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


-- | Easy-to-use reasonable way of emulating approximate in Haskell.
--   
--   Please see the README on GitHub at
--   <a>https://github.com/n-kishaloy/approx#readme</a>
@package approx
@version 0.1.0.1


-- | The library is created to allow for a easy-to-use reasonable way of
--   emulating approx in Haskell. The codes are all in <i>pure</i> Haskell.
--   The idea is to have a natural mathematical feel in writing code, with
--   operators which just works when working with Double and Float and
--   their composite types like lists, vectors etc.
--   
--   The <b>Approx</b> module defines 2 operators <b><tt>=~</tt></b> and
--   <b><tt>/~</tt></b>, which are for checking <i>nearly equal to</i> and
--   <i>not nearly equal to</i> respectively.
--   
--   Both the operators <b>=~</b> and <b>/~</b> are put under the class
--   <b>Approx</b>.
--   
--   At least one of the operators have to be defined and the other gets
--   automatically defined.
--   
--   The library already defines the functions for some of the basic /
--   common types.
--   
--   For types where <b>Eq</b> is defined like <b>Char, Bool, Int, Day,
--   Text</b> the approx is simply replaced with <b>==</b>.
--   
--   For <b>Float</b> and <b>Double</b>, the following formula is used,
--   
--   <pre>
--   if max ( |x|, |y| ) &lt; epsilon_Zero
--   then True
--   else 
--     if |x - y| / max ( |x|, |y| ) &lt; epsilon_Eq
--     then True
--     else False
--   </pre>
--   
--   The motivation for defining Approx for classes for which Eq is also
--   defined is to allow for composite types where both Eq and Approx would
--   be present. For example, the following code evaluates to
--   <b><tt>True</tt></b>, even though the tuple is of type
--   <tt>(Int,Double,Text,[Int],[[Char]],[Double])</tt>.
--   
--   <pre>
--   ((2,5.35,"happ",[1,2],["ret","we"],[6.78,3.5]) 
--       :: (Int,Double,Text,[Int],[[Char]],[Double])) 
--       
--       =~ (2,5.35,"happ",[1,2],["ret","we"],[6.78,3.5])
--   </pre>
--   
--   For UTCTime, the approx operator checks for equality to the nearest
--   minute. The following expression evaluates to <b><tt>True</tt></b>.
--   
--   <pre>
--   (parseTimeM True defaultTimeLocale "%Y-%m-%d %H:%M:%S" "2020-01-15 15:02:15" 
--       :: Maybe UTCTime) 
--   
--       =~ parseTimeM True defaultTimeLocale "%Y-%m-%d %H:%M:%S" "2020-01-15 15:01:50"
--   </pre>
--   
--   The library also provides approx for Complex and common structures
--   like <b>List, Boxed and Unboxed Vector, Hashmap, Tuples</b> and
--   <b>Maybe</b>. For all lists, tuples, hashmaps and vectors, the
--   approximation is checked right down to the elements and the order for
--   lists and vectors are important.
--   
--   For lists, only finite lists are supported. Any use of infinite lists
--   would cause a runtime error.
--   
--   There are addtional functions <b>inRange</b>, <b>safeInRange</b> and
--   <b>inTol</b>, which checks for values within Ranges either
--   <i>explictily</i> defined as in <b>inRange</b> and <b>safeInRange</b>
--   or through tolerances as in <b>inTol</b>.
--   
--   You may see the github repository at
--   <a>https://github.com/n-kishaloy/approx</a>
module Data.Approx

-- | The class <tt>Approx</tt> defines 2 operators <b><tt>=~</tt></b> and
--   <b><tt>/~</tt></b>, which are for checking <i>nearly equal to</i> and
--   <i>not nearly equal to</i> respectively.
class Approx a
(=~) :: Approx a => a -> a -> Bool
(/~) :: Approx a => a -> a -> Bool
infix 4 =~
infix 4 /~

-- | <pre>
--   inRange (u,v) x = check if x is inside the range (u,v)
--   </pre>
--   
--   Note: The function <b>assumes <tt>u &lt; v</tt></b>. This is done to
--   ensure speed of operations. Use safeInRange, otherwise.
inRange :: Ord a => (a, a) -> a -> Bool
infix 4 `inRange`

-- | <pre>
--   safeInRange (u,v) x = check if x is inside the range (u,v)
--   </pre>
--   
--   Note: The function works even if u&gt;v. However, it has addtional
--   checks and is more expensive. Use only if you are not sure that u &lt;
--   v for your use-case.
safeInRange :: Ord a => (a, a) -> a -> Bool
infix 4 `safeInRange`

-- | <pre>
--   inTol t p x = inRange (p - t, p + t) x
--   </pre>
--   
--   The Function checks if <b><tt>x</tt></b> is close to <b><tt>p</tt></b>
--   within a tolerance band <b><tt>t</tt></b>. Please ensure
--   <b><tt>t</tt></b> is <i>positive</i> or there would be
--   <i>incorrect</i> results.
inTol :: (Num a, Ord a) => a -> a -> a -> Bool
infix 4 `inTol`
instance Data.Approx.Approx Data.Time.Calendar.Days.Day
instance Data.Approx.Approx GHC.Types.Char
instance Data.Approx.Approx GHC.Types.Bool
instance Data.Approx.Approx Data.Text.Internal.Text
instance Data.Approx.Approx GHC.Types.Int
instance Data.Approx.Approx GHC.Integer.Type.Integer
instance Data.Approx.Approx Data.Time.Clock.Internal.UTCTime.UTCTime
instance Data.Approx.Approx a => Data.Approx.Approx (Data.Complex.Complex a)
instance Data.Approx.Approx GHC.Types.Float
instance Data.Approx.Approx GHC.Types.Double
instance Data.Approx.Approx a => Data.Approx.Approx (GHC.Maybe.Maybe a)
instance Data.Approx.Approx a => Data.Approx.Approx [a]
instance (Data.Approx.Approx a, Data.Approx.Approx b) => Data.Approx.Approx (a, b)
instance (Data.Approx.Approx a, Data.Approx.Approx b, Data.Approx.Approx c) => Data.Approx.Approx (a, b, c)
instance (Data.Approx.Approx a, Data.Approx.Approx b, Data.Approx.Approx c, Data.Approx.Approx d) => Data.Approx.Approx (a, b, c, d)
instance (Data.Approx.Approx a, Data.Approx.Approx b, Data.Approx.Approx c, Data.Approx.Approx d, Data.Approx.Approx e) => Data.Approx.Approx (a, b, c, d, e)
instance (Data.Approx.Approx a, Data.Approx.Approx b, Data.Approx.Approx c, Data.Approx.Approx d, Data.Approx.Approx e, Data.Approx.Approx f) => Data.Approx.Approx (a, b, c, d, e, f)
instance (Data.Approx.Approx a, Data.Approx.Approx b, Data.Approx.Approx c, Data.Approx.Approx d, Data.Approx.Approx e, Data.Approx.Approx f, Data.Approx.Approx g) => Data.Approx.Approx (a, b, c, d, e, f, g)
instance (Data.Approx.Approx a, Data.Approx.Approx b, Data.Approx.Approx c, Data.Approx.Approx d, Data.Approx.Approx e, Data.Approx.Approx f, Data.Approx.Approx g, Data.Approx.Approx h) => Data.Approx.Approx (a, b, c, d, e, f, g, h)
instance (Data.Approx.Approx a, Data.Approx.Approx b, Data.Approx.Approx c, Data.Approx.Approx d, Data.Approx.Approx e, Data.Approx.Approx f, Data.Approx.Approx g, Data.Approx.Approx h, Data.Approx.Approx i) => Data.Approx.Approx (a, b, c, d, e, f, g, h, i)
instance (Data.Approx.Approx a, Data.Approx.Approx b, Data.Approx.Approx c, Data.Approx.Approx d, Data.Approx.Approx e, Data.Approx.Approx f, Data.Approx.Approx g, Data.Approx.Approx h, Data.Approx.Approx i, Data.Approx.Approx j) => Data.Approx.Approx (a, b, c, d, e, f, g, h, i, j)
instance (Data.Approx.Approx a, Data.Approx.Approx b, Data.Approx.Approx c, Data.Approx.Approx d, Data.Approx.Approx e, Data.Approx.Approx f, Data.Approx.Approx g, Data.Approx.Approx h, Data.Approx.Approx i, Data.Approx.Approx j, Data.Approx.Approx k) => Data.Approx.Approx (a, b, c, d, e, f, g, h, i, j, k)
instance (Data.Vector.Unboxed.Base.Unbox a, Data.Approx.Approx a) => Data.Approx.Approx (Data.Vector.Unboxed.Base.Vector a)
instance Data.Approx.Approx a => Data.Approx.Approx (Data.Vector.Vector a)
instance (GHC.Classes.Eq a, Data.Hashable.Class.Hashable a, Data.Approx.Approx b) => Data.Approx.Approx (Data.HashMap.Internal.HashMap a b)