-- Do not edit! Automatically created with doctest-extract from private/Numeric/FFTW/Extra/NumberTheory.hs
{-# LINE 11 "private/Numeric/FFTW/Extra/NumberTheory.hs" #-}

module DocTest.Numeric.FFTW.Extra.NumberTheory where

import Test.DocTest.Base
import qualified Test.DocTest.Driver as DocTest

{-# LINE 12 "private/Numeric/FFTW/Extra/NumberTheory.hs" #-}
import     Numeric.FFTW.Extra.NumberTheory
import     qualified Test.QuickCheck as QC

test :: DocTest.T ()
test = do
 DocTest.printPrefix "Numeric.FFTW.Extra.NumberTheory:26: "
{-# LINE 26 "private/Numeric/FFTW/Extra/NumberTheory.hs" #-}
 DocTest.example(
{-# LINE 26 "private/Numeric/FFTW/Extra/NumberTheory.hs" #-}
    primeFactors (1::Int)
  )
  [ExpectedLine [LineChunk "[]"]]
 DocTest.printPrefix "Numeric.FFTW.Extra.NumberTheory:28: "
{-# LINE 28 "private/Numeric/FFTW/Extra/NumberTheory.hs" #-}
 DocTest.example(
{-# LINE 28 "private/Numeric/FFTW/Extra/NumberTheory.hs" #-}
    primeFactors (2::Int)
  )
  [ExpectedLine [LineChunk "[(2,1)]"]]
 DocTest.printPrefix "Numeric.FFTW.Extra.NumberTheory:30: "
{-# LINE 30 "private/Numeric/FFTW/Extra/NumberTheory.hs" #-}
 DocTest.example(
{-# LINE 30 "private/Numeric/FFTW/Extra/NumberTheory.hs" #-}
    primeFactors (3::Int)
  )
  [ExpectedLine [LineChunk "[(3,1)]"]]
 DocTest.printPrefix "Numeric.FFTW.Extra.NumberTheory:32: "
{-# LINE 32 "private/Numeric/FFTW/Extra/NumberTheory.hs" #-}
 DocTest.example(
{-# LINE 32 "private/Numeric/FFTW/Extra/NumberTheory.hs" #-}
    primeFactors (4::Int)
  )
  [ExpectedLine [LineChunk "[(2,2)]"]]
 DocTest.printPrefix "Numeric.FFTW.Extra.NumberTheory:34: "
{-# LINE 34 "private/Numeric/FFTW/Extra/NumberTheory.hs" #-}
 DocTest.example(
{-# LINE 34 "private/Numeric/FFTW/Extra/NumberTheory.hs" #-}
    primeFactors (44100::Int)
  )
  [ExpectedLine [LineChunk "[(2,2),(3,2),(5,2),(7,2)]"]]
 DocTest.printPrefix "Numeric.FFTW.Extra.NumberTheory:36: "
{-# LINE 36 "private/Numeric/FFTW/Extra/NumberTheory.hs" #-}
 DocTest.example(
{-# LINE 36 "private/Numeric/FFTW/Extra/NumberTheory.hs" #-}
    primeFactors (48000::Int)
  )
  [ExpectedLine [LineChunk "[(2,7),(3,1),(5,3)]"]]
 DocTest.printPrefix "Numeric.FFTW.Extra.NumberTheory:39: "
{-# LINE 39 "private/Numeric/FFTW/Extra/NumberTheory.hs" #-}
 DocTest.property(
{-# LINE 39 "private/Numeric/FFTW/Extra/NumberTheory.hs" #-}
      \(QC.Positive n) -> all (1<) $ map fst $ primeFactors (n::Int)
  )
 DocTest.printPrefix "Numeric.FFTW.Extra.NumberTheory:41: "
{-# LINE 41 "private/Numeric/FFTW/Extra/NumberTheory.hs" #-}
 DocTest.property(
{-# LINE 41 "private/Numeric/FFTW/Extra/NumberTheory.hs" #-}
      \(QC.Positive n) -> n == product (map (uncurry (^)) (primeFactors (n::Int)))
  )
 DocTest.printPrefix "Numeric.FFTW.Extra.NumberTheory:57: "
{-# LINE 57 "private/Numeric/FFTW/Extra/NumberTheory.hs" #-}
 DocTest.property(
{-# LINE 57 "private/Numeric/FFTW/Extra/NumberTheory.hs" #-}
      \(QC.Positive n) -> elem 1 $ divisors (n::Int)
  )
 DocTest.printPrefix "Numeric.FFTW.Extra.NumberTheory:58: "
{-# LINE 58 "private/Numeric/FFTW/Extra/NumberTheory.hs" #-}
 DocTest.property(
{-# LINE 58 "private/Numeric/FFTW/Extra/NumberTheory.hs" #-}
      \(QC.Positive n) -> elem n $ divisors (n::Int)
  )
 DocTest.printPrefix "Numeric.FFTW.Extra.NumberTheory:59: "
{-# LINE 59 "private/Numeric/FFTW/Extra/NumberTheory.hs" #-}
 DocTest.property(
{-# LINE 59 "private/Numeric/FFTW/Extra/NumberTheory.hs" #-}
      \(QC.Positive n) -> all (\k -> mod n k == 0) $ divisors (n::Int)
  )
 DocTest.printPrefix "Numeric.FFTW.Extra.NumberTheory:68: "
{-# LINE 68 "private/Numeric/FFTW/Extra/NumberTheory.hs" #-}
 DocTest.example(
{-# LINE 68 "private/Numeric/FFTW/Extra/NumberTheory.hs" #-}
    nextDivisor 44100 (1000::Int)
  )
  [ExpectedLine [LineChunk "1050"]]
 DocTest.printPrefix "Numeric.FFTW.Extra.NumberTheory:70: "
{-# LINE 70 "private/Numeric/FFTW/Extra/NumberTheory.hs" #-}
 DocTest.example(
{-# LINE 70 "private/Numeric/FFTW/Extra/NumberTheory.hs" #-}
    nextDivisor 44100 (2000::Int)
  )
  [ExpectedLine [LineChunk "2100"]]
 DocTest.printPrefix "Numeric.FFTW.Extra.NumberTheory:72: "
{-# LINE 72 "private/Numeric/FFTW/Extra/NumberTheory.hs" #-}
 DocTest.example(
{-# LINE 72 "private/Numeric/FFTW/Extra/NumberTheory.hs" #-}
    nextDivisor 44100 (3000::Int)
  )
  [ExpectedLine [LineChunk "3150"]]
 DocTest.printPrefix "Numeric.FFTW.Extra.NumberTheory:74: "
{-# LINE 74 "private/Numeric/FFTW/Extra/NumberTheory.hs" #-}
 DocTest.example(
{-# LINE 74 "private/Numeric/FFTW/Extra/NumberTheory.hs" #-}
    nextDivisor 44100 (4000::Int)
  )
  [ExpectedLine [LineChunk "4410"]]
 DocTest.printPrefix "Numeric.FFTW.Extra.NumberTheory:76: "
{-# LINE 76 "private/Numeric/FFTW/Extra/NumberTheory.hs" #-}
 DocTest.example(
{-# LINE 76 "private/Numeric/FFTW/Extra/NumberTheory.hs" #-}
    nextDivisor 48000 (1000::Int)
  )
  [ExpectedLine [LineChunk "1000"]]
 DocTest.printPrefix "Numeric.FFTW.Extra.NumberTheory:78: "
{-# LINE 78 "private/Numeric/FFTW/Extra/NumberTheory.hs" #-}
 DocTest.example(
{-# LINE 78 "private/Numeric/FFTW/Extra/NumberTheory.hs" #-}
    nextDivisor 48000 (9000::Int)
  )
  [ExpectedLine [LineChunk "9600"]]
 DocTest.printPrefix "Numeric.FFTW.Extra.NumberTheory:81: "
{-# LINE 81 "private/Numeric/FFTW/Extra/NumberTheory.hs" #-}
 DocTest.property(
{-# LINE 81 "private/Numeric/FFTW/Extra/NumberTheory.hs" #-}
        
   \(QC.Positive n) ->
   QC.forAll (QC.choose (1,n::Int)) $ \m ->
      let k = nextDivisor n m
      in m <= k && mod n k == 0
  )
 DocTest.printPrefix "Numeric.FFTW.Extra.NumberTheory:88: "
{-# LINE 88 "private/Numeric/FFTW/Extra/NumberTheory.hs" #-}
 DocTest.property(
{-# LINE 88 "private/Numeric/FFTW/Extra/NumberTheory.hs" #-}
        
   \(QC.Positive n) ->
   QC.forAll (QC.elements (divisors (n::Int))) $ \k ->
      nextDivisor n k == k
  )
 DocTest.printPrefix "Numeric.FFTW.Extra.NumberTheory:99: "
{-# LINE 99 "private/Numeric/FFTW/Extra/NumberTheory.hs" #-}
 DocTest.example(
{-# LINE 99 "private/Numeric/FFTW/Extra/NumberTheory.hs" #-}
    adjacentDivisors 44100 (1000::Int)
  )
  [ExpectedLine [LineChunk "(980,1050)"]]
 DocTest.printPrefix "Numeric.FFTW.Extra.NumberTheory:101: "
{-# LINE 101 "private/Numeric/FFTW/Extra/NumberTheory.hs" #-}
 DocTest.example(
{-# LINE 101 "private/Numeric/FFTW/Extra/NumberTheory.hs" #-}
    adjacentDivisors 44100 (2000::Int)
  )
  [ExpectedLine [LineChunk "(1764,2100)"]]
 DocTest.printPrefix "Numeric.FFTW.Extra.NumberTheory:103: "
{-# LINE 103 "private/Numeric/FFTW/Extra/NumberTheory.hs" #-}
 DocTest.example(
{-# LINE 103 "private/Numeric/FFTW/Extra/NumberTheory.hs" #-}
    adjacentDivisors 44100 (3000::Int)
  )
  [ExpectedLine [LineChunk "(2940,3150)"]]
 DocTest.printPrefix "Numeric.FFTW.Extra.NumberTheory:105: "
{-# LINE 105 "private/Numeric/FFTW/Extra/NumberTheory.hs" #-}
 DocTest.example(
{-# LINE 105 "private/Numeric/FFTW/Extra/NumberTheory.hs" #-}
    adjacentDivisors 44100 (4000::Int)
  )
  [ExpectedLine [LineChunk "(3675,4410)"]]
 DocTest.printPrefix "Numeric.FFTW.Extra.NumberTheory:107: "
{-# LINE 107 "private/Numeric/FFTW/Extra/NumberTheory.hs" #-}
 DocTest.example(
{-# LINE 107 "private/Numeric/FFTW/Extra/NumberTheory.hs" #-}
    adjacentDivisors 48000 (1000::Int)
  )
  [ExpectedLine [LineChunk "(1000,1000)"]]
 DocTest.printPrefix "Numeric.FFTW.Extra.NumberTheory:109: "
{-# LINE 109 "private/Numeric/FFTW/Extra/NumberTheory.hs" #-}
 DocTest.example(
{-# LINE 109 "private/Numeric/FFTW/Extra/NumberTheory.hs" #-}
    adjacentDivisors 48000 (9000::Int)
  )
  [ExpectedLine [LineChunk "(8000,9600)"]]
 DocTest.printPrefix "Numeric.FFTW.Extra.NumberTheory:112: "
{-# LINE 112 "private/Numeric/FFTW/Extra/NumberTheory.hs" #-}
 DocTest.property(
{-# LINE 112 "private/Numeric/FFTW/Extra/NumberTheory.hs" #-}
        
   \(QC.Positive n) ->
   QC.forAll (QC.choose (1,n::Int)) $ \m ->
      let (lower,upper) = adjacentDivisors n m
      in lower <= m && m <= upper
         &&
         mod n lower == 0 && mod n upper == 0
  )
 DocTest.printPrefix "Numeric.FFTW.Extra.NumberTheory:121: "
{-# LINE 121 "private/Numeric/FFTW/Extra/NumberTheory.hs" #-}
 DocTest.property(
{-# LINE 121 "private/Numeric/FFTW/Extra/NumberTheory.hs" #-}
        
   \(QC.Positive n) ->
   QC.forAll (QC.elements (divisors (n::Int))) $ \k ->
      adjacentDivisors n k == (k,k)
  )
 DocTest.printPrefix "Numeric.FFTW.Extra.NumberTheory:134: "
{-# LINE 134 "private/Numeric/FFTW/Extra/NumberTheory.hs" #-}
 DocTest.property(
{-# LINE 134 "private/Numeric/FFTW/Extra/NumberTheory.hs" #-}
      \(QC.NonNegative n) -> elem (ceilingPowerOfTwo (n::Int)) $ iterate (2*) 1
  )
 DocTest.printPrefix "Numeric.FFTW.Extra.NumberTheory:135: "
{-# LINE 135 "private/Numeric/FFTW/Extra/NumberTheory.hs" #-}
 DocTest.property(
{-# LINE 135 "private/Numeric/FFTW/Extra/NumberTheory.hs" #-}
      \(QC.NonNegative n) -> n <= ceilingPowerOfTwo (n::Int)
  )
 DocTest.printPrefix "Numeric.FFTW.Extra.NumberTheory:136: "
{-# LINE 136 "private/Numeric/FFTW/Extra/NumberTheory.hs" #-}
 DocTest.property(
{-# LINE 136 "private/Numeric/FFTW/Extra/NumberTheory.hs" #-}
      \(QC.Positive n) -> ceilingPowerOfTwo (n::Int) < 2*n
  )
 DocTest.printPrefix "Numeric.FFTW.Extra.NumberTheory:155: "
{-# LINE 155 "private/Numeric/FFTW/Extra/NumberTheory.hs" #-}
 DocTest.example(
{-# LINE 155 "private/Numeric/FFTW/Extra/NumberTheory.hs" #-}
    sqrtToPowerOfTwo (0::Integer)
  )
  [ExpectedLine [LineChunk "0"]]
 DocTest.printPrefix "Numeric.FFTW.Extra.NumberTheory:157: "
{-# LINE 157 "private/Numeric/FFTW/Extra/NumberTheory.hs" #-}
 DocTest.example(
{-# LINE 157 "private/Numeric/FFTW/Extra/NumberTheory.hs" #-}
    sqrtToPowerOfTwo (1::Integer)
  )
  [ExpectedLine [LineChunk "1"]]
 DocTest.printPrefix "Numeric.FFTW.Extra.NumberTheory:159: "
{-# LINE 159 "private/Numeric/FFTW/Extra/NumberTheory.hs" #-}
 DocTest.example(
{-# LINE 159 "private/Numeric/FFTW/Extra/NumberTheory.hs" #-}
    map sqrtToPowerOfTwo [7,8,9::Integer]
  )
  [ExpectedLine [LineChunk "[2,4,4]"]]
 DocTest.printPrefix "Numeric.FFTW.Extra.NumberTheory:161: "
{-# LINE 161 "private/Numeric/FFTW/Extra/NumberTheory.hs" #-}
 DocTest.example(
{-# LINE 161 "private/Numeric/FFTW/Extra/NumberTheory.hs" #-}
    map sqrtToPowerOfTwo [15,16,17::Integer]
  )
  [ExpectedLine [LineChunk "[4,4,4]"]]
 DocTest.printPrefix "Numeric.FFTW.Extra.NumberTheory:164: "
{-# LINE 164 "private/Numeric/FFTW/Extra/NumberTheory.hs" #-}
 DocTest.property(
{-# LINE 164 "private/Numeric/FFTW/Extra/NumberTheory.hs" #-}
      \(QC.Positive n) -> snd (divideMaxPower 2 (sqrtToPowerOfTwo (n::Integer))) == 1
  )
 DocTest.printPrefix "Numeric.FFTW.Extra.NumberTheory:165: "
{-# LINE 165 "private/Numeric/FFTW/Extra/NumberTheory.hs" #-}
 DocTest.property(
{-# LINE 165 "private/Numeric/FFTW/Extra/NumberTheory.hs" #-}
      \(QC.NonNegative n) -> let m = sqrtToPowerOfTwo (n::Integer) in m*m <= 2*n && n <= 4*m*m
  )
 DocTest.printPrefix "Numeric.FFTW.Extra.NumberTheory:182: "
{-# LINE 182 "private/Numeric/FFTW/Extra/NumberTheory.hs" #-}
 DocTest.property(
{-# LINE 182 "private/Numeric/FFTW/Extra/NumberTheory.hs" #-}
      \(QC.NonNegative n) -> n <= larger5Smooth (n::Int)
  )
 DocTest.printPrefix "Numeric.FFTW.Extra.NumberTheory:183: "
{-# LINE 183 "private/Numeric/FFTW/Extra/NumberTheory.hs" #-}
 DocTest.property(
{-# LINE 183 "private/Numeric/FFTW/Extra/NumberTheory.hs" #-}
      \(QC.Positive n) -> 4 * larger5Smooth (n::Int) < 5*n
  )
 DocTest.printPrefix "Numeric.FFTW.Extra.NumberTheory:184: "
{-# LINE 184 "private/Numeric/FFTW/Extra/NumberTheory.hs" #-}
 DocTest.property(
{-# LINE 184 "private/Numeric/FFTW/Extra/NumberTheory.hs" #-}
        
   \(QC.Positive n) ->
      (1==) $
      foldl (\k d -> snd $ divideMaxPower d k) (larger5Smooth (n::Int)) [2,3,5]
  )
 DocTest.printPrefix "Numeric.FFTW.Extra.NumberTheory:232: "
{-# LINE 232 "private/Numeric/FFTW/Extra/NumberTheory.hs" #-}
 DocTest.example(
{-# LINE 232 "private/Numeric/FFTW/Extra/NumberTheory.hs" #-}
    map ceilingEfficient [1..(40::Int)]
  )
  [ExpectedLine [LineChunk "[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,18,20,20,24,24,24,24,25,30,30,30,30,30,32,32,36,36,36,36,40,40,40,40]"]]
 DocTest.printPrefix "Numeric.FFTW.Extra.NumberTheory:234: "
{-# LINE 234 "private/Numeric/FFTW/Extra/NumberTheory.hs" #-}
 DocTest.property(
{-# LINE 234 "private/Numeric/FFTW/Extra/NumberTheory.hs" #-}
      \(QC.NonNegative n) -> n <= ceilingEfficient (n::Int)
  )
 DocTest.printPrefix "Numeric.FFTW.Extra.NumberTheory:235: "
{-# LINE 235 "private/Numeric/FFTW/Extra/NumberTheory.hs" #-}
 DocTest.property(
{-# LINE 235 "private/Numeric/FFTW/Extra/NumberTheory.hs" #-}
      \(QC.NonNegative n) -> 5 * ceilingEfficient n <= (6*n :: Int)
  )