add shuffle(::NTuple) to Random

Fixes #56728

stdlib/Random/src/misc.jl

@@ -183,6 +183,36 @@ ltm52(n::Int, mask::Int=nextpow(2, n)-1) = LessThan(n-1, Masked(mask, UInt52Raw(
 
 ## shuffle & shuffle!
 
+function _tuple_without_element_at_index(tup::(Tuple{T, Vararg{T, N}} where {T}), i::Int) where {N}
+    clo = let tup = tup, i = i
+        function closure(j::Int)
+            k = if j < i
+                j
+            else
+                j + 1
+            end
+            tup[k]
+        end
+    end
+    ntuple(clo, Val{N}())
+end
+
+function shuffle(rng::AbstractRNG, tup::(Tuple{Vararg{T, N}} where {T})) where {N}
+    if tup isa Tuple{Any, Vararg}
+        let i = rand(rng, Base.OneTo(N))  # Fisher–Yates shuffle
+            s = _tuple_without_element_at_index(tup, i)
+            t = shuffle(rng, s)
+            (tup[i], t...)
+        end
+    else
+        tup
+    end::typeof(tup)
+end
+
+function shuffle(tup::NTuple)
+    shuffle(default_rng(), tup)
+end
+
 """
     shuffle!([rng=default_rng(),] v::AbstractArray)
 

stdlib/Random/test/runtests.jl

@@ -1032,6 +1032,34 @@ end
     @test maximum(m) <= 0.106
 end
 
+@testset "`shuffle(::NTuple)`" begin
+    @testset "sorted" begin
+        for n ∈ 0:20
+            tup = ntuple(identity, n)
+            @test tup === sort(@inferred shuffle(tup))
+        end
+    end
+    @testset "not identity" begin
+        function is_not_identity_at_least_once()
+            function f(::Any)
+                tup = ntuple(identity, 9)
+                tup !== shuffle(tup)
+            end
+            @test any(f, 1:1000000)
+        end
+        is_not_identity_at_least_once()
+    end
+    @testset "no heap allocation" begin
+        function no_heap_allocation(tup)
+            @test iszero(@allocated shuffle(tup))
+        end
+        for n ∈ 0:9
+            tup = ntuple(identity, n)
+            no_heap_allocation(tup)
+        end
+    end
+end
+
 # issue #42752
 # test that running finalizers that launch tasks doesn't change RNG stream
 function f42752(do_gc::Bool, cell = (()->Any[[]])())