{-# OPTIONS_GHC -fno-warn-orphans #-}
{-
	Copyright (C) 2018 Dr. Alistair Ward

	This file is part of BishBosh.

	BishBosh is free software: you can redistribute it and/or modify
	it under the terms of the GNU General Public License as published by
	the Free Software Foundation, either version 3 of the License, or
	(at your option) any later version.

	BishBosh is distributed in the hope that it will be useful,
	but WITHOUT ANY WARRANTY; without even the implied warranty of
	MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
	GNU General Public License for more details.

	You should have received a copy of the GNU General Public License
	along with BishBosh.  If not, see <http://www.gnu.org/licenses/>.
-}
{- |
 [@AUTHOR@]	Dr. Alistair Ward

 [@DESCRIPTION@]	Defines a /pickler/ for 'Data.Ratio.Ratio'.

 [@CAVEAT@]

	'Rational' numbers are converted imprecisely to floating-point for representation as XML.
	To remedy the loss of precision on reading from XML, they're rounded to the /epsilon/ for IEEE double-precision <https://en.wikipedia.org/wiki/Machine_epsilon>.
-}

module BishBosh.Data.Ratio(
--	round'
) where

import qualified	Data.Ratio
import qualified	Text.XML.HXT.Arrow.Pickle	as HXT

-- | Truncate the rounding-error introduced by conversion to a 'Rational' number.
round' :: RealFrac r => r -> Rational
round' :: r -> Rational
round'	= (r -> r -> Rational
forall a. RealFrac a => a -> a -> Rational
`Data.Ratio.approxRational` r
doublePrecisionEpsilon) where
	doublePrecisionEpsilon :: r
doublePrecisionEpsilon	= r -> r
forall a. Fractional a => a -> a
recip r
2 r -> Int -> r
forall a b. (Num a, Integral b) => a -> b -> a
^ Double -> Int
forall a. RealFloat a => a -> Int
floatDigits (Double
forall a. HasCallStack => a
undefined :: Double)

instance Integral i => HXT.XmlPickler (Data.Ratio.Ratio i) where
	xpickle :: PU (Ratio i)
xpickle	= (Double -> Ratio i, Ratio i -> Double) -> PU Double -> PU (Ratio i)
forall a b. (a -> b, b -> a) -> PU a -> PU b
HXT.xpWrap (
		Rational -> Ratio i
forall a. Fractional a => Rational -> a
fromRational (Rational -> Ratio i) -> (Double -> Rational) -> Double -> Ratio i
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Double -> Rational
forall r. RealFrac r => r -> Rational
round',		-- Construct from a Double.
		\Ratio i
x -> Ratio i -> Double
forall a b. (Real a, Fractional b) => a -> b
realToFrac Ratio i
x :: Double	-- Deconstruct to a Double.
	 ) PU Double
forall a. (Read a, Show a) => PU a
HXT.xpPrim