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range.jl
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# This file is a part of Julia. License is MIT: https://julialang.org/license
(:)(a::Real, b::Real) = (:)(promote(a, b)...)
(:)(start::T, stop::T) where {T<:Real} = UnitRange{T}(start, stop)
(:)(start::T, stop::T) where {T} = (:)(start, oftype(stop >= start ? stop - start : start - stop, 1), stop)
# promote start and stop, leaving step alone
(:)(start::A, step, stop::C) where {A<:Real, C<:Real} =
(:)(convert(promote_type(A, C), start), step, convert(promote_type(A, C), stop))
# AbstractFloat specializations
(:)(a::T, b::T) where {T<:AbstractFloat} = (:)(a, T(1), b)
(:)(a::T, b::AbstractFloat, c::T) where {T<:Real} = (:)(promote(a, b, c)...)
(:)(a::T, b::AbstractFloat, c::T) where {T<:AbstractFloat} = (:)(promote(a, b, c)...)
(:)(a::T, b::Real, c::T) where {T<:AbstractFloat} = (:)(promote(a, b, c)...)
(:)(start::T, step::T, stop::T) where {T<:AbstractFloat} =
_colon(OrderStyle(T), ArithmeticStyle(T), start, step, stop)
(:)(start::T, step::T, stop::T) where {T<:Real} =
_colon(OrderStyle(T), ArithmeticStyle(T), start, step, stop)
_colon(::Ordered, ::Any, start::T, step, stop::T) where {T} = StepRange(start, step, stop)
# for T<:Union{Float16,Float32,Float64} see twiceprecision.jl
_colon(::Ordered, ::ArithmeticRounds, start::T, step, stop::T) where {T} =
StepRangeLen(start, step, convert(Integer, fld(stop - start, step)) + 1)
_colon(::Any, ::Any, start::T, step, stop::T) where {T} =
StepRangeLen(start, step, convert(Integer, fld(stop - start, step)) + 1)
"""
(:)(start, [step], stop)
Range operator. `a:b` constructs a range from `a` to `b` with a step size
equal to +1, which produces:
* a [`UnitRange`](@ref) when `a` and `b` are integers, or
* a [`StepRange`](@ref) when `a` and `b` are characters, or
* a [`StepRangeLen`](@ref) when `a` and/or `b` are floating-point.
`a:s:b` is similar but uses a step size of `s` (a [`StepRange`](@ref) or
[`StepRangeLen`](@ref)). See also [`range`](@ref) for more control.
To create a descending range, use `reverse(a:b)` or a negative step size, e.g. `b:-1:a`.
Otherwise, when `b < a`, an empty range will be constructed and normalized to `a:a-1`.
The operator `:` is also used in indexing to select whole dimensions, e.g. in `A[:, 1]`.
`:` is also used to [`quote`](@ref) code, e.g. `:(x + y) isa Expr` and `:x isa Symbol`.
Since `:2 isa Int`, it does *not* create a range in indexing: `v[:2] == v[2] != v[begin:2]`.
"""
(:)(start::T, step, stop::T) where {T} = _colon(start, step, stop)
(:)(start::T, step, stop::T) where {T<:Real} = _colon(start, step, stop)
# without the second method above, the first method above is ambiguous with
# (:)(start::A, step, stop::C) where {A<:Real,C<:Real}
function _colon(start::T, step, stop::T) where T
T′ = typeof(start+zero(step))
StepRange(convert(T′,start), step, convert(T′,stop))
end
"""
range(start, stop, length)
range(start, stop; length, step)
range(start; length, stop, step)
range(;start, length, stop, step)
Construct a specialized array with evenly spaced elements and optimized storage (an [`AbstractRange`](@ref)) from the arguments.
Mathematically a range is uniquely determined by any three of `start`, `step`, `stop` and `length`.
Valid invocations of range are:
* Call `range` with any three of `start`, `step`, `stop`, `length`.
* Call `range` with two of `start`, `stop`, `length`. In this case `step` will be assumed
to be positive one. If both arguments are Integers, a [`UnitRange`](@ref) will be returned.
* Call `range` with one of `stop` or `length`. `start` and `step` will be assumed to be positive one.
To construct a descending range, specify a negative step size, e.g. `range(5, 1; step = -1)` => [5,4,3,2,1]. Otherwise,
a `stop` value less than the `start` value, with the default `step` of `+1`, constructs an empty range. Empty ranges
are normalized such that the `stop` is one less than the `start`, e.g. `range(5, 1) == 5:4`.
See Extended Help for additional details on the returned type.
See also [`logrange`](@ref) for logarithmically spaced points.
# Examples
```jldoctest
julia> range(1, length=100)
1:100
julia> range(1, stop=100)
1:100
julia> range(1, step=5, length=100)
1:5:496
julia> range(1, step=5, stop=100)
1:5:96
julia> range(1, 10, length=101)
1.0:0.09:10.0
julia> range(1, 100, step=5)
1:5:96
julia> range(stop=10, length=5)
6:10
julia> range(stop=10, step=1, length=5)
6:1:10
julia> range(start=1, step=1, stop=10)
1:1:10
julia> range(; length = 10)
Base.OneTo(10)
julia> range(; stop = 6)
Base.OneTo(6)
julia> range(; stop = 6.5)
1.0:1.0:6.0
```
If `length` is not specified and `stop - start` is not an integer multiple of `step`, a range that ends before `stop` will be produced.
```jldoctest
julia> range(1, 3.5, step=2)
1.0:2.0:3.0
```
Special care is taken to ensure intermediate values are computed rationally.
To avoid this induced overhead, see the [`LinRange`](@ref) constructor.
!!! compat "Julia 1.1"
`stop` as a positional argument requires at least Julia 1.1.
!!! compat "Julia 1.7"
The versions without keyword arguments and `start` as a keyword argument
require at least Julia 1.7.
!!! compat "Julia 1.8"
The versions with `stop` as a sole keyword argument,
or `length` as a sole keyword argument require at least Julia 1.8.
# Extended Help
`range` will produce a `Base.OneTo` when the arguments are Integers and
* Only `length` is provided
* Only `stop` is provided
`range` will produce a `UnitRange` when the arguments are Integers and
* Only `start` and `stop` are provided
* Only `length` and `stop` are provided
A `UnitRange` is not produced if `step` is provided even if specified as one.
"""
function range end
range(start; stop=nothing, length::Union{Integer,Nothing}=nothing, step=nothing) =
_range(start, step, stop, length)
range(start, stop; length::Union{Integer,Nothing}=nothing, step=nothing) = _range(start, step, stop, length)
range(start, stop, length::Integer) = _range(start, nothing, stop, length)
range(;start=nothing, stop=nothing, length::Union{Integer, Nothing}=nothing, step=nothing) =
_range(start, step, stop, length)
_range(start::Nothing, step::Nothing, stop::Nothing, len::Nothing) = range_error(start, step, stop, len)
_range(start::Nothing, step::Nothing, stop::Nothing, len::Any ) = range_length(len)
_range(start::Nothing, step::Nothing, stop::Any , len::Nothing) = range_stop(stop)
_range(start::Nothing, step::Nothing, stop::Any , len::Any ) = range_stop_length(stop, len)
_range(start::Nothing, step::Any , stop::Nothing, len::Nothing) = range_error(start, step, stop, len)
_range(start::Nothing, step::Any , stop::Nothing, len::Any ) = range_error(start, step, stop, len)
_range(start::Nothing, step::Any , stop::Any , len::Nothing) = range_error(start, step, stop, len)
_range(start::Nothing, step::Any , stop::Any , len::Any ) = range_step_stop_length(step, stop, len)
_range(start::Any , step::Nothing, stop::Nothing, len::Nothing) = range_error(start, step, stop, len)
_range(start::Any , step::Nothing, stop::Nothing, len::Any ) = range_start_length(start, len)
_range(start::Any , step::Nothing, stop::Any , len::Nothing) = range_start_stop(start, stop)
_range(start::Any , step::Nothing, stop::Any , len::Any ) = range_start_stop_length(start, stop, len)
_range(start::Any , step::Any , stop::Nothing, len::Nothing) = range_error(start, step, stop, len)
_range(start::Any , step::Any , stop::Nothing, len::Any ) = range_start_step_length(start, step, len)
_range(start::Any , step::Any , stop::Any , len::Nothing) = range_start_step_stop(start, step, stop)
_range(start::Any , step::Any , stop::Any , len::Any ) = range_error(start, step, stop, len)
# Length as the only argument
range_length(len::Integer) = OneTo(len)
# Stop as the only argument
range_stop(stop) = range_start_stop(oftype(stop, 1), stop)
range_stop(stop::Integer) = range_length(stop)
function range_step_stop_length(step, a, len::Integer)
start = a - step * (len - oneunit(len))
if start isa Signed
# overflow in recomputing length from stop is okay
return StepRange{typeof(start),typeof(step)}(start, step, convert(typeof(start), a))
end
return StepRangeLen{typeof(start),typeof(start),typeof(step)}(start, step, len)
end
# Stop and length as the only argument
function range_stop_length(a, len::Integer)
step = oftype(a - a, 1) # assert that step is representable
start = a - (len - oneunit(len))
if start isa Signed
# overflow in recomputing length from stop is okay
return UnitRange(start, oftype(start, a))
end
return StepRangeLen{typeof(start),typeof(start),typeof(step)}(start, step, len)
end
# Start and length as the only argument
function range_start_length(a, len::Integer)
step = oftype(a - a, 1) # assert that step is representable
stop = a + (len - oneunit(len))
if stop isa Signed
# overflow in recomputing length from stop is okay
return UnitRange(oftype(stop, a), stop)
end
return StepRangeLen{typeof(stop),typeof(a),typeof(step)}(a, step, len)
end
range_start_stop(start, stop) = start:stop
function range_start_step_length(a, step, len::Integer)
stop = a + step * (len - oneunit(len))
if stop isa Signed
# overflow in recomputing length from stop is okay
return StepRange{typeof(stop),typeof(step)}(convert(typeof(stop), a), step, stop)
end
return StepRangeLen{typeof(stop),typeof(a),typeof(step)}(a, step, len)
end
range_start_step_stop(start, step, stop) = start:step:stop
function range_error(start, step, stop, length)
hasstart = start !== nothing
hasstep = step !== nothing
hasstop = stop !== nothing
haslength = start !== nothing
hint = if hasstart && hasstep && hasstop && haslength
"Try specifying only three arguments"
elseif !hasstop && !haslength
"At least one of `length` or `stop` must be specified."
elseif !hasstep && !haslength
"At least one of `length` or `step` must be specified."
elseif !hasstart && !hasstop
"At least one of `start` or `stop` must be specified."
else
"Try specifying more arguments."
end
msg = """
Cannot construct range from arguments:
start = $start
step = $step
stop = $stop
length = $length
$hint
"""
throw(ArgumentError(msg))
end
## 1-dimensional ranges ##
"""
AbstractRange{T} <: AbstractVector{T}
Supertype for linear ranges with elements of type `T`.
[`UnitRange`](@ref), [`LinRange`](@ref) and other types are subtypes of this.
All subtypes must define [`step`](@ref).
Thus [`LogRange`](@ref Base.LogRange) is not a subtype of `AbstractRange`.
"""
abstract type AbstractRange{T} <: AbstractArray{T,1} end
RangeStepStyle(::Type{<:AbstractRange}) = RangeStepIrregular()
RangeStepStyle(::Type{<:AbstractRange{<:Integer}}) = RangeStepRegular()
convert(::Type{T}, r::AbstractRange) where {T<:AbstractRange} = r isa T ? r : T(r)::T
## ordinal ranges
"""
OrdinalRange{T, S} <: AbstractRange{T}
Supertype for ordinal ranges with elements of type `T` with
spacing(s) of type `S`. The steps should be always-exact
multiples of [`oneunit`](@ref), and `T` should be a "discrete"
type, which cannot have values smaller than `oneunit`. For example,
`Integer` or `Date` types would qualify, whereas `Float64` would not (since this
type can represent values smaller than `oneunit(Float64)`.
[`UnitRange`](@ref), [`StepRange`](@ref), and other types are subtypes of this.
"""
abstract type OrdinalRange{T,S} <: AbstractRange{T} end
"""
AbstractUnitRange{T} <: OrdinalRange{T, T}
Supertype for ranges with a step size of [`oneunit(T)`](@ref) with elements of type `T`.
[`UnitRange`](@ref) and other types are subtypes of this.
"""
abstract type AbstractUnitRange{T} <: OrdinalRange{T,T} end
"""
StepRange{T, S} <: OrdinalRange{T, S}
Ranges with elements of type `T` with spacing of type `S`. The step
between each element is constant, and the range is defined in terms
of a `start` and `stop` of type `T` and a `step` of type `S`. Neither
`T` nor `S` should be floating point types. The syntax `a:b:c` with `b != 0`
and `a`, `b`, and `c` all integers creates a `StepRange`.
# Examples
```jldoctest
julia> collect(StepRange(1, Int8(2), 10))
5-element Vector{Int64}:
1
3
5
7
9
julia> typeof(StepRange(1, Int8(2), 10))
StepRange{Int64, Int8}
julia> typeof(1:3:6)
StepRange{Int64, Int64}
```
"""
struct StepRange{T,S} <: OrdinalRange{T,S}
start::T
step::S
stop::T
function StepRange{T,S}(start, step, stop) where {T,S}
start = convert(T, start)
step = convert(S, step)
stop = convert(T, stop)
return new(start, step, steprange_last(start, step, stop))
end
end
# to make StepRange constructor inlineable, so optimizer can see `step` value
function steprange_last(start, step, stop)::typeof(stop)
if isa(start, AbstractFloat) || isa(step, AbstractFloat)
throw(ArgumentError("StepRange should not be used with floating point"))
end
if isa(start, Integer) && !isinteger(start + step)
throw(ArgumentError("StepRange{<:Integer} cannot have non-integer step"))
end
z = zero(step)
step == z && throw(ArgumentError("step cannot be zero"))
if stop == start
last = stop
else
if (step > z) != (stop > start)
last = steprange_last_empty(start, step, stop)
else
# Compute absolute value of difference between `start` and `stop`
# (to simplify handling both signed and unsigned T and checking for signed overflow):
absdiff, absstep = stop > start ? (stop - start, step) : (start - stop, -step)
# Compute remainder as a non-negative number:
if absdiff isa Signed && absdiff < zero(absdiff)
# unlikely, but handle the signed overflow case with unsigned rem
overflow_case(absdiff, absstep) = (@noinline; convert(typeof(absdiff), unsigned(absdiff) % absstep))
remain = overflow_case(absdiff, absstep)
else
remain = convert(typeof(absdiff), absdiff % absstep)
end
# Move `stop` closer to `start` if there is a remainder:
last = stop > start ? stop - remain : stop + remain
end
end
return last
end
function steprange_last_empty(start::Integer, step, stop)::typeof(stop)
# empty range has a special representation where stop = start-1,
# which simplifies arithmetic for Signed numbers
if step > zero(step)
last = start - oneunit(step)
else
last = start + oneunit(step)
end
return last
end
steprange_last_empty(start::Bool, step, stop) = start ⊻ (step > zero(step)) # isnegative(step) ? start : !start
# For types where x+oneunit(x) may not be well-defined use the user-given value for stop
steprange_last_empty(start, step, stop) = stop
StepRange{T}(start, step::S, stop) where {T,S} = StepRange{T,S}(start, step, stop)
StepRange(start::T, step::S, stop::T) where {T,S} = StepRange{T,S}(start, step, stop)
"""
UnitRange{T<:Real}
A range parameterized by a `start` and `stop` of type `T`, filled
with elements spaced by `1` from `start` until `stop` is exceeded.
The syntax `a:b` with `a` and `b` both `Integer`s creates a `UnitRange`.
# Examples
```jldoctest
julia> collect(UnitRange(2.3, 5.2))
3-element Vector{Float64}:
2.3
3.3
4.3
julia> typeof(1:10)
UnitRange{Int64}
```
"""
struct UnitRange{T<:Real} <: AbstractUnitRange{T}
start::T
stop::T
UnitRange{T}(start::T, stop::T) where {T<:Real} = new(start, unitrange_last(start, stop))
end
UnitRange{T}(start, stop) where {T<:Real} = UnitRange{T}(convert(T, start), convert(T, stop))
UnitRange(start::T, stop::T) where {T<:Real} = UnitRange{T}(start, stop)
function UnitRange(start, stop)
startstop_promoted = promote(start, stop)
not_sametype((start, stop), startstop_promoted)
UnitRange(startstop_promoted...)
end
# if stop and start are integral, we know that their difference is a multiple of 1
unitrange_last(start::Integer, stop::Integer) =
stop >= start ? stop : convert(typeof(stop), start - oneunit(start - stop))
# otherwise, use `floor` as a more efficient way to compute modulus with step=1
unitrange_last(start, stop) =
stop >= start ? convert(typeof(stop), start + floor(stop - start)) :
convert(typeof(stop), start - oneunit(start - stop))
unitrange(x::AbstractUnitRange) = UnitRange(x) # convenience conversion for promoting the range type
if isdefined(Main, :Base)
# Constant-fold-able indexing into tuples to functionally expose Base.tail and Base.front
function getindex(@nospecialize(t::Tuple), r::AbstractUnitRange)
@inline
require_one_based_indexing(r)
if length(r) <= 10
return ntuple(i -> t[i + first(r) - 1], length(r))
elseif first(r) == 1
last(r) == length(t) && return t
last(r) == length(t)-1 && return front(t)
last(r) == length(t)-2 && return front(front(t))
elseif last(r) == length(t)
first(r) == 2 && return tail(t)
first(r) == 3 && return tail(tail(t))
end
return (eltype(t)[t[ri] for ri in r]...,)
end
end
"""
Base.OneTo(n)
Define an `AbstractUnitRange` that behaves like `1:n`, with the added
distinction that the lower limit is guaranteed (by the type system) to
be 1.
"""
struct OneTo{T<:Integer} <: AbstractUnitRange{T}
stop::T # invariant: stop >= zero(stop)
function OneTo{T}(stop) where {T<:Integer}
throwbool(r) = (@noinline; throw(ArgumentError("invalid index: $r of type Bool")))
T === Bool && throwbool(stop)
return new(max(zero(T), stop))
end
function OneTo{T}(r::AbstractRange) where {T<:Integer}
throwstart(r) = (@noinline; throw(ArgumentError("first element must be 1, got $(first(r))")))
throwstep(r) = (@noinline; throw(ArgumentError("step must be 1, got $(step(r))")))
throwbool(r) = (@noinline; throw(ArgumentError("invalid index: $r of type Bool")))
first(r) == 1 || throwstart(r)
step(r) == 1 || throwstep(r)
T === Bool && throwbool(r)
return new(max(zero(T), last(r)))
end
global unchecked_oneto(stop::Integer) = new{typeof(stop)}(stop)
end
OneTo(stop::T) where {T<:Integer} = OneTo{T}(stop)
OneTo(r::AbstractRange{T}) where {T<:Integer} = OneTo{T}(r)
oneto(r) = OneTo(r)
## Step ranges parameterized by length
"""
StepRangeLen( ref::R, step::S, len, [offset=1]) where { R,S}
StepRangeLen{T,R,S}( ref::R, step::S, len, [offset=1]) where {T,R,S}
StepRangeLen{T,R,S,L}(ref::R, step::S, len, [offset=1]) where {T,R,S,L}
A range `r` where `r[i]` produces values of type `T` (in the first
form, `T` is deduced automatically), parameterized by a `ref`erence
value, a `step`, and the `len`gth. By default `ref` is the starting
value `r[1]`, but alternatively you can supply it as the value of
`r[offset]` for some other index `1 <= offset <= len`. The syntax `a:b`
or `a:b:c`, where any of `a`, `b`, or `c` are floating-point numbers, creates a
`StepRangeLen`.
!!! compat "Julia 1.7"
The 4th type parameter `L` requires at least Julia 1.7.
"""
struct StepRangeLen{T,R,S,L<:Integer} <: AbstractRange{T}
ref::R # reference value (might be smallest-magnitude value in the range)
step::S # step value
len::L # length of the range
offset::L # the index of ref
function StepRangeLen{T,R,S,L}(ref::R, step::S, len::Integer, offset::Integer = 1) where {T,R,S,L}
if T <: Integer && !isinteger(ref + step)
throw(ArgumentError("StepRangeLen{<:Integer} cannot have non-integer step"))
end
len = convert(L, len)
len >= zero(len) || throw(ArgumentError("length cannot be negative, got $len"))
offset = convert(L, offset)
L1 = oneunit(typeof(len))
L1 <= offset <= max(L1, len) || throw(ArgumentError("StepRangeLen: offset must be in [1,$len], got $offset"))
return new(ref, step, len, offset)
end
end
StepRangeLen{T,R,S}(ref::R, step::S, len::Integer, offset::Integer = 1) where {T,R,S} =
StepRangeLen{T,R,S,promote_type(Int,typeof(len))}(ref, step, len, offset)
StepRangeLen(ref::R, step::S, len::Integer, offset::Integer = 1) where {R,S} =
StepRangeLen{typeof(ref+zero(step)),R,S,promote_type(Int,typeof(len))}(ref, step, len, offset)
StepRangeLen{T}(ref::R, step::S, len::Integer, offset::Integer = 1) where {T,R,S} =
StepRangeLen{T,R,S,promote_type(Int,typeof(len))}(ref, step, len, offset)
## range with computed step
"""
LinRange{T,L}
A range with `len` linearly spaced elements between its `start` and `stop`.
The size of the spacing is controlled by `len`, which must
be an `Integer`.
# Examples
```jldoctest
julia> LinRange(1.5, 5.5, 9)
9-element LinRange{Float64, Int64}:
1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5, 5.0, 5.5
```
Compared to using [`range`](@ref), directly constructing a `LinRange` should
have less overhead but won't try to correct for floating point errors:
```jldoctest
julia> collect(range(-0.1, 0.3, length=5))
5-element Vector{Float64}:
-0.1
0.0
0.1
0.2
0.3
julia> collect(LinRange(-0.1, 0.3, 5))
5-element Vector{Float64}:
-0.1
-1.3877787807814457e-17
0.09999999999999999
0.19999999999999998
0.3
```
See also [`Logrange`](@ref Base.LogRange) for logarithmically spaced points.
"""
struct LinRange{T,L<:Integer} <: AbstractRange{T}
start::T
stop::T
len::L
lendiv::L
function LinRange{T,L}(start::T, stop::T, len::L) where {T,L<:Integer}
len >= 0 || throw(ArgumentError("range($start, stop=$stop, length=$len): negative length"))
onelen = oneunit(typeof(len))
if len == onelen
start == stop || throw(ArgumentError("range($start, stop=$stop, length=$len): endpoints differ"))
return new(start, stop, len, len)
end
lendiv = max(len - onelen, onelen)
if T <: Integer && !iszero(mod(stop-start, lendiv))
throw(ArgumentError("LinRange{<:Integer} cannot have non-integer step"))
end
return new(start, stop, len, lendiv)
end
end
function LinRange{T,L}(start, stop, len::Integer) where {T,L}
LinRange{T,L}(convert(T, start), convert(T, stop), convert(L, len))
end
function LinRange{T}(start, stop, len::Integer) where T
LinRange{T,promote_type(Int,typeof(len))}(start, stop, len)
end
function LinRange(start, stop, len::Integer)
T = typeof((zero(stop) - zero(start)) / oneunit(len))
LinRange{T}(start, stop, len)
end
range_start_stop_length(start, stop, len::Integer) =
range_start_stop_length(promote(start, stop)..., len)
range_start_stop_length(start::T, stop::T, len::Integer) where {T} = LinRange(start, stop, len)
range_start_stop_length(start::T, stop::T, len::Integer) where {T<:Integer} =
_linspace(float(T), start, stop, len)
## for Float16, Float32, and Float64 we hit twiceprecision.jl to lift to higher precision StepRangeLen
# for all other types we fall back to a plain old LinRange
_linspace(::Type{T}, start::Integer, stop::Integer, len::Integer) where T = LinRange{T}(start, stop, len)
function show(io::IO, r::LinRange{T}) where {T}
print(io, "LinRange{")
show(io, T)
print(io, "}(")
ioc = IOContext(io, :typeinfo=>T)
show(ioc, first(r))
print(io, ", ")
show(ioc, last(r))
print(io, ", ")
show(io, length(r))
print(io, ')')
end
"""
`print_range(io, r)` prints out a nice looking range r in terms of its elements
as if it were `collect(r)`, dependent on the size of the
terminal, and taking into account whether compact numbers should be shown.
It figures out the width in characters of each element, and if they
end up too wide, it shows the first and last elements separated by a
horizontal ellipsis. Typical output will look like `1.0, 2.0, …, 5.0, 6.0`.
`print_range(io, r, pre, sep, post, hdots)` uses optional
parameters `pre` and `post` characters for each printed row,
`sep` separator string between printed elements,
`hdots` string for the horizontal ellipsis.
"""
function print_range(io::IO, r::AbstractArray,
pre::AbstractString = " ",
sep::AbstractString = ", ",
post::AbstractString = "",
hdots::AbstractString = ", \u2026, ") # horiz ellipsis
# This function borrows from print_matrix() in show.jl
# and should be called by show and display
sz = displaysize(io)
if !haskey(io, :compact)
io = IOContext(io, :compact => true)
end
screenheight, screenwidth = sz[1] - 4, sz[2]
screenwidth -= length(pre) + length(post)
postsp = ""
sepsize = length(sep)
m = 1 # treat the range as a one-row matrix
n = length(r)
# Figure out spacing alignments for r, but only need to examine the
# left and right edge columns, as many as could conceivably fit on the
# screen, with the middle columns summarized by horz, vert, or diag ellipsis
maxpossiblecols = div(screenwidth, 1+sepsize) # assume each element is at least 1 char + 1 separator
colsr = n <= maxpossiblecols ? (1:n) : [1:div(maxpossiblecols,2)+1; (n-div(maxpossiblecols,2)):n]
rowmatrix = reshape(r[colsr], 1, length(colsr)) # treat the range as a one-row matrix for print_matrix_row
nrow, idxlast = size(rowmatrix, 2), last(axes(rowmatrix, 2))
A = alignment(io, rowmatrix, 1:m, 1:length(rowmatrix), screenwidth, screenwidth, sepsize, nrow) # how much space range takes
if n <= length(A) # cols fit screen, so print out all elements
print(io, pre) # put in pre chars
print_matrix_row(io,rowmatrix,A,1,1:n,sep,idxlast) # the entire range
print(io, post) # add the post characters
else # cols don't fit so put horiz ellipsis in the middle
# how many chars left after dividing width of screen in half
# and accounting for the horiz ellipsis
c = div(screenwidth-length(hdots)+1,2)+1 # chars remaining for each side of rowmatrix
alignR = reverse(alignment(io, rowmatrix, 1:m, length(rowmatrix):-1:1, c, c, sepsize, nrow)) # which cols of rowmatrix to put on the right
c = screenwidth - sum(map(sum,alignR)) - (length(alignR)-1)*sepsize - length(hdots)
alignL = alignment(io, rowmatrix, 1:m, 1:length(rowmatrix), c, c, sepsize, nrow) # which cols of rowmatrix to put on the left
print(io, pre) # put in pre chars
print_matrix_row(io, rowmatrix,alignL,1,1:length(alignL),sep,idxlast) # left part of range
print(io, hdots) # horizontal ellipsis
print_matrix_row(io, rowmatrix,alignR,1,length(rowmatrix)-length(alignR)+1:length(rowmatrix),sep,idxlast) # right part of range
print(io, post) # post chars
end
end
## interface implementations
length(r::AbstractRange) = error("length implementation missing") # catch mistakes
size(r::AbstractRange) = (length(r),)
isempty(r::StepRange) =
# steprange_last(r.start, r.step, r.stop) == r.stop
(r.start != r.stop) & ((r.step > zero(r.step)) != (r.stop > r.start))
isempty(r::AbstractUnitRange) = first(r) > last(r)
isempty(r::StepRangeLen) = length(r) == 0
isempty(r::LinRange) = length(r) == 0
"""
step(r)
Get the step size of an [`AbstractRange`](@ref) object.
# Examples
```jldoctest
julia> step(1:10)
1
julia> step(1:2:10)
2
julia> step(2.5:0.3:10.9)
0.3
julia> step(range(2.5, stop=10.9, length=85))
0.1
```
"""
step(r::StepRange) = r.step
step(r::AbstractUnitRange{T}) where {T} = oneunit(T) - zero(T)
step(r::AbstractUnitRange{Bool}) = true
step(r::StepRangeLen) = r.step
step(r::StepRangeLen{T}) where {T<:AbstractFloat} = T(r.step)
step(r::LinRange) = (last(r)-first(r))/r.lendiv
# high-precision step
step_hp(r::StepRangeLen) = r.step
step_hp(r::AbstractRange) = step(r)
# Needed to ensure `has_offset_axes` can constant-fold.
has_offset_axes(::StepRange) = false
# n.b. checked_length for these is defined iff checked_add and checked_sub are
# defined between the relevant types
function checked_length(r::OrdinalRange{T}) where T
s = step(r)
start = first(r)
if isempty(r)
return Integer(div(start - start, oneunit(s)))
end
stop = last(r)
if isless(s, zero(s))
diff = checked_sub(start, stop)
s = -s
else
diff = checked_sub(stop, start)
end
a = div(diff, s)
return Integer(checked_add(a, oneunit(a)))
end
function checked_length(r::AbstractUnitRange{T}) where T
# compiler optimization: remove dead cases from above
if isempty(r)
return Integer(first(r) - first(r))
end
a = checked_sub(last(r), first(r))
return Integer(checked_add(a, oneunit(a)))
end
function length(r::OrdinalRange{T}) where T
s = step(r)
start = first(r)
if isempty(r)
return Integer(div(start - start, oneunit(s)))
end
stop = last(r)
if isless(s, zero(s))
diff = start - stop
s = -s
else
diff = stop - start
end
a = div(diff, s)
return Integer(a + oneunit(a))
end
function length(r::AbstractUnitRange{T}) where T
@inline
start, stop = first(r), last(r)
a = oneunit(zero(stop) - zero(start))
if a isa Signed || stop >= start
a += stop - start # Signed are allowed to go negative
else
a = zero(a) # Unsigned don't necessarily underflow
end
return Integer(a)
end
length(r::OneTo) = Integer(r.stop - zero(r.stop))
length(r::StepRangeLen) = r.len
length(r::LinRange) = r.len
let bigints = Union{Int, UInt, Int64, UInt64, Int128, UInt128},
smallints = (Int === Int64 ?
Union{Int8, UInt8, Int16, UInt16, Int32, UInt32} :
Union{Int8, UInt8, Int16, UInt16}),
bitints = Union{bigints, smallints}
global length, checked_length, firstindex
# compile optimization for which promote_type(T, Int) == T
length(r::OneTo{T}) where {T<:bigints} = r.stop
# slightly more accurate length and checked_length in extreme cases
# (near typemax) for types with known `unsigned` functions
function length(r::OrdinalRange{T}) where T<:bigints
s = step(r)
diff = last(r) - first(r)
isempty(r) && return zero(diff)
# if |s| > 1, diff might have overflowed, but unsigned(diff)÷s should
# therefore still be valid (if the result is representable at all)
# n.b. !(s isa T)
if s isa Unsigned || -1 <= s <= 1 || s == -s
a = div(diff, s) % typeof(diff)
elseif s < 0
a = div(unsigned(-diff), -s) % typeof(diff)
else
a = div(unsigned(diff), s) % typeof(diff)
end
return a + oneunit(a)
end
function checked_length(r::OrdinalRange{T}) where T<:bigints
s = step(r)
stop, start = last(r), first(r)
ET = promote_type(typeof(stop), typeof(start))
isempty(r) && return zero(ET)
# n.b. !(s isa T)
if s > 1
diff = stop - start
a = convert(ET, div(unsigned(diff), s))
elseif s < -1
diff = start - stop
a = convert(ET, div(unsigned(diff), -s))
elseif s > 0
a = convert(ET, div(checked_sub(stop, start), s))
else
a = convert(ET, div(checked_sub(start, stop), -s))
end
return checked_add(a, oneunit(a))
end
firstindex(r::StepRange{<:bigints,<:bitints}) = one(last(r)-first(r))
# some special cases to favor default Int type
function length(r::OrdinalRange{<:smallints})
s = step(r)
isempty(r) && return 0
# n.b. !(step isa T)
return Int(div(Int(last(r)) - Int(first(r)), s)) + 1
end
length(r::AbstractUnitRange{<:smallints}) = Int(last(r)) - Int(first(r)) + 1
length(r::OneTo{<:smallints}) = Int(r.stop)
checked_length(r::OrdinalRange{<:smallints}) = length(r)
checked_length(r::AbstractUnitRange{<:smallints}) = length(r)
checked_length(r::OneTo{<:smallints}) = length(r)
firstindex(::StepRange{<:smallints,<:bitints}) = 1
end
first(r::OrdinalRange{T}) where {T} = convert(T, r.start)
first(r::OneTo{T}) where {T} = oneunit(T)
first(r::StepRangeLen) = unsafe_getindex(r, 1)
first(r::LinRange) = r.start
function first(r::OneTo, n::Integer)
n < 0 && throw(ArgumentError("Number of elements must be non-negative"))
OneTo(oftype(r.stop, min(r.stop, n)))
end
last(r::OrdinalRange{T}) where {T} = convert(T, r.stop) # via steprange_last
last(r::StepRangeLen) = unsafe_getindex(r, length(r))
last(r::LinRange) = r.stop
minimum(r::AbstractUnitRange) = isempty(r) ? throw(ArgumentError("range must be non-empty")) : first(r)
maximum(r::AbstractUnitRange) = isempty(r) ? throw(ArgumentError("range must be non-empty")) : last(r)
minimum(r::AbstractRange) = isempty(r) ? throw(ArgumentError("range must be non-empty")) : min(first(r), last(r))
maximum(r::AbstractRange) = isempty(r) ? throw(ArgumentError("range must be non-empty")) : max(first(r), last(r))
"""
argmin(r::AbstractRange)
Ranges can have multiple minimal elements. In that case
`argmin` will return a minimal index, but not necessarily the
first one.
"""
function argmin(r::AbstractRange)
if isempty(r)
throw(ArgumentError("range must be non-empty"))
elseif step(r) > 0
firstindex(r)
else
lastindex(r)
end
end
"""
argmax(r::AbstractRange)
Ranges can have multiple maximal elements. In that case
`argmax` will return a maximal index, but not necessarily the
first one.
"""
function argmax(r::AbstractRange)
if isempty(r)
throw(ArgumentError("range must be non-empty"))
elseif step(r) > 0
lastindex(r)
else
firstindex(r)
end
end
extrema(r::AbstractRange) = (minimum(r), maximum(r))
# Ranges are immutable
copy(r::AbstractRange) = r
## iteration
function iterate(r::Union{StepRangeLen,LinRange}, i::Integer=zero(length(r)))
@inline
i += oneunit(i)
length(r) < i && return nothing
unsafe_getindex(r, i), i
end
iterate(r::OrdinalRange) = isempty(r) ? nothing : (first(r), first(r))
function iterate(r::OrdinalRange{T}, i) where {T}
@inline
i == last(r) && return nothing
next = convert(T, i + step(r))
(next, next)
end
## indexing
function isassigned(r::AbstractRange, i::Integer)
i isa Bool && throw(ArgumentError("invalid index: $i of type Bool"))
firstindex(r) <= i <= lastindex(r)
end
# `_getindex` is like `getindex` but does not check if `i isa Bool`
function _getindex(v::AbstractRange, i::Integer)
@boundscheck checkbounds(v, i)
unsafe_getindex(v, i)
end
_in_unit_range(v::UnitRange, val, i::Integer) = i > 0 && val <= v.stop && val >= v.start
function _getindex(v::UnitRange{T}, i::Integer) where T
val = convert(T, v.start + (i - oneunit(i)))
@boundscheck _in_unit_range(v, val, i) || throw_boundserror(v, i)
val
end
const OverflowSafe = Union{Bool,Int8,Int16,Int32,Int64,Int128,
UInt8,UInt16,UInt32,UInt64,UInt128}
function _getindex(v::UnitRange{T}, i::Integer) where {T<:OverflowSafe}
val = v.start + (i - oneunit(i))
@boundscheck _in_unit_range(v, val, i) || throw_boundserror(v, i)
val % T
end
let BitInteger64 = Union{Int8,Int16,Int32,Int64,UInt8,UInt16,UInt32,UInt64} # for bootstrapping
global function checkbounds(::Type{Bool}, v::StepRange{<:BitInteger64, <:BitInteger64}, i::BitInteger64)
res = widemul(step(v), i-oneunit(i)) + first(v)
(0 < i) & ifelse(0 < step(v), res <= last(v), res >= last(v))
end
end
# unsafe_getindex is separate to make it useful even when running with --check-bounds=yes
# it assumes the index is inbounds but does not segfault even if the index is out of bounds.
# it does not check if the index isa bool.
unsafe_getindex(v::OneTo{T}, i::Integer) where T = convert(T, i)
unsafe_getindex(v::AbstractRange{T}, i::Integer) where T = convert(T, first(v) + (i - oneunit(i))*step_hp(v))
function unsafe_getindex(r::StepRangeLen{T}, i::Integer) where T
u = oftype(r.offset, i) - r.offset
T(r.ref + u*r.step)
end
unsafe_getindex(r::LinRange, i::Integer) = lerpi(i-oneunit(i), r.lendiv, r.start, r.stop)
function lerpi(j::Integer, d::Integer, a::T, b::T) where T
t = j/d # ∈ [0,1]
# compute approximately fma(t, b, -fma(t, a, a))
return T((1-t)*a + t*b)
end
# non-scalar indexing
getindex(r::AbstractRange, ::Colon) = copy(r)
function getindex(r::AbstractUnitRange, s::AbstractUnitRange{T}) where {T<:Integer}
@inline
@boundscheck checkbounds(r, s)
if T === Bool
return range(first(s) ? first(r) : last(r), length = last(s))
else
f = first(r)
start = oftype(f, f + first(s) - firstindex(r))
len = length(s)
stop = oftype(f, start + (len - oneunit(len)))
return range(start, stop)
end
end
function getindex(r::OneTo{T}, s::OneTo) where T
@inline