Fix big(1)^big(-1) (#50821)

This PR gives BigInt exponentiation the same edge-case behavior as other
integer exponentiation.

The normal integer exponentiation checks if `x` is `1` or `-1` before
erroring if the power is negative.

https://github.com/JuliaLang/julia/blob/9f9e989f241fad1ae03c3920c20a93d8017a5b8f/base/intfuncs.jl#L283-L287

With this PR `big(1)^big(-1) == 1`, `big(-1)^big(-1) == -1` and
`big(-1)^big(-2) == 1`

---------

Co-authored-by: Sukera <[email protected]>

base/gmp.jl

@@ -628,11 +628,11 @@ isqrt(x::BigInt) = MPZ.sqrt(x)
 ^(x::BigInt, y::Culong) = MPZ.pow_ui(x, y)
 
 function bigint_pow(x::BigInt, y::Integer)
+    x == 1 && return x
+    x == -1 && return isodd(y) ? x : -x
     if y<0; throw(DomainError(y, "`y` cannot be negative.")); end
     @noinline throw1(y) =
         throw(OverflowError("exponent $y is too large and computation will overflow"))
-    if x== 1; return x; end
-    if x==-1; return isodd(y) ? x : -x; end
     if y>typemax(Culong)
        x==0 && return x
 

test/gmp.jl

@@ -441,8 +441,25 @@ end
 @test isqrt(big(4)) == 2
 @test isqrt(big(5)) == 2
 
-@test big(5)^true == big(5)
-@test big(5)^false == one(BigInt)
+
+@testset "Exponentiation operator" begin
+    @test big(5)^true == big(5)
+    @test big(5)^false == one(BigInt)
+    testvals = Int8[-128:-126; -3:3; 125:127]
+    @testset "BigInt and Int8 are consistent: $i^$j" for i in testvals, j in testvals
+        int8_res = try
+            i^j
+        catch e
+            e
+        end
+        if int8_res isa Int8
+            @test (big(i)^big(j)) % Int8 === int8_res
+        else
+            # Test both have exception of the same type
+            @test_throws typeof(int8_res) big(i)^big(j)
+        end
+    end
+end
 
 @testset "math ops returning BigFloat" begin
     # operations that when applied to Int64 give Float64, should give BigFloat