Fix up comment

repa-algorithms/Data/Array/Repa/Algorithms/FFT.hs

@@ -1,8 +1,8 @@
 {-# LANGUAGE TypeOperators, PatternGuards, RankNTypes, ScopedTypeVariables, BangPatterns, FlexibleContexts #-}
 {-# OPTIONS -fno-warn-incomplete-patterns #-}
 
--- | Fast computation of Discrete Fourier Transforms using the Cooley-Tuckey algorithm. 
---   Time complexity is O(n log n) in the size of the input. 
+-- | Fast computation of Discrete Fourier Transforms using the Cooley-Tuckey algorithm.
+--   Time complexity is O(n log n) in the size of the input.
 --
 --   This uses a naive divide-and-conquer algorithm, the absolute performance is about
 --   50x slower than FFTW in estimate mode.
@@ -38,8 +38,7 @@ signOfMode mode
 {-# INLINE signOfMode #-}
 
 
--- | Check if an `Int` is a power of two. Assumes `n` is positive
--- and will return `True` when given 0.
+-- | Check if an `Int` is a power of two. Assumes `n` is a natural number.
 
 -- The implementation can be found in Henry S. Warren, Jr.'s book
 -- Hacker's delight, Chapter 2.
@@ -57,29 +56,29 @@ fft3dP  :: (Source r Complex, Monad m)
 fft3dP mode arr
  = let  _ :. depth :. height :. width   = extent arr
         !sign   = signOfMode mode
-        !scale  = fromIntegral (depth * width * height) 
-                
+        !scale  = fromIntegral (depth * width * height)
+
    in   if not (isPowerOfTwo depth && isPowerOfTwo height && isPowerOfTwo width)
          then error $ unlines
                 [ "Data.Array.Repa.Algorithms.FFT: fft3d"
                 , "  Array dimensions must be powers of two,"
-                , "  but the provided array is " 
+                , "  but the provided array is "
                         P.++ show height P.++ "x" P.++ show width P.++ "x" P.++ show depth ]
-                   
-         else arr `deepSeqArray` 
+
+         else arr `deepSeqArray`
                 case mode of
                         Forward -> now $ fftTrans3d sign $ fftTrans3d sign $ fftTrans3d sign arr
                         Reverse -> now $ fftTrans3d sign $ fftTrans3d sign $ fftTrans3d sign arr
                         Inverse -> computeP
-                                $  R.map (/ scale) 
+                                $  R.map (/ scale)
                                 $  fftTrans3d sign $ fftTrans3d sign $ fftTrans3d sign arr
 {-# INLINE fft3dP #-}
 
 
-fftTrans3d 
+fftTrans3d
         :: Source r Complex
         => Double
-        -> Array r DIM3 Complex 
+        -> Array r DIM3 Complex
         -> Array U DIM3 Complex
 
 fftTrans3d sign arr
@@ -88,7 +87,7 @@ fftTrans3d sign arr
 {-# INLINE fftTrans3d #-}
 
 
-rotate3d 
+rotate3d
         :: Source r Complex
         => Array r DIM3 Complex -> Array D DIM3 Complex
 rotate3d arr
@@ -108,15 +107,15 @@ fft2dP  :: (Source r Complex, Monad m)
 fft2dP mode arr
  = let  _ :. height :. width    = extent arr
         sign    = signOfMode mode
-        scale   = fromIntegral (width * height) 
-                
+        scale   = fromIntegral (width * height)
+
    in   if not (isPowerOfTwo height && isPowerOfTwo width)
          then error $ unlines
                 [ "Data.Array.Repa.Algorithms.FFT: fft2d"
                 , "  Array dimensions must be powers of two,"
                 , "  but the provided array is " P.++ show height P.++ "x" P.++ show width ]
-         
-         else arr `deepSeqArray` 
+
+         else arr `deepSeqArray`
                 case mode of
                         Forward -> now $ fftTrans2d sign $ fftTrans2d sign arr
                         Reverse -> now $ fftTrans2d sign $ fftTrans2d sign arr
@@ -127,7 +126,7 @@ fft2dP mode arr
 fftTrans2d
         :: Source r Complex
         => Double
-        -> Array r DIM2 Complex 
+        -> Array r DIM2 Complex
         -> Array U DIM2 Complex
 
 fftTrans2d sign arr
@@ -139,20 +138,20 @@ fftTrans2d sign arr
 -- Vector Transform -------------------------------------------------------------------------------
 -- | Compute the DFT of a vector. Array dimensions must be powers of two else `error`.
 fft1dP  :: (Source r Complex, Monad m)
-        => Mode 
-        -> Array r DIM1 Complex 
+        => Mode
+        -> Array r DIM1 Complex
         -> m (Array U DIM1 Complex)
 fft1dP mode arr
  = let  _ :. len        = extent arr
         sign    = signOfMode mode
         scale   = fromIntegral len
-        
+
    in   if not $ isPowerOfTwo len
-         then error $ unlines 
+         then error $ unlines
                 [ "Data.Array.Repa.Algorithms.FFT: fft1d"
                 , "  Array dimensions must be powers of two, "
                 , "  but the provided array is " P.++ show len ]
-              
+
          else arr `deepSeqArray`
                 case mode of
                         Forward -> now $ fftTrans1d sign arr
@@ -163,7 +162,7 @@ fft1dP mode arr
 
 fftTrans1d
         :: Source r Complex
-        => Double 
+        => Double
         -> Array r DIM1 Complex
         -> Array U DIM1 Complex
 
@@ -175,7 +174,7 @@ fftTrans1d sign arr
 
 -- Rank Generalised Worker ------------------------------------------------------------------------
 fft     :: (Shape sh, Source r Complex)
-        => Double -> sh -> Int 
+        => Double -> sh -> Int
         -> Array r (sh :. Int) Complex
         -> Array U (sh :. Int) Complex
 
@@ -184,9 +183,9 @@ fft !sign !sh !lenVec !vec
  where  go !len !offset !stride
          | len == 2
          = suspendedComputeP $ fromFunction (sh :. 2) swivel
-        
+
          | otherwise
-         = combine len 
+         = combine len
                 (go (len `div` 2) offset            (stride * 2))
                 (go (len `div` 2) (offset + stride) (stride * 2))
 
@@ -198,7 +197,7 @@ fft !sign !sh !lenVec !vec
                 {-# INLINE combine #-}
                 combine !len'   evens odds
                  = evens `deepSeqArray` odds `deepSeqArray`
-                   let  odds'   = unsafeTraverse odds id (\get ix@(_ :. k) -> twiddle sign k len' * get ix) 
+                   let  odds'   = unsafeTraverse odds id (\get ix@(_ :. k) -> twiddle sign k len' * get ix)
                    in   suspendedComputeP $ (evens +^ odds') R.++ (evens -^ odds')
 {-# INLINE fft #-}
 
@@ -214,4 +213,3 @@ twiddle sign k' n'
         where   k       = fromIntegral k'
                 n       = fromIntegral n'
 {-# INLINE twiddle #-}
-