Implement systems for flavor, pointwise extensions, default bound and rounding mode

.gitignore

@@ -1 +1,3 @@
 docs/build/
+
+.vscode/

NEWS.md

@@ -270,7 +270,7 @@ the interval, e.g. `convert(Interval{Float64}, 0.1)`
 
 - Improvements towards conformance with the [IEEE-1788](https://standards.ieee.org/findstds/standard/1788-2015.html) standard for Interval Arithmetic:
 
- - New `special_intervals.jl` file, with definitions of `emptyinterval`, `entireinterval`, `nai` and related functions. Add new interval functions (`<=`, `radius`, `precedes`, `strictprecedes`, `≺`, etc).
+ - New `special_intervals.jl` file, with definitions of `emptyinterval`, `RR`, `nai` and related functions. Add new interval functions (`<=`, `radius`, `precedes`, `strictprecedes`, `≺`, etc).
 
  - Control rounding tighter for arithmetic operations; `*`, `inv` and `/` have been rewritten; this includes changes in `make_interval` and `convert` to get consistent behavior. These functions pass the corresponding tests in the [ITF1788](https://github.com/oheim/ITF1788) test suite.
 - Deprecate the use of `⊊` in favor of `isinterior` (`⪽`).

TODO

@@ -0,0 +1,191 @@
+Review intervals folder: 
+  General:
+    ☐ Choose whether to use x == zero(T) or x == 0 across files
+    ☐ Check that default flavor always return safe result
+    ☐ {F <: Type} -> {F<:Type} (remove spaces)
+    ✔ Replace "IEEE standard" -> "IEEE Std 1788-2015" @done(19-08-22 16:13)
+    ✔ "Corresponds to" -> "Implement" in doc @done(19-08-22 16:13)
+    ✔ Rename `RR` -> `RR` @done(19-08-19 19:14)
+    ☐ Investigate compile time warnings
+    ✔ Check if intervals of different flavor type can/should be equal in the sense of `isidentical` @done(19-12-08 01:12)
+    ☐ Operation on different flavors of interval should always error.
+
+  Discussion:
+    ☐ Do we want to keep `@floatinterval` and `@biginteral` or use `@interval(F, expr1, expr2)` instead ?
+
+  Global precision:
+    ✔ Get rid of it @done(19-08-20 16:49)
+    ✔ Replace pi_interval(T) by Interval{T}(π) everywhere @done(19-12-18 22:59)
+    ✔ Be sure it is done in compliance with #338 @done(19-12-18 22:59)
+
+  Flavors:
+    Implement set based flavor:
+      ☐ Check all requested stuff 10.5.
+      ☐ Error on undefined
+    ☐ Implement cset flavor
+    ☐ Make cset default
+    ☐ Implement all the needed conversions
+      ☐ Automatise with Cassette.jl ?
+
+  macros.jl:
+    ✔ Review @done(19-08-23 01:57)
+    ☐ Clean or open issue for cleaning of the file
+
+  precision.jl:
+    ✔ Review @done(19-08-19 01:49)
+
+  rounding.jl:
+    ✔ Review @done(19-08-19 01:50)
+
+  conversion.jl:
+    ✔ Review @done(19-08-23 03:25)
+    ☐ Fix ambiguous errors
+
+  complex.jl:
+    Should we even bother ?
+    ☐ Review
+
+  9.1. Arithmetic functions:
+    ☐ Distribute everything from arithmetic.jl in other files
+    basic.jl:
+      ✔ Split @done(19-08-19 01:14)
+      ✔ Verify all requested functions are there @done(19-08-19 02:01)
+      ✔ Common @done(19-08-19 01:11)
+      ☐ Adapt for the removal of promotion
+        ☐ Make sure all cases are in the test suite
+      ☐ Solve ambiguity error for real flavors
+      ☐ Flavor dependent *
+      ☐ Flavor dependent /
+      ☐ Flavor dependent inv
+      ☐ Flavor dependent fma
+    power.jl:
+      ✔ Split @done(19-08-19 01:14)
+      ✔ Verify all requested functions are there @done(19-08-19 04:29)
+      ✔ Common @done(19-08-22 16:25)
+      ☐ Add doc to generated funcs
+      ☐ Flavor dependent power (for negative power)
+      ☐ Flavor dependant log
+      ☐ zero(T) or 0 ?
+    trigonometric.jl:
+      ✔ Split @done(19-08-19 02:00)
+      ✔ Verify all requested functions are there @done(19-08-19 02:00)
+      ✔ Clean constants @done(19-08-19 14:13)
+      ✔ Common @done(19-08-19 15:19)
+      ☐ zero(T) or 0 ?
+    hyperbolic.jl:
+      ✔ Split @done(19-08-19 15:23)
+      ✔ Verify all requested functions are there @done(19-08-19 15:23)
+      ✔ Common @done(19-08-19 15:31)
+      ✔ Add docstring to generated funcs @done(19-08-19 16:45)
+      ☐ Flavor dependent atanh
+    integer.jl:
+      ✔ Split @done(19-08-19 17:31)
+      ✔ Verify all requested functions are there @done(19-08-19 17:35)
+      ✔ Common @done(19-08-19 17:43)
+    absmax.jl:
+      ✔ Split @done(19-08-19 17:46)
+      ✔ Verify all requested functions are there @done(19-08-19 17:46)
+      ✔ Common @done(19-08-19 17:48)
+
+  9.2. Cancellative:
+    ✔ Split @done(19-08-19 19:14)
+    ✔ Verify all requested functions are there @done(19-08-19 19:14)
+    ✔ Common @done(19-08-19 19:14)
+    ☐ Check if cancelminus has flavor dependent edge cases
+
+  9.3 Set operations:
+    ✔ Split @done(19-08-19 19:31)
+    ✔ Verify all requested functions are there @done(19-08-19 19:31)
+    ✔ Common @done(19-08-19 19:31)
+
+  9.4. Numeric functions:
+    ✔ Split @done(19-08-19 01:26)
+    ✔ Common @done(19-08-19 01:11)
+    ☐ Solve mid(a, 0.5) != mid(a) discrepency
+    ☐ Flavor dependent mid
+
+  9.5. Boolean functions:
+    These are in the set_operations.jl file
+    ✔ Split @done(19-08-19 19:30)
+    ✔ Verify all requested functions are there @done(19-08-19 19:31)
+    ✔ Common @done(19-08-19 19:36)
+    ✔ equal is not the same as == @done(19-08-19 19:36)
+    ☐ Check `islessprime`
+    ☐ Flavor dependent issubset/isinterior ?
+
+  9.6. Operatons on/with decoration:
+    ☐ Split
+    ☐ Verify all requested functions are there
+    ☐ Review
+
+  9.7. Literals:
+    ☐ Review
+
+  9.8. Constructor:
+    ☐ Review
+    ☐ Check correctness and tightness for Interval{T}(x)
+    ☐ Document flavors
+    ☐ Document constructors
+    ☐ Make `..` work correctly for all input types
+    ☐ Move `DefaultBound` definition before constructors to be able to use them
+    ✔ Add Interval{T}(π) @done(19-08-19 01:58)
+      ✔ Check performance @done(19-12-18 23:00)
+
+  10.5. Required operations in set-based falvor:
+    10.5.1. Literals:
+      ☐ No idea, but do it
+    10.5.2. Constants:
+      ✔ Add ref to doc @done(19-08-21 00:09)
+      ☐ Move deprecation warning to a separated file ?
+    10.5.3. Forward mode elementary functions:
+      ✔ Add ref to doc @done(19-08-21 00:20)
+    10.5.4. Reverse mode elementary functions:
+      ✔ Open issue about their absence @done(19-08-20 03:16)
+      They are in IntervalConstraint.jl
+    10.5.5. Two output division:
+      ✔ Add ref to doc @done(19-08-21 00:23)
+      ☐ Flavor dependent edge case
+      ☐ Recent GH issue
+    10.5.6. Cancellative:
+      ✔ Add ref to doc @done(19-08-22 15:51)
+      ☐ Check that the set-based follow the required behavior for undbounded intervals
+    10.5.7. Set opeations:
+      ✔ Add ref to doc @done(19-08-22 15:55)
+    10.5.8. Constructors:
+      ☐ Review I guess
+    10.5.9. Numeric functions:
+      ✔ Add ref to doc @done(19-08-22 15:55)
+    10.5.10. Boolean:
+      ✔ Check everything required is present @done(19-08-22 16:07)
+      ✔ Add ref to doc @done(19-08-22 16:07)
+  10.6. Recommended operations:
+    ☐ Check all that stuff
+
+
+Other:
+  bisect.jl:
+    ☐ Review
+  display.jl:
+    ☐ Review
+  InteralArithmetic.jl:
+    ☐ Review
+    ☐ Make sure everything is exported correctly
+    ☐ Check renamed/new functions are exported
+  parsing.jl:
+    ✔ parsing of bare interval @done(19-08-23 02:28)
+    ☐ parsing of decorated interval
+  rand.jl:
+    ☐ Review
+  symbols.jl:
+    ☐ Make sure everything is here
+
+
+Review other folders:
+  Check PR #271 for details
+  ☐ Do it
+
+Bugs:
+  ✔ `Int` times `Interval` errors (e.g. `2*a`) @done(19-12-14 23:50)
+
+Tests:
+  ☐ Uncomment complex tests in `construction.jl`

changelog.txt

@@ -0,0 +1,14 @@
+Changelog
+
+- File structure changed to match the IEEE standard
+- Symbols that alias another function moved to `symbols.jl`
+- Removed global precision
+- `make_interval` renamed `wrap_literals`
+- Removed `pi_interval(T)` in favor of `Interval{T}(π)`
+- Renamed `multiply_by_positive_constant` to `scale`
+- `@round` now take the flavor of the returned interval as first argument
+- Removed `find_quadrants_tan` as it was a duplicate of `find_quadrants`
+- Renamed `mid(a, α)` -> `scaled_mid(a, α)` (to avoid discrepency with default parameter)
+- Functions returning intervals based on bound type now required a flavor type as parameter
+- Renamed `entireinterval` -> `RR`
+- Added check of the "IA_DEFAULT_FLAVOR" and "IA_DEFAULT_BOUND_TYPE" keys in `ENV` to get the flavor (`Interval`) and bound type (`DefaultBound`). The default interval type is thus `Interval{DefaultBound}`.

src/IntervalArithmetic.jl

@@ -21,6 +21,7 @@ export ×, dot
 import Base:
     +, -, *, /, //, fma,
     <, >, ==, !=, ⊆, ^, <=,
+    isless,
     in, zero, one, eps, typemin, typemax, abs, abs2, real, min, max,
     sqrt, exp, log, sin, cos, tan, cot, inv, cbrt, csc, hypot, sec, 
     exp2, exp10, log2, log10,
@@ -50,18 +51,19 @@ import Base.MPFR: MPFRRoundUp, MPFRRoundDown, MPFRRoundNearest, MPFRRoundToZero,
 import .Broadcast: broadcasted
 
 export
-    AbstractInterval, Interval,
+    Interval, DefaultBound,
     interval,
-    @interval, @biginterval, @floatinterval, @make_interval,
-    diam, radius, mid, mag, mig, hull,
-    emptyinterval, ∅, ∞, isempty, isinterior, ⪽,
-    precedes, strictprecedes, ≼, ≺, ⊂, ⊃, ⊇, contains_zero,
-    entireinterval, isentire, nai, isnai, isthin, iscommon, isatomic,
+    @interval, @biginterval, @floatinterval,
+    diam, radius, mid, scaled_mid, mag, mig, hull,
+    emptyinterval, ∅, ∞, isempty, isinterior, isdisjoint, ⪽,
+    precedes, strictprecedes, ≺, ⊂, ⊃, ⊇, contains_zero,
+    isidentical, isdistinct,
+    RR, isentire, nai, isnai, isthin, iscommon, isatomic,
     widen, inf, sup, bisect, mince,
-    parameters, eps, dist,
+    eps, dist,
     midpoint_radius, interval_from_midpoint_radius,
     RoundTiesToEven, RoundTiesToAway,
-    cancelminus, cancelplus, isunbounded,
+    cancelminus, cancelplus, isbounded, isunbounded,
     .., @I_str, ±,
     pow, extended_div,
     setformat, @format
@@ -76,8 +78,6 @@ end
 export
     setindex   # re-export from StaticArrays for IntervalBox
 
-
-
 export showfull
 
 import Base: rounding, setrounding, setprecision
@@ -102,28 +102,24 @@ export
 
 function __init__()
     setrounding(BigFloat, RoundNearest)
-
-
-    setprecision(Interval, 256)  # set up pi
-    setprecision(Interval, Float64)
 end
 
 
 ## Includes
 
 include("intervals/intervals.jl")
+
 include("multidim/multidim.jl")
 include("bisect.jl")
 include("decorations/decorations.jl")
 
 include("rand.jl")
 include("parsing.jl")
 include("display.jl")
+include("symbols.jl")
 
 include("plot_recipes/plot_recipes.jl")
 
-include("deprecated.jl")
-
 """
     Region{T} = Union{Interval{T}, IntervalBox{T}}
 """

src/bisect.jl

@@ -10,7 +10,7 @@ Returns a tuple of the new intervals.
 function bisect(X::Interval, α=where_bisect)
     @assert 0 ≤ α ≤ 1
 
-    m = mid(X, α)
+    m = scaled_mid(X, α)
 
     return (Interval(X.lo, m), Interval(m, X.hi))
 end
@@ -40,3 +40,38 @@ function bisect(X::IntervalBox, i::Integer, α=where_bisect)
 
     return (X1, X2)
 end
+
+"""
+    mince(x::Interval, n)
+
+Splits `x` in `n` intervals of the same diameter, which are returned
+as a vector.
+"""
+function mince(x::Interval, n)
+    nodes = range(x.lo, x.hi, length = n+1)
+    return [Interval(nodes[i], nodes[i+1]) for i in 1:length(nodes)-1]
+end
+
+"""
+    mince(x::IntervalBox, n)
+
+Splits `x` in `n` intervals in each dimension of the same diameter. These
+intervals are combined in all possible `IntervalBox`-es, which are returned
+as a vector.
+"""
+@generated function mince(x::IntervalBox{N,T}, n) where {N,T}
+    quote
+        nodes_matrix = Array{Interval{T},2}(undef, n, N)
+        for i in 1:N
+            nodes_matrix[1:n,i] .= mince(x[i], n)
+        end
+
+        nodes = IntervalBox{$N,T}[]
+        Base.Cartesian.@nloops $N i _->(1:n) begin
+            Base.Cartesian.@nextract $N ival d->nodes_matrix[i_d, d]
+            ibox = Base.Cartesian.@ncall $N IntervalBox ival
+            push!(nodes, ibox)
+        end
+        nodes
+    end
+end

src/decorations/decorations.jl

@@ -1,2 +1,16 @@
 include("intervals.jl")
 include("functions.jl")
+
+# TODO Check if it is consistent with #386
+isnan(x::AbstractFlavor) = false  # NaI is always decorated
+
+# TODO adapt for each flavor
+"""`NaI` not-an-interval: [NaN, NaN]."""
+nai(::Type{T}) where T = DecoratedInterval(convert(T, NaN), convert(T, NaN), ill)
+nai(::Type{F}) where {T, F<:Interval{T}} = nai(T)
+nai(::Interval{T}) where T<:Real = nai(T)
+nai(::DecoratedInterval{T}) where T<:Real = nai(T)
+nai() = nai(Interval{DefaultBound})
+
+isnai(x::Interval) = isnan(x.lo) || isnan(x.hi)
+isnai(x::DecoratedInterval) = isnai(interval(x)) && x.decoration == ill