prevent stack overflow in 2-arg promote_type

Don't use recursion, delete the `promote_result` function.

Use loop known to terminate, because of a hardcoded limit on the
iteration count.

Closes JuliaLang#57507, this PR encompasses the fixes from that PR and is more
comprehensive.

Fixes JuliaLang#13193

Author: nsajko

base/promotion.jl

@@ -302,19 +302,44 @@ promote_type(T) = T
 promote_type(T, S, U) = (@inline; promote_type(promote_type(T, S), U))
 promote_type(T, S, U, V...) = (@inline; afoldl(promote_type, promote_type(T, S, U), V...))
 
-promote_type(::Type{Bottom}, ::Type{Bottom}) = Bottom
-promote_type(::Type{T}, ::Type{T}) where {T} = T
-promote_type(::Type{T}, ::Type{Bottom}) where {T} = T
-promote_type(::Type{Bottom}, ::Type{T}) where {T} = T
-
 function promote_type(::Type{T}, ::Type{S}) where {T,S}
-    @inline
-    # Try promote_rule in both orders. Typically only one is defined,
-    # and there is a fallback returning Bottom below, so the common case is
-    #   promote_type(T, S) =>
-    #   promote_result(T, S, result, Bottom) =>
-    #   typejoin(result, Bottom) => result
-    promote_result(T, S, promote_rule(T,S), promote_rule(S,T))
+    @_terminates_locally_meta
+    normalized_type(::Type{Typ}) where {Typ} = Typ
+    types_are_identical(::Type{A}, ::Type{B}) where {A,B} = A === B
+    is_bottom(::Type{Typ}) where {Typ} = Typ <: Bottom
+    left = T
+    right = S
+    for _ ∈ 1:1000
+        if types_are_identical(left, right) || is_bottom(left) || is_bottom(right)
+            break
+        end
+        # Try `promote_rule` in both orders.
+        a = normalized_type(promote_rule(left, right))
+        b = normalized_type(promote_rule(right, left))
+        loop_is_detected_1 = types_are_identical(left, a) && types_are_identical(right, b)
+        loop_is_detected_2 = types_are_identical(left, b) && types_are_identical(right, a)
+        if loop_is_detected_1 || loop_is_detected_2
+            let s = LazyString("`promote_type(", T, ", ", S, ")` failed, there are conflicting `promote_rule` definitions for types ", a, ", ", b)
+                throw(ArgumentError(s))
+            end
+        end
+        if is_bottom(a) && is_bottom(b)
+            # If no `promote_rule` is defined, both directions give `Bottom`. In that
+            # case use `typejoin` on the original types.
+            return typejoin(left, right)
+        end
+        left = a
+        right = b
+    end
+    if (left === right) || is_bottom(left)
+        right
+    elseif is_bottom(right)
+        left
+    else
+        let s = LazyString("`promote_type(", T, ", ", S, ")` failed, ended up with (", left, ", ", right, "), check for faulty `promote_rule` methods")
+            throw(ArgumentError(s))
+        end
+    end
 end
 
 """
@@ -334,11 +359,6 @@ promote_rule(::Type{Bottom}, ::Type{Bottom}, slurp...) = Bottom # not strictly n
 promote_rule(::Type{Bottom}, ::Type{T}, slurp...) where {T} = T
 promote_rule(::Type{T}, ::Type{Bottom}, slurp...) where {T} = T
 
-promote_result(::Type,::Type,::Type{T},::Type{S}) where {T,S} = (@inline; promote_type(T,S))
-# If no promote_rule is defined, both directions give Bottom. In that
-# case use typejoin on the original types instead.
-promote_result(::Type{T},::Type{S},::Type{Bottom},::Type{Bottom}) where {T,S} = (@inline; typejoin(T, S))
-
 """
     promote(xs...)
 

test/core.jl

@@ -2028,6 +2028,37 @@ g4731() = f4731()
 @test f4731() == ""
 @test g4731() == ""
 
+@testset "type promotion" begin
+    @testset "conflicting promote_rule error, PR #57507" begin
+        struct PR57507A end
+        struct PR57507B end
+        struct PR57507C end
+        @testset "error with conflicting promote_rules" begin
+            Base.promote_rule(::Type{PR57507A}, ::Type{PR57507B}) = PR57507A
+            Base.promote_rule(::Type{PR57507B}, ::Type{PR57507A}) = PR57507B
+            @test_throws ArgumentError promote_type(PR57507A, PR57507B)
+            @test_throws ArgumentError promote_type(PR57507B, PR57507A)
+        end
+        @testset "unambiguous cases" begin
+            @test PR57507A === @inferred promote_type(PR57507A, PR57507A)
+            @test PR57507B === @inferred promote_type(PR57507B, PR57507B)
+            Base.promote_rule(::Type{PR57507C}, ::Type{PR57507A}) = PR57507C
+            Base.promote_rule(::Type{PR57507B}, ::Type{PR57507C}) = PR57507C
+            @test PR57507C === @inferred promote_type(PR57507A, PR57507C)
+            @test PR57507C === @inferred promote_type(PR57507C, PR57507B)
+        end
+    end
+    @testset "issue #13193" begin
+        struct Issue13193_SIQuantity{T<:Number} <: Number end
+        Base.promote_rule(::Type{Issue13193_SIQuantity{T}}, ::Type{Issue13193_SIQuantity{S}}) where {T, S} = Issue13193_SIQuantity{promote_type(T,S)}
+        Base.promote_rule(::Type{Issue13193_SIQuantity{T}}, ::Type{S}) where {T, S<:Number} = Issue13193_SIQuantity{promote_type(T,S)}
+        struct Issue13193_Interval{T<:Number} <: Number end
+        Base.promote_rule(::Type{Issue13193_Interval{T}}, ::Type{Issue13193_Interval{S}}) where {T, S} = Issue13193_Interval{promote_type(T,S)}
+        Base.promote_rule(::Type{Issue13193_Interval{T}}, ::Type{S}) where {T, S<:Number} = Issue13193_Interval{promote_type(T,S)}
+        @test_throws ArgumentError promote_type(Issue13193_Interval{Int}, Issue13193_SIQuantity{Int})
+    end
+end
+
 # issue #4675
 f4675(x::StridedArray...) = 1
 f4675(x::StridedArray{T}...) where {T} = 2