Merge branch 'master' into release-1.0

Author: OlivierHnt

Project.toml

@@ -1,7 +1,7 @@
 name = "IntervalArithmetic"
 uuid = "d1acc4aa-44c8-5952-acd4-ba5d80a2a253"
 repo = "https://github.com/JuliaIntervals/IntervalArithmetic.jl.git"
-version = "0.22.23"
+version = "0.22.25"
 
 [deps]
 CRlibm = "96374032-68de-5a5b-8d9e-752f78720389"

docs/src/manual/construction.md

@@ -145,13 +145,12 @@ interval(1) # considered "guaranteed" as the user explicitly constructed the int
 
 In contrast, a [`BareInterval`](@ref) can only be constructed via [`bareinterval`](@ref), it is not a subtype of `Real`, and there are no allowed conversion with `Number`. Thus, this interval type is always guaranteed.
 
-
 !!! danger
-    A user interested in validated numerics should **always** have a resulting interval for which [`isguaranteed`](@ref) is `true`.
+    A user interested in validated numerics should **always** track down the source of an "NG" label.
 
 
 
-## More constructors
+### More constructors
 
 The submodule `IntervalArithmetic.Symbols` exports the infix operator `..` and `±` as an alias for `interval`; this submodule must be explicitly imported.
 

docs/src/manual/usage.md

@@ -123,9 +123,10 @@ One can refer to the following:
 - `setdiff`: cannot be used with intervals. See instead [`interiordiff`](@ref).
 
 
+
 ## Piecewise functions
 
-Since intervals don't play well with `if .. else .. end` statement,
+Since intervals don't play well with `if ... else ... end` statement,
 we provide a utility to define function by pieces:
 
 ```@repl usage
@@ -141,6 +142,7 @@ The resulting function work with both standard numbers and intervals,
 and deal properly with the decorations of intervals.
 
 
+
 ## Custom interval bounds type
 
 A `BareInterval{T}` or `Interval{T}` have the restriction `T <: Union{Rational,AbstractFloat}` which is the parametric type for the bounds of the interval. Supposing one wishes to use their own numeric type `MyNumType <: Union{Rational,AbstractFloat}`, they must provide their own arithmetic operations (with correct rounding!).

src/intervals/construction.jl

@@ -482,7 +482,8 @@ of the form ``m \\pm r``.
 function _interval_midpoint(::Type{T}, m, r, d::Decoration = com) where {T<:BoundTypes}
     x = _interval_infsup(T, m, m, d)
     r = _interval_infsup(T, r, r, d)
-    return _interval_infsup(T, x - r, x + r, d)
+    precedes(zero(r), r) && return _interval_infsup(T, x - r, x + r, d)
+    return throw(DomainError(r, "must be positive"))
 end
 
 _interval_midpoint(::Type{T}, m::Complex, r, d::Decoration = com) where {T<:BoundTypes} =

src/intervals/exact_literals.jl

@@ -58,6 +58,8 @@ ExactReal(x::ExactReal) = x
 
 _value(x::ExactReal) = x.value # hook for interval constructor
 
+isguaranteed(::ExactReal) = true
+
 # utilities
 
 Base.to_index(i::ExactReal{<:Integer}) = i.value # allow to index with ExactReal

src/matmul.jl

@@ -7,7 +7,7 @@ function Base.inv(A::Matrix{<:RealOrComplexI})
     F = A * approx_A⁻¹ - interval(LinearAlgebra.I)
     Y = LinearAlgebra.opnorm(approx_A⁻¹ * F, Inf)
     Z₁ = LinearAlgebra.opnorm(F, Inf)
-    if isbounded(Y) & strictprecedes(Z₁, one(one(Z₁)))
+    if isbounded(Y) & strictprecedes(Z₁, one(Z₁))
         A⁻¹ = interval.(approx_A⁻¹, inf(interval(mag(Y)) / (one(Z₁) - interval(mag(Z₁)))); format = :midpoint)
     else
         A⁻¹ = fill(nai(eltype(approx_A⁻¹)), size(A))
@@ -383,6 +383,7 @@ _2mat(A) = A
 function _call_gem_openblas_upward!(C, A_::AbstractMatrix{Float64}, B_::AbstractMatrix{Float64})
     A = _2mat(A_)
     B = _2mat(B_)
+
     m, k = size(A)
     n = size(B, 2)
 
@@ -414,6 +415,7 @@ end
 function _call_gem_openblas_upward!(C, A_::AbstractMatrix{Float64}, B_::AbstractVector{Float64})
     A = _2mat(A_)
     B = _2mat(B_)
+
     m, k = size(A)
 
     α = 1.0