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+%%
+%% %CopyrightBegin%
+%%
+%% Copyright Ericsson AB 1996-2009. All Rights Reserved.
+%%
+%% The contents of this file are subject to the Erlang Public License,
+%% Version 1.1, (the "License"); you may not use this file except in
+%% compliance with the License. You should have received a copy of the
+%% Erlang Public License along with this software. If not, it can be
+%% retrieved online at http://www.erlang.org/.
+%%
+%% Software distributed under the License is distributed on an "AS IS"
+%% basis, WITHOUT WARRANTY OF ANY KIND, either express or implied. See
+%% the License for the specific language governing rights and limitations
+%% under the License.
+%%
+%% %CopyrightEnd%
+%%
+-module(lists).
+
+-export([append/2, append/1, subtract/2, reverse/1,
+ nth/2, nthtail/2, prefix/2, suffix/2, last/1,
+ seq/2, seq/3, sum/1, duplicate/2, min/1, max/1, sublist/2, sublist/3,
+ delete/2,
+ unzip/1, unzip3/1, zip/2, zip3/3, zipwith/3, zipwith3/4,
+ sort/1, merge/1, merge/2, rmerge/2, merge3/3, rmerge3/3,
+ usort/1, umerge/1, umerge3/3, umerge/2, rumerge3/3, rumerge/2,
+ concat/1, flatten/1, flatten/2, flat_length/1, flatlength/1,
+ keydelete/3, keyreplace/4, keytake/3, keystore/4,
+ keysort/2, keymerge/3, rkeymerge/3, rukeymerge/3,
+ ukeysort/2, ukeymerge/3, keymap/3]).
+
+%% Bifs: member/2, reverse/2
+%% Bifs: keymember/3, keysearch/3, keyfind/3
+
+-export([merge/3, rmerge/3, sort/2, umerge/3, rumerge/3, usort/2]).
+
+-export([all/2,any/2,map/2,flatmap/2,foldl/3,foldr/3,filter/2,
+ partition/2,zf/2,
+ mapfoldl/3,mapfoldr/3,foreach/2,takewhile/2,dropwhile/2,splitwith/2,
+ split/2]).
+
+-deprecated([flat_length/1]).
+
+%% member(X, L) -> (true | false)
+%% test if X is a member of the list L
+%% Now a BIF!
+
+%member(X, [X|_]) -> true;
+%member(X, [_|Y]) ->
+% member(X, Y);
+%member(X, []) -> false.
+
+%% append(X, Y) appends lists X and Y
+
+-spec append([T], [T]) -> [T].
+
+append(L1, L2) -> L1 ++ L2.
+
+%% append(L) appends the list of lists L
+
+-spec append([[T]]) -> [T].
+
+append([E]) -> E;
+append([H|T]) -> H ++ append(T);
+append([]) -> [].
+
+%% subtract(List1, List2) subtract elements in List2 form List1.
+
+-spec subtract([T], [T]) -> [T].
+
+subtract(L1, L2) -> L1 -- L2.
+
+%% reverse(L) reverse all elements in the list L. Is now a BIF!
+
+-spec reverse([T]) -> [T].
+
+reverse([] = L) ->
+ L;
+reverse([_] = L) ->
+ L;
+reverse([A, B]) ->
+ [B, A];
+reverse([A, B | L]) ->
+ lists:reverse(L, [B, A]).
+
+%reverse([H|T], Y) ->
+% reverse(T, [H|Y]);
+%reverse([], X) -> X.
+
+
+%% nth(N, L) returns the N`th element of the list L
+%% nthtail(N, L) returns the N`th tail of the list L
+
+-spec nth(pos_integer(), [T,...]) -> T.
+
+nth(1, [H|_]) -> H;
+nth(N, [_|T]) when N > 1 ->
+ nth(N - 1, T).
+
+-spec nthtail(non_neg_integer(), [T,...]) -> [T].
+
+nthtail(1, [_|T]) -> T;
+nthtail(N, [_|T]) when N > 1 ->
+ nthtail(N - 1, T);
+nthtail(0, L) when is_list(L) -> L.
+
+%% prefix(Prefix, List) -> (true | false)
+
+-spec prefix([T], [T]) -> boolean().
+
+prefix([X|PreTail], [X|Tail]) ->
+ prefix(PreTail, Tail);
+prefix([], List) when is_list(List) -> true;
+prefix([_|_], List) when is_list(List) -> false.
+
+%% suffix(Suffix, List) -> (true | false)
+
+-spec suffix([T], [T]) -> boolean().
+
+suffix(Suffix, List) ->
+ Delta = length(List) - length(Suffix),
+ Delta >= 0 andalso nthtail(Delta, List) =:= Suffix.
+
+%% last(List) returns the last element in a list.
+
+-spec last([T,...]) -> T.
+
+last([E|Es]) -> last(E, Es).
+
+last(_, [E|Es]) -> last(E, Es);
+last(E, []) -> E.
+
+%% seq(Min, Max) -> [Min,Min+1, ..., Max]
+%% seq(Min, Max, Incr) -> [Min,Min+Incr, ..., Max]
+%% returns the sequence Min..Max
+%% Min <= Max and Min and Max must be integers
+
+-spec seq(integer(), integer()) -> [integer()].
+
+seq(First, Last)
+ when is_integer(First), is_integer(Last), First-1 =< Last ->
+ seq_loop(Last-First+1, Last, []).
+
+seq_loop(N, X, L) when N >= 4 ->
+ seq_loop(N-4, X-4, [X-3,X-2,X-1,X|L]);
+seq_loop(N, X, L) when N >= 2 ->
+ seq_loop(N-2, X-2, [X-1,X|L]);
+seq_loop(1, X, L) ->
+ [X|L];
+seq_loop(0, _, L) ->
+ L.
+
+-spec seq(integer(), integer(), integer()) -> [integer()].
+
+seq(First, Last, Inc)
+ when is_integer(First), is_integer(Last), is_integer(Inc) ->
+ if
+ Inc > 0, First - Inc =< Last;
+ Inc < 0, First - Inc >= Last ->
+ N = (Last - First + Inc) div Inc,
+ seq_loop(N, Inc*(N-1)+First, Inc, []);
+ Inc =:= 0, First =:= Last ->
+ seq_loop(1, First, Inc, [])
+ end.
+
+seq_loop(N, X, D, L) when N >= 4 ->
+ Y = X-D, Z = Y-D, W = Z-D,
+ seq_loop(N-4, W-D, D, [W,Z,Y,X|L]);
+seq_loop(N, X, D, L) when N >= 2 ->
+ Y = X-D,
+ seq_loop(N-2, Y-D, D, [Y,X|L]);
+seq_loop(1, X, _, L) ->
+ [X|L];
+seq_loop(0, _, _, L) ->
+ L.
+
+%% sum(L) returns the sum of the elements in L
+
+-spec sum([number()]) -> number().
+
+sum(L) -> sum(L, 0).
+
+sum([H|T], Sum) -> sum(T, Sum + H);
+sum([], Sum) -> Sum.
+
+%% duplicate(N, X) -> [X,X,X,.....,X] (N times)
+%% return N copies of X
+
+-spec duplicate(non_neg_integer(), T) -> [T].
+
+duplicate(N, X) when is_integer(N), N >= 0 -> duplicate(N, X, []).
+
+duplicate(0, _, L) -> L;
+duplicate(N, X, L) -> duplicate(N-1, X, [X|L]).
+
+%% min(L) -> returns the minimum element of the list L
+
+-spec min([T,...]) -> T.
+
+min([H|T]) -> min(T, H).
+
+min([H|T], Min) when H < Min -> min(T, H);
+min([_|T], Min) -> min(T, Min);
+min([], Min) -> Min.
+
+%% max(L) -> returns the maximum element of the list L
+
+-spec max([T,...]) -> T.
+
+max([H|T]) -> max(T, H).
+
+max([H|T], Max) when H > Max -> max(T, H);
+max([_|T], Max) -> max(T, Max);
+max([], Max) -> Max.
+
+%% sublist(List, Start, Length)
+%% Returns the sub-list starting at Start of length Length.
+
+-spec sublist([T], pos_integer(), non_neg_integer()) -> [T].
+
+sublist(List, S, L) when is_integer(L), L >= 0 ->
+ sublist(nthtail(S-1, List), L).
+
+-spec sublist([T], non_neg_integer()) -> [T].
+
+sublist(List, L) when is_integer(L), is_list(List) ->
+ sublist_2(List, L).
+
+sublist_2([H|T], L) when L > 0 ->
+ [H|sublist_2(T, L-1)];
+sublist_2(_, 0) ->
+ [];
+sublist_2(List, L) when is_list(List), L > 0 ->
+ [].
+
+%% delete(Item, List) -> List'
+%% Delete the first occurrence of Item from the list L.
+
+-spec delete(T, [T]) -> [T].
+
+delete(Item, [Item|Rest]) -> Rest;
+delete(Item, [H|Rest]) ->
+ [H|delete(Item, Rest)];
+delete(_, []) -> [].
+
+%% Return [{X0, Y0}, {X1, Y1}, ..., {Xn, Yn}] for lists [X0, X1, ...,
+%% Xn] and [Y0, Y1, ..., Yn].
+
+-spec zip([A], [B]) -> [{A, B}].
+
+zip([X | Xs], [Y | Ys]) -> [{X, Y} | zip(Xs, Ys)];
+zip([], []) -> [].
+
+%% Return {[X0, X1, ..., Xn], [Y0, Y1, ..., Yn]}, for a list [{X0, Y0},
+%% {X1, Y1}, ..., {Xn, Yn}].
+
+-spec unzip([{A, B}]) -> {[A], [B]}.
+
+unzip(Ts) -> unzip(Ts, [], []).
+
+unzip([{X, Y} | Ts], Xs, Ys) -> unzip(Ts, [X | Xs], [Y | Ys]);
+unzip([], Xs, Ys) -> {reverse(Xs), reverse(Ys)}.
+
+%% Return [{X0, Y0, Z0}, {X1, Y1, Z1}, ..., {Xn, Yn, Zn}] for lists [X0,
+%% X1, ..., Xn], [Y0, Y1, ..., Yn] and [Z0, Z1, ..., Zn].
+
+-spec zip3([A], [B], [C]) -> [{A, B, C}].
+
+zip3([X | Xs], [Y | Ys], [Z | Zs]) -> [{X, Y, Z} | zip3(Xs, Ys, Zs)];
+zip3([], [], []) -> [].
+
+%% Return {[X0, X1, ..., Xn], [Y0, Y1, ..., Yn], [Z0, Z1, ..., Zn]}, for
+%% a list [{X0, Y0, Z0}, {X1, Y1, Z1}, ..., {Xn, Yn, Zn}].
+
+-spec unzip3([{A, B, C}]) -> {[A], [B], [C]}.
+
+unzip3(Ts) -> unzip3(Ts, [], [], []).
+
+unzip3([{X, Y, Z} | Ts], Xs, Ys, Zs) ->
+ unzip3(Ts, [X | Xs], [Y | Ys], [Z | Zs]);
+unzip3([], Xs, Ys, Zs) ->
+ {reverse(Xs), reverse(Ys), reverse(Zs)}.
+
+%% Return [F(X0, Y0), F(X1, Y1), ..., F(Xn, Yn)] for lists [X0, X1, ...,
+%% Xn] and [Y0, Y1, ..., Yn].
+
+-spec zipwith(fun((X, Y) -> R), [X], [Y]) -> [R].
+
+zipwith(F, [X | Xs], [Y | Ys]) -> [F(X, Y) | zipwith(F, Xs, Ys)];
+zipwith(F, [], []) when is_function(F, 2) -> [].
+
+%% Return [F(X0, Y0, Z0), F(X1, Y1, Z1), ..., F(Xn, Yn, Zn)] for lists
+%% [X0, X1, ..., Xn], [Y0, Y1, ..., Yn] and [Z0, Z1, ..., Zn].
+
+-spec zipwith3(fun((X, Y, Z) -> R), [X], [Y], [Z]) -> [R].
+
+zipwith3(F, [X | Xs], [Y | Ys], [Z | Zs]) ->
+ [F(X, Y, Z) | zipwith3(F, Xs, Ys, Zs)];
+zipwith3(F, [], [], []) when is_function(F, 3) -> [].
+
+%% sort(List) -> L
+%% sorts the list L
+
+-spec sort([T]) -> [T].
+
+sort([X, Y | L] = L0) when X =< Y ->
+ case L of
+ [] ->
+ L0;
+ [Z] when Y =< Z ->
+ L0;
+ [Z] when X =< Z ->
+ [X, Z, Y];
+ [Z] ->
+ [Z, X, Y];
+ _ when X == Y ->
+ sort_1(Y, L, [X]);
+ _ ->
+ split_1(X, Y, L, [], [])
+ end;
+sort([X, Y | L]) ->
+ case L of
+ [] ->
+ [Y, X];
+ [Z] when X =< Z ->
+ [Y, X | L];
+ [Z] when Y =< Z ->
+ [Y, Z, X];
+ [Z] ->
+ [Z, Y, X];
+ _ ->
+ split_2(X, Y, L, [], [])
+ end;
+sort([_] = L) ->
+ L;
+sort([] = L) ->
+ L.
+
+sort_1(X, [Y | L], R) when X == Y ->
+ sort_1(Y, L, [X | R]);
+sort_1(X, [Y | L], R) when X < Y ->
+ split_1(X, Y, L, R, []);
+sort_1(X, [Y | L], R) ->
+ split_2(X, Y, L, R, []);
+sort_1(X, [], R) ->
+ lists:reverse(R, [X]).
+
+%% merge(List) -> L
+%% merges a list of sorted lists
+
+-spec merge([T]) -> [T].
+
+merge(L) ->
+ mergel(L, []).
+
+%% merge3(X, Y, Z) -> L
+%% merges three sorted lists X, Y and Z
+
+-spec merge3([_], [_], [_]) -> [_].
+
+merge3(L1, [], L3) ->
+ merge(L1, L3);
+merge3(L1, L2, []) ->
+ merge(L1, L2);
+merge3(L1, [H2 | T2], [H3 | T3]) ->
+ lists:reverse(merge3_1(L1, [], H2, T2, H3, T3), []).
+
+%% rmerge3(X, Y, Z) -> L
+%% merges three reversed sorted lists X, Y and Z
+
+-spec rmerge3([_], [_], [_]) -> [_].
+
+rmerge3(L1, [], L3) ->
+ rmerge(L1, L3);
+rmerge3(L1, L2, []) ->
+ rmerge(L1, L2);
+rmerge3(L1, [H2 | T2], [H3 | T3]) ->
+ lists:reverse(rmerge3_1(L1, [], H2, T2, H3, T3), []).
+
+%% merge(X, Y) -> L
+%% merges two sorted lists X and Y
+
+-spec merge([_], [_]) -> [_].
+
+merge(T1, []) ->
+ T1;
+merge(T1, [H2 | T2]) ->
+ lists:reverse(merge2_1(T1, H2, T2, []), []).
+
+%% rmerge(X, Y) -> L
+%% merges two reversed sorted lists X and Y
+
+%% reverse(rmerge(reverse(A),reverse(B))) is equal to merge(I,A,B).
+
+-spec rmerge([_], [_]) -> [_].
+
+rmerge(T1, []) ->
+ T1;
+rmerge(T1, [H2 | T2]) ->
+ lists:reverse(rmerge2_1(T1, H2, T2, []), []).
+
+%% concat(L) concatenate the list representation of the elements
+%% in L - the elements in L can be atoms, numbers of strings.
+%% Returns a list of characters.
+
+-type concat_thing() :: atom() | integer() | float() | string().
+-spec concat([concat_thing()]) -> string().
+
+concat(List) ->
+ flatmap(fun thing_to_list/1, List).
+
+thing_to_list(X) when is_integer(X) -> integer_to_list(X);
+thing_to_list(X) when is_float(X) -> float_to_list(X);
+thing_to_list(X) when is_atom(X) -> atom_to_list(X);
+thing_to_list(X) when is_list(X) -> X. %Assumed to be a string
+
+%% flatten(List)
+%% flatten(List, Tail)
+%% Flatten a list, adding optional tail.
+
+-spec flatten([_]) -> [_].
+
+flatten(List) when is_list(List) ->
+ do_flatten(List, []).
+
+-spec flatten([_], [_]) -> [_].
+
+flatten(List, Tail) when is_list(List), is_list(Tail) ->
+ do_flatten(List, Tail).
+
+do_flatten([H|T], Tail) when is_list(H) ->
+ do_flatten(H, do_flatten(T, Tail));
+do_flatten([H|T], Tail) ->
+ [H|do_flatten(T, Tail)];
+do_flatten([], Tail) ->
+ Tail.
+
+%% flat_length(List) (undocumented can be removed later)
+%% Calculate the length of a list of lists.
+
+-spec flat_length([_]) -> non_neg_integer().
+
+flat_length(List) -> flatlength(List).
+
+%% flatlength(List)
+%% Calculate the length of a list of lists.
+
+-spec flatlength([_]) -> non_neg_integer().
+
+flatlength(List) ->
+ flatlength(List, 0).
+
+flatlength([H|T], L) when is_list(H) ->
+ flatlength(H, flatlength(T, L));
+flatlength([_|T], L) ->
+ flatlength(T, L + 1);
+flatlength([], L) -> L.
+
+%% keymember(Key, Index, [Tuple]) Now a BIF!
+%% keysearch(Key, Index, [Tuple]) Now a BIF!
+%% keydelete(Key, Index, [Tuple])
+%% keyreplace(Key, Index, [Tuple], NewTuple)
+%% keytake(Key, Index, [Tuple])
+%% keystore(Key, Index, [Tuple], NewTuple)
+%% keysort(Index, [Tuple])
+%% keymerge(Index, [Tuple], [Tuple])
+%% ukeysort(Index, [Tuple])
+%% ukeymerge(Index, [Tuple], [Tuple])
+%% keymap(Function, Index, [Tuple])
+%% keymap(Function, ExtraArgs, Index, [Tuple])
+
+%keymember(K,N,L) when is_integer(N), N > 0 ->
+% keymember3(K,N,L).
+
+%keymember3(Key, N, [T|Ts]) when element(N, T) == Key -> true;
+%keymember3(Key, N, [T|Ts]) ->
+% keymember3(Key, N, Ts);
+%keymember3(Key, N, []) -> false.
+
+%keysearch(K, N, L) when is_integer(N), N > 0 ->
+% keysearch3(K, N, L).
+
+%keysearch3(Key, N, [H|T]) when element(N, H) == Key ->
+% {value, H};
+%keysearch3(Key, N, [H|T]) ->
+% keysearch3(Key, N, T);
+%keysearch3(Key, N, []) -> false.
+
+-spec keydelete(_, pos_integer(), [T]) -> [T].
+
+keydelete(K, N, L) when is_integer(N), N > 0 ->
+ keydelete3(K, N, L).
+
+keydelete3(Key, N, [H|T]) when element(N, H) == Key -> T;
+keydelete3(Key, N, [H|T]) ->
+ [H|keydelete3(Key, N, T)];
+keydelete3(_, _, []) -> [].
+
+-spec keyreplace(_, pos_integer(), [_], tuple()) -> [_].
+
+keyreplace(K, N, L, New) when is_integer(N), N > 0, is_tuple(New) ->
+ keyreplace3(K, N, L, New).
+
+keyreplace3(Key, Pos, [Tup|Tail], New) when element(Pos, Tup) == Key ->
+ [New|Tail];
+keyreplace3(Key, Pos, [H|T], New) ->
+ [H|keyreplace3(Key, Pos, T, New)];
+keyreplace3(_, _, [], _) -> [].
+
+-spec keytake(_, pos_integer(), [_]) -> {'value', tuple(), [_]} | 'false'.
+
+keytake(Key, N, L) when is_integer(N), N > 0 ->
+ keytake(Key, N, L, []).
+
+keytake(Key, N, [H|T], L) when element(N, H) == Key ->
+ {value, H, lists:reverse(L, T)};
+keytake(Key, N, [H|T], L) ->
+ keytake(Key, N, T, [H|L]);
+keytake(_K, _N, [], _L) -> false.
+
+-spec keystore(_, pos_integer(), [_], tuple()) -> [_].
+keystore(K, N, L, New) when is_integer(N), N > 0, is_tuple(New) ->
+ keystore2(K, N, L, New).
+
+keystore2(Key, N, [H|T], New) when element(N, H) == Key ->
+ [New|T];
+keystore2(Key, N, [H|T], New) ->
+ [H|keystore2(Key, N, T, New)];
+keystore2(_Key, _N, [], New) ->
+ [New].
+
+-spec keysort(pos_integer(), [T]) -> [T] when is_subtype(T, tuple()).
+
+keysort(I, L) when is_integer(I), I > 0 ->
+ case L of
+ [] -> L;
+ [_] -> L;
+ [X, Y | T] ->
+ case {element(I, X), element(I, Y)} of
+ {EX, EY} when EX =< EY ->
+ case T of
+ [] ->
+ L;
+ [Z] ->
+ case element(I, Z) of
+ EZ when EY =< EZ ->
+ L;
+ EZ when EX =< EZ ->
+ [X, Z, Y];
+ _EZ ->
+ [Z, X, Y]
+ end;
+ _ when X == Y ->
+ keysort_1(I, Y, EY, T, [X]);
+ _ ->
+ keysplit_1(I, X, EX, Y, EY, T, [], [])
+ end;
+ {EX, EY} ->
+ case T of
+ [] ->
+ [Y, X];
+ [Z] ->
+ case element(I, Z) of
+ EZ when EX =< EZ ->
+ [Y, X | T];
+ EZ when EY =< EZ ->
+ [Y, Z, X];
+ _EZ ->
+ [Z, Y, X]
+ end;
+ _ ->
+ keysplit_2(I, X, EX, Y, EY, T, [], [])
+ end
+ end
+ end.
+
+keysort_1(I, X, EX, [Y | L], R) when X == Y ->
+ keysort_1(I, Y, EX, L, [X | R]);
+keysort_1(I, X, EX, [Y | L], R) ->
+ case element(I, Y) of
+ EY when EX =< EY ->
+ keysplit_1(I, X, EX, Y, EY, L, R, []);
+ EY ->
+ keysplit_2(I, X, EX, Y, EY, L, R, [])
+ end;
+keysort_1(_I, X, _EX, [], R) ->
+ lists:reverse(R, [X]).
+
+-spec keymerge(pos_integer(), [X], [Y]) ->
+ [R] when is_subtype(X, tuple()), is_subtype(Y, tuple()), is_subtype(R, tuple()).
+
+keymerge(Index, T1, L2) when is_integer(Index), Index > 0 ->
+ case L2 of
+ [] ->
+ T1;
+ [H2 | T2] ->
+ E2 = element(Index, H2),
+ M = keymerge2_1(Index, T1, E2, H2, T2, []),
+ lists:reverse(M, [])
+ end.
+
+%% reverse(rkeymerge(I,reverse(A),reverse(B))) is equal to keymerge(I,A,B).
+
+-spec rkeymerge(pos_integer(), [X], [Y]) ->
+ [R] when is_subtype(X, tuple()), is_subtype(Y, tuple()), is_subtype(R, tuple()).
+
+rkeymerge(Index, T1, L2) when is_integer(Index), Index > 0 ->
+ case L2 of
+ [] ->
+ T1;
+ [H2 | T2] ->
+ E2 = element(Index, H2),
+ M = rkeymerge2_1(Index, T1, E2, H2, T2, []),
+ lists:reverse(M, [])
+ end.
+
+-spec ukeysort(pos_integer(), [T]) -> [T] when is_subtype(T, tuple()).
+
+ukeysort(I, L) when is_integer(I), I > 0 ->
+ case L of
+ [] -> L;
+ [_] -> L;
+ [X, Y | T] ->
+ case {element(I, X), element(I, Y)} of
+ {EX, EY} when EX == EY ->
+ ukeysort_1(I, X, EX, T);
+ {EX, EY} when EX < EY ->
+ case T of
+ [] ->
+ L;
+ [Z] ->
+ case element(I, Z) of
+ EZ when EY == EZ ->
+ [X, Y];
+ EZ when EY < EZ ->
+ [X, Y, Z];
+ EZ when EZ == EX ->
+ [X, Y];
+ EZ when EX =< EZ ->
+ [X, Z, Y];
+ _EZ ->
+ [Z, X, Y]
+ end;
+ _ ->
+ ukeysplit_1(I, X, EX, Y, EY, T, [], [])
+ end;
+ {EX, EY} ->
+ case T of
+ [] ->
+ [Y, X];
+ [Z] ->
+ case element(I, Z) of
+ EZ when EX == EZ ->
+ [Y, X];
+ EZ when EX < EZ ->
+ [Y, X, Z];
+ EZ when EY == EZ ->
+ [Y, X];
+ EZ when EY =< EZ ->
+ [Y, Z, X];
+ _EZ ->
+ [Z, Y, X]
+ end;
+ _ ->
+ ukeysplit_2(I, Y, EY, T, [X])
+ end
+ end
+ end.
+
+ukeysort_1(I, X, EX, [Y | L]) ->
+ case element(I, Y) of
+ EY when EX == EY ->
+ ukeysort_1(I, X, EX, L);
+ EY when EX < EY ->
+ ukeysplit_1(I, X, EX, Y, EY, L, [], []);
+ EY ->
+ ukeysplit_2(I, Y, EY, L, [X])
+ end;
+ukeysort_1(_I, X, _EX, []) ->
+ [X].
+
+-spec ukeymerge(pos_integer(), [X], [Y]) ->
+ [(X | Y)] when is_subtype(X, tuple()), is_subtype(Y, tuple()).
+
+ukeymerge(Index, L1, T2) when is_integer(Index), Index > 0 ->
+ case L1 of
+ [] ->
+ T2;
+ [H1 | T1] ->
+ E1 = element(Index, H1),
+ M = ukeymerge2_2(Index, T1, E1, H1, T2, []),
+ lists:reverse(M, [])
+ end.
+
+%% reverse(rukeymerge(I,reverse(A),reverse(B))) is equal to ukeymerge(I,A,B).
+
+-spec rukeymerge(pos_integer(), [X], [Y]) ->
+ [(X | Y)] when is_subtype(X, tuple()), is_subtype(Y, tuple()).
+
+rukeymerge(Index, T1, L2) when is_integer(Index), Index > 0 ->
+ case L2 of
+ [] ->
+ T1;
+ [H2 | T2] ->
+ E2 = element(Index, H2),
+ M = rukeymerge2_1(Index, T1, E2, T2, [], H2),
+ lists:reverse(M, [])
+ end.
+
+-spec keymap(fun((_) -> _), pos_integer(), [tuple()]) -> [tuple()].
+
+keymap(Fun, Index, [Tup|Tail]) ->
+ [setelement(Index, Tup, Fun(element(Index, Tup)))|keymap(Fun, Index, Tail)];
+keymap(Fun, Index, []) when is_integer(Index), Index >= 1,
+ is_function(Fun, 1) -> [].
+
+%%% Suggestion from OTP-2948: sort and merge with Fun.
+
+-spec sort(fun((T, T) -> boolean()), [T]) -> [T].
+
+sort(Fun, []) when is_function(Fun, 2) ->
+ [];
+sort(Fun, [_] = L) when is_function(Fun, 2) ->
+ L;
+sort(Fun, [X, Y | T]) ->
+ case Fun(X, Y) of
+ true ->
+ fsplit_1(Y, X, Fun, T, [], []);
+ false ->
+ fsplit_2(Y, X, Fun, T, [], [])
+ end.
+
+-spec merge(fun((X, Y) -> boolean()), [X], [Y]) -> [_].
+
+merge(Fun, T1, [H2 | T2]) when is_function(Fun, 2) ->
+ lists:reverse(fmerge2_1(T1, H2, Fun, T2, []), []);
+merge(Fun, T1, []) when is_function(Fun, 2) ->
+ T1.
+
+%% reverse(rmerge(F,reverse(A),reverse(B))) is equal to merge(F,A,B).
+
+-spec rmerge(fun((X, Y) -> boolean()), [X], [Y]) -> [_].
+
+rmerge(Fun, T1, [H2 | T2]) when is_function(Fun, 2) ->
+ lists:reverse(rfmerge2_1(T1, H2, Fun, T2, []), []);
+rmerge(Fun, T1, []) when is_function(Fun, 2) ->
+ T1.
+
+-spec usort(fun((T, T) -> boolean()), [T]) -> [T].
+
+usort(Fun, [_] = L) when is_function(Fun, 2) ->
+ L;
+usort(Fun, [] = L) when is_function(Fun, 2) ->
+ L;
+usort(Fun, [X | L]) when is_function(Fun, 2) ->
+ usort_1(Fun, X, L).
+
+usort_1(Fun, X, [Y | L]) ->
+ case Fun(X, Y) of
+ true ->
+ case Fun(Y, X) of
+ true -> % X equal to Y
+ case L of
+ [] ->
+ [X];
+ _ ->
+ usort_1(Fun, X, L)
+ end;
+ false ->
+ ufsplit_1(Y, X, Fun, L, [], [])
+ end;
+ false ->
+ ufsplit_2(Y, L, Fun, [X])
+ end.
+
+-spec umerge(fun((X, Y) -> boolean()), [X], [Y]) -> [_].
+
+umerge(Fun, [], T2) when is_function(Fun, 2) ->
+ T2;
+umerge(Fun, [H1 | T1], T2) when is_function(Fun, 2) ->
+ lists:reverse(ufmerge2_2(H1, T1, Fun, T2, []), []).
+
+%% reverse(rumerge(F,reverse(A),reverse(B))) is equal to umerge(F,A,B).
+
+-spec rumerge(fun((X, Y) -> boolean()), [X], [Y]) -> [_].
+
+rumerge(Fun, T1, []) when is_function(Fun, 2) ->
+ T1;
+rumerge(Fun, T1, [H2 | T2]) when is_function(Fun, 2) ->
+ lists:reverse(rufmerge2_1(T1, H2, Fun, T2, []), []).
+
+%% usort(List) -> L
+%% sorts the list L, removes duplicates
+
+-spec usort([T]) -> [T].
+
+usort([X, Y | L] = L0) when X < Y ->
+ case L of
+ [] ->
+ L0;
+ [Z] when Y < Z ->
+ L0;
+ [Z] when Y == Z ->
+ [X, Y];
+ [Z] when Z < X ->
+ [Z, X, Y];
+ [Z] when Z == X ->
+ [X, Y];
+ [Z] ->
+ [X, Z, Y];
+ _ ->
+ usplit_1(X, Y, L, [], [])
+ end;
+usort([X, Y | L]) when X > Y ->
+ case L of
+ [] ->
+ [Y, X];
+ [Z] when X < Z ->
+ [Y, X | L];
+ [Z] when X == Z ->
+ [Y, X];
+ [Z] when Z < Y ->
+ [Z, Y, X];
+ [Z] when Z == Y ->
+ [Y, X];
+ [Z] ->
+ [Y, Z, X];
+ _ ->
+ usplit_2(X, Y, L, [], [])
+ end;
+usort([X, _Y | L]) ->
+ usort_1(X, L);
+usort([_] = L) ->
+ L;
+usort([]) ->
+ [].
+
+usort_1(X, [Y | L]) when X == Y ->
+ usort_1(X, L);
+usort_1(X, [Y | L]) when X < Y ->
+ usplit_1(X, Y, L, [], []);
+usort_1(X, [Y | L]) ->
+ usplit_2(X, Y, L, [], []);
+usort_1(X, []) ->
+ [X].
+
+%% umerge(List) -> L
+%% merges a list of sorted lists without duplicates, removes duplicates
+
+-spec umerge([T]) -> [T].
+
+umerge(L) ->
+ umergel(L).
+
+%% umerge3(X, Y, Z) -> L
+%% merges three sorted lists X, Y and Z without duplicates,
+%% removes duplicates
+
+-spec umerge3([_], [_], [_]) -> [_].
+
+umerge3(L1, [], L3) ->
+ umerge(L1, L3);
+umerge3(L1, L2, []) ->
+ umerge(L1, L2);
+umerge3(L1, [H2 | T2], [H3 | T3]) ->
+ lists:reverse(umerge3_1(L1, [H2 | H3], T2, H2, [], T3, H3), []).
+
+%% rumerge3(X, Y, Z) -> L
+%% merges three reversed sorted lists X, Y and Z without duplicates,
+%% removes duplicates
+
+-spec rumerge3([_], [_], [_]) -> [_].
+
+rumerge3(L1, [], L3) ->
+ rumerge(L1, L3);
+rumerge3(L1, L2, []) ->
+ rumerge(L1, L2);
+rumerge3(L1, [H2 | T2], [H3 | T3]) ->
+ lists:reverse(rumerge3_1(L1, T2, H2, [], T3, H3),[]).
+
+%% umerge(X, Y) -> L
+%% merges two sorted lists X and Y without duplicates, removes duplicates
+
+-spec umerge([_], [_]) -> [_].
+
+umerge([], T2) ->
+ T2;
+umerge([H1 | T1], T2) ->
+ lists:reverse(umerge2_2(T1, T2, [], H1), []).
+
+%% rumerge(X, Y) -> L
+%% merges two reversed sorted lists X and Y without duplicates,
+%% removes duplicates
+
+%% reverse(rumerge(reverse(A),reverse(B))) is equal to umerge(I,A,B).
+
+-spec rumerge([_], [_]) -> [_].
+
+rumerge(T1, []) ->
+ T1;
+rumerge(T1, [H2 | T2]) ->
+ lists:reverse(rumerge2_1(T1, T2, [], H2), []).
+
+%% all(Predicate, List)
+%% any(Predicate, List)
+%% map(Function, List)
+%% flatmap(Function, List)
+%% foldl(Function, First, List)
+%% foldr(Function, Last, List)
+%% filter(Predicate, List)
+%% zf(Function, List)
+%% mapfoldl(Function, First, List)
+%% mapfoldr(Function, Last, List)
+%% foreach(Function, List)
+%% takewhile(Predicate, List)
+%% dropwhile(Predicate, List)
+%% splitwith(Predicate, List)
+%% for list programming. Function here is a 'fun'. For backward compatibility,
+%% {Module,Function} is still accepted.
+%%
+%% The name zf is a joke!
+%%
+%% N.B. Unless where the functions actually needs it only foreach/2/3,
+%% which is meant to be used for its side effects, has a defined order
+%% of evaluation.
+%%
+%% There are also versions with an extra argument, ExtraArgs, which is a
+%% list of extra arguments to each call.
+
+-spec all(fun((T) -> boolean()), [T]) -> boolean().
+
+all(Pred, [Hd|Tail]) ->
+ case Pred(Hd) of
+ true -> all(Pred, Tail);
+ false -> false
+ end;
+all(Pred, []) when is_function(Pred, 1) -> true.
+
+-spec any(fun((T) -> boolean()), [T]) -> boolean().
+
+any(Pred, [Hd|Tail]) ->
+ case Pred(Hd) of
+ true -> true;
+ false -> any(Pred, Tail)
+ end;
+any(Pred, []) when is_function(Pred, 1) -> false.
+
+-spec map(fun((D) -> R), [D]) -> [R].
+
+map(F, [H|T]) ->
+ [F(H)|map(F, T)];
+map(F, []) when is_function(F, 1) -> [].
+
+-spec flatmap(fun((D) -> [R]), [D]) -> [R].
+
+flatmap(F, [Hd|Tail]) ->
+ F(Hd) ++ flatmap(F, Tail);
+flatmap(F, []) when is_function(F, 1) -> [].
+
+-spec foldl(fun((T, _) -> _), _, [T]) -> _.
+
+foldl(F, Accu, [Hd|Tail]) ->
+ foldl(F, F(Hd, Accu), Tail);
+foldl(F, Accu, []) when is_function(F, 2) -> Accu.
+
+-spec foldr(fun((T, _) -> _), _, [T]) -> _.
+
+foldr(F, Accu, [Hd|Tail]) ->
+ F(Hd, foldr(F, Accu, Tail));
+foldr(F, Accu, []) when is_function(F, 2) -> Accu.
+
+-spec filter(Pred :: fun((T) -> boolean()), List :: [T]) -> [T].
+
+filter(Pred, List) when is_function(Pred, 1) ->
+ [ E || E <- List, Pred(E) ].
+
+%% Equivalent to {filter(F, L), filter(NotF, L)}, if NotF = 'fun(X) ->
+%% not F(X) end'.
+
+-spec partition(Pred :: fun((T) -> boolean()), List :: [T]) -> {[T], [T]}.
+
+partition(Pred, L) ->
+ partition(Pred, L, [], []).
+
+partition(Pred, [H | T], As, Bs) ->
+ case Pred(H) of
+ true -> partition(Pred, T, [H | As], Bs);
+ false -> partition(Pred, T, As, [H | Bs])
+ end;
+partition(Pred, [], As, Bs) when is_function(Pred, 1) ->
+ {reverse(As), reverse(Bs)}.
+
+-spec zf(fun((T) -> boolean() | {'true', X}), [T]) -> [(T | X)].
+
+zf(F, [Hd|Tail]) ->
+ case F(Hd) of
+ true ->
+ [Hd|zf(F, Tail)];
+ {true,Val} ->
+ [Val|zf(F, Tail)];
+ false ->
+ zf(F, Tail)
+ end;
+zf(F, []) when is_function(F, 1) -> [].
+
+-spec foreach(F :: fun((T) -> _), List :: [T]) -> 'ok'.
+
+foreach(F, [Hd|Tail]) ->
+ F(Hd),
+ foreach(F, Tail);
+foreach(F, []) when is_function(F, 1) -> ok.
+
+-spec mapfoldl(fun((T, _) -> {_, _}), _, [T]) -> {[_], _}.
+
+mapfoldl(F, Accu0, [Hd|Tail]) ->
+ {R,Accu1} = F(Hd, Accu0),
+ {Rs,Accu2} = mapfoldl(F, Accu1, Tail),
+ {[R|Rs],Accu2};
+mapfoldl(F, Accu, []) when is_function(F, 2) -> {[],Accu}.
+
+-spec mapfoldr(fun((T, _) -> {_, _}), _, [T]) -> {[_], _}.
+
+mapfoldr(F, Accu0, [Hd|Tail]) ->
+ {Rs,Accu1} = mapfoldr(F, Accu0, Tail),
+ {R,Accu2} = F(Hd, Accu1),
+ {[R|Rs],Accu2};
+mapfoldr(F, Accu, []) when is_function(F, 2) -> {[],Accu}.
+
+-spec takewhile(fun((T) -> boolean()), [T]) -> [T].
+
+takewhile(Pred, [Hd|Tail]) ->
+ case Pred(Hd) of
+ true -> [Hd|takewhile(Pred, Tail)];
+ false -> []
+ end;
+takewhile(Pred, []) when is_function(Pred, 1) -> [].
+
+-spec dropwhile(fun((T) -> boolean()), [T]) -> [T].
+
+dropwhile(Pred, [Hd|Tail]=Rest) ->
+ case Pred(Hd) of
+ true -> dropwhile(Pred, Tail);
+ false -> Rest
+ end;
+dropwhile(Pred, []) when is_function(Pred, 1) -> [].
+
+-spec splitwith(fun((T) -> boolean()), [T]) -> {[T], [T]}.
+
+splitwith(Pred, List) when is_function(Pred, 1) ->
+ splitwith(Pred, List, []).
+
+splitwith(Pred, [Hd|Tail], Taken) ->
+ case Pred(Hd) of
+ true -> splitwith(Pred, Tail, [Hd|Taken]);
+ false -> {reverse(Taken), [Hd|Tail]}
+ end;
+splitwith(Pred, [], Taken) when is_function(Pred, 1) ->
+ {reverse(Taken),[]}.
+
+-spec split(non_neg_integer(), [T]) -> {[T], [T]}.
+
+split(N, List) when is_integer(N), N >= 0, is_list(List) ->
+ case split(N, List, []) of
+ {_, _} = Result -> Result;
+ Fault when is_atom(Fault) ->
+ erlang:error(Fault, [N,List])
+ end;
+split(N, List) ->
+ erlang:error(badarg, [N,List]).
+
+split(0, L, R) ->
+ {lists:reverse(R, []), L};
+split(N, [H|T], R) ->
+ split(N-1, T, [H|R]);
+split(_, [], _) ->
+ badarg.
+
+%%% =================================================================
+%%% Here follows the implementation of the sort functions.
+%%%
+%%% These functions used to be in their own module (lists_sort),
+%%% but have now been placed here to allow Dialyzer to produce better
+%%% type information.
+%%% =================================================================
+
+-compile({inline,
+ [{merge3_12,7}, {merge3_21,7}, {rmerge3_12,7}, {rmerge3_21,7}]}).
+
+-compile({inline,
+ [{umerge3_12,8}, {umerge3_21,8},
+ {rumerge3_12a,7}, {rumerge3_12b,8}]}).
+
+-compile({inline,
+ [{keymerge3_12,12}, {keymerge3_21,12},
+ {rkeymerge3_12,12}, {rkeymerge3_21,12}]}).
+
+-compile({inline,
+ [{ukeymerge3_12,13}, {ukeymerge3_21,13},
+ {rukeymerge3_12a,11}, {rukeymerge3_21a,13},
+ {rukeymerge3_12b,12}, {rukeymerge3_21b,12}]}).
+
+%% sort/1
+
+%% Ascending.
+split_1(X, Y, [Z | L], R, Rs) when Z >= Y ->
+ split_1(Y, Z, L, [X | R], Rs);
+split_1(X, Y, [Z | L], R, Rs) when Z >= X ->
+ split_1(Z, Y, L, [X | R], Rs);
+split_1(X, Y, [Z | L], [], Rs) ->
+ split_1(X, Y, L, [Z], Rs);
+split_1(X, Y, [Z | L], R, Rs) ->
+ split_1_1(X, Y, L, R, Rs, Z);
+split_1(X, Y, [], R, Rs) ->
+ rmergel([[Y, X | R] | Rs], []).
+
+split_1_1(X, Y, [Z | L], R, Rs, S) when Z >= Y ->
+ split_1_1(Y, Z, L, [X | R], Rs, S);
+split_1_1(X, Y, [Z | L], R, Rs, S) when Z >= X ->
+ split_1_1(Z, Y, L, [X | R], Rs, S);
+split_1_1(X, Y, [Z | L], R, Rs, S) when S =< Z ->
+ split_1(S, Z, L, [], [[Y, X | R] | Rs]);
+split_1_1(X, Y, [Z | L], R, Rs, S) ->
+ split_1(Z, S, L, [], [[Y, X | R] | Rs]);
+split_1_1(X, Y, [], R, Rs, S) ->
+ rmergel([[S], [Y, X | R] | Rs], []).
+
+%% Descending.
+split_2(X, Y, [Z | L], R, Rs) when Z =< Y ->
+ split_2(Y, Z, L, [X | R], Rs);
+split_2(X, Y, [Z | L], R, Rs) when Z =< X ->
+ split_2(Z, Y, L, [X | R], Rs);
+split_2(X, Y, [Z | L], [], Rs) ->
+ split_2(X, Y, L, [Z], Rs);
+split_2(X, Y, [Z | L], R, Rs) ->
+ split_2_1(X, Y, L, R, Rs, Z);
+split_2(X, Y, [], R, Rs) ->
+ mergel([[Y, X | R] | Rs], []).
+
+split_2_1(X, Y, [Z | L], R, Rs, S) when Z =< Y ->
+ split_2_1(Y, Z, L, [X | R], Rs, S);
+split_2_1(X, Y, [Z | L], R, Rs, S) when Z =< X ->
+ split_2_1(Z, Y, L, [X | R], Rs, S);
+split_2_1(X, Y, [Z | L], R, Rs, S) when S > Z ->
+ split_2(S, Z, L, [], [[Y, X | R] | Rs]);
+split_2_1(X, Y, [Z | L], R, Rs, S) ->
+ split_2(Z, S, L, [], [[Y, X | R] | Rs]);
+split_2_1(X, Y, [], R, Rs, S) ->
+ mergel([[S], [Y, X | R] | Rs], []).
+
+%% merge/1
+
+mergel([[] | L], Acc) ->
+ mergel(L, Acc);
+mergel([T1, [H2 | T2], [H3 | T3] | L], Acc) ->
+ mergel(L, [merge3_1(T1, [], H2, T2, H3, T3) | Acc]);
+mergel([T1, [H2 | T2]], Acc) ->
+ rmergel([merge2_1(T1, H2, T2, []) | Acc], []);
+mergel([L], []) ->
+ L;
+mergel([L], Acc) ->
+ rmergel([lists:reverse(L, []) | Acc], []);
+mergel([], []) ->
+ [];
+mergel([], Acc) ->
+ rmergel(Acc, []);
+mergel([A, [] | L], Acc) ->
+ mergel([A | L], Acc);
+mergel([A, B, [] | L], Acc) ->
+ mergel([A, B | L], Acc).
+
+rmergel([[H3 | T3], [H2 | T2], T1 | L], Acc) ->
+ rmergel(L, [rmerge3_1(T1, [], H2, T2, H3, T3) | Acc]);
+rmergel([[H2 | T2], T1], Acc) ->
+ mergel([rmerge2_1(T1, H2, T2, []) | Acc], []);
+rmergel([L], Acc) ->
+ mergel([lists:reverse(L, []) | Acc], []);
+rmergel([], Acc) ->
+ mergel(Acc, []).
+
+%% merge3/3
+
+%% Take L1 apart.
+merge3_1([H1 | T1], M, H2, T2, H3, T3) when H1 =< H2 ->
+ merge3_12(T1, H1, H2, T2, H3, T3, M);
+merge3_1([H1 | T1], M, H2, T2, H3, T3) ->
+ merge3_21(T1, H1, H2, T2, H3, T3, M);
+merge3_1([], M, H2, T2, H3, T3) when H2 =< H3 ->
+ merge2_1(T2, H3, T3, [H2 | M]);
+merge3_1([], M, H2, T2, H3, T3) ->
+ merge2_2(T2, H3, T3, M, H2).
+
+%% Take L2 apart.
+merge3_2(T1, H1, M, [H2 | T2], H3, T3) when H1 =< H2 ->
+ merge3_12(T1, H1, H2, T2, H3, T3, M);
+merge3_2(T1, H1, M, [H2 | T2], H3, T3) ->
+ merge3_21(T1, H1, H2, T2, H3, T3, M);
+merge3_2(T1, H1, M, [], H3, T3) when H1 =< H3 ->
+ merge2_1(T1, H3, T3, [H1 | M]);
+merge3_2(T1, H1, M, [], H3, T3) ->
+ merge2_2(T1, H3, T3, M, H1).
+
+% H1 =< H2. Inlined.
+merge3_12(T1, H1, H2, T2, H3, T3, M) when H1 =< H3 ->
+ merge3_1(T1, [H1 | M], H2, T2, H3, T3);
+merge3_12(T1, H1, H2, T2, H3, T3, M) ->
+ merge3_12_3(T1, H1, H2, T2, [H3 | M], T3).
+
+% H1 =< H2, take L3 apart.
+merge3_12_3(T1, H1, H2, T2, M, [H3 | T3]) when H1 =< H3 ->
+ merge3_1(T1, [H1 | M], H2, T2, H3, T3);
+merge3_12_3(T1, H1, H2, T2, M, [H3 | T3]) ->
+ merge3_12_3(T1, H1, H2, T2, [H3 | M], T3);
+merge3_12_3(T1, H1, H2, T2, M, []) ->
+ merge2_1(T1, H2, T2, [H1 | M]).
+
+% H1 > H2. Inlined.
+merge3_21(T1, H1, H2, T2, H3, T3, M) when H2 =< H3 ->
+ merge3_2(T1, H1, [H2 | M], T2, H3, T3);
+merge3_21(T1, H1, H2, T2, H3, T3, M) ->
+ merge3_21_3(T1, H1, H2, T2, [H3 | M], T3).
+
+% H1 > H2, take L3 apart.
+merge3_21_3(T1, H1, H2, T2, M, [H3 | T3]) when H2 =< H3 ->
+ merge3_2(T1, H1, [H2 | M], T2, H3, T3);
+merge3_21_3(T1, H1, H2, T2, M, [H3 | T3]) ->
+ merge3_21_3(T1, H1, H2, T2, [H3 | M], T3);
+merge3_21_3(T1, H1, H2, T2, M, []) ->
+ merge2_2(T1, H2, T2, M, H1).
+
+%% rmerge/3
+
+%% Take L1 apart.
+rmerge3_1([H1 | T1], M, H2, T2, H3, T3) when H1 =< H2 ->
+ rmerge3_12(T1, H1, H2, T2, H3, T3, M);
+rmerge3_1([H1 | T1], M, H2, T2, H3, T3) ->
+ rmerge3_21(T1, H1, H2, T2, H3, T3, M);
+rmerge3_1([], M, H2, T2, H3, T3) when H2 =< H3 ->
+ rmerge2_2(T2, H3, T3, M, H2);
+rmerge3_1([], M, H2, T2, H3, T3) ->
+ rmerge2_1(T2, H3, T3, [H2 | M]).
+
+%% Take L2 apart.
+rmerge3_2(T1, H1, M, [H2 | T2], H3, T3) when H1 =< H2 ->
+ rmerge3_12(T1, H1, H2, T2, H3, T3, M);
+rmerge3_2(T1, H1, M, [H2 | T2], H3, T3) ->
+ rmerge3_21(T1, H1, H2, T2, H3, T3, M);
+rmerge3_2(T1, H1, M, [], H3, T3) when H1 =< H3 ->
+ rmerge2_2(T1, H3, T3, M, H1);
+rmerge3_2(T1, H1, M, [], H3, T3) ->
+ rmerge2_1(T1, H3, T3, [H1 | M]).
+
+% H1 =< H2. Inlined.
+rmerge3_12(T1, H1, H2, T2, H3, T3, M) when H2 =< H3 ->
+ rmerge3_12_3(T1, H1, H2, T2, [H3 | M], T3);
+rmerge3_12(T1, H1, H2, T2, H3, T3, M) ->
+ rmerge3_2(T1, H1, [H2 | M], T2, H3, T3).
+
+% H1 =< H2, take L3 apart.
+rmerge3_12_3(T1, H1, H2, T2, M, [H3 | T3]) when H2 =< H3 ->
+ rmerge3_12_3(T1, H1, H2, T2, [H3 | M], T3);
+rmerge3_12_3(T1, H1, H2, T2, M, [H3 | T3]) ->
+ rmerge3_2(T1, H1, [H2 | M], T2, H3, T3);
+rmerge3_12_3(T1, H1, H2, T2, M, []) ->
+ rmerge2_2(T1, H2, T2, M, H1).
+
+% H1 > H2. Inlined.
+rmerge3_21(T1, H1, H2, T2, H3, T3, M) when H1 =< H3 ->
+ rmerge3_21_3(T1, H1, H2, T2, [H3 | M], T3);
+rmerge3_21(T1, H1, H2, T2, H3, T3, M) ->
+ rmerge3_1(T1, [H1 | M], H2, T2, H3, T3).
+
+% H1 > H2, take L3 apart.
+rmerge3_21_3(T1, H1, H2, T2, M, [H3 | T3]) when H1 =< H3 ->
+ rmerge3_21_3(T1, H1, H2, T2, [H3 | M], T3);
+rmerge3_21_3(T1, H1, H2, T2, M, [H3 | T3]) ->
+ rmerge3_1(T1, [H1 | M], H2, T2, H3, T3);
+rmerge3_21_3(T1, H1, H2, T2, M, []) ->
+ rmerge2_1(T1, H2, T2, [H1 | M]).
+
+%% merge/2
+
+merge2_1([H1 | T1], H2, T2, M) when H1 =< H2 ->
+ merge2_1(T1, H2, T2, [H1 | M]);
+merge2_1([H1 | T1], H2, T2, M) ->
+ merge2_2(T1, H2, T2, M, H1);
+merge2_1([], H2, T2, M) ->
+ lists:reverse(T2, [H2 | M]).
+
+merge2_2(T1, HdM, [H2 | T2], M, H1) when H1 =< H2 ->
+ merge2_1(T1, H2, T2, [H1, HdM | M]);
+merge2_2(T1, HdM, [H2 | T2], M, H1) ->
+ merge2_2(T1, H2, T2, [HdM | M], H1);
+merge2_2(T1, HdM, [], M, H1) ->
+ lists:reverse(T1, [H1, HdM | M]).
+
+%% rmerge/2
+
+rmerge2_1([H1 | T1], H2, T2, M) when H1 =< H2 ->
+ rmerge2_2(T1, H2, T2, M, H1);
+rmerge2_1([H1 | T1], H2, T2, M) ->
+ rmerge2_1(T1, H2, T2, [H1 | M]);
+rmerge2_1([], H2, T2, M) ->
+ lists:reverse(T2, [H2 | M]).
+
+rmerge2_2(T1, HdM, [H2 | T2], M, H1) when H1 =< H2 ->
+ rmerge2_2(T1, H2, T2, [HdM | M], H1);
+rmerge2_2(T1, HdM, [H2 | T2], M, H1) ->
+ rmerge2_1(T1, H2, T2, [H1, HdM | M]);
+rmerge2_2(T1, HdM, [], M, H1) ->
+ lists:reverse(T1, [H1, HdM | M]).
+
+%% usort/1
+
+%% Ascending.
+usplit_1(X, Y, [Z | L], R, Rs) when Z > Y ->
+ usplit_1(Y, Z, L, [X | R], Rs);
+usplit_1(X, Y, [Z | L], R, Rs) when Z == Y ->
+ usplit_1(X, Y, L, R, Rs);
+usplit_1(X, Y, [Z | L], R, Rs) when Z > X ->
+ usplit_1(Z, Y, L, [X | R], Rs);
+usplit_1(X, Y, [Z | L], R, Rs) when Z == X ->
+ usplit_1(X, Y, L, R, Rs);
+usplit_1(X, Y, [Z | L], [], Rs) ->
+ usplit_1(X, Y, L, [Z], Rs);
+usplit_1(X, Y, [Z | L], R, Rs) ->
+ usplit_1_1(X, Y, L, R, Rs, Z);
+usplit_1(X, Y, [], R, Rs) ->
+ rumergel([[Y, X | R] | Rs], [], asc).
+
+usplit_1_1(X, Y, [Z | L], R, Rs, S) when Z > Y ->
+ usplit_1_1(Y, Z, L, [X | R], Rs, S);
+usplit_1_1(X, Y, [Z | L], R, Rs, S) when Z == Y ->
+ usplit_1_1(X, Y, L, R, Rs, S);
+usplit_1_1(X, Y, [Z | L], R, Rs, S) when Z > X ->
+ usplit_1_1(Z, Y, L, [X | R], Rs, S);
+usplit_1_1(X, Y, [Z | L], R, Rs, S) when Z == X ->
+ usplit_1_1(X, Y, L, R, Rs, S);
+usplit_1_1(X, Y, [Z | L], R, Rs, S) when Z > S ->
+ usplit_1(S, Z, L, [], [[Y, X | R] | Rs]);
+usplit_1_1(X, Y, [Z | L], R, Rs, S) when Z == S ->
+ usplit_1_1(X, Y, L, R, Rs, S);
+usplit_1_1(X, Y, [Z | L], R, Rs, S) ->
+ usplit_1(Z, S, L, [], [[Y, X | R] | Rs]);
+usplit_1_1(X, Y, [], R, Rs, S) ->
+ rumergel([[S], [Y, X | R] | Rs], [], asc).
+
+%% Descending.
+usplit_2(X, Y, [Z | L], R, Rs) when Z < Y ->
+ usplit_2(Y, Z, L, [X | R], Rs);
+usplit_2(X, Y, [Z | L], R, Rs) when Z == Y ->
+ usplit_2(X, Y, L, R, Rs);
+usplit_2(X, Y, [Z | L], R, Rs) when Z < X ->
+ usplit_2(Z, Y, L, [X | R], Rs);
+usplit_2(X, Y, [Z | L], R, Rs) when Z == X ->
+ usplit_2(X, Y, L, R, Rs);
+usplit_2(X, Y, [Z | L], [], Rs) ->
+ usplit_2(X, Y, L, [Z], Rs);
+usplit_2(X, Y, [Z | L], R, Rs) ->
+ usplit_2_1(X, Y, L, R, Rs, Z);
+usplit_2(X, Y, [], R, Rs) ->
+ umergel([[Y, X | R] | Rs], [], desc).
+
+usplit_2_1(X, Y, [Z | L], R, Rs, S) when Z < Y ->
+ usplit_2_1(Y, Z, L, [X | R], Rs, S);
+usplit_2_1(X, Y, [Z | L], R, Rs, S) when Z == Y ->
+ usplit_2_1(X, Y, L, R, Rs, S);
+usplit_2_1(X, Y, [Z | L], R, Rs, S) when Z < X ->
+ usplit_2_1(Z, Y, L, [X | R], Rs, S);
+usplit_2_1(X, Y, [Z | L], R, Rs, S) when Z == X ->
+ usplit_2_1(X, Y, L, R, Rs, S);
+usplit_2_1(X, Y, [Z | L], R, Rs, S) when Z < S ->
+ usplit_2(S, Z, L, [], [[Y, X | R] | Rs]);
+usplit_2_1(X, Y, [Z | L], R, Rs, S) when Z == S ->
+ usplit_2_1(X, Y, L, R, Rs, S);
+usplit_2_1(X, Y, [Z | L], R, Rs, S) ->
+ usplit_2(Z, S, L, [], [[Y, X | R] | Rs]);
+usplit_2_1(X, Y, [], R, Rs, S) ->
+ umergel([[S], [Y, X | R] | Rs], [], desc).
+
+%% umerge/1
+
+umergel(L) ->
+ umergel(L, [], asc).
+
+umergel([[] | L], Acc, O) ->
+ umergel(L, Acc, O);
+umergel([T1, [H2 | T2], [H3 | T3] | L], Acc, asc) ->
+ umergel(L, [umerge3_1(T1, [H2 | H3], T2, H2, [], T3, H3) | Acc], asc);
+umergel([[H3 | T3], [H2 | T2], T1 | L], Acc, desc) ->
+ umergel(L, [umerge3_1(T1, [H2 | H3], T2, H2, [], T3, H3) | Acc], desc);
+umergel([A, [] | L], Acc, O) ->
+ umergel([A | L], Acc, O);
+umergel([A, B, [] | L], Acc, O) ->
+ umergel([A, B | L], Acc, O);
+umergel([[H1 | T1], T2 | L], Acc, asc) ->
+ umergel(L, [umerge2_2(T1, T2, [], H1) | Acc], asc);
+umergel([T2, [H1 | T1] | L], Acc, desc) ->
+ umergel(L, [umerge2_2(T1, T2, [], H1) | Acc], desc);
+umergel([L], [], _O) ->
+ L;
+umergel([L], Acc, O) ->
+ rumergel([lists:reverse(L, []) | Acc], [], O);
+umergel([], [], _O) ->
+ [];
+umergel([], Acc, O) ->
+ rumergel(Acc, [], O).
+
+rumergel([[H3 | T3], [H2 | T2], T1 | L], Acc, asc) ->
+ rumergel(L, [rumerge3_1(T1, T2, H2, [], T3, H3) | Acc], asc);
+rumergel([T1, [H2 | T2], [H3 | T3] | L], Acc, desc) ->
+ rumergel(L, [rumerge3_1(T1, T2, H2, [], T3, H3) | Acc], desc);
+rumergel([[H2 | T2], T1 | L], Acc, asc) ->
+ rumergel(L, [rumerge2_1(T1, T2, [], H2) | Acc], asc);
+rumergel([T1, [H2 | T2] | L], Acc, desc) ->
+ rumergel(L, [rumerge2_1(T1, T2, [], H2) | Acc], desc);
+rumergel([L], Acc, O) ->
+ umergel([lists:reverse(L, []) | Acc], [], O);
+rumergel([], Acc, O) ->
+ umergel(Acc, [], O).
+
+%% umerge3/3
+
+%% Take L1 apart.
+umerge3_1([H1 | T1], HdM, T2, H2, M, T3, H3) when H1 =< H2 ->
+ umerge3_12(T1, H1, T2, H2, M, T3, H3, HdM);
+umerge3_1([H1 | T1], HdM, T2, H2, M, T3, H3) when H2 == HdM ->
+ umerge3_2(T1, H1, T2, H2, M, T3, H3);
+umerge3_1([H1 | T1], HdM, T2, H2, M, T3, H3) ->
+ umerge3_21(T1, H1, T2, H2, M, T3, H3, HdM);
+umerge3_1([], HdM, T2, H2, M, T3, H3) when H2 == HdM ->
+ umerge2_1(T2, T3, M, HdM, H3);
+umerge3_1([], _HdM, T2, H2, M, T3, H3) when H2 =< H3 ->
+ umerge2_1(T2, T3, [H2 | M], H2, H3);
+umerge3_1([], HdM, T2, H2, M, T3, H3) when H3 == HdM ->
+ umerge2_2(T2, T3, M, H2);
+umerge3_1([], _HdM, T2, H2, M, T3, H3) ->
+ umerge2_2(T2, T3, [H3 | M], H2).
+
+%% Take L2 apart.
+umerge3_2(T1, H1, [H2 | T2], HdM, M, T3, H3) when H1 =< H2 ->
+ umerge3_12(T1, H1, T2, H2, M, T3, H3, HdM);
+umerge3_2(T1, H1, [H2 | T2], HdM, M, T3, H3) ->
+ umerge3_21(T1, H1, T2, H2, M, T3, H3, HdM);
+umerge3_2(T1, H1, [], _HdM, M, T3, H3) when H1 =< H3 ->
+ umerge2_1(T1, T3, [H1 | M], H1, H3);
+umerge3_2(T1, H1, [], HdM, M, T3, H3) when H3 == HdM ->
+ umerge2_2(T1, T3, M, H1);
+umerge3_2(T1, H1, [], _HdM, M, T3, H3) ->
+ umerge2_2(T1, T3, [H3 | M], H1).
+
+% H1 =< H2. Inlined.
+umerge3_12(T1, H1, T2, H2, M, T3, H3, _HdM) when H1 =< H3 ->
+ umerge3_1(T1, H1, T2, H2, [H1 | M], T3, H3);
+umerge3_12(T1, H1, T2, H2, M, T3, H3, HdM) when H3 == HdM ->
+ umerge3_12_3(T1, H1, T2, H2, M, T3);
+umerge3_12(T1, H1, T2, H2, M, T3, H3, _HdM) ->
+ umerge3_12_3(T1, H1, T2, H2, [H3 | M], T3).
+
+% H1 =< H2, take L3 apart.
+umerge3_12_3(T1, H1, T2, H2, M, [H3 | T3]) when H1 =< H3 ->
+ umerge3_1(T1, H1, T2, H2, [H1 | M], T3, H3);
+umerge3_12_3(T1, H1, T2, H2, M, [H3 | T3]) ->
+ umerge3_12_3(T1, H1, T2, H2, [H3 | M], T3);
+umerge3_12_3(T1, H1, T2, H2, M, []) ->
+ umerge2_1(T1, T2, [H1 | M], H1, H2).
+
+% H1 > H2. Inlined.
+umerge3_21(T1, H1, T2, H2, M, T3, H3, _HdM) when H2 =< H3 ->
+ umerge3_2(T1, H1, T2, H2, [H2 | M], T3, H3);
+umerge3_21(T1, H1, T2, H2, M, T3, H3, HdM) when H3 == HdM ->
+ umerge3_21_3(T1, H1, T2, H2, M, T3);
+umerge3_21(T1, H1, T2, H2, M, T3, H3, _HdM) ->
+ umerge3_21_3(T1, H1, T2, H2, [H3 | M], T3).
+
+% H1 > H2, take L3 apart.
+umerge3_21_3(T1, H1, T2, H2, M, [H3 | T3]) when H2 =< H3 ->
+ umerge3_2(T1, H1, T2, H2, [H2 | M], T3, H3);
+umerge3_21_3(T1, H1, T2, H2, M, [H3 | T3]) ->
+ umerge3_21_3(T1, H1, T2, H2, [H3 | M], T3);
+umerge3_21_3(T1, H1, T2, H2, M, []) ->
+ umerge2_2(T1, T2, [H2 | M], H1).
+
+%% Take L1 apart.
+rumerge3_1([H1 | T1], T2, H2, M, T3, H3) when H1 =< H2 ->
+ rumerge3_12a(T1, H1, T2, H2, M, T3, H3);
+rumerge3_1([H1 | T1], T2, H2, M, T3, H3) when H1 =< H3 ->
+ rumerge3_21_3(T1, T2, H2, M, T3, H3, H1);
+rumerge3_1([H1 | T1], T2, H2, M, T3, H3) ->
+ rumerge3_1(T1, T2, H2, [H1 | M], T3, H3);
+rumerge3_1([], T2, H2, M, T3, H3) when H2 =< H3 ->
+ rumerge2_2(T2, T3, M, H3, H2);
+rumerge3_1([], T2, H2, M, T3, H3) ->
+ rumerge2_1(T2, T3, [H2 | M], H3).
+
+% H1 =< H2. Inlined.
+rumerge3_12a(T1, H1, T2, H2, M, T3, H3) when H2 =< H3 ->
+ rumerge3_12_3(T1, T2, H2, M, T3, H3, H1);
+rumerge3_12a(T1, H1, T2, H2, M, T3, H3) ->
+ rumerge3_2(T1, T2, H2, M, T3, H3, H1).
+
+%% Take L2 apart. H2M > H3. H2M > H2.
+rumerge3_2(T1, [H2 | T2], H2M, M, T3, H3, H1) when H1 =< H2 ->
+ % H2M > H1.
+ rumerge3_12b(T1, H1, T2, H2, M, T3, H3, H2M);
+rumerge3_2(T1, [H2 | T2], H2M, M, T3, H3, H1) when H1 == H2M ->
+ rumerge3_1(T1, T2, H2, [H1 | M], T3, H3);
+rumerge3_2(T1, [H2 | T2], H2M, M, T3, H3, H1) when H1 =< H3 ->
+ % H2M > H1.
+ rumerge3_21_3(T1, T2, H2, [H2M | M], T3, H3, H1);
+rumerge3_2(T1, [H2 | T2], H2M, M, T3, H3, H1) ->
+ % H2M > H1.
+ rumerge3_1(T1, T2, H2, [H1, H2M | M], T3, H3);
+rumerge3_2(T1, [], H2M, M, T3, H3, H1) when H1 == H2M ->
+ rumerge2_1(T1, T3, [H1 | M], H3);
+rumerge3_2(T1, [], H2M, M, T3, H3, H1) when H1 =< H3 ->
+ rumerge2_2(T1, T3, [H2M | M], H3, H1);
+rumerge3_2(T1, [], H2M, M, T3, H3, H1) ->
+ rumerge2_1(T1, T3, [H1, H2M | M], H3).
+
+% H1 =< H2. Inlined.
+rumerge3_12b(T1, H1, T2, H2, M, T3, H3, H2M) when H2 =< H3 ->
+ rumerge3_12_3(T1, T2, H2, [H2M | M], T3, H3, H1);
+rumerge3_12b(T1, H1, T2, H2, M, T3, H3, H2M) ->
+ rumerge3_2(T1, T2, H2, [H2M | M], T3, H3, H1).
+
+% H1 =< H2, take L3 apart.
+rumerge3_12_3(T1, T2, H2, M, [H3 | T3], H3M, H1) when H2 =< H3 ->
+ rumerge3_12_3(T1, T2, H2, [H3M | M], T3, H3, H1);
+rumerge3_12_3(T1, T2, H2, M, [H3 | T3], H3M, H1) when H2 == H3M ->
+ rumerge3_2(T1, T2, H2, M, T3, H3, H1);
+rumerge3_12_3(T1, T2, H2, M, [H3 | T3], H3M, H1) ->
+ rumerge3_2(T1, T2, H2, [H3M | M], T3, H3, H1);
+rumerge3_12_3(T1, T2, H2, M, [], H3M, H1) when H2 == H3M ->
+ rumerge2_2(T1, T2, M, H2, H1);
+rumerge3_12_3(T1, T2, H2, M, [], H3M, H1) ->
+ rumerge2_2(T1, T2, [H3M | M], H2, H1).
+
+% H1 > H2, take L3 apart.
+rumerge3_21_3(T1, T2, H2, M, [H3 | T3], H3M, H1) when H1 =< H3 ->
+ rumerge3_21_3(T1, T2, H2, [H3M | M], T3, H3, H1);
+rumerge3_21_3(T1, T2, H2, M, [H3 | T3], H3M, H1) when H1 == H3M ->
+ rumerge3_1(T1, T2, H2, [H1 | M], T3, H3);
+rumerge3_21_3(T1, T2, H2, M, [H3 | T3], H3M, H1) ->
+ rumerge3_1(T1, T2, H2, [H1, H3M | M], T3, H3);
+rumerge3_21_3(T1, T2, H2, M, [], H3M, H1) when H1 == H3M ->
+ rumerge2_1(T1, T2, [H1 | M], H2);
+rumerge3_21_3(T1, T2, H2, M, [], H3M, H1) ->
+ rumerge2_1(T1, T2, [H1, H3M | M], H2).
+
+%% umerge/2
+
+%% Elements from the first list are kept and prioritized.
+umerge2_1([H1 | T1], T2, M, _HdM, H2) when H1 =< H2 ->
+ umerge2_1(T1, T2, [H1 | M], H1, H2);
+umerge2_1([H1 | T1], T2, M, HdM, H2) when H2 == HdM ->
+ umerge2_2(T1, T2, M, H1);
+umerge2_1([H1 | T1], T2, M, _HdM, H2) ->
+ umerge2_2(T1, T2, [H2 | M], H1);
+umerge2_1([], T2, M, HdM, H2) when H2 == HdM ->
+ lists:reverse(T2, M);
+umerge2_1([], T2, M, _HdM, H2) ->
+ lists:reverse(T2, [H2 | M]).
+
+umerge2_2(T1, [H2 | T2], M, H1) when H1 =< H2 ->
+ umerge2_1(T1, T2, [H1 | M], H1, H2);
+umerge2_2(T1, [H2 | T2], M, H1) ->
+ umerge2_2(T1, T2, [H2 | M], H1);
+umerge2_2(T1, [], M, H1) ->
+ lists:reverse(T1, [H1 | M]).
+
+%% rumerge/2
+
+%% Elements from the first list are kept and prioritized.
+rumerge2_1([H1 | T1], T2, M, H2) when H1 =< H2 ->
+ rumerge2_2(T1, T2, M, H2, H1);
+rumerge2_1([H1 | T1], T2, M, H2) ->
+ rumerge2_1(T1, T2, [H1 | M], H2);
+rumerge2_1([], T2, M, H2) ->
+ lists:reverse(T2, [H2 | M]).
+
+% H1 =< H2M.
+rumerge2_2(T1, [H2 | T2], M, H2M, H1) when H1 =< H2 ->
+ rumerge2_2(T1, T2, [H2M | M], H2, H1);
+rumerge2_2(T1, [H2 | T2], M, H2M, H1) when H1 == H2M ->
+ rumerge2_1(T1, T2, [H1 | M], H2);
+rumerge2_2(T1, [H2 | T2], M, H2M, H1) ->
+ rumerge2_1(T1, T2, [H1, H2M | M], H2);
+rumerge2_2(T1, [], M, H2M, H1) when H1 == H2M ->
+ lists:reverse(T1, [H1 | M]);
+rumerge2_2(T1, [], M, H2M, H1) ->
+ lists:reverse(T1, [H1, H2M | M]).
+
+%% keysort/2
+
+%% Ascending.
+keysplit_1(I, X, EX, Y, EY, [Z | L], R, Rs) ->
+ case element(I, Z) of
+ EZ when EY =< EZ ->
+ keysplit_1(I, Y, EY, Z, EZ, L, [X | R], Rs);
+ EZ when EX =< EZ ->
+ keysplit_1(I, Z, EZ, Y, EY, L, [X | R], Rs);
+ _EZ when R == [] ->
+ keysplit_1(I, X, EX, Y, EY, L, [Z], Rs);
+ EZ ->
+ keysplit_1_1(I, X, EX, Y, EY, EZ, R, Rs, Z, L)
+ end;
+keysplit_1(I, X, _EX, Y, _EY, [], R, Rs) ->
+ rkeymergel(I, [[Y, X | R] | Rs], [], asc).
+
+keysplit_1_1(I, X, EX, Y, EY, ES, R, Rs, S, [Z | L]) ->
+ case element(I, Z) of
+ EZ when EY =< EZ ->
+ keysplit_1_1(I, Y, EY, Z, EZ, ES, [X | R], Rs, S, L);
+ EZ when EX =< EZ ->
+ keysplit_1_1(I, Z, EZ, Y, EY, ES, [X | R], Rs, S, L);
+ EZ when ES =< EZ ->
+ keysplit_1(I, S, ES, Z, EZ, L, [], [[Y, X | R] | Rs]);
+ EZ ->
+ keysplit_1(I, Z, EZ, S, ES, L, [], [[Y, X | R] | Rs])
+ end;
+keysplit_1_1(I, X, _EX, Y, _EY, _ES, R, Rs, S, []) ->
+ rkeymergel(I, [[S], [Y, X | R] | Rs], [], asc).
+
+%% Descending.
+keysplit_2(I, X, EX, Y, EY, [Z | L], R, Rs) ->
+ case element(I, Z) of
+ EZ when EY > EZ ->
+ keysplit_2(I, Y, EY, Z, EZ, L, [X | R], Rs);
+ EZ when EX > EZ ->
+ keysplit_2(I, Z, EZ, Y, EY, L, [X | R], Rs);
+ _EZ when R == [] ->
+ keysplit_2(I, X, EX, Y, EY, L, [Z], Rs);
+ EZ ->
+ keysplit_2_1(I, X, EX, Y, EY, EZ, R, Rs, Z, L)
+ end;
+keysplit_2(I, X, _EX, Y, _EY, [], R, Rs) ->
+ keymergel(I, [[Y, X | R] | Rs], [], desc).
+
+keysplit_2_1(I, X, EX, Y, EY, ES, R, Rs, S, [Z | L]) ->
+ case element(I, Z) of
+ EZ when EY > EZ ->
+ keysplit_2_1(I, Y, EY, Z, EZ, ES, [X | R], Rs, S, L);
+ EZ when EX > EZ ->
+ keysplit_2_1(I, Z, EZ, Y, EY, ES, [X | R], Rs, S, L);
+ EZ when ES > EZ ->
+ keysplit_2(I, S, ES, Z, EZ, L, [], [[Y, X | R] | Rs]);
+ EZ ->
+ keysplit_2(I, Z, EZ, S, ES, L, [], [[Y, X | R] | Rs])
+ end;
+keysplit_2_1(I, X, _EX, Y, _EY, _ES, R, Rs, S, []) ->
+ keymergel(I, [[S], [Y, X | R] | Rs], [], desc).
+
+keymergel(I, [T1, [H2 | T2], [H3 | T3] | L], Acc, O) when O == asc ->
+ M = keymerge3_1(I, T1, [],O,element(I,H2), H2, T2, element(I,H3), H3, T3),
+ keymergel(I, L, [M | Acc], O);
+keymergel(I, [[H3 | T3], [H2 | T2], T1 | L], Acc, O) when O == desc ->
+ M = keymerge3_1(I, T1, [],O,element(I,H2), H2, T2, element(I,H3), H3, T3),
+ keymergel(I, L, [M | Acc], O);
+keymergel(I, [T1, [H2 | T2] | L], Acc, asc) ->
+ keymergel(I, L, [keymerge2_1(I, T1, element(I,H2),H2,T2,[]) | Acc], asc);
+keymergel(I, [[H2 | T2], T1 | L], Acc, desc) ->
+ keymergel(I, L, [keymerge2_1(I, T1, element(I,H2),H2,T2,[]) | Acc], desc);
+keymergel(_I, [L], [], _O) ->
+ L;
+keymergel(I, [L], Acc, O) ->
+ rkeymergel(I, [lists:reverse(L, []) | Acc], [], O);
+keymergel(I, [], Acc, O) ->
+ rkeymergel(I, Acc, [], O).
+
+rkeymergel(I, [[H3 | T3], [H2 | T2], T1 | L], Acc, O) when O == asc ->
+ M = rkeymerge3_1(I, T1, [],O,element(I,H2), H2, T2, element(I,H3), H3,T3),
+ rkeymergel(I, L, [M | Acc], O);
+rkeymergel(I, [T1, [H2 | T2], [H3 | T3] | L], Acc, O) when O == desc ->
+ M = rkeymerge3_1(I, T1, [],O,element(I,H2), H2, T2, element(I,H3), H3,T3),
+ rkeymergel(I, L, [M | Acc], O);
+rkeymergel(I, [[H2 | T2], T1 | L], Acc, asc) ->
+ rkeymergel(I, L, [rkeymerge2_1(I, T1, element(I,H2),H2,T2,[]) | Acc],asc);
+rkeymergel(I, [T1, [H2 | T2] | L], Acc, desc) ->
+ rkeymergel(I, L, [rkeymerge2_1(I,T1, element(I,H2),H2,T2,[]) | Acc],desc);
+rkeymergel(I, [L], Acc, O) ->
+ keymergel(I, [lists:reverse(L, []) | Acc], [], O);
+rkeymergel(I, [], Acc, O) ->
+ keymergel(I, Acc, [], O).
+
+%%% An extra argument, D, just to avoid some move instructions.
+
+%% Take L1 apart.
+keymerge3_1(I, [H1 | T1], M, D, E2, H2, T2, E3, H3, T3) ->
+ case element(I, H1) of
+ E1 when E1 =< E2 ->
+ keymerge3_12(I, E1, H1, T1, E2, H2, T2, E3, H3, T3, M, D);
+ E1 ->
+ keymerge3_21(I, E1, H1, T1, E2, H2, T2, E3, H3, T3, M, T2)
+ end;
+keymerge3_1(I, [], M, _D, E2, H2, T2, E3, H3, T3) when E2 =< E3 ->
+ keymerge2_1(I, T2, E3, H3, T3, [H2 | M]);
+keymerge3_1(I, [], M, _D, E2, H2, T2, _E3, H3, T3) ->
+ keymerge2_2(I, T2, E2, H3, T3, M, H2).
+
+%% Take L2 apart.
+keymerge3_2(I, E1, H1, T1, [H2 | T2], M, D, E3, H3, T3) ->
+ case element(I, H2) of
+ E2 when E1 =< E2 ->
+ keymerge3_12(I, E1, H1, T1, E2, H2, T2, E3, H3, T3, M, T1);
+ E2 ->
+ keymerge3_21(I, E1, H1, T1, E2, H2, T2, E3, H3, T3, M, D)
+ end;
+keymerge3_2(I, E1, H1, T1, [], M, _D, E3, H3, T3) when E1 =< E3 ->
+ keymerge2_1(I, T1, E3, H3, T3, [H1 | M]);
+keymerge3_2(I, E1, H1, T1, [], M, _D, _E3, H3, T3) ->
+ keymerge2_2(I, T1, E1, H3, T3, M, H1).
+
+% E1 =< E2. Inlined.
+keymerge3_12(I, E1, H1, T1, E2, H2, T2, E3, H3, T3, M, D) when E1 =< E3 ->
+ keymerge3_1(I, T1, [H1 | M], D, E2, H2, T2, E3, H3, T3);
+keymerge3_12(I, E1, H1, T1, E2, H2, T2, _E3, H3, T3, M, _D) ->
+ keymerge3_12_3(I, E1, H1, T1, E2, H2, T2, T3, [H3 | M]).
+
+% E1 =< E2, take L3 apart.
+keymerge3_12_3(I, E1, H1, T1, E2, H2, T2, [H3 | T3], M) ->
+ case element(I, H3) of
+ E3 when E1 =< E3 ->
+ keymerge3_1(I, T1, [H1 | M], T1, E2, H2, T2, E3, H3, T3);
+ _E3 ->
+ keymerge3_12_3(I, E1, H1, T1, E2, H2, T2, T3, [H3 | M])
+ end;
+keymerge3_12_3(I, _E1, H1, T1, E2, H2, T2, [], M) ->
+ keymerge2_1(I, T1, E2, H2, T2, [H1 | M]).
+
+% E1 > E2. Inlined.
+keymerge3_21(I, E1, H1, T1, E2, H2, T2, E3, H3, T3, M, D) when E2 =< E3 ->
+ keymerge3_2(I, E1, H1, T1, T2, [H2 | M], D, E3, H3, T3);
+keymerge3_21(I, E1, H1, T1, E2, H2, T2, _E3, H3, T3, M, _D) ->
+ keymerge3_21_3(I, E1, H1, T1, E2, H2, T2, T3, [H3 | M]).
+
+% E1 > E2, take L3 apart.
+keymerge3_21_3(I, E1, H1, T1, E2, H2, T2, [H3 | T3], M) ->
+ case element(I, H3) of
+ E3 when E2 =< E3 ->
+ keymerge3_2(I, E1, H1, T1, T2, [H2 | M], T2, E3, H3, T3);
+ _E3 ->
+ keymerge3_21_3(I, E1, H1, T1, E2, H2, T2, T3, [H3 | M])
+ end;
+keymerge3_21_3(I, E1, H1, T1, _E2, H2, T2, [], M) ->
+ keymerge2_2(I, T1, E1, H2, T2, M, H1).
+
+%% Take L1 apart.
+rkeymerge3_1(I, [H1 | T1], M, D, E2, H2, T2, E3, H3, T3) ->
+ case element(I, H1) of
+ E1 when E1 =< E2 ->
+ rkeymerge3_12(I, E1, H1, T1, E2, H2, T2, E3, H3, T3, M, T2);
+ E1 ->
+ rkeymerge3_21(I, E1, H1, T1, E2, H2, T2, E3, H3, T3, M, D)
+ end;
+rkeymerge3_1(I, [], M, _D, E2, H2, T2, E3, H3, T3) when E2 =< E3 ->
+ rkeymerge2_2(I, E2, T2, H3, T3, M, H2);
+rkeymerge3_1(I, [], M, _D, _E2, H2, T2, E3, H3, T3) ->
+ rkeymerge2_1(I, T2, E3, H3, T3, [H2 | M]).
+
+%% Take L2 apart.
+rkeymerge3_2(I, E1, H1, T1, [H2 | T2], M, D, E3, H3, T3) ->
+ case element(I, H2) of
+ E2 when E1 =< E2 ->
+ rkeymerge3_12(I, E1, H1, T1, E2, H2, T2, E3, H3, T3, M, D);
+ E2 ->
+ rkeymerge3_21(I, E1, H1, T1, E2, H2, T2, E3, H3, T3, M, T1)
+ end;
+rkeymerge3_2(I, E1, H1, T1, [], M, _D, E3, H3, T3) when E1 =< E3 ->
+ rkeymerge2_2(I, E1, T1, H3, T3, M, H1);
+rkeymerge3_2(I, _E1, H1, T1, [], M, _D, E3, H3, T3) ->
+ rkeymerge2_1(I, T1, E3, H3, T3, [H1 | M]).
+
+% E1 =< E2. Inlined.
+rkeymerge3_12(I, E1, H1, T1, E2, H2, T2, E3, H3, T3, M, _D) when E2 =< E3 ->
+ rkeymerge3_12_3(I, E1, H1, T1, E2, H2, T2, T3, [H3 | M]);
+rkeymerge3_12(I, E1, H1, T1, _E2, H2, T2, E3, H3, T3, M, D) ->
+ rkeymerge3_2(I, E1, H1, T1, T2, [H2 | M], D, E3, H3, T3).
+
+% E1 =< E2, take L3 apart.
+rkeymerge3_12_3(I, E1, H1, T1, E2, H2, T2, [H3 | T3], M) ->
+ case element(I, H3) of
+ E3 when E2 =< E3 ->
+ rkeymerge3_12_3(I, E1, H1, T1, E2, H2, T2, T3, [H3 | M]);
+ E3 ->
+ rkeymerge3_2(I, E1, H1, T1, T2, [H2 | M], T2, E3, H3, T3)
+ end;
+rkeymerge3_12_3(I, E1, H1, T1, _E2, H2, T2, [], M) ->
+ rkeymerge2_2(I, E1, T1, H2, T2, M, H1).
+
+% E1 > E2. Inlined.
+rkeymerge3_21(I, E1, H1, T1, E2, H2, T2, E3, H3, T3, M, _D) when E1 =< E3 ->
+ rkeymerge3_21_3(I, E1, H1, T1, E2, H2, T2, T3, [H3 | M]);
+rkeymerge3_21(I, _E1, H1, T1, E2, H2, T2, E3, H3, T3, M, D) ->
+ rkeymerge3_1(I, T1, [H1 | M], D, E2, H2, T2, E3, H3, T3).
+
+% E1 > E2, take L3 apart.
+rkeymerge3_21_3(I, E1, H1, T1, E2, H2, T2, [H3 | T3], M) ->
+ case element(I, H3) of
+ E3 when E1 =< E3 ->
+ rkeymerge3_21_3(I, E1, H1, T1, E2, H2, T2, T3, [H3 | M]);
+ E3 ->
+ rkeymerge3_1(I, T1, [H1 | M], T1, E2, H2, T2, E3, H3, T3)
+ end;
+rkeymerge3_21_3(I, _E1, H1, T1, E2, H2, T2, [], M) ->
+ rkeymerge2_1(I, T1, E2, H2, T2, [H1 | M]).
+
+%% keymerge/3
+
+%% Elements from the first list are prioritized.
+keymerge2_1(I, [H1 | T1], E2, H2, T2, M) ->
+ case element(I, H1) of
+ E1 when E1 =< E2 ->
+ keymerge2_1(I, T1, E2, H2, T2, [H1 | M]);
+ E1 ->
+ keymerge2_2(I, T1, E1, H2, T2, M, H1)
+ end;
+keymerge2_1(_I, [], _E2, H2, T2, M) ->
+ lists:reverse(T2, [H2 | M]).
+
+keymerge2_2(I, T1, E1, HdM, [H2 | T2], M, H1) ->
+ case element(I, H2) of
+ E2 when E1 =< E2 ->
+ keymerge2_1(I, T1, E2, H2, T2, [H1, HdM | M]);
+ _E2 ->
+ keymerge2_2(I, T1, E1, H2, T2, [HdM | M], H1)
+ end;
+keymerge2_2(_I, T1, _E1, HdM, [], M, H1) ->
+ lists:reverse(T1, [H1, HdM | M]).
+
+%% rkeymerge/3
+
+rkeymerge2_1(I, [H1 | T1], E2, H2, T2, M) ->
+ case element(I, H1) of
+ E1 when E1 =< E2 ->
+ rkeymerge2_2(I, E1, T1, H2, T2, M, H1);
+ _E1 ->
+ rkeymerge2_1(I, T1, E2, H2, T2, [H1 | M])
+ end;
+rkeymerge2_1(_I, [], _E2, H2, T2, M) ->
+ lists:reverse(T2, [H2 | M]).
+
+rkeymerge2_2(I, E1, T1, HdM, [H2 | T2], M, H1) ->
+ case element(I, H2) of
+ E2 when E1 =< E2 ->
+ rkeymerge2_2(I, E1, T1, H2, T2, [HdM | M], H1);
+ E2 ->
+ rkeymerge2_1(I, T1, E2, H2, T2, [H1, HdM | M])
+ end;
+rkeymerge2_2(_I, _E1, T1, HdM, [], M, H1) ->
+ lists:reverse(T1, [H1, HdM | M]).
+
+%% ukeysort/2
+
+%% Ascending.
+ukeysplit_1(I, X, EX, Y, EY, [Z | L], R, Rs) ->
+ case element(I, Z) of
+ EZ when EY == EZ ->
+ ukeysplit_1(I, X, EX, Y, EY, L, R, Rs);
+ EZ when EY < EZ ->
+ ukeysplit_1(I, Y, EY, Z, EZ, L, [X | R], Rs);
+ EZ when EX == EZ ->
+ ukeysplit_1(I, X, EX, Y, EY, L, R, Rs);
+ EZ when EX < EZ ->
+ ukeysplit_1(I, Z, EZ, Y, EY, L, [X | R], Rs);
+ _EZ when R == [] ->
+ ukeysplit_1(I, X, EX, Y, EY, L, [Z], Rs);
+ EZ ->
+ ukeysplit_1_1(I, X, EX, Y, EY, L, R, Rs, Z, EZ)
+ end;
+ukeysplit_1(I, X, _EX, Y, _EY, [], R, Rs) ->
+ rukeymergel(I, [[Y, X | R] | Rs], []).
+
+ukeysplit_1_1(I, X, EX, Y, EY, [Z | L], R, Rs, S, ES) ->
+ case element(I, Z) of
+ EZ when EY == EZ ->
+ ukeysplit_1_1(I, X, EX, Y, EY, L, R, Rs, S, ES);
+ EZ when EY < EZ ->
+ ukeysplit_1_1(I, Y, EY, Z, EZ, L, [X | R], Rs, S, ES);
+ EZ when EX == EZ ->
+ ukeysplit_1_1(I, X, EX, Y, EY, L, R, Rs, S, ES);
+ EZ when EX < EZ ->
+ ukeysplit_1_1(I, Z, EZ, Y, EY, L, [X | R], Rs, S, ES);
+ EZ when ES == EZ ->
+ ukeysplit_1_1(I, X, EX, Y, EY, L, R, Rs, S, ES);
+ EZ when ES < EZ ->
+ ukeysplit_1(I, S, ES, Z, EZ, L, [], [[Y, X | R] | Rs]);
+ EZ ->
+ ukeysplit_1(I, Z, EZ, S, ES, L, [], [[Y, X | R] | Rs])
+ end;
+ukeysplit_1_1(I, X, _EX, Y, _EY, [], R, Rs, S, _ES) ->
+ rukeymergel(I, [[S], [Y, X | R] | Rs], []).
+
+%% Descending.
+ukeysplit_2(I, Y, EY, [Z | L], R) ->
+ case element(I, Z) of
+ EZ when EY == EZ ->
+ ukeysplit_2(I, Y, EY, L, R);
+ EZ when EY < EZ ->
+ ukeysplit_1(I, Y, EY, Z, EZ, L, [], [lists:reverse(R, [])]);
+ EZ ->
+ ukeysplit_2(I, Z, EZ, L, [Y | R])
+ end;
+ukeysplit_2(_I, Y, _EY, [], R) ->
+ [Y | R].
+
+ukeymergel(I, [T1, [H2 | T2], [H3 | T3] | L], Acc) ->
+ %% The fourth argument, [H2 | H3] (=HdM), may confuse type
+ %% checkers. Its purpose is to ensure that the tests H2 == HdM
+ %% and H3 == HdM in ukeymerge3_1 will always fail as long as M == [].
+ M = ukeymerge3_1(I, T1, Acc, [H2 | H3], element(I, H2), H2, T2, [],
+ element(I, H3), H3, T3),
+ ukeymergel(I, L, [M | Acc]);
+ukeymergel(I, [[H1 | T1], T2 | L], Acc) ->
+ ukeymergel(I, L, [ukeymerge2_2(I, T1, element(I, H1), H1, T2, []) | Acc]);
+ukeymergel(_I, [L], []) ->
+ L;
+ukeymergel(I, [L], Acc) ->
+ rukeymergel(I, [lists:reverse(L, []) | Acc], []);
+ukeymergel(I, [], Acc) ->
+ rukeymergel(I, Acc, []).
+
+rukeymergel(I, [[H3 | T3], [H2 | T2], T1 | L], Acc) ->
+ M = rukeymerge3_1(I, T1, Acc, [], element(I, H2), H2, T2, [],
+ element(I, H3), H3, T3),
+ rukeymergel(I, L, [M | Acc]);
+rukeymergel(I, [[H2 | T2], T1 | L], Acc) ->
+ rukeymergel(I, L, [rukeymerge2_1(I, T1, element(I,H2), T2, [], H2)|Acc]);
+rukeymergel(I, [L], Acc) ->
+ ukeymergel(I, [lists:reverse(L, []) | Acc], []);
+rukeymergel(I, [], Acc) ->
+ ukeymergel(I, Acc, []).
+
+%%% An extra argument, D, just to avoid some move instructions.
+
+%% Take L1 apart.
+ukeymerge3_1(I, [H1 | T1], D, HdM, E2, H2, T2, M, E3, H3, T3) ->
+ case element(I, H1) of
+ E1 when E1 =< E2 ->
+ ukeymerge3_12(I, E1, T1, H1, E2, H2, T2, E3, H3, T3, M, HdM, D);
+ E1 when E2 == HdM ->
+ ukeymerge3_2(I, E1, T1, H1, T2, HdM, T2, M, E3, H3, T3);
+ E1 ->
+ ukeymerge3_21(I, E1, T1, H1, E2, H2, T2, E3, H3, T3, M, HdM, T2)
+ end;
+ukeymerge3_1(I, [], _D, HdM, E2, _H2, T2, M, E3, H3, T3) when E2 == HdM ->
+ ukeymerge2_1(I, T2, E3, HdM, T3, M, H3);
+ukeymerge3_1(I, [], _D, _HdM, E2, H2, T2, M, E3, H3, T3) when E2 =< E3 ->
+ ukeymerge2_1(I, T2, E3, E2, T3, [H2 | M], H3);
+ukeymerge3_1(I, [], _D, HdM, E2, H2, T2, M, E3, _H3, T3) when E3 == HdM ->
+ ukeymerge2_2(I, T2, E2, H2, T3, M);
+ukeymerge3_1(I, [], _D, _HdM, E2, H2, T2, M, _E3, H3, T3) ->
+ ukeymerge2_2(I, T2, E2, H2, T3, [H3 | M]).
+
+%% Take L2 apart.
+ukeymerge3_2(I, E1, T1, H1, [H2 | T2], HdM, D, M, E3, H3, T3) ->
+ case element(I, H2) of
+ E2 when E1 =< E2 ->
+ ukeymerge3_12(I, E1, T1, H1, E2, H2, T2, E3, H3, T3, M, HdM, T1);
+ E2 ->
+ ukeymerge3_21(I, E1, T1, H1, E2, H2, T2, E3, H3, T3, M, HdM, D)
+ end;
+ukeymerge3_2(I, E1, T1, H1, [], _HdM, _D, M, E3, H3, T3) when E1 =< E3 ->
+ ukeymerge2_1(I, T1, E3, E1, T3, [H1 | M], H3);
+ukeymerge3_2(I, E1, T1, H1, [], HdM, _D, M, E3, _H3, T3) when E3 == HdM ->
+ ukeymerge2_2(I, T1, E1, H1, T3, M);
+ukeymerge3_2(I, E1, T1, H1, [], _HdM, _D, M, _E3, H3, T3) ->
+ ukeymerge2_2(I, T1, E1, H1, T3, [H3 | M]).
+
+% E1 =< E2. Inlined.
+ukeymerge3_12(I, E1, T1, H1, E2, H2, T2, E3, H3, T3, M, _HdM, D)
+ when E1 =< E3 ->
+ ukeymerge3_1(I, T1, D, E1, E2, H2, T2, [H1 | M], E3, H3, T3);
+ukeymerge3_12(I, E1, T1, H1, E2, H2, T2, E3, _H3, T3, M, HdM, _D)
+ when E3 == HdM ->
+ ukeymerge3_12_3(I, E1, T1, H1, E2, H2, T2, M, T3);
+ukeymerge3_12(I, E1, T1, H1, E2, H2, T2, _E3, H3, T3, M, _HdM, _D) ->
+ ukeymerge3_12_3(I, E1, T1, H1, E2, H2, T2, [H3 | M], T3).
+
+% E1 =< E2, take L3 apart.
+ukeymerge3_12_3(I, E1, T1, H1, E2, H2, T2, M, [H3 | T3]) ->
+ case element(I, H3) of
+ E3 when E1 =< E3 ->
+ ukeymerge3_1(I, T1, T1, E1, E2, H2, T2, [H1 | M], E3, H3, T3);
+ _E3 ->
+ ukeymerge3_12_3(I, E1, T1, H1, E2, H2, T2, [H3 | M], T3)
+ end;
+ukeymerge3_12_3(I, E1, T1, H1, E2, H2, T2, M, []) ->
+ ukeymerge2_1(I, T1, E2, E1, T2, [H1 | M], H2).
+
+% E1 > E2. Inlined.
+ukeymerge3_21(I, E1, T1, H1, E2, H2, T2, E3, H3, T3, M, _HdM, D)
+ when E2 =< E3 ->
+ ukeymerge3_2(I, E1, T1, H1, T2, E2, D, [H2 | M], E3, H3, T3);
+ukeymerge3_21(I, E1, T1, H1, E2, H2, T2, E3, _H3, T3, M, HdM, _D)
+ when E3 == HdM ->
+ ukeymerge3_21_3(I, E1, T1, H1, E2, H2, T2, M, T3);
+ukeymerge3_21(I, E1, T1, H1, E2, H2, T2, _E3, H3, T3, M, _HdM, _D) ->
+ ukeymerge3_21_3(I, E1, T1, H1, E2, H2, T2, [H3 | M], T3).
+
+% E1 > E2, take L3 apart.
+ukeymerge3_21_3(I, E1, T1, H1, E2, H2, T2, M, [H3 | T3]) ->
+ case element(I, H3) of
+ E3 when E2 =< E3 ->
+ ukeymerge3_2(I, E1, T1, H1, T2, E2, T2, [H2 | M], E3, H3, T3);
+ _E3 ->
+ ukeymerge3_21_3(I, E1, T1, H1, E2, H2, T2, [H3 | M], T3)
+ end;
+ukeymerge3_21_3(I, E1, T1, H1, _E2, H2, T2, M, []) ->
+ ukeymerge2_2(I, T1, E1, H1, T2, [H2 | M]).
+
+%%% Two extra arguments, D1 and D2, just to avoid some move instructions.
+
+%% Take L1 apart.
+rukeymerge3_1(I, [H1 | T1], D1, D2, E2, H2, T2, M, E3, H3, T3) ->
+ case element(I, H1) of
+ E1 when E1 =< E2 ->
+ rukeymerge3_12a(I, E1, H1, T1, E2, H2, T2, E3, H3, T3, M);
+ E1 ->
+ rukeymerge3_21a(I, E1, H1, T1, E2, H2, T2, E3, H3, T3, M, D1, D2)
+ end;
+rukeymerge3_1(I, [], _D1, _D2, E2, H2, T2, M, E3, H3, T3) when E2 =< E3 ->
+ rukeymerge2_2(I, T2, E2, T3, M, E3, H3, H2);
+rukeymerge3_1(I, [], _D1, _D2, _E2, H2, T2, M, E3, H3, T3) ->
+ rukeymerge2_1(I, T2, E3, T3, [H2 | M], H3).
+
+% E1 =< E2. Inlined.
+rukeymerge3_12a(I, E1, H1, T1, E2, H2, T2, E3, H3, T3, M) when E2 =< E3 ->
+ rukeymerge3_12_3(I, E1, H1, T1, E2, H2, T2, M, E3, H3, T3);
+rukeymerge3_12a(I, E1, H1, T1, E2, H2, T2, E3, H3, T3, M) ->
+ rukeymerge3_2(I, E1, H1, T1, T2, H2, E2, M, E3, H3, T3).
+
+% E1 > E2. Inlined
+rukeymerge3_21a(I, E1, H1, T1, E2, H2, T2, E3, H3, T3, M, _D1, _D2)
+ when E1 =< E3 ->
+ rukeymerge3_21_3(I, E1, H1, T1, E2, H2, T2, M, E3, H3, T3);
+rukeymerge3_21a(I, _E1, H1, T1, E2, H2, T2, E3, H3, T3, M, D1, D2) ->
+ rukeymerge3_1(I, T1, D1, D2, E2, H2, T2, [H1 | M], E3, H3, T3).
+
+%% Take L2 apart. E2M > E3. E2M > E2.
+rukeymerge3_2(I, E1, H1, T1, [H2 | T2], H2M, E2M, M, E3, H3, T3) ->
+ case element(I, H2) of
+ E2 when E1 =< E2 ->
+ % E2M > E1.
+ rukeymerge3_12b(I, E1, H1, T1, E2, H2, T2, E3, H3, T3, M, H2M);
+ E2 when E1 == E2M ->
+ rukeymerge3_1(I, T1, H1, T1, E2, H2, T2, [H1 | M], E3, H3, T3);
+ E2 ->
+ % E2M > E1.
+ rukeymerge3_21b(I, E1, H1, T1, E2, H2, T2, E3, H3, T3, M, H2M)
+ end;
+rukeymerge3_2(I, E1, H1, T1, [], _H2M, E2M, M, E3, H3, T3) when E1 == E2M ->
+ rukeymerge2_1(I, T1, E3, T3, [H1 | M], H3);
+rukeymerge3_2(I, E1, H1, T1, [], H2M, _E2M, M, E3, H3, T3) when E1 =< E3 ->
+ rukeymerge2_2(I, T1, E1, T3, [H2M | M], E3, H3, H1);
+rukeymerge3_2(I, _E1, H1, T1, [], H2M, _E2M, M, E3, H3, T3) ->
+ rukeymerge2_1(I, T1, E3, T3, [H1, H2M | M], H3).
+
+% E1 =< E2. Inlined.
+rukeymerge3_12b(I, E1, H1, T1, E2, H2, T2, E3, H3, T3, M, H2M)
+ when E2 =< E3 ->
+ rukeymerge3_12_3(I, E1, H1, T1, E2, H2, T2, [H2M | M], E3, H3, T3);
+rukeymerge3_12b(I, E1, H1, T1, E2, H2, T2, E3, H3, T3, M, H2M) ->
+ rukeymerge3_2(I, E1, H1, T1, T2, H2, E2, [H2M | M], E3, H3, T3).
+
+% E1 > E2. Inlined
+rukeymerge3_21b(I, E1, H1, T1, E2, H2, T2, E3, H3, T3, M,H2M) when E1 =< E3 ->
+ rukeymerge3_21_3(I, E1, H1, T1, E2, H2, T2, [H2M | M], E3, H3, T3);
+rukeymerge3_21b(I, _E1, H1, T1, E2, H2, T2, E3, H3, T3, M, H2M) ->
+ rukeymerge3_1(I, T1, H1, T1, E2, H2, T2, [H1, H2M | M], E3, H3, T3).
+
+% E1 =< E2, take L3 apart.
+rukeymerge3_12_3(I, E1, H1, T1, E2, H2, T2, M, E3M, H3M, [H3 | T3]) ->
+ case element(I, H3) of
+ E3 when E2 =< E3 ->
+ rukeymerge3_12_3(I, E1, H1, T1, E2, H2, T2, [H3M | M], E3, H3, T3);
+ E3 when E2 == E3M ->
+ rukeymerge3_2(I, E1, H1, T1, T2, H2, E2, M, E3, H3, T3);
+ E3 ->
+ rukeymerge3_2(I, E1, H1, T1, T2, H2, E2, [H3M | M], E3, H3, T3)
+ end;
+rukeymerge3_12_3(I, E1, H1, T1, E2, H2, T2, M, E3M, _H3M, []) when E2 == E3M ->
+ rukeymerge2_2(I, T1, E1, T2, M, E2, H2, H1);
+rukeymerge3_12_3(I, E1, H1, T1, E2, H2, T2, M, _E3M, H3M, []) ->
+ rukeymerge2_2(I, T1, E1, T2, [H3M | M], E2, H2, H1).
+
+% E1 > E2, take L3 apart.
+rukeymerge3_21_3(I, E1, H1, T1, E2, H2, T2, M, E3M, H3M, [H3 | T3]) ->
+ case element(I, H3) of
+ E3 when E1 =< E3 ->
+ rukeymerge3_21_3(I, E1, H1, T1, E2, H2, T2, [H3M | M], E3, H3, T3);
+ E3 when E1 == E3M ->
+ rukeymerge3_1(I, T1, H1, T1, E2, H2, T2, [H1 | M], E3, H3, T3);
+ E3 ->
+ rukeymerge3_1(I, T1, H1, T1, E2, H2, T2, [H1,H3M | M], E3, H3, T3)
+ end;
+rukeymerge3_21_3(I, E1, H1, T1, E2, H2, T2, M, E3M, _H3M, []) when E1 == E3M ->
+ rukeymerge2_1(I, T1, E2, T2, [H1 | M], H2);
+rukeymerge3_21_3(I, _E1, H1, T1, E2, H2, T2, M, _E3M, H3M, []) ->
+ rukeymerge2_1(I, T1, E2, T2, [H1, H3M | M], H2).
+
+%% ukeymerge/3
+
+%% Elements from the first list are kept and prioritized.
+ukeymerge2_1(I, [H1 | T1], E2, HdM, T2, M, H2) ->
+ case element(I, H1) of
+ E1 when E1 =< E2 ->
+ ukeymerge2_1(I, T1, E2, E1, T2, [H1 | M], H2);
+ E1 when E2 == HdM ->
+ ukeymerge2_2(I, T1, E1, H1, T2, M);
+ E1 ->
+ ukeymerge2_2(I, T1, E1, H1, T2, [H2 | M])
+ end;
+ukeymerge2_1(_I, [], E2, HdM, T2, M, _H2) when E2 == HdM ->
+ lists:reverse(T2, M);
+ukeymerge2_1(_I, [], _E2, _HdM, T2, M, H2) ->
+ lists:reverse(T2, [H2 | M]).
+
+ukeymerge2_2(I, T1, E1, H1, [H2 | T2], M) ->
+ case element(I, H2) of
+ E2 when E1 =< E2 ->
+ ukeymerge2_1(I, T1, E2, E1, T2, [H1 | M], H2);
+ _E2 ->
+ ukeymerge2_2(I, T1, E1, H1, T2, [H2 | M])
+ end;
+ukeymerge2_2(_I, T1, _E1, H1, [], M) ->
+ lists:reverse(T1, [H1 | M]).
+
+%% rukeymerge/3
+
+rukeymerge2_1(I, [H1 | T1], E2, T2, M, H2) ->
+ case element(I, H1) of
+ E1 when E1 =< E2 ->
+ rukeymerge2_2(I, T1, E1, T2, M, E2, H2, H1);
+ _E1 ->
+ rukeymerge2_1(I, T1, E2, T2, [H1 | M], H2)
+ end;
+rukeymerge2_1(_I, [], _E2, T2, M, H2) ->
+ lists:reverse(T2, [H2 | M]).
+
+rukeymerge2_2(I, T1, E1, [H2 | T2], M, E2M, H2M, H1) ->
+ case element(I, H2) of
+ E2 when E1 =< E2 ->
+ rukeymerge2_2(I, T1, E1, T2, [H2M | M], E2, H2, H1);
+ E2 when E1 == E2M ->
+ rukeymerge2_1(I, T1, E2, T2, [H1 | M], H2);
+ E2 ->
+ rukeymerge2_1(I, T1, E2, T2, [H1, H2M | M], H2)
+ end;
+rukeymerge2_2(_I, T1, E1, [], M, E2M, _H2M, H1) when E1 == E2M ->
+ lists:reverse(T1, [H1 | M]);
+rukeymerge2_2(_I, T1, _E1, [], M, _E2M, H2M, H1) ->
+ lists:reverse(T1, [H1, H2M | M]).
+
+%% sort/2
+
+%% Ascending.
+fsplit_1(Y, X, Fun, [Z | L], R, Rs) ->
+ case Fun(Y, Z) of
+ true ->
+ fsplit_1(Z, Y, Fun, L, [X | R], Rs);
+ false ->
+ case Fun(X, Z) of
+ true ->
+ fsplit_1(Y, Z, Fun, L, [X | R], Rs);
+ false when R == [] ->
+ fsplit_1(Y, X, Fun, L, [Z], Rs);
+ false ->
+ fsplit_1_1(Y, X, Fun, L, R, Rs, Z)
+ end
+ end;
+fsplit_1(Y, X, Fun, [], R, Rs) ->
+ rfmergel([[Y, X | R] | Rs], [], Fun, asc).
+
+fsplit_1_1(Y, X, Fun, [Z | L], R, Rs, S) ->
+ case Fun(Y, Z) of
+ true ->
+ fsplit_1_1(Z, Y, Fun, L, [X | R], Rs, S);
+ false ->
+ case Fun(X, Z) of
+ true ->
+ fsplit_1_1(Y, Z, Fun, L, [X | R], Rs, S);
+ false ->
+ case Fun(S, Z) of
+ true ->
+ fsplit_1(Z, S, Fun, L, [], [[Y, X | R] | Rs]);
+ false ->
+ fsplit_1(S, Z, Fun, L, [], [[Y, X | R] | Rs])
+ end
+ end
+ end;
+fsplit_1_1(Y, X, Fun, [], R, Rs, S) ->
+ rfmergel([[S], [Y, X | R] | Rs], [], Fun, asc).
+
+%% Descending.
+fsplit_2(Y, X, Fun, [Z | L], R, Rs) ->
+ case Fun(Y, Z) of
+ false ->
+ fsplit_2(Z, Y, Fun, L, [X | R], Rs);
+ true ->
+ case Fun(X, Z) of
+ false ->
+ fsplit_2(Y, Z, Fun, L, [X | R], Rs);
+ true when R == [] ->
+ fsplit_2(Y, X, Fun, L, [Z], Rs);
+ true ->
+ fsplit_2_1(Y, X, Fun, L, R, Rs, Z)
+ end
+ end;
+fsplit_2(Y, X, Fun, [], R, Rs) ->
+ fmergel([[Y, X | R] | Rs], [], Fun, desc).
+
+fsplit_2_1(Y, X, Fun, [Z | L], R, Rs, S) ->
+ case Fun(Y, Z) of
+ false ->
+ fsplit_2_1(Z, Y, Fun, L, [X | R], Rs, S);
+ true ->
+ case Fun(X, Z) of
+ false ->
+ fsplit_2_1(Y, Z, Fun, L, [X | R], Rs, S);
+ true ->
+ case Fun(S, Z) of
+ false ->
+ fsplit_2(Z, S, Fun, L, [], [[Y, X | R] | Rs]);
+ true ->
+ fsplit_2(S, Z, Fun, L, [], [[Y, X | R] | Rs])
+ end
+ end
+ end;
+fsplit_2_1(Y, X, Fun, [], R, Rs, S) ->
+ fmergel([[S], [Y, X | R] | Rs], [], Fun, desc).
+
+fmergel([T1, [H2 | T2] | L], Acc, Fun, asc) ->
+ fmergel(L, [fmerge2_1(T1, H2, Fun, T2, []) | Acc], Fun, asc);
+fmergel([[H2 | T2], T1 | L], Acc, Fun, desc) ->
+ fmergel(L, [fmerge2_1(T1, H2, Fun, T2, []) | Acc], Fun, desc);
+fmergel([L], [], _Fun, _O) ->
+ L;
+fmergel([L], Acc, Fun, O) ->
+ rfmergel([lists:reverse(L, []) | Acc], [], Fun, O);
+fmergel([], Acc, Fun, O) ->
+ rfmergel(Acc, [], Fun, O).
+
+rfmergel([[H2 | T2], T1 | L], Acc, Fun, asc) ->
+ rfmergel(L, [rfmerge2_1(T1, H2, Fun, T2, []) | Acc], Fun, asc);
+rfmergel([T1, [H2 | T2] | L], Acc, Fun, desc) ->
+ rfmergel(L, [rfmerge2_1(T1, H2, Fun, T2, []) | Acc], Fun, desc);
+rfmergel([L], Acc, Fun, O) ->
+ fmergel([lists:reverse(L, []) | Acc], [], Fun, O);
+rfmergel([], Acc, Fun, O) ->
+ fmergel(Acc, [], Fun, O).
+
+%% merge/3
+
+%% Elements from the first list are prioritized.
+fmerge2_1([H1 | T1], H2, Fun, T2, M) ->
+ case Fun(H1, H2) of
+ true ->
+ fmerge2_1(T1, H2, Fun, T2, [H1 | M]);
+ false ->
+ fmerge2_2(H1, T1, Fun, T2, [H2 | M])
+ end;
+fmerge2_1([], H2, _Fun, T2, M) ->
+ lists:reverse(T2, [H2 | M]).
+
+fmerge2_2(H1, T1, Fun, [H2 | T2], M) ->
+ case Fun(H1, H2) of
+ true ->
+ fmerge2_1(T1, H2, Fun, T2, [H1 | M]);
+ false ->
+ fmerge2_2(H1, T1, Fun, T2, [H2 | M])
+ end;
+fmerge2_2(H1, T1, _Fun, [], M) ->
+ lists:reverse(T1, [H1 | M]).
+
+%% rmerge/3
+
+rfmerge2_1([H1 | T1], H2, Fun, T2, M) ->
+ case Fun(H1, H2) of
+ true ->
+ rfmerge2_2(H1, T1, Fun, T2, [H2 | M]);
+ false ->
+ rfmerge2_1(T1, H2, Fun, T2, [H1 | M])
+ end;
+rfmerge2_1([], H2, _Fun, T2, M) ->
+ lists:reverse(T2, [H2 | M]).
+
+rfmerge2_2(H1, T1, Fun, [H2 | T2], M) ->
+ case Fun(H1, H2) of
+ true ->
+ rfmerge2_2(H1, T1, Fun, T2, [H2 | M]);
+ false ->
+ rfmerge2_1(T1, H2, Fun, T2, [H1 | M])
+ end;
+rfmerge2_2(H1, T1, _Fun, [], M) ->
+ lists:reverse(T1, [H1 | M]).
+
+%% usort/2
+
+%% Ascending. X < Y
+ufsplit_1(Y, X, Fun, [Z | L], R, Rs) ->
+ case Fun(Y, Z) of
+ true ->
+ case Fun(Z, Y) of
+ true -> % Z equal to Y
+ ufsplit_1(Y, X, Fun, L, R, Rs);
+ false ->
+ ufsplit_1(Z, Y, Fun, L, [X | R], Rs)
+ end;
+ false ->
+ case Fun(X, Z) of
+ true ->
+ case Fun(Z, X) of
+ true -> % Z equal to X
+ ufsplit_1(Y, X, Fun, L, R, Rs);
+ false ->
+ ufsplit_1(Y, Z, Fun, L, [X | R], Rs)
+ end;
+ false when R == [] ->
+ ufsplit_1(Y, X, Fun, L, [Z], Rs);
+ false ->
+ ufsplit_1_1(Y, X, Fun, L, R, Rs, Z)
+ end
+ end;
+ufsplit_1(Y, X, Fun, [], R, Rs) ->
+ rufmergel([[Y, X | R] | Rs], [], Fun).
+
+%% X < Y
+ufsplit_1_1(Y, X, Fun, [Z | L], R, Rs, S) ->
+ case Fun(Y, Z) of
+ true ->
+ case Fun(Z, Y) of
+ true -> % Z equal to Y
+ ufsplit_1_1(Y, X, Fun, L, R, Rs, S);
+ false ->
+ ufsplit_1_1(Z, Y, Fun, L, [X | R], Rs, S)
+ end;
+ false ->
+ case Fun(X, Z) of
+ true ->
+ case Fun(Z, X) of
+ true -> % Z equal to X
+ ufsplit_1_1(Y, X, Fun, L, R, Rs, S);
+ false ->
+ ufsplit_1_1(Y, Z, Fun, L, [X | R], Rs, S)
+ end;
+ false ->
+ case Fun(S, Z) of
+ true ->
+ case Fun(Z, S) of
+ true -> % Z equal to S
+ ufsplit_1_1(Y, X, Fun, L, R, Rs, S);
+ false ->
+ ufsplit_1(Z, S, Fun, L, [], [[Y, X | R] | Rs])
+ end;
+ false ->
+ ufsplit_1(S, Z, Fun, L, [], [[Y, X | R] | Rs])
+ end
+ end
+ end;
+ufsplit_1_1(Y, X, Fun, [], R, Rs, S) ->
+ rufmergel([[S], [Y, X | R] | Rs], [], Fun).
+
+%% Descending.
+ufsplit_2(Y, [Z | L], Fun, R) ->
+ case Fun(Y, Z) of
+ true ->
+ case Fun(Z, Y) of
+ true -> % Z equal to Y
+ ufsplit_2(Y, L, Fun, R);
+ false ->
+ ufsplit_1(Z, Y, Fun, L, [], [lists:reverse(R, [])])
+ end;
+ false ->
+ ufsplit_2(Z, L, Fun, [Y | R])
+ end;
+ufsplit_2(Y, [], _Fun, R) ->
+ [Y | R].
+
+ufmergel([[H1 | T1], T2 | L], Acc, Fun) ->
+ ufmergel(L, [ufmerge2_2(H1, T1, Fun, T2, []) | Acc], Fun);
+ufmergel([L], [], _Fun) ->
+ L;
+ufmergel([L], Acc, Fun) ->
+ rufmergel([lists:reverse(L, []) | Acc], [], Fun);
+ufmergel([], Acc, Fun) ->
+ rufmergel(Acc, [], Fun).
+
+rufmergel([[H2 | T2], T1 | L], Acc, Fun) ->
+ rufmergel(L, [rufmerge2_1(T1, H2, Fun, T2, []) | Acc], Fun);
+rufmergel([L], Acc, Fun) ->
+ ufmergel([lists:reverse(L, []) | Acc], [], Fun);
+rufmergel([], Acc, Fun) ->
+ ufmergel(Acc, [], Fun).
+
+%% umerge/3
+
+%% Elements from the first list are kept and prioritized.
+%% HdM before H2.
+ufmerge2_1([H1 | T1], H2, Fun, T2, M, HdM) ->
+ case Fun(H1, H2) of
+ true ->
+ ufmerge2_1(T1, H2, Fun, T2, [H1 | M], H1);
+ false ->
+ case Fun(H2, HdM) of
+ true -> % HdM equal to H2
+ ufmerge2_2(H1, T1, Fun, T2, M);
+ false ->
+ ufmerge2_2(H1, T1, Fun, T2, [H2 | M])
+ end
+ end;
+ufmerge2_1([], H2, Fun, T2, M, HdM) ->
+ case Fun(H2, HdM) of
+ true -> % HdM equal to H2
+ lists:reverse(T2, M);
+ false ->
+ lists:reverse(T2, [H2 | M])
+ end.
+
+ufmerge2_2(H1, T1, Fun, [H2 | T2], M) ->
+ case Fun(H1, H2) of
+ true ->
+ ufmerge2_1(T1, H2, Fun, T2, [H1 | M], H1);
+ false ->
+ ufmerge2_2(H1, T1, Fun, T2, [H2 | M])
+ end;
+ufmerge2_2(H1, T1, _Fun, [], M) ->
+ lists:reverse(T1, [H1 | M]).
+
+%% rumerge/3
+
+rufmerge2_1([H1 | T1], H2, Fun, T2, M) ->
+ case Fun(H1, H2) of
+ true ->
+ rufmerge2_2(H1, T1, Fun, T2, M, H2);
+ false ->
+ rufmerge2_1(T1, H2, Fun, T2, [H1 | M])
+ end;
+rufmerge2_1([], H2, _Fun, T2, M) ->
+ lists:reverse(T2, [H2 | M]).
+
+%% H1 before H2M
+rufmerge2_2(H1, T1, Fun, [H2 | T2], M, H2M) ->
+ case Fun(H1, H2) of
+ true ->
+ rufmerge2_2(H1, T1, Fun, T2, [H2M | M], H2);
+ false ->
+ case Fun(H2M, H1) of
+ true -> % H2M equal to H1
+ rufmerge2_1(T1, H2, Fun, T2, [H1 | M]);
+ false ->
+ rufmerge2_1(T1, H2, Fun, T2, [H1, H2M | M])
+ end
+ end;
+rufmerge2_2(H1, T1, Fun, [], M, H2M) ->
+ case Fun(H2M, H1) of
+ true ->
+ lists:reverse(T1, [H1 | M]);
+ false ->
+ lists:reverse(T1, [H1, H2M | M])
+ end.
+