fix infinite recursion in promote_type for Irrational (#55870)

Fixes #51001

(cherry picked from commit ca3713e)

base/irrationals.jl

@@ -42,7 +42,16 @@ promote_rule(::Type{<:AbstractIrrational}, ::Type{Float16}) = Float16
 promote_rule(::Type{<:AbstractIrrational}, ::Type{Float32}) = Float32
 promote_rule(::Type{<:AbstractIrrational}, ::Type{<:AbstractIrrational}) = Float64
 promote_rule(::Type{<:AbstractIrrational}, ::Type{T}) where {T<:Real} = promote_type(Float64, T)
-promote_rule(::Type{S}, ::Type{T}) where {S<:AbstractIrrational,T<:Number} = promote_type(promote_type(S, real(T)), T)
+
+function promote_rule(::Type{S}, ::Type{T}) where {S<:AbstractIrrational,T<:Number}
+    U = promote_type(S, real(T))
+    if S <: U
+        # prevent infinite recursion
+        promote_type(Float64, T)
+    else
+        promote_type(U, T)
+    end
+end
 
 AbstractFloat(x::AbstractIrrational) = Float64(x)::Float64
 Float16(x::AbstractIrrational) = Float16(Float32(x)::Float32)

test/numbers.jl

@@ -2886,6 +2886,14 @@ end
     @test log(π,ComplexF32(2)) isa ComplexF32
 end
 
+@testset "irrational promotion shouldn't recurse without bound, issue #51001" begin
+    for s ∈ (:π, :ℯ)
+        T = Irrational{s}
+        @test promote_type(Complex{T}, T) <: Complex
+        @test promote_type(T, Complex{T}) <: Complex
+    end
+end
+
 @testset "printing non finite floats" begin
     let float_types = Set()
         allsubtypes!(Base, AbstractFloat, float_types)