fix digits(n::Unsigned) with neg base for n > typemax(n)÷2 (#29205)

Alternative based on #29187

Tests from rforquet's PR linked above.

base/intfuncs.jl

@@ -744,17 +744,25 @@ julia> digits!([2,2,2,2,2,2], 10, base = 2)
 ```
 """
 function digits!(a::AbstractVector{T}, n::Integer; base::Integer = 10) where T<:Integer
-    base < 0 && isa(n, Unsigned) && return digits!(a, convert(Signed, n), base = base)
     2 <= abs(base) || throw(ArgumentError("base must be ≥ 2 or ≤ -2, got $base"))
     hastypemax(T) && abs(base) - 1 > typemax(T) &&
         throw(ArgumentError("type $T too small for base $base"))
-    for i in eachindex(a)
-        if base > 0
-            a[i] = rem(n, base)
-            n = div(n, base)
-        else
-            a[i] = mod(n, -base)
-            n = cld(n, base)
+    isempty(a) && return a
+
+    if base > 0
+        for i in eachindex(a)
+            n, d = divrem(n, base)
+            a[i] = d
+        end
+    else
+        # manually peel one loop iteration for type stability
+        n, d = fldmod(n, -base)
+        a[firstindex(a)] = d
+        n = -signed(n)
+        for i in firstindex(a)+1:lastindex(a)
+            n, d = fldmod(n, -base)
+            a[i] = d
+            n = -n
         end
     end
     return a

test/intfuncs.jl

@@ -179,11 +179,18 @@ end
     @test digits(5, base = 3) == [2, 1]
 
     @testset "digits/base with negative bases" begin
-        @testset "digits(n::$T, base = b)" for T in (Int, UInt, BigInt, Int32)
+        @testset "digits(n::$T, base = b)" for T in (Int, UInt, BigInt, Int32, UInt32)
             @test digits(T(8163), base = -10) == [3, 4, 2, 2, 1]
             if !(T<:Unsigned)
                 @test digits(T(-8163), base = -10) == [7, 7, 9, 9]
             end
+            if T !== BigInt
+                b = rand(-32:-2)
+                for n = T[rand(T), typemax(T), typemin(T)]
+                    # issue #29183
+                    @test digits(n, base=b) == digits(signed(widen(n)), base=b)
+                end
+            end
         end
         @test [string(n, base = b)
                for n = [-10^9, -10^5, -2^20, -2^10, -100, -83, -50, -34, -27, -16, -7, -3, -2, -1,