diff --git a/ext/AbstractFFTsChainRulesCoreExt.jl b/ext/AbstractFFTsChainRulesCoreExt.jl
index 5ab5d2e..0741584 100644
--- a/ext/AbstractFFTsChainRulesCoreExt.jl
+++ b/ext/AbstractFFTsChainRulesCoreExt.jl
@@ -30,16 +30,20 @@ function ChainRulesCore.rrule(::typeof(rfft), x::AbstractArray{<:Real}, dims)
     halfdim = first(dims)
     d = size(x, halfdim)
     n = size(y, halfdim)
-    scale = 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))
+        ybar_scaled = map(ybar, CartesianIndices(ybar)) do ybar_j, j
+            i = j[halfdim]
+            ybar_scaled_j = if i == 1 || (i == n && 2 * (i - 1) == d)
+                ybar_j
+            else
+                ybar_j / 2
+            end
+            return ybar_scaled_j
+        end
+        x̄ = project_x(brfft(ybar_scaled, d, dims))
         return ChainRulesCore.NoTangent(), x̄, ChainRulesCore.NoTangent()
     end
     return y, rfft_pullback
@@ -74,16 +78,20 @@ function ChainRulesCore.rrule(::typeof(irfft), x::AbstractArray, d::Int, dims)
     n = size(x, halfdim)
     invN = AbstractFFTs.normalization(y, dims)
     twoinvN = 2 * invN
-    scale = 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_scaled = rfft(real.(ybar), dims)
+        x̄ = project_x(map(x̄_scaled, CartesianIndices(x̄_scaled)) do x̄_scaled_j, j
+            i = j[halfdim]
+            x̄_j = if i == 1 || (i == n && 2 * (i - 1) == d)
+                invN * x̄_scaled_j
+            else
+                twoinvN * x̄_scaled_j
+            end
+            return x̄_j
+        end)
         return ChainRulesCore.NoTangent(), x̄, ChainRulesCore.NoTangent(), ChainRulesCore.NoTangent()
     end
     return y, irfft_pullback
@@ -115,14 +123,19 @@ function ChainRulesCore.rrule(::typeof(brfft), x::AbstractArray, d::Int, dims)
     # compute scaling factors
     halfdim = first(dims)
     n = size(x, halfdim)
-    scale = 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)
-        x̄ = project_x(scale .* rfft(real.(ChainRulesCore.unthunk(ȳ)), dims))
+        x̄_scaled = rfft(real.(ChainRulesCore.unthunk(ȳ)), dims)
+        x̄ = project_x(map(x̄_scaled, CartesianIndices(x̄_scaled)) do x̄_scaled_j, j
+            i = j[halfdim]
+            x̄_j = if i == 1 || (i == n && 2 * (i - 1) == d) 
+                x̄_scaled_j
+            else
+                2 * x̄_scaled_j
+            end
+            return x̄_j
+        end)
         return ChainRulesCore.NoTangent(), x̄, ChainRulesCore.NoTangent(), ChainRulesCore.NoTangent()
     end
     return y, brfft_pullback
diff --git a/ext/AbstractFFTsTestExt.jl b/ext/AbstractFFTsTestExt.jl
index ccea93a..a3f427d 100644
--- a/ext/AbstractFFTsTestExt.jl
+++ b/ext/AbstractFFTsTestExt.jl
@@ -60,6 +60,7 @@ function TestUtils.test_plan(P::AbstractFFTs.Plan, x::AbstractArray, x_transform
         _x_out = similar(P * _copy(x))
         @test mul!(_x_out, P, _copy(x)) ≈ x_transformed
         @test _x_out ≈ x_transformed
+        @test P * view(_copy(x), axes(x)...) ≈ x_transformed # test view input
     else
         _x = copy(x)
         @test P * _copy(_x) ≈ x_transformed
@@ -85,6 +86,7 @@ function TestUtils.test_plan_adjoint(P::AbstractFFTs.Plan, x::AbstractArray; rea
         @test _component_dot(y, P * _copy(x)) ≈ _component_dot(P' * _copy(y), x)
         @test _component_dot(x, P \ _copy(y)) ≈ _component_dot(P' \ _copy(x), y) 
     end
+    @test P' * view(_copy(y), axes(y)...) ≈ P' * _copy(y) # test view input (AbstractFFTs.jl#112)
     @test_throws MethodError mul!(x, P', y)
 end
 
diff --git a/src/definitions.jl b/src/definitions.jl
index 5dc703f..943718f 100644
--- a/src/definitions.jl
+++ b/src/definitions.jl
@@ -702,11 +702,16 @@ function adjoint_mul(p::Plan{T}, x::AbstractArray, ::RFFTAdjointStyle) where {T<
     halfdim = first(dims)
     d = size(p, halfdim)
     n = output_size(p, halfdim)
-    scale = reshape(
-        [(i == 1 || (i == n && 2 * (i - 1)) == d) ? N : 2 * N for i in 1:n],
-        ntuple(i -> i == halfdim ? n : 1, Val(ndims(x)))
-    )
-    return p \ (x ./ convert(typeof(x), scale))
+    y = map(x, CartesianIndices(x)) do xj, j
+        i = j[halfdim]
+        yj = if i == 1 || (i == n && 2 * (i - 1) == d)
+            xj / N
+        else
+            xj / (2 * N)
+        end
+        return yj
+    end
+    return p \ y
 end
 
 function adjoint_mul(p::Plan{T}, x::AbstractArray, ::IRFFTAdjointStyle) where {T}
@@ -715,11 +720,17 @@ function adjoint_mul(p::Plan{T}, x::AbstractArray, ::IRFFTAdjointStyle) where {T
     halfdim = first(dims)
     n = size(p, halfdim)
     d = output_size(p, halfdim)
-    scale = reshape(
-        [(i == 1 || (i == n && 2 * (i - 1)) == d) ? 1 : 2 for i in 1:n],
-        ntuple(i -> i == halfdim ? n : 1, Val(ndims(x)))
-    )
-    return (convert(typeof(x), scale) ./ N) .* (p \ x)
+    y = p \ x
+    z = map(y, CartesianIndices(y)) do yj, j
+        i = j[halfdim]
+        zj = if i == 1 || (i == n && 2 * (i - 1) == d)
+            yj / N
+        else
+            2 * yj / N
+        end
+        return zj
+    end
+    return z
 end
 
 adjoint_mul(p::Plan, x::AbstractArray, ::UnitaryAdjointStyle) = p \ x