-- Hoogle documentation, generated by Haddock
-- See Hoogle, http://www.haskell.org/hoogle/


-- | Allows to approximate the fractional numbers in the range [0.005, 1] with sum of 2 or 3 unit fractions of special types.
--   
--   Inspired by the ancient Egyptian mathematics. See the ideas
--   description and formulation in the <a>related draft paper.</a>
@package fractionizer
@version 0.8.0.0

module UnitFractionsDecomposition2

-- | Rounding to thousandth.
threeDigitsK :: Double -> Double

-- | Characterizes the impact of the absolute error sign on the
--   approximation.
type ErrorImpact = Int

-- | Allows to take into account the sign of the absolute error of the
--   aproximation. If the <a>ErrorImpact</a> parameter is equal to 0 , then
--   absolute error can be of any sign, if it is equal to -1 - the absolute
--   error can be only negative, otherwise - only positive
--   
--   <ul>
--   <li></li>
--   </ul>
setOfSolutionsG :: ErrorImpact -> Double -> [(Double, Double)]
setOfSolutions :: Double -> [(Double, Double)]

-- | Partially defined function, if there is no solutions then returns a
--   tuple of <a>undefined</a>. Beter to use <a>suitable21</a>
suitable2 :: Double -> (Double, Double)

-- | Allows to take into account the sign of the absolute error of the
--   aproximation. If the <a>ErrorImpact</a> parameter is equal to 0 , then
--   absolute error can be of any sign, if it is equal to -1 - the absolute
--   error can be only negative, otherwise - only positive
suitable21G :: ErrorImpact -> Double -> Maybe ([Double], Double)
suitable21 :: Double -> Maybe ([Double], Double)
isRangeN :: Double -> Bool

-- | The preferable range of the argument for <a>suitable2</a> and
--   <a>suitable21</a> functions. For arguments in this range the functions
--   always have informative results.
isRangeNPref :: Double -> Bool

-- | Allows to take into account the sign of the absolute error of the
--   aproximation. If the <a>ErrorImpact</a> parameter is equal to 0 , then
--   absolute error can be of any sign, if it is equal to -1 - the absolute
--   error can be only negative, otherwise - only positive
check1FracDecompG :: ErrorImpact -> Double -> Maybe ([Double], Double)

-- | Allows to take into account the sign of the absolute error of the
--   aproximation. If the <a>ErrorImpact</a> parameter is equal to 0 , then
--   absolute error can be of any sign, if it is equal to -1 - the absolute
--   error can be only negative, otherwise - only positive
check3FracDecompPartialG :: ErrorImpact -> Bool -> Double -> Maybe ([Double], Double)

-- | Allows to take into account the sign of the absolute error of the
--   aproximation. If the <a>ErrorImpact</a> parameter is equal to 0 , then
--   absolute error can be of any sign, if it is equal to -1 - the absolute
--   error can be only negative, otherwise - only positive
check3FracDecompPartialPG :: ErrorImpact -> Bool -> [Int] -> Double -> Maybe ([Double], Double)

-- | Allows to take into account the sign of the absolute error of the
--   aproximation. If the <a>ErrorImpact</a> parameter is equal to 0 , then
--   absolute error can be of any sign, if it is equal to -1 - the absolute
--   error can be only negative, otherwise - only positive
lessErrSimpleDecompPG :: ErrorImpact -> [Int] -> Double -> (Int, Maybe ([Double], Double), Double)

-- | Allows to take into account the sign of the absolute error of the
--   aproximation. If the <a>ErrorImpact</a> parameter is equal to 0 , then
--   absolute error can be of any sign, if it is equal to -1 - the absolute
--   error can be only negative, otherwise - only positive
lessErrDenomsPG :: ErrorImpact -> [Int] -> Double -> [Integer]

-- | Tries to approximate the fraction by just one unit fraction. Can be
--   used for the numbers between 0.005 and 0.501.
check1FracDecomp :: Double -> Maybe ([Double], Double)

-- | Function to find the less by absolute value error approximation. One
--   of the denominators is taken from the range [2..10]. The two others
--   are taken from the appropriate <a>suitable21</a> applicattion.
check3FracDecompPartial :: Bool -> Double -> Maybe ([Double], Double)

-- | Extended version of the <a>check3FracDecompPartial</a> with the first
--   denominator being taken not - only from the [2..10], but also from the
--   custom user provided list. -
check3FracDecompPartialP :: Bool -> [Int] -> Double -> Maybe ([Double], Double)
lessErrSimpleDecompP :: [Int] -> Double -> (Int, Maybe ([Double], Double), Double)

-- | Returns a list of denominators for fraction decomposition using also
--   those ones from the the list provided as the first argument. Searches
--   for the least error from the checked ones.
lessErrDenomsP :: [Int] -> Double -> [Integer]