ChrisRackauckas

Julia v0.7's stack-allocation optimizations and escape analysis 

https://github.com/JuliaLang/julia/pull/22684

Watch it in action: stack-allocated mutable static sized arrays. Example thanks to Valentin Churavy.

julia> function f(x::Int64)
         A = MArray{Tuple{3}}(1, 2, 3)
         A[2] += x
         return A[2]-A[1] 

ChrisRackauckas

using Base.Test
using BoundaryValueDiffEq, DiffEqBase, DiffEqDevTools

# First order test
function func_1!(x, y, du)
    du[1] = y[2]
    du[2] = 0
end

# Not able to change the initial condition.

ChrisRackauckas

Variables:
  #self#::OrdinaryDiffEq.#perform_step!
  integrator::OrdinaryDiffEq.ODEIntegrator{OrdinaryDiffEq.Tsit5,Array{Float64,1},Float64,Float64,Float64,Array{Array{Float64,1},1},DiffEqBase.ODESolution{Float64,2,Array{Array{Float64,1},1},Void,Void,Array{Float64,1},Array{Array{Array{Float64,1},1},1},DiffEqBase.ODEProblem{Array{Float64,1},Float64,true,#df,Void,UniformScaling{Int64}},OrdinaryDiffEq.Tsit5,OrdinaryDiffEq.InterpolationData{#df,Array{Array{Float64,1},1},Array{Float64,1},Array{Array{Array{Float64,1},1},1},OrdinaryDiffEq.Tsit5Cache{Array{Float64,1},Array{Float64,1},Array{Float64,1},Array{Float64,1},OrdinaryDiffEq.Tsit5ConstantCache{Float64,Float64}}}},Array{Float64,1},#df,Void,OrdinaryDiffEq.Tsit5Cache{Array{Float64,1},Array{Float64,1},Array{Float64,1},Array{Float64,1},OrdinaryDiffEq.Tsit5ConstantCache{Float64,Float64}},OrdinaryDiffEq.DEOptions{Float64,Float64,Float64,Float64,DiffEqBase.#ODE_DEFAULT_NORM,DiffEqBase.CallbackSet{Tuple{},Tuple{}},DiffEqBase.#ODE_DEFAULT_ISOUTOFDOMAIN,DiffEqBase.#ODE_D

ChrisRackauckas

SymEngine.Basic[x0 + 0.0833333333333333*(1.5*x0 - x0*y0 - (y0 + 0.5*((y0 + 0.25*((x0 + 0.25*(1.5*x0 - x0*y0))*(y0 + 0.25*(-3*y0 + x0*y0)) - 3*(y0 + 0.25*(-3*y0 + x0*y0))))*(x0 + 0.25*(-(x0 + 0.25*(1.5*x0 - x0*y0))*(y0 + 0.25*(-3*y0 + x0*y0)) + 1.5*(x0 + 0.25*(1.5*x0 - x0*y0)))) - 3*(y0 + 0.25*((x0 + 0.25*(1.5*x0 - x0*y0))*(y0 + 0.25*(-3*y0 + x0*y0)) - 3*(y0 + 0.25*(-3*y0 + x0*y0))))))*(x0 + 0.5*(-(y0 + 0.25*((x0 + 0.25*(1.5*x0 - x0*y0))*(y0 + 0.25*(-3*y0 + x0*y0)) - 3*(y0 + 0.25*(-3*y0 + x0*y0))))*(x0 + 0.25*(-(x0 + 0.25*(1.5*x0 - x0*y0))*(y0 + 0.25*(-3*y0 + x0*y0)) + 1.5*(x0 + 0.25*(1.5*x0 - x0*y0)))) + 1.5*(x0 + 0.25*(-(x0 + 0.25*(1.5*x0 - x0*y0))*(y0 + 0.25*(-3*y0 + x0*y0)) + 1.5*(x0 + 0.25*(1.5*x0 - x0*y0)))))) + 1.5*(x0 + 0.5*(-(y0 + 0.25*((x0 + 0.25*(1.5*x0 - x0*y0))*(y0 + 0.25*(-3*y0 + x0*y0)) - 3*(y0 + 0.25*(-3*y0 + x0*y0))))*(x0 + 0.25*(-(x0 + 0.25*(1.5*x0 - x0*y0))*(y0 + 0.25*(-3*y0 + x0*y0)) + 1.5*(x0 + 0.25*(1.5*x0 - x0*y0)))) + 1.5*(x0 + 0.25*(-(x0 + 0.25*(1.5*x0 - x0*y0))*(y0 + 0.25*(-3*y0 + x0*

ChrisRackauckas

SymEngine.Basic[0. + 4.47215104103088*x - 1.36844154947903*x*y + 0.151438560380598*x*y^2 - 0.00923846952746669*x*y^3 + 5.23451694212525e-05*x*y^4 + 1.17843605321514e-05*x*y^5 - 2.92600484558672e-07*x*y^6 + 4.11218785990713e-09*x*y^7 + 7.48501594966537e-11*x*y^8 - 0.672247405107334*x^2*y + 0.370664426736858*x^2*y^2 - 0.0752239972222541*x^2*y^3 + 0.00931494973548523*x^2*y^4 - 0.000773652120635689*x^2*y^5 + 4.1304004934513e-05*x^2*y^6 - 8.80277168398071e-07*x^2*y^7 - 3.07285079704276e-08*x^2*y^8 + 2.48120225104779e-09*x^2*y^9 - 2.22365631233417e-11*x^2*y^10 - 5.3250992844628e-13*x^2*y^11 + 3.88477571287545e-14*x^2*y^12 - 9.64844546215222e-16*x^2*y^13 + 1.87911964770983e-17*x^2*y^14 - 0.192348763958449*x^3*y + 0.169162141060118*x^3*y^2 - 0.0829571943460876*x^3*y^3 + 0.021476513446275*x^3*y^4 - 0.00348656942438397*x^3*y^5 + 0.000403255555876659*x^3*y^6 - 3.48351926640532e-05*x^3*y^7 + 2.32018077215583e-06*x^3*y^8 - 1.16462622982937e-07*x^3*y^9 + 3.49737461145191e-09*x^3*y^10 + 2.02368983871224e-11*x^3*y^11 - 7.563

ChrisRackauckas

SymEngine.Basic[x + 0.0833333333333333*(1.5*x - x*y - (x + 0.5*(-(y + 0.25*((y + 0.25*(-3*y + x*y))*(x + 0.25*(1.5*x - x*y)) - 3*(y + 0.25*(-3*y + x*y))))*(x + 0.25*(-(y + 0.25*(-3*y + x*y))*(x + 0.25*(1.5*x - x*y)) + 1.5*(x + 0.25*(1.5*x - x*y)))) + 1.5*(x + 0.25*(-(y + 0.25*(-3*y + x*y))*(x + 0.25*(1.5*x - x*y)) + 1.5*(x + 0.25*(1.5*x - x*y))))))*(y + 0.5*((y + 0.25*((y + 0.25*(-3*y + x*y))*(x + 0.25*(1.5*x - x*y)) - 3*(y + 0.25*(-3*y + x*y))))*(x + 0.25*(-(y + 0.25*(-3*y + x*y))*(x + 0.25*(1.5*x - x*y)) + 1.5*(x + 0.25*(1.5*x - x*y)))) - 3*(y + 0.25*((y + 0.25*(-3*y + x*y))*(x + 0.25*(1.5*x - x*y)) - 3*(y + 0.25*(-3*y + x*y)))))) + 1.5*(x + 0.5*(-(y + 0.25*((y + 0.25*(-3*y + x*y))*(x + 0.25*(1.5*x - x*y)) - 3*(y + 0.25*(-3*y + x*y))))*(x + 0.25*(-(y + 0.25*(-3*y + x*y))*(x + 0.25*(1.5*x - x*y)) + 1.5*(x + 0.25*(1.5*x - x*y)))) + 1.5*(x + 0.25*(-(y + 0.25*(-3*y + x*y))*(x + 0.25*(1.5*x - x*y)) + 1.5*(x + 0.25*(1.5*x - x*y)))))) + 2*(-(y + 0.25*(-3*y + x*y))*(x + 0.25*(1.5*x - x*y)) - (y + 0.25*((y + 0.25*(-

ChrisRackauckas

# Pkg.add("SpecialMatrices") # Only need to run the first time
using SpecialMatrices, DiffEqBase
A = Strang(11)
function g(t,u)
  for i in eachindex(u)
    2 - u[i]
  end
  u
end
u0 = zeros(11); u0[6] = 10

ChrisRackauckas

julia> cache = init(prob,DP5())
typeof(utilde) = Array{Float64,2}
typeof(cache) = OrdinaryDiffEq.DP5Cache{Array{Float64,2},Any,Array{Float64,2},Any,Any}
cache = OrdinaryDiffEq.DP5Cache{Array{Float64,2},Array{Float64,2},Array{Float64,2},Array{Float64,2},OrdinaryDiffEq.DP5ConstantCache{Float64,Float64}}([0.260125 0.9676; 0.190313 0.645691; 0.660911 0.545968; 0.0671932 0.526845], [0.260125 0.9676; 0.190313 0.645691; 0.660911 0.545968; 0.0671932 0.526845], [0.0 0.0; 0.0 0.0; 0.0 0.0; 0.0 0.0], [0.0 0.0; 0.0 0.0; 0.0 0.0; 0.0 0.0], [0.0 0.0; 0.0 0.0; 0.0 0.0; 0.0 0.0], [0.0 0.0; 0.0 0.0; 0.0 0.0; 0.0 0.0], [0.0 0.0; 0.0 0.0; 0.0 0.0; 0.0 0.0], [0.0 0.0; 0.0 0.0; 0.0 0.0; 0.0 0.0], [0.0 0.0; 0.0 0.0; 0.0 0.0; 0.0 0.0], [0.0 0.0; 0.0 0.0; 0.0 0.0; 0.0 0.0], [0.0 0.0; 0.0 0.0; 0.0 0.0; 0.0 0.0], [0.0 0.0; 0.0 0.0; 0.0 0.0; 0.0 0.0], [0.0 0.0; 0.0 0.0; 0.0 0.0; 0.0 0.0], [0.0 0.0; 0.0 0.0; 0.0 0.0; 0.0 0.0], [0.0 0.0; 0.0 0.0; 0.0 0.0; 0.0 0.0], [0.0 0.0; 0.0 0.0; 0.0 0.0; 0.0 0.0], OrdinaryDiffEq.DP5ConstantCache{Flo

ChrisRackauckas

using DiffEqBase
using OrdinaryDiffEq

###############################################################################
#                                  Variables
###############################################################################

# Global variable to store the acceleration.
# This solution was selected just for the sake of simplification. Don't use
# global variables!

ChrisRackauckas

abstract DEDataArray{T} <: AbstractArray{T,1}

similar(A::DEDataArray) = deepcopy(A)

done(A::DEDataArray, i::Int64) = done(A.x,i)
eachindex(A::DEDataArray)      = eachindex(A.x)
next(A::DEDataArray, i::Int64) = next(A.x,i)
start(A::DEDataArray)          = start(A.x)

length(A::DEDataArray) = length(A.x)