added specialized domain error message for

`^(::Matrix{<:Integer},::Integer)`,
added `@inferred` and comments to test

base/intfuncs.jl

@@ -160,10 +160,15 @@ invmod(n::Integer, m::Integer) = invmod(promote(n,m)...)
 
 # ^ for any x supporting *
 to_power_type(x) = convert(Base.promote_op(*, typeof(x), typeof(x)), x)
-@noinline throw_domerr_powbysq(p) = throw(DomainError(p,
+@noinline throw_domerr_powbysq(::Any, p) = throw(DomainError(p,
     string("Cannot raise an integer x to a negative power ", p, '.',
            "\nMake x a float by adding a zero decimal (e.g., 2.0^$p instead ",
            "of 2^$p), or write 1/x^$(-p), float(x)^$p, or (x//1)^$p")))
+@noinline throw_domerr_powbysq(::AbstractMatrix, p) = throw(DomainError(p,
+   string("Cannot raise an integer matrix x to a negative power ", p, '.',
+          "\nMake x a float matrix by adding a zero decimal ",
+          "(e.g., [2.0 1.0;1.0 0.0]^$p instead ",
+          "of [2 1;1 0]^$p), or write float(x)^$p or Rational.(x)^$p")))
 function power_by_squaring(x_, p::Integer)
     x = to_power_type(x_)
     if p == 1
@@ -175,7 +180,7 @@ function power_by_squaring(x_, p::Integer)
     elseif p < 0
         isone(x) && return copy(x)
         isone(-x) && return iseven(p) ? one(x) : copy(x)
-        throw_domerr_powbysq(p)
+        throw_domerr_powbysq(x, p)
     end
     t = trailing_zeros(p) + 1
     p >>= t
@@ -195,7 +200,7 @@ function power_by_squaring(x_, p::Integer)
 end
 power_by_squaring(x::Bool, p::Unsigned) = ((p==0) | x)
 function power_by_squaring(x::Bool, p::Integer)
-    p < 0 && !x && throw_domerr_powbysq(p)
+    p < 0 && !x && throw_domerr_powbysq(x, p)
     return (p==0) | x
 end
 

test/linalg/dense.jl

@@ -587,16 +587,20 @@ end
                                             UInt128, UInt16, UInt32, UInt64, UInt8,
                                             BigInt)
         @test_throws DomainError elty[1 1;1 0]^-2
-        @test elty[1 1;1 0]^2 == elty[2 1;1 1]
+        @test (@inferred elty[1 1;1 0]^2) == elty[2 1;1 1]
         I_ = elty[1 0;0 1]
         @test I_^-1 == I_
         if !(elty<:Unsigned)
-            @test (-I_)^-1 == -I_
-            @test (-I_)^-2 == I_
+            @test (@inferred (-I_)^-1) == -I_
+            @test (@inferred (-I_)^-2) == I_
         end
+        # make sure that type promotion for ^(::Matrix{<:Integer}, ::Integer)
+        # is analogous to type promotion for ^(::Integer, ::Integer)
+        # e.g. [1 1;1 0]^big(10000) should return Matrix{BigInt}, the same
+        # way as 2^big(10000) returns BigInt
         for elty2 = (Int64, BigInt)
             TT = Base.promote_op(^, elty, elty2)
-            @test Base.return_types(^, (Array{elty,2}, elty2)) == [Array{TT,2}]
+            @test (@inferred elty[1 1;1 0]^elty2(1))::Matrix{TT} == [1 1;1 0]
         end
     end
 end