1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
|
-- |
-- Module: Math.NumberTheory.MoebiusInversionTests
-- Copyright: (c) 2016 Andrew Lelechenko
-- Licence: MIT
-- Maintainer: Andrew Lelechenko <andrew.lelechenko@gmail.com>
--
-- Tests for Math.NumberTheory.MoebiusInversion
--
{-# OPTIONS_GHC -fno-warn-type-defaults #-}
module Math.NumberTheory.MoebiusInversionTests
( testSuite
) where
import Test.Tasty
import Test.Tasty.HUnit
import Test.Tasty.QuickCheck as QC hiding (Positive)
import Data.Proxy
import Data.Vector.Unboxed (Vector)
import Math.NumberTheory.MoebiusInversion
import Math.NumberTheory.ArithmeticFunctions
import Math.NumberTheory.TestUtils
proxy :: Proxy Vector
proxy = Proxy
totientSumProperty :: AnySign Word -> Bool
totientSumProperty (AnySign n) = (totientSum proxy n :: Word) == sum (map totient [1..n])
totientSumSpecialCase1 :: Assertion
totientSumSpecialCase1 = assertEqual "totientSum" 4496 (totientSum proxy 121 :: Word)
totientSumZero :: Assertion
totientSumZero = assertEqual "totientSum" 0 (totientSum proxy 0 :: Word)
generalInversionProperty :: (Word -> Word) -> Positive Word -> Bool
generalInversionProperty g (Positive n)
= g n == sum [f (n `quot` k) | k <- [1 .. n]]
&& f n == sum [runMoebius (moebius k) * g (n `quot` k) | k <- [1 .. n]]
where
f = generalInversion proxy g
testSuite :: TestTree
testSuite = testGroup "MoebiusInversion"
[ testGroup "totientSum"
[ testSmallAndQuick "matches definitions" totientSumProperty
, testCase "special case 1" totientSumSpecialCase1
, testCase "zero" totientSumZero
]
, QC.testProperty "generalInversion" generalInversionProperty
]
|
