Complex powers (#201)

Version 0.7 and 1.0 compatibility including complex powers

Author: dpsanders

.travis.yml

@@ -10,17 +10,18 @@ os:
   - osx
 
 julia:
-  - 0.6
+  - 0.7
+  - 1.0
   - nightly
 
-matrix:
-   allow_failures:
-     - julia: nightly
+#matrix:
+#   allow_failures:
+#     - julia: nightly
 
 notifications:
   email: false
 
 after_success:
-  - julia -e 'Pkg.add("Documenter")'
+  - julia -e 'using Pkg; Pkg.add("Documenter")'
   - julia -e 'cd(Pkg.dir("IntervalArithmetic")); include(joinpath("docs", "make.jl"))'
   - julia -e 'cd(Pkg.dir("IntervalArithmetic")); Pkg.add("Coverage"); using Coverage; Coveralls.submit(Coveralls.process_folder()); Codecov.submit(process_folder())'

NEWS.md

@@ -146,7 +146,7 @@ setdisplay(:full)
 - `bisect` function in `ValidatedNumerics.RootFinding` for bisecting `Interval`s and `IntervalBox`es #217
 
 ### Other
-- Many tests use `Base.Test` instead of `FactCheck` #205
+- Many tests use `Test` instead of `FactCheck` #205
 - Miscellaneous bugfixes
 
 ## v0.6

REQUIRE

@@ -1,7 +1,6 @@
-julia 0.6
-CRlibm 0.6
-StaticArrays 0.5
-FastRounding 0.0.4
-AdjacentFloats 0.0.5
-RecipesBase
-Compat 0.69.0
+julia 0.7
+CRlibm 0.7
+StaticArrays 0.8
+FastRounding 0.1.2
+SetRounding 0.2
+RecipesBase 0.5

appveyor.yml

@@ -1,20 +1,23 @@
 environment:
   matrix:
-  - JULIA_URL: "https://julialang-s3.julialang.org/bin/winnt/x86/0.6/julia-0.6-latest-win32.exe"
-  - JULIA_URL: "https://julialang-s3.julialang.org/bin/winnt/x64/0.6/julia-0.6-latest-win64.exe"
-  - JULIA_URL: "https://julialangnightlies-s3.julialang.org/bin/winnt/x86/julia-latest-win32.exe"
-  - JULIA_URL: "https://julialangnightlies-s3.julialang.org/bin/winnt/x64/julia-latest-win64.exe"
-
-# uncomment the following lines to allow failures on nightly julia
-# (tests will run but not make your overall status red)
-matrix:
- allow_failures:
- - JULIA_URL: "https://julialangnightlies-s3.julialang.org/bin/winnt/x86/julia-latest-win32.exe"
- - JULIA_URL: "https://julialangnightlies-s3.julialang.org/bin/winnt/x64/julia-latest-win64.exe"
+  - julia_version: 0.7
+  - julia_version: 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:
     - master
+    - /release-.*/
 
 notifications:
   - provider: Email
@@ -23,24 +26,18 @@ notifications:
     on_build_status_changed: false
 
 install:
-  - ps: "[System.Net.ServicePointManager]::SecurityProtocol = [System.Net.SecurityProtocolType]::Tls12"
-# If there's a newer build queued for the same PR, cancel this one
-  - ps: if ($env:APPVEYOR_PULL_REQUEST_NUMBER -and $env:APPVEYOR_BUILD_NUMBER -ne ((Invoke-RestMethod `
-        https://ci.appveyor.com/api/projects/$env:APPVEYOR_ACCOUNT_NAME/$env:APPVEYOR_PROJECT_SLUG/history?recordsNumber=50).builds | `
-        Where-Object pullRequestId -eq $env:APPVEYOR_PULL_REQUEST_NUMBER)[0].buildNumber) { `
-        throw "There are newer queued builds for this pull request, failing early." }
-# Download most recent Julia Windows binary
-  - ps: (new-object net.webclient).DownloadFile(
-        $env:JULIA_URL,
-        "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(), \"IntervalArithmetic\"); Pkg.build(\"IntervalArithmetic\")"
+  - echo "%JL_BUILD_SCRIPT%"
+  - C:\julia\bin\julia -e "%JL_BUILD_SCRIPT%"
 
 test_script:
-- C:\projects\julia\bin\julia -e "Pkg.test(\"IntervalArithmetic\")"
+  - 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%"

docs/src/usage.md

@@ -293,7 +293,7 @@ to an `Interval{BigFloat}`, and then use routines from the `MPFR` library
 
 - `^`
 - `exp2`, `exp10`
-- `atan2`, `atanh`
+- `atan`, `atanh`
 
 Note, in particular, that in order to obtain correct rounding for the power function (`^`),
 intervals are converted to and from `BigFloat`; this implies a significant slow-down in this case.

src/IntervalArithmetic.jl

@@ -5,20 +5,16 @@ __precompile__(true)
 module IntervalArithmetic
 
 import CRlibm
+
 using StaticArrays
 using FastRounding
-using AdjacentFloats
-using Compat
-
-if VERSION <= v"0.7.0-DEV.2004"
-    import Base: ×, dot
-    import Compat.Sys
-    export ⊇
-else
-    using Markdown
-    import Base: ⊇
-    import LinearAlgebra: ×, dot
-end
+using SetRounding
+
+using Markdown
+
+using LinearAlgebra
+import LinearAlgebra: ×, dot
+export ×, dot
 
 
 import Base:
@@ -27,24 +23,26 @@ import Base:
     in, zero, one, eps, typemin, typemax, abs, abs2, real, min, max,
     sqrt, exp, log, sin, cos, tan, inv,
     exp2, exp10, log2, log10,
-    asin, acos, atan, atan2,
+    asin, acos, atan,
     sinh, cosh, tanh, asinh, acosh, atanh,
     union, intersect, isempty,
     convert, promote_rule, eltype, size,
     BigFloat, float, widen, big,
-    ∩, ∪, ⊆, eps,
+    ∩, ∪, ⊆, ⊇, eps,
     floor, ceil, trunc, sign, round,
     expm1, log1p,
     precision,
     isfinite, isnan, isinf, iszero,
-    show, showall,
+    show,
     isinteger, setdiff,
     parse, hash
 
 import Base:  # for IntervalBox
     broadcast, length,
     getindex, setindex,
-    start, next, done, eltype
+    iterate, eltype
+
+import .Broadcast: broadcasted
 
 export
     AbstractInterval, Interval,
@@ -67,6 +65,13 @@ export
 export
     setindex   # re-export from StaticArrays for IntervalBox
 
+
+if VERSION < v"1.0-dev"
+    import Base.showall
+end
+
+export showall
+
 import Base: rounding, setrounding, setprecision
 
 

src/bisect.jl

@@ -21,7 +21,7 @@ end
 Bisect the `IntervalBox` `X` at position α ∈ [0,1] along its longest side.
 """
 function bisect(X::IntervalBox, α=where_bisect)
-    i = indmax(diam.(X))  # find longest side
+    i = argmax(diam.(X))  # find longest side
 
     return bisect(X, i, α)
 end

src/decorations/functions.jl

@@ -1,5 +1,8 @@
 # This file is part of the IntervalArithmetic.jl package; MIT licensed
 
+Base.literal_pow(::typeof(^), x::DecoratedInterval{T}, ::Val{p}) where {T,p} = x^p
+
+
 # zero, one
 zero(a::DecoratedInterval{T}) where T<:Real = DecoratedInterval(zero(T))
 zero(::Type{DecoratedInterval{T}}) where T<:Real = DecoratedInterval(zero(T))
@@ -255,7 +258,7 @@ following the IEEE-1788 Standard (see Sect. 11.7.1, pp 47).
 """ union
 
 
-## Functions on unrestricted domains; tan and atan2 are treated separately
+## Functions on unrestricted domains; tan and atan are treated separately
 unrestricted_functions =(
     :exp, :exp2, :exp10,
     :sin, :cos,
@@ -290,10 +293,10 @@ function decay(a::DECORATION)
     ill
 end
 
-function atan2(yy::DecoratedInterval{T}, xx::DecoratedInterval{T}) where T
+function atan(yy::DecoratedInterval{T}, xx::DecoratedInterval{T}) where T
     x = interval_part(xx)
     y = interval_part(yy)
-    r = atan2(y, x)
+    r = atan(y, x)
     d = decoration(r)
     d = min(d, decoration(xx), decoration(yy))
     # Check cases when decoration is trv and decays (from com or dac)

src/display.jl

@@ -109,15 +109,15 @@ end
 function round_string(x::BigFloat, digits::Int, r::RoundingMode)
 
     lng = digits + Int32(8)
-    @compat buf = Array{UInt8}(undef, lng + 1)
+    buf = Array{UInt8}(undef, lng + 1)
 
     lng = ccall((:mpfr_snprintf,:libmpfr), Int32,
     (Ptr{UInt8}, Culong,  Ptr{UInt8}, Int32, Ref{BigFloat}...),
     buf, lng + 1, "%.$(digits)R*g", Base.MPFR.to_mpfr(r), x)
 
     repr = unsafe_string(pointer(buf))
 
-    @compat repr = replace(repr, "nan" => "NaN")
+    repr = replace(repr, "nan" => "NaN")
 
     return repr
 end
@@ -144,8 +144,8 @@ function basic_representation(a::Interval, format=nothing)
         bb = round_string(a.hi, sigfigs, RoundUp)
 
         output = "[$aa, $bb]"
-        @compat output = replace(output, "inf" => "∞")
-        @compat output = replace(output, "Inf" => "∞")
+        output = replace(output, "inf" => "∞")
+        output = replace(output, "Inf" => "∞")
 
     elseif format == :full
         output = "Interval($(a.lo), $(a.hi))"

src/intervals/complex.jl

@@ -1,3 +1,20 @@
+function ^(x::Complex{Interval{T}}, n::Integer) where {T}
+    if n < 0
+        return inv(x)^n
+    end
+
+    return Base.power_by_squaring(x, n)
+end
+
+function ^(x::Complex{Interval{T}}, y::Real) where {T}
+    return exp(y*log(x))
+end
+
+function ^(x::Complex{Interval{T}}, y::Complex) where {T}
+    return exp(y*log(x))
+end
+
+
 function ssqs(x::T, y::T,RND::RoundingMode) where T<:AbstractFloat
     k::Int = 0
     ρ = +(*(x,x,RND),*(y,y,RND),RND)
@@ -75,3 +92,11 @@ function sqrt(z::Complex{Interval{T}}) where T<:AbstractFloat
 
     Complex(ξ,η)
 end
+
+
+function log(z::Complex{T}) where T<:Interval
+    ρ = abs(z)
+    θ = angle(z)
+
+    return log(ρ) + im * θ
+end