我为Haskell的内置exists
列表数据类型编写了量化函数forall
,none
和[]
。在很多情况下,这些方法似乎比Prelude
/ Data.List
的any
和all
效率更高。我天真地怀疑这种性能是由于any
和all
是使用Θ(n)折叠实现的。由于我是Haskell的新手,所以我认为我一定会误会,否则会有这种现象的充分原因。
从Data.Foldable
:
-- | Determines whether any element of the structure satisfies the predicate.
any :: Foldable t => (a -> Bool) -> t a -> Bool
any p = getAny #. foldMap (Any #. p)
-- | Determines whether all elements of the structure satisfy the predicate.
all :: Foldable t => (a -> Bool) -> t a -> Bool
all p = getAll #. foldMap (All #. p)
我的实现:
exists :: (a -> Bool) -> [a] -> Bool
exists _ [] = False
exists pred (x : xs) | pred x = True
| otherwise = exists pred xs
和
forall pred = not . exists (not . pred)
none pred = not . exists pred = forall (not . pred)
消除布尔反演:
forall, none :: (a -> Bool) -> [a] -> Bool
forall _ [] = True
forall pred (x : xs) | pred x = forall pred xs
| otherwise = False
none _ [] = True
none pred (x : xs) | pred x = False
| otherwise = none pred xs
all
:time 327.8 μs (322.4 μs .. 333.0 μs)
0.997 R² (0.996 R² .. 0.998 R²)
mean 328.7 μs (324.1 μs .. 334.2 μs)
std dev 16.95 μs (14.63 μs .. 22.02 μs)
和
forall
:time 113.2 μs (111.2 μs .. 115.0 μs)
0.997 R² (0.996 R² .. 0.998 R²)
mean 112.0 μs (110.0 μs .. 113.9 μs)
std dev 6.333 μs (5.127 μs .. 7.896 μs)
使用标准的
nf
衡量的性能。不出所料,我并没有重蹈覆辙,而是低估了编译器标志,并且天真地希望
-O2
与默认优化级别的性能相比,不会产生如此大的差异,也不会期望单个定制编写方法与库公式之间的优化效果差异。许多高效的专业标准功能优化显然只有在明确启用后才能启动。Haskell标记信息的“性能”部分强调测试代码效率时优化级别编译器标志的重要性。通常建议您信任库函数实现的复杂性,而不是重新布线
RULES
编译指示或重新编写基本形式,而是尝试利用已经培养的优化潜力。 最佳答案
我发现以各种方式重新实现any
具有指导意义:
import Prelude hiding (any)
import Criterion.Main
import Data.Foldable (foldMap)
import Data.Monoid
您的
exists
:exists :: (a -> Bool) -> [a] -> Bool
exists _ [] = False
exists pred (x : xs)
= if pred x
then True
else exists pred xs
使用
(||)
的版本:existsOr :: (a -> Bool) -> [a] -> Bool
existsOr _ [] = False
existsOr pred (x : xs) = pred x || existsOr pred xs
使用
foldr
:any :: (a -> Bool) -> [a] -> Bool
any pred = foldr ((||) . pred) False
使用
foldr
和Any
:anyF :: (a -> Bool) -> [a] -> Bool
anyF pred = getAny . foldr (mappend . (Any . pred)) mempty
使用
foldMap
和Any
:anyFM :: (a -> Bool) -> [a] -> Bool
anyFM pred = getAny . foldMap (Any . pred)
带有
ghc -O0
的基准:benchmarking exists
time 1.552 μs (1.504 μs .. 1.593 μs)
0.989 R² (0.983 R² .. 0.993 R²)
mean 1.482 μs (1.427 μs .. 1.545 μs)
std dev 196.1 ns (168.8 ns .. 229.2 ns)
variance introduced by outliers: 93% (severely inflated)
benchmarking existsOr
time 2.699 μs (2.616 μs .. 2.768 μs)
0.992 R² (0.988 R² .. 0.995 R²)
mean 2.629 μs (2.554 μs .. 2.704 μs)
std dev 277.8 ns (235.8 ns .. 351.1 ns)
variance introduced by outliers: 89% (severely inflated)
benchmarking any
time 5.551 μs (5.354 μs .. 5.777 μs)
0.990 R² (0.986 R² .. 0.995 R²)
mean 5.553 μs (5.395 μs .. 5.750 μs)
std dev 584.2 ns (447.5 ns .. 835.5 ns)
variance introduced by outliers: 88% (severely inflated)
benchmarking anyF
time 7.330 μs (7.081 μs .. 7.612 μs)
0.988 R² (0.982 R² .. 0.994 R²)
mean 7.502 μs (7.272 μs .. 7.762 μs)
std dev 848.2 ns (712.6 ns .. 1.022 μs)
variance introduced by outliers: 89% (severely inflated)
benchmarking anyFM
time 5.668 μs (5.451 μs .. 6.008 μs)
0.987 R² (0.975 R² .. 0.996 R²)
mean 5.807 μs (5.659 μs .. 5.975 μs)
std dev 542.5 ns (446.4 ns .. 721.8 ns)
variance introduced by outliers: 86% (severely inflated)
您的版本(
exists
)确实是最快的,而foldr
版本却相当慢。使用
ghc -O2
,您的版本(exists
)是最慢的,而所有其他功能彼此之间几乎同样快:benchmarking exists
time 753.5 ns (725.4 ns .. 779.9 ns)
0.990 R² (0.986 R² .. 0.995 R²)
mean 762.4 ns (737.0 ns .. 787.0 ns)
std dev 82.47 ns (66.79 ns .. 105.1 ns)
variance introduced by outliers: 91% (severely inflated)
benchmarking existsOr
time 491.5 ns (478.2 ns .. 503.2 ns)
0.994 R² (0.992 R² .. 0.996 R²)
mean 494.5 ns (481.1 ns .. 512.9 ns)
std dev 54.97 ns (42.54 ns .. 80.34 ns)
variance introduced by outliers: 92% (severely inflated)
benchmarking any
time 461.2 ns (442.0 ns .. 479.7 ns)
0.989 R² (0.985 R² .. 0.993 R²)
mean 456.0 ns (439.3 ns .. 476.3 ns)
std dev 60.04 ns (47.27 ns .. 89.47 ns)
variance introduced by outliers: 94% (severely inflated)
benchmarking anyF
time 436.9 ns (415.8 ns .. 461.0 ns)
0.978 R² (0.967 R² .. 0.988 R²)
mean 450.8 ns (430.1 ns .. 472.6 ns)
std dev 70.64 ns (57.04 ns .. 85.92 ns)
variance introduced by outliers: 96% (severely inflated)
benchmarking anyFM
time 438.9 ns (426.9 ns .. 449.5 ns)
0.993 R² (0.989 R² .. 0.996 R²)
mean 435.8 ns (421.4 ns .. 447.6 ns)
std dev 45.32 ns (36.73 ns .. 58.74 ns)
variance introduced by outliers: 90% (severely inflated)
如果人们查看简化的Core代码(
ghc -O2 -ddump-simpl
),就会发现不再有foldr
了(有了-O0
,一切仍然在那里,包括fold
)。因此,我敢说您的代码(在未优化的版本中,
-O0
)比库代码更快,因为它更简单(因为潜在的价格降低了通用性)。经过优化的库代码比您的版本要快,因为它是通过编译器可以识别其优化潜力的方式编写的。 (诚然,这是一些猜测工作)