array.jl

# This file is a part of Julia. License is MIT: https://julialang.org/license

## array.jl: Dense arrays

"""
    DimensionMismatch([msg])

The objects called do not have matching dimensionality. Optional argument `msg` is a
descriptive error string.
"""
mutable struct DimensionMismatch <: Exception
    msg::AbstractString
end
DimensionMismatch() = DimensionMismatch("")

## Type aliases for convenience ##
"""
    AbstractVector{T}

Supertype for one-dimensional arrays (or array-like types) with
elements of type `T`. Alias for [`AbstractArray{T,1}`](@ref).
"""
const AbstractVector{T} = AbstractArray{T,1}

"""
    AbstractMatrix{T}

Supertype for two-dimensional arrays (or array-like types) with
elements of type `T`. Alias for [`AbstractArray{T,2}`](@ref).
"""
const AbstractMatrix{T} = AbstractArray{T,2}
const AbstractVecOrMat{T} = Union{AbstractVector{T}, AbstractMatrix{T}}
const RangeIndex = Union{Int, Range{Int}, AbstractUnitRange{Int}}
const DimOrInd = Union{Integer, AbstractUnitRange}
const IntOrInd = Union{Int, AbstractUnitRange}
const DimsOrInds{N} = NTuple{N,DimOrInd}
const NeedsShaping = Union{Tuple{Integer,Vararg{Integer}}, Tuple{OneTo,Vararg{OneTo}}}

"""
    Array{T,N} <: AbstractArray{T,N}

`N`-dimensional dense array with elements of type `T`.
"""
Array

"""
    Vector{T} <: AbstractVector{T}

One-dimensional dense array with elements of type `T`, often used to represent
a mathematical vector. Alias for [`Array{T,1}`](@ref).
"""
const Vector{T} = Array{T,1}

"""
    Matrix{T} <: AbstractMatrix{T}

Two-dimensional dense array with elements of type `T`, often used to represent
a mathematical matrix. Alias for [`Array{T,2}`](@ref).
"""
const Matrix{T} = Array{T,2}
const VecOrMat{T} = Union{Vector{T}, Matrix{T}}

const DenseVector{T} = DenseArray{T,1}
const DenseMatrix{T} = DenseArray{T,2}
const DenseVecOrMat{T} = Union{DenseVector{T}, DenseMatrix{T}}

## Basic functions ##

"""
    eltype(type)

Determine the type of the elements generated by iterating a collection of the given `type`.
For associative collection types, this will be a `Pair{KeyType,ValType}`. The definition
`eltype(x) = eltype(typeof(x))` is provided for convenience so that instances can be passed
instead of types. However the form that accepts a type argument should be defined for new
types.

# Examples
```jldoctest
julia> eltype(ones(Float32,2,2))
Float32

julia> eltype(ones(Int8,2,2))
Int8
```
"""
eltype(::Type) = Any
eltype(::Type{Any}) = Any
eltype(::Type{Bottom}) = throw(ArgumentError("Union{} does not have elements"))
eltype(t::DataType) = eltype(supertype(t))
eltype(x) = eltype(typeof(x))

import Core: arraysize, arrayset, arrayref

vect() = Array{Any,1}(0)
vect(X::T...) where {T} = T[ X[i] for i = 1:length(X) ]

function vect(X...)
    T = promote_typeof(X...)
    #T[ X[i] for i=1:length(X) ]
    # TODO: this is currently much faster. should figure out why. not clear.
    return copy!(Array{T,1}(length(X)), X)
end

size(a::Array, d) = arraysize(a, d)
size(a::Vector) = (arraysize(a,1),)
size(a::Matrix) = (arraysize(a,1), arraysize(a,2))
size(a::Array{<:Any,N}) where {N} = (@_inline_meta; ntuple(M -> size(a, M), Val(N)))

asize_from(a::Array, n) = n > ndims(a) ? () : (arraysize(a,n), asize_from(a, n+1)...)

"""
    Base.isbitsunion(::Type{T})

Return whether a type is an "is-bits" Union type, meaning each type included in a Union is `isbits`.
"""
function isbitsunion end

function isbitsunion(U::Union)
    for u in Base.uniontypes(U)
        isbits(u) || return false
    end
    return true
end
isbitsunion(T) = false

"""
    Base.bitsunionsize(U::Union)

For a Union of `isbits` types, return the size of the largest type.
"""
function bitsunionsize(U::Union)
    sz = 0
    for u in Base.uniontypes(U)
        sz = max(sz, sizeof(u))
    end
    return sz
end

length(a::Array) = arraylen(a)
elsize(a::Array{T}) where {T} = isbits(T) ? sizeof(T) : (isbitsunion(T) ? bitsunionsize(T) : sizeof(Ptr))
sizeof(a::Array) = Core.sizeof(a)

function isassigned(a::Array, i::Int...)
    @_inline_meta
    ii = (sub2ind(size(a), i...) % UInt) - 1
    @boundscheck ii < length(a) % UInt || return false
    ccall(:jl_array_isassigned, Cint, (Any, UInt), a, ii) == 1
end

## copy ##

"""
    unsafe_copy!(dest::Ptr{T}, src::Ptr{T}, N)

Copy `N` elements from a source pointer to a destination, with no checking. The size of an
element is determined by the type of the pointers.

The `unsafe` prefix on this function indicates that no validation is performed on the
pointers `dest` and `src` to ensure that they are valid. Incorrect usage may corrupt or
segfault your program, in the same manner as C.
"""
function unsafe_copy!(dest::Ptr{T}, src::Ptr{T}, n) where T
    # Do not use this to copy data between pointer arrays.
    # It can't be made safe no matter how carefully you checked.
    ccall(:memmove, Ptr{Void}, (Ptr{Void}, Ptr{Void}, UInt),
          dest, src, n*sizeof(T))
    return dest
end

"""
    unsafe_copy!(dest::Array, do, src::Array, so, N)

Copy `N` elements from a source array to a destination, starting at offset `so` in the
source and `do` in the destination (1-indexed).

The `unsafe` prefix on this function indicates that no validation is performed to ensure
that N is inbounds on either array. Incorrect usage may corrupt or segfault your program, in
the same manner as C.
"""
function unsafe_copy!(dest::Array{T}, doffs, src::Array{T}, soffs, n) where T
    if isbits(T)
        unsafe_copy!(pointer(dest, doffs), pointer(src, soffs), n)
    elseif isbitsunion(T)
        ccall(:memmove, Ptr{Void}, (Ptr{Void}, Ptr{Void}, UInt),
              pointer(dest, doffs), pointer(src, soffs), n * Base.bitsunionsize(T))
        # copy selector bytes
        ccall(:memmove, Ptr{Void}, (Ptr{Void}, Ptr{Void}, UInt),
              convert(Ptr{UInt8}, pointer(dest)) + length(dest) * Base.bitsunionsize(T) + doffs - 1,
              convert(Ptr{UInt8}, pointer(src)) + length(src) * Base.bitsunionsize(T) + soffs - 1,
              n)
    else
        ccall(:jl_array_ptr_copy, Void, (Any, Ptr{Void}, Any, Ptr{Void}, Int),
              dest, pointer(dest, doffs), src, pointer(src, soffs), n)
    end
    return dest
end

"""
    copy!(dest, do, src, so, N)

Copy `N` elements from collection `src` starting at offset `so`, to array `dest` starting at
offset `do`. Returns `dest`.
"""
function copy!(dest::Array{T}, doffs::Integer, src::Array{T}, soffs::Integer, n::Integer) where T
    n == 0 && return dest
    n > 0 || throw(ArgumentError(string("tried to copy n=", n, " elements, but n should be nonnegative")))
    if soffs < 1 || doffs < 1 || soffs+n-1 > length(src) || doffs+n-1 > length(dest)
        throw(BoundsError())
    end
    unsafe_copy!(dest, doffs, src, soffs, n)
end

copy!(dest::Array{T}, src::Array{T}) where {T} = copy!(dest, 1, src, 1, length(src))

"""
    copy(x)

Create a shallow copy of `x`: the outer structure is copied, but not all internal values.
For example, copying an array produces a new array with identically-same elements as the
original.
"""
copy(a::T) where {T<:Array} = ccall(:jl_array_copy, Ref{T}, (Any,), a)

function reinterpret(::Type{T}, a::Array{S,1}) where T where S
    nel = Int(div(length(a) * sizeof(S), sizeof(T)))
    # TODO: maybe check that remainder is zero?
    return reinterpret(T, a, (nel,))
end

function reinterpret(::Type{T}, a::Array{S}) where T where S
    if sizeof(S) != sizeof(T)
        throw(ArgumentError("result shape not specified"))
    end
    reinterpret(T, a, size(a))
end

function reinterpret(::Type{T}, a::Array{S}, dims::NTuple{N,Int}) where T where S where N
    function throwbits(::Type{S}, ::Type{T}, ::Type{U}) where {S,T,U}
        @_noinline_meta
        throw(ArgumentError("cannot reinterpret Array{$(S)} to ::Type{Array{$(T)}}, type $(U) is not a bits type"))
    end
    isbits(T) || throwbits(S, T, T)
    isbits(S) || throwbits(S, T, S)
    nel = div(length(a) * sizeof(S), sizeof(T))
    if prod(dims) != nel
        _throw_dmrsa(dims, nel)
    end
    ccall(:jl_reshape_array, Array{T,N}, (Any, Any, Any), Array{T,N}, a, dims)
end

# reshaping to same # of dimensions
function reshape(a::Array{T,N}, dims::NTuple{N,Int}) where T where N
    if prod(dims) != length(a)
        _throw_dmrsa(dims, length(a))
    end
    if dims == size(a)
        return a
    end
    ccall(:jl_reshape_array, Array{T,N}, (Any, Any, Any), Array{T,N}, a, dims)
end

# reshaping to different # of dimensions
function reshape(a::Array{T}, dims::NTuple{N,Int}) where T where N
    if prod(dims) != length(a)
        _throw_dmrsa(dims, length(a))
    end
    ccall(:jl_reshape_array, Array{T,N}, (Any, Any, Any), Array{T,N}, a, dims)
end

function _throw_dmrsa(dims, len)
    @_noinline_meta
    throw(DimensionMismatch("new dimensions $(dims) must be consistent with array size $len"))
end

## Constructors ##

similar(a::Array{T,1}) where {T}                    = Array{T,1}(size(a,1))
similar(a::Array{T,2}) where {T}                    = Array{T,2}(size(a,1), size(a,2))
similar(a::Array{T,1}, S::Type) where {T}           = Array{S,1}(size(a,1))
similar(a::Array{T,2}, S::Type) where {T}           = Array{S,2}(size(a,1), size(a,2))
similar(a::Array{T}, m::Int) where {T}              = Array{T,1}(m)
similar(a::Array, T::Type, dims::Dims{N}) where {N} = Array{T,N}(dims)
similar(a::Array{T}, dims::Dims{N}) where {T,N}     = Array{T,N}(dims)

# T[x...] constructs Array{T,1}
"""
    getindex(type[, elements...])

Construct a 1-d array of the specified type. This is usually called with the syntax
`Type[]`. Element values can be specified using `Type[a,b,c,...]`.

# Examples
```jldoctest
julia> Int8[1, 2, 3]
3-element Array{Int8,1}:
 1
 2
 3

julia> getindex(Int8, 1, 2, 3)
3-element Array{Int8,1}:
 1
 2
 3
```
"""
function getindex(::Type{T}, vals...) where T
    a = Array{T,1}(length(vals))
    @inbounds for i = 1:length(vals)
        a[i] = vals[i]
    end
    return a
end

getindex(::Type{T}) where {T} = (@_inline_meta; Array{T,1}(0))
getindex(::Type{T}, x) where {T} = (@_inline_meta; a = Array{T,1}(1); @inbounds a[1] = x; a)
getindex(::Type{T}, x, y) where {T} = (@_inline_meta; a = Array{T,1}(2); @inbounds (a[1] = x; a[2] = y); a)
getindex(::Type{T}, x, y, z) where {T} = (@_inline_meta; a = Array{T,1}(3); @inbounds (a[1] = x; a[2] = y; a[3] = z); a)

function getindex(::Type{Any}, @nospecialize vals...)
    a = Array{Any,1}(length(vals))
    @inbounds for i = 1:length(vals)
        a[i] = vals[i]
    end
    return a
end
getindex(::Type{Any}) = Array{Any,1}(0)

function fill!(a::Union{Array{UInt8}, Array{Int8}}, x::Integer)
    ccall(:memset, Ptr{Void}, (Ptr{Void}, Cint, Csize_t), a, x, length(a))
    return a
end

function fill!(a::Array{T}, x) where T<:Union{Integer,AbstractFloat}
    xT = convert(T, x)
    for i in eachindex(a)
        @inbounds a[i] = xT
    end
    return a
end

"""
    fill(x, dims)

Create an array filled with the value `x`. For example, `fill(1.0, (5,5))` returns a 5×5
array of floats, with each element initialized to `1.0`.

# Examples
```jldoctest
julia> fill(1.0, (5,5))
5×5 Array{Float64,2}:
 1.0  1.0  1.0  1.0  1.0
 1.0  1.0  1.0  1.0  1.0
 1.0  1.0  1.0  1.0  1.0
 1.0  1.0  1.0  1.0  1.0
 1.0  1.0  1.0  1.0  1.0
```

If `x` is an object reference, all elements will refer to the same object. `fill(Foo(),
dims)` will return an array filled with the result of evaluating `Foo()` once.
"""
fill(v, dims::Dims)       = fill!(Array{typeof(v)}(dims), v)
fill(v, dims::Integer...) = fill!(Array{typeof(v)}(dims...), v)

"""
    zeros([A::AbstractArray,] [T=eltype(A)::Type,] [dims=size(A)::Tuple])

Create an array of all zeros with the same layout as `A`, element type `T` and size `dims`.
The `A` argument can be skipped, which behaves like `Array{Float64,0}()` was passed.
For convenience `dims` may also be passed in variadic form.

# Examples
```jldoctest
julia> zeros(1)
1-element Array{Float64,1}:
 0.0

julia> zeros(Int8, 2, 3)
2×3 Array{Int8,2}:
 0  0  0
 0  0  0

julia> A = [1 2; 3 4]
2×2 Array{Int64,2}:
 1  2
 3  4

julia> zeros(A)
2×2 Array{Int64,2}:
 0  0
 0  0

julia> zeros(A, Float64)
2×2 Array{Float64,2}:
 0.0  0.0
 0.0  0.0

julia> zeros(A, Bool, (3,))
3-element Array{Bool,1}:
 false
 false
 false
```
See also [`ones`](@ref), [`similar`](@ref).
"""
function zeros end

"""
    ones([A::AbstractArray,] [T=eltype(A)::Type,] [dims=size(A)::Tuple])

Create an array of all ones with the same layout as `A`, element type `T` and size `dims`.
The `A` argument can be skipped, which behaves like `Array{Float64,0}()` was passed.
For convenience `dims` may also be passed in variadic form.

# Examples
```jldoctest
julia> ones(Complex128, 2, 3)
2×3 Array{Complex{Float64},2}:
 1.0+0.0im  1.0+0.0im  1.0+0.0im
 1.0+0.0im  1.0+0.0im  1.0+0.0im

julia> ones(1,2)
1×2 Array{Float64,2}:
 1.0  1.0

julia> A = [1 2; 3 4]
2×2 Array{Int64,2}:
 1  2
 3  4

julia> ones(A)
2×2 Array{Int64,2}:
 1  1
 1  1

julia> ones(A, Float64)
2×2 Array{Float64,2}:
 1.0  1.0
 1.0  1.0

julia> ones(A, Bool, (3,))
3-element Array{Bool,1}:
 true
 true
 true
```
See also [`zeros`](@ref), [`similar`](@ref).
"""
function ones end

for (fname, felt) in ((:zeros,:zero), (:ones,:one))
    @eval begin
        # allow signature of similar
        $fname(a::AbstractArray, T::Type, dims::Tuple) = fill!(similar(a, T, dims), $felt(T))
        $fname(a::AbstractArray, T::Type, dims...) = fill!(similar(a,T,dims...), $felt(T))
        $fname(a::AbstractArray, T::Type=eltype(a)) = fill!(similar(a,T), $felt(T))

        $fname(T::Type, dims::Tuple) = fill!(Array{T}(Dims(dims)), $felt(T))
        $fname(dims::Tuple) = ($fname)(Float64, dims)
        $fname(T::Type, dims...) = $fname(T, dims)
        $fname(dims...) = $fname(dims)
    end
end

"""
    eye([T::Type=Float64,] m::Integer, n::Integer)

`m`-by-`n` identity matrix.
The default element type is [`Float64`](@ref).

# Examples
```jldoctest
julia> eye(3, 4)
3×4 Array{Float64,2}:
 1.0  0.0  0.0  0.0
 0.0  1.0  0.0  0.0
 0.0  0.0  1.0  0.0

julia> eye(2, 2)
2×2 Array{Float64,2}:
 1.0  0.0
 0.0  1.0

julia> eye(Int, 2, 2)
2×2 Array{Int64,2}:
 1  0
 0  1
```
"""
function eye(::Type{T}, m::Integer, n::Integer) where T
    a = zeros(T,m,n)
    for i = 1:min(m,n)
        a[i,i] = oneunit(T)
    end
    return a
end

"""
    eye(m, n)

`m`-by-`n` identity matrix.
"""
eye(m::Integer, n::Integer) = eye(Float64, m, n)
eye(::Type{T}, n::Integer) where {T} = eye(T, n, n)
"""
    eye([T::Type=Float64,] n::Integer)

`n`-by-`n` identity matrix.
The default element type is [`Float64`](@ref).

# Examples
```jldoctest
julia> eye(Int, 2)
2×2 Array{Int64,2}:
 1  0
 0  1

julia> eye(2)
2×2 Array{Float64,2}:
 1.0  0.0
 0.0  1.0
```
"""
eye(n::Integer) = eye(Float64, n)

"""
    eye(A)

Constructs an identity matrix of the same dimensions and type as `A`.

# Examples
```jldoctest
julia> A = [1 2 3; 4 5 6; 7 8 9]
3×3 Array{Int64,2}:
 1  2  3
 4  5  6
 7  8  9

julia> eye(A)
3×3 Array{Int64,2}:
 1  0  0
 0  1  0
 0  0  1
```

Note the difference from [`ones`](@ref).
"""
eye(x::AbstractMatrix{T}) where {T} = eye(typeof(one(T)), size(x, 1), size(x, 2))

function _one(unit::T, x::AbstractMatrix) where T
    m,n = size(x)
    m==n || throw(DimensionMismatch("multiplicative identity defined only for square matrices"))
    eye(T, m)
end

one(x::AbstractMatrix{T}) where {T} = _one(one(T), x)
oneunit(x::AbstractMatrix{T}) where {T} = _one(oneunit(T), x)

## Conversions ##

convert(::Type{Vector}, x::AbstractVector{T}) where {T} = convert(Vector{T}, x)
convert(::Type{Matrix}, x::AbstractMatrix{T}) where {T} = convert(Matrix{T}, x)

convert(::Type{Array{T}}, x::Array{T,n}) where {T,n} = x
convert(::Type{Array{T,n}}, x::Array{T,n}) where {T,n} = x

convert(::Type{Array{T}}, x::AbstractArray{S,n}) where {T,n,S} = convert(Array{T,n}, x)
convert(::Type{Array{T,n}}, x::AbstractArray{S,n}) where {T,n,S} = copy!(Array{T,n}(size(x)), x)

promote_rule(a::Type{Array{T,n}}, b::Type{Array{S,n}}) where {T,n,S} = el_same(promote_type(T,S), a, b)

# constructors should make copies

if module_name(@__MODULE__) === :Base  # avoid method overwrite
(::Type{T})(x::T) where {T<:Array} = copy(x)
end

## copying iterators to containers

"""
    collect(element_type, collection)

Return an `Array` with the given element type of all items in a collection or iterable.
The result has the same shape and number of dimensions as `collection`.

# Examples
```jldoctest
julia> collect(Float64, 1:2:5)
3-element Array{Float64,1}:
 1.0
 3.0
 5.0
```
"""
collect(::Type{T}, itr) where {T} = _collect(T, itr, iteratorsize(itr))

_collect(::Type{T}, itr, isz::HasLength) where {T} = copy!(Array{T,1}(Int(length(itr)::Integer)), itr)
_collect(::Type{T}, itr, isz::HasShape) where {T}  = copy!(similar(Array{T}, indices(itr)), itr)
function _collect(::Type{T}, itr, isz::SizeUnknown) where T
    a = Array{T,1}(0)
    for x in itr
        push!(a,x)
    end
    return a
end

# make a collection similar to `c` and appropriate for collecting `itr`
_similar_for(c::AbstractArray, T, itr, ::SizeUnknown) = similar(c, T, 0)
_similar_for(c::AbstractArray, T, itr, ::HasLength) = similar(c, T, Int(length(itr)::Integer))
_similar_for(c::AbstractArray, T, itr, ::HasShape) = similar(c, T, indices(itr))
_similar_for(c, T, itr, isz) = similar(c, T)

"""
    collect(collection)

Return an `Array` of all items in a collection or iterator. For associative collections, returns
`Pair{KeyType, ValType}`. If the argument is array-like or is an iterator with the `HasShape()`
trait, the result will have the same shape and number of dimensions as the argument.

# Examples
```jldoctest
julia> collect(1:2:13)
7-element Array{Int64,1}:
  1
  3
  5
  7
  9
 11
 13
```
"""
collect(itr) = _collect(1:1 #= Array =#, itr, iteratoreltype(itr), iteratorsize(itr))

collect(A::AbstractArray) = _collect_indices(indices(A), A)

collect_similar(cont, itr) = _collect(cont, itr, iteratoreltype(itr), iteratorsize(itr))

_collect(cont, itr, ::HasEltype, isz::Union{HasLength,HasShape}) =
    copy!(_similar_for(cont, eltype(itr), itr, isz), itr)

function _collect(cont, itr, ::HasEltype, isz::SizeUnknown)
    a = _similar_for(cont, eltype(itr), itr, isz)
    for x in itr
        push!(a,x)
    end
    return a
end

_collect_indices(::Tuple{}, A) = copy!(Vector{eltype(A)}(), A)
_collect_indices(indsA::Tuple{Vararg{OneTo}}, A) =
    copy!(Array{eltype(A)}(length.(indsA)), A)
function _collect_indices(indsA, A)
    B = Array{eltype(A)}(length.(indsA))
    copy!(B, CartesianRange(indices(B)), A, CartesianRange(indsA))
end

if isdefined(Core, :Inference)
    _default_eltype(@nospecialize itrt) = Core.Inference.return_type(first, Tuple{itrt})
else
    _default_eltype(@nospecialize itr) = Any
end

_array_for(::Type{T}, itr, ::HasLength) where {T} = Array{T,1}(Int(length(itr)::Integer))
_array_for(::Type{T}, itr, ::HasShape) where {T} = similar(Array{T}, indices(itr))

function collect(itr::Generator)
    isz = iteratorsize(itr.iter)
    et = _default_eltype(typeof(itr))
    if isa(isz, SizeUnknown)
        return grow_to!(Array{et,1}(0), itr)
    else
        st = start(itr)
        if done(itr,st)
            return _array_for(et, itr.iter, isz)
        end
        v1, st = next(itr, st)
        collect_to_with_first!(_array_for(typeof(v1), itr.iter, isz), v1, itr, st)
    end
end

_collect(c, itr, ::EltypeUnknown, isz::SizeUnknown) =
    grow_to!(_similar_for(c, _default_eltype(typeof(itr)), itr, isz), itr)

function _collect(c, itr, ::EltypeUnknown, isz::Union{HasLength,HasShape})
    st = start(itr)
    if done(itr,st)
        return _similar_for(c, _default_eltype(typeof(itr)), itr, isz)
    end
    v1, st = next(itr, st)
    collect_to_with_first!(_similar_for(c, typeof(v1), itr, isz), v1, itr, st)
end

function collect_to_with_first!(dest::AbstractArray, v1, itr, st)
    i1 = first(linearindices(dest))
    dest[i1] = v1
    return collect_to!(dest, itr, i1+1, st)
end

function collect_to_with_first!(dest, v1, itr, st)
    push!(dest, v1)
    return grow_to!(dest, itr, st)
end

function collect_to!(dest::AbstractArray{T}, itr, offs, st) where T
    # collect to dest array, checking the type of each result. if a result does not
    # match, widen the result type and re-dispatch.
    i = offs
    while !done(itr, st)
        el, st = next(itr, st)
        S = typeof(el)
        if S === T || S <: T
            @inbounds dest[i] = el::T
            i += 1
        else
            R = typejoin(T, S)
            new = similar(dest, R)
            copy!(new,1, dest,1, i-1)
            @inbounds new[i] = el
            return collect_to!(new, itr, i+1, st)
        end
    end
    return dest
end

function grow_to!(dest, itr)
    out = grow_to!(similar(dest,Union{}), itr, start(itr))
    return isempty(out) ? dest : out
end

function grow_to!(dest, itr, st)
    T = eltype(dest)
    while !done(itr, st)
        el, st = next(itr, st)
        S = typeof(el)
        if S === T || S <: T
            push!(dest, el::T)
        else
            new = similar(dest, typejoin(T, S))
            copy!(new, dest)
            push!(new, el)
            return grow_to!(new, itr, st)
        end
    end
    return dest
end

## Iteration ##
start(A::Array) = 1
next(a::Array,i) = (@_propagate_inbounds_meta; (a[i],i+1))
done(a::Array,i) = (@_inline_meta; i == length(a)+1)

## Indexing: getindex ##

"""
    getindex(collection, key...)

Retrieve the value(s) stored at the given key or index within a collection. The syntax
`a[i,j,...]` is converted by the compiler to `getindex(a, i, j, ...)`.

# Examples
```jldoctest
julia> A = Dict("a" => 1, "b" => 2)
Dict{String,Int64} with 2 entries:
  "b" => 2
  "a" => 1

julia> getindex(A, "a")
1
```
"""
function getindex end

# This is more complicated than it needs to be in order to get Win64 through bootstrap
@eval getindex(A::Array, i1::Int) = arrayref($(Expr(:boundscheck)), A, i1)
@eval getindex(A::Array, i1::Int, i2::Int, I::Int...) = (@_inline_meta; arrayref($(Expr(:boundscheck)), A, i1, i2, I...)) # TODO: REMOVE FOR #14770

# Faster contiguous indexing using copy! for UnitRange and Colon
function getindex(A::Array, I::UnitRange{Int})
    @_inline_meta
    @boundscheck checkbounds(A, I)
    lI = length(I)
    X = similar(A, lI)
    if lI > 0
        unsafe_copy!(X, 1, A, first(I), lI)
    end
    return X
end
function getindex(A::Array, c::Colon)
    lI = length(A)
    X = similar(A, lI)
    if lI > 0
        unsafe_copy!(X, 1, A, 1, lI)
    end
    return X
end

# This is redundant with the abstract fallbacks, but needed for bootstrap
function getindex(A::Array{S}, I::Range{Int}) where S
    return S[ A[i] for i in I ]
end

## Indexing: setindex! ##

"""
    setindex!(collection, value, key...)

Store the given value at the given key or index within a collection. The syntax `a[i,j,...] =
x` is converted by the compiler to `(setindex!(a, x, i, j, ...); x)`.
"""
function setindex! end

@eval setindex!(A::Array{T}, x, i1::Int) where {T} = arrayset($(Expr(:boundscheck)), A, convert(T,x)::T, i1)
@eval setindex!(A::Array{T}, x, i1::Int, i2::Int, I::Int...) where {T} =
    (@_inline_meta; arrayset($(Expr(:boundscheck)), A, convert(T,x)::T, i1, i2, I...)) # TODO: REMOVE FOR #14770

# These are redundant with the abstract fallbacks but needed for bootstrap
function setindex!(A::Array, x, I::AbstractVector{Int})
    @_propagate_inbounds_meta
    A === I && (I = copy(I))
    for i in I
        A[i] = x
    end
    return A
end
function setindex!(A::Array, X::AbstractArray, I::AbstractVector{Int})
    @_propagate_inbounds_meta
    @boundscheck setindex_shape_check(X, length(I))
    count = 1
    if X === A
        X = copy(X)
        I===A && (I = X::typeof(I))
    elseif I === A
        I = copy(I)
    end
    for i in I
        @inbounds x = X[count]
        A[i] = x
        count += 1
    end
    return A
end

# Faster contiguous setindex! with copy!
function setindex!(A::Array{T}, X::Array{T}, I::UnitRange{Int}) where T
    @_inline_meta
    @boundscheck checkbounds(A, I)
    lI = length(I)
    @boundscheck setindex_shape_check(X, lI)
    if lI > 0
        unsafe_copy!(A, first(I), X, 1, lI)
    end
    return A
end
function setindex!(A::Array{T}, X::Array{T}, c::Colon) where T
    @_inline_meta
    lI = length(A)
    @boundscheck setindex_shape_check(X, lI)
    if lI > 0
        unsafe_copy!(A, 1, X, 1, lI)
    end
    return A
end

setindex!(A::Array, x::Number, ::Colon) = fill!(A, x)
setindex!(A::Array{T, N}, x::Number, ::Vararg{Colon, N}) where {T, N} = fill!(A, x)

# efficiently grow an array

_growbeg!(a::Vector, delta::Integer) =
    ccall(:jl_array_grow_beg, Void, (Any, UInt), a, delta)
_growend!(a::Vector, delta::Integer) =
    ccall(:jl_array_grow_end, Void, (Any, UInt), a, delta)
_growat!(a::Vector, i::Integer, delta::Integer) =
    ccall(:jl_array_grow_at, Void, (Any, Int, UInt), a, i - 1, delta)

# efficiently delete part of an array

_deletebeg!(a::Vector, delta::Integer) =
    ccall(:jl_array_del_beg, Void, (Any, UInt), a, delta)
_deleteend!(a::Vector, delta::Integer) =
    ccall(:jl_array_del_end, Void, (Any, UInt), a, delta)
_deleteat!(a::Vector, i::Integer, delta::Integer) =
    ccall(:jl_array_del_at, Void, (Any, Int, UInt), a, i - 1, delta)

## Dequeue functionality ##

"""
    push!(collection, items...) -> collection

Insert one or more `items` at the end of `collection`.

# Examples
```jldoctest
julia> push!([1, 2, 3], 4, 5, 6)
6-element Array{Int64,1}:
 1
 2
 3
 4
 5
 6
```

Use [`append!`](@ref) to add all the elements of another collection to
`collection`. The result of the preceding example is equivalent to `append!([1, 2, 3], [4,
5, 6])`.
"""
function push! end

function push!(a::Array{T,1}, item) where T
    # convert first so we don't grow the array if the assignment won't work
    itemT = convert(T, item)
    _growend!(a, 1)
    a[end] = itemT
    return a
end

function push!(a::Array{Any,1}, @nospecialize item)
    _growend!(a, 1)
    arrayset(true, a, item, length(a))
    return a
end

"""
    append!(collection, collection2) -> collection.

Add the elements of `collection2` to the end of `collection`.

# Examples
```jldoctest
julia> append!([1],[2,3])
3-element Array{Int64,1}:
 1
 2
 3

julia> append!([1, 2, 3], [4, 5, 6])
6-element Array{Int64,1}:
 1
 2
 3
 4
 5
 6
```

Use [`push!`](@ref) to add individual items to `collection` which are not already
themselves in another collection. The result is of the preceding example is equivalent to
`push!([1, 2, 3], 4, 5, 6)`.
"""
function append!(a::Array{<:Any,1}, items::AbstractVector)
    itemindices = eachindex(items)
    n = length(itemindices)
    _growend!(a, n)
    copy!(a, length(a)-n+1, items, first(itemindices), n)
    return a
end

append!(a::Vector, iter) = _append!(a, iteratorsize(iter), iter)
push!(a::Vector, iter...) = append!(a, iter)

function _append!(a, ::Union{HasLength,HasShape}, iter)
    n = length(a)
    resize!(a, n+length(iter))
    @inbounds for (i,item) in zip(n+1:length(a), iter)
        a[i] = item
    end
    a
end

function _append!(a, ::IteratorSize, iter)
    for item in iter
        push!(a, item)
    end
    a
end

"""
    prepend!(a::Vector, items) -> collection

Insert the elements of `items` to the beginning of `a`.

# Examples
```jldoctest
julia> prepend!([3],[1,2])
3-element Array{Int64,1}:
 1
 2
 3
```
"""
function prepend! end

function prepend!(a::Array{<:Any,1}, items::AbstractVector)
    itemindices = eachindex(items)
    n = length(itemindices)
    _growbeg!(a, n)
    if a === items
        copy!(a, 1, items, n+1, n)
    else
        copy!(a, 1, items, first(itemindices), n)
    end
    return a
end

prepend!(a::Vector, iter) = _prepend!(a, iteratorsize(iter), iter)
unshift!(a::Vector, iter...) = prepend!(a, iter)

function _prepend!(a, ::Union{HasLength,HasShape}, iter)
    n = length(iter)
    _growbeg!(a, n)
    i = 0
    for item in iter
        @inbounds a[i += 1] = item
    end
    a
end
function _prepend!(a, ::IteratorSize, iter)
    n = 0
    for item in iter
        n += 1
        unshift!(a, item)
    end
    reverse!(a, 1, n)
    a
end

"""
    resize!(a::Vector, n::Integer) -> Vector

Resize `a` to contain `n` elements. If `n` is smaller than the current collection
length, the first `n` elements will be retained. If `n` is larger, the new elements are not
guaranteed to be initialized.

# Examples
```jldoctest
julia> resize!([6, 5, 4, 3, 2, 1], 3)
3-element Array{Int64,1}:
 6
 5
 4

julia> a = resize!([6, 5, 4, 3, 2, 1], 8);

julia> length(a)
8

julia> a[1:6]
6-element Array{Int64,1}:
 6
 5
 4
 3
 2
 1
```
"""
function resize!(a::Vector, nl::Integer)
    l = length(a)
    if nl > l
        ccall(:jl_array_grow_end, Void, (Any, UInt), a, nl-l)
    else
        if nl < 0
            throw(ArgumentError("new length must be ≥ 0"))
        end
        _deleteend!(a, l-nl)
    end
    return a
end

"""
    sizehint!(s, n)

Suggest that collection `s` reserve capacity for at least `n` elements. This can improve performance.
"""
function sizehint! end

function sizehint!(a::Vector, sz::Integer)
    ccall(:jl_array_sizehint, Void, (Any, UInt), a, sz)
    a
end

"""
    pop!(collection) -> item

Remove an item in `collection` and return it. If `collection` is an
ordered container, the last item is returned.

# Examples
```jldoctest
julia> A=[1, 2, 3]
3-element Array{Int64,1}:
 1
 2
 3

julia> pop!(A)
3

julia> A
2-element Array{Int64,1}:
 1
 2

julia> S = Set([1, 2])
Set([2, 1])

julia> pop!(S)
2

julia> S
Set([1])

julia> pop!(Dict(1=>2))
1 => 2
```
"""
function pop!(a::Vector)
    if isempty(a)
        throw(ArgumentError("array must be non-empty"))
    end
    item = a[end]
    _deleteend!(a, 1)
    return item
end

"""
    unshift!(collection, items...) -> collection

Insert one or more `items` at the beginning of `collection`.

# Examples
```jldoctest
julia> unshift!([1, 2, 3, 4], 5, 6)
6-element Array{Int64,1}:
 5
 6
 1
 2
 3
 4
```
"""
function unshift!(a::Array{T,1}, item) where T
    item = convert(T, item)
    _growbeg!(a, 1)
    a[1] = item
    return a
end

"""
    shift!(collection) -> item

Remove the first `item` from `collection`.

# Examples
```jldoctest
julia> A = [1, 2, 3, 4, 5, 6]
6-element Array{Int64,1}:
 1
 2
 3
 4
 5
 6

julia> shift!(A)
1

julia> A
5-element Array{Int64,1}:
 2
 3
 4
 5
 6
```
"""
function shift!(a::Vector)
    if isempty(a)
        throw(ArgumentError("array must be non-empty"))
    end
    item = a[1]
    _deletebeg!(a, 1)
    return item
end

"""
    insert!(a::Vector, index::Integer, item)

Insert an `item` into `a` at the given `index`. `index` is the index of `item` in
the resulting `a`.

# Examples
```jldoctest
julia> insert!([6, 5, 4, 2, 1], 4, 3)
6-element Array{Int64,1}:
 6
 5
 4
 3
 2
 1
```
"""
function insert!(a::Array{T,1}, i::Integer, item) where T
    # Throw convert error before changing the shape of the array
    _item = convert(T, item)
    _growat!(a, i, 1)
    # _growat! already did bound check
    @inbounds a[i] = _item
    return a
end

"""
    deleteat!(a::Vector, i::Integer)

Remove the item at the given `i` and return the modified `a`. Subsequent items
are shifted to fill the resulting gap.

# Examples
```jldoctest
julia> deleteat!([6, 5, 4, 3, 2, 1], 2)
5-element Array{Int64,1}:
 6
 4
 3
 2
 1
```
"""
deleteat!(a::Vector, i::Integer) = (_deleteat!(a, i, 1); a)

function deleteat!(a::Vector, r::UnitRange{<:Integer})
    n = length(a)
    isempty(r) || _deleteat!(a, first(r), length(r))
    return a
end

"""
    deleteat!(a::Vector, inds)

Remove the items at the indices given by `inds`, and return the modified `a`.
Subsequent items are shifted to fill the resulting gap.

`inds` can be either an iterator or a collection of sorted and unique integer indices,
or a boolean vector of the same length as `a` with `true` indicating entries to delete.

# Examples
```jldoctest
julia> deleteat!([6, 5, 4, 3, 2, 1], 1:2:5)
3-element Array{Int64,1}:
 5
 3
 1

julia> deleteat!([6, 5, 4, 3, 2, 1], [true, false, true, false, true, false])
3-element Array{Int64,1}:
 5
 3
 1

julia> deleteat!([6, 5, 4, 3, 2, 1], (2, 2))
ERROR: ArgumentError: indices must be unique and sorted
Stacktrace:
 [1] _deleteat!(::Array{Int64,1}, ::Tuple{Int64,Int64}) at ./array.jl:926
 [2] deleteat!(::Array{Int64,1}, ::Tuple{Int64,Int64}) at ./array.jl:913
```
"""
deleteat!(a::Vector, inds) = _deleteat!(a, inds)
deleteat!(a::Vector, inds::AbstractVector) = _deleteat!(a, to_indices(a, (inds,))[1])

function _deleteat!(a::Vector, inds)
    n = length(a)
    s = start(inds)
    done(inds, s) && return a
    (p, s) = next(inds, s)
    q = p+1
    while !done(inds, s)
        (i,s) = next(inds, s)
        if !(q <= i <= n)
            if i < q
                throw(ArgumentError("indices must be unique and sorted"))
            else
                throw(BoundsError())
            end
        end
        while q < i
            @inbounds a[p] = a[q]
            p += 1; q += 1
        end
        q = i+1
    end
    while q <= n
        @inbounds a[p] = a[q]
        p += 1; q += 1
    end
    _deleteend!(a, n-p+1)
    return a
end

# Simpler and more efficient version for logical indexing
function deleteat!(a::Vector, inds::AbstractVector{Bool})
    n = length(a)
    length(inds) == n || throw(BoundsError(a, inds))
    p = 1
    for (q, i) in enumerate(inds)
        @inbounds a[p] = a[q]
        p += !i
    end
    _deleteend!(a, n-p+1)
    return a
end

const _default_splice = []

"""
    splice!(a::Vector, index::Integer, [replacement]) -> item

Remove the item at the given index, and return the removed item.
Subsequent items are shifted left to fill the resulting gap.
If specified, replacement values from an ordered
collection will be spliced in place of the removed item.

# Examples
```jldoctest splice!
julia> A = [6, 5, 4, 3, 2, 1]; splice!(A, 5)
2

julia> A
5-element Array{Int64,1}:
 6
 5
 4
 3
 1

julia> splice!(A, 5, -1)
1

julia> A
5-element Array{Int64,1}:
  6
  5
  4
  3
 -1

julia> splice!(A, 1, [-1, -2, -3])
6

julia> A
7-element Array{Int64,1}:
 -1
 -2
 -3
  5
  4
  3
 -1
```

To insert `replacement` before an index `n` without removing any items, use
`splice!(collection, n:n-1, replacement)`.
"""
function splice!(a::Vector, i::Integer, ins=_default_splice)
    v = a[i]
    m = length(ins)
    if m == 0
        _deleteat!(a, i, 1)
    elseif m == 1
        a[i] = ins[1]
    else
        _growat!(a, i, m-1)
        k = 1
        for x in ins
            a[i+k-1] = x
            k += 1
        end
    end
    return v
end

"""
    splice!(a::Vector, range, [replacement]) -> items

Remove items in the specified index range, and return a collection containing
the removed items.
Subsequent items are shifted left to fill the resulting gap.
If specified, replacement values from an ordered collection will be spliced in
place of the removed items.

To insert `replacement` before an index `n` without removing any items, use
`splice!(collection, n:n-1, replacement)`.

# Examples
```jldoctest splice!
julia> splice!(A, 4:3, 2)
0-element Array{Int64,1}

julia> A
8-element Array{Int64,1}:
 -1
 -2
 -3
  2
  5
  4
  3
 -1
```
"""
function splice!(a::Vector, r::UnitRange{<:Integer}, ins=_default_splice)
    v = a[r]
    m = length(ins)
    if m == 0
        deleteat!(a, r)
        return v
    end

    n = length(a)
    f = first(r)
    l = last(r)
    d = length(r)

    if m < d
        delta = d - m
        _deleteat!(a, (f - 1 < n - l) ? f : (l - delta + 1), delta)
    elseif m > d
        _growat!(a, (f - 1 < n - l) ? f : (l + 1), m - d)
    end

    k = 1
    for x in ins
        a[f+k-1] = x
        k += 1
    end
    return v
end

function empty!(a::Vector)
    _deleteend!(a, length(a))
    return a
end

# use memcmp for lexcmp on byte arrays
function lexcmp(a::Array{UInt8,1}, b::Array{UInt8,1})
    c = ccall(:memcmp, Int32, (Ptr{UInt8}, Ptr{UInt8}, UInt),
              a, b, min(length(a),length(b)))
    return c < 0 ? -1 : c > 0 ? +1 : cmp(length(a),length(b))
end

const BitIntegerArray{N} = Union{map(T->Array{T,N}, BitInteger_types)...} where N
# use memcmp for == on bit integer types
function ==(a::Arr, b::Arr) where Arr <: BitIntegerArray
    size(a) == size(b) && 0 == ccall(
        :memcmp, Int32, (Ptr{Void}, Ptr{Void}, UInt), a, b, sizeof(eltype(Arr)) * length(a))
end

# this is ~20% faster than the generic implementation above for very small arrays
function ==(a::Arr, b::Arr) where Arr <: BitIntegerArray{1}
    len = length(a)
    len == length(b) && 0 == ccall(
        :memcmp, Int32, (Ptr{Void}, Ptr{Void}, UInt), a, b, sizeof(eltype(Arr)) * len)
end

"""
    reverse(v [, start=1 [, stop=length(v) ]] )

Return a copy of `v` reversed from start to stop.

# Examples
```jldoctest
julia> A = collect(1:5)
5-element Array{Int64,1}:
 1
 2
 3
 4
 5

julia> reverse(A)
5-element Array{Int64,1}:
 5
 4
 3
 2
 1

julia> reverse(A, 1, 4)
5-element Array{Int64,1}:
 4
 3
 2
 1
 5

julia> reverse(A, 3, 5)
5-element Array{Int64,1}:
 1
 2
 5
 4
 3
```
"""
function reverse(A::AbstractVector, s=first(linearindices(A)), n=last(linearindices(A)))
    B = similar(A)
    for i = first(linearindices(A)):s-1
        B[i] = A[i]
    end
    for i = s:n
        B[i] = A[n+s-i]
    end
    for i = n+1:last(linearindices(A))
        B[i] = A[i]
    end
    return B
end
function reverseind(a::AbstractVector, i::Integer)
    li = linearindices(a)
    first(li) + last(li) - i
end

"""
    reverse!(v [, start=1 [, stop=length(v) ]]) -> v

In-place version of [`reverse`](@ref).
"""
function reverse!(v::AbstractVector, s=first(linearindices(v)), n=last(linearindices(v)))
    liv = linearindices(v)
    if n <= s  # empty case; ok
    elseif !(first(liv) ≤ s ≤ last(liv))
        throw(BoundsError(v, s))
    elseif !(first(liv) ≤ n ≤ last(liv))
        throw(BoundsError(v, n))
    end
    r = n
    @inbounds for i in s:div(s+n-1, 2)
        v[i], v[r] = v[r], v[i]
        r -= 1
    end
    return v
end

# concatenations of homogeneous combinations of vectors, horizontal and vertical

vcat() = Array{Any,1}(0)
hcat() = Array{Any,1}(0)

function hcat(V::Vector{T}...) where T
    height = length(V[1])
    for j = 2:length(V)
        if length(V[j]) != height
            throw(DimensionMismatch("vectors must have same lengths"))
        end
    end
    return [ V[j][i]::T for i=1:length(V[1]), j=1:length(V) ]
end

function vcat(arrays::Vector{T}...) where T
    n = 0
    for a in arrays
        n += length(a)
    end
    arr = Array{T,1}(n)
    ptr = pointer(arr)
    if isbits(T)
        elsz = Core.sizeof(T)
    elseif isbitsunion(T)
        elsz = bitsunionsize(T)
        selptr = convert(Ptr{UInt8}, ptr) + n * elsz
    else
        elsz = Core.sizeof(Ptr{Void})
    end
    for a in arrays
        na = length(a)
        nba = na * elsz
        if isbits(T)
            ccall(:memcpy, Ptr{Void}, (Ptr{Void}, Ptr{Void}, UInt),
                  ptr, a, nba)
        elseif isbitsunion(T)
            ccall(:memcpy, Ptr{Void}, (Ptr{Void}, Ptr{Void}, UInt),
                  ptr, a, nba)
            # copy selector bytes
            ccall(:memcpy, Ptr{Void}, (Ptr{Void}, Ptr{Void}, UInt),
                  selptr, convert(Ptr{UInt8}, pointer(a)) + nba, na)
            selptr += na
        else
            ccall(:jl_array_ptr_copy, Void, (Any, Ptr{Void}, Any, Ptr{Void}, Int),
                  arr, ptr, a, pointer(a), na)
        end
        ptr += nba
    end
    return arr
end

cat(n::Integer, x::Integer...) = reshape([x...], (ntuple(x->1, n-1)..., length(x)))

## find ##

"""
    findnext(A, i::Integer)

Find the next linear index >= `i` of a non-zero element of `A`, or `0` if not found.

# Examples
```jldoctest
julia> A = [0 0; 1 0]
2×2 Array{Int64,2}:
 0  0
 1  0

julia> findnext(A,1)
2

julia> findnext(A,3)
0
```
"""
function findnext(A, start::Integer)
    l = endof(A)
    i = start
    while i <= l
        if A[i] != 0
            return i
        end
        i = nextind(A, i)
    end
    return 0
end

"""
    findfirst(A)

Return the linear index of the first non-zero value in `A` (determined by `A[i]!=0`).
Returns `0` if no such value is found.

# Examples
```jldoctest
julia> A = [0 0; 1 0]
2×2 Array{Int64,2}:
 0  0
 1  0

julia> findfirst(A)
2

julia> findfirst(zeros(3))
0
```
"""
findfirst(A) = findnext(A, 1)

"""
    findnext(A, v, i::Integer)

Find the next linear index >= `i` of an element of `A` equal to `v` (using `==`), or `0` if not found.

# Examples
```jldoctest
julia> A = [1 4; 2 2]
2×2 Array{Int64,2}:
 1  4
 2  2

julia> findnext(A,4,4)
0

julia> findnext(A,4,3)
3
```
"""
function findnext(A, v, start::Integer)
    l = endof(A)
    i = start
    while i <= l
        if A[i] == v
            return i
        end
        i = nextind(A, i)
    end
    return 0
end
"""
    findfirst(A, v)

Return the linear index of the first element equal to `v` in `A`.
Returns `0` if `v` is not found.

# Examples
```jldoctest
julia> A = [4 6; 2 2]
2×2 Array{Int64,2}:
 4  6
 2  2

julia> findfirst(A,2)
2

julia> findfirst(A,3)
0
```
"""
findfirst(A, v) = findnext(A, v, 1)

"""
    findnext(predicate::Function, A, i::Integer)

Find the next linear index >= `i` of an element of `A` for which `predicate` returns `true`, or `0` if not found.

# Examples
```jldoctest
julia> A = [1 4; 2 2]
2×2 Array{Int64,2}:
 1  4
 2  2

julia> findnext(isodd, A, 1)
1

julia> findnext(isodd, A, 2)
0
```
"""
function findnext(testf::Function, A, start::Integer)
    l = endof(A)
    i = start
    while i <= l
        if testf(A[i])
            return i
        end
        i = nextind(A, i)
    end
    return 0
end

"""
    findfirst(predicate::Function, A)

Return the linear index of the first element of `A` for which `predicate` returns `true`.
Returns `0` if there is no such element.

# Examples
```jldoctest
julia> A = [1 4; 2 2]
2×2 Array{Int64,2}:
 1  4
 2  2

julia> findfirst(iseven, A)
2

julia> findfirst(x -> x>10, A)
0
```
"""
findfirst(testf::Function, A) = findnext(testf, A, 1)

"""
    findprev(A, i::Integer)

Find the previous linear index <= `i` of a non-zero element of `A`, or `0` if not found.

# Examples
```jldoctest
julia> A = [0 0; 1 2]
2×2 Array{Int64,2}:
 0  0
 1  2

julia> findprev(A,2)
2

julia> findprev(A,1)
0
```
"""
function findprev(A, start::Integer)
    i = start
    while i >= 1
        A[i] != 0 && return i
        i = prevind(A, i)
    end
    return 0
end

"""
    findlast(A)

Return the linear index of the last non-zero value in `A` (determined by `A[i]!=0`).
Returns `0` if there is no non-zero value in `A`.

# Examples
```jldoctest
julia> A = [1 0; 1 0]
2×2 Array{Int64,2}:
 1  0
 1  0

julia> findlast(A)
2

julia> A = zeros(2,2)
2×2 Array{Float64,2}:
 0.0  0.0
 0.0  0.0

julia> findlast(A)
0
```
"""
findlast(A) = findprev(A, endof(A))

"""
    findprev(A, v, i::Integer)

Find the previous linear index <= `i` of an element of `A` equal to `v` (using `==`), or `0` if not found.

# Examples
```jldoctest
julia> A = [0 0; 1 2]
2×2 Array{Int64,2}:
 0  0
 1  2

julia> findprev(A, 1, 4)
2

julia> findprev(A, 1, 1)
0
```
"""
function findprev(A, v, start::Integer)
    i = start
    while i >= 1
        A[i] == v && return i
        i = prevind(A, i)
    end
    return 0
end

"""
    findlast(A, v)

Return the linear index of the last element equal to `v` in `A`.
Returns `0` if there is no element of `A` equal to `v`.

# Examples
```jldoctest
julia> A = [1 2; 2 1]
2×2 Array{Int64,2}:
 1  2
 2  1

julia> findlast(A,1)
4

julia> findlast(A,2)
3

julia> findlast(A,3)
0
```
"""
findlast(A, v) = findprev(A, v, endof(A))

"""
    findprev(predicate::Function, A, i::Integer)

Find the previous linear index <= `i` of an element of `A` for which `predicate` returns `true`, or
`0` if not found.

# Examples
```jldoctest
julia> A = [4 6; 1 2]
2×2 Array{Int64,2}:
 4  6
 1  2

julia> findprev(isodd, A, 1)
0

julia> findprev(isodd, A, 3)
2
```
"""
function findprev(testf::Function, A, start::Integer)
    i = start
    while i >= 1
        testf(A[i]) && return i
        i = prevind(A, i)
    end
    return 0
end

"""
    findlast(predicate::Function, A)

Return the linear index of the last element of `A` for which `predicate` returns `true`.
Returns `0` if there is no such element.

# Examples
```jldoctest
julia> A = [1 2; 3 4]
2×2 Array{Int64,2}:
 1  2
 3  4

julia> findlast(isodd, A)
2

julia> findlast(x -> x > 5, A)
0
```
"""
findlast(testf::Function, A) = findprev(testf, A, endof(A))

"""
    find(f::Function, A)

Return a vector `I` of the linear indexes of `A` where `f(A[I])` returns `true`.
If there are no such elements of `A`, find returns an empty array.

# Examples
```jldoctest
julia> A = [1 2; 3 4]
2×2 Array{Int64,2}:
 1  2
 3  4

julia> find(isodd,A)
2-element Array{Int64,1}:
 1
 2

julia> find(isodd, [2, 4])
0-element Array{Int64,1}
```
"""
function find(testf::Function, A)
    # use a dynamic-length array to store the indexes, then copy to a non-padded
    # array for the return
    tmpI = Array{Int,1}(0)
    inds = _index_remapper(A)
    for (i,a) = enumerate(A)
        if testf(a)
            push!(tmpI, inds[i])
        end
    end
    I = Array{Int,1}(length(tmpI))
    copy!(I, tmpI)
    return I
end
_index_remapper(A::AbstractArray) = linearindices(A)
_index_remapper(iter) = OneTo(typemax(Int))  # safe for objects that don't implement length

"""
    find(A)

Return a vector of the linear indexes of the non-zeros in `A` (determined by `A[i]!=0`). A
common use of this is to convert a boolean array to an array of indexes of the `true`
elements. If there are no non-zero elements of `A`, `find` returns an empty array.

# Examples
```jldoctest
julia> A = [true false; false true]
2×2 Array{Bool,2}:
  true  false
 false   true

julia> find(A)
2-element Array{Int64,1}:
 1
 4

julia> find(zeros(3))
0-element Array{Int64,1}
```
"""
function find(A)
    nnzA = count(t -> t != 0, A)
    I = Vector{Int}(nnzA)
    cnt = 1
    inds = _index_remapper(A)
    for (i,a) in enumerate(A)
        if a != 0
            I[cnt] = inds[i]
            cnt += 1
        end
    end
    return I
end

find(x::Number) = x == 0 ? Array{Int,1}(0) : [1]
find(testf::Function, x::Number) = !testf(x) ? Array{Int,1}(0) : [1]

findn(A::AbstractVector) = find(A)

"""
    findn(A)

Return a vector of indexes for each dimension giving the locations of the non-zeros in `A`
(determined by `A[i]!=0`).
If there are no non-zero elements of `A`, `findn` returns a 2-tuple of empty arrays.

# Examples
```jldoctest
julia> A = [1 2 0; 0 0 3; 0 4 0]
3×3 Array{Int64,2}:
 1  2  0
 0  0  3
 0  4  0

julia> findn(A)
([1, 1, 3, 2], [1, 2, 2, 3])

julia> A = zeros(2,2)
2×2 Array{Float64,2}:
 0.0  0.0
 0.0  0.0

julia> findn(A)
(Int64[], Int64[])
```
"""
function findn(A::AbstractMatrix)
    nnzA = count(t -> t != 0, A)
    I = similar(A, Int, nnzA)
    J = similar(A, Int, nnzA)
    cnt = 1
    for j=indices(A,2), i=indices(A,1)
        if A[i,j] != 0
            I[cnt] = i
            J[cnt] = j
            cnt += 1
        end
    end
    return (I, J)
end

"""
    findnz(A)

Return a tuple `(I, J, V)` where `I` and `J` are the row and column indexes of the non-zero
values in matrix `A`, and `V` is a vector of the non-zero values.

# Examples
```jldoctest
julia> A = [1 2 0; 0 0 3; 0 4 0]
3×3 Array{Int64,2}:
 1  2  0
 0  0  3
 0  4  0

julia> findnz(A)
([1, 1, 3, 2], [1, 2, 2, 3], [1, 2, 4, 3])
```
"""
function findnz(A::AbstractMatrix{T}) where T
    nnzA = count(t -> t != 0, A)
    I = zeros(Int, nnzA)
    J = zeros(Int, nnzA)
    NZs = Array{T,1}(nnzA)
    cnt = 1
    if nnzA > 0
        for j=indices(A,2), i=indices(A,1)
            Aij = A[i,j]
            if Aij != 0
                I[cnt] = i
                J[cnt] = j
                NZs[cnt] = Aij
                cnt += 1
            end
        end
    end
    return (I, J, NZs)
end

"""
    findmax(itr) -> (x, index)

Returns the maximum element of the collection `itr` and its index. If there are multiple
maximal elements, then the first one will be returned.
If any data element is `NaN`, this element is returned.
The result is in line with `max`.

The collection must not be empty.

# Examples
```jldoctest
julia> findmax([8,0.1,-9,pi])
(8.0, 1)

julia> findmax([1,7,7,6])
(7, 2)

julia> findmax([1,7,7,NaN])
(NaN, 4)
```
"""
function findmax(a)
    if isempty(a)
        throw(ArgumentError("collection must be non-empty"))
    end
    p = pairs(a)
    s = start(p)
    (mi, m), s = next(p, s)
    i = mi
    while !done(p, s)
        m != m && break
        (i, ai), s = next(p, s)
        if ai != ai || isless(m, ai)
            m = ai
            mi = i
        end
    end
    return (m, mi)
end

"""
    findmin(itr) -> (x, index)

Returns the minimum element of the collection `itr` and its index. If there are multiple
minimal elements, then the first one will be returned.
If any data element is `NaN`, this element is returned.
The result is in line with `min`.

The collection must not be empty.

# Examples
```jldoctest
julia> findmin([8,0.1,-9,pi])
(-9.0, 3)

julia> findmin([7,1,1,6])
(1, 2)

julia> findmin([7,1,1,NaN])
(NaN, 4)
```
"""
function findmin(a)
    if isempty(a)
        throw(ArgumentError("collection must be non-empty"))
    end
    p = pairs(a)
    s = start(p)
    (mi, m), s = next(p, s)
    i = mi
    while !done(p, s)
        m != m && break
        (i, ai), s = next(p, s)
        if ai != ai || isless(ai, m)
            m = ai
            mi = i
        end
    end
    return (m, mi)
end

"""
    indmax(itr) -> Integer

Returns the index of the maximum element in a collection. If there are multiple maximal
elements, then the first one will be returned.

The collection must not be empty.

# Examples
```jldoctest
julia> indmax([8,0.1,-9,pi])
1

julia> indmax([1,7,7,6])
2

julia> indmax([1,7,7,NaN])
4
```
"""
indmax(a) = findmax(a)[2]

"""
    indmin(itr) -> Integer

Returns the index of the minimum element in a collection. If there are multiple minimal
elements, then the first one will be returned.

The collection must not be empty.

# Examples
```jldoctest
julia> indmin([8,0.1,-9,pi])
3

julia> indmin([7,1,1,6])
2

julia> indmin([7,1,1,NaN])
4
```
"""
indmin(a) = findmin(a)[2]

# similar to Matlab's ismember
"""
    indexin(a, b)

Returns a vector containing the highest index in `b` for
each value in `a` that is a member of `b` . The output
vector contains 0 wherever `a` is not a member of `b`.

# Examples
```jldoctest
julia> a = ['a', 'b', 'c', 'b', 'd', 'a'];

julia> b = ['a','b','c'];

julia> indexin(a,b)
6-element Array{Int64,1}:
 1
 2
 3
 2
 0
 1

julia> indexin(b,a)
3-element Array{Int64,1}:
 6
 4
 3
```
"""
function indexin(a::AbstractArray, b::AbstractArray)
    bdict = Dict(zip(b, 1:length(b)))
    [get(bdict, i, 0) for i in a]
end

function _findin(a, b)
    ind  = Int[]
    bset = Set(b)
    @inbounds for (i,ai) in enumerate(a)
        ai in bset && push!(ind, i)
    end
    ind
end

# If two collections are already sorted, findin can be computed with
# a single traversal of the two collections. This is much faster than
# using a hash table (although it has the same complexity).
function _sortedfindin(v, w)
    viter, witer = eachindex(v), eachindex(w)
    out  = eltype(viter)[]
    i, j = start(viter), start(witer)
    if done(viter, i) || done(witer, j)
        return out
    end
    viteri, i = next(viter, i)
    witerj, j = next(witer, j)
    @inbounds begin
        vi, wj = v[viteri], w[witerj]
        while true
            if isless(vi, wj)
                if done(viter, i)
                    break
                end
                viteri, i = next(viter, i)
                vi        = v[viteri]
            elseif isless(wj, vi)
                if done(witer, j)
                    break
                end
                witerj, j = next(witer, j)
                wj        = w[witerj]
            else
                push!(out, viteri)
                if done(viter, i)
                    break
                end
                # We only increment the v iterator because v can have
                # repeated matches to a single value in w
                viteri, i = next(viter, i)
                vi        = v[viteri]
            end
        end
    end
    return out
end

"""
    findin(a, b)

Returns the indices of elements in collection `a` that appear in collection `b`.

# Examples
```jldoctest
julia> a = collect(1:3:15)
5-element Array{Int64,1}:
  1
  4
  7
 10
 13

julia> b = collect(2:4:10)
3-element Array{Int64,1}:
  2
  6
 10

julia> findin(a,b) # 10 is the only common element
1-element Array{Int64,1}:
 4
```
"""
function findin(a::Array{<:Real}, b::Union{Array{<:Real},Real})
    if issorted(a, Sort.Forward) && issorted(b, Sort.Forward)
        return _sortedfindin(a, b)
    else
        return _findin(a, b)
    end
end
# issorted fails for some element types so the method above has to be restricted
# to element with isless/< defined.
findin(a, b) = _findin(a, b)

# Copying subregions
# TODO: DEPRECATE FOR #14770
function indcopy(sz::Dims, I::Vector)
    n = length(I)
    s = sz[n]
    for i = n+1:length(sz)
        s *= sz[i]
    end
    dst = eltype(I)[findin(I[i], i < n ? (1:sz[i]) : (1:s)) for i = 1:n]
    src = eltype(I)[I[i][findin(I[i], i < n ? (1:sz[i]) : (1:s))] for i = 1:n]
    dst, src
end

function indcopy(sz::Dims, I::Tuple{Vararg{RangeIndex}})
    n = length(I)
    s = sz[n]
    for i = n+1:length(sz)
        s *= sz[i]
    end
    dst::typeof(I) = ntuple(i-> findin(I[i], i < n ? (1:sz[i]) : (1:s)), n)::typeof(I)
    src::typeof(I) = ntuple(i-> I[i][findin(I[i], i < n ? (1:sz[i]) : (1:s))], n)::typeof(I)
    dst, src
end

## Filter ##

"""
    filter(f, a::AbstractArray)

Return a copy of `a`, removing elements for which `f` is `false`.
The function `f` is passed one argument.

# Examples
```jldoctest
julia> a = 1:10
1:10

julia> filter(isodd, a)
5-element Array{Int64,1}:
 1
 3
 5
 7
 9
```
"""
filter(f, As::AbstractArray) = As[map(f, As)::AbstractArray{Bool}]

"""
    filter!(f, a::AbstractVector)

Update `a`, removing elements for which `f` is `false`.
The function `f` is passed one argument.

# Examples
```jldoctest
julia> filter!(isodd, collect(1:10))
5-element Array{Int64,1}:
 1
 3
 5
 7
 9
```
"""
function filter!(f, a::AbstractVector)
    isempty(a) && return a

    idx = eachindex(a)
    state = start(idx)
    i, state = next(idx, state)

    for acurr in a
        if f(acurr)
            a[i] = acurr
            i, state = next(idx, state)
        end
    end

    deleteat!(a, i:last(idx))

    return a
end

function filter(f, a::Vector)
    r = Vector{eltype(a)}(0)
    for ai in a
        if f(ai)
            push!(r, ai)
        end
    end
    return r
end

# set-like operators for vectors
# These are moderately efficient, preserve order, and remove dupes.

function intersect(v1, vs...)
    ret = Vector{promote_eltype(v1, vs...)}(0)
    for v_elem in v1
        inall = true
        for vsi in vs
            if !in(v_elem, vsi)
                inall=false; break
            end
        end
        if inall
            push!(ret, v_elem)
        end
    end
    ret
end

function union(vs...)
    ret = Vector{promote_eltype(vs...)}(0)
    seen = Set()
    for v in vs
        for v_elem in v
            if !in(v_elem, seen)
                push!(ret, v_elem)
                push!(seen, v_elem)
            end
        end
    end
    ret
end
# setdiff only accepts two args

"""
    setdiff(a, b)

Construct the set of elements in `a` but not `b`. Maintains order with arrays. Note that
both arguments must be collections, and both will be iterated over. In particular,
`setdiff(set,element)` where `element` is a potential member of `set`, will not work in
general.

# Examples
```jldoctest
julia> setdiff([1,2,3],[3,4,5])
2-element Array{Int64,1}:
 1
 2
```
"""
function setdiff(a, b)
    args_type = promote_type(eltype(a), eltype(b))
    bset = Set(b)
    ret = Array{args_type,1}(0)
    seen = Set{eltype(a)}()
    for a_elem in a
        if !in(a_elem, seen) && !in(a_elem, bset)
            push!(ret, a_elem)
            push!(seen, a_elem)
        end
    end
    ret
end
# symdiff is associative, so a relatively clean
# way to implement this is by using setdiff and union, and
# recursing. Has the advantage of keeping order, too, but
# not as fast as other methods that make a single pass and
# store counts with a Dict.
symdiff(a) = a
symdiff(a, b) = union(setdiff(a,b), setdiff(b,a))
"""
    symdiff(a, b, rest...)

Construct the symmetric difference of elements in the passed in sets or arrays.
Maintains order with arrays.

# Examples
```jldoctest
julia> symdiff([1,2,3],[3,4,5],[4,5,6])
3-element Array{Int64,1}:
 1
 2
 6
```
"""
symdiff(a, b, rest...) = symdiff(a, symdiff(b, rest...))