{- |
Copyright   :  (c) Henning Thielemann 2007

Maintainer  :  haskell@henning-thielemann.de
Stability   :  stable
Portability :  Haskell 98

Event lists starting with a time difference and ending with a body.

The time is stored in differences between the events.
Thus there is no increase of time information for long,
or even infinite, streams of events.
Further on, the time difference is stored
in the latter of two neighbouring events.
This is necessary for real-time computing
where it is not known whether and when the next event happens.

module Data.EventList.Relative.TimeBody
    empty, singleton, null,
    viewL, viewR, switchL, switchR, cons, snoc,
    fromPairList, toPairList,
    getTimes, getBodies, duration,
    mapBody, mapTime,
    concatMapMonoid, mapM, mapM_, mapBodyM, mapTimeM,
    foldr, foldrPair,
    merge, mergeBy, insert, insertBy,
    decreaseStart, delay, filter, partition, slice, span,
    mapMaybe, catMaybes,
    normalize, isNormalized,
    collectCoincident, flatten, mapCoincident,
    append, concat, cycle,
    discretize, resample,
    toAbsoluteEventList, fromAbsoluteEventList,
   ) where

import Data.EventList.Relative.TimeBodyPrivate
import qualified Data.EventList.Relative.BodyBodyPrivate as BodyBodyPriv

import qualified Data.EventList.Absolute.TimeBodyPrivate as AbsoluteEventPriv
import qualified Data.EventList.Absolute.TimeBody as AbsoluteEventList

import qualified Data.AlternatingList.List.Disparate as Disp
import qualified Data.AlternatingList.List.Uniform as Uniform
import qualified Data.AlternatingList.List.Mixed as Mixed

import qualified Data.List as List
import qualified Data.EventList.Utility as Utility

import Data.Monoid (Monoid, )

import qualified Numeric.NonNegative.Class as NonNeg
import Data.Tuple.HT (mapFst, mapSnd, mapPair, )
import Data.Maybe.HT (toMaybe, )
import Data.List.HT (isAscending, )
import Data.EventList.Utility (floorDiff, beforeBy, )
import Control.Monad.Trans.State (evalState, modify, get, put, )

import Prelude hiding (mapM, mapM_, null, foldr, filter, concat, cycle, span, )

empty :: T time body
empty = Cons Disp.empty

null :: T time body -> Bool
null = Disp.null . decons

singleton :: time -> body -> T time body
singleton time body = Cons $ Disp.singleton time body

cons :: time -> body -> T time body -> T time body
cons time body = lift (Disp.cons time body)

snoc :: T time body -> time -> body -> T time body
snoc xs time body = Cons $ (Disp.snoc $~* xs) time body

viewL :: T time body -> Maybe ((time, body), T time body)
viewL = fmap (mapSnd Cons) . Disp.viewL . decons

viewR :: T time body -> Maybe (T time body, (time, body))
viewR = fmap (mapFst Cons) . Disp.viewR . decons

{-# INLINE switchL #-}
switchL :: c -> ((time, body) -> T time body -> c) -> T time body -> c
switchL f g = Disp.switchL f (\ t b  -> g (t,b) . Cons) . decons

{-# INLINE switchR #-}
switchR :: c -> (T time body -> (time, body) -> c) -> T time body -> c
switchR f g = Disp.switchR f (\xs t b -> g (Cons xs) (t,b)) . decons

fromPairList :: [(a,b)] -> T a b
fromPairList = Cons . Disp.fromPairList

toPairList :: T a b -> [(a,b)]
toPairList = Disp.toPairList . decons

getBodies :: T time body -> [body]
getBodies = Disp.getSeconds . decons

getTimes :: T time body -> [time]
getTimes = Disp.getFirsts . decons

duration :: Num time => T time body -> time
duration = sum . getTimes

mapBody :: (body0 -> body1) -> T time body0 -> T time body1
mapBody f = lift (Disp.mapSecond f)

mapTime :: (time0 -> time1) -> T time0 body -> T time1 body
mapTime f = lift (Disp.mapFirst f)

concatMapMonoid :: Monoid m =>
   (time -> m) -> (body -> m) ->
   T time body -> m
concatMapMonoid f g =
   Disp.concatMapMonoid f g . decons

mapM :: Monad m =>
   (time0 -> m time1) -> (body0 -> m body1) ->
   T time0 body0 -> m (T time1 body1)
mapM f g = liftM (Disp.mapM f g)

mapM_ :: Monad m =>
   (time -> m ()) -> (body -> m ()) ->
   T time body -> m ()
mapM_ f g = Disp.mapM_ f g . decons

mapBodyM :: Monad m =>
   (body0 -> m body1) -> T time body0 -> m (T time body1)
mapBodyM f = liftM (Disp.mapSecondM f)

mapTimeM :: Monad m =>
   (time0 -> m time1) -> T time0 body -> m (T time1 body)
mapTimeM f = liftM (Disp.mapFirstM f)

foldr :: (time -> a -> b) -> (body -> b -> a) -> b -> T time body -> b
foldr f g x = Disp.foldr f g x . decons

foldrPair :: (time -> body -> a -> a) -> a -> T time body -> a
foldrPair f x = Disp.foldrPair f x . decons

{- |
Keep only events that match a predicate while preserving absolute times.
filter :: (Num time) =>
   (body -> Bool) -> T time body -> T time body
filter p = mapMaybe (\b -> toMaybe (p b) b)
-- filter p = fst . partition p

mapMaybe :: (Num time) =>
   (body0 -> Maybe body1) ->
   T time body0 -> T time body1
mapMaybe f = catMaybes . mapBody f

{- |
Adds times in a left-associative fashion.
Use this if the time is a strict data type.
catMaybes :: (Num time) =>
   T time (Maybe body) -> T time body
catMaybes =
   Cons .
   fst . Mixed.viewSecondR .
   Uniform.mapSecond sum .
   Uniform.catMaybesFirst .
   flip Mixed.snocSecond (error "catMaybes: no trailing time") .

The function 'partition' is somehow the inverse to 'merge'.
It is similar to 'List.partition'.
We could use the List function if the event times would be absolute,
because then the events need not to be altered on splits.
But absolute time points can't be used for infinite music
thus we take the burden of adapting the time differences
when an event is removed from the performance list and
put to the list of events of a particular instrument.
@t0@ is the time gone since the last event in the first partition,
@t1@ is the time gone since the last event in the second partition.

Note, that using 'Data.EventList.Utility.mapPair' we circumvent the following problem:
Since the recursive call to 'partition'
may end up with Bottom,
pattern matching with, say \expression{(es0,es1)},
will halt the bounding of the variables
until the most inner call to 'partition' is finished.
This never happens.
If the pair constructor is made strict,
that is we write \expression{~(es0,es1)},
then everything works.
Also avoiding pattern matching and
using 'fst' and 'snd' would help.


Could be implemented more easily in terms of Uniform.partition
partition :: (Num time) =>
   (body -> Bool) -> T time body -> (T time body, T time body)
partition p = partitionRec p 0 0

partitionRec :: (Num time) =>
   (body -> Bool) -> time -> time ->
       T time body -> (T time body, T time body)
partitionRec p =
   let recourse t0 t1 =
             (empty, empty)
             (\ (t, b) es ->
                let t0' = t0 + t
                    t1' = t1 + t
                in  if p b
                      then mapFst (cons t0' b) (recourse 0 t1' es)
                      else mapSnd (cons t1' b) (recourse t0' 0 es))
   in  recourse

{- |
Using a classification function
we splice the event list into lists, each containing the same class.
Absolute time stamps are preserved.
slice :: (Eq a, Num time) =>
   (body -> a) -> T time body -> [(a, T time body)]
slice = Utility.slice (fmap (snd . fst) . viewL) partition

span :: (body -> Bool) -> T time body -> (T time body, T time body)
span p = mapPair (Cons, Cons) . Disp.spanSecond p . decons

{- |
Group events that have equal start times
(that is zero time differences).
collectCoincident :: (NonNeg.C time) => T time body -> T time [body]
collectCoincident =
   mapTimeTail $ BodyBodyPriv.lift $ Uniform.filterFirst (0<)

{- |
Reverse to collectCoincident:
Turn each @body@ into a separate event.

>   xs  ==  flatten (collectCoincident xs)
flatten :: (NonNeg.C time) => T time [body] -> T time body
flatten =
   Cons .
      (\time ->
         unlift (delay time) .
         fst . Mixed.viewSecondR .
            (Mixed.appendUniformUniform . Uniform.fromSecondList 0)
            Mixed.consSecond Disp.empty .
         Uniform.mapSecond sum .
         Uniform.filterSecond (not . List.null)) .

{- |
Apply a function to the lists of coincident events.
mapCoincident :: (NonNeg.C time) =>
   ([a] -> [b]) -> T time a -> T time b
mapCoincident f = flatten . mapBody f . collectCoincident

{- |
'List.sort' sorts a list of coinciding events,
that is all events but the first one have time difference 0.
'normalize' sorts all coinciding events in a list
thus yielding a canonical representation of a time ordered list.
normalize :: (NonNeg.C time, Ord body) => T time body -> T time body
normalize = mapCoincident List.sort

isNormalized :: (NonNeg.C time, Ord body) =>
   T time body -> Bool
isNormalized =
   all isAscending . getBodies . collectCoincident

{- |
This function merges the events of two lists into a new event list.
Note that 'merge' compares entire events rather than just start times.
This is to ensure that it is commutative,
one of the properties we test for.
merge :: (NonNeg.C time, Ord body) =>
   T time body -> T time body -> T time body
merge = mergeBy (<)

{- |
'mergeBy' is like 'merge' but does not simply use the methods of the 'Ord' class
but allows a custom comparison function.

Could be implemented using 'splitAt' and 'insert'.
mergeBy :: (NonNeg.C time) =>
   (body -> body -> Bool) ->
   T time body -> T time body -> T time body
mergeBy before xs0 ys0 =
   case (viewL xs0, viewL ys0) of
      (Nothing, _) -> ys0
      (_, Nothing) -> xs0
      (Just (x@(xt,xb),xs), Just (y@(yt,yb),ys)) ->
         if beforeBy before x y
           then uncurry cons x $ mergeBy before xs $ cons (yt-xt) yb ys
           else uncurry cons y $ mergeBy before ys $ cons (xt-yt) xb xs

{- |
'insert' inserts an event into an event list at the given time.
insert :: (NonNeg.C time, Ord body) =>
   time -> body -> T time body -> T time body
insert t0 me0 =
      (singleton t0 me0)
      (\ mev1@(t1, me1) mevs ->
          let mev0 = (t0, me0)
          in  if mev0 < mev1
                then uncurry cons mev0 $ cons   (t1-t0) me1 mevs
                else uncurry cons mev1 $ insert (t0-t1) me0 mevs)

insertBy :: (NonNeg.C time, Ord body) =>
   (body -> body -> Bool) ->
   time -> body -> T time body -> T time body
insertBy before t0 me0 =
      (singleton t0 me0)
      (\ mev1@(t1, me1) mevs ->
          if beforeBy before (t0, me0) mev1
            then cons t0 me0 $ cons   (t1-t0) me1 mevs
            else cons t1 me1 $ insert (t0-t1) me0 mevs)

{- |
Move events towards the front of the event list.
You must make sure, that no event is moved before time zero.
This works only for finite lists.
moveForward :: (NonNeg.C time) =>
   T time (time, body) -> T time body
moveForward =
   fromAbsoluteEventList .
   AbsoluteEventList.moveForward .
   toAbsoluteEventList 0

Like 'moveForward' but restricts the look-ahead time.
For @moveForwardRestricted maxTimeDiff xs@
all time differences (aka the moveForward offsets) in @xs@
must be at most @maxTimeDiff@.
With this restriction the function is lazy enough
for handling infinite event lists.
However the larger @maxTimeDiff@ the more memory and time is consumed.
{- for implementation notes see TimeTime

This implementation requires TimeTime.duration, TimeMixed.appendBodyEnd, TimeMixed.splitAtTime
and thus we would need a lot of movement of functions between modules

moveForwardRestricted :: (NonNeg.C time) =>
   time -> T time (time, body) -> T time body
moveForwardRestricted maxTime xs =
   let (prefix,suffix) = splitAtTime maxTime xs
       prefixDur = duration prefix
       getChunk t =
          do (toEmit,toKeep) <- gets (splitAtTime t)
             put toKeep
             return (pad t toEmit)
       insertEvent (t,b) =
          insertBy (\ _ _ -> False) (maxTime - t) b
   in  evalState
             (\t m -> liftM2 append (getChunk t) m)
             (\b m -> modify (insertEvent b) >> m)
             (gets (pad prefixDur)) suffix)
          (moveForward (seq prefixDur prefix))

append :: T time body -> T time body -> T time body
append xs = lift (Disp.append $~* xs)

concat :: [T time body] -> T time body
concat = Cons . Disp.concat . map decons

cycle :: T time body -> T time body
cycle = lift Disp.cycle

decreaseStart :: (NonNeg.C time) =>
   time -> T time body -> T time body
decreaseStart dif =
   mapTimeHead (subtract dif)

delay :: (NonNeg.C time) =>
   time -> T time body -> T time body
delay dif =
   mapTimeHead (dif+)

{- |
We provide 'discretize' and 'resample' for discretizing the time information.
When converting the precise relative event times
to the integer relative event times
we have to prevent accumulation of rounding errors.
We avoid this problem with a stateful conversion
which remembers each rounding error we make.
This rounding error is used to correct the next rounding.
Given the relative time and duration of an event
the function 'floorDiff' creates a 'Control.Monad.State.State'
which computes the rounded relative time.
It is corrected by previous rounding errors.

The resulting event list may have differing time differences
which were equal before discretization,
but the overall timing is uniformly close to the original.

We use 'floorDiff' rather than 'Utility.roundDiff'
in order to compute exclusively with non-negative numbers.

discretize :: (NonNeg.C time, RealFrac time, NonNeg.C i, Integral i) =>
   T time body -> T i body
discretize =
   flip evalState 0.5 . mapTimeM floorDiff

resample :: (NonNeg.C time, RealFrac time, NonNeg.C i, Integral i) =>
   time -> T time body -> T i body
resample rate =
   discretize . mapTime (rate*)

{- |
We tried hard to compute everything with respect to relative times.
However sometimes we need absolute time values.
toAbsoluteEventList :: (Num time) =>
   time -> T time body -> AbsoluteEventList.T time body
toAbsoluteEventList start =
   AbsoluteEventPriv.Cons . decons .
   flip evalState start .
   mapTimeM (\dur -> modify (dur+) >> get)

fromAbsoluteEventList :: (Num time) =>
   AbsoluteEventList.T time body -> T time body
fromAbsoluteEventList =
   flip evalState 0 .
      (\time -> do lastTime <- get; put time; return (time-lastTime)) .
   Cons . AbsoluteEventPriv.decons