%% Licensed under the Apache License, Version 2.0 (the "License"); %% you may not use this file except in compliance with the License. %% You may obtain a copy of the License at %% %% http://www.apache.org/licenses/LICENSE-2.0 %% %% Unless required by applicable law or agreed to in writing, software %% distributed under the License is distributed on an "AS IS" BASIS, %% WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. %% See the License for the specific language governing permissions and %% limitations under the License. %% %% Copyright (C) 2006-2016 Richard Carlsson and Ericsson AB %% %% @author Richard Carlsson %% @author Dan Gudmundsson %% %% @doc Functional, extendible arrays. Arrays can have fixed size, or %% can grow automatically as needed. A default value is used for entries %% that have not been explicitly set. %% %% Arrays uses zero based indexing. This is a deliberate design %% choice and differs from other erlang datastructures, e.g. tuples. %% %% Unless specified by the user when the array is created, the default %% value is the atom `undefined'. There is no difference between an %% unset entry and an entry which has been explicitly set to the same %% value as the default one (cf. {@link reset/2}). If you need to %% differentiate between unset and set entries, you must make sure that %% the default value cannot be confused with the values of set entries. %% %% The array never shrinks automatically; if an index `I' has been used %% successfully to set an entry, all indices in the range [0,`I'] will %% stay accessible unless the array size is explicitly changed by %% calling {@link resize/2}. %% %% Examples: %% ``` %% %% Create a fixed-size array with entries 0-9 set to 'undefined' %% A0 = array:new(10). %% 10 = array:size(A0). %% %% %% Create an extendible array and set entry 17 to 'true', %% %% causing the array to grow automatically %% A1 = array:set(17, true, array:new()). %% 18 = array:size(A1). %% %% %% Read back a stored value %% true = array:get(17, A1). %% %% %% Accessing an unset entry returns the default value %% undefined = array:get(3, A1). %% %% %% Accessing an entry beyond the last set entry also returns the %% %% default value, if the array does not have fixed size %% undefined = array:get(18, A1). %% %% %% "sparse" functions ignore default-valued entries %% A2 = array:set(4, false, A1). %% [{4, false}, {17, true}] = array:sparse_to_orddict(A2). %% %% %% An extendible array can be made fixed-size later %% A3 = array:fix(A2). %% %% %% A fixed-size array does not grow automatically and does not %% %% allow accesses beyond the last set entry %% {'EXIT',{badarg,_}} = (catch array:set(18, true, A3)). %% {'EXIT',{badarg,_}} = (catch array:get(18, A3)). %% ''' %% @type array(). A functional, extendible array. The representation is %% not documented and is subject to change without notice. Note that %% arrays cannot be directly compared for equality. -module(array). -export([new/0, new/1, new/2, is_array/1, set/3, get/2, size/1, sparse_size/1, default/1, reset/2, to_list/1, sparse_to_list/1, from_list/1, from_list/2, to_orddict/1, sparse_to_orddict/1, from_orddict/1, from_orddict/2, map/2, sparse_map/2, foldl/3, foldr/3, sparse_foldl/3, sparse_foldr/3, fix/1, relax/1, is_fix/1, resize/1, resize/2]). -export_type([array/0, array/1]). %%-define(TEST,1). -ifdef(TEST). -include_lib("eunit/include/eunit.hrl"). -endif. %% Developers: %% %% For OTP devs: Both tests and documentation is extracted from this %% file, keep and update this file, %% test are extracted with array_SUITE:extract_tests(). %% Doc with docb_gen array.erl %% %% The key to speed is to minimize the number of tests, on %% large input. Always make the most probable path as short as possible. %% In particular, keep in mind that for large trees, the probability of %% a leaf node is small relative to that of an internal node. %% %% If you try to tweak the set_1 and get_1 loops: Measure, look at the %% generated Beam code, and measure again! The argument order matters! %% Representation: %% %% A tree is either a leaf, with LEAFSIZE elements (the "base"), an %% internal node with LEAFSIZE+1 elements, or an unexpanded tree, %% represented by a single integer: the number of elements that may be %% stored in the tree when it is expanded. The last element of an %% internal node caches the number of elements that may be stored in %% each of its subtrees. %% %% Note that to update an entry in a tree of height h = log[b] n, the %% total number of written words is (b+1)+(h-1)*(b+2), since tuples use %% a header word on the heap. 4 is the optimal base for minimizing the %% number of words written, but causes higher trees, which takes time. %% The best compromise between speed and memory usage seems to lie %% around 8-10. Measurements indicate that the optimum base for speed is %% 24 - above that, it gets slower again due to the high memory usage. %% Base 10 is a good choice, giving 2/3 of the possible speedup from %% base 4, but only using 1/3 more memory. (Base 24 uses 65% more memory %% per write than base 10, but the speedup is only 21%.) -define(DEFAULT, undefined). -define(LEAFSIZE, 10). % the "base" -define(NODESIZE, ?LEAFSIZE). % (no reason to have a different size) -define(NODEPATTERN(S), {_,_,_,_,_,_,_,_,_,_,S}). % NODESIZE+1 elements! -define(NEW_NODE(S), % beware of argument duplication! setelement((?NODESIZE+1),erlang:make_tuple((?NODESIZE+1),(S)),(S))). -define(NEW_LEAF(D), erlang:make_tuple(?LEAFSIZE,(D))). -define(NODELEAFS, ?NODESIZE*?LEAFSIZE). %% These make the code a little easier to experiment with. %% It turned out that using shifts (when NODESIZE=2^n) was not faster. -define(reduce(X), ((X) div (?NODESIZE))). -define(extend(X), ((X) * (?NODESIZE))). %%-------------------------------------------------------------------------- -type element_tuple(T) :: {T, T, T, T, T, T, T, T, T, T} | {element_tuple(T), element_tuple(T), element_tuple(T), element_tuple(T), element_tuple(T), element_tuple(T), element_tuple(T), element_tuple(T), element_tuple(T), element_tuple(T), non_neg_integer()}. -type elements(T) :: non_neg_integer() | element_tuple(T) | nil(). % kill reference, for GC -record(array, {size :: non_neg_integer(), %% number of defined entries max :: non_neg_integer(), %% maximum number of entries %% in current tree default, %% the default value (usually 'undefined') elements :: elements(_) %% the tuple tree }). -type array() :: array(term()). -opaque array(Type) :: #array{default :: Type, elements :: elements(Type)}. %% %% Types %% -type array_indx() :: non_neg_integer(). -type array_opt() :: {'fixed', boolean()} | 'fixed' | {'default', Type :: term()} | {'size', N :: non_neg_integer()} | (N :: non_neg_integer()). -type array_opts() :: array_opt() | [array_opt()]. -type indx_pair(Type) :: {Index :: array_indx(), Type}. -type indx_pairs(Type) :: [indx_pair(Type)]. %%-------------------------------------------------------------------------- %% @doc Create a new, extendible array with initial size zero. %% @equiv new([]) %% %% @see new/1 %% @see new/2 -spec new() -> array(). new() -> new([]). %% @doc Create a new array according to the given options. By default, %% the array is extendible and has initial size zero. Array indices %% start at 0. %% %% `Options' is a single term or a list of terms, selected from the %% following: %%
%%
`N::integer()' or `{size, N::integer()}'
%%
Specifies the initial size of the array; this also implies %% `{fixed, true}'. If `N' is not a nonnegative integer, the call %% fails with reason `badarg'.
%%
`fixed' or `{fixed, true}'
%%
Creates a fixed-size array; see also {@link fix/1}.
%%
`{fixed, false}'
%%
Creates an extendible (non fixed-size) array.
%%
`{default, Value}'
%%
Sets the default value for the array to `Value'.
%%
%% Options are processed in the order they occur in the list, i.e., %% later options have higher precedence. %% %% The default value is used as the value of uninitialized entries, and %% cannot be changed once the array has been created. %% %% Examples: %% ```array:new(100)''' creates a fixed-size array of size 100. %% ```array:new({default,0})''' creates an empty, extendible array %% whose default value is 0. %% ```array:new([{size,10},{fixed,false},{default,-1}])''' creates an %% extendible array with initial size 10 whose default value is -1. %% %% @see new/0 %% @see new/2 %% @see set/3 %% @see get/2 %% @see from_list/2 %% @see fix/1 -spec new(Options :: array_opts()) -> array(). new(Options) -> new_0(Options, 0, false). %% @doc Create a new array according to the given size and options. If %% `Size' is not a nonnegative integer, the call fails with reason %% `badarg'. By default, the array has fixed size. Note that any size %% specifications in `Options' will override the `Size' parameter. %% %% If `Options' is a list, this is simply equivalent to `new([{size, %% Size} | Options]', otherwise it is equivalent to `new([{size, Size} | %% [Options]]'. However, using this function directly is more efficient. %% %% Example: %% ```array:new(100, {default,0})''' creates a fixed-size array of size %% 100, whose default value is 0. %% %% @see new/1 -spec new(Size :: non_neg_integer(), Options :: array_opts()) -> array(). new(Size, Options) when is_integer(Size), Size >= 0 -> new_0(Options, Size, true); new(_, _) -> erlang:error(badarg). new_0(Options, Size, Fixed) when is_list(Options) -> new_1(Options, Size, Fixed, ?DEFAULT); new_0(Options, Size, Fixed) -> new_1([Options], Size, Fixed, ?DEFAULT). new_1([fixed | Options], Size, _, Default) -> new_1(Options, Size, true, Default); new_1([{fixed, Fixed} | Options], Size, _, Default) when is_boolean(Fixed) -> new_1(Options, Size, Fixed, Default); new_1([{default, Default} | Options], Size, Fixed, _) -> new_1(Options, Size, Fixed, Default); new_1([{size, Size} | Options], _, _, Default) when is_integer(Size), Size >= 0 -> new_1(Options, Size, true, Default); new_1([Size | Options], _, _, Default) when is_integer(Size), Size >= 0 -> new_1(Options, Size, true, Default); new_1([], Size, Fixed, Default) -> new(Size, Fixed, Default); new_1(_Options, _Size, _Fixed, _Default) -> erlang:error(badarg). new(0, false, undefined) -> %% Constant empty array #array{size=0, max=?LEAFSIZE, elements=?LEAFSIZE}; new(Size, Fixed, Default) -> E = find_max(Size - 1, ?LEAFSIZE), M = if Fixed -> 0; true -> E end, #array{size = Size, max = M, default = Default, elements = E}. -spec find_max(integer(), integer()) -> integer(). find_max(I, M) when I >= M -> find_max(I, ?extend(M)); find_max(_I, M) -> M. %% @doc Returns `true' if `X' appears to be an array, otherwise `false'. %% Note that the check is only shallow; there is no guarantee that `X' %% is a well-formed array representation even if this function returns %% `true'. -spec is_array(X :: term()) -> boolean(). is_array(#array{size = Size, max = Max}) when is_integer(Size), is_integer(Max) -> true; is_array(_) -> false. %% @doc Get the number of entries in the array. Entries are numbered %% from 0 to `size(Array)-1'; hence, this is also the index of the first %% entry that is guaranteed to not have been previously set. %% @see set/3 %% @see sparse_size/1 -spec size(Array :: array()) -> non_neg_integer(). size(#array{size = N}) -> N; size(_) -> erlang:error(badarg). %% @doc Get the value used for uninitialized entries. %% %% @see new/2 -spec default(Array :: array(Type)) -> Value :: Type. default(#array{default = D}) -> D; default(_) -> erlang:error(badarg). -ifdef(EUNIT). new_test_() -> N0 = ?LEAFSIZE, N01 = N0+1, N1 = ?NODESIZE*N0, N11 = N1+1, N2 = ?NODESIZE*N1, [?_test(new()), ?_test(new([])), ?_test(new(10)), ?_test(new({size,10})), ?_test(new(fixed)), ?_test(new({fixed,true})), ?_test(new({fixed,false})), ?_test(new({default,undefined})), ?_test(new([{size,100},{fixed,false},{default,undefined}])), ?_test(new([100,fixed,{default,0}])), ?_assert(new() =:= new([])), ?_assert(new() =:= new([{size,0},{default,undefined},{fixed,false}])), ?_assert(new() =:= new(0, {fixed,false})), ?_assert(new(fixed) =:= new(0)), ?_assert(new(fixed) =:= new(0, [])), ?_assert(new(10) =:= new([{size,0},{size,5},{size,10}])), ?_assert(new(10) =:= new(0, {size,10})), ?_assert(new(10, []) =:= new(10, [{default,undefined},{fixed,true}])), ?_assertError(badarg, new(-1)), ?_assertError(badarg, new(10.0)), ?_assertError(badarg, new(undefined)), ?_assertError(badarg, new([undefined])), ?_assertError(badarg, new([{default,0} | fixed])), ?_assertError(badarg, new(-1, [])), ?_assertError(badarg, new(10.0, [])), ?_assertError(badarg, new(undefined, [])), ?_assertMatch(#array{size=0,max=N0,default=undefined,elements=N0}, new()), ?_assertMatch(#array{size=0,max=0,default=undefined,elements=N0}, new(fixed)), ?_assertMatch(#array{size=N0,max=N0,elements=N0}, new(N0, {fixed,false})), ?_assertMatch(#array{size=N01,max=N1,elements=N1}, new(N01, {fixed,false})), ?_assertMatch(#array{size=N1,max=N1,elements=N1}, new(N1, {fixed,false})), ?_assertMatch(#array{size=N11,max=N2,elements=N2}, new(N11, {fixed,false})), ?_assertMatch(#array{size=N2, max=N2, default=42,elements=N2}, new(N2, [{fixed,false},{default,42}])), ?_assert(0 =:= array:size(new())), ?_assert(17 =:= array:size(new(17))), ?_assert(100 =:= array:size(array:set(99,0,new()))), ?_assertError(badarg, array:size({bad_data,gives_error})), ?_assert(undefined =:= default(new())), ?_assert(4711 =:= default(new({default,4711}))), ?_assert(0 =:= default(new(10, {default,0}))), ?_assertError(badarg, default({bad_data,gives_error})), ?_assert(is_array(new())), ?_assert(false =:= is_array({foobar, 23, 23})), ?_assert(false =:= is_array(#array{size=bad})), ?_assert(false =:= is_array(#array{max=bad})), ?_assert(is_array(new(10))), ?_assert(is_array(new(10, {fixed,false}))) ]. -endif. %% @doc Fix the size of the array. This prevents it from growing %% automatically upon insertion; see also {@link set/3}. %% @see relax/1 -spec fix(Array :: array(Type)) -> array(Type). fix(#array{}=A) -> A#array{max = 0}. %% @doc Check if the array has fixed size. %% Returns `true' if the array is fixed, otherwise `false'. %% @see fix/1 -spec is_fix(Array :: array()) -> boolean(). is_fix(#array{max = 0}) -> true; is_fix(#array{}) -> false. -ifdef(EUNIT). fix_test_() -> [?_assert(is_array(fix(new()))), ?_assert(fix(new()) =:= new(fixed)), ?_assertNot(is_fix(new())), ?_assertNot(is_fix(new([]))), ?_assertNot(is_fix(new({fixed,false}))), ?_assertNot(is_fix(new(10, {fixed,false}))), ?_assert(is_fix(new({fixed,true}))), ?_assert(is_fix(new(fixed))), ?_assert(is_fix(new(10))), ?_assert(is_fix(new(10, []))), ?_assert(is_fix(new(10, {fixed,true}))), ?_assert(is_fix(fix(new()))), ?_assert(is_fix(fix(new({fixed,false})))), ?_test(set(0, 17, new())), ?_assertError(badarg, set(0, 17, new(fixed))), ?_assertError(badarg, set(1, 42, fix(set(0, 17, new())))), ?_test(set(9, 17, new(10))), ?_assertError(badarg, set(10, 17, new(10))), ?_assertError(badarg, set(10, 17, fix(new(10, {fixed,false})))) ]. -endif. %% @doc Make the array resizable. (Reverses the effects of {@link %% fix/1}.) %% @see fix/1 -spec relax(Array :: array(Type)) -> array(Type). relax(#array{size = N}=A) -> A#array{max = find_max(N-1, ?LEAFSIZE)}. -ifdef(EUNIT). relax_test_() -> [?_assert(is_array(relax(new(fixed)))), ?_assertNot(is_fix(relax(fix(new())))), ?_assertNot(is_fix(relax(new(fixed)))), ?_assert(new() =:= relax(new(fixed))), ?_assert(new() =:= relax(new(0))), ?_assert(new(17, {fixed,false}) =:= relax(new(17))), ?_assert(new(100, {fixed,false}) =:= relax(fix(new(100, {fixed,false})))) ]. -endif. %% @doc Change the size of the array. If `Size' is not a nonnegative %% integer, the call fails with reason `badarg'. If the given array has %% fixed size, the resulting array will also have fixed size. -spec resize(Size :: non_neg_integer(), Array :: array(Type)) -> array(Type). resize(Size, #array{size = N, max = M, elements = E}=A) when is_integer(Size), Size >= 0 -> if Size > N -> {E1, M1} = grow(Size-1, E, if M > 0 -> M; true -> find_max(N-1, ?LEAFSIZE) end), A#array{size = Size, max = if M > 0 -> M1; true -> M end, elements = E1}; Size < N -> %% TODO: shrink physical representation when shrinking the array A#array{size = Size}; true -> A end; resize(_Size, _) -> erlang:error(badarg). %% @doc Change the size of the array to that reported by {@link %% sparse_size/1}. If the given array has fixed size, the resulting %% array will also have fixed size. %% @equiv resize(sparse_size(Array), Array) %% @see resize/2 %% @see sparse_size/1 -spec resize(Array :: array(Type)) -> array(Type). resize(Array) -> resize(sparse_size(Array), Array). -ifdef(EUNIT). resize_test_() -> [?_assert(resize(0, new()) =:= new()), ?_assert(resize(99, new(99)) =:= new(99)), ?_assert(resize(99, relax(new(99))) =:= relax(new(99))), ?_assert(is_fix(resize(100, new(10)))), ?_assertNot(is_fix(resize(100, relax(new(10))))), ?_assert(array:size(resize(100, new())) =:= 100), ?_assert(array:size(resize(0, new(100))) =:= 0), ?_assert(array:size(resize(99, new(10))) =:= 99), ?_assert(array:size(resize(99, new(1000))) =:= 99), ?_assertError(badarg, set(99, 17, new(10))), ?_test(set(99, 17, resize(100, new(10)))), ?_assertError(badarg, set(100, 17, resize(100, new(10)))), ?_assert(array:size(resize(new())) =:= 0), ?_assert(array:size(resize(new(8))) =:= 0), ?_assert(array:size(resize(array:set(7, 0, new()))) =:= 8), ?_assert(array:size(resize(array:set(7, 0, new(10)))) =:= 8), ?_assert(array:size(resize(array:set(99, 0, new(10,{fixed,false})))) =:= 100), ?_assert(array:size(resize(array:set(7, undefined, new()))) =:= 0), ?_assert(array:size(resize(array:from_list([1,2,3,undefined]))) =:= 3), ?_assert(array:size( resize(array:from_orddict([{3,0},{17,0},{99,undefined}]))) =:= 18), ?_assertError(badarg, resize(foo, bad_argument)) ]. -endif. %% @doc Set entry `I' of the array to `Value'. If `I' is not a %% nonnegative integer, or if the array has fixed size and `I' is larger %% than the maximum index, the call fails with reason `badarg'. %% %% If the array does not have fixed size, and `I' is greater than %% `size(Array)-1', the array will grow to size `I+1'. %% %% @see get/2 %% @see reset/2 -spec set(I :: array_indx(), Value :: Type, Array :: array(Type)) -> array(Type). set(I, Value, #array{size = N, max = M, default = D, elements = E}=A) when is_integer(I), I >= 0 -> if I < N -> A#array{elements = set_1(I, E, Value, D)}; I < M -> %% (note that this cannot happen if M == 0, since N >= 0) A#array{size = I+1, elements = set_1(I, E, Value, D)}; M > 0 -> {E1, M1} = grow(I, E, M), A#array{size = I+1, max = M1, elements = set_1(I, E1, Value, D)}; true -> erlang:error(badarg) end; set(_I, _V, _A) -> erlang:error(badarg). %% See get_1/3 for details about switching and the NODEPATTERN macro. set_1(I, E=?NODEPATTERN(S), X, D) -> I1 = I div S + 1, setelement(I1, E, set_1(I rem S, element(I1, E), X, D)); set_1(I, E, X, D) when is_integer(E) -> expand(I, E, X, D); set_1(I, E, X, _D) -> setelement(I+1, E, X). %% Enlarging the array upwards to accommodate an index `I' grow(I, E, _M) when is_integer(E) -> M1 = find_max(I, E), {M1, M1}; grow(I, E, M) -> grow_1(I, E, M). grow_1(I, E, M) when I >= M -> grow(I, setelement(1, ?NEW_NODE(M), E), ?extend(M)); grow_1(_I, E, M) -> {E, M}. %% Insert an element in an unexpanded node, expanding it as necessary. expand(I, S, X, D) when S > ?LEAFSIZE -> S1 = ?reduce(S), setelement(I div S1 + 1, ?NEW_NODE(S1), expand(I rem S1, S1, X, D)); expand(I, _S, X, D) -> setelement(I+1, ?NEW_LEAF(D), X). %% @doc Get the value of entry `I'. If `I' is not a nonnegative %% integer, or if the array has fixed size and `I' is larger than the %% maximum index, the call fails with reason `badarg'. %% %% If the array does not have fixed size, this function will return the %% default value for any index `I' greater than `size(Array)-1'. %% @see set/3 -spec get(I :: array_indx(), Array :: array(Type)) -> Value :: Type. get(I, #array{size = N, max = M, elements = E, default = D}) when is_integer(I), I >= 0 -> if I < N -> get_1(I, E, D); M > 0 -> D; true -> erlang:error(badarg) end; get(_I, _A) -> erlang:error(badarg). %% The use of NODEPATTERN(S) to select the right clause is just a hack, %% but it is the only way to get the maximum speed out of this loop %% (using the Beam compiler in OTP 11). get_1(I, E=?NODEPATTERN(S), D) -> get_1(I rem S, element(I div S + 1, E), D); get_1(_I, E, D) when is_integer(E) -> D; get_1(I, E, _D) -> element(I+1, E). %% @doc Reset entry `I' to the default value for the array. %% If the value of entry `I' is the default value the array will be %% returned unchanged. Reset will never change size of the array. %% Shrinking can be done explicitly by calling {@link resize/2}. %% %% If `I' is not a nonnegative integer, or if the array has fixed size %% and `I' is larger than the maximum index, the call fails with reason %% `badarg'; cf. {@link set/3} %% %% @see new/2 %% @see set/3 %% TODO: a reset_range function -spec reset(I :: array_indx(), Array :: array(Type)) -> array(Type). reset(I, #array{size = N, max = M, default = D, elements = E}=A) when is_integer(I), I >= 0 -> if I < N -> try A#array{elements = reset_1(I, E, D)} catch throw:default -> A end; M > 0 -> A; true -> erlang:error(badarg) end; reset(_I, _A) -> erlang:error(badarg). reset_1(I, E=?NODEPATTERN(S), D) -> I1 = I div S + 1, setelement(I1, E, reset_1(I rem S, element(I1, E), D)); reset_1(_I, E, _D) when is_integer(E) -> throw(default); reset_1(I, E, D) -> Indx = I+1, case element(Indx, E) of D -> throw(default); _ -> setelement(I+1, E, D) end. -ifdef(EUNIT). set_get_test_() -> N0 = ?LEAFSIZE, N1 = ?NODESIZE*N0, [?_assert(array:get(0, new()) =:= undefined), ?_assert(array:get(1, new()) =:= undefined), ?_assert(array:get(99999, new()) =:= undefined), ?_assert(array:get(0, new(1)) =:= undefined), ?_assert(array:get(0, new(1,{default,0})) =:= 0), ?_assert(array:get(9, new(10)) =:= undefined), ?_assertError(badarg, array:get(0, new(fixed))), ?_assertError(badarg, array:get(1, new(1))), ?_assertError(badarg, array:get(-1, new(1))), ?_assertError(badarg, array:get(10, new(10))), ?_assertError(badarg, array:set(-1, foo, new(10))), ?_assertError(badarg, array:set(10, foo, no_array)), ?_assert(array:size(set(0, 17, new())) =:= 1), ?_assert(array:size(set(N1-1, 17, new())) =:= N1), ?_assert(array:size(set(0, 42, set(0, 17, new()))) =:= 1), ?_assert(array:size(set(9, 42, set(0, 17, new()))) =:= 10), ?_assert(array:get(0, set(0, 17, new())) =:= 17), ?_assert(array:get(0, set(1, 17, new())) =:= undefined), ?_assert(array:get(1, set(1, 17, new())) =:= 17), ?_assert(array:get(0, fix(set(0, 17, new()))) =:= 17), ?_assertError(badarg, array:get(1, fix(set(0, 17, new())))), ?_assert(array:get(N1-2, set(N1-1, 17, new())) =:= undefined), ?_assert(array:get(N1-1, set(N1-1, 17, new())) =:= 17), ?_assertError(badarg, array:get(N1, fix(set(N1-1, 17, new())))), ?_assert(array:get(0, set(0, 42, set(0, 17, new()))) =:= 42), ?_assertError(badarg, array:get(0, reset(11, new([{size,10}])))), ?_assertError(badarg, array:get(0, reset(-1, new([{size,10}])))), ?_assert(array:get(0, reset(0, new())) =:= undefined), ?_assert(array:get(0, reset(0, set(0, 17, new()))) =:= undefined), ?_assert(array:get(0, reset(9, set(9, 17, new()))) =:= undefined), ?_assert(array:get(0, reset(11, set(11, 17, new()))) =:= undefined), ?_assert(array:get(0, reset(11, set(12, 17, new()))) =:= undefined), ?_assert(array:get(0, reset(1, set(12, 17, new()))) =:= undefined), ?_assert(array:get(0, reset(11, new())) =:= undefined), ?_assert(array:get(0, reset(0, set(0, 17, new({default,42})))) =:= 42), ?_assert(array:get(0, reset(0, new({default,42}))) =:= 42) ]. -endif. %% @doc Converts the array to a list. %% %% @see from_list/2 %% @see sparse_to_list/1 -spec to_list(Array :: array(Type)) -> list(Value :: Type). to_list(#array{size = 0}) -> []; to_list(#array{size = N, elements = E, default = D}) -> to_list_1(E, D, N - 1); to_list(_) -> erlang:error(badarg). %% this part handles the rightmost subtrees to_list_1(E=?NODEPATTERN(S), D, I) -> N = I div S, to_list_3(N, D, to_list_1(element(N+1, E), D, I rem S), E); to_list_1(E, D, I) when is_integer(E) -> push(I+1, D, []); to_list_1(E, _D, I) -> push_tuple(I+1, E, []). %% this part handles full trees only to_list_2(E=?NODEPATTERN(_S), D, L) -> to_list_3(?NODESIZE, D, L, E); to_list_2(E, D, L) when is_integer(E) -> push(E, D, L); to_list_2(E, _D, L) -> push_tuple(?LEAFSIZE, E, L). to_list_3(0, _D, L, _E) -> L; to_list_3(N, D, L, E) -> to_list_3(N-1, D, to_list_2(element(N, E), D, L), E). push(0, _E, L) -> L; push(N, E, L) -> push(N - 1, E, [E | L]). push_tuple(0, _T, L) -> L; push_tuple(N, T, L) -> push_tuple(N - 1, T, [element(N, T) | L]). -ifdef(EUNIT). to_list_test_() -> N0 = ?LEAFSIZE, [?_assert([] =:= to_list(new())), ?_assert([undefined] =:= to_list(new(1))), ?_assert([undefined,undefined] =:= to_list(new(2))), ?_assert(lists:duplicate(N0,0) =:= to_list(new(N0,{default,0}))), ?_assert(lists:duplicate(N0+1,1) =:= to_list(new(N0+1,{default,1}))), ?_assert(lists:duplicate(N0+2,2) =:= to_list(new(N0+2,{default,2}))), ?_assert(lists:duplicate(666,6) =:= to_list(new(666,{default,6}))), ?_assert([1,2,3] =:= to_list(set(2,3,set(1,2,set(0,1,new()))))), ?_assert([3,2,1] =:= to_list(set(0,3,set(1,2,set(2,1,new()))))), ?_assert([1|lists:duplicate(N0-2,0)++[1]] =:= to_list(set(N0-1,1,set(0,1,new({default,0}))))), ?_assert([1|lists:duplicate(N0-1,0)++[1]] =:= to_list(set(N0,1,set(0,1,new({default,0}))))), ?_assert([1|lists:duplicate(N0,0)++[1]] =:= to_list(set(N0+1,1,set(0,1,new({default,0}))))), ?_assert([1|lists:duplicate(N0*3,0)++[1]] =:= to_list(set((N0*3)+1,1,set(0,1,new({default,0}))))), ?_assertError(badarg, to_list(no_array)) ]. -endif. %% @doc Converts the array to a list, skipping default-valued entries. %% %% @see to_list/1 -spec sparse_to_list(Array :: array(Type)) -> list(Value :: Type). sparse_to_list(#array{size = 0}) -> []; sparse_to_list(#array{size = N, elements = E, default = D}) -> sparse_to_list_1(E, D, N - 1); sparse_to_list(_) -> erlang:error(badarg). %% see to_list/1 for details sparse_to_list_1(E=?NODEPATTERN(S), D, I) -> N = I div S, sparse_to_list_3(N, D, sparse_to_list_1(element(N+1, E), D, I rem S), E); sparse_to_list_1(E, _D, _I) when is_integer(E) -> []; sparse_to_list_1(E, D, I) -> sparse_push_tuple(I+1, D, E, []). sparse_to_list_2(E=?NODEPATTERN(_S), D, L) -> sparse_to_list_3(?NODESIZE, D, L, E); sparse_to_list_2(E, _D, L) when is_integer(E) -> L; sparse_to_list_2(E, D, L) -> sparse_push_tuple(?LEAFSIZE, D, E, L). sparse_to_list_3(0, _D, L, _E) -> L; sparse_to_list_3(N, D, L, E) -> sparse_to_list_3(N-1, D, sparse_to_list_2(element(N, E), D, L), E). sparse_push_tuple(0, _D, _T, L) -> L; sparse_push_tuple(N, D, T, L) -> case element(N, T) of D -> sparse_push_tuple(N - 1, D, T, L); E -> sparse_push_tuple(N - 1, D, T, [E | L]) end. -ifdef(EUNIT). sparse_to_list_test_() -> N0 = ?LEAFSIZE, [?_assert([] =:= sparse_to_list(new())), ?_assert([] =:= sparse_to_list(new(1))), ?_assert([] =:= sparse_to_list(new(1,{default,0}))), ?_assert([] =:= sparse_to_list(new(2))), ?_assert([] =:= sparse_to_list(new(2,{default,0}))), ?_assert([] =:= sparse_to_list(new(N0,{default,0}))), ?_assert([] =:= sparse_to_list(new(N0+1,{default,1}))), ?_assert([] =:= sparse_to_list(new(N0+2,{default,2}))), ?_assert([] =:= sparse_to_list(new(666,{default,6}))), ?_assert([1,2,3] =:= sparse_to_list(set(2,3,set(1,2,set(0,1,new()))))), ?_assert([3,2,1] =:= sparse_to_list(set(0,3,set(1,2,set(2,1,new()))))), ?_assert([0,1] =:= sparse_to_list(set(N0-1,1,set(0,0,new())))), ?_assert([0,1] =:= sparse_to_list(set(N0,1,set(0,0,new())))), ?_assert([0,1] =:= sparse_to_list(set(N0+1,1,set(0,0,new())))), ?_assert([0,1,2] =:= sparse_to_list(set(N0*10+1,2,set(N0*2+1,1,set(0,0,new()))))), ?_assertError(badarg, sparse_to_list(no_array)) ]. -endif. %% @equiv from_list(List, undefined) -spec from_list(List :: list(Value :: Type)) -> array(Type). from_list(List) -> from_list(List, undefined). %% @doc Convert a list to an extendible array. `Default' is used as the value %% for uninitialized entries of the array. If `List' is not a proper list, %% the call fails with reason `badarg'. %% %% @see new/2 %% @see to_list/1 -spec from_list(List :: list(Value :: Type), Default :: term()) -> array(Type). from_list([], Default) -> new({default,Default}); from_list(List, Default) when is_list(List) -> {E, N, M} = from_list_1(?LEAFSIZE, List, Default, 0, [], []), #array{size = N, max = M, default = Default, elements = E}; from_list(_, _) -> erlang:error(badarg). %% Note: A cleaner but slower algorithm is to first take the length of %% the list and compute the max size of the final tree, and then %% decompose the list. The below algorithm is almost twice as fast, %% however. %% Building the leaf nodes (padding the last one as necessary) and %% counting the total number of elements. from_list_1(0, Xs, D, N, As, Es) -> E = list_to_tuple(lists:reverse(As)), case Xs of [] -> case Es of [] -> {E, N, ?LEAFSIZE}; _ -> from_list_2_0(N, [E | Es], ?LEAFSIZE) end; [_|_] -> from_list_1(?LEAFSIZE, Xs, D, N, [], [E | Es]); _ -> erlang:error(badarg) end; from_list_1(I, Xs, D, N, As, Es) -> case Xs of [X | Xs1] -> from_list_1(I-1, Xs1, D, N+1, [X | As], Es); _ -> from_list_1(I-1, Xs, D, N, [D | As], Es) end. %% Building the internal nodes (note that the input is reversed). from_list_2_0(N, Es, S) -> from_list_2(?NODESIZE, pad((N-1) div S + 1, ?NODESIZE, S, Es), S, N, [S], []). from_list_2(0, Xs, S, N, As, Es) -> E = list_to_tuple(As), case Xs of [] -> case Es of [] -> {E, N, ?extend(S)}; _ -> from_list_2_0(N, lists:reverse([E | Es]), ?extend(S)) end; _ -> from_list_2(?NODESIZE, Xs, S, N, [S], [E | Es]) end; from_list_2(I, [X | Xs], S, N, As, Es) -> from_list_2(I-1, Xs, S, N, [X | As], Es). %% left-padding a list Es with elements P to the nearest multiple of K %% elements from N (adding 0 to K-1 elements). pad(N, K, P, Es) -> push((K - (N rem K)) rem K, P, Es). -ifdef(EUNIT). from_list_test_() -> N0 = ?LEAFSIZE, N1 = ?NODESIZE*N0, N2 = ?NODESIZE*N1, N3 = ?NODESIZE*N2, N4 = ?NODESIZE*N3, [?_assert(array:size(from_list([])) =:= 0), ?_assert(array:is_fix(from_list([])) =:= false), ?_assert(array:size(from_list([undefined])) =:= 1), ?_assert(array:is_fix(from_list([undefined])) =:= false), ?_assert(array:size(from_list(lists:seq(1,N1))) =:= N1), ?_assert(to_list(from_list(lists:seq(1,N0))) =:= lists:seq(1,N0)), ?_assert(to_list(from_list(lists:seq(1,N0+1))) =:= lists:seq(1,N0+1)), ?_assert(to_list(from_list(lists:seq(1,N0+2))) =:= lists:seq(1,N0+2)), ?_assert(to_list(from_list(lists:seq(1,N2))) =:= lists:seq(1,N2)), ?_assert(to_list(from_list(lists:seq(1,N2+1))) =:= lists:seq(1,N2+1)), ?_assert(to_list(from_list(lists:seq(0,N3))) =:= lists:seq(0,N3)), ?_assert(to_list(from_list(lists:seq(0,N4))) =:= lists:seq(0,N4)), ?_assertError(badarg, from_list([a,b,a,c|d])), ?_assertError(badarg, from_list(no_array)) ]. -endif. %% @doc Convert the array to an ordered list of pairs `{Index, Value}'. %% %% @see from_orddict/2 %% @see sparse_to_orddict/1 -spec to_orddict(Array :: array(Type)) -> indx_pairs(Value :: Type). to_orddict(#array{size = 0}) -> []; to_orddict(#array{size = N, elements = E, default = D}) -> I = N - 1, to_orddict_1(E, I, D, I); to_orddict(_) -> erlang:error(badarg). %% see to_list/1 for comparison to_orddict_1(E=?NODEPATTERN(S), R, D, I) -> N = I div S, I1 = I rem S, to_orddict_3(N, R - I1 - 1, D, to_orddict_1(element(N+1, E), R, D, I1), E, S); to_orddict_1(E, R, D, I) when is_integer(E) -> push_pairs(I+1, R, D, []); to_orddict_1(E, R, _D, I) -> push_tuple_pairs(I+1, R, E, []). to_orddict_2(E=?NODEPATTERN(S), R, D, L) -> to_orddict_3(?NODESIZE, R, D, L, E, S); to_orddict_2(E, R, D, L) when is_integer(E) -> push_pairs(E, R, D, L); to_orddict_2(E, R, _D, L) -> push_tuple_pairs(?LEAFSIZE, R, E, L). to_orddict_3(0, _R, _D, L, _E, _S) -> %% when is_integer(R) -> L; to_orddict_3(N, R, D, L, E, S) -> to_orddict_3(N-1, R - S, D, to_orddict_2(element(N, E), R, D, L), E, S). -spec push_pairs(non_neg_integer(), array_indx(), term(), indx_pairs(Type)) -> indx_pairs(Type). push_pairs(0, _I, _E, L) -> L; push_pairs(N, I, E, L) -> push_pairs(N-1, I-1, E, [{I, E} | L]). -spec push_tuple_pairs(non_neg_integer(), array_indx(), term(), indx_pairs(Type)) -> indx_pairs(Type). push_tuple_pairs(0, _I, _T, L) -> L; push_tuple_pairs(N, I, T, L) -> push_tuple_pairs(N-1, I-1, T, [{I, element(N, T)} | L]). -ifdef(EUNIT). to_orddict_test_() -> N0 = ?LEAFSIZE, [?_assert([] =:= to_orddict(new())), ?_assert([{0,undefined}] =:= to_orddict(new(1))), ?_assert([{0,undefined},{1,undefined}] =:= to_orddict(new(2))), ?_assert([{N,0}||N<-lists:seq(0,N0-1)] =:= to_orddict(new(N0,{default,0}))), ?_assert([{N,1}||N<-lists:seq(0,N0)] =:= to_orddict(new(N0+1,{default,1}))), ?_assert([{N,2}||N<-lists:seq(0,N0+1)] =:= to_orddict(new(N0+2,{default,2}))), ?_assert([{N,6}||N<-lists:seq(0,665)] =:= to_orddict(new(666,{default,6}))), ?_assert([{0,1},{1,2},{2,3}] =:= to_orddict(set(2,3,set(1,2,set(0,1,new()))))), ?_assert([{0,3},{1,2},{2,1}] =:= to_orddict(set(0,3,set(1,2,set(2,1,new()))))), ?_assert([{0,1}|[{N,0}||N<-lists:seq(1,N0-2)]++[{N0-1,1}]] =:= to_orddict(set(N0-1,1,set(0,1,new({default,0}))))), ?_assert([{0,1}|[{N,0}||N<-lists:seq(1,N0-1)]++[{N0,1}]] =:= to_orddict(set(N0,1,set(0,1,new({default,0}))))), ?_assert([{0,1}|[{N,0}||N<-lists:seq(1,N0)]++[{N0+1,1}]] =:= to_orddict(set(N0+1,1,set(0,1,new({default,0}))))), ?_assert([{0,0} | [{N,undefined}||N<-lists:seq(1,N0*2)]] ++ [{N0*2+1,1} | [{N,undefined}||N<-lists:seq(N0*2+2,N0*10)]] ++ [{N0*10+1,2}] =:= to_orddict(set(N0*10+1,2,set(N0*2+1,1,set(0,0,new()))))), ?_assertError(badarg, to_orddict(no_array)) ]. -endif. %% @doc Convert the array to an ordered list of pairs `{Index, Value}', %% skipping default-valued entries. %% %% @see to_orddict/1 -spec sparse_to_orddict(Array :: array(Type)) -> indx_pairs(Value :: Type). sparse_to_orddict(#array{size = 0}) -> []; sparse_to_orddict(#array{size = N, elements = E, default = D}) -> I = N - 1, sparse_to_orddict_1(E, I, D, I); sparse_to_orddict(_) -> erlang:error(badarg). %% see to_orddict/1 for details sparse_to_orddict_1(E=?NODEPATTERN(S), R, D, I) -> N = I div S, I1 = I rem S, sparse_to_orddict_3(N, R - I1 - 1, D, sparse_to_orddict_1(element(N+1, E), R, D, I1), E, S); sparse_to_orddict_1(E, _R, _D, _I) when is_integer(E) -> []; sparse_to_orddict_1(E, R, D, I) -> sparse_push_tuple_pairs(I+1, R, D, E, []). sparse_to_orddict_2(E=?NODEPATTERN(S), R, D, L) -> sparse_to_orddict_3(?NODESIZE, R, D, L, E, S); sparse_to_orddict_2(E, _R, _D, L) when is_integer(E) -> L; sparse_to_orddict_2(E, R, D, L) -> sparse_push_tuple_pairs(?LEAFSIZE, R, D, E, L). sparse_to_orddict_3(0, _R, _D, L, _E, _S) -> % when is_integer(R) -> L; sparse_to_orddict_3(N, R, D, L, E, S) -> sparse_to_orddict_3(N-1, R - S, D, sparse_to_orddict_2(element(N, E), R, D, L), E, S). -spec sparse_push_tuple_pairs(non_neg_integer(), array_indx(), _, _, indx_pairs(Type)) -> indx_pairs(Type). sparse_push_tuple_pairs(0, _I, _D, _T, L) -> L; sparse_push_tuple_pairs(N, I, D, T, L) -> case element(N, T) of D -> sparse_push_tuple_pairs(N-1, I-1, D, T, L); E -> sparse_push_tuple_pairs(N-1, I-1, D, T, [{I, E} | L]) end. -ifdef(EUNIT). sparse_to_orddict_test_() -> N0 = ?LEAFSIZE, [?_assert([] =:= sparse_to_orddict(new())), ?_assert([] =:= sparse_to_orddict(new(1))), ?_assert([] =:= sparse_to_orddict(new(1,{default,0}))), ?_assert([] =:= sparse_to_orddict(new(2))), ?_assert([] =:= sparse_to_orddict(new(2,{default,0}))), ?_assert([] =:= sparse_to_orddict(new(N0,{default,0}))), ?_assert([] =:= sparse_to_orddict(new(N0+1,{default,1}))), ?_assert([] =:= sparse_to_orddict(new(N0+2,{default,2}))), ?_assert([] =:= sparse_to_orddict(new(666,{default,6}))), ?_assert([{0,1},{1,2},{2,3}] =:= sparse_to_orddict(set(2,3,set(1,2,set(0,1,new()))))), ?_assert([{0,3},{1,2},{2,1}] =:= sparse_to_orddict(set(0,3,set(1,2,set(2,1,new()))))), ?_assert([{0,1},{N0-1,1}] =:= sparse_to_orddict(set(N0-1,1,set(0,1,new({default,0}))))), ?_assert([{0,1},{N0,1}] =:= sparse_to_orddict(set(N0,1,set(0,1,new({default,0}))))), ?_assert([{0,1},{N0+1,1}] =:= sparse_to_orddict(set(N0+1,1,set(0,1,new({default,0}))))), ?_assert([{0,0},{N0*2+1,1},{N0*10+1,2}] =:= sparse_to_orddict(set(N0*10+1,2,set(N0*2+1,1,set(0,0,new()))))), ?_assertError(badarg, sparse_to_orddict(no_array)) ]. -endif. %% @equiv from_orddict(Orddict, undefined) -spec from_orddict(Orddict :: indx_pairs(Value :: Type)) -> array(Type). from_orddict(Orddict) -> from_orddict(Orddict, undefined). %% @doc Convert an ordered list of pairs `{Index, Value}' to a %% corresponding extendible array. `Default' is used as the value for %% uninitialized entries of the array. If `List' is not a proper, %% ordered list of pairs whose first elements are nonnegative %% integers, the call fails with reason `badarg'. %% %% @see new/2 %% @see to_orddict/1 -spec from_orddict(Orddict :: indx_pairs(Value :: Type), Default :: Type) -> array(Type). from_orddict([], Default) -> new({default,Default}); from_orddict(List, Default) when is_list(List) -> {E, N, M} = from_orddict_0(List, 0, ?LEAFSIZE, Default, []), #array{size = N, max = M, default = Default, elements = E}; from_orddict(_, _) -> erlang:error(badarg). %% 2 pass implementation, first pass builds the needed leaf nodes %% and adds hole sizes. %% (inserts default elements for missing list entries in the leafs %% and pads the last tuple if necessary). %% Second pass builds the tree from the leafs and the holes. %% %% Doesn't build/expand unnecessary leaf nodes which costs memory %% and time for sparse arrays. from_orddict_0([], N, _Max, _D, Es) -> %% Finished, build the resulting tree case Es of [E] -> {E, N, ?LEAFSIZE}; _ -> collect_leafs(N, Es, ?LEAFSIZE) end; from_orddict_0(Xs=[{Ix1, _}|_], Ix, Max0, D, Es0) when Ix1 > Max0, is_integer(Ix1) -> %% We have a hole larger than a leaf Hole = Ix1-Ix, Step = Hole - (Hole rem ?LEAFSIZE), Next = Ix+Step, from_orddict_0(Xs, Next, Next+?LEAFSIZE, D, [Step|Es0]); from_orddict_0(Xs0=[{_, _}|_], Ix0, Max, D, Es) -> %% Fill a leaf {Xs,E,Ix} = from_orddict_1(Ix0, Max, Xs0, Ix0, D, []), from_orddict_0(Xs, Ix, Ix+?LEAFSIZE, D, [E|Es]); from_orddict_0(Xs, _, _, _,_) -> erlang:error({badarg, Xs}). from_orddict_1(Ix, Ix, Xs, N, _D, As) -> %% Leaf is full E = list_to_tuple(lists:reverse(As)), {Xs, E, N}; from_orddict_1(Ix, Max, Xs, N0, D, As) -> case Xs of [{Ix, Val} | Xs1] -> N = Ix+1, from_orddict_1(N, Max, Xs1, N, D, [Val | As]); [{Ix1, _} | _] when is_integer(Ix1), Ix1 > Ix -> N = Ix+1, from_orddict_1(N, Max, Xs, N, D, [D | As]); [_ | _] -> erlang:error({badarg, Xs}); _ -> from_orddict_1(Ix+1, Max, Xs, N0, D, [D | As]) end. %% Es is reversed i.e. starting from the largest leafs collect_leafs(N, Es, S) -> I = (N-1) div S + 1, Pad = ((?NODESIZE - (I rem ?NODESIZE)) rem ?NODESIZE) * S, case Pad of 0 -> collect_leafs(?NODESIZE, Es, S, N, [S], []); _ -> %% Pad the end collect_leafs(?NODESIZE, [Pad|Es], S, N, [S], []) end. collect_leafs(0, Xs, S, N, As, Es) -> E = list_to_tuple(As), case Xs of [] -> case Es of [] -> {E, N, ?extend(S)}; _ -> collect_leafs(N, lists:reverse([E | Es]), ?extend(S)) end; _ -> collect_leafs(?NODESIZE, Xs, S, N, [S], [E | Es]) end; collect_leafs(I, [X | Xs], S, N, As0, Es0) when is_integer(X) -> %% A hole, pad accordingly. Step0 = (X div S), if Step0 < I -> As = push(Step0, S, As0), collect_leafs(I-Step0, Xs, S, N, As, Es0); I =:= ?NODESIZE -> Step = Step0 rem ?NODESIZE, As = push(Step, S, As0), collect_leafs(I-Step, Xs, S, N, As, [X|Es0]); I =:= Step0 -> As = push(I, S, As0), collect_leafs(0, Xs, S, N, As, Es0); true -> As = push(I, S, As0), Step = Step0 - I, collect_leafs(0, [Step*S|Xs], S, N, As, Es0) end; collect_leafs(I, [X | Xs], S, N, As, Es) -> collect_leafs(I-1, Xs, S, N, [X | As], Es); collect_leafs(?NODESIZE, [], S, N, [_], Es) -> collect_leafs(N, lists:reverse(Es), ?extend(S)). -ifdef(EUNIT). from_orddict_test_() -> N0 = ?LEAFSIZE, N1 = ?NODESIZE*N0, N2 = ?NODESIZE*N1, N3 = ?NODESIZE*N2, N4 = ?NODESIZE*N3, [?_assert(array:size(from_orddict([])) =:= 0), ?_assert(array:is_fix(from_orddict([])) =:= false), ?_assert(array:size(from_orddict([{0,undefined}])) =:= 1), ?_assert(array:is_fix(from_orddict([{0,undefined}])) =:= false), ?_assert(array:size(from_orddict([{N0-1,undefined}])) =:= N0), ?_assert(array:size(from_orddict([{N,0}||N<-lists:seq(0,N1-1)])) =:= N1), ?_assertError({badarg,_}, from_orddict([foo])), ?_assertError({badarg,_}, from_orddict([{200,foo},{1,bar}])), ?_assertError({badarg,_}, from_orddict([{N,0}||N<-lists:seq(0,N0-1)] ++ not_a_list)), ?_assertError(badarg, from_orddict(no_array)), ?_assert(?LET(L, [{N,0}||N<-lists:seq(0,N0-1)], L =:= to_orddict(from_orddict(L)))), ?_assert(?LET(L, [{N,0}||N<-lists:seq(0,N0)], L =:= to_orddict(from_orddict(L)))), ?_assert(?LET(L, [{N,0}||N<-lists:seq(0,N2-1)], L =:= to_orddict(from_orddict(L)))), ?_assert(?LET(L, [{N,0}||N<-lists:seq(0,N2)], L =:= to_orddict(from_orddict(L)))), ?_assert(?LET(L, [{N,0}||N<-lists:seq(0,N3-1)], L =:= to_orddict(from_orddict(L)))), ?_assert(?LET(L, [{N,0}||N<-lists:seq(0,N4-1)], L =:= to_orddict(from_orddict(L)))), %% Hole in the begining ?_assert(?LET(L, [{0,0}], L =:= sparse_to_orddict(from_orddict(L)))), ?_assert(?LET(L, [{N0,0}], L =:= sparse_to_orddict(from_orddict(L)))), ?_assert(?LET(L, [{N1,0}], L =:= sparse_to_orddict(from_orddict(L)))), ?_assert(?LET(L, [{N3,0}], L =:= sparse_to_orddict(from_orddict(L)))), ?_assert(?LET(L, [{N4,0}], L =:= sparse_to_orddict(from_orddict(L)))), ?_assert(?LET(L, [{N0-1,0}], L =:= sparse_to_orddict(from_orddict(L)))), ?_assert(?LET(L, [{N1-1,0}], L =:= sparse_to_orddict(from_orddict(L)))), ?_assert(?LET(L, [{N3-1,0}], L =:= sparse_to_orddict(from_orddict(L)))), ?_assert(?LET(L, [{N4-1,0}], L =:= sparse_to_orddict(from_orddict(L)))), %% Hole in middle ?_assert(?LET(L, [{0,0},{N0,0}], L =:= sparse_to_orddict(from_orddict(L)))), ?_assert(?LET(L, [{0,0},{N1,0}], L =:= sparse_to_orddict(from_orddict(L)))), ?_assert(?LET(L, [{0,0},{N3,0}], L =:= sparse_to_orddict(from_orddict(L)))), ?_assert(?LET(L, [{0,0},{N4,0}], L =:= sparse_to_orddict(from_orddict(L)))), ?_assert(?LET(L, [{0,0},{N0-1,0}], L =:= sparse_to_orddict(from_orddict(L)))), ?_assert(?LET(L, [{0,0},{N1-1,0}], L =:= sparse_to_orddict(from_orddict(L)))), ?_assert(?LET(L, [{0,0},{N3-1,0}], L =:= sparse_to_orddict(from_orddict(L)))), ?_assert(?LET(L, [{0,0},{N4-1,0}], L =:= sparse_to_orddict(from_orddict(L)))) ]. -endif. %% Function = (Index::integer(), Value::term()) -> term() %% @doc Map the given function onto each element of the array. The %% elements are visited in order from the lowest index to the highest. %% If `Function' is not a function, the call fails with reason `badarg'. %% %% @see foldl/3 %% @see foldr/3 %% @see sparse_map/2 -spec map(Function, Array :: array(Type1)) -> array(Type2) when Function :: fun((Index :: array_indx(), Type1) -> Type2). map(Function, Array=#array{size = N, elements = E, default = D}) when is_function(Function, 2) -> if N > 0 -> A = Array#array{elements = []}, % kill reference, for GC A#array{elements = map_1(N-1, E, 0, Function, D)}; true -> Array end; map(_, _) -> erlang:error(badarg). %% It might be simpler to traverse the array right-to-left, as done e.g. %% in the to_orddict/1 function, but it is better to guarantee %% left-to-right application over the elements - that is more likely to %% be a generally useful property. map_1(N, E=?NODEPATTERN(S), Ix, F, D) -> list_to_tuple(lists:reverse([S | map_2(1, E, Ix, F, D, [], N div S + 1, N rem S, S)])); map_1(N, E, Ix, F, D) when is_integer(E) -> map_1(N, unfold(E, D), Ix, F, D); map_1(N, E, Ix, F, D) -> list_to_tuple(lists:reverse(map_3(1, E, Ix, F, D, N+1, []))). map_2(I, E, Ix, F, D, L, I, R, _S) -> map_2_1(I+1, E, [map_1(R, element(I, E), Ix, F, D) | L]); map_2(I, E, Ix, F, D, L, N, R, S) -> map_2(I+1, E, Ix + S, F, D, [map_1(S-1, element(I, E), Ix, F, D) | L], N, R, S). map_2_1(I, E, L) when I =< ?NODESIZE -> map_2_1(I+1, E, [element(I, E) | L]); map_2_1(_I, _E, L) -> L. -spec map_3(pos_integer(), _, array_indx(), fun((array_indx(),_) -> _), _, non_neg_integer(), [X]) -> [X]. map_3(I, E, Ix, F, D, N, L) when I =< N -> map_3(I+1, E, Ix+1, F, D, N, [F(Ix, element(I, E)) | L]); map_3(I, E, Ix, F, D, N, L) when I =< ?LEAFSIZE -> map_3(I+1, E, Ix+1, F, D, N, [D | L]); map_3(_I, _E, _Ix, _F, _D, _N, L) -> L. unfold(S, _D) when S > ?LEAFSIZE -> ?NEW_NODE(?reduce(S)); unfold(_S, D) -> ?NEW_LEAF(D). -ifdef(EUNIT). map_test_() -> N0 = ?LEAFSIZE, Id = fun (_,X) -> X end, Plus = fun(N) -> fun (_,X) -> X+N end end, Default = fun(_K,undefined) -> no_value; (K,V) -> K+V end, [?_assertError(badarg, map([], new())), ?_assertError(badarg, map([], new(10))), ?_assert(to_list(map(Id, new())) =:= []), ?_assert(to_list(map(Id, new(1))) =:= [undefined]), ?_assert(to_list(map(Id, new(5,{default,0}))) =:= [0,0,0,0,0]), ?_assert(to_list(map(Id, from_list([1,2,3,4]))) =:= [1,2,3,4]), ?_assert(to_list(map(Plus(1), from_list([0,1,2,3]))) =:= [1,2,3,4]), ?_assert(to_list(map(Plus(-1), from_list(lists:seq(1,11)))) =:= lists:seq(0,10)), ?_assert(to_list(map(Plus(11), from_list(lists:seq(0,99999)))) =:= lists:seq(11,100010)), ?_assert([{0,0},{N0*2+1,N0*2+1+1},{N0*100+1,N0*100+1+2}] =:= sparse_to_orddict((map(Default, set(N0*100+1,2, set(N0*2+1,1, set(0,0,new())))))#array{default = no_value})) ]. -endif. %% Function = (Index::integer(), Value::term()) -> term() %% @doc Map the given function onto each element of the array, skipping %% default-valued entries. The elements are visited in order from the %% lowest index to the highest. If `Function' is not a function, the %% call fails with reason `badarg'. %% %% @see map/2 -spec sparse_map(Function, Array :: array(Type1)) -> array(Type2) when Function :: fun((Index :: array_indx(), Type1) -> Type2). sparse_map(Function, Array=#array{size = N, elements = E, default = D}) when is_function(Function, 2) -> if N > 0 -> A = Array#array{elements = []}, % kill reference, for GC A#array{elements = sparse_map_1(N-1, E, 0, Function, D)}; true -> Array end; sparse_map(_, _) -> erlang:error(badarg). %% see map/2 for details %% TODO: we can probably optimize away the use of div/rem here sparse_map_1(N, E=?NODEPATTERN(S), Ix, F, D) -> list_to_tuple(lists:reverse([S | sparse_map_2(1, E, Ix, F, D, [], N div S + 1, N rem S, S)])); sparse_map_1(_N, E, _Ix, _F, _D) when is_integer(E) -> E; sparse_map_1(_N, E, Ix, F, D) -> list_to_tuple(lists:reverse(sparse_map_3(1, E, Ix, F, D, []))). sparse_map_2(I, E, Ix, F, D, L, I, R, _S) -> sparse_map_2_1(I+1, E, [sparse_map_1(R, element(I, E), Ix, F, D) | L]); sparse_map_2(I, E, Ix, F, D, L, N, R, S) -> sparse_map_2(I+1, E, Ix + S, F, D, [sparse_map_1(S-1, element(I, E), Ix, F, D) | L], N, R, S). sparse_map_2_1(I, E, L) when I =< ?NODESIZE -> sparse_map_2_1(I+1, E, [element(I, E) | L]); sparse_map_2_1(_I, _E, L) -> L. -spec sparse_map_3(pos_integer(), _, array_indx(), fun((array_indx(),_) -> _), _, [X]) -> [X]. sparse_map_3(I, T, Ix, F, D, L) when I =< ?LEAFSIZE -> case element(I, T) of D -> sparse_map_3(I+1, T, Ix+1, F, D, [D | L]); E -> sparse_map_3(I+1, T, Ix+1, F, D, [F(Ix, E) | L]) end; sparse_map_3(_I, _E, _Ix, _F, _D, L) -> L. -ifdef(EUNIT). sparse_map_test_() -> N0 = ?LEAFSIZE, Id = fun (_,X) -> X end, Plus = fun(N) -> fun (_,X) -> X+N end end, KeyPlus = fun (K,X) -> K+X end, [?_assertError(badarg, sparse_map([], new())), ?_assertError(badarg, sparse_map([], new(10))), ?_assert(to_list(sparse_map(Id, new())) =:= []), ?_assert(to_list(sparse_map(Id, new(1))) =:= [undefined]), ?_assert(to_list(sparse_map(Id, new(5,{default,0}))) =:= [0,0,0,0,0]), ?_assert(to_list(sparse_map(Id, from_list([1,2,3,4]))) =:= [1,2,3,4]), ?_assert(to_list(sparse_map(Plus(1), from_list([0,1,2,3]))) =:= [1,2,3,4]), ?_assert(to_list(sparse_map(Plus(-1), from_list(lists:seq(1,11)))) =:= lists:seq(0,10)), ?_assert(to_list(sparse_map(Plus(11), from_list(lists:seq(0,99999)))) =:= lists:seq(11,100010)), ?_assert(to_list(sparse_map(Plus(1), set(1,1,new({default,0})))) =:= [0,2]), ?_assert(to_list(sparse_map(Plus(1), set(3,4,set(0,1,new({default,0}))))) =:= [2,0,0,5]), ?_assert(to_list(sparse_map(Plus(1), set(9,9,set(1,1,new({default,0}))))) =:= [0,2,0,0,0,0,0,0,0,10]), ?_assert([{0,0},{N0*2+1,N0*2+1+1},{N0*100+1,N0*100+1+2}] =:= sparse_to_orddict(sparse_map(KeyPlus, set(N0*100+1,2, set(N0*2+1,1, set(0,0,new())))))) ]. -endif. %% @doc Fold the elements of the array using the given function and %% initial accumulator value. The elements are visited in order from the %% lowest index to the highest. If `Function' is not a function, the %% call fails with reason `badarg'. %% %% @see foldr/3 %% @see map/2 %% @see sparse_foldl/3 -spec foldl(Function, InitialAcc :: A, Array :: array(Type)) -> B when Function :: fun((Index :: array_indx(), Value :: Type, Acc :: A) -> B). foldl(Function, A, #array{size = N, elements = E, default = D}) when is_function(Function, 3) -> if N > 0 -> foldl_1(N-1, E, A, 0, Function, D); true -> A end; foldl(_, _, _) -> erlang:error(badarg). foldl_1(N, E=?NODEPATTERN(S), A, Ix, F, D) -> foldl_2(1, E, A, Ix, F, D, N div S + 1, N rem S, S); foldl_1(N, E, A, Ix, F, D) when is_integer(E) -> foldl_1(N, unfold(E, D), A, Ix, F, D); foldl_1(N, E, A, Ix, F, _D) -> foldl_3(1, E, A, Ix, F, N+1). foldl_2(I, E, A, Ix, F, D, I, R, _S) -> foldl_1(R, element(I, E), A, Ix, F, D); foldl_2(I, E, A, Ix, F, D, N, R, S) -> foldl_2(I+1, E, foldl_1(S-1, element(I, E), A, Ix, F, D), Ix + S, F, D, N, R, S). -spec foldl_3(pos_integer(), _, A, array_indx(), fun((array_indx(), _, A) -> B), integer()) -> B. foldl_3(I, E, A, Ix, F, N) when I =< N -> foldl_3(I+1, E, F(Ix, element(I, E), A), Ix+1, F, N); foldl_3(_I, _E, A, _Ix, _F, _N) -> A. -ifdef(EUNIT). foldl_test_() -> N0 = ?LEAFSIZE, Count = fun (_,_,N) -> N+1 end, Sum = fun (_,X,N) -> N+X end, Reverse = fun (_,X,L) -> [X|L] end, Vals = fun(_K,undefined,{C,L}) -> {C+1,L}; (K,X,{C,L}) -> {C,[K+X|L]} end, [?_assertError(badarg, foldl([], 0, new())), ?_assertError(badarg, foldl([], 0, new(10))), ?_assert(foldl(Count, 0, new()) =:= 0), ?_assert(foldl(Count, 0, new(1)) =:= 1), ?_assert(foldl(Count, 0, new(10)) =:= 10), ?_assert(foldl(Count, 0, from_list([1,2,3,4])) =:= 4), ?_assert(foldl(Count, 10, from_list([0,1,2,3,4,5,6,7,8,9])) =:= 20), ?_assert(foldl(Count, 1000, from_list(lists:seq(0,999))) =:= 2000), ?_assert(foldl(Sum, 0, from_list(lists:seq(0,10))) =:= 55), ?_assert(foldl(Reverse, [], from_list(lists:seq(0,1000))) =:= lists:reverse(lists:seq(0,1000))), ?_assert({999,[N0*100+1+2,N0*2+1+1,0]} =:= foldl(Vals, {0,[]}, set(N0*100+1,2, set(N0*2+1,1, set(0,0,new()))))) ]. -endif. %% @doc Fold the elements of the array using the given function and %% initial accumulator value, skipping default-valued entries. The %% elements are visited in order from the lowest index to the highest. %% If `Function' is not a function, the call fails with reason `badarg'. %% %% @see foldl/3 %% @see sparse_foldr/3 -spec sparse_foldl(Function, InitialAcc :: A, Array :: array(Type)) -> B when Function :: fun((Index :: array_indx(), Value :: Type, Acc :: A) -> B). sparse_foldl(Function, A, #array{size = N, elements = E, default = D}) when is_function(Function, 3) -> if N > 0 -> sparse_foldl_1(N-1, E, A, 0, Function, D); true -> A end; sparse_foldl(_, _, _) -> erlang:error(badarg). %% see foldl/3 for details %% TODO: this can be optimized sparse_foldl_1(N, E=?NODEPATTERN(S), A, Ix, F, D) -> sparse_foldl_2(1, E, A, Ix, F, D, N div S + 1, N rem S, S); sparse_foldl_1(_N, E, A, _Ix, _F, _D) when is_integer(E) -> A; sparse_foldl_1(N, E, A, Ix, F, D) -> sparse_foldl_3(1, E, A, Ix, F, D, N+1). sparse_foldl_2(I, E, A, Ix, F, D, I, R, _S) -> sparse_foldl_1(R, element(I, E), A, Ix, F, D); sparse_foldl_2(I, E, A, Ix, F, D, N, R, S) -> sparse_foldl_2(I+1, E, sparse_foldl_1(S-1, element(I, E), A, Ix, F, D), Ix + S, F, D, N, R, S). sparse_foldl_3(I, T, A, Ix, F, D, N) when I =< N -> case element(I, T) of D -> sparse_foldl_3(I+1, T, A, Ix+1, F, D, N); E -> sparse_foldl_3(I+1, T, F(Ix, E, A), Ix+1, F, D, N) end; sparse_foldl_3(_I, _T, A, _Ix, _F, _D, _N) -> A. -ifdef(EUNIT). sparse_foldl_test_() -> N0 = ?LEAFSIZE, Count = fun (_,_,N) -> N+1 end, Sum = fun (_,X,N) -> N+X end, Reverse = fun (_,X,L) -> [X|L] end, Vals = fun(_K,undefined,{C,L}) -> {C+1,L}; (K,X,{C,L}) -> {C,[K+X|L]} end, [?_assertError(badarg, sparse_foldl([], 0, new())), ?_assertError(badarg, sparse_foldl([], 0, new(10))), ?_assert(sparse_foldl(Count, 0, new()) =:= 0), ?_assert(sparse_foldl(Count, 0, new(1)) =:= 0), ?_assert(sparse_foldl(Count, 0, new(10,{default,1})) =:= 0), ?_assert(sparse_foldl(Count, 0, from_list([0,1,2,3,4],0)) =:= 4), ?_assert(sparse_foldl(Count, 0, from_list([0,1,2,3,4,5,6,7,8,9,0],0)) =:= 9), ?_assert(sparse_foldl(Count, 0, from_list(lists:seq(0,999),0)) =:= 999), ?_assert(sparse_foldl(Sum, 0, from_list(lists:seq(0,10), 5)) =:= 50), ?_assert(sparse_foldl(Reverse, [], from_list(lists:seq(0,1000), 0)) =:= lists:reverse(lists:seq(1,1000))), ?_assert({0,[N0*100+1+2,N0*2+1+1,0]} =:= sparse_foldl(Vals, {0,[]}, set(N0*100+1,2, set(N0*2+1,1, set(0,0,new()))))) ]. -endif. %% @doc Fold the elements of the array right-to-left using the given %% function and initial accumulator value. The elements are visited in %% order from the highest index to the lowest. If `Function' is not a %% function, the call fails with reason `badarg'. %% %% @see foldl/3 %% @see map/2 -spec foldr(Function, InitialAcc :: A, Array :: array(Type)) -> B when Function :: fun((Index :: array_indx(), Value :: Type, Acc :: A) -> B). foldr(Function, A, #array{size = N, elements = E, default = D}) when is_function(Function, 3) -> if N > 0 -> I = N - 1, foldr_1(I, E, I, A, Function, D); true -> A end; foldr(_, _, _) -> erlang:error(badarg). %% this is based on to_orddict/1 foldr_1(I, E=?NODEPATTERN(S), Ix, A, F, D) -> foldr_2(I div S + 1, E, Ix, A, F, D, I rem S, S-1); foldr_1(I, E, Ix, A, F, D) when is_integer(E) -> foldr_1(I, unfold(E, D), Ix, A, F, D); foldr_1(I, E, Ix, A, F, _D) -> I1 = I+1, foldr_3(I1, E, Ix-I1, A, F). foldr_2(0, _E, _Ix, A, _F, _D, _R, _R0) -> A; foldr_2(I, E, Ix, A, F, D, R, R0) -> foldr_2(I-1, E, Ix - R - 1, foldr_1(R, element(I, E), Ix, A, F, D), F, D, R0, R0). -spec foldr_3(array_indx(), term(), integer(), A, fun((array_indx(), _, A) -> B)) -> B. foldr_3(0, _E, _Ix, A, _F) -> A; foldr_3(I, E, Ix, A, F) -> foldr_3(I-1, E, Ix, F(Ix+I, element(I, E), A), F). -ifdef(EUNIT). foldr_test_() -> N0 = ?LEAFSIZE, Count = fun (_,_,N) -> N+1 end, Sum = fun (_,X,N) -> N+X end, List = fun (_,X,L) -> [X|L] end, Vals = fun(_K,undefined,{C,L}) -> {C+1,L}; (K,X,{C,L}) -> {C,[K+X|L]} end, [?_assertError(badarg, foldr([], 0, new())), ?_assertError(badarg, foldr([], 0, new(10))), ?_assert(foldr(Count, 0, new()) =:= 0), ?_assert(foldr(Count, 0, new(1)) =:= 1), ?_assert(foldr(Count, 0, new(10)) =:= 10), ?_assert(foldr(Count, 0, from_list([1,2,3,4])) =:= 4), ?_assert(foldr(Count, 10, from_list([0,1,2,3,4,5,6,7,8,9])) =:= 20), ?_assert(foldr(Count, 1000, from_list(lists:seq(0,999))) =:= 2000), ?_assert(foldr(Sum, 0, from_list(lists:seq(0,10))) =:= 55), ?_assert(foldr(List, [], from_list(lists:seq(0,1000))) =:= lists:seq(0,1000)), ?_assert({999,[0,N0*2+1+1,N0*100+1+2]} =:= foldr(Vals, {0,[]}, set(N0*100+1,2, set(N0*2+1,1, set(0,0,new()))))) ]. -endif. %% @doc Fold the elements of the array right-to-left using the given %% function and initial accumulator value, skipping default-valued %% entries. The elements are visited in order from the highest index to %% the lowest. If `Function' is not a function, the call fails with %% reason `badarg'. %% %% @see foldr/3 %% @see sparse_foldl/3 -spec sparse_foldr(Function, InitialAcc :: A, Array :: array(Type)) -> B when Function :: fun((Index :: array_indx(), Value :: Type, Acc :: A) -> B). sparse_foldr(Function, A, #array{size = N, elements = E, default = D}) when is_function(Function, 3) -> if N > 0 -> I = N - 1, sparse_foldr_1(I, E, I, A, Function, D); true -> A end; sparse_foldr(_, _, _) -> erlang:error(badarg). %% see foldr/3 for details %% TODO: this can be optimized sparse_foldr_1(I, E=?NODEPATTERN(S), Ix, A, F, D) -> sparse_foldr_2(I div S + 1, E, Ix, A, F, D, I rem S, S-1); sparse_foldr_1(_I, E, _Ix, A, _F, _D) when is_integer(E) -> A; sparse_foldr_1(I, E, Ix, A, F, D) -> I1 = I+1, sparse_foldr_3(I1, E, Ix-I1, A, F, D). sparse_foldr_2(0, _E, _Ix, A, _F, _D, _R, _R0) -> A; sparse_foldr_2(I, E, Ix, A, F, D, R, R0) -> sparse_foldr_2(I-1, E, Ix - R - 1, sparse_foldr_1(R, element(I, E), Ix, A, F, D), F, D, R0, R0). -spec sparse_foldr_3(array_indx(), _, array_indx(), A, fun((array_indx(), _, A) -> B), _) -> B. sparse_foldr_3(0, _T, _Ix, A, _F, _D) -> A; sparse_foldr_3(I, T, Ix, A, F, D) -> case element(I, T) of D -> sparse_foldr_3(I-1, T, Ix, A, F, D); E -> sparse_foldr_3(I-1, T, Ix, F(Ix+I, E, A), F, D) end. %% @doc Get the number of entries in the array up until the last %% non-default valued entry. In other words, returns `I+1' if `I' is the %% last non-default valued entry in the array, or zero if no such entry %% exists. %% @see size/1 %% @see resize/1 -spec sparse_size(Array :: array()) -> non_neg_integer(). sparse_size(A) -> F = fun (I, _V, _A) -> throw({value, I}) end, try sparse_foldr(F, [], A) of [] -> 0 catch {value, I} -> I + 1 end. -ifdef(EUNIT). sparse_foldr_test_() -> N0 = ?LEAFSIZE, Count = fun (_,_,N) -> N+1 end, Sum = fun (_,X,N) -> N+X end, List = fun (_,X,L) -> [X|L] end, Vals = fun(_K,undefined,{C,L}) -> {C+1,L}; (K,X,{C,L}) -> {C,[K+X|L]} end, [?_assertError(badarg, sparse_foldr([], 0, new())), ?_assertError(badarg, sparse_foldr([], 0, new(10))), ?_assert(sparse_foldr(Count, 0, new()) =:= 0), ?_assert(sparse_foldr(Count, 0, new(1)) =:= 0), ?_assert(sparse_foldr(Count, 0, new(10,{default,1})) =:= 0), ?_assert(sparse_foldr(Count, 0, from_list([0,1,2,3,4],0)) =:= 4), ?_assert(sparse_foldr(Count, 0, from_list([0,1,2,3,4,5,6,7,8,9,0],0)) =:= 9), ?_assert(sparse_foldr(Count, 0, from_list(lists:seq(0,999),0)) =:= 999), ?_assert(sparse_foldr(Sum, 0, from_list(lists:seq(0,10),5)) =:= 50), ?_assert(sparse_foldr(List, [], from_list(lists:seq(0,1000),0)) =:= lists:seq(1,1000)), ?_assert(sparse_size(new()) =:= 0), ?_assert(sparse_size(new(8)) =:= 0), ?_assert(sparse_size(array:set(7, 0, new())) =:= 8), ?_assert(sparse_size(array:set(7, 0, new(10))) =:= 8), ?_assert(sparse_size(array:set(99, 0, new(10,{fixed,false}))) =:= 100), ?_assert(sparse_size(array:set(7, undefined, new())) =:= 0), ?_assert(sparse_size(array:from_list([1,2,3,undefined])) =:= 3), ?_assert(sparse_size(array:from_orddict([{3,0},{17,0},{99,undefined}])) =:= 18), ?_assert({0,[0,N0*2+1+1,N0*100+1+2]} =:= sparse_foldr(Vals, {0,[]}, set(N0*100+1,2, set(N0*2+1,1, set(0,0,new()))))) ]. -endif.