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Tip revision: 63b33a2ef51b66d06cc075f9a36efb480515f887 authored by Tony Kelman on 04 November 2016, 23:38:30 UTC
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range.jl
# This file is a part of Julia. License is MIT: http://julialang.org/license
## 1-dimensional ranges ##
typealias Dims Tuple{Vararg{Int}}
abstract Range{T} <: AbstractArray{T,1}
## ordinal ranges
abstract OrdinalRange{T,S} <: Range{T}
immutable StepRange{T,S} <: OrdinalRange{T,S}
start::T
step::S
stop::T
function StepRange(start::T, step::S, stop::T)
new(start, step, steprange_last(start,step,stop))
end
end
# to make StepRange constructor inlineable, so optimizer can see `step` value
function steprange_last{T}(start::T, step, stop)
if isa(start,AbstractFloat) || isa(step,AbstractFloat)
throw(ArgumentError("StepRange should not be used with floating point"))
end
z = zero(step)
step == z && throw(ArgumentError("step cannot be zero"))
if stop == start
last = stop
else
if (step > z) != (stop > start)
# empty range has a special representation where stop = start-1
# this is needed to avoid the wrap-around that can happen computing
# start - step, which leads to a range that looks very large instead
# of empty.
if step > z
last = start - one(stop-start)
else
last = start + one(stop-start)
end
else
diff = stop - start
if T<:Signed && (diff > zero(diff)) != (stop > start)
# handle overflowed subtraction with unsigned rem
if diff > zero(diff)
remain = -convert(T, unsigned(-diff) % step)
else
remain = convert(T, unsigned(diff) % step)
end
else
remain = steprem(start,stop,step)
end
last = stop - remain
end
end
last
end
steprem(start,stop,step) = (stop-start) % step
StepRange{T,S}(start::T, step::S, stop::T) = StepRange{T,S}(start, step, stop)
immutable UnitRange{T<:Real} <: OrdinalRange{T,Int}
start::T
stop::T
UnitRange(start, stop) = new(start, unitrange_last(start,stop))
end
UnitRange{T<:Real}(start::T, stop::T) = UnitRange{T}(start, stop)
unitrange_last(::Bool, stop::Bool) = stop
unitrange_last{T<:Integer}(start::T, stop::T) =
ifelse(stop >= start, stop, convert(T,start-one(stop-start)))
unitrange_last{T}(start::T, stop::T) =
ifelse(stop >= start, convert(T,start+floor(stop-start)),
convert(T,start-one(stop-start)))
colon(a::Real, b::Real) = colon(promote(a,b)...)
colon{T<:Real}(start::T, stop::T) = UnitRange{T}(start, stop)
range(a::Real, len::Integer) = UnitRange{typeof(a)}(a, oftype(a, a+len-1))
colon{T}(start::T, stop::T) = StepRange(start, one(stop-start), stop)
range{T}(a::T, len::Integer) =
StepRange{T, typeof(a-a)}(a, one(a-a), a+oftype(a-a,(len-1)))
# first promote start and stop, leaving step alone
# this is for non-numeric ranges where step can be quite different
colon{A<:Real,C<:Real}(a::A, b, c::C) = colon(convert(promote_type(A,C),a), b, convert(promote_type(A,C),c))
colon{T<:Real}(start::T, step, stop::T) = StepRange(start, step, stop)
colon{T<:Real}(start::T, step::T, stop::T) = StepRange(start, step, stop)
colon{T<:Real}(start::T, step::Real, stop::T) = StepRange(promote(start, step, stop)...)
colon{T}(start::T, step, stop::T) = StepRange(start, step, stop)
range{T,S}(a::T, step::S, len::Integer) = StepRange{T,S}(a, step, convert(T, a+step*(len-1)))
## floating point ranges
immutable FloatRange{T<:AbstractFloat} <: Range{T}
start::T
step::T
len::T
divisor::T
end
FloatRange(a::AbstractFloat, s::AbstractFloat, l::Real, d::AbstractFloat) =
FloatRange{promote_type(typeof(a),typeof(s),typeof(d))}(a,s,l,d)
# float rationalization helper
function rat(x)
y = x
a = d = 1
b = c = 0
m = maxintfloat(Float32)
while abs(y) <= m
f = trunc(Int,y)
y -= f
a, c = f*a + c, a
b, d = f*b + d, b
max(abs(a),abs(b)) <= convert(Int,m) || return c, d
oftype(x,a)/oftype(x,b) == x && break
y = inv(y)
end
return a, b
end
function colon{T<:AbstractFloat}(start::T, step::T, stop::T)
step == 0 && throw(ArgumentError("range step cannot be zero"))
start == stop && return FloatRange{T}(start,step,1,1)
(0 < step) != (start < stop) && return FloatRange{T}(start,step,0,1)
# float range "lifting"
r = (stop-start)/step
n = round(r)
lo = prevfloat((prevfloat(stop)-nextfloat(start))/n)
hi = nextfloat((nextfloat(stop)-prevfloat(start))/n)
if lo <= step <= hi
a0, b = rat(start)
a = convert(T,a0)
if a/convert(T,b) == start
c0, d = rat(step)
c = convert(T,c0)
if c/convert(T,d) == step
e = lcm(b,d)
a *= div(e,b)
c *= div(e,d)
eT = convert(T,e)
if (a+n*c)/eT == stop
return FloatRange{T}(a, c, n+1, eT)
end
end
end
end
FloatRange{T}(start, step, floor(r)+1, one(step))
end
colon{T<:AbstractFloat}(a::T, b::T) = colon(a, one(a), b)
colon{T<:Real}(a::T, b::AbstractFloat, c::T) = colon(promote(a,b,c)...)
colon{T<:AbstractFloat}(a::T, b::AbstractFloat, c::T) = colon(promote(a,b,c)...)
colon{T<:AbstractFloat}(a::T, b::Real, c::T) = colon(promote(a,b,c)...)
range(a::AbstractFloat, len::Integer) = FloatRange(a,one(a),len,one(a))
range(a::AbstractFloat, st::AbstractFloat, len::Integer) = FloatRange(a,st,len,one(a))
range(a::Real, st::AbstractFloat, len::Integer) = FloatRange(float(a), st, len, one(st))
range(a::AbstractFloat, st::Real, len::Integer) = FloatRange(a, float(st), len, one(a))
## linspace and logspace
immutable LinSpace{T<:AbstractFloat} <: Range{T}
start::T
stop::T
len::T
divisor::T
end
function linspace{T<:AbstractFloat}(start::T, stop::T, len::T)
len == round(len) || throw(InexactError())
0 <= len || error("linspace($start, $stop, $len): negative length")
if len == 0
n = convert(T, 2)
if isinf(n*start) || isinf(n*stop)
start /= n; stop /= n; n = one(T)
end
return LinSpace(-start, -stop, -one(T), n)
end
if len == 1
start == stop || error("linspace($start, $stop, $len): endpoints differ")
return LinSpace(-start, -start, zero(T), one(T))
end
n = convert(T, len - 1)
len - n == 1 || error("linspace($start, $stop, $len): too long for $T")
a0, b = rat(start)
a = convert(T,a0)
if a/convert(T,b) == start
c0, d = rat(stop)
c = convert(T,c0)
if c/convert(T,d) == stop
e = lcm(b,d)
a *= div(e,b)
c *= div(e,d)
s = convert(T,n*e)
if isinf(a*n) || isinf(c*n)
s, p = frexp(s)
p2 = oftype(s,2)^p
a /= p2; c /= p2
end
if a*n/s == start && c*n/s == stop
return LinSpace(a, c, len, s)
end
end
end
a, c, s = start, stop, n
if isinf(a*n) || isinf(c*n)
s, p = frexp(s)
p2 = oftype(s,2)^p
a /= p2; c /= p2
end
if a*n/s == start && c*n/s == stop
return LinSpace(a, c, len, s)
end
return LinSpace(start, stop, len, n)
end
function linspace{T<:AbstractFloat}(start::T, stop::T, len::Real)
T_len = convert(T, len)
T_len == len || throw(InexactError())
linspace(start, stop, T_len)
end
linspace(start::Real, stop::Real, len::Real=50) =
linspace(promote(AbstractFloat(start), AbstractFloat(stop))..., len)
function show(io::IO, r::LinSpace)
print(io, "linspace(")
show(io, first(r))
print(io, ',')
show(io, last(r))
print(io, ',')
show(io, length(r))
print(io, ')')
end
logspace(start::Real, stop::Real, n::Integer=50) = 10.^linspace(start, stop, n)
## interface implementations
similar(r::Range, T::Type, dims::Tuple{Vararg{Integer}}) = Array(T, dims...)
similar(r::Range, T::Type, dims::Dims) = Array(T, dims)
size(r::Range) = (length(r),)
isempty(r::StepRange) =
(r.start != r.stop) & ((r.step > zero(r.step)) != (r.stop > r.start))
isempty(r::UnitRange) = r.start > r.stop
isempty(r::FloatRange) = length(r) == 0
isempty(r::LinSpace) = length(r) == 0
step(r::StepRange) = r.step
step(r::UnitRange) = 1
step(r::FloatRange) = r.step/r.divisor
step{T}(r::LinSpace{T}) = ifelse(r.len <= 0, convert(T,NaN), (r.stop-r.start)/r.divisor)
function length(r::StepRange)
n = Integer(div(r.stop+r.step - r.start, r.step))
isempty(r) ? zero(n) : n
end
length(r::UnitRange) = Integer(r.stop - r.start + 1)
length(r::FloatRange) = Integer(r.len)
length(r::LinSpace) = Integer(r.len + signbit(r.len - 1))
function length{T<:Union{Int,UInt,Int64,UInt64}}(r::StepRange{T})
isempty(r) && return zero(T)
if r.step > 1
return checked_add(convert(T, div(unsigned(r.stop - r.start), r.step)), one(T))
elseif r.step < -1
return checked_add(convert(T, div(unsigned(r.start - r.stop), -r.step)), one(T))
else
checked_add(div(checked_sub(r.stop, r.start), r.step), one(T))
end
end
length{T<:Union{Int,Int64}}(r::UnitRange{T}) =
checked_add(checked_sub(r.stop, r.start), one(T))
length{T<:Union{UInt,UInt64}}(r::UnitRange{T}) =
r.stop < r.start ? zero(T) : checked_add(r.stop - r.start, one(T))
# some special cases to favor default Int type
let smallint = (Int === Int64 ?
Union{Int8,UInt8,Int16,UInt16,Int32,UInt32} :
Union{Int8,UInt8,Int16,UInt16})
global length
function length{T <: smallint}(r::StepRange{T})
isempty(r) && return Int(0)
div(Int(r.stop)+Int(r.step) - Int(r.start), Int(r.step))
end
length{T <: smallint}(r::UnitRange{T}) = Int(r.stop) - Int(r.start) + 1
end
first{T}(r::OrdinalRange{T}) = convert(T, r.start)
first{T}(r::FloatRange{T}) = convert(T, r.start/r.divisor)
first{T}(r::LinSpace{T}) = convert(T, (r.len-1)*r.start/r.divisor)
last{T}(r::StepRange{T}) = r.stop
last(r::UnitRange) = r.stop
last{T}(r::FloatRange{T}) = convert(T, (r.start + (r.len-1)*r.step)/r.divisor)
last{T}(r::LinSpace{T}) = convert(T, (r.len-1)*r.stop/r.divisor)
minimum(r::UnitRange) = isempty(r) ? throw(ArgumentError("range must be non-empty")) : first(r)
maximum(r::UnitRange) = isempty(r) ? throw(ArgumentError("range must be non-empty")) : last(r)
minimum(r::Range) = isempty(r) ? throw(ArgumentError("range must be non-empty")) : min(first(r), last(r))
maximum(r::Range) = isempty(r) ? throw(ArgumentError("range must be non-empty")) : max(first(r), last(r))
ctranspose(r::Range) = [x for _=1, x=r]
transpose(r::Range) = r'
# Ranges are immutable
copy(r::Range) = r
## iteration
start(r::FloatRange) = 0
done(r::FloatRange, i::Int) = length(r) <= i
next{T}(r::FloatRange{T}, i::Int) =
(convert(T, (r.start + i*r.step)/r.divisor), i+1)
start(r::LinSpace) = 1
done(r::LinSpace, i::Int) = length(r) < i
next{T}(r::LinSpace{T}, i::Int) =
(convert(T, ((r.len-i)*r.start + (i-1)*r.stop)/r.divisor), i+1)
# NOTE: For ordinal ranges, we assume start+step might be from a
# lifted domain (e.g. Int8+Int8 => Int); use that for iterating.
start(r::StepRange) = convert(typeof(r.start+r.step), r.start)
next{T}(r::StepRange{T}, i) = (convert(T,i), i+r.step)
done{T,S}(r::StepRange{T,S}, i) = isempty(r) | (i < min(r.start, r.stop)) | (i > max(r.start, r.stop))
done{T,S}(r::StepRange{T,S}, i::Integer) = isempty(r) | (i == r.stop+r.step)
start(r::UnitRange) = oftype(r.start+1, r.start)
next{T}(r::UnitRange{T}, i) = (convert(T,i), i+1)
done(r::UnitRange, i) = i==oftype(i,r.stop)+1
## indexing
getindex(r::Range, i::Integer) = (checkbounds(r, i); unsafe_getindex(r, i))
unsafe_getindex{T}(v::Range{T}, i::Integer) = convert(T, first(v) + (i-1)*step(v))
getindex{T}(r::FloatRange{T}, i::Integer) = (checkbounds(r, i); unsafe_getindex(r, i))
unsafe_getindex{T}(r::FloatRange{T}, i::Integer) = convert(T, (r.start + (i-1)*r.step)/r.divisor)
getindex{T}(r::LinSpace{T}, i::Integer) = (checkbounds(r, i); unsafe_getindex(r, i))
unsafe_getindex{T}(r::LinSpace{T}, i::Integer) = convert(T, ((r.len-i)*r.start + (i-1)*r.stop)/r.divisor)
getindex(r::Range, ::Colon) = copy(r)
unsafe_getindex(r::Range, ::Colon) = copy(r)
getindex(r::UnitRange, s::UnitRange{Int}) = (checkbounds(r, s); unsafe_getindex(r, s))
function unsafe_getindex(r::UnitRange, s::UnitRange{Int})
st = oftype(r.start, r.start + s.start-1)
range(st, length(s))
end
getindex(r::UnitRange, s::StepRange{Int}) = (checkbounds(r, s); unsafe_getindex(r, s))
function unsafe_getindex(r::UnitRange, s::StepRange{Int})
st = oftype(r.start, r.start + s.start-1)
range(st, step(s), length(s))
end
getindex(r::StepRange, s::Range{Int}) = (checkbounds(r, s); unsafe_getindex(r, s))
function unsafe_getindex(r::StepRange, s::Range{Int})
st = oftype(r.start, r.start + (first(s)-1)*step(r))
range(st, step(r)*step(s), length(s))
end
getindex(r::FloatRange, s::OrdinalRange) = (checkbounds(r, s); unsafe_getindex(r, s))
function unsafe_getindex(r::FloatRange, s::OrdinalRange)
FloatRange(r.start + (first(s)-1)*r.step, step(s)*r.step, length(s), r.divisor)
end
getindex(r::LinSpace, s::OrdinalRange) = (checkbounds(r, s); unsafe_getindex(r, s))
function unsafe_getindex{T}(r::LinSpace{T}, s::OrdinalRange)
sl::T = length(s)
ifirst = first(s)
ilast = last(s)
vfirst::T = ((r.len - ifirst) * r.start + (ifirst - 1) * r.stop) / r.divisor
vlast::T = ((r.len - ilast) * r.start + (ilast - 1) * r.stop) / r.divisor
return linspace(vfirst, vlast, sl)
end
function show(io::IO, r::Range)
print(io, repr(first(r)), ':', repr(step(r)), ':', repr(last(r)))
end
show(io::IO, r::UnitRange) = print(io, repr(first(r)), ':', repr(last(r)))
=={T<:Range}(r::T, s::T) = (first(r) == first(s)) & (step(r) == step(s)) & (last(r) == last(s))
==(r::OrdinalRange, s::OrdinalRange) = (first(r) == first(s)) & (step(r) == step(s)) & (last(r) == last(s))
=={T<:LinSpace}(r::T, s::T) = (first(r) == first(s)) & (length(r) == length(s)) & (last(r) == last(s))
function ==(r::Range, s::Range)
lr = length(r)
if lr != length(s)
return false
end
u, v = start(r), start(s)
while !done(r, u)
x, u = next(r, u)
y, v = next(s, v)
if x != y
return false
end
end
return true
end
intersect{T1<:Integer, T2<:Integer}(r::UnitRange{T1}, s::UnitRange{T2}) = max(r.start,s.start):min(last(r),last(s))
intersect{T<:Integer}(i::Integer, r::UnitRange{T}) =
i < first(r) ? (first(r):i) :
i > last(r) ? (i:last(r)) : (i:i)
intersect{T<:Integer}(r::UnitRange{T}, i::Integer) = intersect(i, r)
function intersect{T1<:Integer, T2<:Integer}(r::UnitRange{T1}, s::StepRange{T2})
if isempty(s)
range(first(r), 0)
elseif step(s) == 0
intersect(first(s), r)
elseif step(s) < 0
intersect(r, reverse(s))
else
sta = first(s)
ste = step(s)
sto = last(s)
lo = first(r)
hi = last(r)
i0 = max(sta, lo + mod(sta - lo, ste))
i1 = min(sto, hi - mod(hi - sta, ste))
i0:ste:i1
end
end
function intersect{T1<:Integer, T2<:Integer}(r::StepRange{T1}, s::UnitRange{T2})
if step(r) < 0
reverse(intersect(s, reverse(r)))
else
intersect(s, r)
end
end
function intersect(r::StepRange, s::StepRange)
if isempty(r) || isempty(s)
return range(first(r), step(r), 0)
elseif step(s) < 0
return intersect(r, reverse(s))
elseif step(r) < 0
return reverse(intersect(reverse(r), s))
end
start1 = first(r)
step1 = step(r)
stop1 = last(r)
start2 = first(s)
step2 = step(s)
stop2 = last(s)
a = lcm(step1, step2)
# if a == 0
# # One or both ranges have step 0.
# if step1 == 0 && step2 == 0
# return start1 == start2 ? r : Range(start1, 0, 0)
# elseif step1 == 0
# return start2 <= start1 <= stop2 && rem(start1 - start2, step2) == 0 ? r : Range(start1, 0, 0)
# else
# return start1 <= start2 <= stop1 && rem(start2 - start1, step1) == 0 ? (start2:step1:start2) : Range(start1, step1, 0)
# end
# end
g, x, y = gcdx(step1, step2)
if rem(start1 - start2, g) != 0
# Unaligned, no overlap possible.
return range(start1, a, 0)
end
z = div(start1 - start2, g)
b = start1 - x * z * step1
# Possible points of the intersection of r and s are
# ..., b-2a, b-a, b, b+a, b+2a, ...
# Determine where in the sequence to start and stop.
m = max(start1 + mod(b - start1, a), start2 + mod(b - start2, a))
n = min(stop1 - mod(stop1 - b, a), stop2 - mod(stop2 - b, a))
m:a:n
end
function intersect(r1::Range, r2::Range, r3::Range, r::Range...)
i = intersect(intersect(r1, r2), r3)
for t in r
i = intersect(i, t)
end
i
end
# findin (the index of intersection)
function _findin{T1<:Integer, T2<:Integer}(r::Range{T1}, span::UnitRange{T2})
local ifirst
local ilast
fspan = first(span)
lspan = last(span)
fr = first(r)
lr = last(r)
sr = step(r)
if sr > 0
ifirst = fr >= fspan ? 1 : ceil(Integer,(fspan-fr)/sr)+1
ilast = lr <= lspan ? length(r) : length(r) - ceil(Integer,(lr-lspan)/sr)
elseif sr < 0
ifirst = fr <= lspan ? 1 : ceil(Integer,(lspan-fr)/sr)+1
ilast = lr >= fspan ? length(r) : length(r) - ceil(Integer,(lr-fspan)/sr)
else
ifirst = fr >= fspan ? 1 : length(r)+1
ilast = fr <= lspan ? length(r) : 0
end
ifirst, ilast
end
function findin{T1<:Integer, T2<:Integer}(r::UnitRange{T1}, span::UnitRange{T2})
ifirst, ilast = _findin(r, span)
ifirst:ilast
end
function findin{T1<:Integer, T2<:Integer}(r::Range{T1}, span::UnitRange{T2})
ifirst, ilast = _findin(r, span)
ifirst:1:ilast
end
## linear operations on ranges ##
-(r::OrdinalRange) = range(-r.start, -step(r), length(r))
-(r::FloatRange) = FloatRange(-r.start, -r.step, r.len, r.divisor)
-(r::LinSpace) = LinSpace(-r.start, -r.stop, r.len, r.divisor)
.+(x::Real, r::UnitRange) = range(x + r.start, length(r))
.+(x::Real, r::Range) = (x+first(r)):step(r):(x+last(r))
#.+(x::Real, r::StepRange) = range(x + r.start, r.step, length(r))
.+(x::Real, r::FloatRange) = FloatRange(r.divisor*x + r.start, r.step, r.len, r.divisor)
function .+{T}(x::Real, r::LinSpace{T})
x2 = x * r.divisor / (r.len - 1)
LinSpace(x2 + r.start, x2 + r.stop, r.len, r.divisor)
end
.+(r::Range, x::Real) = x + r
#.+(r::FloatRange, x::Real) = x + r
.-(x::Real, r::Range) = (x-first(r)):-step(r):(x-last(r))
.-(x::Real, r::FloatRange) = FloatRange(r.divisor*x - r.start, -r.step, r.len, r.divisor)
function .-(x::Real, r::LinSpace)
x2 = x * r.divisor / (r.len - 1)
LinSpace(x2 - r.start, x2 - r.stop, r.len, r.divisor)
end
.-(r::UnitRange, x::Real) = range(r.start-x, length(r))
.-(r::StepRange , x::Real) = range(r.start-x, r.step, length(r))
.-(r::FloatRange, x::Real) = FloatRange(r.start - r.divisor*x, r.step, r.len, r.divisor)
function .-(r::LinSpace, x::Real)
x2 = x * r.divisor / (r.len - 1)
LinSpace(r.start - x2, r.stop - x2, r.len, r.divisor)
end
.*(x::Real, r::OrdinalRange) = range(x*r.start, x*step(r), length(r))
.*(x::Real, r::FloatRange) = FloatRange(x*r.start, x*r.step, r.len, r.divisor)
.*(x::Real, r::LinSpace) = LinSpace(x * r.start, x * r.stop, r.len, r.divisor)
.*(r::Range, x::Real) = x .* r
.*(r::FloatRange, x::Real) = x .* r
.*(r::LinSpace, x::Real) = x .* r
./(r::OrdinalRange, x::Real) = range(r.start/x, step(r)/x, length(r))
./(r::FloatRange, x::Real) = FloatRange(r.start/x, r.step/x, r.len, r.divisor)
./(r::LinSpace, x::Real) = LinSpace(r.start / x, r.stop / x, r.len, r.divisor)
promote_rule{T1,T2}(::Type{UnitRange{T1}},::Type{UnitRange{T2}}) =
UnitRange{promote_type(T1,T2)}
convert{T}(::Type{UnitRange{T}}, r::UnitRange{T}) = r
convert{T}(::Type{UnitRange{T}}, r::UnitRange) = UnitRange{T}(r.start, r.stop)
promote_rule{T1a,T1b,T2a,T2b}(::Type{StepRange{T1a,T1b}},::Type{StepRange{T2a,T2b}}) =
StepRange{promote_type(T1a,T2a),promote_type(T1b,T2b)}
convert{T1,T2}(::Type{StepRange{T1,T2}}, r::StepRange{T1,T2}) = r
promote_rule{T1a,T1b,T2}(::Type{StepRange{T1a,T1b}},::Type{UnitRange{T2}}) =
StepRange{promote_type(T1a,T2),promote_type(T1b,T2)}
convert{T1,T2}(::Type{StepRange{T1,T2}}, r::Range) =
StepRange{T1,T2}(convert(T1, first(r)), convert(T2, step(r)), convert(T1, last(r)))
convert{T}(::Type{StepRange}, r::UnitRange{T}) =
StepRange{T,T}(first(r), step(r), last(r))
promote_rule{T1,T2}(::Type{FloatRange{T1}},::Type{FloatRange{T2}}) =
FloatRange{promote_type(T1,T2)}
convert{T}(::Type{FloatRange{T}}, r::FloatRange{T}) = r
convert{T}(::Type{FloatRange{T}}, r::FloatRange) =
FloatRange{T}(r.start,r.step,r.len,r.divisor)
promote_rule{F,OR<:OrdinalRange}(::Type{FloatRange{F}}, ::Type{OR}) =
FloatRange{promote_type(F,eltype(OR))}
convert{T}(::Type{FloatRange{T}}, r::OrdinalRange) =
FloatRange{T}(first(r), step(r), length(r), one(T))
convert{T}(::Type{FloatRange}, r::OrdinalRange{T}) =
FloatRange{typeof(float(first(r)))}(first(r), step(r), length(r), one(T))
promote_rule{T1,T2}(::Type{LinSpace{T1}},::Type{LinSpace{T2}}) =
LinSpace{promote_type(T1,T2)}
convert{T}(::Type{LinSpace{T}}, r::LinSpace{T}) = r
convert{T}(::Type{LinSpace{T}}, r::LinSpace) =
LinSpace{T}(r.start, r.stop, r.len, r.divisor)
promote_rule{F,OR<:OrdinalRange}(::Type{LinSpace{F}}, ::Type{OR}) =
LinSpace{promote_type(F,eltype(OR))}
convert{T}(::Type{LinSpace{T}}, r::OrdinalRange) =
linspace(convert(T, first(r)), convert(T, last(r)), convert(T, length(r)))
convert{T}(::Type{LinSpace}, r::OrdinalRange{T}) =
convert(LinSpace{typeof(float(first(r)))}, r)
# Promote FloatRange to LinSpace
promote_rule{F,OR<:FloatRange}(::Type{LinSpace{F}}, ::Type{OR}) =
LinSpace{promote_type(F,eltype(OR))}
convert{T}(::Type{LinSpace{T}}, r::FloatRange) =
linspace(convert(T, first(r)), convert(T, last(r)), convert(T, length(r)))
convert{T}(::Type{LinSpace}, r::FloatRange{T}) =
convert(LinSpace{T}, r)
# +/- of ranges is defined in operators.jl (to be able to use @eval etc.)
## non-linear operations on ranges and fallbacks for non-real numbers ##
.+(x::Number, r::Range) = [ x+y for y=r ]
.+(r::Range, y::Number) = [ x+y for x=r ]
.-(x::Number, r::Range) = [ x-y for y=r ]
.-(r::Range, y::Number) = [ x-y for x=r ]
.*(x::Number, r::Range) = [ x*y for y=r ]
.*(r::Range, y::Number) = [ x*y for x=r ]
./(x::Number, r::Range) = [ x/y for y=r ]
./(r::Range, y::Number) = [ x/y for x=r ]
.^(x::Number, r::Range) = [ x^y for y=r ]
.^(r::Range, y::Number) = [ x^y for x=r ]
## concatenation ##
function vcat{T}(rs::Range{T}...)
n::Int = 0
for ra in rs
n += length(ra)
end
a = Array(T,n)
i = 1
for ra in rs, x in ra
@inbounds a[i] = x
i += 1
end
return a
end
convert{T}(::Type{Array{T,1}}, r::Range{T}) = vcat(r)
collect(r::Range) = vcat(r)
reverse(r::OrdinalRange) = colon(last(r), -step(r), first(r))
reverse(r::FloatRange) = FloatRange(r.start + (r.len-1)*r.step, -r.step, r.len, r.divisor)
reverse(r::LinSpace) = LinSpace(r.stop, r.start, r.len, r.divisor)
## sorting ##
issorted(r::UnitRange) = true
issorted(r::Range) = step(r) >= zero(step(r))
sort(r::UnitRange) = r
sort!(r::UnitRange) = r
sort(r::Range) = issorted(r) ? r : reverse(r)
sortperm(r::UnitRange) = 1:length(r)
sortperm(r::Range) = issorted(r) ? (1:1:length(r)) : (length(r):-1:1)
function sum{T<:Real}(r::Range{T})
l = length(r)
# note that a little care is required to avoid overflow in l*(l-1)/2
return l * first(r) + (iseven(l) ? (step(r) * (l-1)) * (l>>1)
: (step(r) * l) * ((l-1)>>1))
end
function sum(r::FloatRange)
l = length(r)
if iseven(l)
s = r.step * (l-1) * (l>>1)
else
s = (r.step * l) * ((l-1)>>1)
end
return (l * r.start + s)/r.divisor
end
function mean{T<:Real}(r::Range{T})
isempty(r) && throw(ArgumentError("mean of an empty range is undefined"))
(first(r) + last(r)) / 2
end
median{T<:Real}(r::Range{T}) = mean(r)
function in(x, r::Range)
n = step(r) == 0 ? 1 : round(Integer,(x-first(r))/step(r))+1
n >= 1 && n <= length(r) && r[n] == x
end
in{T<:Integer}(x, r::Range{T}) = isinteger(x) && !isempty(r) && x>=minimum(r) && x<=maximum(r) && (mod(convert(T,x),step(r))-mod(first(r),step(r)) == 0)
in(x::Char, r::Range{Char}) = !isempty(r) && x >= minimum(r) && x <= maximum(r) && (mod(Int(x) - Int(first(r)), step(r)) == 0)