! Copyright (C) 2019 Michael Raitza
!
! * Crit-bit trees
! ** Rationale
! Critbit trees are described in [[https://cr.yp.to/critbit.html][djb's crit-bit tree]]. They are an evolution of
! PATRICIA trees showing that fast insertion, deletion, exact searching and suffix
! searching is possible with this data structure.

! The strength of this datastructure, according to its author, lies in its simple
! design and its optimisation to be machine parsable using machine word-sized
! operations where possible. Like PATRICIA trees, crit-bit trees are
! prefix-compressed, with internal nodes storing next decision point (the critical
! bit) in a length field (encoded as an integer and a mask) and two successor
! pointers. Arbitrary data objects make up its leaves.

USING: accessors fry kernel math sequences serialize ;
IN: critbit

TUPLE: critbit root ;

<PRIVATE

: new-critbit ( class -- critbit )
    new
    f >>root ; inline

PRIVATE>

: <critbit> ( -- critbit )
    critbit new-critbit ;

<PRIVATE

TUPLE: node left right { byte# integer } { bits integer } ;

: empty? ( tree -- ? )
    root>> f = ; inline

: new-node ( bits byte# class -- node )
    new
    swap >>byte#
    swap >>bits ; inline

: <node> ( bits byte# -- node )
    node new-node ;

: get-child ( node direction -- child )
    0 = [ right>> ] [ left>> ] if ;

: set-child ( node child direction -- node )
    0 = [ >>right ] [ >>left ] if ;

: set-child-opposite ( node child direction -- node )
    1 swap - set-child ;

: direction ( byte bits -- direction )
    bitor 1 + -8 shift ;

! ** Walking the tree
! Extract the split byte number and bit from node and return the proper child the
! proper child corresponding to the bytestring's prefix.

: successor ( bytes node -- bytes successor via-direction )
    2dup [ byte#>> ] [ bits>> ] bi
    [ swap ?nth [ 0 ] unless* ] dip
    direction [ get-child ] keep ;

! Walk the tree until we find a leaf.

: walk-critbit ( obj tree -- objbytes leaf )
    [ object>bytes ] [ root>> ] bi*
    [ dup node? ] [ successor drop ] while ;

PRIVATE>

: member? ( obj tree -- ? )
    dup critbit?
    [ walk-critbit = ]
    [ 2drop f ] if ;

<PRIVATE

! Produce a byte with all bits set except the msb from bits*.
! See MAGIC Algorithms for rationale.

: msb0 ( bits* -- bits )
    dup -1 shift bitor
    dup -2 shift bitor
    dup -4 shift bitor
    dup -1 shift bitnot bitand 255 bitxor ;

: byte-diff ( newbyte oldbyte -- direction bits )
    swap over
    bitxor msb0
    [ direction ] keep ;

: node-params ( newbytes oldbytes -- direction bits byte# )
    2dup mismatch
    [ [ '[ _ swap nth ] bi@ byte-diff ] keep ]
    ! Equal prefix over full (shorter) byte sequence.
    [ [ 1 255 ] 2dip shorter length 1 - ] if* ;

: derive-node ( obj newbytes leaf -- node direction )
    object>bytes
    node-params <node> -rot [ set-child-opposite ] keep ;

: insert-node ( node split-node direction -- successor ? )
    [
        [ [ byte#>> ] bi@ - [ 0 < ] [ 0 = ] bi ] 2keep
        [ bits>> ] > and
        or
    ] dip drop
    ;

: insertion-walk ( tree split-node new-direction -- tree )
    ! FIXME Unfinished. We need obj to calculate succession :(
    rot [
        root>> dup node?
        [ ] [ 2over insert-node ] while 3drop
    ] keep ;

:: walk-on? ( split-node node -- ? )
    node node? not
    node byte#>> split-node byte#>> >
    or
    node byte#>> split-node byte#>> =
    node bits>> split-node bits>> >
    and
    or
    not ;

:: insertion-walk ( obj split-node new-direction -- ? )
    obj obj>bytes :> objbytes
    tree root>> :> node
    [ split-node node walk-on? ] [
        node :> predecessor
        objbytes node successor :> node-direction :> node drop
    ] while
    node split-node new-direction set-child
    ;

! :: insertion-successor ( objbytes bits byte# node -- split-node )
!     node node? not
!     [ node ]
!     [
!         node byte#>>
!         [ byte# > ] keep
!         byte# = node bits>> bits > and
!         or
!         ! objbytes no longer matches prefix?
!         [ node ]
!         [
!             ! FIXME: complete node insertion
!         ] if
!     ] if ;

! :: (insert-node) ( obj tree objbytes treebytes direction bits byte# -- tree )
!     bits byte# <node>
!     direction 0 = [ obj >>right ] [ obj >>left ] if :> node
!     tree root>> [ dup node? ] [ insertion-successor]
!     ;

! : insert-node ( obj tree objbytes treebytes -- tree )
!     2dup node-params (insert-node)
!     ;

PRIVATE>

: (put) ( tree obj -- tree )
    swap dup empty?
    [ swap >>root ]
    [ [ 2dup walk-critbit
        derive-node
        ! FIXME Unfinished, this node must now be inserted into the tree
      ] 2keep
      2drop ! <- remove;
      ! insert-node
    ] if ;

: put ( obj tree -- tree )
    dup critbit? [ (put) ] [ 2drop "Not a critbit tree" throw ] if ;