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random.jl
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random.jl
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# Issue #6573
srand(0); rand(); x = rand(384);
@test find(x .== rand()) == []
@test rand() != rand()
@test 0.0 <= rand() < 1.0
@test rand(UInt32) >= 0
@test -10 <= rand(-10:-5) <= -5
@test -10 <= rand(-10:5) <= 5
@test minimum([rand(Int32(1):Int32(7^7)) for i = 1:100000]) > 0
@test(typeof(rand(false:true)) == Bool)
@test length(randn(4, 5)) == 20
@test length(bitrand(4, 5)) == 20
@test rand(MersenneTwister()) == 0.8236475079774124
@test rand(MersenneTwister(0)) == 0.8236475079774124
@test rand(MersenneTwister(42)) == 0.5331830160438613
# Try a seed larger than 2^32
@test rand(MersenneTwister(5294967296)) == 0.3498809918210497
# Test array filling, Issues #7643, #8360
@test rand(MersenneTwister(0), 1) == [0.8236475079774124]
A = zeros(2, 2)
rand!(MersenneTwister(0), A)
@test A == [0.8236475079774124 0.16456579813368521;
0.9103565379264364 0.17732884646626457]
@test rand(MersenneTwister(0), Int64, 1) == [4439861565447045202]
A = zeros(Int64, 2, 2)
rand!(MersenneTwister(0), A)
@test A == [858542123778948672 5715075217119798169;
8690327730555225005 8435109092665372532]
# rand from AbstractArray
let mt = MersenneTwister()
srand(mt)
@test rand(mt, 0:3:1000) in 0:3:1000
@test issubset(rand!(mt, Array(Int, 100), 0:3:1000), 0:3:1000)
coll = Any[2, UInt128(128), big(619), "string", 'c']
@test rand(mt, coll) in coll
@test issubset(rand(mt, coll, 2, 3), coll)
# check API with default RNG:
rand(0:3:1000)
rand!(Array(Int, 100), 0:3:1000)
rand(coll)
rand(coll, 2, 3)
end
# randn
@test randn(MersenneTwister(42)) == -0.5560268761463861
A = zeros(2, 2)
randn!(MersenneTwister(42), A)
@test A == [-0.5560268761463861 0.027155338009193845;
-0.444383357109696 -0.29948409035891055]
for T in (Int8, UInt8, Int16, UInt16, Int32, UInt32, Int64, UInt64, Int128, UInt128, BigInt,
Float16, Float32, Float64, Rational{Int})
r = rand(convert(T, 97):convert(T, 122))
@test typeof(r) == T
@test 97 <= r <= 122
r = rand(convert(T, 97):convert(T,2):convert(T, 122),2)[1]
@test typeof(r) == T
@test 97 <= r <= 122
@test mod(r,2)==1
if T<:Integer && !(T===BigInt)
x = rand(typemin(T):typemax(T))
@test isa(x,T)
@test typemin(T) <= x <= typemax(T)
end
end
@test !any([(Base.Random.maxmultiple(i)+i) > 0xFF for i in 0x00:0xFF])
@test all([(Base.Random.maxmultiple(i)+1) % i for i in 0x01:0xFF] .== 0)
@test all([(Base.Random.maxmultiple(i)+1+i) > 0xFF for i in 0x00:0xFF])
@test length(0x00:0xFF)== Base.Random.maxmultiple(0x0)+1
if sizeof(Int32) < sizeof(Int)
r = rand(Int32(-1):typemax(Int32))
@test typeof(r) == Int32
@test -1 <= r <= typemax(Int32)
@test all([div(0x00010000000000000000,k)*k - 1 == Base.Random.RangeGenerator(map(UInt64,1:k)).u for k in 13 .+ Int64(2).^(32:62)])
@test all([div(0x00010000000000000000,k)*k - 1 == Base.Random.RangeGenerator(map(Int64,1:k)).u for k in 13 .+ Int64(2).^(32:61)])
@test Base.Random.maxmultiplemix(0x000100000000) === 0xffffffffffffffff
@test Base.Random.maxmultiplemix(0x0000FFFFFFFF) === 0x00000000fffffffe
@test Base.Random.maxmultiplemix(0x000000000000) === 0xffffffffffffffff
end
# BigInt specific
for T in [UInt32, UInt64, UInt128, Int128]
s = big(typemax(T)-1000) : big(typemax(T)) + 10000
@test rand(s) != rand(s)
@test big(typemax(T)-1000) <= rand(s) <= big(typemax(T)) + 10000
r = rand(s, 1, 2)
@test size(r) == (1, 2)
@test typeof(r) == Matrix{BigInt}
srand(0)
r = rand(s)
srand(0)
@test rand(s) == r
end
# Test ziggurat tables
ziggurat_table_size = 256
nmantissa = Int64(2)^51 # one bit for the sign
ziggurat_nor_r = BigFloat("3.65415288536100879635194725185604664812733315920964488827246397029393565706474")
nor_section_area = ziggurat_nor_r*exp(-ziggurat_nor_r^2/2) + erfc(ziggurat_nor_r/sqrt(BigFloat(2)))*sqrt(big(π)/2)
emantissa = Int64(2)^52
ziggurat_exp_r = BigFloat("7.69711747013104971404462804811408952334296818528283253278834867283241051210533")
exp_section_area = (ziggurat_exp_r + 1)*exp(-ziggurat_exp_r)
const ki = Array(UInt64, ziggurat_table_size)
const wi = Array(Float64, ziggurat_table_size)
const fi = Array(Float64, ziggurat_table_size)
# Tables for exponential variates
const ke = Array(UInt64, ziggurat_table_size)
const we = Array(Float64, ziggurat_table_size)
const fe = Array(Float64, ziggurat_table_size)
function randmtzig_fill_ziggurat_tables() # Operates on the global arrays
wib = big(wi)
fib = big(fi)
web = big(we)
feb = big(fe)
# Ziggurat tables for the normal distribution
x1 = ziggurat_nor_r
wib[256] = x1/nmantissa
fib[256] = exp(-0.5*x1*x1)
# Index zero is special for tail strip, where Marsaglia and Tsang
# defines this as
# k_0 = 2^31 * r * f(r) / v, w_0 = 0.5^31 * v / f(r), f_0 = 1,
# where v is the area of each strip of the ziggurat.
ki[1] = trunc(UInt64,x1*fib[256]/nor_section_area*nmantissa)
wib[1] = nor_section_area/fib[256]/nmantissa
fib[1] = one(BigFloat)
for i = 255:-1:2
# New x is given by x = f^{-1}(v/x_{i+1} + f(x_{i+1})), thus
# need inverse operator of y = exp(-0.5*x*x) -> x = sqrt(-2*ln(y))
x = sqrt(-2.0*log(nor_section_area/x1 + fib[i+1]))
ki[i+1] = trunc(UInt64,x/x1*nmantissa)
wib[i] = x/nmantissa
fib[i] = exp(-0.5*x*x)
x1 = x
end
ki[2] = UInt64(0)
# Zigurrat tables for the exponential distribution
x1 = ziggurat_exp_r
web[256] = x1/emantissa
feb[256] = exp(-x1)
# Index zero is special for tail strip, where Marsaglia and Tsang
# defines this as
# k_0 = 2^32 * r * f(r) / v, w_0 = 0.5^32 * v / f(r), f_0 = 1,
# where v is the area of each strip of the ziggurat.
ke[1] = trunc(UInt64,x1*feb[256]/exp_section_area*emantissa)
web[1] = exp_section_area/feb[256]/emantissa
feb[1] = one(BigFloat)
for i = 255:-1:2
# New x is given by x = f^{-1}(v/x_{i+1} + f(x_{i+1})), thus
# need inverse operator of y = exp(-x) -> x = -ln(y)
x = -log(exp_section_area/x1 + feb[i+1])
ke[i+1] = trunc(UInt64,x/x1*emantissa)
web[i] = x/emantissa
feb[i] = exp(-x)
x1 = x
end
ke[2] = zero(UInt64)
wi[:] = wib
fi[:] = fib
we[:] = web
fe[:] = feb
return nothing
end
randmtzig_fill_ziggurat_tables()
@test all(ki == Base.Random.ki)
@test all(wi == Base.Random.wi)
@test all(fi == Base.Random.fi)
@test all(ke == Base.Random.ke)
@test all(we == Base.Random.we)
@test all(fe == Base.Random.fe)
#same random numbers on for small ranges on all systems
seed = rand(UInt) #leave state nondeterministic as above
srand(seed)
r = map(Int64,rand(map(Int32,97:122)))
srand(seed)
@test r == rand(map(Int64,97:122))
srand(seed)
r = map(UInt64,rand(map(UInt32,97:122)))
srand(seed)
@test r == rand(map(UInt64,97:122))
@test all([div(0x000100000000,k)*k - 1 == Base.Random.RangeGenerator(map(UInt64,1:k)).u for k in 13 .+ Int64(2).^(1:30)])
@test all([div(0x000100000000,k)*k - 1 == Base.Random.RangeGenerator(map(Int64,1:k)).u for k in 13 .+ Int64(2).^(1:30)])
import Base.Random: uuid4, UUID
# UUID
a = uuid4()
@test a == UUID(string(a)) == UUID(utf16(string(a))) == UUID(utf32(string(a)))
@test_throws ArgumentError UUID("550e8400e29b-41d4-a716-446655440000")
@test_throws ArgumentError UUID("550e8400e29b-41d4-a716-44665544000098")
@test_throws ArgumentError UUID("z50e8400-e29b-41d4-a716-446655440000")
#issue 8257
i8257 = 1:1/3:100
for i = 1:100
@test rand(i8257) in i8257
end
# test code paths of rand!
let mt = MersenneTwister(0)
A128 = Array(UInt128, 0)
@test length(rand!(mt, A128)) == 0
for (i,n) in enumerate([1, 3, 5, 6, 10, 11, 30])
resize!(A128, n)
rand!(mt, A128)
@test length(A128) == n
@test A128[end] == UInt128[0x15de6b23025813ad129841f537a04e40,
0xcfa4db38a2c65bc4f18c07dc91125edf,
0x33bec08136f19b54290982449b3900d5,
0xde41af3463e74cb830dad4add353ca20,
0x066d8695ebf85f833427c93416193e1f,
0x48fab49cc9fcee1c920d6dae629af446,
0x4b54632b4619f4eca22675166784d229][i]
end
srand(mt,0)
for (i,T) in enumerate([Int8, UInt8, Int16, UInt16, Int32, UInt32, Int64, UInt64, Int128, Float16, Float32])
A = Array(T, 16)
B = Array(T, 31)
rand!(mt, A)
rand!(mt, B)
@test A[end] == Any[21,0x7b,17385,0x3086,-1574090021,0xadcb4460,6797283068698303107,0x4e91c9c4d4f5f759,
-3482609696641744459568613291754091152,Float16(0.03125),0.68733835f0][i]
@test B[end] == Any[49,0x65,-3725,0x719d,814246081,0xdf61843a,-3010919637398300844,0x61b367cf8810985d,
-33032345278809823492812856023466859769,Float16(0.95),0.51829386f0][i]
end
srand(mt,0)
AF64 = Array(Float64, Base.Random.dsfmt_get_min_array_size()-1)
@test rand!(mt, AF64)[end] == 0.957735065345398
@test rand!(mt, AF64)[end] == 0.6492481059865669
resize!(AF64, 2*length(mt.vals))
@test Base.Random.rand_AbstractArray_Float64!(mt, AF64)[end] == 0.432757268470779
end
# Issue #9037
let mt = MersenneTwister()
a = Array(Float64, 0)
resize!(a, 1000) # could be 8-byte aligned
b = Array(Float64, 1000) # should be 16-byte aligned
c8 = Array(UInt8, 8001)
c = pointer_to_array(Ptr{Float64}(pointer(c8, 2)), 1000) # Int(pointer(c)) % 16 == 1
for A in (a, b, c)
srand(mt, 0)
rand(mt) # this is to fill mt.vals, cf. #9040
rand!(mt, A) # must not segfault even if Int(pointer(A)) % 16 != 0
@test A[end-4:end] == [0.49508297796349776,0.3408340446375888,0.3211229457075784,0.9103565379264364,0.16456579813368521]
end
end
# test all rand APIs
for rng in ([], [MersenneTwister()], [RandomDevice()])
for f in [rand, randn, randexp]
f(rng...) ::Float64
f(rng..., 5) ::Vector{Float64}
f(rng..., 2, 3) ::Array{Float64, 2}
end
for f! in [randn!, randexp!]
f!(rng..., Array(Float64, 5)) ::Vector{Float64}
f!(rng..., Array(Float64, 2, 3)) ::Array{Float64, 2}
end
bitrand(rng..., 5) ::BitArray{1}
bitrand(rng..., 2, 3) ::BitArray{2}
rand!(rng..., BitArray(5)) ::BitArray{1}
rand!(rng..., BitArray(2, 3)) ::BitArray{2}
for T in [Base.IntTypes..., Bool, Float16, Float32, Float64]
a0 = rand(rng..., T) ::T
a1 = rand(rng..., T, 5) ::Vector{T}
a2 = rand(rng..., T, 2, 3) ::Array{T, 2}
if T <: FloatingPoint
for a in [a0, a1..., a2...]
@test 0.0 <= a < 1.0
end
end
for A in (Array(T, 5), Array(T, 2, 3))
rand!(rng..., A) ::typeof(A)
rand!(rng..., A, T[0,1,2]) ::typeof(A)
rand!(rng..., sparse(A)) ::typeof(sparse(A))
rand!(rng..., sparse(A), T[0,1,2]) ::typeof(sparse(A))
end
end
end
# test uniform distribution of floats
let bins = [prevfloat(0.0):0.25:1.0;]
for rng in [srand(MersenneTwister()), RandomDevice()]
for T in [Float16,Float32,Float64]
# array version
_, counts = hist(rand(rng, T, 2000), bins)
@test minimum(counts) > 300 # should fail with proba < 1e-26
# scalar version
_, counts = hist([rand(rng, T) for i in 1:2000], bins)
@test minimum(counts) > 300
end
end
end
# test reproducility of methods
let mta = MersenneTwister(42), mtb = MersenneTwister(42)
@test rand(mta) == rand(mtb)
@test rand(mta,10) == rand(mtb,10)
@test randn(mta) == randn(mtb)
@test randn(mta,10) == randn(mtb,10)
@test randexp(mta) == randexp(mtb)
@test randexp(mta,10) == randexp(mtb,10)
@test rand(mta,1:100) == rand(mtb,1:100)
@test rand(mta,1:10,10) == rand(mtb,1:10,10)
@test rand(mta,Bool) == rand(mtb,Bool)
@test bitrand(mta,10) == bitrand(mtb,10)
@test randstring(mta) == randstring(mtb)
@test randstring(mta,10) == randstring(mtb,10)
@test randsubseq(mta,1:10,0.4) == randsubseq(mtb,1:10,0.4)
@test randsubseq!(mta,Int[],1:10,0.4) == randsubseq!(mtb,Int[],1:10,0.4)
@test shuffle(mta,collect(1:10)) == shuffle(mtb,collect(1:10))
@test shuffle!(mta,collect(1:10)) == shuffle!(mtb,collect(1:10))
@test randperm(mta,10) == randperm(mtb,10)
@test randcycle(mta,10) == randcycle(mtb,10)
@test sprand(mta,1,1,0.9) == sprand(mtb,1,1,0.9)
@test sprand(mta,10,10,0.3) == sprand(mtb,10,10,0.3)
end