Add 2-arg versions of findmax/min, argmax/min (#35316)

Defines a descending total order, `isgreater` (not exported), where unordered values like NaNs and missing are last. This makes defining min, argmin, etc, simpler and more consistent. Also adds 2-arg versions of findmax/min, argmax/min. Defines and exports the `isunordered` predicate for testing whether a value is unordered like NaN and missing. Fixes #27613. Related: #27639, #27612, #34674.

Thanks to @tkf, @StefanKarpinski and @drewrobson for their assistance with this PR.

Co-authored-by: Jameson Nash <jameson@juliacomputing.com>
Co-authored-by: Takafumi Arakaki <takafumi.a@gmail.com>

NEWS.md

@@ -28,6 +28,8 @@ Build system changes
 New library functions
 ---------------------
 
+* Two argument methods `findmax(f, domain)`, `argmax(f, domain)` and the corresponding `min` versions ([#27613]).
+* `isunordered(x)` returns true if `x` is value that is normally unordered, such as `NaN` or `missing`.
 
 New library features
 --------------------

base/array.jl

@@ -2205,140 +2205,6 @@ findall(x::Bool) = x ? [1] : Vector{Int}()
 findall(testf::Function, x::Number) = testf(x) ? [1] : Vector{Int}()
 findall(p::Fix2{typeof(in)}, x::Number) = x in p.x ? [1] : Vector{Int}()
 
-"""
-    findmax(itr) -> (x, index)
-
-Return the maximum element of the collection `itr` and its index or key.
-If there are multiple maximal elements, then the first one will be returned.
-If any data element is `NaN`, this element is returned.
-The result is in line with `max`.
-
-The collection must not be empty.
-
-# Examples
-```jldoctest
-julia> findmax([8,0.1,-9,pi])
-(8.0, 1)
-
-julia> findmax([1,7,7,6])
-(7, 2)
-
-julia> findmax([1,7,7,NaN])
-(NaN, 4)
-```
-"""
-findmax(a) = _findmax(a, :)
-
-function _findmax(a, ::Colon)
-    p = pairs(a)
-    y = iterate(p)
-    if y === nothing
-        throw(ArgumentError("collection must be non-empty"))
-    end
-    (mi, m), s = y
-    i = mi
-    while true
-        y = iterate(p, s)
-        y === nothing && break
-        m != m && break
-        (i, ai), s = y
-        if ai != ai || isless(m, ai)
-            m = ai
-            mi = i
-        end
-    end
-    return (m, mi)
-end
-
-"""
-    findmin(itr) -> (x, index)
-
-Return the minimum element of the collection `itr` and its index or key.
-If there are multiple minimal elements, then the first one will be returned.
-If any data element is `NaN`, this element is returned.
-The result is in line with `min`.
-
-The collection must not be empty.
-
-# Examples
-```jldoctest
-julia> findmin([8,0.1,-9,pi])
-(-9.0, 3)
-
-julia> findmin([7,1,1,6])
-(1, 2)
-
-julia> findmin([7,1,1,NaN])
-(NaN, 4)
-```
-"""
-findmin(a) = _findmin(a, :)
-
-function _findmin(a, ::Colon)
-    p = pairs(a)
-    y = iterate(p)
-    if y === nothing
-        throw(ArgumentError("collection must be non-empty"))
-    end
-    (mi, m), s = y
-    i = mi
-    while true
-        y = iterate(p, s)
-        y === nothing && break
-        m != m && break
-        (i, ai), s = y
-        if ai != ai || isless(ai, m)
-            m = ai
-            mi = i
-        end
-    end
-    return (m, mi)
-end
-
-"""
-    argmax(itr)
-
-Return the index or key of the maximum element in a collection.
-If there are multiple maximal elements, then the first one will be returned.
-
-The collection must not be empty.
-
-# Examples
-```jldoctest
-julia> argmax([8,0.1,-9,pi])
-1
-
-julia> argmax([1,7,7,6])
-2
-
-julia> argmax([1,7,7,NaN])
-4
-```
-"""
-argmax(a) = findmax(a)[2]
-
-"""
-    argmin(itr)
-
-Return the index or key of the minimum element in a collection.
-If there are multiple minimal elements, then the first one will be returned.
-
-The collection must not be empty.
-
-# Examples
-```jldoctest
-julia> argmin([8,0.1,-9,pi])
-3
-
-julia> argmin([7,1,1,6])
-2
-
-julia> argmin([7,1,1,NaN])
-4
-```
-"""
-argmin(a) = findmin(a)[2]
-
 # similar to Matlab's ismember
 """
     indexin(a, b)

base/exports.jl

@@ -657,6 +657,7 @@ export
     isequal,
     ismutable,
     isless,
+    isunordered,
     ifelse,
     objectid,
     sizeof,

base/operators.jl

@@ -141,7 +141,7 @@ is defined, it is expected to satisfy the following:
   `isless(x, y) && isless(y, z)` implies `isless(x, z)`.
 
 Values that are normally unordered, such as `NaN`,
-are ordered in an arbitrary but consistent fashion.
+are ordered after regular values.
 [`missing`](@ref) values are ordered last.
 
 This is the default comparison used by [`sort`](@ref).
@@ -168,6 +168,63 @@ isless(x::AbstractFloat, y::AbstractFloat) = (!isnan(x) & (isnan(y) | signless(x
 isless(x::Real,          y::AbstractFloat) = (!isnan(x) & (isnan(y) | signless(x, y))) | (x < y)
 isless(x::AbstractFloat, y::Real         ) = (!isnan(x) & (isnan(y) | signless(x, y))) | (x < y)
 
+"""
+    isgreater(x, y)
+
+Not the inverse of `isless`! Test whether `x` is greater than `y`, according to
+a fixed total order compatible with `min`.
+
+Defined with `isless`, this function is usually `isless(y, x)`, but `NaN` and
+[`missing`](@ref) are ordered as smaller than any ordinary value with `missing`
+smaller than `NaN`.
+
+So `isless` defines an ascending total order with `NaN` and `missing` as the
+largest values and `isgreater` defines a descending total order with `NaN` and
+`missing` as the smallest values.
+
+!!! note
+
+    Like `min`, `isgreater` orders containers (tuples, vectors, etc)
+    lexigraphically with `isless(y, x)` rather than recursively with itself:
+
+    ```jldoctest
+    julia> Base.isgreater(1, NaN) # 1 is greater than NaN
+    true
+
+    julia> Base.isgreater((1,), (NaN,)) # But (1,) is not greater than (NaN,)
+    false
+
+    julia> sort([1, 2, 3, NaN]; lt=Base.isgreater)
+    4-element Vector{Float64}:
+       3.0
+       2.0
+       1.0
+     NaN
+
+    julia> sort(tuple.([1, 2, 3, NaN]); lt=Base.isgreater)
+    4-element Vector{Tuple{Float64}}:
+     (NaN,)
+     (3.0,)
+     (2.0,)
+     (1.0,)
+    ```
+
+# Implementation
+This is unexported. Types should not usually implement this function. Instead, implement `isless`.
+"""
+isgreater(x, y) = isunordered(x) || isunordered(y) ? isless(x, y) : isless(y, x)
+
+"""
+    isunordered(x)
+
+Return true if `x` is a value that is not normally orderable, such as `NaN` or `missing`.
+
+!!! compat "Julia 1.7"
+    This function requires Julia 1.7 or later.
+"""
+isunordered(x) = false
+isunordered(x::AbstractFloat) = isnan(x)
+isunordered(x::Missing) = true
 
 function ==(T::Type, S::Type)
     @_pure_meta