Introduce closure function, extracted out of convert (#114)

* Introduce `closure` function, separate from convert.

* Fix find_quadrants (implicit convert -> explicit closure).

* Add docstring to closure.

* Remove tests with undesired behavior.

* Remove one convert method, test another.

* closure -> atomic

Author: tkoolen

src/decorations/intervals.jl

@@ -112,7 +112,7 @@ convert(::Type{DecoratedInterval{T}}, x::S) where {T<:Real, S<:Integer} =
 # end
 function convert(::Type{DecoratedInterval{T}}, xx::DecoratedInterval) where T<:Real
     x = interval_part(xx)
-    x = convert(Interval{T},x)
+    x = atomic(Interval{T},x)
     DecoratedInterval( x, decoration(xx) )
 end
 

src/intervals/conversion.jl

@@ -12,23 +12,77 @@ promote_rule(::Type{BigFloat}, ::Type{Interval{T}}) where T<:Real =
     Interval{promote_type(T, BigFloat)}
 
 
+# convert methods:
+convert(::Type{Interval{T}}, x) where {T} = atomic(Interval{T}, x)
+convert(::Type{Interval{T}}, x::T) where {T} = Interval{T}(x)
+convert(::Type{Interval{T}}, x::Interval{T}) where {T} = x
+convert(::Type{Interval{T}}, x::Interval) where {T} = atomic(Interval{T}, x)
 
-# Floating point intervals:
+convert(::Type{Interval}, x::Real) = (T = typeof(float(x)); convert(Interval{T}, x))
+convert(::Type{Interval}, x::Interval) = x
 
-convert(::Type{Interval{T}}, x::AbstractString) where T<:AbstractFloat =
-    parse(Interval{T}, x)
+"""
+    atomic(::Type{<:Interval}, x)
+
+Construct the tightest interval of a given type that contains the value `x`.
+
+If `x` is an `AbstractString`, the interval will be created by calling `parse`.
+
+# Examples
+
+Construct an `Interval{Float64}` containing a given `BigFloat`:
+
+```julia
+julia> x = big"0.1"
+1.000000000000000000000000000000000000000000000000000000000000000000000000000002e-01
+
+julia> i = IntervalArithmetic.atomic(Interval{Float64}, x)
+[0.0999999, 0.100001]
+
+julia> i isa Interval{Float64}
+true
+
+julia> i.lo <= x <= i.hi
+true
+
+julia> i.hi === nextfloat(i.lo)
+true
+```
+
+Construct an `Interval{Float32}` containing a the real number 0.1 in two ways:
+
+```julia
+julia> i1 = IntervalArithmetic.atomic(Interval{Float32}, "0.1")
+[0.0999999, 0.100001]
 
-convert(::Type{Interval}, x::AbstractString) = convert(Interval{Float64}, x)
+julia> i2 = IntervalArithmetic.atomic(Interval{Float32}, 1//10)
+[0.0999999, 0.100001]
 
-function convert(::Type{Interval{T}}, x::S) where {T<:AbstractFloat, S<:Real}
+julia> i1 === i2
+true
+
+julia> i.lo <= 1//10 <= i.hi
+true
+```
+"""
+function atomic end
+
+# Integer intervals:
+atomic(::Type{Interval{T}}, x::T) where {T<:Integer} = Interval{T}(x)
+
+# Floating point intervals:
+atomic(::Type{Interval{T}}, x::AbstractString) where T<:AbstractFloat =
+    parse(Interval{T}, x)
+
+function atomic(::Type{Interval{T}}, x::S) where {T<:AbstractFloat, S<:Real}
     isinf(x) && return wideinterval(T(x))
 
     Interval{T}( T(x, RoundDown), T(x, RoundUp) )
     # the rounding up could be done as nextfloat of the rounded down one?
     # use @round_up and @round_down here?
 end
 
-function convert(::Type{Interval{T}}, x::S) where {T<:AbstractFloat, S<:AbstractFloat}
+function atomic(::Type{Interval{T}}, x::S) where {T<:AbstractFloat, S<:AbstractFloat}
     isinf(x) && return wideinterval(x)#Interval{T}(prevfloat(T(x)), nextfloat(T(x)))
     # isinf(x) && return Interval{T}(prevfloat(x), nextfloat(x))
 
@@ -41,50 +95,37 @@ function convert(::Type{Interval{T}}, x::S) where {T<:AbstractFloat, S<:Abstract
         return Interval(parse(T, xstr, RoundDown), parse(T, xstr, RoundUp))
     end
 
-    return convert(Interval{T}, xrat)
+    return atomic(Interval{T}, xrat)
 end
 
-convert(::Type{Interval{T}}, x::Interval{T}) where T<:AbstractFloat = x
-
-function convert(::Type{Interval{T}}, x::Interval) where T<:AbstractFloat
+function atomic(::Type{Interval{T}}, x::Interval) where T<:AbstractFloat
     Interval{T}( T(x.lo, RoundDown), T(x.hi, RoundUp) )
 end
 
-
 # Complex numbers:
-convert(::Type{Interval{T}}, x::Complex{Bool}) where T<:AbstractFloat =
+atomic(::Type{Interval{T}}, x::Complex{Bool}) where T<:AbstractFloat =
     (x == im) ? one(T)*im : throw(ArgumentError("Complex{Bool} not equal to im"))
 
 
 # Rational intervals
-function convert(::Type{Interval{Rational{Int}}}, x::Irrational)
-    a = float(convert(Interval{BigFloat}, x))
-    convert(Interval{Rational{Int}}, a)
+function atomic(::Type{Interval{Rational{Int}}}, x::Irrational)
+    a = float(atomic(Interval{BigFloat}, x))
+    atomic(Interval{Rational{Int}}, a)
 end
 
-function convert(::Type{Interval{Rational{BigInt}}}, x::Irrational)
-    a = convert(Interval{BigFloat}, x)
-    convert(Interval{Rational{BigInt}}, a)
+function atomic(::Type{Interval{Rational{BigInt}}}, x::Irrational)
+    a = atomic(Interval{BigFloat}, x)
+    atomic(Interval{Rational{BigInt}}, a)
 end
 
-convert(::Type{Interval{Rational{T}}}, x::S) where {T<:Integer, S<:Integer} =
+atomic(::Type{Interval{Rational{T}}}, x::S) where {T<:Integer, S<:Integer} =
     Interval(x*one(Rational{T}))
 
-convert(::Type{Interval{Rational{T}}}, x::Rational{S}) where
+atomic(::Type{Interval{Rational{T}}}, x::Rational{S}) where
     {T<:Integer, S<:Integer} = Interval(x*one(Rational{T}))
 
-convert(::Type{Interval{Rational{T}}}, x::S) where {T<:Integer, S<:Float64} =
+atomic(::Type{Interval{Rational{T}}}, x::S) where {T<:Integer, S<:Float64} =
     Interval(rationalize(T, x))
 
-convert(::Type{Interval{Rational{T}}}, x::S) where {T<:Integer, S<:BigFloat} =
+atomic(::Type{Interval{Rational{T}}}, x::S) where {T<:Integer, S<:BigFloat} =
     Interval(rationalize(T, x))
-
-
-# conversion to Interval without explicit type:
-function convert(::Type{Interval}, x::Real)
-    T = typeof(float(x))
-
-    return convert(Interval{T}, x)
-end
-
-convert(::Type{Interval}, x::Interval) = x

src/intervals/functions.jl

@@ -7,7 +7,7 @@
 
 # Write explicitly like this to avoid ambiguity warnings:
 for T in (:Integer, :Rational, :Float64, :BigFloat, :Interval)
-    @eval ^(a::Interval{Float64}, x::$T) = convert(Interval{Float64}, big53(a)^x)
+    @eval ^(a::Interval{Float64}, x::$T) = atomic(Interval{Float64}, big53(a)^x)
 end
 
 
@@ -98,7 +98,7 @@ function ^(a::Interval{BigFloat}, x::BigFloat)
     a = a ∩ domain
     (isempty(x) || isempty(a)) && return emptyinterval(a)
 
-    xx = convert(Interval{BigFloat}, x)
+    xx = atomic(Interval{BigFloat}, x)
 
     # @round() can't be used directly, because both arguments may
     # Inf or -Inf, which throws an error
@@ -135,7 +135,7 @@ end
 function ^(a::Interval{Rational{T}}, x::AbstractFloat) where T<:Integer
     a = Interval(a.lo.num/a.lo.den, a.hi.num/a.hi.den)
     a = a^x
-    convert(Interval{Rational{T}}, a)
+    atomic(Interval{Rational{T}}, a)
 end
 
 # Rational power
@@ -149,13 +149,13 @@ function ^(a::Interval{BigFloat}, r::Rational{S}) where S<:Integer
         return emptyinterval(a)
     end
 
-    isinteger(r) && return convert(Interval{T}, a^round(S,r))
+    isinteger(r) && return atomic(Interval{T}, a^round(S,r))
     r == one(S)//2 && return sqrt(a)
 
     a = a ∩ domain
     (isempty(r) || isempty(a)) && return emptyinterval(a)
 
-    y = convert(Interval{BigFloat}, r)
+    y = atomic(Interval{BigFloat}, r)
 
     a^y
 end
@@ -245,7 +245,7 @@ for f in (:exp2, :exp10)
             end
         end
 
-    @eval ($f)(a::Interval{Float64}) = convert(Interval{Float64}, $f(big53(a)))  # no CRlibm version
+    @eval ($f)(a::Interval{Float64}) = atomic(Interval{Float64}, $f(big53(a)))  # no CRlibm version
 
     @eval function ($f)(a::Interval{BigFloat})
             isempty(a) && return a

src/intervals/hyperbolic.jl

@@ -64,6 +64,6 @@ for f in (:tanh, :asinh, :acosh, :atanh)
     @eval function ($f)(a::Interval{Float64})
         isempty(a) && return a
 
-        convert(Interval{Float64}, ($f)(big53(a)) )
+        atomic(Interval{Float64}, ($f)(big53(a)) )
     end
 end

src/intervals/intervals.jl

@@ -56,7 +56,7 @@ Interval(x::Complex) = Interval(real(x)) + im*Interval(imag(x))
 
 Interval{T}(x) where T = Interval(convert(T, x))
 
-Interval{T}(x::Interval) where T = convert(Interval{T}, x)
+Interval{T}(x::Interval) where T = atomic(Interval{T}, x)
 
 """
     is_valid_interval(a::Real, b::Real)
@@ -122,7 +122,9 @@ include("hyperbolic.jl")
 
 # Syntax for intervals
 
-a..b = interval(convert(Interval, a).lo, convert(Interval, b).hi)
+function ..(a::T, b::S) where {T, S}
+    interval(atomic(Interval{T}, a).lo, atomic(Interval{S}, b).hi)
+end
 
 # ..(a::Integer, b::Integer) = interval(a, b)
 # ..(a::Integer, b::Real) = interval(a, nextfloat(float(b)))
@@ -135,3 +137,4 @@ macro I_str(ex)  # I"[3,4]"
 end
 
 a ± b = (a-b)..(a+b)
+±(a::Interval, b) = (a.lo - b)..(a.hi + b)

src/intervals/macros.jl

@@ -81,13 +81,13 @@ by calling `transform`."""
 function make_interval(T, expr1, expr2)
     # @show expr1, expr2
 
-    expr1 = transform(expr1, :convert, :(Interval{$T}))
+    expr1 = transform(expr1, :atomic, :(Interval{$T}))
 
     if isempty(expr2)  # only one argument
         return :(Interval($expr1))
     end
 
-    expr2 = transform(expr2[1], :convert, :(Interval{$T}))
+    expr2 = transform(expr2[1], :atomic, :(Interval{$T}))
 
     :(interval(($expr1).lo, ($expr2).hi))
 end

src/intervals/precision.jl

@@ -18,7 +18,7 @@ const parameters = IntervalParameters()
 doc"`big53` creates an equivalent `BigFloat` interval to a given `Float64` interval."
 function big53(a::Interval{Float64})
     setprecision(Interval, 53) do  # precision of Float64
-        convert(Interval{BigFloat}, a)
+        atomic(Interval{BigFloat}, a)
     end
 end
 
@@ -41,7 +41,7 @@ function setprecision(::Type{Interval}, ::Type{T}, prec::Integer) where T<:Abstr
 
     parameters.precision_type = T
     parameters.precision = prec
-    parameters.pi = convert(Interval{BigFloat}, pi)
+    parameters.pi = atomic(Interval{BigFloat}, pi)
 
     prec
 end
@@ -69,7 +69,7 @@ setprecision(::Type{Interval}, t::Tuple) = setprecision(Interval, t...)
 precision(::Type{Interval}) = (parameters.precision_type, parameters.precision)
 
 
-const float_interval_pi = convert(Interval{Float64}, pi)  # does not change
+const float_interval_pi = atomic(Interval{Float64}, pi)  # does not change
 
 pi_interval(::Type{BigFloat}) = parameters.pi
 pi_interval(::Type{Float64})  = float_interval_pi
@@ -82,6 +82,6 @@ end
 
 
 
-float(x::Interval{T}) where T = convert( Interval{float(T)}, x)  # https://github.com/dpsanders/IntervalArithmetic.jl/issues/174
+float(x::Interval{T}) where T = atomic( Interval{float(T)}, x)  # https://github.com/dpsanders/IntervalArithmetic.jl/issues/174
 
-big(x::Interval) = convert(Interval{BigFloat}, x)
+big(x::Interval) = atomic(Interval{BigFloat}, x)

src/intervals/trigonometric.jl

@@ -19,8 +19,8 @@ This is a rather indirect way to determine if π/2 and 3π/2 are contained
 in the interval; cf. the formula for sine of an interval in
 Tucker, *Validated Numerics*."""
 
-function find_quadrants(x::AbstractFloat)
-    temp = x / half_pi(x)
+function find_quadrants(x::T) where {T<:AbstractFloat}
+    temp = atomic(Interval{T}, x) / half_pi(x)
     (floor(temp.lo), floor(temp.hi))
 end
 
@@ -172,7 +172,7 @@ end
 function atan2(y::Interval{Float64}, x::Interval{Float64})
     (isempty(y) || isempty(x)) && return emptyinterval(Float64)
 
-    convert(Interval{Float64}, atan2(big53(y), big53(x)))
+    atomic(Interval{Float64}, atan2(big53(y), big53(x)))
 end
 
 

test/interval_tests/construction.jl

@@ -64,17 +64,14 @@ using Base.Test
     @test convert(Interval, eu) == @interval(eu)
     @test convert(Interval, BigInt(1)) == Interval(BigInt(1))
     @test convert(Interval, 1//10) == @interval(1//10)
-    @test convert(Interval, 0.1) == Interval(0.09999999999999999, 0.1)
-    @test convert(Interval, big"0.1") == big"0.1"..big"0.1"
+    @test convert(Interval, Interval(0.1, 0.2)) === Interval(0.1, 0.2)
 
     @test convert(Interval{Rational{Int}}, 0.1) == Interval(1//10)
     # @test convert(Interval{Rational{BigInt}}, pi) == Interval{Rational{BigInt}}(pi)
 
     ## promotion
     @test promote(Interval(2//1,3//1), Interval(1, 2)) ==
         (Interval(2.0,3.0), Interval(1.0,2.0))
-    @test promote(Interval(1.5), parse(BigFloat, "2.1")) ==
-        (Interval(BigFloat(1.5)), big"2.1"..big"2.1")
     @test promote(Interval(1.0), pi) == (Interval(1.0), @interval(pi))
 
     # Constructors from the macros @interval, @floatinterval @biginterval