, zero, one, abs, real, min, max,
+    in, zero, one, abs, abs2, real, min, max,
     sqrt, exp, log, sin, cos, tan, inv,
     exp2, exp10, log2, log10,
     asin, acos, atan, atan2,

src/intervals/arithmetic.jl

@@ -235,6 +235,10 @@ function abs(a::Interval)
     Interval(mig(a), mag(a))
 end
 
+function abs2(a::Interval)
+    sqr(a)
+end
+
 function min(a::Interval, b::Interval)
     (isempty(a) || isempty(b)) && return emptyinterval(a)
     Interval( min(a.lo, b.lo), min(a.hi, b.hi))

test/interval_tests/consistency.jl

@@ -243,6 +243,8 @@ c = @interval(0.25, 4.0)
         @test abs(emptyinterval()) == emptyinterval()
         @test abs(Interval(-3.0,1.0)) == Interval(0.0, 3.0)
         @test abs(Interval(-3.0,-1.0)) == Interval(1.0, 3.0)
+        @test abs2(Interval(-3.0,1.0)) == Interval(0.0, 9.0)
+        @test abs2(Interval(-3.0,-1.0)) == Interval(1.0, 9.0)
         @test min(entireinterval(), Interval(3.0,4.0)) == Interval(-Inf, 4.0)
         @test min(emptyinterval(), Interval(3.0,4.0)) == emptyinterval()
         @test min(Interval(-3.0,1.0), Interval(3.0,4.0)) == Interval(-3.0, 1.0)