WIP: Add erf and erfc (#118)

* Add erf and erfc

* Add test file

* Add SpecialFunctions to REQUIRE

* Fix Interval{Float64} case

-Also fix line endings for test file

* Add tests

Author: SebastianM-C

REQUIRE

@@ -4,4 +4,4 @@ StaticArrays 0.5
 FastRounding 0.0.4
 AdjacentFloats 0.0.5
 RecipesBase
-
+SpecialFunctions

src/IntervalArithmetic.jl

@@ -29,6 +29,9 @@ import Base:
     isinteger, setdiff,
     parse
 
+import SpecialFunctions: 
+    erf, erfc
+
 export
     AbstractInterval, Interval,
     interval,

src/intervals/functions.jl

@@ -266,3 +266,24 @@ for f in (:log, :log2, :log10, :log1p)
 
         end
 end
+
+for f in (:erf, :erfc)
+    @eval function($f)(x::BigFloat, r::RoundingMode)
+        setrounding(BigFloat, r) do
+            ($f)(x)
+        end
+    end
+
+    @eval ($f)(a::Interval{Float64}) = convert(Interval{Float64}, ($f)(big53(a)))
+
+end
+
+function erf(a::Interval{T}) where T
+    isempty(a) && return a
+    @round( erf(a.lo), erf(a.hi) )
+end
+
+function erfc(a::Interval{T}) where T
+    isempty(a) && return a
+    @round( erfc(a.hi), erfc(a.lo) )
+end

test/interval_tests/intervals.jl

@@ -5,6 +5,7 @@ include("consistency.jl")
 include("numeric.jl")
 include("trig.jl")
 include("hyperbolic.jl")
+include("special_functions.jl")
 include("non_BigFloat.jl")
 include("linear_algebra.jl")
 include("loops.jl")

test/interval_tests/special_functions.jl

@@ -0,0 +1,21 @@
+# This file is part of the IntervalArithmetic.jl package; MIT licensed
+
+using IntervalArithmetic
+using Base.Test
+
+setprecision(Interval, 128)
+setprecision(Interval, Float64)
+
+@testset "Special Functions tests" begin
+    @test erf(emptyinterval()) == emptyinterval()
+    @test erf(1..2) == Interval(0.8427007929497148, 0.9953222650189528)
+    @test erf(@interval(0.5)) == Interval(5.2049987781304652e-01, 5.2049987781304663e-01)
+    @test erf(0..0) == Interval(0.0, 0.0)
+    @test erf(@biginterval(-1, 1)) ⊆ Interval(-8.4270079294971489e-01, 8.4270079294971489e-01)
+
+    @test erfc(emptyinterval()) == emptyinterval()
+    @test erfc(1..2) == Interval(0.004677734981047265, 0.15729920705028513)
+    @test erfc(@interval(0.5)) == Interval(4.7950012218695343e-01, 4.7950012218695348e-01)
+    @test erfc(0..0) == Interval(1.0, 1.0)
+    @test erfc(@biginterval(-1, 1)) ⊆ Interval(1.5729920705028511e-01, 1.842700792949715)
+end