All geek questions in one place

Efficient folding of the sum tree

In this earlier question, I asked how to write a function that sums a non-binary integer tree, and several answers came up.

@ Sibi said:

data Tree a = Empty | Node a [Tree a] deriving (Eq, Show)

addNums :: (Num a) => Tree a -> a
addNums Empty = 0
addNums (Node n []) = n
addNums (Node n (x:xs)) = n + (addNums x) + addNums (Node 0 xs)

@ user3237465 said:

data Tree a = Empty | Node a [Tree a] deriving (Eq, Show, Foldable)

myNums :: (Num a) => Tree a
myNums = ...

main = print $ sum myNums

and @chi said:

addNums :: (Num a) => Tree a -> a
addNums Empty = 0
addNums (Node n xs) = n + sum (map addNums xs)

How to find the most effective solution? Does Haskell have its own benchmarking tool?

+4
source share
2 answers

Although so.com is not a recommendation site, I suggest you take a look at the criterion https://hackage.haskell.org/package/criterion

I can give an example of use tomorrow

, llvm, --ddump-llvm, , .

- criterion

, , haskell, github/epsilonhalbe

, ( data Tree, data Tree' data Tree''). . Chi.hs :

module Chi where

data Tree a = Empty | Node a [Tree a] deriving (Eq, Show)

addNums :: (Num a) => Tree a -> a
addNums Empty = 0
addNums (Node n xs) = n + sum (map addNums xs)

myInts :: Tree Int
myInts =
    Node 1 [
           Node 2 [
             Node 4 [Empty], Node 5 [Empty]
           ],
           Node 3 [
             Node 6 [Empty], Node 7 [Empty], Node 8 [Empty]
           ]
        ]

myDouble :: Tree Double
myDouble =
    Node 1 [
           Node 2 [
             Node 4 [Empty], Node 5 [Empty]
           ],
           Node 3 [
             Node 6 [Empty], Node 7 [Empty], Node 8 [Empty]
           ]
        ]

: User3237465.hs Pragma

{-# LANGUAGE DeriveFoldable #-}
module User3237465 where

data Tree a = Empty | Node a [Tree a] deriving (Eq, Show, Foldable)

addNums :: Num a => Tree a -> a
addNums = sum

myInts ..
myDouble ..

/, ( stack new critExample //)

../haskell/critExample/
▾ src/
    Chi.hs
    Sibi.hs
    User3237465.hs
▾ bench/
    Benchmarks.hs
  critExample.cabal
  LICENSE
  Setup.hs
  stack.yaml

critExample.cabal ,

name:                critExample
[... non-important stuff ...]

library
  hs-source-dirs:      src
  -- don't forget to adjust the exposed modules
  exposed-modules:     Chi
                 ,     Sibi
                 ,     User3237465
  build-depends:       base >= 4.7 && < 5
  default-language:    Haskell2010

-- and add the following benchmark part
benchmark addNums
  type:                exitcode-stdio-1.0
  hs-source-dirs:      bench
  main-is:             Benchmarks.hs
  build-depends:       base
                     , critExample
                     , criterion
  default-language:    Haskell2010
  [...]

Benchmarks.hs

module Main where

import Criterion
import Criterion.Main

import qualified Chi
import qualified Sibi
import qualified User3237465


main :: IO ()
main = defaultMain [
    bgroup "myInts" [ bench "Sibi"        $ whnf Sibi.addNums Sibi.myInts
                    , bench "Chi"         $ whnf Chi.addNums Chi.myInts
                    , bench "User3237465" $ whnf User3237465.addNums User3237465.myInts
                    ],

    bgroup "myDouble" [ bench "Sibi"        $ whnf Sibi.addNums Sibi.myDouble
                      , bench "Chi"         $ whnf Chi.addNums Chi.myDouble
                      , bench "User3237465" $ whnf User3237465.addNums User3237465.myDouble ]
    ]

, whnf , , - , (:) , Int Double . "" , nf whnf - , , whnf, , (, - ).

stack build, stack bench ( ) stack bench critExample:addNums (, ), projectname:name of benchmarks given in cabal-file.

html (, , , bryan o'sullivan , ) :

./.stack-work/dist/x86_64-linux/Cabal-1.22.4.0/build/addNums/addNums --output index.html

, , Linux.

Update2

- , - Linux!

Running 1 benchmarks...
Benchmark addNums: RUNNING...
benchmarking myInts/Sibi
time                 616.7 ns   (614.1 ns .. 619.2 ns)
                     1.000 R²   (1.000 R² .. 1.000 R²)
mean                 619.1 ns   (615.4 ns .. 626.8 ns)
std dev              17.09 ns   (9.625 ns .. 31.62 ns)
variance introduced by outliers: 38% (moderately inflated)

benchmarking myInts/Chi
time                 582.6 ns   (576.5 ns .. 592.1 ns)
                     0.998 R²   (0.996 R² .. 1.000 R²)
mean                 586.2 ns   (581.5 ns .. 595.5 ns)
std dev              21.14 ns   (11.56 ns .. 33.61 ns)
variance introduced by outliers: 52% (severely inflated)

benchmarking myInts/User3237465
time                 606.5 ns   (604.9 ns .. 608.2 ns)
                     1.000 R²   (1.000 R² .. 1.000 R²)
mean                 607.0 ns   (605.5 ns .. 609.2 ns)
std dev              5.915 ns   (3.992 ns .. 9.798 ns)

benchmarking myInts/User3237465 -- folding variant see comments
time                 371.0 ns   (370.2 ns .. 371.7 ns)
                     1.000 R²   (1.000 R² .. 1.000 R²)
mean                 372.5 ns   (370.8 ns .. 375.0 ns)
std dev              6.824 ns   (4.076 ns .. 11.19 ns)
variance introduced by outliers: 22% (moderately inflated)

benchmarking myDouble/Sibi
time                 678.9 ns   (642.3 ns .. 743.8 ns)
                     0.978 R²   (0.958 R² .. 1.000 R²)
mean                 649.9 ns   (641.1 ns .. 681.6 ns)
std dev              50.99 ns   (12.60 ns .. 105.0 ns)
variance introduced by outliers: 84% (severely inflated)

benchmarking myDouble/Chi
time                 643.3 ns   (617.4 ns .. 673.6 ns)
                     0.987 R²   (0.979 R² .. 0.996 R²)
mean                 640.6 ns   (626.7 ns .. 665.6 ns)
std dev              58.35 ns   (40.63 ns .. 87.82 ns)
variance introduced by outliers: 88% (severely inflated)

benchmarking myDouble/User3237465
time                 630.4 ns   (622.9 ns .. 638.5 ns)
                     0.997 R²   (0.994 R² .. 0.999 R²)
mean                 637.8 ns   (625.4 ns .. 659.8 ns)
std dev              53.15 ns   (33.46 ns .. 78.36 ns)
variance introduced by outliers: 85% (severely inflated)

benchmarking myDouble/User3237465 -- folding variant see comments
time                 398.1 ns   (380.7 ns .. 422.0 ns)
                     0.988 R²   (0.980 R² .. 0.996 R²)
mean                 400.6 ns   (389.1 ns .. 428.6 ns)
std dev              55.83 ns   (28.94 ns .. 103.6 ns)
variance introduced by outliers: 94% (severely inflated)

Benchmark addNums: FINISH
Completed all 2 actions.

, import Data.Foldable (foldl') addNums' = foldl' (+) 0 ( @User3237465!!)

+2

, , . , . :

newtype Tree a = Tree {fold :: forall r. r -> (a -> [r] -> r) -> r}

:

newtype Tree a = Tree {fold :: forall r. r -> (a -> ChurchList r -> r) -> r}

:

newtype Tree a = Tree {fold :: forall tree list. tree -> (a -> list -> tree) -> list -> (tree -> list -> list) -> tree}

, .

+1

Source: https://habr.com/ru/post/1621176/

More articles:


All Articles