defmodule A.Vector do @moduledoc """ A Clojure-like persistent vector with efficient appends and random access. [Persistent vectors](https://hypirion.com/musings/understanding-persistent-vector-pt-1) are an efficient alternative to lists. Many operations for `A.Vector` run in effective constant time (length, random access, appends...), unlike linked lists for which most operations run in linear time. Functions that need to go through the whole collection like `map/2` or `foldl/3` are as often fast as their list equivalents, or sometimes even slightly faster. Vectors also use less memory than lists for "big" collections (see the [Memory usage section](#module-memory-usage)). Make sure to read the [Efficiency guide section](#module-efficiency-guide) to get the best performance out of vectors. Erlang's [`:array`](http://erlang.org/doc/man/array.html) module offer similar functionalities. However `A.Vector`: - is a better Elixir citizen: pipe-friendliness, `Access` behaviour, `Enum` / `Inspect` / `Collectable` protocols - should have higher performance in most use cases, especially "loops" like `map/2` / `to_list/1` / `foldl/3` - mirrors the `Enum` module API, with highly optimized versions for vectors (`join/1`, `sum/1`, `random/1`...) - supports negative indexing (e.g. `-1` corresponds to the last element) - optionally implements the `Jason.Encoder` protocol if `Jason` is installed Note: most of the design is inspired by [this series of blog posts](https://hypirion.com/musings/understanding-persistent-vector-pt-1), but a branching factor of `16 = 2 ^ 4` has been picked instead of `32 = 2 ^ 5`. This choice was made following performance benchmarking that showed better overall performance for this particular implementation. ## Examples iex> vector = A.Vector.new(1..10) #A iex> A.Vector.append(vector, :foo) #A iex> vector[3] 4 iex> A.Vector.replace_at(vector, -1, :bar) #A iex> 3 in vector true ## Access behaviour `A.Vector` implements the `Access` behaviour. iex> vector = A.Vector.new(1..10) iex> vector[3] 4 iex> put_in(vector[5], :foo) #A iex> {9, updated} = pop_in(vector[8]); updated #A ## Convenience [`vec/1`](`A.vec/1`) and [`vec_size/1`](`A.vec_size/1`) macros The `A.Vector` module can be used without any macro. The `A.vec/1` macro does however provide some syntactic sugar to make it more convenient to work with vectors of known size, namely: - pattern match on elements for vectors of known size - construct new vectors of known size faster, by generating the AST at compile time Examples: iex> import A iex> vec([1, 2, 3]) #A iex> vec([1, 2, var, _, _, _]) = A.Vector.new(1..6); var 3 The `A.vec_size/1` macro can be used in guards: iex> import A iex> match?(v when vec_size(v) > 99, A.Vector.new(1..100)) true ## Pattern-matching and opaque type An `A.Vector` is represented internally using the `%A.Vector{}` struct. This struct can be used whenever there's a need to pattern match on something being an `A.Vector`: iex> match?(%A.Vector{}, A.Vector.new()) true Note, however, than `A.Vector` is an [opaque type](https://hexdocs.pm/elixir/typespecs.html#user-defined-types): its struct internal fields must not be accessed directly. As discussed in the previous section, [`vec/1`](`A.vec/1`) makes it possible to pattern match on size and elements as well as checking the type. ## Memory usage Vectors have a small overhead over lists for smaller collections, but are using far less memory for bigger collections: iex> memory_for = fn n -> [Enum.to_list(1..n), A.Vector.new(1..n)] |> Enum.map(&:erts_debug.size/1) end iex> memory_for.(1) [2, 28] iex> memory_for.(10) [20, 28] iex> memory_for.(100) [200, 150] iex> memory_for.(10_000) [20000, 11370] If you need to work with vectors containing mostly the same value, `A.Vector.duplicate/2` is highly efficient both in time and memory (logarithmic). It minimizes the number of actual copies and reuses the same nested structures under the hood: iex> A.Vector.duplicate(0, 10_000) |> :erts_debug.size() 116 iex> A.Vector.duplicate(0, 10_000) |> :erts_debug.flat_size() # when shared over processes / ETS 11370 Even a 1B x 1B matrix of the same element costs virtually nothing! big_n = 1_000_000_000 0 |> A.Vector.duplicate(big_n) |> A.Vector.duplicate(big_n) |> :erts_debug.size() 538 ## Efficiency guide If you are using vectors and not lists, chances are that you care about performance. Here are a couple notes about how to use vectors in an optimal way. Most functions from this module are highly efficient, those that are not will indicate it in their documentation. But remember the golden rule: **in case of doubt, always benchmark**. ### Avoid prepending Appending is very efficient, but prepending is highly inefficient since the whole array needs to be reconstructed. **DON'T** A.Vector.prepend(vector, :foo) **DO** [:foo | list] # use lists A.Vector.append(vector, :foo) ### Avoid deletions This implementation of persistent vectors has many advantages, but it does not support efficient deletion, with the exception of the last element that can be popped very efficiently (`A.Vector.pop_last/1`, `A.Vector.delete_last/1`). Deleting close to the end of the vector is still fairly fast, but deleting near the beginning needs to reconstruct most of the vector. Deletion functionality is provided through functions like `A.Vector.pop_at/3` and `A.Vector.delete_at/2` for the sake of completion, but please note that they are inefficient and their usage is discouraged. If you need to be able to pop arbitrary indexes, chances are you should consider an alternative data structure. Another possibility could be to use sparse arrays, defining `nil` as a deleted value (but then the indexing and size won't reflect this). **DON'T** A.Vector.pop_at(vector, 3) A.Vector.delete_at(vector, 3) pop_in(vector[3]) **DO** A.Vector.pop_last(vector) A.Vector.delete_last(vector) A.Vector.delete_at(vector, -3) # close to the end A.Vector.replace_at(vector, 3, nil) ### Successive appends If you just need to append all elements of an enumerable, it is more efficient to use `A.Vector.concat/2` than successive calls to `A.Vector.append/2`: **DON'T** Enum.reduce(enumerable, vector, fn val, acc -> A.Vector.append(acc, val) end) Enum.into(enumerable, vector) **DO** A.Vector.concat(vector, enumerable) ### Prefer `A.Vector` to `Enum` for vectors Many functions provided in this module are very efficient and should be used over `Enum` functions whenever possible, even if `A.Vector` implements the `Enumerable` and `Collectable` protocols for convienience: **DON'T** Enum.sum(vector) Enum.to_list(vector) Enum.reduce(vector, [], fun) Enum.into(enumerable, %A.Vector.new()) Enum.into(enumerable, vector) **DO** A.Vector.sum(vector) A.Vector.to_list(vector) A.Vector.foldl(vector, [], fun) A.Vector.new(enumerable) A.Vector.concat(vector, enumerable) `for` comprehensions are actually using `Enumerable` as well, so the same advice holds: **DON'T** for value <- vector do do_stuff() end **DO** for value <- A.Vector.to_list(vector) do do_stuff() end ### Exceptions: `Enum` optimized functions `Enum.member?/2` is implemented in an efficient way, so `in/2` is optimal: **DO** 33 in vector `Enum.slice/2` and `Enum.slice/3` are optimized and their use is encouraged, other "slicing" functions like `Enum.take/2` or `Enum.drop/2` however are inefficient: **DON'T** Enum.take(vector, 10) Enum.drop(vector, 25) **DO** Enum.slice(vector, 0, 10) Enum.slice(vector, 0..10) Enum.slice(vector, 25..-1) ### Slicing optimization Slicing any subset on the left on the vector using methods from `A.Vector` is extremely efficient as the vector internals can be reused: **DO** A.Vector.take(vector, 10) # take a positive amount A.Vector.drop(vector, -20) # drop a negative amount A.Vector.slice(vector, 0, 10) # slicing from 0 A.Vector.slice(vector, 0..-5) # slicing from 0 ### `A.Vector` and `Enum` APIs Not all `Enum` functions have been mirrored in `A.Vector`, but you can try either to: - use `A.Vector.foldl/3` or `A.Vector.foldr/3` to implement it (the latter is better to build lists) - call `A.Vector.to_list/1` before using `Enum` Also, it is worth noting that several `A.Vector` functions return vectors, not lists like their `Enum` counterpart: iex> vector = A.Vector.new(1..10) iex> A.Vector.map(vector, & (&1 * 7)) #A iex> A.Vector.reverse(vector) #A ### Additional notes * If you need to work with vectors containing mostly the same value, use `A.Vector.duplicate/2` (more details in the [Memory usage section](#module-memory-usage)). * If you work with functions returning vectors of known size, you can use the `A.vec/1` macro to defer the generation of the AST for the internal structure to compile time instead of runtime. A.Vector.new([a, 1, 2, 3, 4]) # structure created at runtime vec([a, 1, 2, 3, 4]) # structure AST defined at compile time """ alias A.Vector.{EmptyError, IndexError, Raw} require Raw @behaviour Access @type index :: integer @type value :: term @opaque t(value) :: %__MODULE__{__vector__: Raw.t(value)} @enforce_keys [:__vector__] defstruct [:__vector__] @type t :: t(value) @empty_raw Raw.empty() @doc """ Returns the number of elements in `vector`. Runs in constant time. ## Examples iex> A.Vector.new(10_000..20_000) |> A.Vector.size() 10001 iex> A.Vector.new() |> A.Vector.size() 0 """ @compile {:inline, size: 1} @spec size(t()) :: non_neg_integer def size(%__MODULE__{__vector__: internal}) do Raw.size(internal) end @doc """ Returns a new empty vector. ## Examples iex> A.Vector.new() #A """ @compile {:inline, new: 0} @spec new :: t() def new() do %__MODULE__{__vector__: @empty_raw} end @doc """ Creates a vector from an `enumerable`. Runs in linear time. ## Examples iex> A.Vector.new(10..25) #A """ @spec new(Enumerable.t()) :: t() def new(%__MODULE__{} = vector) do vector end def new(enumerable) do %__MODULE__{ __vector__: Raw.new(enumerable) } end @doc """ Creates a vector from an `enumerable` via the given `transform` function. ## Examples iex> A.Vector.new(1..10, &(&1 * &1)) #A """ @spec new(Enumerable.t(), (v1 -> v2)) :: t(v2) when v1: value, v2: value def new(enumerable, fun) when is_function(fun, 1) do case enumerable do %__MODULE__{} -> map(enumerable, fun) _ -> %__MODULE__{ __vector__: Raw.new(enumerable, fun) } end end @doc """ Duplicates the given element `n` times in a vector. `n` is an integer greater than or equal to `0`. If `n` is `0`, an empty list is returned. Runs in logarithmic time regarding `n`. It is very fast and memory efficient (see [Memory usage](#module-memory-usage)). ## Examples iex> A.Vector.duplicate(nil, 10) #A iex> A.Vector.duplicate(:foo, 0) #A """ @spec duplicate(val, non_neg_integer) :: t(val) when val: value def duplicate(value, n) when is_integer(n) and n >= 0 do %__MODULE__{ __vector__: Raw.duplicate(value, n) } end @doc """ Populates a vector of size `n` by calling `generator_fun` repeatedly. ## Examples # Although not necessary, let's seed the random algorithm iex> :rand.seed(:exsplus, {1, 2, 3}) iex> A.Vector.repeatedly(&:rand.uniform/0, 3) #A """ def repeatedly(generator_fun, n) when is_function(generator_fun, 0) and is_integer(n) and n >= 0 do %__MODULE__{ __vector__: A.List.repeatedly(generator_fun, n) |> Raw.from_list() } end @doc """ Appends a `value` at the end of a `vector`. Runs in effective constant time. ## Examples iex> A.Vector.new() |> A.Vector.append(:foo) #A iex> A.Vector.new(1..5) |> A.Vector.append(:foo) #A """ @spec append(t(val), val) :: t(val) when val: value def append(%__MODULE__{__vector__: internal}, value) do %__MODULE__{ __vector__: Raw.append(internal, value) } end @doc """ Appends all values from an `enumerable` at the end of a `vector`. Runs in effective linear time in respect with the length of `enumerable`, disregarding the size of the `vector`. ## Examples iex> A.Vector.new(1..5) |> A.Vector.concat(10..15) #A iex> A.Vector.new() |> A.Vector.concat(10..15) #A """ @spec concat(t(val), Enumerable.t()) :: t(val) when val: value def concat(%__MODULE__{__vector__: internal}, enumerable) do list = A.FastEnum.to_list(enumerable) %__MODULE__{ __vector__: Raw.concat(internal, list) } end @deprecated "Use A.Vector.concat/2 instead" defdelegate append_many(vector, enumerable), to: __MODULE__, as: :concat @doc """ (Inefficient) Prepends `value` at the beginning of the `vector`. Runs in linear time because the whole vector needs to be reconstructuded, and should be avoided. ## Examples iex> A.Vector.new() |> A.Vector.prepend(:foo) #A iex> A.Vector.new(1..5) |> A.Vector.prepend(:foo) #A """ @spec prepend(t(val), val) :: t(val) when val: value def prepend(%__MODULE__{__vector__: internal}, value) do %__MODULE__{ __vector__: Raw.prepend(internal, value) } end @doc """ Returns the first element in the `vector` or `default` if `vector` is empty. Runs in effective constant time. ## Examples iex> A.Vector.new(1..10_000) |> A.Vector.first() 1 iex> A.Vector.new() |> A.Vector.first() nil """ @spec first(t(val), default) :: val | default when val: value, default: term def first(vector, default \\ nil) def first(%__MODULE__{__vector__: internal}, default) do Raw.first(internal, default) end @doc """ Returns the last element in the `vector` or `default` if `vector` is empty. Runs in constant time (actual, not effective). ## Examples iex> A.Vector.new(1..10_000) |> A.Vector.last() 10_000 iex> A.Vector.new() |> A.Vector.last() nil """ @spec last(t(val), default) :: val | default when val: value, default: term def last(vector, default \\ nil) def last(%__MODULE__{__vector__: internal}, default) do Raw.last(internal, default) end @doc """ Finds the element at the given `index` (zero-based), and returns it in a ok-entry. If the `index` does not exist, returns `:error`. Supports negative indexing from the end of the `vector`. Runs in effective constant time. ## Examples iex> A.Vector.new(1..1_000) |> A.Vector.fetch(555) {:ok, 556} iex> A.Vector.new(1..1_000) |> A.Vector.fetch(1_000) :error iex> A.Vector.new(1..1_000) |> A.Vector.fetch(-1) {:ok, 1000} """ @impl Access @spec fetch(t(val), index) :: {:ok, val} | :error when val: value def fetch(vector, index) def fetch(%__MODULE__{__vector__: internal}, index) when is_integer(index) do Raw.fetch_any(internal, index) end @doc """ Finds the element at the given `index` (zero-based). Returns `default` if `index` is out of bounds. Supports negative indexing from the end of the `vector`. Runs in effective constant time. ## Examples iex> A.Vector.new(1..1_000) |> A.Vector.at(555) 556 iex> A.Vector.new(1..1_000) |> A.Vector.at(1_000) nil """ @spec at(t(val), index, default) :: val | default when val: value, default: term def at(vector, index, default \\ nil) def at(%__MODULE__{__vector__: internal}, index, default) when is_integer(index) do case Raw.fetch_any(internal, index) do {:ok, value} -> value :error -> default end end @doc """ Finds the element at the given `index` (zero-based). Raises an `A.Vector.IndexError` if `index` is out of bounds. Supports negative indexing from the end of the `vector`. Runs in effective constant time. ## Examples iex> A.Vector.new(1..1_000) |> A.Vector.at!(555) 556 iex> A.Vector.new(1..1_000) |> A.Vector.at!(-10) 991 iex> A.Vector.new(1..1_000) |> A.Vector.at!(1_000) ** (A.Vector.IndexError) out of bound index: 1000 not in -1000..999 """ @spec at(t(val), index) :: val when val: value def at!(vector, index) def at!(%__MODULE__{__vector__: internal}, index) when is_integer(index) do case Raw.fetch_any(internal, index) do {:ok, value} -> value :error -> raise IndexError, index: index, size: Raw.size(internal) end end @doc """ Returns a copy of `vector` with a replaced `value` at the specified `index`. Returns the `vector` untouched if `index` is out of bounds. Supports negative indexing from the end of the `vector`. Runs in effective constant time. ## Examples iex> A.Vector.new(1..8) |> A.Vector.replace_at(5, :foo) #A iex> A.Vector.new(1..8) |> A.Vector.replace_at(8, :foo) #A iex> A.Vector.new(1..8) |> A.Vector.replace_at(-2, :foo) #A """ @spec replace_at(t(val), index, val) :: t(val) when val: value def replace_at(%__MODULE__{__vector__: internal} = vector, index, value) when is_integer(index) do case Raw.replace_any(internal, index, value) do {:ok, updated} -> %__MODULE__{__vector__: updated} :error -> vector end end @doc """ Returns a copy of `vector` with a replaced `value` at the specified `index`. Raises an `A.Vector.IndexError` if `index` is out of bounds. Supports negative indexing from the end of the `vector`. Runs in effective constant time. ## Examples iex> A.Vector.new(1..8) |> A.Vector.replace_at!(5, :foo) #A iex> A.Vector.new(1..8) |> A.Vector.replace_at!(-2, :foo) #A iex> A.Vector.new(1..8) |> A.Vector.replace_at!(8, :foo) ** (A.Vector.IndexError) out of bound index: 8 not in -8..7 """ @spec replace_at!(t(val), index, val) :: t(val) when val: value def replace_at!(%__MODULE__{__vector__: internal}, index, value) when is_integer(index) do case Raw.replace_any(internal, index, value) do {:ok, updated} -> %__MODULE__{__vector__: updated} :error -> raise IndexError, index: index, size: Raw.size(internal) end end @doc """ Returns a copy of `vector` with an updated value at the specified `index`. Returns the `vector` untouched if `index` is out of bounds. Supports negative indexing from the end of the `vector`. Runs in effective constant time. ## Examples iex> A.Vector.new(1..8) |> A.Vector.update_at(2, &(&1 * 1000)) #A iex> A.Vector.new(1..8) |> A.Vector.update_at(8, &(&1 * 1000)) #A iex> A.Vector.new(1..8) |> A.Vector.update_at(-1, &(&1 * 1000)) #A """ @spec update_at(t(val), index, (val -> val)) :: t(val) when val: value def update_at(%__MODULE__{__vector__: internal} = vector, index, fun) when is_integer(index) and is_function(fun) do case Raw.update_any(internal, index, fun) do {:ok, updated} -> %__MODULE__{__vector__: updated} :error -> vector end end @doc """ Returns a copy of `vector` with an updated value at the specified `index`. Raises an `A.Vector.IndexError` if `index` is out of bounds. Supports negative indexing from the end of the `vector`. Runs in effective constant time. ## Examples iex> A.Vector.new(1..8) |> A.Vector.update_at!(2, &(&1 * 1000)) #A iex> A.Vector.new(1..8) |> A.Vector.update_at!(-1, &(&1 * 1000)) #A iex> A.Vector.new(1..8) |> A.Vector.update_at!(-9, &(&1 * 1000)) ** (A.Vector.IndexError) out of bound index: -9 not in -8..7 """ @spec update_at!(t(val), index, (val -> val)) :: t(val) when val: value def update_at!(%__MODULE__{__vector__: internal}, index, fun) when is_integer(index) and is_function(fun) do case Raw.update_any(internal, index, fun) do {:ok, updated} -> %__MODULE__{__vector__: updated} :error -> raise IndexError, index: index, size: Raw.size(internal) end end @doc """ Removes the last value from the `vector` and returns both the value and the updated vector. Leaves the `vector` untouched if empty. Runs in effective constant time. ## Examples iex> vector = A.Vector.new(1..8) iex> {8, updated} = A.Vector.pop_last(vector); updated #A iex> {nil, updated} = A.Vector.pop_last(A.Vector.new()); updated #A """ @spec pop_last(t(val), default) :: {val | default, t(val)} when val: value, default: term def pop_last(vector, default \\ nil) def pop_last(%__MODULE__{__vector__: internal} = vector, default) do case Raw.pop_last(internal) do {value, new_internal} -> {value, %__MODULE__{__vector__: new_internal}} :error -> {default, vector} end end @doc """ Removes the last value from the `vector` and returns both the value and the updated vector. Raises an `A.Vector.EmptyError` if empty. Runs in effective constant time. ## Examples iex> vector = A.Vector.new(1..8) iex> {8, updated} = A.Vector.pop_last!(vector); updated #A iex> {nil, updated} = A.Vector.pop_last!(A.Vector.new()); updated ** (A.Vector.EmptyError) empty vector error """ @spec pop_last!(t(val)) :: {val, t(val)} when val: value def pop_last!(vector) def pop_last!(%__MODULE__{__vector__: internal}) do case Raw.pop_last(internal) do {value, new_internal} -> {value, %__MODULE__{__vector__: new_internal}} :error -> raise EmptyError end end @doc """ Removes the last value from the `vector` and returns the updated vector. Leaves the `vector` untouched if empty. Runs in effective constant time. ## Examples iex> vector = A.Vector.new(1..8) iex> A.Vector.delete_last(vector) #A iex> A.Vector.delete_last(A.Vector.new()) #A """ @spec delete_last(t(val)) :: t(val) when val: value def delete_last(vector) def delete_last(%__MODULE__{__vector__: internal} = vector) do case Raw.pop_last(internal) do {_value, new_internal} -> %__MODULE__{__vector__: new_internal} :error -> vector end end @doc """ Removes the last value from the `vector` and returns the updated vector. Raises an `A.Vector.EmptyError` if empty. Runs in effective constant time. ## Examples iex> vector = A.Vector.new(1..8) iex> A.Vector.delete_last!(vector) #A iex> A.Vector.delete_last!(A.Vector.new()) ** (A.Vector.EmptyError) empty vector error """ @spec delete_last!(t(val)) :: t(val) when val: value def delete_last!(vector) def delete_last!(%__MODULE__{__vector__: internal}) do case Raw.pop_last(internal) do {_value, new_internal} -> %__MODULE__{__vector__: new_internal} :error -> raise EmptyError end end @doc """ (Inefficient) Returns and removes the value at the specified `index` in the `vector`. Returns the `vector` untouched if `index` is out of bounds. Supports negative indexing from the end of the `vector`. Runs in linear time. Its usage is discouraged, see the [Efficiency guide](#module-efficiency-guide). ## Examples iex> vector = A.Vector.new(1..8) iex> {5, updated} = A.Vector.pop_at(vector, 4); updated #A iex> {nil, updated} = A.Vector.pop_at(vector, -9); updated #A """ @spec pop_at(t(val), index, default) :: {val | default, t(val)} when val: value, default: term def pop_at(vector, index, default \\ nil) def pop_at(%__MODULE__{__vector__: internal} = vector, index, default) when is_integer(index) do case Raw.pop_any(internal, index) do {value, new_internal} -> {value, %__MODULE__{__vector__: new_internal}} :error -> {default, vector} end end @doc """ (Inefficient) Returns and removes the value at the specified `index` in the `vector`. Raises an `A.Vector.IndexError` if `index` is out of bounds. Supports negative indexing from the end of the `vector`. Runs in linear time. Its usage is discouraged, see the [Efficiency guide](#module-efficiency-guide). ## Examples iex> vector = A.Vector.new(1..8) iex> {5, updated} = A.Vector.pop_at!(vector, 4); updated #A iex> A.Vector.pop_at!(vector, -9) ** (A.Vector.IndexError) out of bound index: -9 not in -8..7 """ @spec pop_at!(t(val), index) :: {val, t(val)} when val: value def pop_at!(vector, index) def pop_at!(%__MODULE__{__vector__: internal}, index) when is_integer(index) do case Raw.pop_any(internal, index) do {value, new_internal} -> {value, %__MODULE__{__vector__: new_internal}} :error -> raise IndexError, index: index, size: Raw.size(internal) end end @doc false @impl Access @spec pop(t(val), index) :: {val | nil, t(val)} when val: value defdelegate pop(vector, key), to: __MODULE__, as: :pop_at @doc """ (Inefficient) Returns a copy of `vector` without the value at the specified `index`. Returns the `vector` untouched if `index` is out of bounds. Supports negative indexing from the end of the `vector`. Runs in linear time. Its usage is discouraged, see the [Efficiency guide](#module-efficiency-guide). ## Examples iex> vector = A.Vector.new(1..8) iex> A.Vector.delete_at(vector, 4) #A iex> A.Vector.delete_at(vector, -9) #A """ @spec delete_at(t(val), index) :: t(val) when val: value def delete_at(%__MODULE__{__vector__: internal} = vector, index) when is_integer(index) do case Raw.delete_any(internal, index) do {:ok, new_internal} -> %__MODULE__{__vector__: new_internal} :error -> vector end end @doc """ (Inefficient) Returns a copy of `vector` without the value at the specified `index`. Raises an `A.Vector.IndexError` if `index` is out of bounds. Supports negative indexing from the end of the `vector`. Runs in linear time. Its usage is discouraged, see the [Efficiency guide](#module-efficiency-guide). ## Examples iex> vector = A.Vector.new(1..8) iex> A.Vector.delete_at!(vector, 4) #A iex> A.Vector.delete_at!(vector, -9) ** (A.Vector.IndexError) out of bound index: -9 not in -8..7 """ @spec delete_at!(t(val), index) :: t(val) when val: value def delete_at!(vector, index) def delete_at!(%__MODULE__{__vector__: internal}, index) when is_integer(index) do case Raw.delete_any(internal, index) do {:ok, new_internal} -> %__MODULE__{__vector__: new_internal} :error -> raise IndexError, index: index, size: Raw.size(internal) end end @doc """ Gets the value from key and updates it, all in one pass. See `Access.get_and_update/3` for more details. ## Examples iex> vector = A.Vector.new(1..8) iex> {6, updated} = A.Vector.get_and_update(vector, 5, fn current_value -> ...> {current_value, current_value && current_value * 100} ...> end); updated #A iex> {nil, updated} = A.Vector.get_and_update(vector, 8, fn current_value -> ...> {current_value, current_value && current_value * 100} ...> end); updated #A iex> {4, updated} = A.Vector.get_and_update(vector, 3, fn _ -> :pop end); updated #A iex> {nil, updated} = A.Vector.get_and_update(vector, 8, fn _ -> :pop end); updated #A """ @impl Access @spec get_and_update(t(v), index, (v -> {returned, v} | :pop)) :: {returned, t(v)} when v: value, returned: term def get_and_update(%__MODULE__{__vector__: internal}, index, fun) when is_integer(index) and is_function(fun, 1) do {returned, new_internal} = Raw.get_and_update_any(internal, index, fun) {returned, %__MODULE__{__vector__: new_internal}} end @doc """ Converts the `vector` to a list. Runs in linear time. ## Examples iex> A.Vector.new(10..25) |> A.Vector.to_list() [10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25] iex> A.Vector.new() |> A.Vector.to_list() [] """ @spec to_list(t(val)) :: [val] when val: value def to_list(%__MODULE__{__vector__: internal}) do Raw.to_list(internal) end @doc """ Returns a new vector where each element is the result of invoking `fun` on each corresponding element of `vector`. Runs in linear time. ## Examples iex> A.Vector.new(1..10) |> A.Vector.map(&(&1 * &1)) #A """ @spec map(t(v1), (v1 -> v2)) :: t(v2) when v1: value, v2: value def map(%__MODULE__{__vector__: internal}, fun) when is_function(fun, 1) do %__MODULE__{ __vector__: Raw.map(internal, fun) } end @doc """ Filters the `vector`, i.e. return a new vector containing only elements for which `fun` returns a truthy (neither `false` nor `nil`) value. Runs in linear time. ## Examples iex> vector = A.Vector.new(1..100) iex> A.Vector.filter(vector, fn i -> rem(i, 13) == 0 end) #A """ @spec filter(t(val), (val -> boolean)) :: t(val) when val: value def filter(%__MODULE__{__vector__: internal}, fun) when is_function(fun, 1) do %__MODULE__{ __vector__: Raw.filter(internal, fun) } end @doc """ Filters the `vector`, i.e. return a new vector containing only elements for which `fun` returns a falsy (either `false` or `nil`) value. Runs in linear time. ## Examples iex> vector = A.Vector.new(1..12) iex> A.Vector.reject(vector, fn i -> rem(i, 3) == 0 end) #A """ @spec reject(t(val), (val -> boolean)) :: t(val) when val: value def reject(%__MODULE__{__vector__: internal}, fun) when is_function(fun, 1) do %__MODULE__{ __vector__: Raw.reject(internal, fun) } end @doc """ Sorts the `vector` in the same way as `Enum.sort/1`. ## Examples iex> A.Vector.new(9..1) |> A.Vector.sort() #A """ @spec sort(t(val)) :: t(val) when val: value def sort(%__MODULE__{__vector__: internal}) do new_internal = internal |> Raw.to_list() |> Enum.sort() |> Raw.from_list() %__MODULE__{__vector__: new_internal} end @doc """ Sorts the `vector` in the same way as `Enum.sort/2`. See `Enum.sort/2` documentation for detailled usage. ## Examples iex> A.Vector.new(1..9) |> A.Vector.sort(:desc) #A """ @spec sort( t(val), (val, val -> boolean) | :asc | :desc | module | {:asc | :desc, module} ) :: t(val) when val: value def sort(%__MODULE__{__vector__: internal}, fun) do new_internal = internal |> Raw.to_list() |> Enum.sort(fun) |> Raw.from_list() %__MODULE__{__vector__: new_internal} end @doc """ Sorts the `vector` in the same way as `Enum.sort_by/3`. See `Enum.sort_by/3` documentation for detailled usage. ## Examples iex> vector = A.Vector.new(["some", "kind", "of", "monster"]) iex> A.Vector.sort_by(vector, &byte_size/1) #A iex> A.Vector.sort_by(vector, &{byte_size(&1), String.first(&1)}) #A """ @spec sort_by( t(val), (val -> mapped_val), (val, val -> boolean) | :asc | :desc | module | {:asc | :desc, module} ) :: t(val) when val: value, mapped_val: value def sort_by(%__MODULE__{__vector__: internal}, mapper, sorter \\ &<=/2) do new_internal = internal |> Raw.to_list() |> Enum.sort_by(mapper, sorter) |> Raw.from_list() %__MODULE__{__vector__: new_internal} end @doc """ Returns a copy of the vector without any duplicated element. The first occurrence of each element is kept. Runs in linear time. ## Examples iex> A.Vector.new([1, 1, 2, 1, 2, 3, 2]) |> A.Vector.uniq() #A """ @spec uniq(t(val)) :: t(val) when val: value def uniq(%__MODULE__{__vector__: internal}) do # TODO optimize (take until found a dupe, and concat the rest) new_internal = internal |> Raw.to_list() |> Enum.uniq() |> Raw.from_list() %__MODULE__{__vector__: new_internal} end @doc """ Returns a copy of the vector without elements for which the function `fun` returned duplicate elements. The first occurrence of each element is kept. Runs in linear time. ## Examples iex> vector = A.Vector.new([x: 1, y: 2, z: 1]) #A iex> A.Vector.uniq_by(vector, fn {_x, y} -> y end) #A """ @spec uniq_by(t(val), (val -> term)) :: t(val) when val: value def uniq_by(%__MODULE__{__vector__: internal}, fun) when is_function(fun, 1) do new_internal = internal |> Raw.to_list() |> Enum.uniq_by(fun) |> Raw.from_list() %__MODULE__{__vector__: new_internal} end @doc """ Intersperses `separator` between each element of the `vector`. Runs in linear time. ## Examples iex> A.Vector.new(1..6) |> A.Vector.intersperse(nil) #A """ @spec intersperse( t(val), separator ) :: t(val | separator) when val: value, separator: value def intersperse(%__MODULE__{__vector__: internal}, separator) do new_internal = internal |> Raw.intersperse(separator) |> Raw.from_list() %__MODULE__{__vector__: new_internal} end @doc """ Maps and intersperses the `vector` in one pass. Runs in linear time. ## Examples iex> A.Vector.new(1..6) |> A.Vector.map_intersperse(nil, &(&1 * 10)) #A """ @spec map_intersperse( t(val), separator, (val -> mapped_val) ) :: t(mapped_val | separator) when val: value, separator: value, mapped_val: value def map_intersperse(%__MODULE__{__vector__: internal}, separator, mapper) when is_function(mapper, 1) do new_internal = internal |> Raw.map(mapper) |> Raw.intersperse(separator) |> Raw.from_list() %__MODULE__{__vector__: new_internal} end @doc """ Folds (reduces) the given `vector` from the left with the function `fun`. Requires an accumulator `acc`. Runs in linear time. ## Examples iex> A.Vector.new(1..10) |> A.Vector.foldl(0, &+/2) 55 iex> A.Vector.new(1..10) |> A.Vector.foldl([], & [&1 | &2]) [10, 9, 8, 7, 6, 5, 4, 3, 2, 1] """ @spec foldl(t(val), acc, (val, acc -> acc)) :: acc when val: value, acc: term def foldl(%__MODULE__{__vector__: internal}, acc, fun) when is_function(fun, 2) do Raw.foldl(internal, acc, fun) end @doc """ Folds (reduces) the given `vector` from the right with the function `fun`. Requires an accumulator `acc`. Unlike linked lists, this is as efficient as `foldl/3`. This can typically save a call to `Enum.reverse/1` on the result when building a list. Runs in linear time. ## Examples iex> A.Vector.new(1..10) |> A.Vector.foldr(0, &+/2) 55 iex> A.Vector.new(1..10) |> A.Vector.foldr([], & [&1 | &2]) [1, 2, 3, 4, 5, 6, 7, 8, 9, 10] """ @spec foldr(t(val), acc, (val, acc -> acc)) :: acc when val: value, acc: term def foldr(%__MODULE__{__vector__: internal}, acc, fun) when is_function(fun, 2) do Raw.foldr(internal, acc, fun) end @doc """ Invokes the given `fun` for each element in the `vector`. Returns `:ok`. Runs in linear time. ## Examples A.Vector.new(1..3) |> A.Vector.each(&IO.inspect/1) 1 2 3 :ok """ @spec each(t(val), (val -> term)) :: :ok when val: value def each(%__MODULE__{__vector__: internal}, fun) when is_function(fun, 1) do Raw.each(internal, fun) end @doc """ Returns the sum of all elements in the `vector`. Raises `ArithmeticError` if `vector` contains a non-numeric value. Runs in linear time. ## Examples iex> A.Vector.new(1..10) |> A.Vector.sum() 55 iex> A.Vector.new() |> A.Vector.sum() 0 """ @spec sum(t(num)) :: num when num: number def sum(%__MODULE__{__vector__: internal}) do Raw.sum(internal) end @doc """ Returns the product of all elements in the `vector`. Raises `ArithmeticError` if `vector` contains a non-numeric value. Runs in linear time. ## Examples iex> A.Vector.new(1..5) |> A.Vector.product() 120 iex> A.Vector.new() |> A.Vector.product() 1 """ @spec product(t(num)) :: num when num: number def product(%__MODULE__{__vector__: internal}) do Raw.product(internal) end @doc """ Joins the given `vector` into a string using `joiner` as a separator. If `joiner` is not passed at all, it defaults to an empty string. All elements in the `vector` must be convertible to a string, otherwise an error is raised. Runs in linear time. ## Examples iex> A.Vector.new(1..6) |> A.Vector.join() "123456" iex> A.Vector.new(1..6) |> A.Vector.join(" + ") "1 + 2 + 3 + 4 + 5 + 6" iex> A.Vector.new() |> A.Vector.join(" + ") "" """ @spec join(t(val), String.t()) :: String.t() when val: String.Chars.t() def join(%__MODULE__{__vector__: internal}, joiner \\ "") when is_binary(joiner) do Raw.join_as_iodata(internal, joiner) |> IO.iodata_to_binary() end @doc """ Maps and joins the given `vector` into a string using `joiner` as a separator. If `joiner` is not passed at all, it defaults to an empty string. `mapper` should only return values that are convertible to a string, otherwise an error is raised. Runs in linear time. ## Examples iex> A.Vector.new(1..6) |> A.Vector.map_join(fn x -> x * 10 end) "102030405060" iex> A.Vector.new(1..6) |> A.Vector.map_join(" + ", fn x -> x * 10 end) "10 + 20 + 30 + 40 + 50 + 60" iex> A.Vector.new() |> A.Vector.map_join(" + ", fn x -> x * 10 end) "" """ @spec map_join(t(val), String.t(), (val -> String.Chars.t())) :: String.t() when val: value def map_join(%__MODULE__{__vector__: internal}, joiner \\ "", mapper) when is_binary(joiner) and is_function(mapper, 1) do internal |> Raw.map(mapper) |> Raw.join_as_iodata(joiner) |> IO.iodata_to_binary() end @doc """ Returns the maximal element in the `vector` according to Erlang's term ordering. Runs in linear time. ## Examples iex> A.Vector.new(1..10) |> A.Vector.max() 10 iex> A.Vector.new() |> A.Vector.max() ** (A.Vector.EmptyError) empty vector error """ @spec max(t(val)) :: val when val: value def max(%__MODULE__{__vector__: internal}) do Raw.max(internal) end @doc """ Returns the minimal element in the `vector` according to Erlang's term ordering. Runs in linear time. ## Examples iex> A.Vector.new(1..10) |> A.Vector.min() 1 iex> A.Vector.new() |> A.Vector.min() ** (A.Vector.EmptyError) empty vector error """ @spec min(t(val)) :: val when val: value def min(%__MODULE__{__vector__: internal}) do # TODO mirror Enum API Raw.min(internal) end @doc """ Returns `true` if at least one element in `enumerable` is truthy. Runs in linear time, but stops evaluating when finds the first truthy value. Iterates over the `enumerable`, and when it finds a truthy value (neither `false` nor `nil`), `true` is returned. In all other cases `false` is returned. ## Examples iex> A.Vector.new([false, false, true]) |> A.Vector.any?() true iex> A.Vector.new([false, nil]) |> A.Vector.any?() false iex> A.Vector.new() |> A.Vector.any?() false """ @spec any?(t(val)) :: boolean when val: value def any?(%__MODULE__{__vector__: internal}) do Raw.any?(internal) end @doc """ Returns `true` if `fun.(element)` is truthy for at least one element in `enumerable`. Runs in linear time, but stops evaluating when finds the first truthy value. Iterates over the `enumerable` and invokes `fun` on each element. When an invocation of `fun` returns a truthy value (neither `false` nor `nil`) iteration stops immediately and `true` is returned. In all other cases `false` is returned. ## Examples iex> vector = A.Vector.new(1..10) iex> A.Vector.any?(vector, fn i -> rem(i, 7) == 0 end) true iex> A.Vector.any?(vector, fn i -> rem(i, 13) == 0 end) false iex> A.Vector.new() |> A.Vector.any?(fn i -> rem(i, 7) == 0 end) false """ @spec any?(t(val), (val -> as_boolean(term))) :: boolean when val: value def any?(%__MODULE__{__vector__: internal}, fun) when is_function(fun, 1) do Raw.any?(internal, fun) end @doc """ Returns `true` if all elements in `enumerable` are truthy. Runs in linear time, but stops evaluating when finds the first falsy value. Iterates over the `enumerable`, and when it finds a falsy value (`false` or `nil`), `false` is returned. In all other cases `true` is returned. ## Examples iex> A.Vector.new([true, true, false]) |> A.Vector.all?() false iex> A.Vector.new([true, [], %{}, 5]) |> A.Vector.all?() true iex> A.Vector.new() |> A.Vector.all?() true """ @spec all?(t(val)) :: boolean when val: value def all?(%__MODULE__{__vector__: internal}) do Raw.all?(internal) end @doc """ Returns `true` if `fun.(element)` is truthy for all elements in `enumerable`. Runs in linear time, but stops evaluating when finds the first falsy value. Iterates over the `enumerable` and invokes `fun` on each element. When an invocation of `fun` returns a falsy value (`false` or `nil`) iteration stops immediately and `false` is returned. In all other cases `true` is returned. ## Examples iex> vector = A.Vector.new(1..10) iex> A.Vector.all?(vector, fn i -> rem(i, 13) != 0 end) true iex> A.Vector.all?(vector, fn i -> rem(i, 7) != 0 end) false iex> A.Vector.new() |> A.Vector.all?(fn i -> rem(i, 7) != 0 end) true """ @spec all?(t(val), (val -> as_boolean(term))) :: boolean when val: value def all?(%__MODULE__{__vector__: internal}, fun) when is_function(fun, 1) do Raw.all?(internal, fun) end @doc """ Returns the `vector` in reverse order. Runs in linear time. ## Examples iex> A.Vector.new(1..12) |> A.Vector.reverse() #A """ @spec reverse(t(val)) :: t(val) when val: value def reverse(%__MODULE__{__vector__: internal}) do internal |> Raw.to_reverse_list() |> new() end @doc """ Returns a subset of the given `vector` by `index_range`. Works the same as `Enum.slice/2`, see its documentation for more details. Runs in linear time regarding the size of the returned subset. ## Examples iex> A.Vector.new(0..100) |> A.Vector.slice(80..90) #A iex> A.Vector.new(0..100) |> A.Vector.slice(-40..-30) #A iex> A.Vector.new([:only_one]) |> A.Vector.slice(0..1000) #A """ @spec slice(t(val), Range.t()) :: t(val) when val: value def slice(%__MODULE__{} = vector, first..last = index_range) do case first do 0 -> amount = last + 1 if last < 0 do drop(vector, amount) else take(vector, amount) end _ -> vector |> Enum.slice(index_range) |> new() end end @doc """ Returns a subset of the given `vector`, from `start_index` (zero-based) with `amount number` of elements if available. Works the same as `Enum.slice/3`, see its documentation for more details. Runs in linear time regarding the size of the returned subset. ## Examples iex> A.Vector.new(0..100) |> A.Vector.slice(80, 10) #A iex> A.Vector.new(0..100) |> A.Vector.slice(-40, 10) #A iex> A.Vector.new([:only_one]) |> A.Vector.slice(0, 1000) #A """ @spec slice(t(val), index, non_neg_integer) :: t(val) when val: value def slice(%__MODULE__{__vector__: internal} = vector, start_index, amount) when is_integer(start_index) and is_integer(amount) and amount >= 0 do if start_index == 0 or start_index == -Raw.size(internal) do new_internal = Raw.take(internal, amount) %__MODULE__{__vector__: new_internal} else vector |> Enum.slice(start_index, amount) |> new() end end @doc """ Takes an `amount` of elements from the beginning or the end of the `vector`. If a positive `amount` is given, it takes the amount elements from the beginning of the `vector`. If a negative `amount` is given, the amount of elements will be taken from the end. If amount is 0, it returns the empty vector. Time complexity is: - effective constant time when `amount` is positive, as the vector structure can be shared - linear when `amount` is negative, as the vector needs to be reconstructed. ## Examples iex> A.Vector.new(0..100) |> A.Vector.take(10) #A iex> A.Vector.new([:only_one]) |> A.Vector.take(1000) #A iex> A.Vector.new(0..10) |> A.Vector.take(-5) #A """ @spec take(t(val), integer) :: t(val) when val: value def take(%__MODULE__{__vector__: internal}, amount) when is_integer(amount) do new_internal = do_take(internal, amount) %__MODULE__{__vector__: new_internal} end defp do_take(internal, amount) when amount < 0 do size = Raw.size(internal) case size + amount do start when start > 0 -> internal |> Raw.slice(start, size - 1) |> Raw.from_list() _ -> internal end end defp do_take(internal, amount) do Raw.take(internal, amount) end @doc """ Drops the amount of elements from the `vector`. If a negative `amount` is given, the amount of last values will be dropped. Time complexity is: - linear when `amount` is positive, as the vector needs to be reconstructed. - effective constant time when `amount` is negative, as the vector structure can be shared ## Examples iex> A.Vector.new(0..15) |> A.Vector.drop(10) #A iex> A.Vector.new(0..5) |> A.Vector.drop(0) #A iex> A.Vector.new(0..10) |> A.Vector.drop(-5) #A """ @spec drop(t(val), integer) :: t(val) when val: value def drop(%__MODULE__{__vector__: internal}, amount) when is_integer(amount) do new_internal = do_drop(internal, amount) %__MODULE__{__vector__: new_internal} end defp do_drop(internal, _amount = 0) do internal end defp do_drop(internal, amount) when amount < 0 do size = Raw.size(internal) case size + amount do keep when keep > 0 -> Raw.take(internal, size + amount) _ -> @empty_raw end end defp do_drop(internal, amount) do size = Raw.size(internal) if amount >= size do @empty_raw else internal |> Raw.slice(amount, size - 1) |> Raw.from_list() end end @doc """ Returns the `vector` with each element wrapped in a tuple alongside its index. If an `offset` is given, we will index from the given `offset` instead of from zero. Runs in linear time. ## Examples iex> A.Vector.new(["foo", "bar", "baz"]) |> A.Vector.with_index() #A iex> A.Vector.new() |> A.Vector.with_index() #A iex> A.Vector.new(["foo", "bar", "baz"]) |> A.Vector.with_index(100) #A """ @spec with_index(t(val), index) :: t({val, index}) when val: value def with_index(%__MODULE__{__vector__: internal}, offset \\ 0) when is_integer(offset) do new_internal = Raw.with_index(internal, offset) %__MODULE__{__vector__: new_internal} end @doc """ Returns a random element of a `vector`. Raises `Vector.EmptyError` if `vector` is empty. Like `Enum.random/1`, this function uses Erlang's [`:rand` module](http://www.erlang.org/doc/man/rand.html) to calculate the random value. Check its documentation for setting a different random algorithm or a different seed. Runs in effective constant time, and is therefore more efficient than `Enum.random/1` on lists. ## Examples # Although not necessary, let's seed the random algorithm iex>:rand.seed(:exrop, {101, 102, 103}) iex> A.Vector.new([1, 2, 3]) |> A.Vector.random() 3 iex> A.Vector.new([1, 2, 3]) |> A.Vector.random() 2 iex> A.Vector.new(1..1_000) |> A.Vector.random() 846 iex> A.Vector.new([]) |> A.Vector.random() ** (A.Vector.EmptyError) empty vector error """ @spec random(t(val)) :: val when val: value def random(%__MODULE__{__vector__: internal}) do Raw.random(internal) end @doc """ Takes `amount` random elements from `vector`. Note that, unless `amount` is `0` or `1`, this function will traverse the whole `vector` to get the random sub-vector. If `amount` is more than the `vector` size, this is equivalent to shuffling the `vector`: the returned vector cannot be bigger than the original one. See `Enum.random/1` for notes on implementation and random seed. Runs in linerar time (except for `amount <= 1`, which is effective constant time). ## Examples # Although not necessary, let's seed the random algorithm iex> :rand.seed(:exrop, {1, 2, 3}) iex> A.Vector.new(1..10) |> A.Vector.take_random(2) #A iex> A.Vector.new([:foo, :bar, :baz]) |> A.Vector.take_random(100) #A """ @spec take_random(t(val), non_neg_integer) :: t(val) when val: value def take_random(%__MODULE__{__vector__: internal}, amount) when is_integer(amount) and amount >= 0 do new_internal = Raw.take_random(internal, amount) %__MODULE__{__vector__: new_internal} end @doc """ Returns a new vector with the elements of `vector` shuffled. See `Enum.shuffle/1` for notes on implementation and random seed. ## Examples # Although not necessary, let's seed the random algorithm iex> :rand.seed(:exrop, {1, 2, 3}) iex> A.Vector.new([1, 2, 3]) |> A.Vector.shuffle() #A iex> A.Vector.new([1, 2, 3]) |> A.Vector.shuffle() #A """ @spec shuffle(t(val)) :: t(val) when val: value def shuffle(%__MODULE__{__vector__: internal}) do # Note: benchmarks suggest that this is already fast without further optimization new_internal = internal |> Raw.to_list() |> Enum.shuffle() |> Raw.from_list() %__MODULE__{__vector__: new_internal} end defimpl Inspect do import Inspect.Algebra def inspect(vector, opts) do opts = %Inspect.Opts{opts | charlists: :as_lists} concat(["#A"]) end end defimpl Enumerable do def count(vector) do {:ok, A.Vector.size(vector)} end def member?(%A.Vector{__vector__: internal}, value) do {:ok, Raw.member?(internal, value)} end def slice(%A.Vector{__vector__: internal}) do size = A.Vector.Raw.size(internal) {:ok, size, fn start, length -> A.Vector.Raw.slice(internal, start, start + length - 1) end} end def reduce(%A.Vector{__vector__: internal}, acc, fun) do internal |> A.Vector.Raw.to_list() |> Enumerable.List.reduce(acc, fun) end end defimpl Collectable do alias A.Vector.Raw def into(%A.Vector{__vector__: internal}) do {{[], internal}, &collector_fun/2} end @compile {:inline, collector_fun: 2} defp collector_fun({acc, internal}, {:cont, value}), do: {[value | acc], internal} defp collector_fun({acc, internal}, :done) do new_internal = Raw.concat(internal, :lists.reverse(acc)) %A.Vector{__vector__: new_internal} end defp collector_fun(_acc, :halt), do: :ok end if Code.ensure_loaded?(Jason.Encoder) do defimpl Jason.Encoder do def encode(vector, opts) do vector |> A.Vector.to_list() |> Jason.Encode.list(opts) end end end end