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

module Random

using Base.dSFMT
using Base.GMP: GMP_VERSION, Limb
import Base: copymutable, copy, copy!, ==

export srand,
       rand, rand!,
       randn, randn!,
       randexp, randexp!,
       bitrand,
       randstring,
       randsubseq,randsubseq!,
       shuffle,shuffle!,
       randperm, randcycle,
       AbstractRNG, MersenneTwister, RandomDevice,
       GLOBAL_RNG, randjump

abstract type AbstractRNG end

abstract type FloatInterval end
mutable struct CloseOpen <: FloatInterval end
mutable struct Close1Open2 <: FloatInterval end

## RandomDevice

if is_windows()

    struct RandomDevice <: AbstractRNG
        buffer::Vector{UInt128}

        RandomDevice() = new(Vector{UInt128}(1))
    end

    function rand{T<:Union{Bool, Base.BitInteger}}(rd::RandomDevice, ::Type{T})
        win32_SystemFunction036!(rd.buffer)
        @inbounds return rd.buffer[1] % T
    end

    rand!(rd::RandomDevice, A::Array{<:Union{Bool, Base.BitInteger}}) = (win32_SystemFunction036!(A); A)
else # !windows
    struct RandomDevice <: AbstractRNG
        file::IOStream
        unlimited::Bool

        RandomDevice(unlimited::Bool=true) = new(open(unlimited ? "/dev/urandom" : "/dev/random"), unlimited)
    end

    rand{T<:Union{Bool, Base.BitInteger}}(rd::RandomDevice, ::Type{T}) = read( rd.file, T)
    rand!(rd::RandomDevice, A::Array{<:Union{Bool, Base.BitInteger}})  = read!(rd.file, A)
end # os-test

"""
    RandomDevice()

Create a `RandomDevice` RNG object. Two such objects will always generate different streams of random numbers.
"""
RandomDevice

rand(rng::RandomDevice, ::Type{Close1Open2}) =
    reinterpret(Float64, 0x3ff0000000000000 | rand(rng, UInt64) & 0x000fffffffffffff)

rand(rng::RandomDevice, ::Type{CloseOpen}) = rand(rng, Close1Open2) - 1.0

## MersenneTwister

const MTCacheLength = dsfmt_get_min_array_size()

mutable struct MersenneTwister <: AbstractRNG
    seed::Vector{UInt32}
    state::DSFMT_state
    vals::Vector{Float64}
    idx::Int

    function MersenneTwister(seed, state, vals, idx)
        length(vals) == MTCacheLength &&  0 <= idx <= MTCacheLength || throw(DomainError())
        new(seed, state, vals, idx)
    end
end

MersenneTwister(seed::Vector{UInt32}, state::DSFMT_state) =
    MersenneTwister(seed, state, zeros(Float64, MTCacheLength), MTCacheLength)

"""
    MersenneTwister(seed)

Create a `MersenneTwister` RNG object. Different RNG objects can have their own seeds, which
may be useful for generating different streams of random numbers.
"""
MersenneTwister(seed) = srand(MersenneTwister(Vector{UInt32}(), DSFMT_state()), seed)

function copy!(dst::MersenneTwister, src::MersenneTwister)
    copy!(resize!(dst.seed, length(src.seed)), src.seed)
    copy!(dst.state, src.state)
    copy!(dst.vals, src.vals)
    dst.idx = src.idx
    dst
end

copy(src::MersenneTwister) =
    MersenneTwister(copy(src.seed), copy(src.state), copy(src.vals), src.idx)

==(r1::MersenneTwister, r2::MersenneTwister) =
    r1.seed == r2.seed && r1.state == r2.state && isequal(r1.vals, r2.vals) && r1.idx == r2.idx

## Low level API for MersenneTwister

@inline mt_avail(r::MersenneTwister) = MTCacheLength - r.idx
@inline mt_empty(r::MersenneTwister) = r.idx == MTCacheLength
@inline mt_setfull!(r::MersenneTwister) = r.idx = 0
@inline mt_setempty!(r::MersenneTwister) = r.idx = MTCacheLength
@inline mt_pop!(r::MersenneTwister) = @inbounds return r.vals[r.idx+=1]

function gen_rand(r::MersenneTwister)
    dsfmt_fill_array_close1_open2!(r.state, pointer(r.vals), length(r.vals))
    mt_setfull!(r)
end

@inline reserve_1(r::MersenneTwister) = mt_empty(r) && gen_rand(r)
# `reserve` allows one to call `rand_inbounds` n times
# precondition: n <= MTCacheLength
@inline reserve(r::MersenneTwister, n::Int) = mt_avail(r) < n && gen_rand(r)

# precondition: !mt_empty(r)
@inline rand_inbounds(r::MersenneTwister, ::Type{Close1Open2}) = mt_pop!(r)
@inline rand_inbounds(r::MersenneTwister, ::Type{CloseOpen}) = rand_inbounds(r, Close1Open2) - 1.0
@inline rand_inbounds(r::MersenneTwister) = rand_inbounds(r, CloseOpen)

# produce Float64 values
@inline rand{I<:FloatInterval}(r::MersenneTwister, ::Type{I}) = (reserve_1(r); rand_inbounds(r, I))

@inline rand_ui52_raw_inbounds(r::MersenneTwister) = reinterpret(UInt64, rand_inbounds(r, Close1Open2))
@inline rand_ui52_raw(r::MersenneTwister) = (reserve_1(r); rand_ui52_raw_inbounds(r))
@inline rand_ui2x52_raw(r::MersenneTwister) = rand_ui52_raw(r) % UInt128 << 64 | rand_ui52_raw(r)

function srand(r::MersenneTwister, seed::Vector{UInt32})
    copy!(resize!(r.seed, length(seed)), seed)
    dsfmt_init_by_array(r.state, r.seed)
    mt_setempty!(r)
    return r
end

# MersenneTwister jump

"""
    randjump(r::MersenneTwister, jumps::Integer, [jumppoly::AbstractString=dSFMT.JPOLY1e21]) -> Vector{MersenneTwister}

Create an array of the size `jumps` of initialized `MersenneTwister` RNG objects. The
first RNG object given as a parameter and following `MersenneTwister` RNGs in the array are
initialized such that a state of the RNG object in the array would be moved forward (without
generating numbers) from a previous RNG object array element on a particular number of steps
encoded by the jump polynomial `jumppoly`.

Default jump polynomial moves forward `MersenneTwister` RNG state by `10^20` steps.
"""
function randjump(mt::MersenneTwister, jumps::Integer, jumppoly::AbstractString)
    mts = MersenneTwister[]
    push!(mts, mt)
    for i in 1:jumps-1
        cmt = mts[end]
        push!(mts, MersenneTwister(cmt.seed, dSFMT.dsfmt_jump(cmt.state, jumppoly)))
    end
    return mts
end
randjump(r::MersenneTwister, jumps::Integer) = randjump(r, jumps, dSFMT.JPOLY1e21)

## initialization

function __init__()
    try
        srand()
    catch ex
        Base.showerror_nostdio(ex,
            "WARNING: Error during initialization of module Random")
    end
end

## make_seed()
# make_seed methods produce values of type Array{UInt32}, suitable for MersenneTwister seeding

function make_seed()
    try
        return rand(RandomDevice(), UInt32, 4)
    catch
        println(STDERR, "Entropy pool not available to seed RNG; using ad-hoc entropy sources.")
        seed = reinterpret(UInt64, time())
        seed = hash(seed, UInt64(getpid()))
        try
        seed = hash(seed, parse(UInt64, readstring(pipeline(`ifconfig`, `sha1sum`))[1:40], 16))
        end
        return make_seed(seed)
    end
end

function make_seed(n::Integer)
    n < 0 && throw(DomainError())
    seed = UInt32[]
    while true
        push!(seed, n & 0xffffffff)
        n >>= 32
        if n == 0
            return seed
        end
    end
end

function make_seed(filename::AbstractString, n::Integer)
    read!(filename, Vector{UInt32}(Int(n)))
end

## srand()

"""
    srand([rng=GLOBAL_RNG], [seed]) -> rng
    srand([rng=GLOBAL_RNG], filename, n=4) -> rng

Reseed the random number generator. If a `seed` is provided, the RNG will give a
reproducible sequence of numbers, otherwise Julia will get entropy from the system. For
`MersenneTwister`, the `seed` may be a non-negative integer, a vector of `UInt32` integers
or a filename, in which case the seed is read from a file (`4n` bytes are read from the file,
where `n` is an optional argument). `RandomDevice` does not support seeding.
"""
srand(r::MersenneTwister) = srand(r, make_seed())
srand(r::MersenneTwister, n::Integer) = srand(r, make_seed(n))
srand(r::MersenneTwister, filename::AbstractString, n::Integer=4) = srand(r, make_seed(filename, n))

function dsfmt_gv_srand()
    # Temporary fix for #8874 and #9124: update global RNG for Rmath
    dsfmt_gv_init_by_array(GLOBAL_RNG.seed+UInt32(1))
    return GLOBAL_RNG
end

function srand()
    srand(GLOBAL_RNG)
    dsfmt_gv_srand()
end

function srand(seed::Union{Integer, Vector{UInt32}})
    srand(GLOBAL_RNG, seed)
    dsfmt_gv_srand()
end

function srand(filename::AbstractString, n::Integer=4)
    srand(GLOBAL_RNG, filename, n)
    dsfmt_gv_srand()
end

## Global RNG

const GLOBAL_RNG = MersenneTwister(0)
globalRNG() = GLOBAL_RNG

# rand: a non-specified RNG defaults to GLOBAL_RNG

"""
    rand([rng=GLOBAL_RNG], [S], [dims...])

Pick a random element or array of random elements from the set of values specified by `S`; `S` can be

* an indexable collection (for example `1:n` or `['x','y','z']`), or
* a type: the set of values to pick from is then equivalent to `typemin(S):typemax(S)` for
  integers (this is not applicable to `BigInt`), and to ``[0, 1)`` for floating point numbers;

`S` defaults to `Float64`.
"""
@inline rand() = rand(GLOBAL_RNG, CloseOpen)
@inline rand(T::Type) = rand(GLOBAL_RNG, T)
rand(dims::Dims) = rand(GLOBAL_RNG, dims)
rand(dims::Integer...) = rand(convert(Tuple{Vararg{Int}}, dims))
rand(T::Type, dims::Dims) = rand(GLOBAL_RNG, T, dims)
rand(T::Type, d1::Integer, dims::Integer...) = rand(T, tuple(Int(d1), convert(Tuple{Vararg{Int}}, dims)...))
rand!(A::AbstractArray) = rand!(GLOBAL_RNG, A)

rand(r::AbstractArray) = rand(GLOBAL_RNG, r)

"""
    rand!([rng=GLOBAL_RNG], A, [coll])

Populate the array `A` with random values. If the indexable collection `coll` is specified,
the values are picked randomly from `coll`. This is equivalent to `copy!(A, rand(rng, coll, size(A)))`
or `copy!(A, rand(rng, eltype(A), size(A)))` but without allocating a new array.
"""
rand!(A::AbstractArray, r::AbstractArray) = rand!(GLOBAL_RNG, A, r)

rand(r::AbstractArray, dims::Dims) = rand(GLOBAL_RNG, r, dims)
rand(r::AbstractArray, dims::Integer...) = rand(GLOBAL_RNG, r, convert(Tuple{Vararg{Int}}, dims))

## random floating point values

@inline rand(r::AbstractRNG) = rand(r, CloseOpen)

# MersenneTwister & RandomDevice
@inline rand(r::Union{RandomDevice,MersenneTwister}, ::Type{Float64}) = rand(r, CloseOpen)

rand_ui10_raw(r::MersenneTwister) = rand_ui52_raw(r)
rand_ui23_raw(r::MersenneTwister) = rand_ui52_raw(r)
rand_ui10_raw(r::AbstractRNG)    = rand(r, UInt16)
rand_ui23_raw(r::AbstractRNG)    = rand(r, UInt32)

rand(r::Union{RandomDevice,MersenneTwister}, ::Type{Float16}) =
    Float16(reinterpret(Float32, (rand_ui10_raw(r) % UInt32 << 13) & 0x007fe000 | 0x3f800000) - 1)

rand(r::Union{RandomDevice,MersenneTwister}, ::Type{Float32}) =
    reinterpret(Float32, rand_ui23_raw(r) % UInt32 & 0x007fffff | 0x3f800000) - 1

## random integers

@inline rand_ui52_raw(r::AbstractRNG) = reinterpret(UInt64, rand(r, Close1Open2))
@inline rand_ui52(r::AbstractRNG) = rand_ui52_raw(r) & 0x000fffffffffffff

# MersenneTwister

@inline rand{T<:Union{Bool, Int8, UInt8, Int16, UInt16, Int32, UInt32}}(r::MersenneTwister, ::Type{T}) = rand_ui52_raw(r) % T

function rand(r::MersenneTwister, ::Type{UInt64})
    reserve(r, 2)
    rand_ui52_raw_inbounds(r) << 32 ⊻ rand_ui52_raw_inbounds(r)
end

function rand(r::MersenneTwister, ::Type{UInt128})
    reserve(r, 3)
    xor(rand_ui52_raw_inbounds(r) % UInt128 << 96,
        rand_ui52_raw_inbounds(r) % UInt128 << 48,
        rand_ui52_raw_inbounds(r))
end

rand(r::MersenneTwister, ::Type{Int64})   = reinterpret(Int64,  rand(r, UInt64))
rand(r::MersenneTwister, ::Type{Int128})  = reinterpret(Int128, rand(r, UInt128))

## random Complex values

rand{T<:Real}(r::AbstractRNG, ::Type{Complex{T}}) = complex(rand(r, T), rand(r, T))

# random Char values
# returns a random valid Unicode scalar value (i.e. 0 - 0xd7ff, 0xe000 - # 0x10ffff)
function rand(r::AbstractRNG, ::Type{Char})
    c = rand(r, 0x00000000:0x0010f7ff)
    (c < 0xd800) ? Char(c) : Char(c+0x800)
end

# random values from Dict or Set (for efficiency)
function rand(r::AbstractRNG, t::Dict)
    isempty(t) && throw(ArgumentError("dict must be non-empty"))
    n = length(t.slots)
    while true
        i = rand(r, 1:n)
        Base.isslotfilled(t, i) && return (t.keys[i] => t.vals[i])
    end
end
rand(t::Dict) = rand(GLOBAL_RNG, t)
rand(r::AbstractRNG, s::Set) = rand(r, s.dict).first
rand(s::Set) = rand(GLOBAL_RNG, s)

## Arrays of random numbers

rand(r::AbstractRNG, dims::Dims) = rand(r, Float64, dims)
rand(r::AbstractRNG, dims::Integer...) = rand(r, convert(Tuple{Vararg{Int}}, dims))

rand(r::AbstractRNG, T::Type, dims::Dims) = rand!(r, Array{T}(dims))
rand(r::AbstractRNG, T::Type, d1::Integer, dims::Integer...) = rand(r, T, tuple(Int(d1), convert(Tuple{Vararg{Int}}, dims)...))
# note: the above method would trigger an ambiguity warning if d1 was not separated out:
# rand(r, ()) would match both this method and rand(r, dims::Dims)
# moreover, a call like rand(r, NotImplementedType()) would be an infinite loop

function rand!{T}(r::AbstractRNG, A::AbstractArray{T})
    for i in eachindex(A)
        @inbounds A[i] = rand(r, T)
    end
    A
end

# MersenneTwister

function rand_AbstractArray_Float64!{I<:FloatInterval}(r::MersenneTwister, A::AbstractArray{Float64}, n=length(A), ::Type{I}=CloseOpen)
    # what follows is equivalent to this simple loop but more efficient:
    # for i=1:n
    #     @inbounds A[i] = rand(r, I)
    # end
    m = 0
    while m < n
        s = mt_avail(r)
        if s == 0
            gen_rand(r)
            s = mt_avail(r)
        end
        m2 = min(n, m+s)
        for i=m+1:m2
            @inbounds A[i] = rand_inbounds(r, I)
        end
        m = m2
    end
    A
end

rand!(r::MersenneTwister, A::AbstractArray{Float64}) = rand_AbstractArray_Float64!(r, A)

fill_array!(s::DSFMT_state, A::Ptr{Float64}, n::Int, ::Type{CloseOpen}) = dsfmt_fill_array_close_open!(s, A, n)
fill_array!(s::DSFMT_state, A::Ptr{Float64}, n::Int, ::Type{Close1Open2}) = dsfmt_fill_array_close1_open2!(s, A, n)

function rand!{I<:FloatInterval}(r::MersenneTwister, A::Array{Float64}, n::Int=length(A), ::Type{I}=CloseOpen)
    # depending on the alignment of A, the data written by fill_array! may have
    # to be left-shifted by up to 15 bytes (cf. unsafe_copy! below) for
    # reproducibility purposes;
    # so, even for well aligned arrays, fill_array! is used to generate only
    # the n-2 first values (or n-3 if n is odd), and the remaining values are
    # generated by the scalar version of rand
    if n > length(A)
        throw(BoundsError(A,n))
    end
    n2 = (n-2) ÷ 2 * 2
    if n2 < dsfmt_get_min_array_size()
        rand_AbstractArray_Float64!(r, A, n, I)
    else
        pA = pointer(A)
        align = Csize_t(pA) % 16
        if align > 0
            pA2 = pA + 16 - align
            fill_array!(r.state, pA2, n2, I) # generate the data in-place, but shifted
            unsafe_copy!(pA, pA2, n2) # move the data to the beginning of the array
        else
            fill_array!(r.state, pA, n2, I)
        end
        for i=n2+1:n
            @inbounds A[i] = rand(r, I)
        end
    end
    A
end

@inline mask128(u::UInt128, ::Type{Float16}) = (u & 0x03ff03ff03ff03ff03ff03ff03ff03ff) | 0x3c003c003c003c003c003c003c003c00
@inline mask128(u::UInt128, ::Type{Float32}) = (u & 0x007fffff007fffff007fffff007fffff) | 0x3f8000003f8000003f8000003f800000

function rand!{T<:Union{Float16, Float32}}(r::MersenneTwister, A::Array{T}, ::Type{Close1Open2})
    n = length(A)
    n128 = n * sizeof(T) ÷ 16
    rand!(r, unsafe_wrap(Array, convert(Ptr{Float64}, pointer(A)), 2*n128), 2*n128, Close1Open2)
    A128 = unsafe_wrap(Array, convert(Ptr{UInt128}, pointer(A)), n128)
    @inbounds for i in 1:n128
        u = A128[i]
        u ⊻= u << 26
        # at this point, the 64 low bits of u, "k" being the k-th bit of A128[i] and "+" the bit xor, are:
        # [..., 58+32,..., 53+27, 52+26, ..., 33+7, 32+6, ..., 27+1, 26, ..., 1]
        # the bits needing to be random are
        # [1:10, 17:26, 33:42, 49:58] (for Float16)
        # [1:23, 33:55] (for Float32)
        # this is obviously satisfied on the 32 low bits side, and on the high side, the entropy comes
        # from bits 33:52 of A128[i] and then from bits 27:32 (which are discarded on the low side)
        # this is similar for the 64 high bits of u
        A128[i] = mask128(u, T)
    end
    for i in 16*n128÷sizeof(T)+1:n
        @inbounds A[i] = rand(r, T) + oneunit(T)
    end
    A
end

function rand!{T<:Union{Float16, Float32}}(r::MersenneTwister, A::Array{T}, ::Type{CloseOpen})
    rand!(r, A, Close1Open2)
    I32 = one(Float32)
    for i in eachindex(A)
        @inbounds A[i] = T(Float32(A[i])-I32) # faster than "A[i] -= one(T)" for T==Float16
    end
    A
end

rand!(r::MersenneTwister, A::Array{<:Union{Float16, Float32}}) = rand!(r, A, CloseOpen)

function rand!(r::MersenneTwister, A::Array{UInt128}, n::Int=length(A))
    if n > length(A)
        throw(BoundsError(A,n))
    end
    Af = unsafe_wrap(Array, convert(Ptr{Float64}, pointer(A)), 2n)
    i = n
    while true
        rand!(r, Af, 2i, Close1Open2)
        n < 5 && break
        i = 0
        @inbounds while n-i >= 5
            u = A[i+=1]
            A[n]    ⊻= u << 48
            A[n-=1] ⊻= u << 36
            A[n-=1] ⊻= u << 24
            A[n-=1] ⊻= u << 12
            n-=1
        end
    end
    if n > 0
        u = rand_ui2x52_raw(r)
        for i = 1:n
            @inbounds A[i] ⊻= u << 12*i
        end
    end
    A
end

function rand!{T<:Union{Int8, UInt8, Int16, UInt16, Int32, UInt32, Int64, UInt64, Int128}}(r::MersenneTwister, A::Array{T})
    n=length(A)
    n128 = n * sizeof(T) ÷ 16
    rand!(r, unsafe_wrap(Array, convert(Ptr{UInt128}, pointer(A)), n128))
    for i = 16*n128÷sizeof(T)+1:n
        @inbounds A[i] = rand(r, T)
    end
    A
end

## Generate random integer within a range

# remainder function according to Knuth, where rem_knuth(a, 0) = a
rem_knuth(a::UInt, b::UInt) = a % (b + (b == 0)) + a * (b == 0)
rem_knuth(a::T, b::T) where {T<:Unsigned} = b != 0 ? a % b : a

# maximum multiple of k <= 2^bits(T) decremented by one,
# that is 0xFFFF...FFFF if k = typemax(T) - typemin(T) with intentional underflow
# see http://stackoverflow.com/questions/29182036/integer-arithmetic-add-1-to-uint-max-and-divide-by-n-without-overflow
maxmultiple(k::T) where {T<:Unsigned} = (div(typemax(T) - k + oneunit(k), k + (k == 0))*k + k - oneunit(k))::T

# maximum multiple of k within 1:2^32 or 1:2^64 decremented by one, depending on size
maxmultiplemix(k::UInt64) = if k >> 32 != 0; maxmultiple(k); else (div(0x0000000100000000, k + (k == 0))*k - oneunit(k))::UInt64; end

abstract type RangeGenerator end

struct RangeGeneratorInt{T<:Integer,U<:Unsigned} <: RangeGenerator
    a::T   # first element of the range
    k::U   # range length or zero for full range
    u::U   # rejection threshold
end
# generators with 32, 128 bits entropy
RangeGeneratorInt(a::T, k::U) where {T,U<:Union{UInt32,UInt128}} = RangeGeneratorInt{T,U}(a, k, maxmultiple(k))
# mixed 32/64 bits entropy generator
RangeGeneratorInt(a::T, k::UInt64) where {T} = RangeGeneratorInt{T,UInt64}(a, k, maxmultiplemix(k))
# generator for ranges
function RangeGenerator(r::UnitRange{T}) where T<:Unsigned
    if isempty(r)
        throw(ArgumentError("range must be non-empty"))
    end
    RangeGeneratorInt(first(r), last(r) - first(r) + oneunit(T))
end

# specialized versions
for (T, U) in [(UInt8, UInt32), (UInt16, UInt32),
               (Int8, UInt32), (Int16, UInt32), (Int32, UInt32), (Int64, UInt64), (Int128, UInt128),
               (Bool, UInt32)]

    @eval RangeGenerator(r::UnitRange{$T}) = begin
        if isempty(r)
            throw(ArgumentError("range must be non-empty"))
        end
        RangeGeneratorInt(first(r), convert($U, unsigned(last(r) - first(r)) + one($U))) # overflow ok
    end
end

if GMP_VERSION.major >= 6
    struct RangeGeneratorBigInt <: RangeGenerator
        a::BigInt             # first
        m::BigInt             # range length - 1
        nlimbs::Int           # number of limbs in generated BigInt's
        mask::Limb            # applied to the highest limb
    end

else
    struct RangeGeneratorBigInt <: RangeGenerator
        a::BigInt             # first
        m::BigInt             # range length - 1
        limbs::Vector{Limb}   # buffer to be copied into generated BigInt's
        mask::Limb            # applied to the highest limb

        RangeGeneratorBigInt(a, m, nlimbs, mask) = new(a, m, Vector{Limb}(nlimbs), mask)
    end
end

function RangeGenerator(r::UnitRange{BigInt})
    m = last(r) - first(r)
    m < 0 && throw(ArgumentError("range must be non-empty"))
    nd = ndigits(m, 2)
    nlimbs, highbits = divrem(nd, 8*sizeof(Limb))
    highbits > 0 && (nlimbs += 1)
    mask = highbits == 0 ? ~zero(Limb) : one(Limb)<<highbits - one(Limb)
    return RangeGeneratorBigInt(first(r), m, nlimbs, mask)
end

# this function uses 32 bit entropy for small ranges of length <= typemax(UInt32) + 1
# RangeGeneratorInt is responsible for providing the right value of k
function rand{T<:Union{UInt64, Int64}}(rng::AbstractRNG, g::RangeGeneratorInt{T,UInt64})
    local x::UInt64
    if (g.k - 1) >> 32 == 0
        x = rand(rng, UInt32)
        while x > g.u
            x = rand(rng, UInt32)
        end
    else
        x = rand(rng, UInt64)
        while x > g.u
            x = rand(rng, UInt64)
        end
    end
    return reinterpret(T, reinterpret(UInt64, g.a) + rem_knuth(x, g.k))
end

function rand{T<:Integer, U<:Unsigned}(rng::AbstractRNG, g::RangeGeneratorInt{T,U})
    x = rand(rng, U)
    while x > g.u
        x = rand(rng, U)
    end
    (unsigned(g.a) + rem_knuth(x, g.k)) % T
end

if GMP_VERSION.major >= 6
    # mpz_limbs_write and mpz_limbs_finish are available only in GMP version 6
    function rand(rng::AbstractRNG, g::RangeGeneratorBigInt)
        x = BigInt()
        while true
            # note: on CRAY computers, the second argument may be of type Cint (48 bits) and not Clong
            xd = ccall((:__gmpz_limbs_write, :libgmp), Ptr{Limb}, (Ptr{BigInt}, Clong), &x, g.nlimbs)
            limbs = unsafe_wrap(Array, xd, g.nlimbs)
            rand!(rng, limbs)
            limbs[end] &= g.mask
            ccall((:__gmpz_limbs_finish, :libgmp), Void, (Ptr{BigInt}, Clong), &x, g.nlimbs)
            x <= g.m && break
        end
        ccall((:__gmpz_add, :libgmp), Void, (Ptr{BigInt}, Ptr{BigInt}, Ptr{BigInt}), &x, &x, &g.a)
        return x
    end
else
    function rand(rng::AbstractRNG, g::RangeGeneratorBigInt)
        x = BigInt()
        while true
            rand!(rng, g.limbs)
            g.limbs[end] &= g.mask
            ccall((:__gmpz_import, :libgmp), Void,
                  (Ptr{BigInt}, Csize_t, Cint, Csize_t, Cint, Csize_t, Ptr{Limb}),
                  &x, length(g.limbs), -1, sizeof(Limb), 0, 0, g.limbs)
            x <= g.m && break
        end
        ccall((:__gmpz_add, :libgmp), Void, (Ptr{BigInt}, Ptr{BigInt}, Ptr{BigInt}), &x, &x, &g.a)
        return x
    end
end

rand(rng::AbstractRNG, r::UnitRange{<:Union{Signed,Unsigned,BigInt,Bool}}) = rand(rng, RangeGenerator(r))

# Randomly draw a sample from an AbstractArray r
# (e.g. r is a range 0:2:8 or a vector [2, 3, 5, 7])
rand(rng::AbstractRNG, r::AbstractArray) = @inbounds return r[rand(rng, 1:length(r))]

function rand!(rng::AbstractRNG, A::AbstractArray, g::RangeGenerator)
    for i in eachindex(A)
        @inbounds A[i] = rand(rng, g)
    end
    return A
end

rand!(rng::AbstractRNG, A::AbstractArray, r::UnitRange{<:Union{Signed,Unsigned,BigInt,Bool,Char}}) = rand!(rng, A, RangeGenerator(r))

function rand!(rng::AbstractRNG, A::AbstractArray, r::AbstractArray)
    g = RangeGenerator(1:(length(r)))
    for i in eachindex(A)
        @inbounds A[i] = r[rand(rng, g)]
    end
    return A
end

rand{T}(rng::AbstractRNG, r::AbstractArray{T}, dims::Dims) = rand!(rng, Array{T}(dims), r)
rand(rng::AbstractRNG, r::AbstractArray, dims::Int...) = rand(rng, r, dims)

## random BitArrays (AbstractRNG)

function rand!(rng::AbstractRNG, B::BitArray)
    isempty(B) && return B
    Bc = B.chunks
    rand!(rng, Bc)
    Bc[end] &= Base._msk_end(B)
    return B
end

"""
    bitrand([rng=GLOBAL_RNG], [dims...])

Generate a `BitArray` of random boolean values.
"""
bitrand(r::AbstractRNG, dims::Dims)   = rand!(r, BitArray(dims))
bitrand(r::AbstractRNG, dims::Int...) = rand!(r, BitArray(dims))

bitrand(dims::Dims)   = rand!(BitArray(dims))
bitrand(dims::Int...) = rand!(BitArray(dims))

## randn() - Normally distributed random numbers using Ziggurat algorithm

# The Ziggurat Method for generating random variables - Marsaglia and Tsang
# Paper and reference code: http://www.jstatsoft.org/v05/i08/

# randmtzig (covers also exponential variates)
## Tables for normal variates
const ki =
    UInt64[0x0007799ec012f7b2,0x0000000000000000,0x0006045f4c7de363,0x0006d1aa7d5ec0a5,
           0x000728fb3f60f777,0x0007592af4e9fbc0,0x000777a5c0bf655d,0x00078ca3857d2256,
           0x00079bf6b0ffe58b,0x0007a7a34ab092ad,0x0007b0d2f20dd1cb,0x0007b83d3aa9cb52,
           0x0007be597614224d,0x0007c3788631abe9,0x0007c7d32bc192ee,0x0007cb9263a6e86d,
           0x0007ced483edfa84,0x0007d1b07ac0fd39,0x0007d437ef2da5fc,0x0007d678b069aa6e,
           0x0007d87db38c5c87,0x0007da4fc6a9ba62,0x0007dbf611b37f3b,0x0007dd7674d0f286,
           0x0007ded5ce8205f6,0x0007e018307fb62b,0x0007e141081bd124,0x0007e2533d712de8,
           0x0007e3514bbd7718,0x0007e43d54944b52,0x0007e5192f25ef42,0x0007e5e67481118d,
           0x0007e6a6897c1ce2,0x0007e75aa6c7f64c,0x0007e803df8ee498,0x0007e8a326eb6272,
           0x0007e93954717a28,0x0007e9c727f8648f,0x0007ea4d4cc85a3c,0x0007eacc5c4907a9,
           0x0007eb44e0474cf6,0x0007ebb754e47419,0x0007ec242a3d8474,0x0007ec8bc5d69645,
           0x0007ecee83d3d6e9,0x0007ed4cb8082f45,0x0007eda6aee0170f,0x0007edfcae2dfe68,
           0x0007ee4ef5dccd3e,0x0007ee9dc08c394e,0x0007eee9441a17c7,0x0007ef31b21b4fb1,
           0x0007ef773846a8a7,0x0007efba00d35a17,0x0007effa32ccf69f,0x0007f037f25e1278,
           0x0007f0736112d12c,0x0007f0ac9e145c25,0x0007f0e3c65e1fcc,0x0007f118f4ed8e54,
           0x0007f14c42ed0dc8,0x0007f17dc7daa0c3,0x0007f1ad99aac6a5,0x0007f1dbcce80015,
           0x0007f20874cf56bf,0x0007f233a36a3b9a,0x0007f25d69a604ad,0x0007f285d7694a92,
           0x0007f2acfba75e3b,0x0007f2d2e4720909,0x0007f2f79f09c344,0x0007f31b37ec883b,
           0x0007f33dbae36abc,0x0007f35f330f08d5,0x0007f37faaf2fa79,0x0007f39f2c805380,
           0x0007f3bdc11f4f1c,0x0007f3db71b83850,0x0007f3f846bba121,0x0007f4144829f846,
           0x0007f42f7d9a8b9d,0x0007f449ee420432,0x0007f463a0f8675e,0x0007f47c9c3ea77b,
           0x0007f494e643cd8e,0x0007f4ac84e9c475,0x0007f4c37dc9cd50,0x0007f4d9d638a432,
           0x0007f4ef934a5b6a,0x0007f504b9d5f33d,0x0007f5194e78b352,0x0007f52d55994a96,
           0x0007f540d36aba0c,0x0007f553cbef0e77,0x0007f56642f9ec8f,0x0007f5783c32f31e,
           0x0007f589bb17f609,0x0007f59ac2ff1525,0x0007f5ab5718b15a,0x0007f5bb7a71427c,
           0x0007f5cb2ff31009,0x0007f5da7a67cebe,0x0007f5e95c7a24e7,0x0007f5f7d8b7171e,
           0x0007f605f18f5ef4,0x0007f613a958ad0a,0x0007f621024ed7e9,0x0007f62dfe94f8cb,
           0x0007f63aa036777a,0x0007f646e928065a,0x0007f652db488f88,0x0007f65e786213ff,
           0x0007f669c22a7d8a,0x0007f674ba446459,0x0007f67f623fc8db,0x0007f689bb9ac294,
           0x0007f693c7c22481,0x0007f69d881217a6,0x0007f6a6fdd6ac36,0x0007f6b02a4c61ee,
           0x0007f6b90ea0a7f4,0x0007f6c1abf254c0,0x0007f6ca03521664,0x0007f6d215c2db82,
           0x0007f6d9e43a3559,0x0007f6e16fa0b329,0x0007f6e8b8d23729,0x0007f6efc09e4569,
           0x0007f6f687c84cbf,0x0007f6fd0f07ea09,0x0007f703570925e2,0x0007f709606cad03,
           0x0007f70f2bc8036f,0x0007f714b9a5b292,0x0007f71a0a85725d,0x0007f71f1edc4d9e,
           0x0007f723f714c179,0x0007f728938ed843,0x0007f72cf4a03fa0,0x0007f7311a945a16,
           0x0007f73505ac4bf8,0x0007f738b61f03bd,0x0007f73c2c193dc0,0x0007f73f67bd835c,
           0x0007f74269242559,0x0007f745305b31a1,0x0007f747bd666428,0x0007f74a103f12ed,
           0x0007f74c28d414f5,0x0007f74e0709a42d,0x0007f74faab939f9,0x0007f75113b16657,
           0x0007f75241b5a155,0x0007f753347e16b8,0x0007f753ebb76b7c,0x0007f75467027d05,
           0x0007f754a5f4199d,0x0007f754a814b207,0x0007f7546ce003ae,0x0007f753f3c4bb29,
           0x0007f7533c240e92,0x0007f75245514f41,0x0007f7510e91726c,0x0007f74f971a9012,
           0x0007f74dde135797,0x0007f74be2927971,0x0007f749a39e051c,0x0007f747202aba8a,
           0x0007f744571b4e3c,0x0007f741473f9efe,0x0007f73def53dc43,0x0007f73a4dff9bff,
           0x0007f73661d4deaf,0x0007f732294f003f,0x0007f72da2d19444,0x0007f728cca72bda,
           0x0007f723a5000367,0x0007f71e29f09627,0x0007f7185970156b,0x0007f7123156c102,
           0x0007f70baf5c1e2c,0x0007f704d1150a23,0x0007f6fd93f1a4e5,0x0007f6f5f53b10b6,
           0x0007f6edf211023e,0x0007f6e587671ce9,0x0007f6dcb2021679,0x0007f6d36e749c64,
           0x0007f6c9b91bf4c6,0x0007f6bf8e1c541b,0x0007f6b4e95ce015,0x0007f6a9c68356ff,
           0x0007f69e20ef5211,0x0007f691f3b517eb,0x0007f6853997f321,0x0007f677ed03ff19,
           0x0007f66a08075bdc,0x0007f65b844ab75a,0x0007f64c5b091860,0x0007f63c8506d4bc,
           0x0007f62bfa8798fe,0x0007f61ab34364b0,0x0007f608a65a599a,0x0007f5f5ca4737e8,
           0x0007f5e214d05b48,0x0007f5cd7af7066e,0x0007f5b7f0e4c2a1,0x0007f5a169d68fcf,
           0x0007f589d80596a5,0x0007f5712c8d0174,0x0007f557574c912b,0x0007f53c46c77193,
           0x0007f51fe7feb9f2,0x0007f5022646ecfb,0x0007f4e2eb17ab1d,0x0007f4c21dd4a3d1,
           0x0007f49fa38ea394,0x0007f47b5ebb62eb,0x0007f4552ee27473,0x0007f42cf03d58f5,
           0x0007f4027b48549f,0x0007f3d5a44119df,0x0007f3a63a8fb552,0x0007f37408155100,
           0x0007f33ed05b55ec,0x0007f3064f9c183e,0x0007f2ca399c7ba1,0x0007f28a384bb940,
           0x0007f245ea1b7a2b,0x0007f1fcdffe8f1b,0x0007f1ae9af758cd,0x0007f15a8917f27e,
           0x0007f10001ccaaab,0x0007f09e413c418a,0x0007f034627733d7,0x0007efc15815b8d5,
           0x0007ef43e2bf7f55,0x0007eeba84e31dfe,0x0007ee237294df89,0x0007ed7c7c170141,
           0x0007ecc2f0d95d3a,0x0007ebf377a46782,0x0007eb09d6deb285,0x0007ea00a4f17808,
           0x0007e8d0d3da63d6,0x0007e771023b0fcf,0x0007e5d46c2f08d8,0x0007e3e937669691,
           0x0007e195978f1176,0x0007deb2c0e05c1c,0x0007db0362002a19,0x0007d6202c151439,
           0x0007cf4b8f00a2cb,0x0007c4fd24520efd,0x0007b362fbf81816,0x00078d2d25998e24]
const wi =
    [1.7367254121602630e-15,9.5586603514556339e-17,1.2708704834810623e-16,
     1.4909740962495474e-16,1.6658733631586268e-16,1.8136120810119029e-16,
     1.9429720153135588e-16,2.0589500628482093e-16,2.1646860576895422e-16,
     2.2622940392218116e-16,2.3532718914045892e-16,2.4387234557428771e-16,
     2.5194879829274225e-16,2.5962199772528103e-16,2.6694407473648285e-16,
     2.7395729685142446e-16,2.8069646002484804e-16,2.8719058904113930e-16,
     2.9346417484728883e-16,2.9953809336782113e-16,3.0543030007192440e-16,
     3.1115636338921572e-16,3.1672988018581815e-16,3.2216280350549905e-16,
     3.2746570407939751e-16,3.3264798116841710e-16,3.3771803417353232e-16,
     3.4268340353119356e-16,3.4755088731729758e-16,3.5232663846002031e-16,
     3.5701624633953494e-16,3.6162480571598339e-16,3.6615697529653540e-16,
     3.7061702777236077e-16,3.7500889278747798e-16,3.7933619401549554e-16,
     3.8360228129677279e-16,3.8781025861250247e-16,3.9196300853257678e-16,
     3.9606321366256378e-16,4.0011337552546690e-16,4.0411583124143332e-16,
     4.0807276830960448e-16,4.1198623774807442e-16,4.1585816580828064e-16,
     4.1969036444740733e-16,4.2348454071520708e-16,4.2724230518899761e-16,
     4.3096517957162941e-16,4.3465460355128760e-16,4.3831194100854571e-16,
     4.4193848564470665e-16,4.4553546609579137e-16,4.4910405058828750e-16,
     4.5264535118571397e-16,4.5616042766900381e-16,4.5965029108849407e-16,
     4.6311590702081647e-16,4.6655819856008752e-16,4.6997804906941950e-16,
     4.7337630471583237e-16,4.7675377680908526e-16,4.8011124396270155e-16,
     4.8344945409350080e-16,4.8676912627422087e-16,4.9007095245229938e-16,
     4.9335559904654139e-16,4.9662370843221783e-16,4.9987590032409088e-16,
     5.0311277306593187e-16,5.0633490483427195e-16,5.0954285476338923e-16,
     5.1273716399787966e-16,5.1591835667857364e-16,5.1908694086703434e-16,
     5.2224340941340417e-16,5.2538824077194543e-16,5.2852189976823820e-16,
     5.3164483832166176e-16,5.3475749612647295e-16,5.3786030129452348e-16,
     5.4095367096239933e-16,5.4403801186554671e-16,5.4711372088173611e-16,
     5.5018118554603362e-16,5.5324078453927836e-16,5.5629288815190902e-16,
     5.5933785872484621e-16,5.6237605106900435e-16,5.6540781286489604e-16,
     5.6843348504368141e-16,5.7145340215092040e-16,5.7446789269419609e-16,
     5.7747727947569648e-16,5.8048187991076857e-16,5.8348200633338921e-16,
     5.8647796628943653e-16,5.8947006281858718e-16,5.9245859472561339e-16,
     5.9544385684180598e-16,5.9842614027720281e-16,6.0140573266426640e-16,
     6.0438291839361250e-16,6.0735797884236057e-16,6.1033119259564394e-16,
     6.1330283566179110e-16,6.1627318168165963e-16,6.1924250213258470e-16,
     6.2221106652737879e-16,6.2517914260879998e-16,6.2814699653988953e-16,
     6.3111489309056042e-16,6.3408309582080600e-16,6.3705186726088149e-16,
     6.4002146908880247e-16,6.4299216230548961e-16,6.4596420740788321e-16,
     6.4893786456033965e-16,6.5191339376461587e-16,6.5489105502874154e-16,
     6.5787110853507413e-16,6.6085381480782587e-16,6.6383943488035057e-16,
     6.6682823046247459e-16,6.6982046410815579e-16,6.7281639938375311e-16,
     6.7581630103719006e-16,6.7882043516829803e-16,6.8182906940062540e-16,
     6.8484247305500383e-16,6.8786091732516637e-16,6.9088467545571690e-16,
     6.9391402292275690e-16,6.9694923761748294e-16,6.9999060003307640e-16,
     7.0303839345521508e-16,7.0609290415654822e-16,7.0915442159548734e-16,
     7.1222323861967788e-16,7.1529965167453030e-16,7.1838396101720629e-16,
     7.2147647093647067e-16,7.2457748997883870e-16,7.2768733118146927e-16,
     7.3080631231227429e-16,7.3393475611774048e-16,7.3707299057898310e-16,
     7.4022134917657997e-16,7.4338017116476479e-16,7.4654980185558890e-16,
     7.4973059291369793e-16,7.5292290266240584e-16,7.5612709640179217e-16,
     7.5934354673958895e-16,7.6257263393567558e-16,7.6581474626104873e-16,
     7.6907028037219191e-16,7.7233964170182985e-16,7.7562324486711744e-16,
     7.7892151409638524e-16,7.8223488367564108e-16,7.8556379841610841e-16,
     7.8890871414417552e-16,7.9227009821522709e-16,7.9564843005293662e-16,
     7.9904420171571300e-16,8.0245791849212591e-16,8.0589009952726568e-16,
     8.0934127848215009e-16,8.1281200422845008e-16,8.1630284158098775e-16,
     8.1981437207065329e-16,8.2334719476060504e-16,8.2690192710884700e-16,
     8.3047920588053737e-16,8.3407968811366288e-16,8.3770405214202216e-16,
     8.4135299867980282e-16,8.4502725197240968e-16,8.4872756101861549e-16,
     8.5245470086955962e-16,8.5620947401062333e-16,8.5999271183276646e-16,
     8.6380527620052589e-16,8.6764806112455816e-16,8.7152199454736980e-16,
     8.7542804025171749e-16,8.7936719990210427e-16,8.8334051523084080e-16,
     8.8734907038131345e-16,8.9139399442240861e-16,8.9547646404950677e-16,
     8.9959770648910994e-16,9.0375900262601175e-16,9.0796169037400680e-16,
     9.1220716831348461e-16,9.1649689962191353e-16,9.2083241632623076e-16,
     9.2521532390956933e-16,9.2964730630864167e-16,9.3413013134252651e-16,
     9.3866565661866598e-16,9.4325583596767065e-16,9.4790272646517382e-16,
     9.5260849610662787e-16,9.5737543220974496e-16,9.6220595062948384e-16,
     9.6710260588230542e-16,9.7206810229016259e-16,9.7710530627072088e-16,
     9.8221725991905411e-16,9.8740719604806711e-16,9.9267855488079765e-16,
     9.9803500261836449e-16,1.0034804521436181e-15,1.0090190861637457e-15,
     1.0146553831467086e-15,1.0203941464683124e-15,1.0262405372613567e-15,
     1.0322001115486456e-15,1.0382788623515399e-15,1.0444832676000471e-15,
     1.0508203448355195e-15,1.0572977139009890e-15,1.0639236690676801e-15,
     1.0707072623632994e-15,1.0776584002668106e-15,1.0847879564403425e-15,
     1.0921079038149563e-15,1.0996314701785628e-15,1.1073733224935752e-15,
     1.1153497865853155e-15,1.1235791107110833e-15,1.1320817840164846e-15,
     1.1408809242582780e-15,1.1500027537839792e-15,1.1594771891449189e-15,
     1.1693385786910960e-15,1.1796266352955801e-15,1.1903876299282890e-15,
     1.2016759392543819e-15,1.2135560818666897e-15,1.2261054417450561e-15,
     1.2394179789163251e-15,1.2536093926602567e-15,1.2688244814255010e-15,
     1.2852479319096109e-15,1.3031206634689985e-15,1.3227655770195326e-15,
     1.3446300925011171e-15,1.3693606835128518e-15,1.3979436672775240e-15,
     1.4319989869661328e-15,1.4744848603597596e-15,1.5317872741611144e-15,
     1.6227698675312968e-15]
const fi =
    [1.0000000000000000e+00,9.7710170126767082e-01,9.5987909180010600e-01,
     9.4519895344229909e-01,9.3206007595922991e-01,9.1999150503934646e-01,
     9.0872644005213032e-01,8.9809592189834297e-01,8.8798466075583282e-01,
     8.7830965580891684e-01,8.6900868803685649e-01,8.6003362119633109e-01,
     8.5134625845867751e-01,8.4291565311220373e-01,8.3471629298688299e-01,
     8.2672683394622093e-01,8.1892919160370192e-01,8.1130787431265572e-01,
     8.0384948317096383e-01,7.9654233042295841e-01,7.8937614356602404e-01,
     7.8234183265480195e-01,7.7543130498118662e-01,7.6863731579848571e-01,
     7.6195334683679483e-01,7.5537350650709567e-01,7.4889244721915638e-01,
     7.4250529634015061e-01,7.3620759812686210e-01,7.2999526456147568e-01,
     7.2386453346862967e-01,7.1781193263072152e-01,7.1183424887824798e-01,
     7.0592850133275376e-01,7.0009191813651117e-01,6.9432191612611627e-01,
     6.8861608300467136e-01,6.8297216164499430e-01,6.7738803621877308e-01,
     6.7186171989708166e-01,6.6639134390874977e-01,6.6097514777666277e-01,
     6.5561147057969693e-01,6.5029874311081637e-01,6.4503548082082196e-01,
     6.3982027745305614e-01,6.3465179928762327e-01,6.2952877992483625e-01,
     6.2445001554702606e-01,6.1941436060583399e-01,6.1442072388891344e-01,
     6.0946806492577310e-01,6.0455539069746733e-01,5.9968175261912482e-01,
     5.9484624376798689e-01,5.9004799633282545e-01,5.8528617926337090e-01,
     5.8055999610079034e-01,5.7586868297235316e-01,5.7121150673525267e-01,
     5.6658776325616389e-01,5.6199677581452390e-01,5.5743789361876550e-01,
     5.5291049042583185e-01,5.4841396325526537e-01,5.4394773119002582e-01,
     5.3951123425695158e-01,5.3510393238045717e-01,5.3072530440366150e-01,
     5.2637484717168403e-01,5.2205207467232140e-01,5.1775651722975591e-01,
     5.1348772074732651e-01,5.0924524599574761e-01,5.0502866794346790e-01,
     5.0083757512614835e-01,4.9667156905248933e-01,4.9253026364386815e-01,
     4.8841328470545758e-01,4.8432026942668288e-01,4.8025086590904642e-01,
     4.7620473271950547e-01,4.7218153846772976e-01,4.6818096140569321e-01,
     4.6420268904817391e-01,4.6024641781284248e-01,4.5631185267871610e-01,
     4.5239870686184824e-01,4.4850670150720273e-01,4.4463556539573912e-01,
     4.4078503466580377e-01,4.3695485254798533e-01,4.3314476911265209e-01,
     4.2935454102944126e-01,4.2558393133802180e-01,4.2183270922949573e-01,
     4.1810064983784795e-01,4.1438753404089090e-01,4.1069314827018799e-01,
     4.0701728432947315e-01,4.0335973922111429e-01,3.9972031498019700e-01,
     3.9609881851583223e-01,3.9249506145931540e-01,3.8890886001878855e-01,
     3.8534003484007706e-01,3.8178841087339344e-01,3.7825381724561896e-01,
     3.7473608713789086e-01,3.7123505766823922e-01,3.6775056977903225e-01,
     3.6428246812900372e-01,3.6083060098964775e-01,3.5739482014578022e-01,
     3.5397498080007656e-01,3.5057094148140588e-01,3.4718256395679348e-01,
     3.4380971314685055e-01,3.4045225704452164e-01,3.3711006663700588e-01,
     3.3378301583071823e-01,3.3047098137916342e-01,3.2717384281360129e-01,
     3.2389148237639104e-01,3.2062378495690530e-01,3.1737063802991350e-01,
     3.1413193159633707e-01,3.1090755812628634e-01,3.0769741250429189e-01,
     3.0450139197664983e-01,3.0131939610080288e-01,2.9815132669668531e-01,
     2.9499708779996164e-01,2.9185658561709499e-01,2.8872972848218270e-01,
     2.8561642681550159e-01,2.8251659308370741e-01,2.7943014176163772e-01,
     2.7635698929566810e-01,2.7329705406857691e-01,2.7025025636587519e-01,
     2.6721651834356114e-01,2.6419576399726080e-01,2.6118791913272082e-01,
     2.5819291133761890e-01,2.5521066995466168e-01,2.5224112605594190e-01,
     2.4928421241852824e-01,2.4633986350126363e-01,2.4340801542275012e-01,
     2.4048860594050039e-01,2.3758157443123795e-01,2.3468686187232990e-01,
     2.3180441082433859e-01,2.2893416541468023e-01,2.2607607132238020e-01,
     2.2323007576391746e-01,2.2039612748015194e-01,2.1757417672433113e-01,
     2.1476417525117358e-01,2.1196607630703015e-01,2.0917983462112499e-01,
     2.0640540639788071e-01,2.0364274931033485e-01,2.0089182249465656e-01,
     1.9815258654577511e-01,1.9542500351413428e-01,1.9270903690358912e-01,
     1.9000465167046496e-01,1.8731181422380025e-01,1.8463049242679927e-01,
     1.8196065559952254e-01,1.7930227452284767e-01,1.7665532144373500e-01,
     1.7401977008183875e-01,1.7139559563750595e-01,1.6878277480121151e-01,
     1.6618128576448205e-01,1.6359110823236570e-01,1.6101222343751107e-01,
     1.5844461415592431e-01,1.5588826472447920e-01,1.5334316106026283e-01,
     1.5080929068184568e-01,1.4828664273257453e-01,1.4577520800599403e-01,
     1.4327497897351341e-01,1.4078594981444470e-01,1.3830811644855071e-01,
     1.3584147657125373e-01,1.3338602969166913e-01,1.3094177717364430e-01,
     1.2850872227999952e-01,1.2608687022018586e-01,1.2367622820159654e-01,
     1.2127680548479021e-01,1.1888861344290998e-01,1.1651166562561080e-01,
     1.1414597782783835e-01,1.1179156816383801e-01,1.0944845714681163e-01,
     1.0711666777468364e-01,1.0479622562248690e-01,1.0248715894193508e-01,
     1.0018949876880981e-01,9.7903279038862284e-02,9.5628536713008819e-02,
     9.3365311912690860e-02,9.1113648066373634e-02,8.8873592068275789e-02,
     8.6645194450557961e-02,8.4428509570353374e-02,8.2223595813202863e-02,
     8.0030515814663056e-02,7.7849336702096039e-02,7.5680130358927067e-02,
     7.3522973713981268e-02,7.1377949058890375e-02,6.9245144397006769e-02,
     6.7124653827788497e-02,6.5016577971242842e-02,6.2921024437758113e-02,
     6.0838108349539864e-02,5.8767952920933758e-02,5.6710690106202902e-02,
     5.4666461324888914e-02,5.2635418276792176e-02,5.0617723860947761e-02,
     4.8613553215868521e-02,4.6623094901930368e-02,4.4646552251294443e-02,
     4.2684144916474431e-02,4.0736110655940933e-02,3.8802707404526113e-02,
     3.6884215688567284e-02,3.4980941461716084e-02,3.3093219458578522e-02,
     3.1221417191920245e-02,2.9365939758133314e-02,2.7527235669603082e-02,
     2.5705804008548896e-02,2.3902203305795882e-02,2.2117062707308864e-02,
     2.0351096230044517e-02,1.8605121275724643e-02,1.6880083152543166e-02,
     1.5177088307935325e-02,1.3497450601739880e-02,1.1842757857907888e-02,
     1.0214971439701471e-02,8.6165827693987316e-03,7.0508754713732268e-03,
     5.5224032992509968e-03,4.0379725933630305e-03,2.6090727461021627e-03,
     1.2602859304985975e-03]

## Tables for exponential variates
const ke =
    UInt64[0x000e290a13924be3,0x0000000000000000,0x0009beadebce18bf,0x000c377ac71f9e08,
           0x000d4ddb99075857,0x000de893fb8ca23e,0x000e4a8e87c4328d,0x000e8dff16ae1cb9,
           0x000ebf2deab58c59,0x000ee49a6e8b9638,0x000f0204efd64ee4,0x000f19bdb8ea3c1b,
           0x000f2d458bbe5bd1,0x000f3da104b78236,0x000f4b86d784571f,0x000f577ad8a7784f,
           0x000f61de83da32ab,0x000f6afb7843cce7,0x000f730a57372b44,0x000f7a37651b0e68,
           0x000f80a5bb6eea52,0x000f867189d3cb5b,0x000f8bb1b4f8fbbd,0x000f9079062292b8,
           0x000f94d70ca8d43a,0x000f98d8c7dcaa99,0x000f9c8928abe083,0x000f9ff175b734a6,
           0x000fa319996bc47d,0x000fa6085f8e9d07,0x000fa8c3a62e1991,0x000fab5084e1f660,
           0x000fadb36c84cccb,0x000faff041086846,0x000fb20a6ea22bb9,0x000fb404fb42cb3c,
           0x000fb5e295158173,0x000fb7a59e99727a,0x000fb95038c8789d,0x000fbae44ba684eb,
           0x000fbc638d822e60,0x000fbdcf89209ffa,0x000fbf29a303cfc5,0x000fc0731df1089c,
           0x000fc1ad1ed6c8b1,0x000fc2d8b02b5c89,0x000fc3f6c4d92131,0x000fc5083ac9ba7d,
           0x000fc60ddd1e9cd6,0x000fc7086622e825,0x000fc7f881009f0b,0x000fc8decb41ac70,
           0x000fc9bbd623d7ec,0x000fca9027c5b26d,0x000fcb5c3c319c49,0x000fcc20864b4449,
           0x000fccdd70a35d40,0x000fcd935e34bf80,0x000fce42ab0db8bd,0x000fceebace7ec01,
           0x000fcf8eb3b0d0e7,0x000fd02c0a049b60,0x000fd0c3f59d199c,0x000fd156b7b5e27e,
           0x000fd1e48d670341,0x000fd26daff73551,0x000fd2f2552684be,0x000fd372af7233c1,
           0x000fd3eeee528f62,0x000fd4673e73543a,0x000fd4dbc9e72ff7,0x000fd54cb856dc2c,
           0x000fd5ba2f2c4119,0x000fd62451ba02c2,0x000fd68b415fcff4,0x000fd6ef1dabc160,
           0x000fd75004790eb6,0x000fd7ae120c583f,0x000fd809612dbd09,0x000fd8620b40effa,
           0x000fd8b8285b78fd,0x000fd90bcf594b1d,0x000fd95d15efd425,0x000fd9ac10bfa70c,
           0x000fd9f8d364df06,0x000fda437086566b,0x000fda8bf9e3c9fe,0x000fdad28062fed5,
           0x000fdb17141bff2c,0x000fdb59c4648085,0x000fdb9a9fda83cc,0x000fdbd9b46e3ed4,
           0x000fdc170f6b5d04,0x000fdc52bd81a3fb,0x000fdc8ccacd07ba,0x000fdcc542dd3902,
           0x000fdcfc30bcb793,0x000fdd319ef77143,0x000fdd6597a0f60b,0x000fdd98245a48a2,
           0x000fddc94e575271,0x000fddf91e64014f,0x000fde279ce914ca,0x000fde54d1f0a06a,
           0x000fde80c52a47cf,0x000fdeab7def394e,0x000fded50345eb35,0x000fdefd5be59fa0,
           0x000fdf248e39b26f,0x000fdf4aa064b4af,0x000fdf6f98435894,0x000fdf937b6f30ba,
           0x000fdfb64f414571,0x000fdfd818d48262,0x000fdff8dd07fed8,0x000fe018a08122c4,
           0x000fe03767adaa59,0x000fe05536c58a13,0x000fe07211ccb4c5,0x000fe08dfc94c532,
           0x000fe0a8fabe8ca1,0x000fe0c30fbb87a5,0x000fe0dc3ecf3a5a,0x000fe0f48b107521,
           0x000fe10bf76a82ef,0x000fe122869e41ff,0x000fe1383b4327e1,0x000fe14d17c83187,
           0x000fe1611e74c023,0x000fe1745169635a,0x000fe186b2a09176,0x000fe19843ef4e07,
           0x000fe1a90705bf63,0x000fe1b8fd6fb37c,0x000fe1c828951443,0x000fe1d689ba4bfd,
           0x000fe1e4220099a4,0x000fe1f0f26655a0,0x000fe1fcfbc726d4,0x000fe2083edc2830,
           0x000fe212bc3bfeb4,0x000fe21c745adfe3,0x000fe225678a8895,0x000fe22d95fa23f4,
           0x000fe234ffb62282,0x000fe23ba4a800d9,0x000fe2418495fddc,0x000fe2469f22bffb,
           0x000fe24af3cce90d,0x000fe24e81ee9858,0x000fe25148bcda19,0x000fe253474703fe,
           0x000fe2547c75fdc6,0x000fe254e70b754f,0x000fe25485a0fd1a,0x000fe25356a71450,
           0x000fe2515864173a,0x000fe24e88f316f1,0x000fe24ae64296fa,0x000fe2466e132f60,
           0x000fe2411df611bd,0x000fe23af34b6f73,0x000fe233eb40bf41,0x000fe22c02cee01b,
           0x000fe22336b81710,0x000fe2198385e5cc,0x000fe20ee586b707,0x000fe20358cb5dfb,
           0x000fe1f6d92465b1,0x000fe1e9621f2c9e,0x000fe1daef02c8da,0x000fe1cb7accb0a6,
           0x000fe1bb002d22c9,0x000fe1a9798349b8,0x000fe196e0d9140c,0x000fe1832fdebc44,
           0x000fe16e5fe5f931,0x000fe15869dccfcf,0x000fe1414647fe78,0x000fe128ed3cf8b2,
           0x000fe10f565b69cf,0x000fe0f478c633ab,0x000fe0d84b1bdd9e,0x000fe0bac36e6688,
           0x000fe09bd73a6b5b,0x000fe07b7b5d920a,0x000fe059a40c26d2,0x000fe03644c5d7f8,
           0x000fe011504979b2,0x000fdfeab887b95c,0x000fdfc26e94a447,0x000fdf986297e305,
           0x000fdf6c83bb8663,0x000fdf3ec0193eed,0x000fdf0f04a5d30a,0x000fdedd3d1aa204,
           0x000fdea953dcfc13,0x000fde7331e3100d,0x000fde3abe9626f2,0x000fddffdfb1dbd5,
           0x000fddc2791ff351,0x000fdd826cd068c6,0x000fdd3f9a8d3856,0x000fdcf9dfc95b0c,
           0x000fdcb1176a55fe,0x000fdc65198ba50b,0x000fdc15bb3b2daa,0x000fdbc2ce2dc4ae,
           0x000fdb6c206aaaca,0x000fdb117becb4a1,0x000fdab2a6379bf0,0x000fda4f5fdfb4e9,
           0x000fd9e76401f3a3,0x000fd97a67a9ce1f,0x000fd90819221429,0x000fd8901f2d4b02,
           0x000fd812182170e1,0x000fd78d98e23cd3,0x000fd7022bb3f082,0x000fd66f4edf96b9,
           0x000fd5d473200305,0x000fd530f9ccff94,0x000fd48432b7b351,0x000fd3cd59a8469e,
           0x000fd30b9368f90a,0x000fd23dea45f500,0x000fd16349e2e04a,0x000fd07a7a3ef98a,
           0x000fcf8219b5df05,0x000fce7895bcfcde,0x000fcd5c220ad5e2,0x000fcc2aadbc17dc,
           0x000fcae1d5e81fbc,0x000fc97ed4e778f9,0x000fc7fe6d4d720e,0x000fc65ccf39c2fc,
           0x000fc4957623cb03,0x000fc2a2fc826dc7,0x000fc07ee19b01cd,0x000fbe213c1cf493,
           0x000fbb8051ac1566,0x000fb890078d120e,0x000fb5411a5b9a95,0x000fb18000547133,
           0x000fad334827f1e2,0x000fa839276708b9,0x000fa263b32e37ed,0x000f9b72d1c52cd1,
           0x000f930a1a281a05,0x000f889f023d820a,0x000f7b577d2be5f3,0x000f69c650c40a8f,
           0x000f51530f0916d8,0x000f2cb0e3c5933e,0x000eeefb15d605d8,0x000e6da6ecf27460]

const we =
    [1.9311480126418366e-15,1.4178028487910829e-17,2.3278824993382448e-17,
     3.0487830247064320e-17,3.6665697714474878e-17,4.2179302189289733e-17,
     4.7222561556862764e-17,5.1911915446217879e-17,5.6323471083955047e-17,
     6.0510082606427647e-17,6.4510165096727506e-17,6.8352646803700541e-17,
     7.2059939574689050e-17,7.5649815537392981e-17,7.9136643961951065e-17,
     8.2532235563518929e-17,8.5846436168850513e-17,8.9087554865647428e-17,
     9.2262679629663719e-17,9.5377914505292719e-17,9.8438560874559257e-17,
     1.0144925809006294e-16,1.0441409405585343e-16,1.0733669323436384e-16,
     1.1022028745670189e-16,1.1306777346479334e-16,1.1588176009705533e-16,
     1.1866460730417886e-16,1.2141845865694359e-16,1.2414526862326387e-16,
     1.2684682560606153e-16,1.2952477151912284e-16,1.3218061851538810e-16,
     1.3481576335745444e-16,1.3743149982367625e-16,1.4002902946807859e-16,
     1.4260947099321287e-16,1.4517386844829297e-16,1.4772319842763584e-16,
     1.5025837641447456e-16,1.5278026239101652e-16,1.5528966581595696e-16,
     1.5778735005459581e-16,1.6027403633350909e-16,1.6275040728083524e-16,
     1.6521711010420076e-16,1.6767475945078279e-16,1.7012393998770646e-16,
     1.7256520873568226e-16,1.7499909718432365e-16,1.7742611321380505e-16,
     1.7984674284430714e-16,1.8226145183195818e-16,1.8467068712763576e-16,
     1.8707487821298258e-16,1.8947443832625899e-16,1.9186976558915995e-16,
     1.9426124404443042e-16,1.9664924461299023e-16,1.9903412597830144e-16,
     2.0141623540485899e-16,2.0379590949693882e-16,2.0617347490308439e-16,
     2.0854924897123771e-16,2.1092354035891528e-16,2.1329664960238294e-16,
     2.1566886964838970e-16,2.1804048635167009e-16,2.2041177894111562e-16,
     2.2278302045723950e-16,2.2515447816331350e-16,2.2752641393233694e-16,
     2.2989908461180186e-16,2.3227274236804366e-16,2.3464763501180916e-16,
     2.3702400630653389e-16,2.3940209626069303e-16,2.4178214140547710e-16,
     2.4416437505894123e-16,2.4654902757768304e-16,2.4893632659702250e-16,
     2.5132649726057970e-16,2.5371976244007951e-16,2.5611634294614988e-16,
     2.5851645773082391e-16,2.6092032408240577e-16,2.6332815781331452e-16,
     2.6574017344147618e-16,2.6815658436579989e-16,2.7057760303623509e-16,
     2.7300344111887955e-16,2.7543430965657619e-16,2.7787041922541278e-16,
     2.8031198008751431e-16,2.8275920234049704e-16,2.8521229606393309e-16,
     2.8767147146315804e-16,2.9013693901073754e-16,2.9260890958589514e-16,
     2.9508759461219033e-16,2.9757320619372521e-16,3.0006595725014739e-16,
     3.0256606165070789e-16,3.0507373434762511e-16,3.0758919150899939e-16,
     3.1011265065151543e-16,3.1264433077316750e-16,3.1518445248623523e-16,
     3.1773323815073683e-16,3.2029091200858335e-16,3.2285770031865573e-16,
     3.2543383149302610e-16,3.2801953623454359e-16,3.3061504767600738e-16,
     3.3322060152114841e-16,3.3583643618764577e-16,3.3846279295240445e-16,
     3.4109991609932597e-16,3.4374805306980633e-16,3.4640745461620167e-16,
     3.4907837495850680e-16,3.5176107194449828e-16,3.5445580721360130e-16,
     3.5716284636474652e-16,3.5988245912849274e-16,3.6261491954370031e-16,
     3.6536050613905045e-16,3.6811950211971757e-16,3.7089219555951389e-16,
     3.7367887959883854e-16,3.7647985264877841e-16,3.7929541860172334e-16,
     3.8212588704887531e-16,3.8497157350504876e-16,3.8783279964117988e-16,
     3.9070989352498183e-16,3.9360318987020748e-16,3.9651303029500381e-16,
     3.9943976358986842e-16,4.0238374599574693e-16,4.0534534149283966e-16,
     4.0832492210071775e-16,4.1132286819038357e-16,4.1433956880894741e-16,
     4.1737542201763194e-16,4.2043083524385856e-16,4.2350622564821518e-16,
     4.2660202050715582e-16,4.2971865761233266e-16,4.3285658568752094e-16,
     4.3601626482415681e-16,4.3919816693657415e-16,4.4240277623809919e-16,
     4.4563058973923611e-16,4.4888211776926172e-16,4.5215788452263475e-16,
     4.5545842863172421e-16,4.5878430376746227e-16,4.6213607926964266e-16,
     4.6551434080870692e-16,4.6891969108099157e-16,4.7235275053955480e-16,
     4.7581415816285534e-16,4.7930457226372470e-16,4.8282467134125866e-16,
     4.8637515497845119e-16,4.8995674478861404e-16,4.9357018541385775e-16,
     4.9721624557917034e-16,5.0089571920591141e-16,5.0460942658884340e-16,
     5.0835821564116245e-16,5.1214296321235415e-16,5.1596457648410618e-16,
     5.1982399444994938e-16,5.2372218948478484e-16,5.2766016901098856e-16,
     5.3163897726836902e-16,5.3565969719590503e-16,5.3972345243389779e-16,
     5.4383140945596370e-16,5.4798477984116296e-16,5.5218482269752343e-16,
     5.5643284724928722e-16,5.6073021560139669e-16,5.6507834569605064e-16,
     5.6947871447763482e-16,5.7393286128396354e-16,5.7844239148359912e-16,
     5.8300898038105864e-16,5.8763437741400573e-16,5.9232041066909314e-16,
     5.9706899174600906e-16,6.0188212100252363e-16,6.0676189321700068e-16,
     6.1171050370897217e-16,6.1673025496306200e-16,6.2182356380685327e-16,
     6.2699296919933262e-16,6.3224114069342115e-16,6.3757088764394262e-16,
     6.4298516924135947e-16,6.4848710546189033e-16,6.5407998903644809e-16,
     6.5976729855445663e-16,6.6555271283433428e-16,6.7144012671064882e-16,
     6.7743366840910103e-16,6.8353771870512740e-16,6.8975693209068478e-16,
     6.9609626020748846e-16,7.0256097784459588e-16,7.0915671184495837e-16,
     7.1588947332085531e-16,7.2276569364381212e-16,7.2979226475290851e-16,
     7.3697658441912426e-16,7.4432660721604146e-16,7.5185090208325131e-16,
     7.5955871753377488e-16,7.6746005575784274e-16,7.7556575712157906e-16,
     7.8388759686228577e-16,7.9243839615735500e-16,8.0123215021130834e-16,
     8.1028417659131464e-16,8.1961128778061250e-16,8.2923199285818092e-16,
     8.3916673441467979e-16,8.4943816836487701e-16,8.6007149633349414e-16,
     8.7109486293879040e-16,8.8253983380721398e-16,8.9444197485198646e-16,
     9.0684155971316690e-16,9.1978444098118649e-16,9.3332313294229516e-16,
     9.4751817065249841e-16,9.6243983456584759e-16,9.7817036547844198e-16,
     9.9480684723838795e-16,1.0124650144288319e-15,1.0312843657756166e-15,
     1.0514351604044550e-15,1.0731281954224043e-15,1.0966288068517408e-15,
     1.1222774909350319e-15,1.1505212963006663e-15,1.1819635283304206e-15,
     1.2174462832361815e-15,1.2581958069755114e-15,1.3060984107128082e-15,
     1.3642786158057857e-15,1.4384889932178723e-15,1.5412190700064194e-15,
     1.7091034077168055e-15]
const fe =
    [1.0000000000000000e+00,9.3814368086217470e-01,9.0046992992574648e-01,
     8.7170433238120359e-01,8.4778550062398961e-01,8.2699329664305032e-01,
     8.0842165152300838e-01,7.9152763697249562e-01,7.7595685204011555e-01,
     7.6146338884989628e-01,7.4786862198519510e-01,7.3503809243142348e-01,
     7.2286765959357202e-01,7.1127476080507601e-01,7.0019265508278816e-01,
     6.8956649611707799e-01,6.7935057226476536e-01,6.6950631673192473e-01,
     6.6000084107899970e-01,6.5080583341457110e-01,6.4189671642726609e-01,
     6.3325199421436607e-01,6.2485273870366598e-01,6.1668218091520766e-01,
     6.0872538207962201e-01,6.0096896636523223e-01,5.9340090169173343e-01,
     5.8601031847726803e-01,5.7878735860284503e-01,5.7172304866482582e-01,
     5.6480919291240017e-01,5.5803828226258745e-01,5.5140341654064129e-01,
     5.4489823767243961e-01,5.3851687200286191e-01,5.3225388026304332e-01,
     5.2610421398361973e-01,5.2006317736823360e-01,5.1412639381474856e-01,
     5.0828977641064288e-01,5.0254950184134772e-01,4.9690198724154955e-01,
     4.9134386959403253e-01,4.8587198734188491e-01,4.8048336393045421e-01,
     4.7517519303737737e-01,4.6994482528395998e-01,4.6478975625042618e-01,
     4.5970761564213769e-01,4.5469615747461550e-01,4.4975325116275500e-01,
     4.4487687341454851e-01,4.4006510084235390e-01,4.3531610321563657e-01,
     4.3062813728845883e-01,4.2599954114303434e-01,4.2142872899761658e-01,
     4.1691418643300288e-01,4.1245446599716118e-01,4.0804818315203240e-01,
     4.0369401253053028e-01,3.9939068447523107e-01,3.9513698183329016e-01,
     3.9093173698479711e-01,3.8677382908413765e-01,3.8266218149600983e-01,
     3.7859575940958079e-01,3.7457356761590216e-01,3.7059464843514600e-01,
     3.6665807978151416e-01,3.6276297335481777e-01,3.5890847294874978e-01,
     3.5509375286678746e-01,3.5131801643748334e-01,3.4758049462163698e-01,
     3.4388044470450241e-01,3.4021714906678002e-01,3.3658991402867761e-01,
     3.3299806876180899e-01,3.2944096426413633e-01,3.2591797239355619e-01,
     3.2242848495608917e-01,3.1897191284495724e-01,3.1554768522712895e-01,
     3.1215524877417955e-01,3.0879406693456019e-01,3.0546361924459026e-01,
     3.0216340067569353e-01,2.9889292101558179e-01,2.9565170428126120e-01,
     2.9243928816189257e-01,2.8925522348967775e-01,2.8609907373707683e-01,
     2.8297041453878075e-01,2.7986883323697292e-01,2.7679392844851736e-01,
     2.7374530965280297e-01,2.7072259679906002e-01,2.6772541993204479e-01,
     2.6475341883506220e-01,2.6180624268936298e-01,2.5888354974901623e-01,
     2.5598500703041538e-01,2.5311029001562946e-01,2.5025908236886230e-01,
     2.4743107566532763e-01,2.4462596913189211e-01,2.4184346939887721e-01,
     2.3908329026244918e-01,2.3634515245705964e-01,2.3362878343743335e-01,
     2.3093391716962741e-01,2.2826029393071670e-01,2.2560766011668407e-01,
     2.2297576805812019e-01,2.2036437584335949e-01,2.1777324714870053e-01,
     2.1520215107537868e-01,2.1265086199297828e-01,2.1011915938898826e-01,
     2.0760682772422204e-01,2.0511365629383771e-01,2.0263943909370902e-01,
     2.0018397469191127e-01,1.9774706610509887e-01,1.9532852067956322e-01,
     1.9292814997677135e-01,1.9054576966319539e-01,1.8818119940425432e-01,
     1.8583426276219711e-01,1.8350478709776746e-01,1.8119260347549629e-01,
     1.7889754657247831e-01,1.7661945459049488e-01,1.7435816917135349e-01,
     1.7211353531532006e-01,1.6988540130252766e-01,1.6767361861725019e-01,
     1.6547804187493600e-01,1.6329852875190182e-01,1.6113493991759203e-01,
     1.5898713896931421e-01,1.5685499236936523e-01,1.5473836938446808e-01,
     1.5263714202744286e-01,1.5055118500103989e-01,1.4848037564386679e-01,
     1.4642459387834494e-01,1.4438372216063478e-01,1.4235764543247220e-01,
     1.4034625107486245e-01,1.3834942886358020e-01,1.3636707092642886e-01,
     1.3439907170221363e-01,1.3244532790138752e-01,1.3050573846833077e-01,
     1.2858020454522817e-01,1.2666862943751067e-01,1.2477091858083096e-01,
     1.2288697950954514e-01,1.2101672182667483e-01,1.1916005717532768e-01,
     1.1731689921155557e-01,1.1548716357863353e-01,1.1367076788274431e-01,
     1.1186763167005630e-01,1.1007767640518538e-01,1.0830082545103380e-01,
     1.0653700405000166e-01,1.0478613930657017e-01,1.0304816017125772e-01,
     1.0132299742595363e-01,9.9610583670637132e-02,9.7910853311492199e-02,
     9.6223742550432798e-02,9.4549189376055859e-02,9.2887133556043541e-02,
     9.1237516631040155e-02,8.9600281910032858e-02,8.7975374467270218e-02,
     8.6362741140756913e-02,8.4762330532368119e-02,8.3174093009632383e-02,
     8.1597980709237419e-02,8.0033947542319905e-02,7.8481949201606421e-02,
     7.6941943170480503e-02,7.5413888734058410e-02,7.3897746992364746e-02,
     7.2393480875708738e-02,7.0901055162371829e-02,6.9420436498728755e-02,
     6.7951593421936601e-02,6.6494496385339774e-02,6.5049117786753749e-02,
     6.3615431999807334e-02,6.2193415408540995e-02,6.0783046445479633e-02,
     5.9384305633420266e-02,5.7997175631200659e-02,5.6621641283742877e-02,
     5.5257689676697037e-02,5.3905310196046087e-02,5.2564494593071692e-02,
     5.1235237055126281e-02,4.9917534282706372e-02,4.8611385573379497e-02,
     4.7316792913181548e-02,4.6033761076175170e-02,4.4762297732943282e-02,
     4.3502413568888183e-02,4.2254122413316234e-02,4.1017441380414819e-02,
     3.9792391023374125e-02,3.8578995503074857e-02,3.7377282772959361e-02,
     3.6187284781931423e-02,3.5009037697397410e-02,3.3842582150874330e-02,
     3.2687963508959535e-02,3.1545232172893609e-02,3.0414443910466604e-02,
     2.9295660224637393e-02,2.8188948763978636e-02,2.7094383780955800e-02,
     2.6012046645134217e-02,2.4942026419731783e-02,2.3884420511558171e-02,
     2.2839335406385240e-02,2.1806887504283581e-02,2.0787204072578117e-02,
     1.9780424338009743e-02,1.8786700744696030e-02,1.7806200410911362e-02,
     1.6839106826039948e-02,1.5885621839973163e-02,1.4945968011691148e-02,
     1.4020391403181938e-02,1.3109164931254991e-02,1.2212592426255381e-02,
     1.1331013597834597e-02,1.0464810181029979e-02,9.6144136425022099e-03,
     8.7803149858089753e-03,7.9630774380170400e-03,7.1633531836349839e-03,
     6.3819059373191791e-03,5.6196422072054830e-03,4.8776559835423923e-03,
     4.1572951208337953e-03,3.4602647778369040e-03,2.7887987935740761e-03,
     2.1459677437189063e-03,1.5362997803015724e-03,9.6726928232717454e-04,
     4.5413435384149677e-04]

const ziggurat_nor_r      = 3.6541528853610087963519472518
const ziggurat_nor_inv_r  = inv(ziggurat_nor_r)
const ziggurat_exp_r      = 7.6971174701310497140446280481

"""
    randn([rng=GLOBAL_RNG], [T=Float64], [dims...])

Generate a normally-distributed random number of type `T` with mean 0 and standard deviation 1.
Optionally generate an array of normally-distributed random numbers.
The `Base` module currently provides an implementation for the types
`Float16`, `Float32`, and `Float64` (the default).
"""
@inline function randn(rng::AbstractRNG=GLOBAL_RNG)
    @inbounds begin
        r = rand_ui52(rng)
        rabs = Int64(r>>1) # One bit for the sign
        idx = rabs & 0xFF
        x = ifelse(r % Bool, -rabs, rabs)*wi[idx+1]
        rabs < ki[idx+1] && return x # 99.3% of the time we return here 1st try
        return randn_unlikely(rng, idx, rabs, x)
    end
end

# this unlikely branch is put in a separate function for better efficiency
function randn_unlikely(rng, idx, rabs, x)
    @inbounds if idx == 0
        while true
            xx = -ziggurat_nor_inv_r*log(rand(rng))
            yy = -log(rand(rng))
            yy+yy > xx*xx && return (rabs >> 8) % Bool ? -ziggurat_nor_r-xx : ziggurat_nor_r+xx
        end
    elseif (fi[idx] - fi[idx+1])*rand(rng) + fi[idx+1] < exp(-0.5*x*x)
        return x # return from the triangular area
    else
        return randn(rng)
    end
end

"""
    randexp([rng=GLOBAL_RNG], [T=Float64], [dims...])

Generate a random number of type `T` according to the exponential distribution with scale 1.
Optionally generate an array of such random numbers.
The `Base` module currently provides an implementation for the types
`Float16`, `Float32`, and `Float64` (the default).
"""
@inline function randexp(rng::AbstractRNG=GLOBAL_RNG)
    @inbounds begin
        ri = rand_ui52(rng)
        idx = ri & 0xFF
        x = ri*we[idx+1]
        ri < ke[idx+1] && return x # 98.9% of the time we return here 1st try
        return randexp_unlikely(rng, idx, x)
    end
end

function randexp_unlikely(rng, idx, x)
    @inbounds if idx == 0
        return ziggurat_exp_r - log(rand(rng))
    elseif (fe[idx] - fe[idx+1])*rand(rng) + fe[idx+1] < exp(-x)
        return x # return from the triangular area
    else
        return randexp(rng)
    end
end

"""
    randn!([rng=GLOBAL_RNG], A::AbstractArray) -> A

Fill the array `A` with normally-distributed (mean 0, standard deviation 1) random numbers.
Also see the [`rand`](@ref) function.
"""
function randn! end

"""
    randexp!([rng=GLOBAL_RNG], A::AbstractArray) -> A

Fill the array `A` with random numbers following the exponential distribution (with scale 1).
"""
function randexp! end

let Floats = Union{Float16,Float32,Float64}
    for randfun in [:randn, :randexp]
        randfun! = Symbol(randfun, :!)
        @eval begin
            # scalars
            $randfun(rng::AbstractRNG, ::Type{T}) where {T<:$Floats} = convert(T, $randfun(rng))
            $randfun(::Type{T}) where {T} = $randfun(GLOBAL_RNG, T)

            # filling arrays
            function $randfun!(rng::AbstractRNG, A::AbstractArray{T}) where T
                for i in eachindex(A)
                    @inbounds A[i] = $randfun(rng, T)
                end
                A
            end

            $randfun!(A::AbstractArray) = $randfun!(GLOBAL_RNG, A)

            # generating arrays
            $randfun(rng::AbstractRNG, ::Type{T}, dims::Dims                     ) where {T} = $randfun!(rng, Array{T}(dims))
            # Note that this method explicitly does not define $randfun(rng, T), in order to prevent an infinite recursion.
            $randfun(rng::AbstractRNG, ::Type{T}, dim1::Integer, dims::Integer...) where {T} = $randfun!(rng, Array{T}(dim1, dims...))
            $randfun(                  ::Type{T}, dims::Dims                     ) where {T} = $randfun(GLOBAL_RNG, T, dims)
            $randfun(                  ::Type{T}, dims::Integer...               ) where {T} = $randfun(GLOBAL_RNG, T, dims...)
            $randfun(rng::AbstractRNG,            dims::Dims                     )           = $randfun(rng, Float64, dims)
            $randfun(rng::AbstractRNG,            dims::Integer...               )           = $randfun(rng, Float64, dims...)
            $randfun(                             dims::Dims                     )           = $randfun(GLOBAL_RNG, Float64, dims)
            $randfun(                             dims::Integer...               )           = $randfun(GLOBAL_RNG, Float64, dims...)
        end
    end
end

## random UUID generation

struct UUID
    value::UInt128

    UUID(u::UInt128) = new(u)
end

"""
    uuid1([rng::AbstractRNG=GLOBAL_RNG]) -> UUID

Generates a version 1 (time-based) universally unique identifier (UUID), as specified
by RFC 4122. Note that the Node ID is randomly generated (does not identify the host)
according to section 4.5 of the RFC.
"""
function uuid1(rng::AbstractRNG=GLOBAL_RNG)
    u = rand(rng, UInt128)

    # mask off clock sequence and node
    u &= 0x00000000000000003fffffffffffffff

    # set the unicast/multicast bit and version
    u |= 0x00000000000010000000010000000000

    # 0x01b21dd213814000 is the number of 100 nanosecond intervals
    # between the UUID epoch and Unix epoch
    timestamp = round(UInt64, time() * 1e7) + 0x01b21dd213814000
    ts_low = timestamp & typemax(UInt32)
    ts_mid = (timestamp >> 32) & typemax(UInt16)
    ts_hi = (timestamp >> 48) & 0x0fff

    u |= UInt128(ts_low) << 96
    u |= UInt128(ts_mid) << 80
    u |= UInt128(ts_hi) << 64

    UUID(u)
end

"""
    uuid4([rng::AbstractRNG=GLOBAL_RNG]) -> UUID

Generates a version 4 (random or pseudo-random) universally unique identifier (UUID),
as specified by RFC 4122.
"""
function uuid4(rng::AbstractRNG=GLOBAL_RNG)
    u = rand(rng, UInt128)
    u &= 0xffffffffffff0fff3fffffffffffffff
    u |= 0x00000000000040008000000000000000
    UUID(u)
end

"""
    uuid_version(u::UUID) -> Integer

Inspects the given UUID and returns its version (see RFC 4122).
"""
function uuid_version(u::UUID)
    Int((u.value >> 76) & 0xf)
end

Base.convert(::Type{UInt128}, u::UUID) = u.value

function Base.convert(::Type{UUID}, s::AbstractString)
    s = lowercase(s)

    if !ismatch(r"^[0-9a-f]{8}(?:-[0-9a-f]{4}){3}-[0-9a-f]{12}$", s)
        throw(ArgumentError("Malformed UUID string"))
    end

    u = UInt128(0)
    for i in [1:8; 10:13; 15:18; 20:23; 25:36]
        u <<= 4
        d = s[i]-'0'
        u |= 0xf & (d-39*(d>9))
    end
    return UUID(u)
end

function Base.repr(u::UUID)
    u = u.value
    a = Vector{UInt8}(36)
    for i = [36:-1:25; 23:-1:20; 18:-1:15; 13:-1:10; 8:-1:1]
        d = u & 0xf
        a[i] = '0'+d+39*(d>9)
        u >>= 4
    end
    a[[24,19,14,9]] = '-'

    return String(a)
end

Base.show(io::IO, u::UUID) = write(io, Base.repr(u))

# return a random string (often useful for temporary filenames/dirnames)
let b = UInt8['0':'9';'A':'Z';'a':'z']
    global randstring
    randstring(r::AbstractRNG, n::Int) = String(b[rand(r, 1:length(b), n)])
    randstring(r::AbstractRNG) = randstring(r,8)
    randstring(n::Int) = randstring(GLOBAL_RNG, n)
    randstring() = randstring(GLOBAL_RNG)
end

# Fill S (resized as needed) with a random subsequence of A, where
# each element of A is included in S with independent probability p.
# (Note that this is different from the problem of finding a random
#  size-m subset of A where m is fixed!)
function randsubseq!(r::AbstractRNG, S::AbstractArray, A::AbstractArray, p::Real)
    0 <= p <= 1 || throw(ArgumentError("probability $p not in [0,1]"))
    n = length(A)
    p == 1 && return copy!(resize!(S, n), A)
    empty!(S)
    p == 0 && return S
    nexpected = p * length(A)
    sizehint!(S, round(Int,nexpected + 5*sqrt(nexpected)))
    if p > 0.15 # empirical threshold for trivial O(n) algorithm to be better
        for i = 1:n
            rand(r) <= p && push!(S, A[i])
        end
    else
        # Skip through A, in order, from each element i to the next element i+s
        # included in S. The probability that the next included element is
        # s==k (k > 0) is (1-p)^(k-1) * p, and hence the probability (CDF) that
        # s is in {1,...,k} is 1-(1-p)^k = F(k).   Thus, we can draw the skip s
        # from this probability distribution via the discrete inverse-transform
        # method: s = ceil(F^{-1}(u)) where u = rand(), which is simply
        # s = ceil(log(rand()) / log1p(-p)).
        # -log(rand()) is an exponential variate, so can use randexp().
        L = -1 / log1p(-p) # L > 0
        i = 0
        while true
            s = randexp(r) * L
            s >= n - i && return S # compare before ceil to avoid overflow
            push!(S, A[i += ceil(Int,s)])
        end
        # [This algorithm is similar in spirit to, but much simpler than,
        #  the one by Vitter for a related problem in "Faster methods for
        #  random sampling," Comm. ACM Magazine 7, 703-718 (1984).]
    end
    return S
end
randsubseq!(S::AbstractArray, A::AbstractArray, p::Real) = randsubseq!(GLOBAL_RNG, S, A, p)

randsubseq(r::AbstractRNG, A::AbstractArray{T}, p::Real) where {T} = randsubseq!(r, T[], A, p)

"""
    randsubseq(A, p) -> Vector

Return a vector consisting of a random subsequence of the given array `A`, where each
element of `A` is included (in order) with independent probability `p`. (Complexity is
linear in `p*length(A)`, so this function is efficient even if `p` is small and `A` is
large.) Technically, this process is known as "Bernoulli sampling" of `A`.
"""
randsubseq(A::AbstractArray, p::Real) = randsubseq(GLOBAL_RNG, A, p)

"Return a random `Int` (masked with `mask`) in ``[0, n)``, when `n <= 2^52`."
@inline function rand_lt(r::AbstractRNG, n::Int, mask::Int=nextpow2(n)-1)
    # this duplicates the functionality of RangeGenerator objects,
    # to optimize this special case
    while true
        x = (rand_ui52_raw(r) % Int) & mask
        x < n && return x
    end
end

"""
    shuffle!([rng=GLOBAL_RNG,] v)

In-place version of [`shuffle`](@ref): randomly permute the array `v` in-place,
optionally supplying the random-number generator `rng`.
"""
function shuffle!(r::AbstractRNG, a::AbstractVector)
    n = length(a)
    @assert n <= Int64(2)^52
    mask = nextpow2(n) - 1
    for i = n:-1:2
        (mask >> 1) == i && (mask >>= 1)
        j = 1 + rand_lt(r, i, mask)
        a[i], a[j] = a[j], a[i]
    end
    return a
end

shuffle!(a::AbstractVector) = shuffle!(GLOBAL_RNG, a)

"""
    shuffle([rng=GLOBAL_RNG,] v)

Return a randomly permuted copy of `v`. The optional `rng` argument specifies a random
number generator (see [Random Numbers](@ref)).
To permute `v` in-place, see [`shuffle!`](@ref).  To obtain randomly permuted
indices, see [`randperm`](@ref).
"""
shuffle(r::AbstractRNG, a::AbstractVector) = shuffle!(r, copymutable(a))
shuffle(a::AbstractVector) = shuffle(GLOBAL_RNG, a)

"""
    randperm([rng=GLOBAL_RNG,] n::Integer)

Construct a random permutation of length `n`. The optional `rng` argument specifies a random
number generator (see [Random Numbers](@ref)).
To randomly permute a arbitrary vector, see [`shuffle`](@ref)
or [`shuffle!`](@ref).
"""
function randperm(r::AbstractRNG, n::Integer)
    a = Vector{typeof(n)}(n)
    @assert n <= Int64(2)^52
    if n == 0
       return a
    end
    a[1] = 1
    mask = 3
    @inbounds for i = 2:Int(n)
        j = 1 + rand_lt(r, i, mask)
        if i != j # a[i] is uninitialized (and could be #undef)
            a[i] = a[j]
        end
        a[j] = i
        i == 1+mask && (mask = 2mask + 1)
    end
    return a
end
randperm(n::Integer) = randperm(GLOBAL_RNG, n)

"""
    randcycle([rng=GLOBAL_RNG,] n::Integer)

Construct a random cyclic permutation of length `n`. The optional `rng`
argument specifies a random number generator, see [Random Numbers](@ref).
"""
function randcycle(r::AbstractRNG, n::Integer)
    a = Vector{typeof(n)}(n)
    n == 0 && return a
    @assert n <= Int64(2)^52
    a[1] = 1
    mask = 3
    @inbounds for i = 2:Int(n)
        j = 1 + rand_lt(r, i-1, mask)
        a[i] = a[j]
        a[j] = i
        i == 1+mask && (mask = 2mask + 1)
    end
    return a
end
randcycle(n::Integer) = randcycle(GLOBAL_RNG, n)

end # module

max_stars_repo_name: odow/julia

max_issues_repo_name: odow/julia

max_forks_repo_name: odow/julia


text:
using Printf
using LinearAlgebra
using DelimitedFiles
using Quaternions

#EXERCISE MADE BY ERIK MARTÍN GARZÓN & DAVID BOCES OBIS

function to_2d(V3)
    #we calculate de matrix (see the first exercise)

    a = 0.5*cosd(42)
    b = 0.5*sind(42)
    c = cosd(7)
    d = sind(7)
    e = 0
    f = 1

    M = [-a c e;
        -b -d f]
     #matrix found in the first exercise

    V2 = M*V3 #operation to transform V3 of R3 in V2 in R2

    # println("The vector ", V3, " representated in R2 is: ", V2)
    # println()

    return V2
end

function rotate_phi_z(phi, z, V)

    global z_norm
    global z_module

    z_module = sqrt(z[1]*z[1]+z[2]*z[2]+z[3]*z[3])

    z_norm = z/z_module

    Z = [0.0 -z_norm[3] z_norm[2];
         z_norm[3] 0.0 -z_norm[1];
        -z_norm[2] z_norm[1] 0.0]

    #formula de Rodriges to find "R", the rotation matrix
    R = I + sind(phi)*Z + (1-cosd(phi))*(Z^2)
    #just above, we multiply pi/180 to the angle (in degrees) to obtain the angle in radians
    #so julia can do the operation we want

    #next, we will check if R is a rotation matrix: R*R'=I and det(R)=1
    #For this comprobation, we needed to round R*R' and det(R). That's because much times
    #the result was 0.999999 and not 1
    if(phi==0)
        return V
    end
    if (z != [0.0;0.0;0.0])
        if (round.(R*R') == I && round(det(R)) == 1)
            #we find the rotated matrix:
            U = R*V
            # print("V rotated is = ", U)
            # println()
            return U
        else

            print("R = ", R, "\nis NOT a rotation matrix\n")
            println("R*R'= ", round.(R*R'))
            println("det(R)= ", round(det(R)))

        end
    else

            return [0.0 0.0 0.0; 0.0 0.0 0.0;0.0 0.0 0.0]
    end
end

# FUNCTION TO DRAW WHAT THE CAMERA IS SEEING  (EX 3.1)
function focal_camera(cameraMatrixInv, focus, point)
    projMat=[focus 0 0 0; 0 focus 0 0;  0 0 1 0]

    pointHomo = vcat(point, [1])

    finalPoint=projMat*cameraMatrixInv*pointHomo

    finalPointHomo = [finalPoint[1]/finalPoint[3];finalPoint[2]/finalPoint[3]; finalPoint[3]/finalPoint[3]]

    return finalPointHomo
end

# FUNCTION TO DRAW FOCAL CAMERA POINTS IN SPACE (EX 3.2)
function focal_camera_points_in_space(cameraMatrix, focus, point2d)
    pointHomo = vcat(point2d, [focus; 1])

    point_in_space = cameraMatrix * pointHomo

    return point_in_space
end

# # FUNCTION TO KNOW THE CAMERA PLANE WITHOUT FOCUS (EX 4.3)
# function camera_plane_without_focus(cameraMatrixInv, point)
#     pointHomo = vcat(point, [1])
#
#     finalPoint=cameraMatrixInv*pointHomo
#
#     finalPointHomo = [finalPoint[1]/finalPoint[3];finalPoint[2]/finalPoint[3]; finalPoint[3]/finalPoint[3]]
#
#     return finalPointHomo
#     end

ext: jl


text:
using BayesianDataFusion
using CSV
using DataFrames
using DelimitedFiles
using JLD
using SparseArrays
using Test

# see https://docs.julialang.org/en/v0.4/stdlib/io-network/?highlight=readdlm#Base.readdlm
function readdlm(path, delim)
    res = []
    open(path) do file
        while !eof(file)
            l = parse.(Float64, split(readline(file), delim))
            ls = reshape(l, 1, length(l))
            push!(res, ls)
        end
    end
    reduce(vcat, res)
end

# IndexedDF
X = IndexedDF(DataFrame(A=[2,2,3], B=[1,3,4], C=[0., -1., 0.5]), [4,4])
@test BayesianDataFusion.nnz(X) == 3
@test size(getData(X, 1, 1)) == (0,3)
@test size(getData(X, 1, 4)) == (0,3)

x12 = getData(X, 1, 2)
@test size(x12) == (2,3)
@test x12[:,1] == [2,2]
@test x12[:,2] == [1,3]
@test x12[:,3] == [0., -1.]

@test size(getData(X, 2, 2)) == (0,3)

@test BayesianDataFusion.rep_int([2, 4, 1, 10], [3, 2, 1, 0]) == [2, 2, 2, 4, 4, 1]

# FastIDF
Xf = FastIDF(X)
@test BayesianDataFusion.nnz(Xf) == 3
@test size(getData(Xf, 1, 1)[1]) == (0,2)
@test size(getData(Xf, 1, 1)[2]) == (0,)
x12f = getData(Xf, 1, 2)
@test x12f[1][:,1] == [2,2]
@test x12f[1][:,2] == [1,3]
@test x12f[2] == [0., -1.]

Xf32 = FastIDF(IndexedDF(DataFrame(A=Int32[1,2,3], B=Int32[1,2,3], C=Float32[0.5, -0.1, 0.0])))
@test typeof(Xf32) == FastIDF{Int32, Float32}

Xf32b = FastIDF(DataFrame(A=Int32[1,2,3], B=Int32[1,2,3], C=Float32[0.5, -0.1, 0.0]), [3, 3])
@test typeof(Xf32b) == FastIDF{Int32, Float32}

@test size(Xf32b) == (3, 3)
@test size(Xf32b, 2) == 3

# IndexedDF with tuple input
X2 = IndexedDF(DataFrame(A=[2,2,3], B=[1,3,4], C=[0., -1., 0.5]), (4,4))
@test size(X2) == (4,4)

# IndexedDF with plain DataFrame
X2a = IndexedDF(DataFrame(A=[2,2,3], B=[1,1,4], C=[0.4, -1, -9]))
@test size(X2a) == (3,4)

# testing removing rows
X3 = removeSamples(X2, [2])
@test BayesianDataFusion.nnz(X3) == 2
@test size(X3) == (4,4)
x12 = getData(X3, 1, 2)
@test size(x12) == (1,3)
@test size(x12,1) == getCount(X3, 1, 2)

# creating relation from DataFrame
a = DataFrame(A=[1,2,2,3,2], B=[1,3,1,4,4], v=[0.4, 1.0, -1.9, 1.4, 0.85])
r = Relation(a, "a")
@test size(r) == (3,4)

r.F = [1.0 2.5; -1 -2; 0 1; 3 -3]
assignToTest!(r, [1, 4])
@test r.F == [-1.0 -2; 0 1]
@test r.test_F == [1.0 2.5; 3 -3]

# creating empty Entity
e1 = Entity("e1")
e2 = Entity("e2")
e3 = Entity("e3")

# creating Relation from two entities
r2 = Relation(a, "r2", [e1, e2])
@test e1.count == size(r2, 1)
@test e2.count == size(r2, 2)
@test size(r2) == (3,4)

# testing setTest!
atest = DataFrame(A=[1,2], B=[3,4], v=[0.1, -0.2])
setTest!(r2, atest)
@test size(r2.test_vec) == size(atest)
@test numData(r2) == size(a, 1)

# testing setTest! with SparseMatrixCSC
atest_sp = sparse([3,2,2], [1,2,1], [-0.4, 0.6, 0.7])
setTest!(r2, atest_sp)
# @test numTest(r2) == BayesianDataFusion.nnz(atest_sp)
@test numData(r2) == size(a, 1)

# testing precision setting
setPrecision!(r2, 1.75)
@test r2.model.alpha == 1.75

a3 = DataFrame(B=[1], C=[5], v=[0.1])
r3 = Relation(a3, "r3", [e2, e3])
@test e3.count == 5
@test size(r3) == (4, 5)

a4 = DataFrame(A=[5], C=[4], v=[0.1])
@test_throws ArgumentError Relation(a4, "r4", [e1, e3])

# testing RelationData from sparse matrix
Y  = sprand(15,10, 0.1)
rd = RelationData(Y, class_cut = 0.5)
assignToTest!(rd.relations[1], 2)
@test numTest(rd.relations[1]) == 2
@test length(rd.relations[1].test_label) == 2

# running the data
result = macau(rd, burnin = 10, psamples = 10, verbose = false)
@test size(result["predictions"],1) == 2
@test length(result["predictions"][!, :stdev]) == 2
@test all(result["predictions"][!, :stdev] .>= 0)

# testing pred_all
Yhat = pred_all(rd.relations[1])
@test size(Yhat) == (15, 10)
@test Yhat[2,3] ≈ (rd.entities[1].model.sample[:,2]' * rd.entities[2].model.sample[:,3])[1] + rd.relations[1].model.mean_value

# predict all
result1 = macau(rd, burnin = 10, psamples = 10, verbose = false, full_prediction = true)
@test size(result1["predictions_full"]) == (15, 10)
x1 = result1["predictions"][1, 1:2]
y1 = result1["predictions"][!, :pred][1]
@test result1["predictions_full"][x1[1], x1[2]] ≈ y1

# rmse_train works
result1a = macau(rd, burnin = 1, psamples = 2, verbose = false, rmse_train = true)
@test result1a["RMSE_train"] >= 0

# writing output (latent vectors) works
tmpdir = mktempdir()  # TODO: cleanup=true
try
  rd2 = RelationData(Y, class_cut = 0.5, entity1 = "e1", entity2 = "e2")
  result1b = macau(rd2, burnin = 1, psamples = 10, verbose = false, num_latent = 5, output = "$tmpdir/macau-runtest", output_type="binary")
  @test isfile("$tmpdir/macau-runtest-e1-01.jld")
  @test isfile("$tmpdir/macau-runtest-e1-02.jld")
  @test isfile("$tmpdir/macau-runtest-e2-01.jld")
  @test isfile("$tmpdir/macau-runtest-e2-02.jld")
  e1_sample = load("$tmpdir/macau-runtest-e1-01.jld", "sample")
  @test size(Y,1) == size(e1_sample,2) ## number of instances
  @test 5         == size(e1_sample,1) ## number of latents
  e1_sample2 = load("$tmpdir/macau-runtest-e1-10.jld", "sample")
  e1_last    = convert(Array{Float32}, rd2.entities[1].model.sample)
  @test e1_sample2 ≈ e1_last
finally
  rm(tmpdir, recursive = true)
end

# writing output (latent vectors) works
tmpdir = mktempdir()
try
  rd2 = RelationData(Y, class_cut = 0.5, entity1 = "e1", entity2 = "e2")
  result1b = macau(rd2, burnin = 1, psamples = 10, verbose = false, num_latent = 5, output = "$tmpdir/macau-runtest", output_type="csv")
  @test isfile("$tmpdir/macau-runtest-e1-01.csv")
  @test isfile("$tmpdir/macau-runtest-e1-02.csv")
  @test isfile("$tmpdir/macau-runtest-e2-01.csv")
  @test isfile("$tmpdir/macau-runtest-e2-02.csv")
  df1 = CSV.read("$tmpdir/macau-runtest-e1-01.csv", header=false)
  e1_sample = convert(Matrix{Float64}, df1)

  @test size(Y,1) == size(e1_sample,2) ## number of instances
  @test 5         == size(e1_sample,1) ## number of latents
  df2 = CSV.read("$tmpdir/macau-runtest-e1-10.csv", header=false)
  e1_sample2 = convert(Matrix{Float64}, df2)
  e1_last    = convert(Array{Float32}, rd2.entities[1].model.sample)
  @test e1_sample2 ≈ e1_last
finally
  rm(tmpdir, recursive = true)
end

# custom function on latent variables
f1(a) = length(a.entities)
result2 = macau(rd, burnin = 5, psamples = 6, verbose = false, f = f1)
@test length(result2["f_output"]) == 6

# pred for training set
ytrain_hat = pred(rd.relations[1])
@test length(ytrain_hat) == numData(rd.relations[1])
row = rd.relations[1].data.df[1,1]
col = rd.relations[1].data.df[1,2]
y1 = sum(rd.entities[1].model.sample[:,row] .* rd.entities[2].model.sample[:,col]) + valueMean(rd.relations[1].data)
@test y1 ≈ ytrain_hat[1]


text:
module EverestCustomNPC

using ..Ahorn, Maple

const placements = Ahorn.PlacementDict(
    "Custom NPC (Everest)" => Ahorn.EntityPlacement(
        Maple.EverestCustomNPC
    )
)

function getSpriteName(entity::Maple.EverestCustomNPC)
    spriteName = get(entity.data, "sprite", "")

    return "characters/$(spriteName)00"
end

function Ahorn.selection(entity::Maple.EverestCustomNPC)
    x, y = Ahorn.position(entity)

    scaleX, scaleY = get(entity.data, "flipX", false) ? -1 : 1, get(entity.data, "flipY", false) ? -1 : 1

    spriteName = getSpriteName(entity)
    sprite = Ahorn.getSprite(spriteName, "Gameplay")

    if sprite.width == 0 || sprite.height == 0
        return Ahorn.Rectangle(x - 4, y - 4, 8, 8)

    else
        return Ahorn.getSpriteRectangle(spriteName, x, y, jx=0.5, jy=1.0, sx=scaleX, sy=scaleY)
    end
end

function Ahorn.render(ctx::Ahorn.Cairo.CairoContext, entity::Maple.EverestCustomNPC, room::Maple.Room)
    scaleX, scaleY = get(entity.data, "flipX", false) ? -1 : 1, get(entity.data, "flipY", false) ? -1 : 1
    spriteName = getSpriteName(entity)

    Ahorn.drawSprite(ctx, spriteName, 0, 0, jx=0.5, jy=1.0, sx=scaleX, sy=scaleY)
end

end


text:
using HSL

HSL_solvers = Function[]

include("ARCMA97.jl")
push!(HSL_solvers,eval(fname))

include("ARCMA97_abs.jl")
push!(HSL_solvers,eval(fname))

include("TRMA97.jl")
push!(HSL_solvers,eval(fname))

include("TRMA97_abs.jl")
push!(HSL_solvers,eval(fname))


text:
module LanguageServer
using JSON
using REPL
import URIParser
import DocumentFormat
import CSTParser
using CSTParser: TopLevel, Block, Call, FileH, EXPR, UnaryOpCall, UnarySyntaxOpCall, BinaryOpCall, BinarySyntaxOpCall, WhereOpCall, ConditionalOpCall, IDENTIFIER, KEYWORD, LITERAL, OPERATOR, PUNCTUATION, Quotenode, contributes_scope
import CSTParser.Tokenize.Tokens

import StaticLint

export LanguageServerInstance

include("uri2.jl")
include("protocol/protocol.jl")
include("document.jl")
include("languageserverinstance.jl")
include("jsonrpc.jl")

include("requests/misc.jl")
include("requests/init.jl")
include("requests/textDocument.jl")
include("requests/workspace.jl")
include("parsing.jl")
include("utilities.jl")
include("jmd.jl")
include("display.jl")

function __init__()
    StaticLint.loadpkgs()
end

end


text:
@with_kw immutable SymmetricNormalResampler
    n::Int
    std::Float64
end

function ParticleFilters.resample(r::SymmetricNormalResampler, b::WeightedParticleBelief, rng::AbstractRNG)
    collection = resample(LowVarianceResampler(r.n), b, rng)
    ps = particles(collection)
    for i in 1:r.n
        ps[i] += r.std*randn(rng, 2)
    end
    return collection
end

@with_kw immutable MinPopResampler
    n::Int
    min_pop::Int
    std::Float64
end

function ParticleFilters.resample(r::MinPopResampler, b, rng::AbstractRNG)
    collection = resample(LowVarianceResampler(r.n), b, rng)
    ps = particles(collection)
    nu = length(unique(ps))
    if r.min_pop > nu
        is = rand(rng, 1:r.n, r.min_pop - nu)
        for i in is
            ps[i] += r.std*randn(rng, 2)
        end
    end
    @show length(unique(ps))
    @show length(ps)
    return collection
end

immutable ObsAdaptiveParticleFilter{P<:POMDP,S,R,RNG<:AbstractRNG} <: Updater
    pomdp::P
    resample::R
    max_frac_replaced::Float64
    rng::RNG
    _pm::Vector{S}
    _wm::Vector{Float64}
end

function ObsAdaptiveParticleFilter(p::POMDP, resample, max_frac_replaced, rng::AbstractRNG)
    S = state_type(p)
    return ObsAdaptiveParticleFilter(p, resample, max_frac_replaced, rng, S[], Float64[])
end

POMDPs.initialize_belief{S}(up::ObsAdaptiveParticleFilter{S}, d::Any) = resample(up.resample, d, up.rng)
POMDPs.update(up::ObsAdaptiveParticleFilter, b, a, o) = update(up, resample(up.resample, b, up.rng), a, o)

function POMDPs.update(up::ObsAdaptiveParticleFilter, b::ParticleFilters.ParticleCollection, a, o)
    if n_particles(b) > 2*up.resample.n
        b = resample(up.resample, b, up.rng)
    end

    ps = particles(b)
    pm = up._pm
    wm = up._wm
    resize!(pm, 0)
    resize!(wm, 0)

    all_terminal = true
    for i in 1:n_particles(b)
        s = ps[i]
        if !isterminal(up.pomdp, s)
            all_terminal = false
            sp = generate_s(up.pomdp, s, a, up.rng)
            push!(pm, sp)
            od = observation(up.pomdp, s, a, sp)
            push!(wm, pdf(od, o))
        end
    end
    ws = sum(wm)
    if all_terminal || ws < eps(1.0/length(wm))
        # warn("All states in particle collection were terminal.")
        return initialize_belief(up, reset_distribution(up.pomdp, b, a, o))
    end

    pc = resample(up.resample, WeightedParticleBelief{state_type(up.pomdp)}(pm, wm, ws, nothing), up.rng)
    ps = particles(pc)

    mpw = max_possible_weight(up.pomdp, a, o)
    frac_replaced = up.max_frac_replaced*max(0.0, 1.0 - maximum(wm)/mpw)
    n_replaced = floor(Int, frac_replaced*length(ps))
    is = randperm(up.rng, length(ps))[1:n_replaced]
    for i in is
        ps[i] = new_particle(up.pomdp, b, a, o, up.rng)
    end
    return pc
end

# POMCPOW.belief_type(::Type{ObsAdaptiveParticleFilter{Vec2}}, ::Type{LightDark2DTarget}) = POWNodeBelief{Vec2, Vec2, Vec2, LightDark2DTarget}

function max_possible_weight(pomdp::AbstractLD2, a, o)
    od = observation(pomdp, a, o) # will only work for LightDark
    return pdf(od, o)
end

function new_particle(pomdp::AbstractLD2, b, a, o, rng)
    return o + LightDarkPOMDPs.obs_std(pomdp, o[1])*randn(rng, 2)
end

reset_distribution(p::POMDP, b, a, o) = initial_state_distribution(p)

function max_possible_weight(pomdp::SimpleLightDark, a, o)
    return pdf(observation(pomdp, o), o)
end

function new_particle(p::SimpleLightDark, b, a, o, rng)
    return clamp(round(Int, o + rand(rng, observation(p, o))), -p.radius, p.radius)
end

function max_possible_weight(pomdp::SubHuntPOMDP, a, o)
    if a == SubHunt.PING
        return pdf(Normal(0.0, pomdp.active_std), 0.0)^8
    else
        return pdf(Normal(0.0, pomdp.passive_std), 0.0)^7 * pdf(Normal(0.0, pomdp.passive_detected_std), 0.0)
    end
end

function new_particle(p::SubHuntPOMDP, b, a, o, rng)
    nonterm = filter(s->!isterminal(p, s), particles(b))
    own = first(nonterm).own
    aware = first(nonterm).aware || a == SubHunt.PING
    target = SVector(rand(rng, 1:p.size), rand(rng, 1:p.size))
    return SubState(own, target, rand(rng, 1:4), aware)
end

function reset_distribution(p::SubHuntPOMDP, b, a, o, rng)
    nonterm = filter(s->!isterminal(p, s), particles(b))
    own = first(nonterm).own
    aware = first(nonterm).aware || a == SubHunt.PING
    ps = SubState[]
    for i in 1:100
        target = SVector(rand(rng, 1:p.size), rand(rng, 1:p.size))
        push!(ps, SubState(own, target, rand(rng, 1:4), aware))
    end
    return ParticleCollection(ps)
end

#=
max_possible_weight(pomdp::PowseekerPOMDP, a::GPSOrAngle, o::SkierObs) = 0.0

function new_particle(pomdp::PowseekerPOMDP, a::GPSOrAngle, o::SkierObs, rng::AbstractRNG)
    if a.gps
        return SkierState(o.time, get(o.pos)+pomdp.gps_std*randn(rng, 1), 2*pi*rand(rng))
    else
        is = initial_state(pomdp, rng)
        return SkierState(o.time, is.pos, is.psi)
    end
end

reset_distribution(p::PowseekerPOMDP, a::GPSOrAngle, o::SkierObs) = SkierUnif(o.time, mdp(p).xlim, mdp(p).ylim)
=#

max_possible_weight(pomdp::VDPTagPOMDP, a::TagAction, o) = 0.0

new_particle(pomdp::VDPTagPOMDP, a::TagAction, o) = error("shouldn't get here")

function reset_distribution(p::LaserTagPOMDP, b::ParticleCollection, a, o)
    # warn("Resetting Particle Filter Distribution")
    rob = first(particles(b)).robot
    nextrob = LaserTag.add_if_inside(p.floor, rob, LaserTag.ACTION_DIRS[a])
    if o == LaserTag.C_SAME_LOC
        return ParticleCollection{LaserTag.LTState}([LaserTag.LTState(nextrob, nextrob, false)])
    else
        return LaserTag.LTInitialBelief(nextrob, p.floor)
    end
end

max_possible_weight(pomdp::LaserTagPOMDP, a::Int, o) = 0.0

new_particle(pomdp::LaserTagPOMDP, a::Int, o) = error("tried to generate a new particle (shouldn't get here)")

#=
max_possible_weight(pomdp::LaserTagPOMDP, a::Int, o::Float64) = max(1.0, pdf(Normal(0.0, pomdp.return_std), 0.0))

function new_particle(pomdp::VDPTagPOMDP, a::Int, o::Float64)
    if o == C_SAME_LOC
        return LTState(
end
=#

#=
function POMCPOW.init_node_belief(::ObsAdaptiveParticleFilter, p::LightDark2DTarget, s::Vec2, a::Vec2, o::Vec2, sp::Vec2)
    POWNodeBelief(p, s, a, o, sp)
end

function POMCPOW.push_weighted!(b::POWNodeBelief, up::ObsAdaptiveParticleFilter, s::Vec2, sp::Vec2)
    od = observation(b.model, s, b.a, sp)
    w = pdf(od, b.o)
    ood = observation(b.model, b.a, b.o)
    frac_replaced = up.max_frac_replaced*max(0.0, 1.0 - w/pdf(ood, b.o))
    insert!(b.dist, sp, w*(1.0-frac_replaced))
    sp2 = rand(up.rng, ood)
    insert!(b.dist, sp2, w*frac_replaced)
end
=#