From 5f216791305b80c670a4b8e05978c5c10eece70c Mon Sep 17 00:00:00 2001
From: Antoine Levitt <antoine.levitt@gmail.com>
Date: Thu, 16 Jul 2026 11:56:31 +0200
Subject: [PATCH 1/2] Don't widen the primal when differentiating `x^y` with a
 real base

`2^x` is `Float32` for a `Float32` `x`, but `2^Dual{T,Float32,N}` came back
`Dual{T,Float64,N}`: `expv = x^v` honours Base's promotion, while `log(x)` was
evaluated from `x` alone, so an integer base gave a Float64 partial and the
`Dual` constructor unified value and partials upward. Differentiating should
not change the primal's type.

Take the log in `expv`'s type instead, which is the promotion `^` already chose
for this base/exponent pair. Float64 results are bit-identical; only bases
narrower than the exponent's own promotion (e.g. `Integer`) change, and only in
type. `NaNMath.pow` shares the definition and is fixed too.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_017an8Gie5b1ULeSjhep3Sjb
---
 src/dual.jl      | 2 +-
 test/DualTest.jl | 8 ++++++++
 2 files changed, 9 insertions(+), 1 deletion(-)

diff --git a/src/dual.jl b/src/dual.jl
index 7552dd5f..0c5d5ebc 100644
--- a/src/dual.jl
+++ b/src/dual.jl
@@ -576,7 +576,7 @@ for (f, log) in ((:(Base.:^), :(Base.log)), (:(NaNMath.pow), :(NaNMath.log)))
             begin
                 v = value(y)
                 expv = ($f)(x, v)
-                deriv = (iszero(x) && v > 0) ? zero(expv) : expv*($log)(x)
+                deriv = (iszero(x) && v > 0) ? zero(expv) : expv*($log)(oftype(expv, x))
                 return Dual{Ty}(expv, deriv * partials(y))
             end
         )
diff --git a/test/DualTest.jl b/test/DualTest.jl
index df9f9dcb..03021b9d 100644
--- a/test/DualTest.jl
+++ b/test/DualTest.jl
@@ -499,6 +499,14 @@ ForwardDiff.:≺(::Type{OuterTestTag}, ::Type{TestTag}) = false
 
     @test partials(NaNMath.pow(Dual{TestTag}(-2.0, 1.0), Dual{TestTag}(2.0, 0.0)), 1) == -4.0
 
+    # differentiating must not widen the primal: `2^x` is Float32 for a Float32 `x`
+    @testset "$f: real base keeps $W exponent" for f in (^, NaNMath.pow),
+                                                   W in (Float16, Float32, Float64)
+        w = W(4)/W(3)
+        @test typeof(value(f(2, Dual{TestTag}(w, one(W))))) === typeof(f(2, w))
+        @test typeof(value(f(2.0f0, Dual{TestTag}(w, one(W))))) === typeof(f(2.0f0, w))
+    end
+
     ###################################
     # General Mathematical Operations #
     ###################################

From 5e05ba55c73767367dfdcf1ebdda881af3f305b5 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?David=20M=C3=BCller-Widmann?=
 <devmotion@users.noreply.github.com>
Date: Mon, 27 Jul 2026 15:15:19 +0200
Subject: [PATCH 2/2] Bump version to 1.4.2

---
 Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Project.toml b/Project.toml
index 77f40590..05ab97c0 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,6 +1,6 @@
 name = "ForwardDiff"
 uuid = "f6369f11-7733-5829-9624-2563aa707210"
-version = "1.4.1"
+version = "1.4.2"
 
 [deps]
 CommonSubexpressions = "bbf7d656-a473-5ed7-a52c-81e309532950"