don't throw DomainError for negative integer powers of ±1 (#18342)

* don't throw DomainError for negative integer powers of ±1

* fix replutil test that was expecting 1^(-1) to fail

Author: stevengj

base/intfuncs.jl

@@ -165,6 +165,8 @@ function power_by_squaring(x_, p::Integer)
     elseif p == 2
         return x*x
     elseif p < 0
+        x == 1 && return copy(x)
+        x == -1 && return iseven(p) ? one(x) : copy(x)
         throw(DomainError())
     end
     t = trailing_zeros(p) + 1
@@ -185,7 +187,7 @@ 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 && throw(DomainError())
+    p < 0 && !x && throw(DomainError())
     return (p==0) | x
 end
 

test/math.jl

@@ -827,6 +827,10 @@ end
 @test_throws DomainError 2 ^ -2
 @test_throws DomainError (-2)^(2.2)
 @test_throws DomainError (-2.0)^(2.2)
+@test_throws DomainError false ^ -2
+@test 1 ^ -2 === (-1) ^ -2 === 1
+@test (-1) ^ -3 === -1
+@test true ^ -2 === true
 
 # issue #13748
 let A = [1 2; 3 4]; B = [5 6; 7 8]; C = [9 10; 11 12]

test/replutil.jl

@@ -257,7 +257,7 @@ immutable TypeWithIntParam{T <: Integer} end
 let undefvar
     err_str = @except_strbt sqrt(-1) DomainError
     @test contains(err_str, "Try sqrt(complex(x)).")
-    err_str = @except_strbt 1^(-1) DomainError
+    err_str = @except_strbt 2^(-1) DomainError
     @test contains(err_str, "Cannot raise an integer x to a negative power -n")
     err_str = @except_strbt (-1)^0.25 DomainError
     @test contains(err_str, "Exponentiation yielding a complex result requires a complex argument")