Release 1.0

.github/workflows/CI.yml

@@ -11,7 +11,7 @@ jobs:
       fail-fast: false
       matrix:
         version:
-          - '1.9'
+          - '1.10'
           - '1'
           - 'nightly'
         os:

Project.toml

@@ -8,6 +8,7 @@ CRlibm = "96374032-68de-5a5b-8d9e-752f78720389"
 MacroTools = "1914dd2f-81c6-5fcd-8719-6d5c9610ff09"
 OpenBLASConsistentFPCSR_jll = "6cdc7f73-28fd-5e50-80fb-958a8875b1af"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
+Printf = "de0858da-6303-5e67-8744-51eddeeeb8d7"
 RoundingEmulator = "5eaf0fd0-dfba-4ccb-bf02-d820a40db705"
 
 [weakdeps]
@@ -32,13 +33,14 @@ IntervalArithmeticSparseArraysExt = "SparseArrays"
 Arblib = "1.3.0"
 CRlibm = "1.0.2"
 DiffRules = "1"
-ForwardDiff = "0.10, 1"
+ForwardDiff = "1"
 IntervalSets = "0.7"
-LinearAlgebra = "1.9"
+LinearAlgebra = "1.10"
 MacroTools = "0.5"
 OpenBLASConsistentFPCSR_jll = "0.3.29"
-Random = "1.9"
+Random = "1.10"
+Printf = "1.10"
 RecipesBase = "1"
 RoundingEmulator = "0.2"
-SparseArrays = "1.9.0"
-julia = "1.9"
+SparseArrays = "1.10"
+julia = "1.10"

README.md

@@ -19,7 +19,7 @@ The official documentation is available online: https://juliaintervals.github.io
 
 ## Installation
 
-The IntervalArithmetic.jl package requires to [install Julia](https://julialang.org/downloads/) (v1.9 or above).
+The IntervalArithmetic.jl package requires to [install Julia](https://julialang.org/downloads/) (v1.10 or above).
 
 Then, start Julia and execute the following command in the REPL:
 

docs/src/index.md

@@ -7,7 +7,7 @@ IntervalArithmetic.jl is a Julia package for validated numerics in Julia. All ca
 ## Installation
 
 ```@repl
-using Pkg # Julia v1.9 or above
+using Pkg # Julia v1.10 or above
 redirect_stderr(devnull) do # hide
 Pkg.add("IntervalArithmetic")
 end # hide

ext/IntervalArithmeticForwardDiffExt.jl

@@ -23,8 +23,10 @@ Base.promote_rule(::Type{ExactReal{S}}, ::Type{Dual{T, V, N}}) where {S<:Real, T
 Base.promote_rule(::Type{Dual{T, V, N}}, ::Type{ExactReal{S}}) where {S<:Real, T, V, N} =
     Dual{T,ExactReal{IntervalArithmetic.promote_numtype(V, S)},N}
 
-Base.:(==)(x::Union{BareInterval,Interval}, y::Dual) = x == value(y)
-Base.:(==)(x::Dual, y::Union{BareInterval,Interval}) = value(x) == y
+Base.:(==)(x::Interval, y::Dual) = x == value(y)
+Base.:(==)(x::Dual, y::Interval) = value(x) == y
+Base.:<(x::Interval, y::Dual) = x < value(y)
+Base.:<(x::Dual, y::Interval) = value(x) < y
 
 function Base.:(^)(x::Dual{Txy,<:Interval}, y::Dual{Txy,<:Interval}) where {Txy}
     vx, vy = value(x), value(y)
@@ -91,10 +93,9 @@ function Base.:(^)(x::ExactReal, y::Dual{<:Ty}) where {Ty}
     end
 end
 
-
 # Piecewise functions
 
-function (constant::Constant)(::Dual{T, Interval{S}}) where {T, S}
+function (constant::Constant)(::Dual{T,Interval{S}}) where {T, S}
     return Dual{T}(interval(S, constant.value), interval(S, 0.0))
 end
 

src/IntervalArithmetic.jl

@@ -77,6 +77,8 @@ include("piecewise.jl")
 
 #
 
+import Printf
+
 include("display.jl")
     export setdisplay
 
@@ -228,7 +230,7 @@ Configure the default behavior for:
   [`IntervalArithmetic.MatMulMode`](@ref).
   Keyword: `matmul`. Available options: `:fast` (default), `:slow`.
 """
-function configure(; numtype::Type{<:NumTypes}=Float64, flavor::Symbol=:set_based, rounding::Symbol=:correct, power::Symbol=:fast, matmul::Symbol=:slow)
+function configure(; numtype::Type{<:NumTypes}=Float64, flavor::Symbol=:set_based, rounding::Symbol=:correct, power::Symbol=:fast, matmul::Symbol=:fast)
     configure_numtype(numtype)
     configure_flavor(flavor)
     configure_rounding(rounding)

src/display.jl

@@ -49,7 +49,7 @@ Display options:
   - significant digits: 6
 
 julia> x = interval(0.1, 0.3)
-[0.0999999, 0.300001]_com
+[0.1, 0.3]_com
 
 julia> setdisplay(:full)
 Display options:
@@ -69,7 +69,7 @@ Display options:
   - significant digits: 3
 
 julia> x
-[0.0999, 0.301]_com
+[0.1, 0.3]_com
 
 julia> setdisplay(; decorations = false)
 Display options:
@@ -79,7 +79,7 @@ Display options:
   - significant digits: 3
 
 julia> x
-[0.0999, 0.301]
+[0.1, 0.3]
 ```
 """
 function setdisplay(format::Symbol = display_options.format;
@@ -196,14 +196,14 @@ function _str_basic_repr(a::BareInterval{<:AbstractFloat}, format::Symbol)
         return string(str_lo, ", ", str_hi)
     elseif format === :midpoint
         m = mid(a)
-        str_m = _round_string(m, sigdigits, RoundNearest)
+        str_m = _round_string(m, sigdigits)
         # str_m = ifelse(m ≥ 0, string('+', str_m), str_m)
-        output = string(str_m, " ± ", _round_string(radius(a), sigdigits, RoundUp))
+        output = string(str_m, " ± ", _round_string(radius(a), sigdigits))
         return replace(output, "Inf" => '∞')
     else
-        str_lo = _round_string(lo, sigdigits, RoundDown)
+        str_lo = _round_string(lo, sigdigits)
         # str_lo = ifelse(lo ≥ 0, string('+', str_lo), str_lo)
-        str_hi = _round_string(hi, sigdigits, RoundUp)
+        str_hi = _round_string(hi, sigdigits)
         # str_hi = ifelse(hi ≥ 0, string('+', str_hi), str_hi)
         output = string('[', str_lo, ", ", str_hi, ']')
         return replace(output, "Inf]" => "∞)", "[-Inf" => "(-∞")
@@ -231,26 +231,26 @@ function _str_basic_repr(a::BareInterval{Float32}, format::Symbol)
         return string(str_lo, ", ", str_hi)
     elseif format === :midpoint
         m = mid(a)
-        str_m = _round_string(m, sigdigits, RoundNearest)
+        str_m = _round_string(m, sigdigits)
         str_m = replace(string(str_m, "f0"), "NaNf0" => "NaN32", "Inff0" => "Inf32")
         if contains(str_m, 'e')
             str_m = replace(str_m, 'e' => 'f', "f0" => "")
         end
         # str_m = ifelse(m ≥ 0, string('+', str_m), str_m)
-        str_r = _round_string(radius(a), sigdigits, RoundUp)
+        str_r = _round_string(radius(a), sigdigits)
         str_r = replace(string(str_r, "f0"), "NaNf0" => "NaN32", "Inff0" => "Inf32")
         if contains(str_r, 'e')
             str_r = replace(str_r, 'e' => 'f', "f0" => "")
         end
         return string(str_m, " ± ", str_r)
     else
-        str_lo = _round_string(lo, sigdigits, RoundDown)
+        str_lo = _round_string(lo, sigdigits)
         str_lo = replace(string('[', str_lo, "f0"), "NaNf0" => "NaN32", "[-Inff0" => "(-∞")
         if contains(str_lo, 'e')
             str_lo = replace(str_lo, 'e' => 'f', "f0" => "")
         end
         # str_lo = ifelse(lo ≥ 0, string('+', str_lo), str_lo)
-        str_hi = _round_string(hi, sigdigits, RoundUp)
+        str_hi = _round_string(hi, sigdigits)
         str_hi = replace(string(str_hi, "f0]"), "NaNf0" => "NaN32", "Inff0]" => "∞)")
         if contains(str_hi, 'e')
             str_hi = replace(str_hi, 'e' => 'f', "f0" => "")
@@ -274,14 +274,14 @@ function _str_basic_repr(a::BareInterval{Float16}, format::Symbol)
         return replace(output, "Float16(NaN)" => "NaN16", "Float16(-Inf)" => "-Inf16", "Float16(Inf)" => "Inf16")
     elseif format === :midpoint
         m = mid(a)
-        str_m = _round_string(m, sigdigits, RoundNearest)
+        str_m = _round_string(m, sigdigits)
         # str_m = ifelse(m ≥ 0, string('+', str_m), str_m)
-        output = string("Float16(", str_m, ") ± Float16(", _round_string(radius(a), sigdigits, RoundUp), ')')
+        output = string("Float16(", str_m, ") ± Float16(", _round_string(radius(a), sigdigits), ')')
         return replace(output, "Float16(NaN)" => "NaN16", "Float16(Inf)" => '∞')
     else
-        str_lo = _round_string(lo, sigdigits, RoundDown)
+        str_lo = _round_string(lo, sigdigits)
         # str_lo = ifelse(lo ≥ 0, string('+', str_lo), str_lo)
-        str_hi = _round_string(sup(a), sigdigits, RoundUp)
+        str_hi = _round_string(sup(a), sigdigits)
         # str_hi = ifelse(hi ≥ 0, string('+', str_hi), str_hi)
         output = string("[Float16(", str_lo, "), Float16(", str_hi, ")]")
         return replace(output, "Float16(NaN)" => "NaN16", "[Float16(-Inf)" => "(-∞", "Float16(Inf)]" => "∞)")
@@ -308,102 +308,19 @@ function _str_basic_repr(a::BareInterval{<:Rational}, format::Symbol)
     end
 end
 
-# round to the prescribed significant digits
-# code inspired by `_string(x::BigFloat, k::Integer)` in base/mpfr.jl
-
-function _round_string(x::T, sigdigits::Int, r::RoundingMode) where {T<:AbstractFloat}
-    str_x = string(x)
-    str_digits = split(contains(str_x, '.') ? split(str_x, '.'; limit = 2)[2] : str_x, 'e'; limit = 2)[1]
-    len = length(str_digits)
-    if isinteger(x) && sigdigits ≥ len # `x` is exactly representable
-        return replace(_round_string(big(x), length(str_x), RoundNearest), "e-0" => "e-")
-    elseif ispow2(abs(x)) && sigdigits ≥ len # `x` is exactly representable
-        return replace(_round_string(big(x), len + 1, RoundNearest), "e-0" => "e-")
-    else
-        return _round_string(big(x), sigdigits, r)
-    end
-end
+# truncate to the prescribed significant digits
 
-_round_string(x::BigFloat, sigdigits::Int, ::RoundingMode{:Nearest}) =
-    Base.MPFR._string(x, sigdigits-1) # `sigdigits-1` digits after the decimal
-
-function _round_string(x::BigFloat, sigdigits::Int, r::RoundingMode)
-    if !isfinite(x)
-        return string(Float64(x))
-    else
-        str_x = string(x)
-        str_digits = split(split(str_x, '.'; limit = 2)[2], 'e'; limit = 2)[1]
-        len = length(str_digits)
-        if isinteger(x) && sigdigits ≥ len # `x` is exactly representable
-            return _round_string(big(x), length(str_x), RoundNearest)
-        elseif ispow2(abs(x)) && sigdigits ≥ len # `x` is exactly representable
-            return _round_string(big(x), len + 1, RoundNearest)
-        else
-            # `sigdigits` digits after the decimal
-            str = Base.MPFR.string_mpfr(x, "%.$(sigdigits)Re")
-            rounded_str = _round_string(str, r)
-            return Base.MPFR._prettify_bigfloat(rounded_str)
-        end
-    end
+function _round_string(x::AbstractFloat, sigdigits::Int)
+    !isfinite(x) && return string(x)
+    max_sig_digits = _count_sigdigits(string(x))
+    ndigits = min(sigdigits, max_sig_digits)
+    str = Printf.@sprintf("%.*g", ndigits, x)
+    occursin(r"[eE]", str) && return replace(str, r"^([+-]?\d+)(?=[eE])" => s"\1.0", r"([eE][+-])0+(\d+)" => s"\1\2")
+    !occursin(r"\.", str) && return str * ".0"
+    return str
 end
 
-_round_string(s::String, ::RoundingMode{:Up}) =
-    startswith(s, '-') ? string('-', _round_string_down(s[2:end])) : _round_string_up(s)
-
-_round_string(s::String, ::RoundingMode{:Down}) =
-    startswith(s, '-') ? string('-', _round_string_up(s[2:end])) : _round_string_down(s)
-
-function _round_string_up(s::String)
-    # `s` has one extra significant digit to control the rounding
-    mantissa, exponent = eachsplit(s, 'e')
-    mantissa = mantissa[1:end-1]
-    len = length(mantissa)
-    idx = findlast(d -> (d !== '9') & (d !== '.'), mantissa)
-    if idx == len # last significant digit is not `9`
-        d = parse(Int, mantissa[len]) + 1 # increase the last significant digit
-        return string(view(mantissa, 1:len-1), d, 'e', exponent)
-    else
-        if isnothing(idx) # all significant digits are `9`
-            expo = parse(Int, exponent) + 1 # increase the exponent by `1`
-            expo_str = string(expo; pad = 2)
-            exponent = expo < 0 ? expo_str : string('+', expo_str)
-            return string("1.", '0'^(len - 2), 'e', exponent)
-        else
-            new_mantissa = string(
-                view(mantissa, 1:idx-1),
-                parse(Int, mantissa[idx]) + 1,
-                # add `"."` if the last significant digit not equal to `9` is before the decimal point
-                idx == 1 ? "." : "",
-                '0'^(len - idx))
-            return string(new_mantissa, 'e', exponent)
-        end
-    end
-end
-
-function _round_string_down(s::String)
-    # `s` has one extra significant digit to control the rounding
-    mantissa, exponent = eachsplit(s, 'e')
-    len = length(mantissa)
-    idx = findlast(d -> (d !== '0') & (d !== '.'), mantissa)
-    if idx == len # last significant digit is not `0`
-        return string(view(mantissa, 1:len-1), 'e', exponent) # truncate
-    else
-        if isnothing(idx) # all significant digits are `0`
-            expo = parse(Int, exponent) - 1 # decrease the exponent by `1`
-            expo_str = string(expo; pad = 2)
-            exponent = expo < 0 ? expo_str : string('+', expo_str)
-            return string("9.", '9'^(len - 3), 'e', exponent)
-        else
-            new_mantissa = string(
-                    view(mantissa, 1:idx-1),
-                    parse(Int, mantissa[idx]) - 1,
-                    # add `"."` if the last significant digit not equal to `0` is before the decimal point
-                    idx == 1 ? "." : "",
-                    '9'^(len - (idx + 1)))
-            return string(new_mantissa, 'e', exponent)
-        end
-    end
-end
+_count_sigdigits(s::AbstractString) = length(replace(split(s, r"[eE]")[1], '-' => "", '.' => "", r"^0+" => ""))
 
 #