Replace division with multiplication in adjoint loop

src/definitions.jl

@@ -692,43 +692,43 @@ end
 
 function adjoint_mul(p::Plan{T}, x::AbstractArray, ::RFFTAdjointStyle) where {T<:Real}
  dims = fftdims(p)
- _N = normalization(T, size(p), dims)
+ N = normalization(T, size(p), dims)
  halfdim = first(dims)
  d = size(p, halfdim)
  pinv = inv(p)
  n = size(pinv, halfdim)
  # Optimization: when pinv is a ScaledPlan, fuse the scaling into our map to ensure we do not loop over x twice.
- N = pinv isa ScaledPlan ? _N / pinv.scale : _N
- scaled_pinv = pinv isa ScaledPlan ? pinv.p : pinv 
+ scale = pinv isa ScaledPlan ? pinv.scale / 2N : 1 / 2N
+ unscaled_pinv = pinv isa ScaledPlan ? pinv.p : pinv 
  y = map(x, CartesianIndices(x)) do xj, j
  i = j[halfdim]
  yj = if i == 1 || (i == n && 2 * (i - 1) == d)
- xj / N
+ xj * scale * 2
  else
- xj / (2 * N)
+ xj * scale
  end
  return yj
  end
- return scaled_pinv * y
+ return unscaled_pinv * y
 end
 
 function adjoint_mul(p::Plan{T}, x::AbstractArray, ::IRFFTAdjointStyle) where {T}
  dims = fftdims(p)
- _N = normalization(real(T), size(inv(p)), dims)
+ N = normalization(real(T), size(inv(p)), dims)
  halfdim = first(dims)
  n = size(p, halfdim)
  pinv = inv(p)
  d = size(pinv, halfdim)
  # Optimization: when pinv is a ScaledPlan, fuse the scaling into our map to ensure we do not loop over x twice.
- N = pinv isa ScaledPlan ? _N / pinv.scale : _N
- scaled_pinv = pinv isa ScaledPlan ? pinv.p : pinv 
- y = scaled_pinv * x
+ scale = pinv isa ScaledPlan ? pinv.scale / N : 1 / N
+ unscaled_pinv = pinv isa ScaledPlan ? pinv.p : pinv 
+ y = unscaled_pinv * x
  z = map(y, CartesianIndices(y)) do yj, j
  i = j[halfdim]
  zj = if i == 1 || (i == n && 2 * (i - 1) == d)
- yj / N
+ yj * scale
  else
- 2 * yj / N
+ yj * scale * 2
  end
  return zj
  end