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faster randn!(::MersenneTwister, ::Array{Float64}) #35078

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Apr 24, 2020
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faster randn!(::MersenneTwister, ::Array{Float64}) #35078

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aaa8f3a
faster randn!(::MersenneTwister, ::Array{Float64})
rfourquet Mar 11, 2020
b89e35c
try make LinearAlgebra tests pass
rfourquet Apr 23, 2020
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2 changes: 2 additions & 0 deletions NEWS.md
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Expand Up @@ -154,6 +154,8 @@ Standard library changes

#### Random

* `randn!(::MersenneTwister, ::Array{Float64})` is faster, and as a result, for a given state of the RNG,
the corresponding generated numbers have changed ([#35078]).

#### REPL

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2 changes: 1 addition & 1 deletion stdlib/LinearAlgebra/test/cholesky.jl
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Expand Up @@ -39,7 +39,7 @@ end
n1 = div(n, 2)
n2 = 2*n1

Random.seed!(1234321)
Random.seed!(12343)

areal = randn(n,n)/2
aimg = randn(n,n)/2
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2 changes: 1 addition & 1 deletion stdlib/LinearAlgebra/test/symmetric.jl
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Expand Up @@ -4,7 +4,7 @@ module TestSymmetric

using Test, LinearAlgebra, SparseArrays, Random

Random.seed!(101)
Random.seed!(1010)

@testset "Pauli σ-matrices: $σ" for σ in map(Hermitian,
Any[ [1 0; 0 1], [0 1; 1 0], [0 -im; im 0], [1 0; 0 -1] ])
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28 changes: 24 additions & 4 deletions stdlib/Random/src/normal.jl
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Expand Up @@ -35,9 +35,11 @@ julia> randn(rng, ComplexF32, (2, 3))
0.611224+1.56403im 0.355204-0.365563im 0.0905552+1.31012im
```
"""
@inline function randn(rng::AbstractRNG=default_rng())
@inline randn(rng::AbstractRNG=default_rng()) = _randn(rng, rand(rng, UInt52Raw()))

@inline function _randn(rng::AbstractRNG, r::UInt64)
@inbounds begin
r = rand(rng, UInt52())
r &= 0x000fffffffffffff
rabs = Int64(r>>1) # One bit for the sign
idx = rabs & 0xFF
x = ifelse(r % Bool, -rabs, rabs)*wi[idx+1]
Expand Down Expand Up @@ -95,9 +97,11 @@ julia> randexp(rng, 3, 3)
0.695867 0.693292 0.643644
```
"""
function randexp(rng::AbstractRNG=default_rng())
randexp(rng::AbstractRNG=default_rng()) = _randexp(rng, rand(rng, UInt52Raw()))

function _randexp(rng::AbstractRNG, ri::UInt64)
@inbounds begin
ri = rand(rng, UInt52())
ri &= 0x000fffffffffffff
idx = ri & 0xFF
x = ri*we[idx+1]
ri < ke[idx+1] && return x # 98.9% of the time we return here 1st try
Expand Down Expand Up @@ -162,6 +166,7 @@ function randexp! end

for randfun in [:randn, :randexp]
randfun! = Symbol(randfun, :!)
_randfun = Symbol(:_, randfun)
@eval begin
# scalars
$randfun(rng::AbstractRNG, T::BitFloatType) = convert(T, $randfun(rng))
Expand All @@ -175,6 +180,21 @@ for randfun in [:randn, :randexp]
A
end

# optimization for MersenneTwister, which randomizes natively Array{Float64}
function $randfun!(rng::MersenneTwister, A::Array{Float64})
if length(A) < 13
for i in eachindex(A)
@inbounds A[i] = $randfun(rng, Float64)
end
else
rand!(rng, A, CloseOpen12())
for i in eachindex(A)
@inbounds A[i] = $_randfun(rng, reinterpret(UInt64, A[i]))
end
end
A
end

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

# generating arrays
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