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Julia-Intro
Raw
#README
From
https://github.com/JuliaComputing/JuliaBoxTutorials/tree/master/introductory-tutorials/intro-to-julia/short-version
lightly adapted.
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00.Jupyter_notebooks.ipynb
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01.Getting_to_know_Julia.ipynb
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02.Linear_Algebra.ipynb
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03.Using_packages.ipynb
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04.Intro_to_plotting.ipynb
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05.Julia_is_fast.ipynb
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Julia is fast\n",
"\n",
"Very often, benchmarks are used to compare languages. These benchmarks can lead to long discussions, first as to exactly what is being benchmarked and secondly what explains the differences. These simple questions can sometimes get more complicated than you at first might imagine.\n",
"\n",
"The purpose of this notebook is for you to see a simple benchmark for yourself. One can read the notebook and see what happened on the author's Macbook Pro with a 4-core Intel Core I7, or run the notebook yourself.\n",
"\n",
"(This material began life as a wonderful lecture by Steven Johnson at MIT: https://github.com/stevengj/18S096/blob/master/lectures/lecture1/Boxes-and-registers.ipynb.)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Outline of this notebook\n",
"\n",
"- Define the sum function\n",
"- Implementations & benchmarking of sum in...\n",
" - C (hand-written)\n",
" - C (hand-written with -ffast-math)\n",
" - python (built-in)\n",
" - python (numpy)\n",
" - python (hand-written)\n",
" - Julia (built-in)\n",
" - Julia (hand-written)\n",
" - Julia (hand-written with SIMD)\n",
"- Summary of benchmarks"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# `sum`: An easy enough function to understand"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Consider the **sum** function `sum(a)`, which computes\n",
"$$\n",
"\\mathrm{sum}(a) = \\sum_{i=1}^n a_i,\n",
"$$\n",
"where $n$ is the length of `a`."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"scrolled": false
},
"outputs": [
{
"data": {
"text/plain": [
"10000000-element Array{Float64,1}:\n",
" 0.29537308739291657 \n",
" 0.6222946431219714 \n",
" 0.994901236995569 \n",
" 0.8423773757016357 \n",
" 0.376362069462733 \n",
" 0.8878365850980467 \n",
" 0.5479896278606624 \n",
" 0.5292467771845317 \n",
" 0.1587866913317426 \n",
" 0.7289068946404345 \n",
" 0.3316223201559607 \n",
" 0.07231933734350471 \n",
" 0.082867557700953 \n",
" ⋮ \n",
" 0.8877975347567155 \n",
" 0.05052784236033103 \n",
" 0.1575147170030966 \n",
" 0.7142387156192505 \n",
" 0.3371085457226555 \n",
" 0.24799745462979916 \n",
" 0.4302614718615332 \n",
" 0.19020630043223075 \n",
" 0.8811645437498168 \n",
" 0.022302398214089303\n",
" 0.8928006901655872 \n",
" 0.09523210998675635 "
]
},
"execution_count": 1,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"a = rand(10^7) # 1D vector of random numbers, uniform on [0,1)"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
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"5.00129166729673e6"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
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],
"source": [
"sum(a)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The expected result is 0.5 * 10^7, since the mean of each entry is 0.5"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Benchmarking a few ways in a few languages"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" 0.005898 seconds (5 allocations: 176 bytes)\n"
]
},
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"5.00129166729673e6"
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},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"@time sum(a)"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" 0.006157 seconds (5 allocations: 176 bytes)\n"
]
},
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"data": {
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"execution_count": 8,
"metadata": {},
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],
"source": [
"@time sum(a)"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" 0.006957 seconds (5 allocations: 176 bytes)\n"
]
},
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"data": {
"text/plain": [
"5.00129166729673e6"
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"execution_count": 9,
"metadata": {},
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],
"source": [
"@time sum(a)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The `@time` macro can yield noisy results, so it's not our best choice for benchmarking!\n",
"\n",
"Luckily, Julia has a `BenchmarkTools.jl` package to make benchmarking easy and accurate:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# using Pkg\n",
"# Pkg.add(\"BenchmarkTools\")"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"scrolled": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" 4.436 ms (0 allocations: 0 bytes)\n"
]
},
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"data": {
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"5.00129166729673e6"
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"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"using BenchmarkTools \n",
"@btime sum($a)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# 1. The C language\n",
"\n",
"C is often considered the gold standard: difficult on the human, nice for the machine. Getting within a factor of 2 of C is often satisfying. Nonetheless, even within C, there are many kinds of optimizations possible that a naive C writer may or may not get the advantage of.\n",
"\n",
"The current author does not speak C, so he does not read the cell below, but is happy to know that you can put C code in a Julia session, compile it, and run it. Note that the `\"\"\"` wrap a multi-line string."
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"scrolled": false
},
"outputs": [
{
"data": {
"text/plain": [
"c_sum (generic function with 1 method)"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"using Libdl\n",
"C_code = \"\"\"\n",
"#include <stddef.h>\n",
"double c_sum(size_t n, double *X) {\n",
" double s = 0.0;\n",
" for (size_t i = 0; i < n; ++i) {\n",
" s += X[i];\n",
" }\n",
" return s;\n",
"}\n",
"\"\"\"\n",
"\n",
"const Clib = tempname() # make a temporary file\n",
"\n",
"\n",
"# compile to a shared library by piping C_code to gcc\n",
"# (works only if you have gcc installed):\n",
"\n",
"open(`gcc -fPIC -O3 -msse3 -xc -shared -o $(Clib * \".\" * Libdl.dlext) -`, \"w\") do f\n",
" print(f, C_code) \n",
"end\n",
"\n",
"# define a Julia function that calls the C function:\n",
"c_sum(X::Array{Float64}) = ccall((\"c_sum\", Clib), Float64, (Csize_t, Ptr{Float64}), length(X), X)"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"scrolled": false
},
"outputs": [
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"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"c_sum(a)"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"scrolled": false
},
"outputs": [
{
"data": {
"text/plain": [
"true"
]
},
"execution_count": 15,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"c_sum(a) ≈ sum(a) # type \\approx and then <TAB> to get the ≈ symbolb"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"c_sum(a) - sum(a) "
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"scrolled": true
},
"outputs": [],
"source": [
"≈ # alias for the `isapprox` function"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"scrolled": true
},
"outputs": [],
"source": [
"?isapprox"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can now benchmark the C code directly from Julia:"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"scrolled": false
},
"outputs": [
{
"data": {
"text/plain": [
"BenchmarkTools.Trial: \n",
" memory estimate: 0 bytes\n",
" allocs estimate: 0\n",
" --------------\n",
" minimum time: 8.652 ms (0.00% GC)\n",
" median time: 8.772 ms (0.00% GC)\n",
" mean time: 8.812 ms (0.00% GC)\n",
" maximum time: 9.737 ms (0.00% GC)\n",
" --------------\n",
" samples: 567\n",
" evals/sample: 1"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"c_bench = @benchmark c_sum($a)"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"scrolled": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"C: Fastest time was 8.652178 msec\n"
]
}
],
"source": [
"println(\"C: Fastest time was $(minimum(c_bench.times) / 1e6) msec\")"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
"text/plain": [
"Dict{Any,Any} with 1 entry:\n",
" \"C\" => 8.65218"
]
},
"execution_count": 18,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"d = Dict() # a \"dictionary\", i.e. an associative array\n",
"d[\"C\"] = minimum(c_bench.times) / 1e6 # in milliseconds\n",
"d"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
"text/plain": [
"Plots.GRBackend()"
]
},
"execution_count": 19,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"using Plots\n",
"gr()"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {},
"outputs": [
{
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},
"execution_count": 21,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"using Statistics # bring in statistical support for standard deviations\n",
"t = c_bench.times / 1e6 # times in milliseconds\n",
"m, σ = minimum(t), std(t)\n",
"\n",
"histogram(t, bins=500,\n",
" xlim=(m - 0.01, m + σ),\n",
" xlabel=\"milliseconds\", ylabel=\"count\", label=\"\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# 2. C with -ffast-math\n",
"\n",
"If we allow C to re-arrange the floating point operations, then it'll vectorize with SIMD (single instruction, multiple data) instructions."
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"c_sum_fastmath (generic function with 1 method)"
]
},
"execution_count": 22,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"const Clib_fastmath = tempname() # make a temporary file\n",
"\n",
"# The same as above but with a -ffast-math flag added\n",
"open(`gcc -fPIC -O3 -msse3 -xc -shared -ffast-math -o $(Clib_fastmath * \".\" * Libdl.dlext) -`, \"w\") do f\n",
" print(f, C_code) \n",
"end\n",
"\n",
"# define a Julia function that calls the C function:\n",
"c_sum_fastmath(X::Array{Float64}) = ccall((\"c_sum\", Clib_fastmath), Float64, (Csize_t, Ptr{Float64}), length(X), X)"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"BenchmarkTools.Trial: \n",
" memory estimate: 0 bytes\n",
" allocs estimate: 0\n",
" --------------\n",
" minimum time: 4.796 ms (0.00% GC)\n",
" median time: 4.975 ms (0.00% GC)\n",
" mean time: 5.054 ms (0.00% GC)\n",
" maximum time: 7.738 ms (0.00% GC)\n",
" --------------\n",
" samples: 987\n",
" evals/sample: 1"
]
},
"execution_count": 23,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"c_fastmath_bench = @benchmark $c_sum_fastmath($a)"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"4.796354"
]
},
"execution_count": 24,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"d[\"C -ffast-math\"] = minimum(c_fastmath_bench.times) / 1e6 # in milliseconds"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# 3. Python's built in `sum` "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The `PyCall` package provides a Julia interface to Python:"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {
"scrolled": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\u001b[32m\u001b[1m Updating\u001b[22m\u001b[39m registry at `~/.julia/registries/General`\n",
"\u001b[32m\u001b[1m Updating\u001b[22m\u001b[39m git-repo `https://github.com/JuliaRegistries/General.git`\n",
"\u001b[2K\u001b[?25h[1mFetching:\u001b[22m\u001b[39m [========================================>] 100.0 %.0 %\u001b[32m\u001b[1m Resolving\u001b[22m\u001b[39m package versions...\n",
"\u001b[32m\u001b[1m Updating\u001b[22m\u001b[39m `~/.julia/environments/v1.1/Project.toml`\n",
" \u001b[90m [438e738f]\u001b[39m\u001b[92m + PyCall v1.91.2\u001b[39m\n",
"\u001b[32m\u001b[1m Updating\u001b[22m\u001b[39m `~/.julia/environments/v1.1/Manifest.toml`\n",
"\u001b[90m [no changes]\u001b[39m\n"
]
}
],
"source": [
"using Pkg; Pkg.add(\"PyCall\")\n",
"using PyCall"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {
"scrolled": false
},
"outputs": [
{
"data": {
"text/plain": [
"PyObject <built-in function sum>"
]
},
"execution_count": 27,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# get the Python built-in \"sum\" function:\n",
"pysum = pybuiltin(\"sum\")"
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {
"scrolled": false
},
"outputs": [
{
"data": {
"text/plain": [
"5.001291667296473e6"
]
},
"execution_count": 28,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pysum(a)"
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {
"scrolled": false
},
"outputs": [
{
"data": {
"text/plain": [
"true"
]
},
"execution_count": 29,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pysum(a) ≈ sum(a)"
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {
"scrolled": false
},
"outputs": [
{
"data": {
"text/plain": [
"BenchmarkTools.Trial: \n",
" memory estimate: 368 bytes\n",
" allocs estimate: 8\n",
" --------------\n",
" minimum time: 817.063 ms (0.00% GC)\n",
" median time: 840.961 ms (0.00% GC)\n",
" mean time: 846.405 ms (0.00% GC)\n",
" maximum time: 888.676 ms (0.00% GC)\n",
" --------------\n",
" samples: 6\n",
" evals/sample: 1"
]
},
"execution_count": 30,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"py_list_bench = @benchmark $pysum($a)"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {
"scrolled": false
},
"outputs": [
{
"data": {
"text/plain": [
"Dict{Any,Any} with 3 entries:\n",
" \"C\" => 8.65218\n",
" \"Python built-in\" => 817.063\n",
" \"C -ffast-math\" => 4.79635"
]
},
"execution_count": 31,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"d[\"Python built-in\"] = minimum(py_list_bench.times) / 1e6\n",
"d"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# 4. Python: `numpy` \n",
"\n",
"## Takes advantage of hardware \"SIMD\", but only works when it works.\n",
"\n",
"`numpy` is an optimized C library, callable from Python.\n",
"It may be installed within Julia as follows:"
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {
"scrolled": false
},
"outputs": [
{
"ename": "ArgumentError",
"evalue": "ArgumentError: Package Conda not found in current path:\n- Run `import Pkg; Pkg.add(\"Conda\")` to install the Conda package.\n",
"output_type": "error",
"traceback": [
"ArgumentError: Package Conda not found in current path:\n- Run `import Pkg; Pkg.add(\"Conda\")` to install the Conda package.\n",
"",
"Stacktrace:",
" [1] require(::Module, ::Symbol) at ./loading.jl:823",
" [2] top-level scope at In[32]:1"
]
}
],
"source": [
"# using Pkg; Pkg.add(\"Conda\")\n",
"using Conda"
]
},
{
"cell_type": "code",
"execution_count": 33,
"metadata": {},
"outputs": [],
"source": [
"# Conda.add(\"numpy\")"
]
},
{
"cell_type": "code",
"execution_count": 34,
"metadata": {
"scrolled": false
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"┌ Warning: `getindex(o::PyObject, s::AbstractString)` is deprecated in favor of dot overloading (`getproperty`) so elements should now be accessed as e.g. `o.\"s\"` instead of `o[\"s\"]`.\n",
"│ caller = top-level scope at In[34]:1\n",
"└ @ Core In[34]:1\n"
]
},
{
"data": {
"text/plain": [
"BenchmarkTools.Trial: \n",
" memory estimate: 368 bytes\n",
" allocs estimate: 8\n",
" --------------\n",
" minimum time: 4.536 ms (0.00% GC)\n",
" median time: 4.721 ms (0.00% GC)\n",
" mean time: 4.811 ms (0.00% GC)\n",
" maximum time: 6.929 ms (0.00% GC)\n",
" --------------\n",
" samples: 1036\n",
" evals/sample: 1"
]
},
"execution_count": 34,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"numpy_sum = pyimport(\"numpy\")[\"sum\"]\n",
"\n",
"py_numpy_bench = @benchmark $numpy_sum($a)"
]
},
{
"cell_type": "code",
"execution_count": 35,
"metadata": {
"scrolled": false
},
"outputs": [
{
"data": {
"text/plain": [
"5.001291667296729e6"
]
},
"execution_count": 35,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"numpy_sum(a)"
]
},
{
"cell_type": "code",
"execution_count": 36,
"metadata": {
"scrolled": false
},
"outputs": [
{
"data": {
"text/plain": [
"true"
]
},
"execution_count": 36,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"numpy_sum(a) ≈ sum(a)"
]
},
{
"cell_type": "code",
"execution_count": 37,
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
"text/plain": [
"Dict{Any,Any} with 4 entries:\n",
" \"C\" => 8.65218\n",
" \"Python numpy\" => 4.53581\n",
" \"Python built-in\" => 817.063\n",
" \"C -ffast-math\" => 4.79635"
]
},
"execution_count": 37,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"d[\"Python numpy\"] = minimum(py_numpy_bench.times) / 1e6\n",
"d"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# 5. Python, hand-written "
]
},
{
"cell_type": "code",
"execution_count": 38,
"metadata": {
"scrolled": false
},
"outputs": [
{
"data": {
"text/plain": [
"PyObject <function py_sum at 0x7ff6d1c150d0>"
]
},
"execution_count": 38,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"py\"\"\"\n",
"def py_sum(A):\n",
" s = 0.0\n",
" for a in A:\n",
" s += a\n",
" return s\n",
"\"\"\"\n",
"\n",
"sum_py = py\"py_sum\""
]
},
{
"cell_type": "code",
"execution_count": 39,
"metadata": {
"scrolled": false
},
"outputs": [
{
"data": {
"text/plain": [
"BenchmarkTools.Trial: \n",
" memory estimate: 368 bytes\n",
" allocs estimate: 8\n",
" --------------\n",
" minimum time: 1.149 s (0.00% GC)\n",
" median time: 1.163 s (0.00% GC)\n",
" mean time: 1.169 s (0.00% GC)\n",
" maximum time: 1.210 s (0.00% GC)\n",
" --------------\n",
" samples: 5\n",
" evals/sample: 1"
]
},
"execution_count": 39,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"py_hand = @benchmark $sum_py($a)"
]
},
{
"cell_type": "code",
"execution_count": 40,
"metadata": {
"scrolled": false
},
"outputs": [
{
"data": {
"text/plain": [
"5.001291667296473e6"
]
},
"execution_count": 40,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"sum_py(a)"
]
},
{
"cell_type": "code",
"execution_count": 41,
"metadata": {
"scrolled": false
},
"outputs": [
{
"data": {
"text/plain": [
"true"
]
},
"execution_count": 41,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"sum_py(a) ≈ sum(a)"
]
},
{
"cell_type": "code",
"execution_count": 42,
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
"text/plain": [
"Dict{Any,Any} with 5 entries:\n",
" \"C\" => 8.65218\n",
" \"Python numpy\" => 4.53581\n",
" \"Python hand-written\" => 1148.87\n",
" \"Python built-in\" => 817.063\n",
" \"C -ffast-math\" => 4.79635"
]
},
"execution_count": 42,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"d[\"Python hand-written\"] = minimum(py_hand.times) / 1e6\n",
"d"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# 6. Julia (built-in) \n",
"\n",
"## Written directly in Julia, not in C!"
]
},
{
"cell_type": "code",
"execution_count": 43,
"metadata": {
"scrolled": false
},
"outputs": [
{
"data": {
"text/html": [
"sum(a::<b>AbstractArray</b>) in Base at <a href=\"https://github.com/JuliaLang/julia/tree/80516ca20297a67b996caa08c38786332379b6a5/base/reducedim.jl#L648\" target=\"_blank\">reducedim.jl:648</a>"
],
"text/plain": [
"sum(a::AbstractArray) in Base at reducedim.jl:648"
]
},
"execution_count": 43,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"@which sum(a)"
]
},
{
"cell_type": "code",
"execution_count": 44,
"metadata": {
"scrolled": false
},
"outputs": [
{
"data": {
"text/plain": [
"BenchmarkTools.Trial: \n",
" memory estimate: 0 bytes\n",
" allocs estimate: 0\n",
" --------------\n",
" minimum time: 4.409 ms (0.00% GC)\n",
" median time: 4.549 ms (0.00% GC)\n",
" mean time: 4.613 ms (0.00% GC)\n",
" maximum time: 6.061 ms (0.00% GC)\n",
" --------------\n",
" samples: 1081\n",
" evals/sample: 1"
]
},
"execution_count": 44,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"j_bench = @benchmark sum($a)"
]
},
{
"cell_type": "code",
"execution_count": 45,
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
"text/plain": [
"Dict{Any,Any} with 6 entries:\n",
" \"C\" => 8.65218\n",
" \"Python numpy\" => 4.53581\n",
" \"Python hand-written\" => 1148.87\n",
" \"Python built-in\" => 817.063\n",
" \"Julia built-in\" => 4.40938\n",
" \"C -ffast-math\" => 4.79635"
]
},
"execution_count": 45,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"d[\"Julia built-in\"] = minimum(j_bench.times) / 1e6\n",
"d"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# 7. Julia (hand-written) "
]
},
{
"cell_type": "code",
"execution_count": 46,
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
"text/plain": [
"mysum (generic function with 1 method)"
]
},
"execution_count": 46,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"function mysum(A) \n",
" s = 0.0 # s = zero(eltype(a))\n",
" for a in A\n",
" s += a\n",
" end\n",
" s\n",
"end"
]
},
{
"cell_type": "code",
"execution_count": 47,
"metadata": {
"scrolled": false
},
"outputs": [
{
"data": {
"text/plain": [
"BenchmarkTools.Trial: \n",
" memory estimate: 0 bytes\n",
" allocs estimate: 0\n",
" --------------\n",
" minimum time: 8.684 ms (0.00% GC)\n",
" median time: 8.893 ms (0.00% GC)\n",
" mean time: 8.981 ms (0.00% GC)\n",
" maximum time: 10.601 ms (0.00% GC)\n",
" --------------\n",
" samples: 556\n",
" evals/sample: 1"
]
},
"execution_count": 47,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"j_bench_hand = @benchmark mysum($a)"
]
},
{
"cell_type": "code",
"execution_count": 48,
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
"text/plain": [
"Dict{Any,Any} with 7 entries:\n",
" \"C\" => 8.65218\n",
" \"Python numpy\" => 4.53581\n",
" \"Julia hand-written\" => 8.68355\n",
" \"Python hand-written\" => 1148.87\n",
" \"Python built-in\" => 817.063\n",
" \"Julia built-in\" => 4.40938\n",
" \"C -ffast-math\" => 4.79635"
]
},
"execution_count": 48,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"d[\"Julia hand-written\"] = minimum(j_bench_hand.times) / 1e6\n",
"d"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# 8. Julia (hand-written w. simd) "
]
},
{
"cell_type": "code",
"execution_count": 49,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"mysum_simd (generic function with 1 method)"
]
},
"execution_count": 49,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"function mysum_simd(A) \n",
" s = 0.0 # s = zero(eltype(A))\n",
" @simd for a in A\n",
" s += a\n",
" end\n",
" s\n",
"end"
]
},
{
"cell_type": "code",
"execution_count": 50,
"metadata": {
"scrolled": false
},
"outputs": [
{
"data": {
"text/plain": [
"BenchmarkTools.Trial: \n",
" memory estimate: 0 bytes\n",
" allocs estimate: 0\n",
" --------------\n",
" minimum time: 4.295 ms (0.00% GC)\n",
" median time: 4.501 ms (0.00% GC)\n",
" mean time: 4.582 ms (0.00% GC)\n",
" maximum time: 7.126 ms (0.00% GC)\n",
" --------------\n",
" samples: 1088\n",
" evals/sample: 1"
]
},
"execution_count": 50,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"j_bench_hand_simd = @benchmark mysum_simd($a)"
]
},
{
"cell_type": "code",
"execution_count": 51,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"5.001291667296788e6"
]
},
"execution_count": 51,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"mysum_simd(a)"
]
},
{
"cell_type": "code",
"execution_count": 52,
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
"text/plain": [
"Dict{Any,Any} with 8 entries:\n",
" \"Julia hand-written simd\" => 4.29476\n",
" \"C\" => 8.65218\n",
" \"Python numpy\" => 4.53581\n",
" \"Julia hand-written\" => 8.68355\n",
" \"Python hand-written\" => 1148.87\n",
" \"Python built-in\" => 817.063\n",
" \"Julia built-in\" => 4.40938\n",
" \"C -ffast-math\" => 4.79635"
]
},
"execution_count": 52,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"d[\"Julia hand-written simd\"] = minimum(j_bench_hand_simd.times) / 1e6\n",
"d"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Summary"
]
},
{
"cell_type": "code",
"execution_count": 53,
"metadata": {
"scrolled": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Julia hand-written simd.....4.3\n",
"Julia built-in..............4.4\n",
"Python numpy................4.5\n",
"C -ffast-math...............4.8\n",
"C...........................8.7\n",
"Julia hand-written..........8.7\n",
"Python built-in...........817.1\n",
"Python hand-written......1148.9\n"
]
}
],
"source": [
"for (key, value) in sort(collect(d), by=last)\n",
" println(rpad(key, 25, \".\"), lpad(round(value; digits=1), 6, \".\"))\n",
"end"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"anaconda-cloud": {},
"kernelspec": {
"display_name": "Julia 1.1.0",
"language": "julia",
"name": "julia-1.1"
},
"language_info": {
"file_extension": ".jl",
"mimetype": "application/julia",
"name": "julia",
"version": "1.1.0"
},
"toc": {
"colors": {
"hover_highlight": "#DAA520",
"running_highlight": "#FF0000",
"selected_highlight": "#FFD700"
},
"moveMenuLeft": true,
"nav_menu": {
"height": "212px",
"width": "252px"
},
"navigate_menu": true,
"number_sections": true,
"sideBar": true,
"threshold": "2",
"toc_cell": false,
"toc_section_display": "block",
"toc_window_display": false
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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