diff --git a/ext/AbstractFFTsChainRulesCoreExt.jl b/ext/AbstractFFTsChainRulesCoreExt.jl
index 5ab5d2e..a26bc59 100644
--- a/ext/AbstractFFTsChainRulesCoreExt.jl
+++ b/ext/AbstractFFTsChainRulesCoreExt.jl
@@ -30,16 +30,15 @@ function ChainRulesCore.rrule(::typeof(rfft), x::AbstractArray{<:Real}, dims)
     halfdim = first(dims)
     d = size(x, halfdim)
     n = size(y, halfdim)
-    scale = reshape(
+    scale = convert(typeof(y), reshape(
         [i == 1 || (i == n && 2 * (i - 1) == d) ? 1 : 2 for i in 1:n],
         ntuple(i -> i == first(dims) ? n : 1, Val(ndims(x))),
-    )
+    ))
 
     project_x = ChainRulesCore.ProjectTo(x)
     function rfft_pullback(ȳ)
         ybar = ChainRulesCore.unthunk(ȳ)
-        _scale = convert(typeof(ybar),scale)
-        x̄ = project_x(brfft(ybar ./ _scale, d, dims))
+        x̄ = project_x(brfft(ybar ./ scale, d, dims))
         return ChainRulesCore.NoTangent(), x̄, ChainRulesCore.NoTangent()
     end
     return y, rfft_pullback
@@ -74,16 +73,15 @@ function ChainRulesCore.rrule(::typeof(irfft), x::AbstractArray, d::Int, dims)
     n = size(x, halfdim)
     invN = AbstractFFTs.normalization(y, dims)
     twoinvN = 2 * invN
-    scale = reshape(
+    scale = convert(typeof(y), reshape(
         [i == 1 || (i == n && 2 * (i - 1) == d) ? invN : twoinvN for i in 1:n],
         ntuple(i -> i == first(dims) ? n : 1, Val(ndims(x))),
-    )
+    ))
 
     project_x = ChainRulesCore.ProjectTo(x)
     function irfft_pullback(ȳ)
         ybar = ChainRulesCore.unthunk(ȳ)
-        _scale = convert(typeof(ybar),scale)
-        x̄ = project_x(_scale .* rfft(real.(ybar), dims))
+        x̄ = project_x(scale .* rfft(real.(ybar), dims))
         return ChainRulesCore.NoTangent(), x̄, ChainRulesCore.NoTangent(), ChainRulesCore.NoTangent()
     end
     return y, irfft_pullback
@@ -115,10 +113,10 @@ function ChainRulesCore.rrule(::typeof(brfft), x::AbstractArray, d::Int, dims)
     # compute scaling factors
     halfdim = first(dims)
     n = size(x, halfdim)
-    scale = reshape(
+    scale = convert(typeof(y), reshape(
         [i == 1 || (i == n && 2 * (i - 1) == d) ? 1 : 2 for i in 1:n],
         ntuple(i -> i == first(dims) ? n : 1, Val(ndims(x))),
-    )
+    ))
 
     project_x = ChainRulesCore.ProjectTo(x)
     function brfft_pullback(ȳ)