make ^ and .^ types consistent (part of #3274)

For example, before this patch:

    julia> typeof(int32(2) ^ int64(3))
    Int32

    julia> eltype([int32(2)] .^ [int64(3)])
    Int64  # Int32 after this patch

    julia> typeof(complex(2) ^ complex(3))
    Complex{Float64}

    julia> eltype([complex(2)] .^ [complex(3)])
    Complex{Int}  # Complex{Float64} after this patch

base/broadcast.jl

@@ -328,8 +328,9 @@ function .//(A::AbstractArray, B::AbstractArray)
     broadcast!(//, Array(type_rdiv(eltype(A), eltype(B)), broadcast_shape(A, B)), A, B)
 end
 
-type_pow(T,S) = promote_type(T,S)
-type_pow{S<:Integer}(::Type{Bool},::Type{S}) = Bool
+@generated function type_pow(T,S)
+    :(promote_type(Base.return_types(^,(T,S))...))
+end
 type_pow{S}(T,::Type{Rational{S}}) = type_pow(T, type_div(S, S))
 
 function .^(A::AbstractArray, B::AbstractArray)

base/gmp.jl

@@ -385,13 +385,15 @@ function isqrt(x::BigInt)
     return z
 end
 
+^(x::BigInt, y::Bool) = y ? x : one(x)
+
 function ^(x::BigInt, y::Culong)
     z = BigInt()
     ccall((:__gmpz_pow_ui, :libgmp), Void, (Ptr{BigInt}, Ptr{BigInt}, Culong), &z, &x, y)
     return z
 end
 
-function bigint_pow(x::BigInt, y::Integer)
+function ^(x::BigInt, y::Integer)
     if y<0; throw(DomainError()); end
     if x== 1; return x; end
     if x==-1; return isodd(y) ? x : -x; end
@@ -411,10 +413,6 @@ function bigint_pow(x::BigInt, y::Integer)
     return x^convert(Culong, y)
 end
 
-^(x::BigInt , y::BigInt ) = bigint_pow(x, y)
-^(x::BigInt , y::Bool   ) = y ? x : one(x)
-^(x::BigInt , y::Integer) = bigint_pow(x, y)
-
 function powermod(x::BigInt, p::BigInt, m::BigInt)
     p < 0 && throw(DomainError())
     r = BigInt()

test/numbers.jl

@@ -2504,3 +2504,16 @@ end
 
 # fix 0x2^big(9) = big(512), while 0x2^9 = 0x0
 @test 0x2^9 === 0x2^big(9) === 0x0
+
+# issue #3274
+let
+    realtypes = [Int8,  Int16,  Int32,  Int64,  Int128,
+                 UInt8, UInt16, UInt32, UInt64, UInt128,
+                 Float32, Float64, BigInt, BigFloat]
+    alltypes = [realtypes; [Complex{T} for T in realtypes]]
+
+    for T in alltypes, S in alltypes
+        a,b = T(2),S(3)
+        @test typeof(a^b) === eltype([a].^[b])
+    end
+end