From 34f8126ffd11bf19b13ccd1a4b78668e1f831579 Mon Sep 17 00:00:00 2001
From: oscarddssmith <oscar.smith@juliacomputing.com>
Date: Thu, 14 Mar 2024 15:40:48 -0400
Subject: [PATCH 1/3] fix literal-pow to return the right type when the base is
 -1

---
 base/intfuncs.jl | 19 ++++++++++++++++---
 1 file changed, 16 insertions(+), 3 deletions(-)

diff --git a/base/intfuncs.jl b/base/intfuncs.jl
index 916cd28a32c6f..be2f1a218a51e 100644
--- a/base/intfuncs.jl
+++ b/base/intfuncs.jl
@@ -369,8 +369,19 @@ const HWNumber = Union{HWReal, Complex{<:HWReal}, Rational{<:HWReal}}
 @inline literal_pow(::typeof(^), x::HWNumber, ::Val{1}) = x
 @inline literal_pow(::typeof(^), x::HWNumber, ::Val{2}) = x*x
 @inline literal_pow(::typeof(^), x::HWNumber, ::Val{3}) = x*x*x
-@inline literal_pow(::typeof(^), x::HWNumber, ::Val{-1}) = inv(x)
-@inline literal_pow(::typeof(^), x::HWNumber, ::Val{-2}) = (i=inv(x); i*i)
+@inline function literal_pow(::typeof(^), x::HWNumber, ::Val{-1})
+    if x == -one(x)
+        return isodd(p) ? one(x) : -one(x)
+    end
+    inv(x)
+end
+@inline function literal_pow(::typeof(^), x::HWNumber, ::Val{-2})
+    if x == -one(x)
+        return isodd(p) ? one(x) : -one(x)
+    end
+    i=inv(x)
+    return i*i
+end
 
 # don't use the inv(x) transformation here since float^p is slightly more accurate
 @inline literal_pow(::typeof(^), x::AbstractFloat, ::Val{p}) where {p} = x^p
@@ -379,7 +390,9 @@ const HWNumber = Union{HWReal, Complex{<:HWReal}, Rational{<:HWReal}}
 # for other types, define x^-n as inv(x)^n so that negative literal powers can
 # be computed in a type-stable way even for e.g. integers.
 @inline function literal_pow(f::typeof(^), x, ::Val{p}) where {p}
-    if p < 0
+    if x == -one(x)
+        return isodd(p) ? one(x) : -one(x)
+    elseif p < 0
         if x isa BitInteger64
             f(Float64(x), p) # inv would cause rounding, while Float64^Integer is able to compensate the inverse
         else

From a5f8b2a0b7ed69a99dbd5adae9ab21e3d7a80ba5 Mon Sep 17 00:00:00 2001
From: oscarddssmith <oscar.smith@juliacomputing.com>
Date: Thu, 14 Mar 2024 15:44:03 -0400
Subject: [PATCH 2/3] add tests

---
 test/math.jl | 7 +++++++
 1 file changed, 7 insertions(+)

diff --git a/test/math.jl b/test/math.jl
index f551bb3a5d4b7..eeed7b5f0f916 100644
--- a/test/math.jl
+++ b/test/math.jl
@@ -1459,6 +1459,13 @@ end
     # two cases where we have observed > 1 ULP in the past
     @test 0.0013653274095082324^-97.60372292227069 == 4.088393948750035e279
     @test 8.758520413376658e-5^70.55863059215994 == 5.052076767078296e-287
+    # test literal pow for base = -1
+    @test (-1)^(-1) === (-1)^((-1,)[1])
+    @test (-1)^(-2) === (-1)^((-2,)[1])
+    @test (-1)^(-3) === (-1)^((-3,)[1])
+    @test (-1)^(1) === (-1)^((1,)[1])
+    @test (-1)^(2) === (-1)^((2,)[1])
+    @test (-1)^(3) === (-1)^((3,)[1])
 end
 
 # Test that sqrt behaves correctly and doesn't exhibit fp80 double rounding.

From db3677b505da297f6db6850aff2d241ce646969d Mon Sep 17 00:00:00 2001
From: Oscar Smith <oscardssmith@gmail.com>
Date: Fri, 15 Mar 2024 09:50:30 -0400
Subject: [PATCH 3/3] Update base/intfuncs.jl

Co-authored-by: Max Horn <max@quendi.de>
---
 base/intfuncs.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/base/intfuncs.jl b/base/intfuncs.jl
index be2f1a218a51e..7a3c9d3ed7816 100644
--- a/base/intfuncs.jl
+++ b/base/intfuncs.jl
@@ -371,7 +371,7 @@ const HWNumber = Union{HWReal, Complex{<:HWReal}, Rational{<:HWReal}}
 @inline literal_pow(::typeof(^), x::HWNumber, ::Val{3}) = x*x*x
 @inline function literal_pow(::typeof(^), x::HWNumber, ::Val{-1})
     if x == -one(x)
-        return isodd(p) ? one(x) : -one(x)
+        return x
     end
     inv(x)
 end