From 9511405d57d2ac110f1743712593f8eb137c400e Mon Sep 17 00:00:00 2001
From: Fabian Greimel <fabgrei@gmail.com>
Date: Fri, 1 Apr 2022 09:41:01 +0200
Subject: [PATCH 1/2] maximum & minimum & extrema with init

---
 test/reduce.jl | 9 +++++++++
 1 file changed, 9 insertions(+)

diff --git a/test/reduce.jl b/test/reduce.jl
index 3a8f9532b4710..7791bacc8c1ab 100644
--- a/test/reduce.jl
+++ b/test/reduce.jl
@@ -400,6 +400,15 @@ A = circshift(reshape(1:24,2,3,4), (0,1,1))
     maximum([NaN;zeros(255);missing]) === missing
 end
 
+@testset "maximum & minimum & extrema with init" begin
+    @test maximum(1:10, init=11)      == 11
+    @test maximum(1:10, init=0)       == 10
+    @test minimum(1:10, init=11)      == 1
+    @test minimum(1:10, init=0)       == 0
+    @test extrema(1:10, init=(0, 5))  == (0, 10)
+    @test extrema(1:10, init=(5, 11)) == (1, 11)
+end
+
 # findmin, findmax, argmin, argmax
 
 @testset "findmin(f, domain)" begin

From ada79a0164c77fb77dad1eaa95ea5ee77a2feb18 Mon Sep 17 00:00:00 2001
From: Fabian Greimel <fabgrei@gmail.com>
Date: Fri, 1 Apr 2022 09:51:16 +0200
Subject: [PATCH 2/2] update docstrings for minimum, maximum, extrema

---
 base/reduce.jl | 57 ++++++++++++++++++++++++++++++++++++++++----------
 1 file changed, 46 insertions(+), 11 deletions(-)

diff --git a/base/reduce.jl b/base/reduce.jl
index 13e1b69c79ede..fca04bd7f120b 100644
--- a/base/reduce.jl
+++ b/base/reduce.jl
@@ -724,19 +724,29 @@ Returns the largest element in a collection.
 The value returned for empty `itr` can be specified by `init`. It must be
 a neutral element for `max` (i.e. which is less than or equal to any
 other element) as it is unspecified whether `init` is used
-for non-empty collections.
+for non-empty collections. If `init > maximum(itr)`, return `init`.
 
 !!! compat "Julia 1.6"
     Keyword argument `init` requires Julia 1.6 or later.
 
 # Examples
 ```jldoctest
-julia> maximum(-20.5:10)
+julia> x = -20.5:10
+-20.5:1.0:9.5
+
+julia> maximum(x)
 9.5
 
-julia> maximum([1,2,3])
+julia> y = [1 2 3]
+1×3 Matrix{Int64}:
+ 1  2  3
+
+julia> maximum(y)
 3
 
+julia> maximum(y, init=maximum(x)) == maximum(x ∪ y) == 9.5
+true
+
 julia> maximum(())
 ERROR: MethodError: reducing over an empty collection is not allowed; consider supplying `init` to the reducer
 Stacktrace:
@@ -756,19 +766,29 @@ Returns the smallest element in a collection.
 The value returned for empty `itr` can be specified by `init`. It must be
 a neutral element for `min` (i.e. which is greater than or equal to any
 other element) as it is unspecified whether `init` is used
-for non-empty collections.
+for non-empty collections. If `init < minimum(itr)`, return `init`.
 
 !!! compat "Julia 1.6"
     Keyword argument `init` requires Julia 1.6 or later.
 
 # Examples
 ```jldoctest
-julia> minimum(-20.5:10)
+julia> x = -20.5:10
+-20.5:1.0:9.5
+
+julia> minimum(x)
 -20.5
 
-julia> minimum([1,2,3])
+julia> y = [1 2 3]
+1×3 Matrix{Int64}:
+ 1  2  3
+
+julia> minimum(y)
 1
 
+julia> minimum(y, init=minimum(x)) == minimum(x ∪ y) == -20.5
+true
+
 julia> minimum([])
 ERROR: MethodError: reducing over an empty collection is not allowed; consider supplying `init` to the reducer
 Stacktrace:
@@ -789,20 +809,35 @@ 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`.
+`itr` is empty the returned `(mn, mx)` tuple will satisfy `mn ≥ mx`. If the `init` contains
+a non-neutral element, this element is returned as appropriate. (If `init[1] < minimum(itr)`,
+`mn == init[1]`. If `init[2] > maximum(itr)`, `mx == init[2]`.) 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> x = 1:5
+1:5
+
+julia> extrema(x)
+(1, 5)
+
+julia> y = [9 pi 4.5]
+1×3 Matrix{Float64}:
+ 9.0  3.14159  4.5
 
-julia> extrema([9,pi,4.5])
+julia> extrema(x)
+(1, 5)
+
+julia> extrema(y)
 (3.141592653589793, 9.0)
 
+julia> extrema(y, init=extrema(x)) == extrema(x ∪ y) == (1.0, 9.0)
+true
+
 julia> extrema([]; init = (Inf, -Inf))
 (Inf, -Inf)
 ```