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ranges.jl
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ranges.jl
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# This file is a part of Julia. License is MIT: https://julialang.org/license
using Dates, Random
# Compare precision in a manner sensitive to subnormals, which lose
# precision compared to widening.
function cmp_sn(w, hi, lo, slopbits=0)
if !isfinite(hi)
if abs(w) > realmax(typeof(hi))
return isinf(hi) && sign(w) == sign(hi)
end
if isnan(w) && isnan(hi)
return true
end
return w == hi
end
if abs(w) < subnormalmin(typeof(hi))
return (hi == zero(hi) || abs(w - widen(hi)) < abs(w)) && lo == zero(hi)
end
# Compare w == hi + lo unless `lo` issubnormal
z = widen(hi) + widen(lo)
if !issubnormal(lo) && lo != 0
if slopbits == 0
return z == w
end
wr, zr = roundshift(w, slopbits), roundshift(z, slopbits)
return max(wr-1, zero(wr)) <= zr <= wr+1
end
# round w to the same number of bits as z
zu = asbits(z)
wu = asbits(w)
lastbit = false
while zu > 0 && !isodd(zu)
lastbit = isodd(wu)
zu = zu >> 1
wu = wu >> 1
end
return wu <= zu <= wu + lastbit
end
asbits(x) = reinterpret(Base.uinttype(typeof(x)), x)
function roundshift(x, n)
xu = asbits(x)
lastbit = false
for i = 1:n
lastbit = isodd(xu)
xu = xu >> 1
end
xu + lastbit
end
subnormalmin(::Type{T}) where T = reinterpret(T, Base.uinttype(T)(1))
function highprec_pair(x, y)
slopbits = (Base.Math.significand_bits(typeof(widen(x))) + 1) -
2*(Base.Math.significand_bits(typeof(x)) + 1)
hi, lo = Base.add12(x, y)
@test cmp_sn(widen(x) + widen(y), hi, lo)
hi, lo = Base.mul12(x, y)
@test cmp_sn(widen(x) * widen(y), hi, lo)
y == 0 && return nothing
hi, lo = Base.div12(x, y)
@test cmp_sn(widen(x) / widen(y), hi, lo, slopbits)
nothing
end
@testset "high precision" begin
# Because ranges rely on high precision arithmetic, test those utilities first
for (I, T) in ((Int16, Float16), (Int32, Float32), (Int64, Float64)), i = 1:10^3
i = rand(I) >> 1 # test large values below
hi, lo = Base.splitprec(T, i)
@test widen(hi) + widen(lo) == i
@test endswith(bitstring(hi), repeat('0', Base.Math.significand_bits(T) ÷ 2))
end
for (I, T) in ((Int16, Float16), (Int32, Float32), (Int64, Float64))
x = T(typemax(I))
Δi = ceil(I, eps(x))
for i = typemax(I)-2Δi:typemax(I)-Δi
hi, lo = Base.splitprec(T, i)
@test widen(hi) + widen(lo) == i
@test endswith(bitstring(hi), repeat('0', Base.Math.significand_bits(T) ÷ 2))
end
for i = typemin(I):typemin(I)+Δi
hi, lo = Base.splitprec(T, i)
@test widen(hi) + widen(lo) == i
@test endswith(bitstring(hi), repeat('0', Base.Math.significand_bits(T) ÷ 2))
end
end
# # This tests every possible pair of Float16s. It takes too long for
# # ordinary use, which is why it's commented out.
# function pair16()
# for yu in 0x0000:0xffff
# for xu in 0x0000:0xffff
# x, y = reinterpret(Float16, xu), reinterpret(Float16, yu)
# highprec_pair(x, y)
# end
# end
# end
for T in (Float16, Float32) # skip Float64 (bit representation of BigFloat is not available)
for i = 1:10^5
x, y = rand(T), rand(T)
highprec_pair(x, y)
highprec_pair(-x, y)
highprec_pair(x, -y)
highprec_pair(-x, -y)
end
# Make sure we test dynamic range too
for i = 1:10^5
x, y = rand(T), rand(T)
x == 0 || y == 0 && continue
x, y = log(x), log(y)
highprec_pair(x, y)
end
end
end
asww(x) = widen(widen(x.hi)) + widen(widen(x.lo))
astuple(x) = (x.hi, x.lo)
function cmp_sn2(w, hi, lo, slopbits=0)
if !isfinite(hi)
if abs(w) > realmax(typeof(hi))
return isinf(hi) && sign(w) == sign(hi)
end
if isnan(w) && isnan(hi)
return true
end
return w == hi
end
if abs(w) < subnormalmin(typeof(hi))
return (hi == zero(hi) || abs(w - widen(hi)) < abs(w)) && lo == zero(hi)
end
z = widen(hi) + widen(lo)
w == z && return true
zu, wu = asbits(z), asbits(w)
while zu > 0 && !isodd(zu)
zu = zu >> 1
wu = wu >> 1
end
zu = zu >> slopbits
wu = wu >> slopbits
return wu - 1 <= zu <= wu + 1
end
@testset "TwicePrecision" begin
# TwicePrecision test. These routines lose accuracy if you form
# intermediate subnormals; with Float16, this happens so frequently,
# let's only test Float32.
let T = Float32
Tw = widen(T)
slopbits = (Base.Math.significand_bits(Tw) + 1) -
2*(Base.Math.significand_bits(T) + 1)
for i = 1:10^5
x = Base.TwicePrecision{T}(rand())
y = Base.TwicePrecision{T}(rand())
xw, yw = asww(x), asww(y)
@test cmp_sn2(Tw(xw+yw), astuple(x+y)..., slopbits)
@test cmp_sn2(Tw(xw-yw), astuple(x-y)..., slopbits)
@test cmp_sn2(Tw(xw*yw), astuple(x*y)..., slopbits)
@test cmp_sn2(Tw(xw/yw), astuple(x/y)..., slopbits)
y = rand(T)
yw = widen(widen(y))
@test cmp_sn2(Tw(xw+yw), astuple(x+y)..., slopbits)
@test cmp_sn2(Tw(xw-yw), astuple(x-y)..., slopbits)
@test cmp_sn2(Tw(xw*yw), astuple(x*y)..., slopbits)
@test cmp_sn2(Tw(xw/yw), astuple(x/y)..., slopbits)
end
end
x1 = Base.TwicePrecision{Float64}(1)
x0 = Base.TwicePrecision{Float64}(0)
xinf = Base.TwicePrecision{Float64}(Inf)
@test Float64(x1+x0) == 1
@test Float64(x1+0) == 1
@test Float64(x1+0.0) == 1
@test Float64(x1*x0) == 0
@test Float64(x1*0) == 0
@test Float64(x1*0.0) == 0
@test Float64(x1/x0) == Inf
@test Float64(x1/0) == Inf
@test Float64(xinf*x1) == Inf
@test isnan(Float64(xinf*x0))
@test isnan(Float64(xinf*0))
@test isnan(Float64(xinf*0.0))
@test isnan(Float64(x0/x0))
@test isnan(Float64(x0/0))
@test isnan(Float64(x0/0.0))
end
@testset "ranges" begin
@test size(10:1:0) == (0,)
@testset "colon" begin
@inferred((:)(10, 1, 0))
@inferred((:)(1, .2, 2))
@inferred((:)(1., .2, 2.))
@inferred((:)(2, -.2, 1))
@inferred((:)(1, 0))
@inferred((:)(0.0, -0.5))
end
@testset "indexing" begin
L32 = @inferred(range(Int32(1), stop=Int32(4), length=4))
L64 = @inferred(range(Int64(1), stop=Int64(4), length=4))
@test @inferred(L32[1]) === 1.0 && @inferred(L64[1]) === 1.0
@test L32[2] == 2 && L64[2] == 2
@test L32[3] == 3 && L64[3] == 3
@test L32[4] == 4 && L64[4] == 4
@test @inferred(range(1.0, stop=2.0, length=2))[1] === 1.0
@test @inferred(range(1.0f0, stop=2.0f0, length=2))[1] === 1.0f0
@test @inferred(range(Float16(1.0), stop=Float16(2.0), length=2))[1] === Float16(1.0)
let r = 5:-1:1
@test r[1]==5
@test r[2]==4
@test r[3]==3
@test r[4]==2
@test r[5]==1
end
@test @inferred((0.1:0.1:0.3)[2]) === 0.2
@test @inferred((0.1f0:0.1f0:0.3f0)[2]) === 0.2f0
@test @inferred((1:5)[1:4]) === 1:4
@test @inferred((1.0:5)[1:4]) === 1.0:4
@test (2:6)[1:4] == 2:5
@test (1:6)[2:5] === 2:5
@test (1:6)[2:2:5] === 2:2:4
@test (1:2:13)[2:6] === 3:2:11
@test (1:2:13)[2:3:7] === 3:6:13
@test isempty((1:4)[5:4])
@test_throws BoundsError (1:10)[8:-1:-2]
let r = typemax(Int)-5:typemax(Int)-1
@test_throws BoundsError r[7]
end
end
@testset "length" begin
@test length(.1:.1:.3) == 3
@test length(1.1:1.1:3.3) == 3
@test length(1.1:1.3:3) == 2
@test length(1:1:1.8) == 1
@test length(1:.2:2) == 6
@test length(1.:.2:2.) == 6
@test length(2:-.2:1) == 6
@test length(2.:-.2:1.) == 6
@test length(2:.2:1) == 0
@test length(2.:.2:1.) == 0
@test length(1:0) == 0
@test length(0.0:-0.5) == 0
@test length(1:2:0) == 0
end
@testset "findall(::Base.Fix2{typeof(in)}, ::Array)" begin
@test findall(in(3:20), [5.2, 3.3]) == findall(in(Vector(3:20)), [5.2, 3.3])
let span = 5:20,
r = -7:3:42
@test findall(in(span), r) == 5:10
r = 15:-2:-38
@test findall(in(span), r) == 1:6
end
end
@testset "reverse" begin
@test reverse(reverse(1:10)) == 1:10
@test reverse(reverse(typemin(Int):typemax(Int))) == typemin(Int):typemax(Int)
@test reverse(reverse(typemin(Int):2:typemax(Int))) == typemin(Int):2:typemax(Int)
end
@testset "intersect" begin
@test intersect(1:5, 2:3) == 2:3
@test intersect(-3:5, 2:8) == 2:5
@test intersect(-8:-3, -8:-3) == -8:-3
@test intersect(1:5, 5:13) == 5:5
@test isempty(intersect(-8:-3, -2:2))
@test isempty(intersect(-3:7, 2:1))
@test intersect(1:11, -2:3:15) == 1:3:10
@test intersect(1:11, -2:2:15) == 2:2:10
@test intersect(1:11, -2:1:15) == 1:11
@test intersect(1:11, 15:-1:-2) == 1:11
@test intersect(1:11, 15:-4:-2) == 3:4:11
@test intersect(-20:-5, -10:3:-2) == -10:3:-7
@test isempty(intersect(-5:5, -6:13:20))
@test isempty(intersect(1:11, 15:4:-2))
@test isempty(intersect(11:1, 15:-4:-2))
#@test intersect(-5:5, 1+0*(1:3)) == 1:1
#@test isempty(intersect(-5:5, 6+0*(1:3)))
@test intersect(-15:4:7, -10:-2) == -7:4:-3
@test intersect(13:-2:1, -2:8) == 7:-2:1
@test isempty(intersect(13:2:1, -2:8))
@test isempty(intersect(13:-2:1, 8:-2))
#@test intersect(5+0*(1:4), 2:8) == 5+0*(1:4)
#@test isempty(intersect(5+0*(1:4), -7:3))
@test intersect(0:3:24, 0:4:24) == 0:12:24
@test intersect(0:4:24, 0:3:24) == 0:12:24
@test intersect(0:3:24, 24:-4:0) == 0:12:24
@test intersect(24:-3:0, 0:4:24) == 24:-12:0
@test intersect(24:-3:0, 24:-4:0) == 24:-12:0
@test intersect(1:3:24, 0:4:24) == 4:12:16
@test intersect(0:6:24, 0:4:24) == 0:12:24
@test isempty(intersect(1:6:2400, 0:4:2400))
@test intersect(-51:5:100, -33:7:125) == -26:35:79
@test intersect(-51:5:100, -32:7:125) == -11:35:94
#@test intersect(0:6:24, 6+0*(0:4:24)) == 6:6:6
#@test intersect(12+0*(0:6:24), 0:4:24) == AbstractRange(12, 0, 5)
#@test isempty(intersect(6+0*(0:6:24), 0:4:24))
@test intersect(-10:3:24, -10:3:24) == -10:3:23
@test isempty(intersect(-11:3:24, -10:3:24))
@test intersect(typemin(Int):2:typemax(Int),1:10) == 2:2:10
@test intersect(1:10,typemin(Int):2:typemax(Int)) == 2:2:10
@test intersect(reverse(typemin(Int):2:typemax(Int)),typemin(Int):2:typemax(Int)) == reverse(typemin(Int):2:typemax(Int))
@test intersect(typemin(Int):2:typemax(Int),reverse(typemin(Int):2:typemax(Int))) == typemin(Int):2:typemax(Int)
@test intersect(UnitRange(1,2),3) == UnitRange(3,2)
@test intersect(UnitRange(1,2), UnitRange(1,5), UnitRange(3,7), UnitRange(4,6)) == UnitRange(4,3)
@test intersect(1:3, 2) === intersect(2, 1:3) === 2:2
@test intersect(1.0:3.0, 2) == intersect(2, 1.0:3.0) == [2.0]
end
@testset "sort/sort!/partialsort" begin
@test sort(UnitRange(1,2)) == UnitRange(1,2)
@test sort!(UnitRange(1,2)) == UnitRange(1,2)
@test sort(1:10, rev=true) == 10:-1:1
@test sort(-3:3, by=abs) == [0,-1,1,-2,2,-3,3]
@test partialsort(1:10, 4) == 4
end
@testset "in" begin
@test 0 in UInt(0):100:typemax(UInt)
@test last(UInt(0):100:typemax(UInt)) in UInt(0):100:typemax(UInt)
@test -9223372036854775790 in -9223372036854775790:100:9223372036854775710
@test -9223372036854775690 in -9223372036854775790:100:9223372036854775710
@test -90 in -9223372036854775790:100:9223372036854775710
@test 10 in -9223372036854775790:100:9223372036854775710
@test 110 in -9223372036854775790:100:9223372036854775710
@test 9223372036854775610 in -9223372036854775790:100:9223372036854775710
@test 9223372036854775710 in -9223372036854775790:100:9223372036854775710
@test !(3.5 in 1:5)
@test (3 in 1:5)
@test (3 in 5:-1:1)
#@test (3 in 3+0*(1:5))
#@test !(4 in 3+0*(1:5))
let r = 0.0:0.01:1.0
@test (r[30] in r)
end
let r = (-4*Int64(maxintfloat(Int === Int32 ? Float32 : Float64))):5
@test (3 in r)
@test (3.0 in r)
end
@test !(1 in 1:0)
@test !(1.0 in 1.0:0.0)
end
@testset "in() works across types, including non-numeric types (#21728)" begin
@test 1//1 in 1:3
@test 1//1 in 1.0:3.0
@test !(5//1 in 1:3)
@test !(5//1 in 1.0:3.0)
@test Complex(1, 0) in 1:3
@test Complex(1, 0) in 1.0:3.0
@test Complex(1.0, 0.0) in 1:3
@test Complex(1.0, 0.0) in 1.0:3.0
@test !(Complex(1, 1) in 1:3)
@test !(Complex(1, 1) in 1.0:3.0)
@test !(Complex(1.0, 1.0) in 1:3)
@test !(Complex(1.0, 1.0) in 1.0:3.0)
@test !(π in 1:3)
@test !(π in 1.0:3.0)
@test !("a" in 1:3)
@test !("a" in 1.0:3.0)
@test !(1 in Date(2017, 01, 01):Dates.Day(1):Date(2017, 01, 05))
@test !(Complex(1, 0) in Date(2017, 01, 01):Dates.Day(1):Date(2017, 01, 05))
@test !(π in Date(2017, 01, 01):Dates.Day(1):Date(2017, 01, 05))
@test !("a" in Date(2017, 01, 01):Dates.Day(1):Date(2017, 01, 05))
end
end
@testset "indexing range with empty range (#4309)" begin
@test (3:6)[5:4] == 7:6
@test_throws BoundsError (3:6)[5:5]
@test_throws BoundsError (3:6)[5]
@test (0:2:10)[7:6] == 12:2:10
@test_throws BoundsError (0:2:10)[7:7]
end
# indexing with negative ranges (#8351)
for a=AbstractRange[3:6, 0:2:10], b=AbstractRange[0:1, 2:-1:0]
@test_throws BoundsError a[b]
end
# avoiding intermediate overflow (#5065)
@test length(1:4:typemax(Int)) == div(typemax(Int),4) + 1
@testset "overflow in length" begin
@test_throws OverflowError length(0:typemax(Int))
@test_throws OverflowError length(typemin(Int):typemax(Int))
@test_throws OverflowError length(-1:typemax(Int)-1)
end
@testset "loops involving typemin/typemax" begin
n = 0
s = 0
# loops ending at typemax(Int)
for i = (typemax(Int)-1):typemax(Int)
s += 1
@test s <= 2
end
@test s == 2
s = 0
for i = (typemax(Int)-2):(typemax(Int)-1)
s += 1
@test s <= 2
end
@test s == 2
s = 0
for i = typemin(Int):(typemin(Int)+1)
s += 1
@test s <= 2
end
@test s == 2
# loops covering the full range of smaller integer types
s = 0
for i = typemin(UInt8):typemax(UInt8)
s += 1
end
@test s == 256
s = 0
for i = typemin(UInt8):one(UInt8):typemax(UInt8)
s += 1
end
@test s == 256
# loops past typemax(Int)
n = 0
s = Int128(0)
for i = typemax(UInt64)-2:typemax(UInt64)
n += 1
s += i
end
@test n == 3
@test s == 3*Int128(typemax(UInt64)) - 3
# loops over empty ranges
s = 0
for i = 0xff:0x00
s += 1
end
@test s == 0
s = 0
for i = Int128(typemax(Int128)):Int128(typemin(Int128))
s += 1
end
@test s == 0
end
@testset "sums of ranges" begin
@test sum(1:100) == 5050
@test sum(0:100) == 5050
@test sum(-100:100) == 0
@test sum(0:2:100) == 2550
end
@testset "overflowing sums (see #5798)" begin
if Sys.WORD_SIZE == 64
@test sum(Int128(1):10^18) == div(10^18 * (Int128(10^18)+1), 2)
@test sum(Int128(1):10^18-1) == div(10^18 * (Int128(10^18)-1), 2)
else
@test sum(Int64(1):10^9) == div(10^9 * (Int64(10^9)+1), 2)
@test sum(Int64(1):10^9-1) == div(10^9 * (Int64(10^9)-1), 2)
end
end
@testset "Tricky sums of StepRangeLen #8272" begin
@test sum(10000.:-0.0001:0) == 5.00000005e11
@test sum(0:0.001:1) == 500.5
@test sum(0:0.000001:1) == 500000.5
@test sum(0:0.1:10) == 505.
end
@testset "broadcasted operations with scalars" begin
@test broadcast(-, 1:3, 2) == -1:1
@test broadcast(-, 1:3, 0.25) == 1-0.25:3-0.25
@test broadcast(+, 1:3, 2) == 3:5
@test broadcast(+, 1:3, 0.25) == 1+0.25:3+0.25
@test broadcast(+, 1:2:6, 1) == 2:2:6
@test broadcast(+, 1:2:6, 0.3) == 1+0.3:2:5+0.3
@test broadcast(-, 1:2:6, 1) == 0:2:4
@test broadcast(-, 1:2:6, 0.3) == 1-0.3:2:5-0.3
@test broadcast(-, 2, 1:3) == 1:-1:-1
end
@testset "operations between ranges and arrays" begin
@test all(([1:5;] + (5:-1:1)) .== 6)
@test all(((5:-1:1) + [1:5;]) .== 6)
@test all(([1:5;] - (1:5)) .== 0)
@test all(((1:5) - [1:5;]) .== 0)
end
@testset "tricky floating-point ranges" begin
for (start, step, stop, len) in ((1, 1, 3, 3), (0, 1, 3, 4),
(3, -1, -1, 5), (1, -1, -3, 5),
(0, 1, 10, 11), (0, 7, 21, 4),
(0, 11, 33, 4), (1, 11, 34, 4),
(0, 13, 39, 4), (1, 13, 40, 4),
(11, 11, 33, 3), (3, 1, 11, 9),
(0, 10, 55, 0), (0, -1, 5, 0), (0, 10, 5, 0),
(0, 1, 5, 0), (0, -10, 5, 0), (0, -10, 0, 1),
(0, -1, 1, 0), (0, 1, -1, 0), (0, -1, -10, 11))
r = start/10:step/10:stop/10
a = Vector(start:step:stop)./10
ra = Vector(r)
@test r == a
@test isequal(r, a)
@test r == ra
@test isequal(r, ra)
@test hash(r) == hash(a)
@test hash(r) == hash(ra)
if len > 0
l = range(start/10, stop=stop/10, length=len)
la = Vector(l)
@test a == l
@test r == l
@test isequal(a, l)
@test isequal(r, l)
@test l == la
@test isequal(l, la)
@test hash(l) == hash(a)
@test hash(l) == hash(la)
end
end
@test 1.0:1/49:27.0 == range(1.0, stop=27.0, length=1275) == [49:1323;]./49
@test isequal(1.0:1/49:27.0, range(1.0, stop=27.0, length=1275))
@test isequal(1.0:1/49:27.0, Vector(49:1323)./49)
@test hash(1.0:1/49:27.0) == hash(range(1.0, stop=27.0, length=1275)) == hash(Vector(49:1323)./49)
@test [prevfloat(0.1):0.1:0.3;] == [prevfloat(0.1), 0.2, 0.3]
@test [nextfloat(0.1):0.1:0.3;] == [nextfloat(0.1), 0.2]
@test [prevfloat(0.0):0.1:0.3;] == [prevfloat(0.0), 0.1, 0.2]
@test [nextfloat(0.0):0.1:0.3;] == [nextfloat(0.0), 0.1, 0.2]
@test [0.1:0.1:prevfloat(0.3);] == [0.1, 0.2]
@test [0.1:0.1:nextfloat(0.3);] == [0.1, 0.2, nextfloat(0.3)]
@test [0.0:0.1:prevfloat(0.3);] == [0.0, 0.1, 0.2]
@test [0.0:0.1:nextfloat(0.3);] == [0.0, 0.1, 0.2, nextfloat(0.3)]
@test [0.1:prevfloat(0.1):0.3;] == [0.1, 0.2, 0.3]
@test [0.1:nextfloat(0.1):0.3;] == [0.1, 0.2]
@test [0.0:prevfloat(0.1):0.3;] == [0.0, prevfloat(0.1), prevfloat(0.2), 0.3]
@test [0.0:nextfloat(0.1):0.3;] == [0.0, nextfloat(0.1), nextfloat(0.2)]
end
@testset "issue #7420 for type $T" for T = (Float32, Float64,), # BigFloat),
a = -5:25,
s = [-5:-1; 1:25; ],
d = 1:25,
n = -1:15
denom = convert(T, d)
strt = convert(T, a)/denom
Δ = convert(T, s)/denom
stop = convert(T, (a + (n - 1) * s)) / denom
vals = T[a:s:(a + (n - 1) * s); ] ./ denom
r = strt:Δ:stop
@test [r;] == vals
@test [range(strt, stop=stop, length=length(r));] == vals
n = length(r)
@test [r[1:n];] == [r;]
@test [r[2:n];] == [r;][2:end]
@test [r[1:3:n];] == [r;][1:3:n]
@test [r[2:2:n];] == [r;][2:2:n]
@test [r[n:-1:2];] == [r;][n:-1:2]
@test [r[n:-2:1];] == [r;][n:-2:1]
end
@testset "issue #20373 (unliftable ranges with exact end points)" begin
@test [3*0.05:0.05:0.2;] == [range(3*0.05, stop=0.2, length=2);] == [3*0.05,0.2]
@test [0.2:-0.05:3*0.05;] == [range(0.2, stop=3*0.05, length=2);] == [0.2,3*0.05]
@test [-3*0.05:-0.05:-0.2;] == [range(-3*0.05, stop=-0.2, length=2);] == [-3*0.05,-0.2]
@test [-0.2:0.05:-3*0.05;] == [range(-0.2, stop=-3*0.05, length=2);] == [-0.2,-3*0.05]
end
function range_fuzztests(::Type{T}, niter, nrange) where {T}
for i = 1:niter, n in nrange
strt, Δ = randn(T), randn(T)
Δ == 0 && continue
stop = strt + (n-1)*Δ
# `n` is not necessarily unique s.t. `strt + (n-1)*Δ == stop`
# so test that `length(strt:Δ:stop)` satisfies this identity
# and is the closest value to `(stop-strt)/Δ` to do so
lo = hi = n
while strt + (lo-1)*Δ == stop; lo -= 1; end
while strt + (hi-1)*Δ == stop; hi += 1; end
m = clamp(round(Int, (stop-strt)/Δ) + 1, lo+1, hi-1)
r = strt:Δ:stop
@test m == length(r)
@test strt == first(r)
@test Δ == step(r)
@test_skip stop == last(r)
l = range(strt, stop=stop, length=n)
@test n == length(l)
@test strt == first(l)
@test stop == last(l)
end
end
@testset "range fuzztests for $T" for T = (Float32, Float64,)
range_fuzztests(T, 2^15, 1:5)
end
@testset "Inexact errors on 32 bit architectures. #22613" begin
@test first(range(log(0.2), stop=log(10.0), length=10)) == log(0.2)
@test last(range(log(0.2), stop=log(10.0), length=10)) == log(10.0)
@test length(Base.floatrange(-3e9, 1.0, 1, 1.0)) == 1
end
@testset "ranges with very small endpoints for type $T" for T = (Float32, Float64)
z = zero(T)
u = eps(z)
@test first(range(u, stop=u, length=0)) == u
@test last(range(u, stop=u, length=0)) == u
@test first(range(-u, stop=u, length=0)) == -u
@test last(range(-u, stop=u, length=0)) == u
@test [range(-u, stop=u, length=0);] == []
@test [range(-u, stop=-u, length=1);] == [-u]
@test [range(-u, stop=u, length=2);] == [-u,u]
@test [range(-u, stop=u, length=3);] == [-u,0,u]
@test first(range(-u, stop=-u, length=0)) == -u
@test last(range(-u, stop=-u, length=0)) == -u
@test first(range(u, stop=-u, length=0)) == u
@test last(range(u, stop=-u, length=0)) == -u
@test [range(u, stop=-u, length=0);] == []
@test [range(u, stop=u, length=1);] == [u]
@test [range(u, stop=-u, length=2);] == [u,-u]
@test [range(u, stop=-u, length=3);] == [u,0,-u]
v = range(-u, stop=u, length=12)
@test length(v) == 12
@test [-3u:u:3u;] == [range(-3u, stop=3u, length=7);] == [-3:3;].*u
@test [3u:-u:-3u;] == [range(3u, stop=-3u, length=7);] == [3:-1:-3;].*u
end
@testset "range with very large endpoints for type $T" for T = (Float32, Float64)
largeint = Int(min(maxintfloat(T), typemax(Int)))
a = realmax()
for i = 1:5
@test [range(a, stop=a, length=1);] == [a]
@test [range(-a, stop=-a, length=1);] == [-a]
b = realmax()
for j = 1:5
@test [range(-a, stop=b, length=0);] == []
@test [range(-a, stop=b, length=2);] == [-a,b]
@test [range(-a, stop=b, length=3);] == [-a,(b-a)/2,b]
@test [range(a, stop=-b, length=0);] == []
@test [range(a, stop=-b, length=2);] == [a,-b]
@test [range(a, stop=-b, length=3);] == [a,(a-b)/2,-b]
for c = largeint-3:largeint
s = range(-a, stop=b, length=c)
@test first(s) == -a
@test last(s) == b
@test length(s) == c
s = range(a, stop=-b, length=c)
@test first(s) == a
@test last(s) == -b
@test length(s) == c
end
b = prevfloat(b)
end
a = prevfloat(a)
end
end
# issue #20380
let r = LinRange(1,4,4)
@test isa(r[1:4], LinRange)
end
@testset "range with 1 or 0 elements (whose step length is NaN)" begin
@test issorted(range(1, stop=1, length=0))
@test issorted(range(1, stop=1, length=1))
end
# near-equal ranges
@test 0.0:0.1:1.0 != 0.0f0:0.1f0:1.0f0
# comparing and hashing ranges
@testset "comparing and hashing ranges" begin
Rs = AbstractRange[1:1, 1:1:1, 1:2, 1:1:2,
map(Int32,1:3:17), map(Int64,1:3:17), 1:0, 1:-1:0, 17:-3:0,
0.0:0.1:1.0, map(Float32,0.0:0.1:1.0),
1.0:eps():1.0 .+ 10eps(), 9007199254740990.:1.0:9007199254740994,
range(0, stop=1, length=20), map(Float32, range(0, stop=1, length=20))]
for r in Rs
local r
ar = Vector(r)
@test r == ar
@test isequal(r,ar)
@test hash(r) == hash(ar)
for s in Rs
as = Vector(s)
@test isequal(r,s) == (hash(r)==hash(s))
@test (r==s) == (ar==as)
end
end
end
@testset "comparing UnitRanges and OneTo" begin
@test 1:2:10 == 1:2:10 != 1:3:10 != 1:3:13 != 2:3:13 == 2:3:11 != 2:11
@test 1:1:10 == 1:10 == 1:10 == Base.OneTo(10) == Base.OneTo(10)
@test 1:10 != 2:10 != 2:11 != Base.OneTo(11)
@test Base.OneTo(10) != Base.OneTo(11) != 1:10
end
# issue #2959
@test 1.0:1.5 == 1.0:1.0:1.5 == 1.0:1.0
#@test 1.0:(.3-.1)/.1 == 1.0:2.0
@testset "length with typemin/typemax" begin
let r = typemin(Int64):2:typemax(Int64), s = typemax(Int64):-2:typemin(Int64)
@test first(r) == typemin(Int64)
@test last(r) == (typemax(Int64)-1)
@test_throws OverflowError length(r)
@test first(s) == typemax(Int64)
@test last(s) == (typemin(Int64)+1)
@test_throws OverflowError length(s)
end
@test length(typemin(Int64):3:typemax(Int64)) == 6148914691236517206
@test length(typemax(Int64):-3:typemin(Int64)) == 6148914691236517206
for s in 3:100
@test length(typemin(Int):s:typemax(Int)) == length(big(typemin(Int)):big(s):big(typemax(Int)))
@test length(typemax(Int):-s:typemin(Int)) == length(big(typemax(Int)):big(-s):big(typemin(Int)))
end
@test length(UInt(1):UInt(1):UInt(0)) == 0
@test length(typemax(UInt):UInt(1):(typemax(UInt)-1)) == 0
@test length(typemax(UInt):UInt(2):(typemax(UInt)-1)) == 0
@test length((typemin(Int)+3):5:(typemin(Int)+1)) == 0
end
# issue #6364
@test length((1:64)*(pi/5)) == 64
@testset "issue #6973" begin
r1 = 1.0:0.1:2.0
r2 = 1.0f0:0.2f0:3.0f0
r3 = 1:2:21
@test r1 + r1 == 2*r1
@test r1 + r2 == 2.0:0.3:5.0
@test (r1 + r2) - r2 == r1
@test r1 + r3 == convert(StepRangeLen{Float64}, r3) + r1
@test r3 + r3 == 2 * r3
end
@testset "issue #7114" begin
let r = -0.004532318104333742:1.2597349521122731e-5:0.008065031416788989
@test length(r[1:end-1]) == length(r) - 1
@test isa(r[1:2:end],AbstractRange) && length(r[1:2:end]) == div(length(r)+1, 2)
@test r[3:5][2] ≈ r[4]
@test r[5:-2:1][2] ≈ r[3]
@test_throws BoundsError r[0:10]
@test_throws BoundsError r[1:10000]
end
let r = range(1/3, stop=5/7, length=6)
@test length(r) == 6
@test r[1] == 1/3
@test abs(r[end] - 5/7) <= eps(5/7)
end
let r = range(0.25, stop=0.25, length=1)
@test length(r) == 1
@test_throws ArgumentError range(0.25, stop=0.5, length=1)
end
end
# issue #7426
@test [typemax(Int):1:typemax(Int);] == [typemax(Int)]
#issue #7484
let r7484 = 0.1:0.1:1
@test [reverse(r7484);] == reverse([r7484;])
end
@testset "issue #7387" begin
for r in (0:1, 0.0:1.0)
local r
@test [r .+ im;] == [r;] .+ im
@test [r .- im;] == [r;] .- im
@test [r * im;] == [r;] * im
@test [r / im;] == [r;] / im
end
end
# Preservation of high precision upon addition
let r = (-0.1:0.1:0.3) + broadcast(+, -0.3:0.1:0.1, 1e-12)
@test r[3] == 1e-12
end
@testset "issue #7709" begin
@test length(map(identity, 0x01:0x05)) == 5
@test length(map(identity, 0x0001:0x0005)) == 5
@test length(map(identity, UInt64(1):UInt64(5))) == 5
@test length(map(identity, UInt128(1):UInt128(5))) == 5
end
@testset "mean/median" begin
for f in (mean, median)
for n = 2:5
@test f(2:n) == f([2:n;])
@test f(2:0.1:n) ≈ f([2:0.1:n;])
end
end
end
@testset "issue #8531" begin
smallint = (Int === Int64 ?
(Int8,UInt8,Int16,UInt16,Int32,UInt32) :
(Int8,UInt8,Int16,UInt16))
for T in smallint
@test length(typemin(T):typemax(T)) == 2^(8*sizeof(T))
end
end
# issue #8584
@test (0:1//2:2)[1:2:3] == 0:1//1:1
# issue #12278
@test length(1:UInt(0)) == 0
@testset "zip" begin
i = 0
x = 1:2:8
y = 2:2:8
xy = 1:8
for (thisx, thisy) in zip(x, y)
@test thisx == xy[i+=1]
@test thisy == xy[i+=1]
end
end
@testset "issue #9962" begin
@test eltype(0:1//3:10) <: Rational
@test (0:1//3:10)[1] == 0
@test (0:1//3:10)[2] == 1//3
end
@testset "converting ranges (issue #10965)" begin
@test promote(0:1, UInt8(2):UInt8(5)) === (0:1, 2:5)
@test convert(UnitRange{Int}, 0:5) === 0:5
@test convert(UnitRange{Int128}, 0:5) === Int128(0):Int128(5)
@test promote(0:1:1, UInt8(2):UInt8(1):UInt8(5)) === (0:1:1, 2:1:5)
@test convert(StepRange{Int,Int}, 0:1:1) === 0:1:1
@test convert(StepRange{Int128,Int128}, 0:1:1) === Int128(0):Int128(1):Int128(1)
@test promote(0:1:1, 2:5) === (0:1:1, 2:1:5)
@test convert(StepRange{Int128,Int128}, 0:5) === Int128(0):Int128(1):Int128(5)
@test convert(StepRange, 0:5) === 0:1:5
@test convert(StepRange{Int128,Int128}, 0.:5) === Int128(0):Int128(1):Int128(5)
@test_throws ArgumentError StepRange(1.1,1,5.1)
@test promote(0f0:inv(3f0):1f0, 0.:2.:5.) === (0:1/3:1, 0.:2.:5.)
@test convert(StepRangeLen{Float64}, 0:1/3:1) === 0:1/3:1
@test convert(StepRangeLen{Float64}, 0f0:inv(3f0):1f0) === 0:1/3:1
@test promote(0:1/3:1, 0:5) === (0:1/3:1, 0.:1.:5.)
@test convert(StepRangeLen{Float64}, 0:5) === 0.:1.:5.
@test convert(StepRangeLen{Float64}, 0:1:5) === 0.:1.:5.
@test convert(StepRangeLen, 0:5) == 0:5
@test convert(StepRangeLen, 0:1:5) == 0:1:5
@test convert(LinRange{Float64}, 0.0:0.1:0.3) === LinRange{Float64}(0.0, 0.3, 4)
@test convert(LinRange, 0.0:0.1:0.3) === LinRange{Float64}(0.0, 0.3, 4)
@test convert(LinRange, 0:3) === LinRange{Int}(0, 3, 4)
@test promote('a':'z', 1:2) === ('a':'z', 1:1:2)
@test eltype(['a':'z', 1:2]) == (StepRange{T,Int} where T)
end
@testset "LinRange ops" begin
@test start(LinRange(0,3,4)) == 1
@test 2*LinRange(0,3,4) == LinRange(0,6,4)
@test LinRange(0,3,4)*2 == LinRange(0,6,4)
@test LinRange(0,3,4)/3 == LinRange(0,1,4)
@test broadcast(-, 2, LinRange(0,3,4)) == LinRange(2,-1,4)
@test broadcast(+, 2, LinRange(0,3,4)) == LinRange(2,5,4)
@test -LinRange(0,3,4) == LinRange(0,-3,4)
@test reverse(LinRange(0,3,4)) == LinRange(3,0,4)
end
@testset "Issue #11245" begin
io = IOBuffer()
show(io, range(1, stop=2, length=3))
str = String(take!(io))
# @test str == "range(1.0, stop=2.0, length=3)"
@test str == "1.0:0.5:2.0"
end
@testset "issue 10950" begin
r = 1//2:3
@test length(r) == 3
i = 1
for x in r
@test x == i//2
i += 2
end
@test i == 7
end
@testset "repr" begin
# repr/show should display the range nicely
# to test print_range in range.jl
replrepr(x) = repr("text/plain", x; context=IOContext(stdout, :limit=>true, :displaysize=>(24, 80)))
@test replrepr(1:4) == "1:4"
@test repr("text/plain", 1:4) == "1:4"
@test repr("text/plain", range(1, stop=5, length=7)) == "1.0:0.6666666666666666:5.0"
@test repr("text/plain", LinRange{Float64}(1,5,7)) == "7-element LinRange{Float64}:\n 1.0,1.66667,2.33333,3.0,3.66667,4.33333,5.0"
@test repr(range(1, stop=5, length=7)) == "1.0:0.6666666666666666:5.0"
@test repr(LinRange{Float64}(1,5,7)) == "range(1.0, stop=5.0, length=7)"
@test replrepr(0:100.) == "0.0:1.0:100.0"
# next is to test a very large range, which should be fast because print_range
# only examines spacing of the left and right edges of the range, sufficient
# to cover the designated screen size.
@test replrepr(range(0, stop=100, length=10000)) == "0.0:0.010001000100010001:100.0"
@test replrepr(LinRange{Float64}(0,100, 10000)) == "10000-element LinRange{Float64}:\n 0.0,0.010001,0.020002,0.030003,0.040004,…,99.95,99.96,99.97,99.98,99.99,100.0"
@test sprint(show, UnitRange(1, 2)) == "1:2"
@test sprint(show, StepRange(1, 2, 5)) == "1:2:5"
end
@testset "Issue 11049 and related" begin
@test promote(range(0f0, stop=1f0, length=3), range(0., stop=5., length=2)) ===
(range(0., stop=1., length=3), range(0., stop=5., length=2))
@test convert(LinRange{Float64}, range(0., stop=1., length=3)) === LinRange(0., 1., 3)
@test convert(LinRange{Float64}, range(0f0, stop=1f0, length=3)) === LinRange(0., 1., 3)
@test promote(range(0., stop=1., length=3), 0:5) === (range(0., stop=1., length=3),
range(0., stop=5., length=6))
@test convert(LinRange{Float64}, 0:5) === LinRange(0., 5., 6)
@test convert(LinRange{Float64}, 0:1:5) === LinRange(0., 5., 6)
@test convert(LinRange, 0:5) === LinRange{Int}(0, 5, 6)
@test convert(LinRange, 0:1:5) === LinRange{Int}(0, 5, 6)
function test_range_index(r, s)
@test typeof(r[s]) == typeof(r)
@test [r;][s] == [r[s];]
end
test_range_index(range(0.1, stop=0.3, length=3), 1:2)
test_range_index(range(0.1, stop=0.3, length=3), 1:0)
test_range_index(range(1.0, stop=1.0, length=1), 1:1)
test_range_index(range(1.0, stop=1.0, length=1), 1:0)
test_range_index(range(1.0, stop=2.0, length=0), 1:0)
function test_range_identity(r::AbstractRange{T}, mr) where T
@test -r == mr
@test -Vector(r) == Vector(mr)
@test isa(-r, typeof(r))
@test broadcast(+, broadcast(+, 1, r), -1) == r
@test 1 .+ Vector(r) == Vector(1 .+ r) == Vector(r .+ 1)
@test isa(broadcast(+, broadcast(+, 1, r), -1), typeof(r))
@test broadcast(-, broadcast(-, 1, r), 1) == mr
@test 1 .- Vector(r) == Vector(1 .- r) == Vector(1 .+ mr)
@test Vector(r) .- 1 == Vector(r .- 1) == -Vector(mr .+ 1)
@test isa(broadcast(-, broadcast(-, 1, r), 1), typeof(r))
@test 1 * r * 1 == r
@test 2 * r * T(0.5) == r
@test isa(1 * r * 1, typeof(r))
@test r / 1 == r
@test r / 2 * 2 == r
@test r / T(0.5) * T(0.5) == r
@test isa(r / 1, typeof(r))
@test (2 * Vector(r) == Vector(r * 2) == Vector(2 * r) ==
Vector(r * T(2.0)) == Vector(T(2.0) * r) ==
Vector(r / T(0.5)) == -Vector(mr * T(2.0)))
end
test_range_identity(range(1.0, stop=27.0, length=10), range(-1.0, stop=-27.0, length=10))
test_range_identity(range(1f0, stop=27f0, length=10), range(-1f0, stop=-27f0, length=10))
test_range_identity(range(1.0, stop=27.0, length=0), range(-1.0, stop=-27.0, length=0))
test_range_identity(range(1f0, stop=27f0, length=0), range(-1f0, stop=-27f0, length=0))
test_range_identity(range(1.0, stop=1.0, length=1), range(-1.0, stop=-1.0, length=1))
test_range_identity(range(1f0, stop=1f0, length=1), range(-1f0, stop=-1f0, length=1))
@test reverse(range(1.0, stop=27.0, length=1275)) == range(27.0, stop=1.0, length=1275)
@test [reverse(range(1.0, stop=27.0, length=1275));] ==
reverse([range(1.0, stop=27.0, length=1275);])
end
@testset "PR 12200 and related" begin
for _r in (1:2:100, 1:100, 1f0:2f0:100f0, 1.0:2.0:100.0,
range(1, stop=100, length=10), range(1f0, stop=100f0, length=10))
float_r = float(_r)
big_r = big.(_r)
@test typeof(big_r).name === typeof(_r).name
if eltype(_r) <: AbstractFloat
@test isa(float_r, typeof(_r))
@test eltype(big_r) === BigFloat
else
@test isa(float_r, AbstractRange)
@test eltype(float_r) <: AbstractFloat