Question

我有以下矩阵乘法函数

winograd :: M.Matrix Int -> M.Matrix Int -> M.Matrix Int
winograd a b = c
where
  ra = M.nrows a
  ca = M.ncols a
  rb = M.nrows b
  cb = M.ncols b

  isEven = even ca

  avs = V.generate ra $ \i -> M.getRow (i+1) a
  bvs = V.generate cb $ \j -> M.getCol (j+1) b

  rows = V.generate ra $ \i -> wgdGroup $ V.unsafeIndex avs i
  cols = V.generate cb $ \j -> wgdGroup $ V.unsafeIndex bvs j

  wgdGroup x = let
                 finish = (V.length x - 1)
               in
                 forLoopFold 0 (<finish) (+2) 0 $
                 \acc i -> acc
                 - V.unsafeIndex x i *  V.unsafeIndex x (i+1)

  c = if isEven then
        M.matrix ra cb $
        \(i,j) ->
        V.unsafeIndex rows (i-1) +
        V.unsafeIndex cols (j-1)  +
        g (V.unsafeIndex avs (i-1)) (V.unsafeIndex bvs (j-1))
      else
        M.matrix ra cb $
        \(i,j) ->
        V.unsafeIndex rows (i-1) +
        V.unsafeIndex cols (j-1) +
        g (V.unsafeIndex avs (i-1)) (V.unsafeIndex bvs (j-1)) +
        V.last (V.unsafeIndex avs (i-1)) * V.last (V.unsafeIndex bvs (j-1))

  g r c = forLoopFold 0 (<(ca-1)) (+2) 0 $ \acc i ->
            let
              x1 = V.unsafeIndex r i
              x2 = V.unsafeIndex r (i+1)
              y1 = V.unsafeIndex c i
              y2 = V.unsafeIndex c (i+1)
            in
            acc + (x1+y2)*(x2+y1)

我使用clock和formatting包来测量此函数的执行时间如下（是的，我知道Criterion，但现在我需要以这种方式测量它）：

main :: IO ()
main = do
  let a = simple 2 (-1) 1000
  let b = simple 2 (-3) 1000
  start <- getTime Realtime
  let
    c = winograd a b
  end <- c `deepseq` getTime Realtime
  fprint (timeSpecs % "\n") start end

其中simple是

simple :: Int -> Int -> Int -> M.Matrix Int
simple x y size = M.matrix size size $ \(i,j) -> x*i+y*j

我得到的结果大约5秒钟。但是当我摆脱函数simple并且这样做时：

main :: IO ()
main = do
  let a = M.matrix 1000 1000 $ \(i,j) -> 2*i-1*j
  let b = M.matrix 1000 1000 $ \(i,j) -> 2*i-3*j
  start <- getTime Realtime
  let
    c = winograd a b
  end <- c `deepseq` getTime Realtime
  fprint (timeSpecs % "\n") start end

时间增加到15秒！

非常有趣的原因。用标志-O2编译。

Haskell时间测量

0 个答案: