Add integer powers (JuliaIntervals#7)

* ValidatedNumerics -> IntervalArithmetic

* Add powers and tests

* Rewrite tests for small powers / range

* Update appveyor.yml

Project.toml

@@ -6,8 +6,14 @@ version = "0.1.0"
 [deps]
 IntervalArithmetic = "d1acc4aa-44c8-5952-acd4-ba5d80a2a253"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
-Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
 [compat]
 IntervalArithmetic = "≥ 0.15.0"
 julia = "≥ 1.0.0"
+
+[extras]
+Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
+Polynomials = "f27b6e38-b328-58d1-80ce-0feddd5e7a45"
+
+[targets]
+test = ["Test", "Polynomials"]

appveyor.yml

@@ -1,9 +1,18 @@
 environment:
   matrix:
-  - JULIAVERSION: "julialang/bin/winnt/x86/0.5/julia-0.5-latest-win32.exe"
-  - JULIAVERSION: "julialang/bin/winnt/x64/0.5/julia-0.5-latest-win64.exe"
-  - JULIAVERSION: "julianightlies/bin/winnt/x86/julia-latest-win32.exe"
-  - JULIAVERSION: "julianightlies/bin/winnt/x64/julia-latest-win64.exe"
+  - julia_version: 1
+  - julia_version: 1.1
+  - julia_version: nightly
+
+platform:
+  - x86 # 32-bit
+  - x64 # 64-bit
+
+# # Uncomment the following lines to allow failures on nightly julia
+# # (tests will run but not make your overall status red)
+# matrix:
+#   allow_failures:
+#   - julia_version: nightly
 
 branches:
   only:
@@ -17,18 +26,18 @@ notifications:
     on_build_status_changed: false
 
 install:
-# Download most recent Julia Windows binary
-  - ps: (new-object net.webclient).DownloadFile(
-        $("http://s3.amazonaws.com/"+$env:JULIAVERSION),
-        "C:\projects\julia-binary.exe")
-# Run installer silently, output to C:\projects\julia
-  - C:\projects\julia-binary.exe /S /D=C:\projects\julia
+  - ps: iex ((new-object net.webclient).DownloadString("https://raw.githubusercontent.com/JuliaCI/Appveyor.jl/version-1/bin/install.ps1"))
 
 build_script:
-# Need to convert from shallow to complete for Pkg.clone to work
-  - IF EXIST .git\shallow (git fetch --unshallow)
-  - C:\projects\julia\bin\julia -e "versioninfo();
-      Pkg.clone(pwd(), \"AffineArithmetic\"); Pkg.build(\"AffineArithmetic\")"
+  - echo "%JL_BUILD_SCRIPT%"
+  - C:\julia\bin\julia -e "%JL_BUILD_SCRIPT%"
 
 test_script:
-  - C:\projects\julia\bin\julia -e "Pkg.test(\"AffineArithmetic\")"
+  - echo "%JL_TEST_SCRIPT%"
+  - C:\julia\bin\julia -e "%JL_TEST_SCRIPT%"
+
+# # Uncomment to support code coverage upload. Should only be enabled for packages
+# # which would have coverage gaps without running on Windows
+# on_success:
+#   - echo "%JL_CODECOV_SCRIPT%"
+#   - C:\julia\bin\julia -e "%JL_CODECOV_SCRIPT%"

src/AffineArithmetic.jl

@@ -2,7 +2,7 @@ module AffineArithmetic
 
 using IntervalArithmetic
 
-import Base: +, -, *, /, ==,
+import Base: +, -, *, /, ^, ==,
             zero, one, range,
             show
 
@@ -54,6 +54,8 @@ Affine(c::Real) = Affine(c, Float64[])
 
 range(C::Affine) = C.c + sum(abs.(C.γ))*(-1..1)
 
+range(X::Interval) = X
+
 # morally:
 # +(C::Affine, D::Afine) = Affine(C.c + D.c, C.γ + D.γ)
 
@@ -76,6 +78,12 @@ for op in (:+, :-)
     end
 end
 
++(C::Affine, α::Real) = Affine(C.c + α, C.γ)
++(α::Real, C::Affine) = C + α
+
+-(C::Affine, α::Real) = Affine(C.c - α, C.γ)
+-(α::Real, C::Affine) = Affine(α - C.c, [-x for x in C.γ])
+
 function *(C::Affine, D::Affine)
 
     c = C.c
@@ -102,6 +110,11 @@ function *(C::Affine, D::Affine)
 end
 
 *(α::Real, C::Affine) = Affine(α*C.c, α*C.γ)
+*(C::Affine, α::Real) = α * C
+
+^(x::Affine, n::Integer) = Base.power_by_squaring(x, n)
+
+Base.literal_pow(::typeof(^), x::Affine{T}, ::Val{p}) where {T,p} = x^p
 
 eltype(C::Affine{T}) where T = T
 zero(C::Affine{T}) where T = Affine(zero(T))

test/runtests.jl

@@ -1,5 +1,6 @@
 using AffineArithmetic
 using IntervalArithmetic
+using Polynomials
 
 using Test
 
@@ -13,6 +14,8 @@ using Test
     C = Affine(1.0, [3.0, 4.0])
     @test C.c == 1.0
     @test C.γ == [3.0, 4.0]
+
+    reset_affine_index()
 end
 
 reset_affine_index()
@@ -31,36 +34,21 @@ reset_affine_index()
     @test X_a * Y_a == Affine(6.0, [3.0, 2.0, 1.0])
 end
 
-sqr(x) = x * x
-
-X = 1..3
-    X_a = Affine(X)
-
-    Y = sqr(X_a) - 2X_a + one(X_a)
-    r1 = range(Y)
+@testset "Small powers and range" begin
 
-    Z = sqr(X_a - one(X_a))
-    range(Z)
-
-    Y3 = sqr(X - 1)
-
-@testset "range" begin
     X = 1..3
-    X_a = Affine(X)
+    Y = Affine(X)
 
-    Y1 = sqr(X_a) - 2X_a + one(X_a)
-    r1 = range(Y)
+    f(x) = x^2 - x + 1
 
-    Y2 = sqr(X_a - one(X_a))
-    r2 = range(Z)
+    @test range(f(X)) == -1..9
+    @test range(f(Y)) == -1..7   # affine is a little better
 
-    @test r1 == (-2..4)
-    @test r2 == r1
 
-    Y3 = sqr(X - 1)
-    @test Y3 == 0..4
+    g(x) = (x - 1)^3
 
-    @test Y3 ⊆ range(Y1)
+    @test range(g(X)) == 0..8
+    @test range(g(Y)) == -6..8   # affine is significantly worse
 end
 
 reset_affine_index()
@@ -76,3 +64,18 @@ reset_affine_index()
 
     @test A * XX == [Affine(0.0, [0.5, 1.0]), Affine(0.0, [-0.5, 0.5])]
 end
+
+
+reset_affine_index()
+
+@testset "Range of polynomial" begin
+    # example from Rump 2015
+    p = Poly([-3, 1])   # x - 3
+    p2 = p^8
+
+    x = 4 ± 1e-4
+    y = Affine(x)
+
+    @test (-70..70) ⊆ range(p2(x))
+    @test range(p2(y)) ⊆ 0.998..1.002   # affine is extremely much better!
+end