array.jl

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

## array.jl: Dense arrays

## Type aliases for convenience ##

typealias AbstractVector{T} AbstractArray{T,1}
typealias AbstractMatrix{T} AbstractArray{T,2}
typealias AbstractVecOrMat{T} Union{AbstractVector{T}, AbstractMatrix{T}}
typealias RangeIndex Union{Int, Range{Int}, AbstractUnitRange{Int}, Colon}
typealias DimOrInd Union{Integer, AbstractUnitRange}
typealias IntOrInd Union{Int, AbstractUnitRange}
typealias DimsOrInds{N} NTuple{N,DimOrInd}
typealias NeedsShaping Union{Tuple{Integer,Vararg{Integer}}, Tuple{OneTo,Vararg{OneTo}}}

typealias Vector{T} Array{T,1}
typealias Matrix{T} Array{T,2}
typealias VecOrMat{T} Union{Vector{T}, Matrix{T}}

typealias DenseVector{T} DenseArray{T,1}
typealias DenseMatrix{T} DenseArray{T,2}
typealias DenseVecOrMat{T} Union{DenseVector{T}, DenseMatrix{T}}

## Basic functions ##

import Core: arraysize, arrayset, arrayref

vect() = Array{Any,1}(0)
vect{T}(X::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) = (@_inline_meta; _size((), a))
_size{_,N}(out::NTuple{N}, A::Array{_,N}) = out
function _size{_,M,N}(out::NTuple{M}, A::Array{_,N})
    @_inline_meta
    _size((out..., size(A,M+1)), A)
end

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

length(a::Array) = arraylen(a)
elsize{T}(a::Array{T}) = isbits(T) ? sizeof(T) : sizeof(Ptr)
sizeof(a::Array) = elsize(a) * length(a)

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

## copy ##

function unsafe_copy!{T}(dest::Ptr{T}, src::Ptr{T}, n)
    # 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

function unsafe_copy!{T}(dest::Array{T}, doffs, src::Array{T}, soffs, n)
    if isbits(T)
        unsafe_copy!(pointer(dest, doffs), pointer(src, soffs), 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

function copy!{T}(dest::Array{T}, doffs::Integer, src::Array{T}, soffs::Integer, n::Integer)
    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!{T}(dest::Array{T}, src::Array{T}) = copy!(dest, 1, src, 1, length(src))

copy{T<:Array}(a::T) = ccall(:jl_array_copy, Ref{T}, (Any,), a)

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

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

function reinterpret{T,S,N}(::Type{T}, a::Array{S}, dims::NTuple{N,Int})
    if !isbits(T)
        throw(ArgumentError("cannot reinterpret Array{$(S)} to ::Type{Array{$(T)}}, type $(T) is not a bitstype"))
    end
    if !isbits(S)
        throw(ArgumentError("cannot reinterpret Array{$(S)} to ::Type{Array{$(T)}}, type $(S) is not a bitstype"))
    end
    nel = div(length(a)*sizeof(S),sizeof(T))
    if prod(dims) != nel
        throw(DimensionMismatch("new dimensions $(dims) must be consistent with array size $(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{T,N}(a::Array{T,N}, dims::NTuple{N,Int})
    if prod(dims) != length(a)
        throw(DimensionMismatch("new dimensions $(dims) must be consistent with array size $(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{T,N}(a::Array{T}, dims::NTuple{N,Int})
    if prod(dims) != length(a)
        throw(DimensionMismatch("new dimensions $(dims) must be consistent with array size $(length(a))"))
    end
    ccall(:jl_reshape_array, Array{T,N}, (Any, Any, Any), Array{T,N}, a, dims)
end

## Constructors ##

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

# T[x...] constructs Array{T,1}
function getindex{T}(::Type{T}, vals...)
    a = Array{T,1}(length(vals))
    @inbounds for i = 1:length(vals)
        a[i] = vals[i]
    end
    return a
end

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

function getindex(::Type{Any}, vals::ANY...)
    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!{T<:Union{Integer,AbstractFloat}}(a::Array{T}, x)
    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`.

```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)

for (fname, felt) in ((:zeros,:zero), (:ones,:one))
    @eval begin
        ($fname)(T::Type, dims...)       = fill!(Array{T}(dims...), ($felt)(T))
        ($fname)(dims...)                = fill!(Array{Float64}(dims...), ($felt)(Float64))
        ($fname){T}(A::AbstractArray{T}) = fill!(similar(A), ($felt)(T))
    end
end

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

`m`-by-`n` identity matrix.
The default element type is `Float64`.
"""
function eye(T::Type, m::Integer, n::Integer)
    a = zeros(T,m,n)
    for i = 1:min(m,n)
        a[i,i] = one(T)
    end
    return a
end

"""
    eye(m, n)

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

`n`-by-`n` identity matrix.
The default element type is `Float64`.
"""
eye(n::Integer) = eye(Float64, n)

"""
    eye(A)

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

```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`](:func:`ones`).
"""
eye{T}(x::AbstractMatrix{T}) = eye(T, size(x, 1), size(x, 2))

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

## Conversions ##

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

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

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

promote_rule{T,n,S}(::Type{Array{T,n}}, ::Type{Array{S,n}}) = Array{promote_type(T,S),n}

## 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`.
"""
collect{T}(::Type{T}, itr) = _collect(T, itr, iteratorsize(itr))

_collect{T}(::Type{T}, itr, isz::HasLength) = copy!(Array{T,1}(Int(length(itr)::Integer)), itr)
_collect{T}(::Type{T}, itr, isz::HasShape)  = copy!(similar(Array{T}, indices(itr)), itr)
function _collect{T}(::Type{T}, itr, isz::SizeUnknown)
    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.

```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_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

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

_array_for{T}(::Type{T}, itr, ::HasLength) = Array{T,1}(Int(length(itr)::Integer))
_array_for{T}(::Type{T}, itr, ::HasShape) = 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!{T}(dest::AbstractArray{T}, itr, offs, st)
    # 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 ##

# This is more complicated than it needs to be in order to get Win64 through bootstrap
getindex(A::Array, i1::Real) = arrayref(A, to_index(i1))
getindex(A::Array, i1::Real, i2::Real, I::Real...) = (@_inline_meta; arrayref(A, to_index(i1), to_index(i2), to_indexes(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{S,T<:Real}(A::Array{S}, I::Range{T})
    return S[ A[to_index(i)] for i in I ]
end

## Indexing: setindex! ##
setindex!{T}(A::Array{T}, x, i1::Real) = arrayset(A, convert(T,x)::T, to_index(i1))
setindex!{T}(A::Array{T}, x, i1::Real, i2::Real, I::Real...) = (@_inline_meta; arrayset(A, convert(T,x)::T, to_index(i1), to_index(i2), to_indexes(I...)...)) # TODO: REMOVE FOR #14770

# These are redundant with the abstract fallbacks but needed for bootstrap
function setindex!(A::Array, x, I::AbstractVector{Int})
    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})
    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
        A[i] = X[count]
        count += 1
    end
    return A
end

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

# efficiently grow an array

_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

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

## Dequeue functionality ##

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

function push!(a::Array{Any,1}, item::ANY)
    ccall(:jl_array_grow_end, Void, (Any, UInt), a, 1)
    arrayset(a, item, length(a))
    return a
end

function append!{T}(a::Array{T,1}, items::AbstractVector)
    n = length(items)
    ccall(:jl_array_grow_end, Void, (Any, UInt), a, n)
    copy!(a, length(a)-n+1, items, 1, n)
    return a
end

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

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

```jldoctest
julia> prepend!([3],[1,2])
3-element Array{Int64,1}:
 1
 2
 3
```
"""
function prepend!{T}(a::Array{T,1}, items::AbstractVector)
    n = length(items)
    ccall(:jl_array_grow_beg, Void, (Any, UInt), a, n)
    if a === items
        copy!(a, 1, items, n+1, n)
    else
        copy!(a, 1, items, 1, n)
    end
    return 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.

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

```julia
julia> resize!([6, 5, 4, 3, 2, 1], 8)
8-element Array{Int64,1}:
 6
 5
 4
 3
 2
 1
 0
 0
```
"""
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
        ccall(:jl_array_del_end, Void, (Any, UInt), a, l-nl)
    end
    return a
end

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

function pop!(a::Vector)
    if isempty(a)
        throw(ArgumentError("array must be non-empty"))
    end
    item = a[end]
    ccall(:jl_array_del_end, Void, (Any, UInt), a, 1)
    return item
end

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

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

```jldoctest
  julia> unshift!([1, 2, 3, 4], 5, 6)
  6-element Array{Int64,1}:
   5
   6
   1
   2
   3
   4
```
"""
function unshift!{T}(a::Array{T,1}, item)
    item = convert(T, item)
    ccall(:jl_array_grow_beg, Void, (Any, UInt), a, 1)
    a[1] = item
    return a
end

function shift!(a::Vector)
    if isempty(a)
        throw(ArgumentError("array must be non-empty"))
    end
    item = a[1]
    ccall(:jl_array_del_beg, Void, (Any, UInt), 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`.

```jldoctest
julia> insert!([6, 5, 4, 2, 1], 4, 3)
6-element Array{Int64,1}:
 6
 5
 4
 3
 2
 1
```
"""
function insert!{T}(a::Array{T,1}, i::Integer, item)
    # 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.

```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!{T<:Integer}(a::Vector, r::UnitRange{T})
    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` must be sorted and unique.

```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], (2, 2))
ERROR: ArgumentError: indices must be unique and sorted
 in deleteat!(::Array{Int64,1}, ::Tuple{Int64,Int64}) at ./array.jl:748
 ...
```
"""
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
    ccall(:jl_array_del_end, Void, (Any, UInt), 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.

```jldoctest
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)`.

```jldoctest
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!{T<:Integer}(a::Vector, r::UnitRange{T}, 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)
    ccall(:jl_array_del_end, Void, (Any, UInt), 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

# use memcmp for == on bit integer types
function =={T<:BitInteger,N}(a::Array{T,N}, b::Array{T,N})
    size(a) == size(b) && 0 == ccall(
        :memcmp, Int32, (Ptr{T}, Ptr{T}, UInt), a, b, sizeof(T) * length(a))
end

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

function reverse(A::AbstractVector, s=1, n=length(A))
    B = similar(A)
    for i = 1:s-1
        B[i] = A[i]
    end
    for i = s:n
        B[i] = A[n+s-i]
    end
    for i = n+1:length(A)
        B[i] = A[i]
    end
    return B
end
reverseind(a::AbstractVector, i::Integer) = length(a) + 1 - i

function reverse!(v::AbstractVector, s=1, n=length(v))
    if n <= s  # empty case; ok
    elseif !(1 ≤ s ≤ endof(v))
        throw(BoundsError(v, s))
    elseif !(1 ≤ n ≤ endof(v))
        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
function hcat{T}(V::Vector{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{T}(arrays::Vector{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)
    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)
        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


## find ##

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

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

```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)
    for i = start:length(A)
        if A[i] != 0
            return i
        end
    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.

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

julia> findfirst(A)
2
```
"""
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.

```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)
    for i = start:length(A)
        if A[i] == v
            return i
        end
    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.

```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.

```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)
    for i = start:length(A)
        if testf(A[i])
            return i
        end
    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.

```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.

```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)
    for i = start:-1:1
        A[i] != 0 && return 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`.

```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, length(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.

```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)
    for i = start:-1:1
        A[i] == v && return 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`.

```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, length(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.

```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)
    for i = start:-1:1
        testf(A[i]) && return 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.

```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, length(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.

```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
```
"""
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) = Colon()  # 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.

```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
```
"""
function find(A)
    nnzA = countnz(A)
    I = Vector{Int}(nnzA)
    count = 1
    inds = _index_remapper(A)
    for (i,a) in enumerate(A)
        if a != 0
            I[count] = inds[i]
            count += 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.

```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 = countnz(A)
    I = similar(A, Int, nnzA)
    J = similar(A, Int, nnzA)
    count = 1
    for j=indices(A,2), i=indices(A,1)
        if A[i,j] != 0
            I[count] = i
            J[count] = j
            count += 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.

```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{T}(A::AbstractMatrix{T})
    nnzA = countnz(A)
    I = zeros(Int, nnzA)
    J = zeros(Int, nnzA)
    NZs = Array{T,1}(nnzA)
    count = 1
    if nnzA > 0
        for j=indices(A,2), i=indices(A,1)
            Aij = A[i,j]
            if Aij != 0
                I[count] = i
                J[count] = j
                NZs[count] = Aij
                count += 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. `NaN` values are ignored, unless
all elements are `NaN`.

The collection must not be empty.

```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])
(7.0,2)
```
"""
function findmax(a)
    if isempty(a)
        throw(ArgumentError("collection must be non-empty"))
    end
    s = start(a)
    mi = i = 1
    m, s = next(a, s)
    while !done(a, s)
        ai, s = next(a, s)
        i += 1
        if ai > m || m!=m
            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. `NaN` values are ignored, unless
all elements are `NaN`.

The collection must not be empty.

```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])
(1.0,2)
```
"""
function findmin(a)
    if isempty(a)
        throw(ArgumentError("collection must be non-empty"))
    end
    s = start(a)
    mi = i = 1
    m, s = next(a, s)
    while !done(a, s)
        ai, s = next(a, s)
        i += 1
        if ai < m || m!=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. `NaN` values are ignored, unless all
elements are `NaN`.

The collection must not be empty.

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

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

julia> indmax([1,7,7,NaN])
2
```
"""
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. `NaN` values are ignored, unless all
elements are `NaN`.

The collection must not be empty.

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

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

julia> indmin([7,1,1,NaN])
2
```
"""
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`.

```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

"""
    findin(a, b)

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

```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, b)
    ind = Array{Int,1}(0)
    bset = Set(b)
    @inbounds for (i,ai) in enumerate(a)
        ai in bset && push!(ind, i)
    end
    ind
end

# 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(function, collection)

Return a copy of `collection`, removing elements for which `function` is `false`. For
associative collections, the function is passed two arguments (key and value).

```jldocttest
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}]

function filter!(f, a::Vector)
    insrt = 1
    for acurr in a
        if f(acurr)
            a[insrt] = acurr
            insrt += 1
        end
    end
    deleteat!(a, insrt:length(a))
    return a
end

function filter(f, a::Vector)
    r = Array{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 = Array{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 = Array{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.

```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.

```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...))