Fix extrema(x; dims) for inputs with NaN/missing

NEWS.md

@@ -99,6 +99,7 @@ Standard library changes
   arithmetic to error if the result may be wrapping. Or use a package such as SaferIntegers.jl when
   constructing the range. ([#40382])
 * TCP socket objects now expose `closewrite` functionality and support half-open mode usage ([#40783]).
+* `extrema` now supports `init` keyword argument ([#36265], [#43604]).
 * Intersect returns a result with the eltype of the type-promoted eltypes of the two inputs ([#41769]).
 * `Iterators.countfrom` now accepts any type that defines `+`. ([#37747])
 

base/compiler/compiler.jl

@@ -131,6 +131,19 @@ include("compiler/abstractinterpretation.jl")
 include("compiler/typeinfer.jl")
 include("compiler/optimize.jl") # TODO: break this up further + extract utilities
 
+# required for bootstrap
+# TODO: find why this is needed and remove it.
+function extrema(x::Array)
+    isempty(x) && throw(ArgumentError("collection must be non-empty"))
+    vmin = vmax = x[1]
+    for i in 2:length(x)
+        xi = x[i]
+        vmax = max(vmax, xi)
+        vmin = min(vmin, xi)
+    end
+    return vmin, vmax
+end
+
 include("compiler/bootstrap.jl")
 ccall(:jl_set_typeinf_func, Cvoid, (Any,), typeinf_ext_toplevel)
 

base/exports.jl

@@ -385,6 +385,7 @@ export
     eachindex,
     eachrow,
     eachslice,
+    extrema!,
     extrema,
     fill!,
     fill,

base/multidimensional.jl

@@ -1695,80 +1695,6 @@ _unique_dims(A::AbstractArray, dims::Colon) = invoke(unique, Tuple{Any}, A)
     end
 end
 
-"""
-    extrema(A::AbstractArray; dims) -> Array{Tuple}
-
-Compute the minimum and maximum elements of an array over the given dimensions.
-
-# Examples
-```jldoctest
-julia> A = reshape(Vector(1:2:16), (2,2,2))
-2×2×2 Array{Int64, 3}:
-[:, :, 1] =
- 1  5
- 3  7
-
-[:, :, 2] =
-  9  13
- 11  15
-
-julia> extrema(A, dims = (1,2))
-1×1×2 Array{Tuple{Int64, Int64}, 3}:
-[:, :, 1] =
- (1, 7)
-
-[:, :, 2] =
- (9, 15)
-```
-"""
-extrema(A::AbstractArray; dims = :) = _extrema_dims(identity, A, dims)
-
-"""
-    extrema(f, A::AbstractArray; dims) -> Array{Tuple}
-
-Compute the minimum and maximum of `f` applied to each element in the given dimensions
-of `A`.
-
-!!! compat "Julia 1.2"
-    This method requires Julia 1.2 or later.
-"""
-extrema(f, A::AbstractArray; dims=:) = _extrema_dims(f, A, dims)
-
-_extrema_dims(f, A::AbstractArray, ::Colon) = _extrema_itr(f, A)
-
-function _extrema_dims(f, A::AbstractArray, dims)
-    sz = size(A)
-    for d in dims
-        sz = setindex(sz, 1, d)
-    end
-    T = promote_op(f, eltype(A))
-    B = Array{Tuple{T,T}}(undef, sz...)
-    return extrema!(f, B, A)
-end
-
-@noinline function extrema!(f, B, A)
-    require_one_based_indexing(B, A)
-    sA = size(A)
-    sB = size(B)
-    for I in CartesianIndices(sB)
-        fAI = f(A[I])
-        B[I] = (fAI, fAI)
-    end
-    Bmax = CartesianIndex(sB)
-    @inbounds @simd for I in CartesianIndices(sA)
-        J = min(Bmax,I)
-        BJ = B[J]
-        fAI = f(A[I])
-        if fAI < BJ[1]
-            B[J] = (fAI, BJ[2])
-        elseif fAI > BJ[2]
-            B[J] = (BJ[1], fAI)
-        end
-    end
-    return B
-end
-extrema!(B, A) = extrema!(identity, B, A)
-
 # Show for pairs() with Cartesian indices. Needs to be here rather than show.jl for bootstrap order
 function Base.showarg(io::IO, r::Iterators.Pairs{<:Integer, <:Any, <:Any, T}, toplevel) where T <: Union{AbstractVector, Tuple}
     print(io, "pairs(::$T)")

base/operators.jl

@@ -504,58 +504,6 @@ julia> minmax('c','b')
 """
 minmax(x,y) = isless(y, x) ? (y, x) : (x, y)
 
-"""
-    extrema(itr) -> Tuple
-
-Compute both the minimum and maximum element in a single pass, and return them as a 2-tuple.
-
-# Examples
-```jldoctest
-julia> extrema(2:10)
-(2, 10)
-
-julia> extrema([9,pi,4.5])
-(3.141592653589793, 9.0)
-```
-"""
-extrema(itr) = _extrema_itr(identity, itr)
-
-"""
-    extrema(f, itr) -> Tuple
-
-Compute both the minimum and maximum of `f` applied to each element in `itr` and return
-them as a 2-tuple. Only one pass is made over `itr`.
-
-!!! compat "Julia 1.2"
-    This method requires Julia 1.2 or later.
-
-# Examples
-```jldoctest
-julia> extrema(sin, 0:π)
-(0.0, 0.9092974268256817)
-```
-"""
-extrema(f, itr) = _extrema_itr(f, itr)
-
-function _extrema_itr(f, itr)
-    y = iterate(itr)
-    y === nothing && throw(ArgumentError("collection must be non-empty"))
-    (v, s) = y
-    vmin = vmax = f(v)
-    while true
-        y = iterate(itr, s)
-        y === nothing && break
-        (x, s) = y
-        fx = f(x)
-        vmax = max(fx, vmax)
-        vmin = min(fx, vmin)
-    end
-    return (vmin, vmax)
-end
-
-extrema(x::Real) = (x, x)
-extrema(f, x::Real) = (y = f(x); (y, y))
-
 ## definitions providing basic traits of arithmetic operators ##
 
 """

base/reduce.jl

@@ -604,7 +604,7 @@ julia> prod(1:5; init = 1.0)
 """
 prod(a; kw...) = mapreduce(identity, mul_prod, a; kw...)
 
-## maximum & minimum
+## maximum, minimum, & extrema
 _fast(::typeof(min),x,y) = min(x,y)
 _fast(::typeof(max),x,y) = max(x,y)
 function _fast(::typeof(max), x::AbstractFloat, y::AbstractFloat)
@@ -634,11 +634,6 @@ function mapreduce_impl(f, op::Union{typeof(max), typeof(min)},
     start = first + 1
     simdstop  = start + chunk_len - 4
     while simdstop <= last - 3
-        # short circuit in case of NaN or missing
-        (v1 == v1) === true || return v1
-        (v2 == v2) === true || return v2
-        (v3 == v3) === true || return v3
-        (v4 == v4) === true || return v4
         @inbounds for i in start:4:simdstop
             v1 = _fast(op, v1, f(A[i+0]))
             v2 = _fast(op, v2, f(A[i+1]))
@@ -785,6 +780,76 @@ Inf
 """
 minimum(a; kw...) = mapreduce(identity, min, a; kw...)
 
+"""
+    extrema(itr; [init]) -> (mn, mx)
+
+Compute both the minimum `mn` and maximum `mx` element in a single pass, and return them
+as a 2-tuple.
+
+The value returned for empty `itr` can be specified by `init`. It must be a 2-tuple whose
+first and second elements are neutral elements for `min` and `max` respectively
+(i.e. which are greater/less than or equal to any other element). As a consequence, when
+`itr` is empty the returned `(mn, mx)` tuple will satisfy `mn ≥ mx`. When `init` is
+specified it may be used even for non-empty `itr`.
+
+!!! compat "Julia 1.8"
+    Keyword argument `init` requires Julia 1.8 or later.
+
+# Examples
+```jldoctest
+julia> extrema(2:10)
+(2, 10)
+
+julia> extrema([9,pi,4.5])
+(3.141592653589793, 9.0)
+
+julia> extrema([]; init = (Inf, -Inf))
+(Inf, -Inf)
+```
+"""
+extrema(itr; kw...) = extrema(identity, itr; kw...)
+
+"""
+    extrema(f, itr; [init]) -> (mn, mx)
+
+Compute both the minimum `mn` and maximum `mx` of `f` applied to each element in `itr` and
+return them as a 2-tuple. Only one pass is made over `itr`.
+
+The value returned for empty `itr` can be specified by `init`. It must be a 2-tuple whose
+first and second elements are neutral elements for `min` and `max` respectively
+(i.e. which are greater/less than or equal to any other element). It is used for non-empty
+collections. Note: it implies that, for empty `itr`, the returned value `(mn, mx)` satisfies
+`mn ≥ mx` even though for non-empty `itr` it  satisfies `mn ≤ mx`.  This is a "paradoxical"
+but yet expected result.
+
+!!! compat "Julia 1.2"
+    This method requires Julia 1.2 or later.
+
+!!! compat "Julia 1.8"
+    Keyword argument `init` requires Julia 1.8 or later.
+
+# Examples
+```jldoctest
+julia> extrema(sin, 0:π)
+(0.0, 0.9092974268256817)
+
+julia> extrema(sin, Real[]; init = (1.0, -1.0))  # good, since -1 ≤ sin(::Real) ≤ 1
+(1.0, -1.0)
+```
+"""
+extrema(f, itr; kw...) = mapreduce(ExtremaMap(f), _extrema_rf, itr; kw...)
+
+# Not using closure since `extrema(type, itr)` is a very likely use-case and it's better
+# to avoid type-instability (#23618).
+struct ExtremaMap{F} <: Function
+    f::F
+end
+ExtremaMap(::Type{T}) where {T} = ExtremaMap{Type{T}}(T)
+@inline (f::ExtremaMap)(x) = (y = f.f(x); (y, y))
+
+# TODO: optimize for inputs <: AbstractFloat
+@inline _extrema_rf((min1, max1), (min2, max2)) = (min(min1, min2), max(max1, max2))
+
 ## findmax, findmin, argmax & argmin
 
 """