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Notebook benchmarking C, Python, Julia and R
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9 - Julia is fast (modified).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",
"_Note_: I (jmcastagnetto) run this notebook on an HP laptop witha a 4-core Ryzen 3 3200U with Radeon Vega Mobile Gfx, 16GB (14GB accessible, 2GB for graphics) RAM, and SSD Drive. Using Julia 1.7.0, Python 3.8.10 and R 4.1.2\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",
" - R base sum\n",
" - R hand-written sum\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": 58,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"10000000-element Vector{Float64}:\n",
" 0.23554841155162087\n",
" 0.4144761515203421\n",
" 0.6209139843388389\n",
" 0.7587124999975389\n",
" 0.5132166436202502\n",
" 0.8978720084048397\n",
" 0.9556059573349612\n",
" 0.7871201114775244\n",
" 0.821826879968898\n",
" 0.3315031832122076\n",
" 0.8058013898958418\n",
" 0.2522187421336839\n",
" 0.3577025114637479\n",
" ⋮\n",
" 0.10902044017456214\n",
" 0.37427152416749687\n",
" 0.00721461542946189\n",
" 0.19167172337865035\n",
" 0.9578601054015895\n",
" 0.5075592977642448\n",
" 0.13686593615379727\n",
" 0.2378202144283894\n",
" 0.6567190147170613\n",
" 0.8031968001870893\n",
" 0.7493721234931605\n",
" 0.3323185237701626"
]
},
"execution_count": 58,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"a = rand(10^7) # 1D vector of random numbers, uniform on [0,1)"
]
},
{
"cell_type": "code",
"execution_count": 59,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"4.998784559011245e6"
]
},
"execution_count": 59,
"metadata": {},
"output_type": "execute_result"
}
],
"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": 60,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" 0.006959 seconds (1 allocation: 16 bytes)\n"
]
},
{
"data": {
"text/plain": [
"4.998784559011245e6"
]
},
"execution_count": 60,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"@time sum(a)"
]
},
{
"cell_type": "code",
"execution_count": 61,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" 0.007074 seconds (1 allocation: 16 bytes)\n"
]
},
{
"data": {
"text/plain": [
"4.998784559011245e6"
]
},
"execution_count": 61,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"@time sum(a)"
]
},
{
"cell_type": "code",
"execution_count": 62,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" 0.008090 seconds (1 allocation: 16 bytes)\n"
]
},
{
"data": {
"text/plain": [
"4.998784559011245e6"
]
},
"execution_count": 62,
"metadata": {},
"output_type": "execute_result"
}
],
"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": 63,
"metadata": {},
"outputs": [],
"source": [
"#using Pkg\n",
"#Pkg.add(\"BenchmarkTools\")"
]
},
{
"cell_type": "code",
"execution_count": 64,
"metadata": {},
"outputs": [],
"source": [
"using BenchmarkTools "
]
},
{
"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": 65,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"WARNING: redefinition of constant Clib. This may fail, cause incorrect answers, or produce other errors.\n"
]
},
{
"data": {
"text/plain": [
"c_sum (generic function with 1 method)"
]
},
"execution_count": 65,
"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": 66,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"4.998784559011017e6"
]
},
"execution_count": 66,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"c_sum(a)"
]
},
{
"cell_type": "code",
"execution_count": 67,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"true"
]
},
"execution_count": 67,
"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": 68,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"-2.2817403078079224e-7"
]
},
"execution_count": 68,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"c_sum(a) - sum(a) "
]
},
{
"cell_type": "code",
"execution_count": 69,
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
"text/plain": [
"isapprox (generic function with 19 methods)"
]
},
"execution_count": 69,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"≈ # alias for the `isapprox` function"
]
},
{
"cell_type": "code",
"execution_count": 70,
"metadata": {
"scrolled": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"search: \u001b[0m\u001b[1mi\u001b[22m\u001b[0m\u001b[1ms\u001b[22m\u001b[0m\u001b[1ma\u001b[22m\u001b[0m\u001b[1mp\u001b[22m\u001b[0m\u001b[1mp\u001b[22m\u001b[0m\u001b[1mr\u001b[22m\u001b[0m\u001b[1mo\u001b[22m\u001b[0m\u001b[1mx\u001b[22m\n",
"\n"
]
},
{
"data": {
"text/latex": [
"\\begin{verbatim}\n",
"isapprox(x, y; atol::Real=0, rtol::Real=atol>0 ? 0 : √eps, nans::Bool=false[, norm::Function])\n",
"\\end{verbatim}\n",
"Inexact equality comparison. Two numbers compare equal if their relative distance \\emph{or} their absolute distance is within tolerance bounds: \\texttt{isapprox} returns \\texttt{true} if \\texttt{norm(x-y) <= max(atol, rtol*max(norm(x), norm(y)))}. The default \\texttt{atol} is zero and the default \\texttt{rtol} depends on the types of \\texttt{x} and \\texttt{y}. The keyword argument \\texttt{nans} determines whether or not NaN values are considered equal (defaults to false).\n",
"\n",
"For real or complex floating-point values, if an \\texttt{atol > 0} is not specified, \\texttt{rtol} defaults to the square root of \\href{@ref}{\\texttt{eps}} of the type of \\texttt{x} or \\texttt{y}, whichever is bigger (least precise). This corresponds to requiring equality of about half of the significand digits. Otherwise, e.g. for integer arguments or if an \\texttt{atol > 0} is supplied, \\texttt{rtol} defaults to zero.\n",
"\n",
"The \\texttt{norm} keyword defaults to \\texttt{abs} for numeric \\texttt{(x,y)} and to \\texttt{LinearAlgebra.norm} for arrays (where an alternative \\texttt{norm} choice is sometimes useful). When \\texttt{x} and \\texttt{y} are arrays, if \\texttt{norm(x-y)} is not finite (i.e. \\texttt{±Inf} or \\texttt{NaN}), the comparison falls back to checking whether all elements of \\texttt{x} and \\texttt{y} are approximately equal component-wise.\n",
"\n",
"The binary operator \\texttt{≈} is equivalent to \\texttt{isapprox} with the default arguments, and \\texttt{x ≉ y} is equivalent to \\texttt{!isapprox(x,y)}.\n",
"\n",
"Note that \\texttt{x ≈ 0} (i.e., comparing to zero with the default tolerances) is equivalent to \\texttt{x == 0} since the default \\texttt{atol} is \\texttt{0}. In such cases, you should either supply an appropriate \\texttt{atol} (or use \\texttt{norm(x) ≤ atol}) or rearrange your code (e.g. use \\texttt{x ≈ y} rather than \\texttt{x - y ≈ 0}). It is not possible to pick a nonzero \\texttt{atol} automatically because it depends on the overall scaling (the \"units\") of your problem: for example, in \\texttt{x - y ≈ 0}, \\texttt{atol=1e-9} is an absurdly small tolerance if \\texttt{x} is the \\href{https://en.wikipedia.org/wiki/Earth_radius}{radius of the Earth} in meters, but an absurdly large tolerance if \\texttt{x} is the \\href{https://en.wikipedia.org/wiki/Bohr_radius}{radius of a Hydrogen atom} in meters.\n",
"\n",
"\\begin{quote}\n",
"\\textbf{compat}\n",
"\n",
"Julia 1.6\n",
"\n",
"Passing the \\texttt{norm} keyword argument when comparing numeric (non-array) arguments requires Julia 1.6 or later.\n",
"\n",
"\\end{quote}\n",
"\\section{Examples}\n",
"\\begin{verbatim}\n",
"julia> isapprox(0.1, 0.15; atol=0.05)\n",
"true\n",
"\n",
"julia> isapprox(0.1, 0.15; rtol=0.34)\n",
"true\n",
"\n",
"julia> isapprox(0.1, 0.15; rtol=0.33)\n",
"false\n",
"\n",
"julia> 0.1 + 1e-10 ≈ 0.1\n",
"true\n",
"\n",
"julia> 1e-10 ≈ 0\n",
"false\n",
"\n",
"julia> isapprox(1e-10, 0, atol=1e-8)\n",
"true\n",
"\n",
"julia> isapprox([10.0^9, 1.0], [10.0^9, 2.0]) # using `norm`\n",
"true\n",
"\\end{verbatim}\n",
"\\rule{\\textwidth}{1pt}\n",
"\\begin{verbatim}\n",
"isapprox(x; kwargs...) / ≈(x; kwargs...)\n",
"\\end{verbatim}\n",
"Create a function that compares its argument to \\texttt{x} using \\texttt{≈}, i.e. a function equivalent to \\texttt{y -> y ≈ x}.\n",
"\n",
"The keyword arguments supported here are the same as those in the 2-argument \\texttt{isapprox}.\n",
"\n",
"\\begin{quote}\n",
"\\textbf{compat}\n",
"\n",
"Julia 1.5\n",
"\n",
"This method requires Julia 1.5 or later.\n",
"\n",
"\\end{quote}\n",
"\\rule{\\textwidth}{1pt}\n",
"\\begin{verbatim}\n",
"isapprox(x::FixedPoint, y::FixedPoint; rtol=0, atol=max(eps(x), eps(y)))\n",
"\\end{verbatim}\n",
"For FixedPoint numbers, the default criterion is that \\texttt{x} and \\texttt{y} differ by no more than \\texttt{eps}, the separation between adjacent fixed-point numbers.\n",
"\n",
"\\rule{\\textwidth}{1pt}\n",
"\\begin{verbatim}\n",
"isapprox(df1::AbstractDataFrame, df2::AbstractDataFrame;\n",
" rtol::Real=atol>0 ? 0 : √eps, atol::Real=0,\n",
" nans::Bool=false, norm::Function=norm)\n",
"\\end{verbatim}\n",
"Inexact equality comparison. \\texttt{df1} and \\texttt{df2} must have the same size and column names. Return \\texttt{true} if \\texttt{isapprox} with given keyword arguments applied to all pairs of columns stored in \\texttt{df1} and \\texttt{df2} returns \\texttt{true}.\n",
"\n"
],
"text/markdown": [
"```\n",
"isapprox(x, y; atol::Real=0, rtol::Real=atol>0 ? 0 : √eps, nans::Bool=false[, norm::Function])\n",
"```\n",
"\n",
"Inexact equality comparison. Two numbers compare equal if their relative distance *or* their absolute distance is within tolerance bounds: `isapprox` returns `true` if `norm(x-y) <= max(atol, rtol*max(norm(x), norm(y)))`. The default `atol` is zero and the default `rtol` depends on the types of `x` and `y`. The keyword argument `nans` determines whether or not NaN values are considered equal (defaults to false).\n",
"\n",
"For real or complex floating-point values, if an `atol > 0` is not specified, `rtol` defaults to the square root of [`eps`](@ref) of the type of `x` or `y`, whichever is bigger (least precise). This corresponds to requiring equality of about half of the significand digits. Otherwise, e.g. for integer arguments or if an `atol > 0` is supplied, `rtol` defaults to zero.\n",
"\n",
"The `norm` keyword defaults to `abs` for numeric `(x,y)` and to `LinearAlgebra.norm` for arrays (where an alternative `norm` choice is sometimes useful). When `x` and `y` are arrays, if `norm(x-y)` is not finite (i.e. `±Inf` or `NaN`), the comparison falls back to checking whether all elements of `x` and `y` are approximately equal component-wise.\n",
"\n",
"The binary operator `≈` is equivalent to `isapprox` with the default arguments, and `x ≉ y` is equivalent to `!isapprox(x,y)`.\n",
"\n",
"Note that `x ≈ 0` (i.e., comparing to zero with the default tolerances) is equivalent to `x == 0` since the default `atol` is `0`. In such cases, you should either supply an appropriate `atol` (or use `norm(x) ≤ atol`) or rearrange your code (e.g. use `x ≈ y` rather than `x - y ≈ 0`). It is not possible to pick a nonzero `atol` automatically because it depends on the overall scaling (the \"units\") of your problem: for example, in `x - y ≈ 0`, `atol=1e-9` is an absurdly small tolerance if `x` is the [radius of the Earth](https://en.wikipedia.org/wiki/Earth_radius) in meters, but an absurdly large tolerance if `x` is the [radius of a Hydrogen atom](https://en.wikipedia.org/wiki/Bohr_radius) in meters.\n",
"\n",
"!!! compat \"Julia 1.6\"\n",
" Passing the `norm` keyword argument when comparing numeric (non-array) arguments requires Julia 1.6 or later.\n",
"\n",
"\n",
"# Examples\n",
"\n",
"```jldoctest\n",
"julia> isapprox(0.1, 0.15; atol=0.05)\n",
"true\n",
"\n",
"julia> isapprox(0.1, 0.15; rtol=0.34)\n",
"true\n",
"\n",
"julia> isapprox(0.1, 0.15; rtol=0.33)\n",
"false\n",
"\n",
"julia> 0.1 + 1e-10 ≈ 0.1\n",
"true\n",
"\n",
"julia> 1e-10 ≈ 0\n",
"false\n",
"\n",
"julia> isapprox(1e-10, 0, atol=1e-8)\n",
"true\n",
"\n",
"julia> isapprox([10.0^9, 1.0], [10.0^9, 2.0]) # using `norm`\n",
"true\n",
"```\n",
"\n",
"---\n",
"\n",
"```\n",
"isapprox(x; kwargs...) / ≈(x; kwargs...)\n",
"```\n",
"\n",
"Create a function that compares its argument to `x` using `≈`, i.e. a function equivalent to `y -> y ≈ x`.\n",
"\n",
"The keyword arguments supported here are the same as those in the 2-argument `isapprox`.\n",
"\n",
"!!! compat \"Julia 1.5\"\n",
" This method requires Julia 1.5 or later.\n",
"\n",
"\n",
"---\n",
"\n",
"```\n",
"isapprox(x::FixedPoint, y::FixedPoint; rtol=0, atol=max(eps(x), eps(y)))\n",
"```\n",
"\n",
"For FixedPoint numbers, the default criterion is that `x` and `y` differ by no more than `eps`, the separation between adjacent fixed-point numbers.\n",
"\n",
"---\n",
"\n",
"```\n",
"isapprox(df1::AbstractDataFrame, df2::AbstractDataFrame;\n",
" rtol::Real=atol>0 ? 0 : √eps, atol::Real=0,\n",
" nans::Bool=false, norm::Function=norm)\n",
"```\n",
"\n",
"Inexact equality comparison. `df1` and `df2` must have the same size and column names. Return `true` if `isapprox` with given keyword arguments applied to all pairs of columns stored in `df1` and `df2` returns `true`.\n"
],
"text/plain": [
"\u001b[36m isapprox(x, y; atol::Real=0, rtol::Real=atol>0 ? 0 : √eps, nans::Bool=false[, norm::Function])\u001b[39m\n",
"\n",
" Inexact equality comparison. Two numbers compare equal if their relative\n",
" distance \u001b[4mor\u001b[24m their absolute distance is within tolerance bounds: \u001b[36misapprox\u001b[39m\n",
" returns \u001b[36mtrue\u001b[39m if \u001b[36mnorm(x-y) <= max(atol, rtol*max(norm(x), norm(y)))\u001b[39m. The\n",
" default \u001b[36matol\u001b[39m is zero and the default \u001b[36mrtol\u001b[39m depends on the types of \u001b[36mx\u001b[39m and \u001b[36my\u001b[39m.\n",
" The keyword argument \u001b[36mnans\u001b[39m determines whether or not NaN values are\n",
" considered equal (defaults to false).\n",
"\n",
" For real or complex floating-point values, if an \u001b[36matol > 0\u001b[39m is not specified,\n",
" \u001b[36mrtol\u001b[39m defaults to the square root of \u001b[36meps\u001b[39m of the type of \u001b[36mx\u001b[39m or \u001b[36my\u001b[39m, whichever is\n",
" bigger (least precise). This corresponds to requiring equality of about half\n",
" of the significand digits. Otherwise, e.g. for integer arguments or if an\n",
" \u001b[36matol > 0\u001b[39m is supplied, \u001b[36mrtol\u001b[39m defaults to zero.\n",
"\n",
" The \u001b[36mnorm\u001b[39m keyword defaults to \u001b[36mabs\u001b[39m for numeric \u001b[36m(x,y)\u001b[39m and to \u001b[36mLinearAlgebra.norm\u001b[39m\n",
" for arrays (where an alternative \u001b[36mnorm\u001b[39m choice is sometimes useful). When \u001b[36mx\u001b[39m\n",
" and \u001b[36my\u001b[39m are arrays, if \u001b[36mnorm(x-y)\u001b[39m is not finite (i.e. \u001b[36m±Inf\u001b[39m or \u001b[36mNaN\u001b[39m), the\n",
" comparison falls back to checking whether all elements of \u001b[36mx\u001b[39m and \u001b[36my\u001b[39m are\n",
" approximately equal component-wise.\n",
"\n",
" The binary operator \u001b[36m≈\u001b[39m is equivalent to \u001b[36misapprox\u001b[39m with the default arguments,\n",
" and \u001b[36mx ≉ y\u001b[39m is equivalent to \u001b[36m!isapprox(x,y)\u001b[39m.\n",
"\n",
" Note that \u001b[36mx ≈ 0\u001b[39m (i.e., comparing to zero with the default tolerances) is\n",
" equivalent to \u001b[36mx == 0\u001b[39m since the default \u001b[36matol\u001b[39m is \u001b[36m0\u001b[39m. In such cases, you should\n",
" either supply an appropriate \u001b[36matol\u001b[39m (or use \u001b[36mnorm(x) ≤ atol\u001b[39m) or rearrange your\n",
" code (e.g. use \u001b[36mx ≈ y\u001b[39m rather than \u001b[36mx - y ≈ 0\u001b[39m). It is not possible to pick a\n",
" nonzero \u001b[36matol\u001b[39m automatically because it depends on the overall scaling (the\n",
" \"units\") of your problem: for example, in \u001b[36mx - y ≈ 0\u001b[39m, \u001b[36matol=1e-9\u001b[39m is an\n",
" absurdly small tolerance if \u001b[36mx\u001b[39m is the radius of the Earth\n",
" (https://en.wikipedia.org/wiki/Earth_radius) in meters, but an absurdly\n",
" large tolerance if \u001b[36mx\u001b[39m is the radius of a Hydrogen atom\n",
" (https://en.wikipedia.org/wiki/Bohr_radius) in meters.\n",
"\n",
"\u001b[39m\u001b[1m │ \u001b[22m\u001b[39m\u001b[1mJulia 1.6\u001b[22m\n",
"\u001b[39m\u001b[1m │\u001b[22m\n",
"\u001b[39m\u001b[1m │\u001b[22m Passing the \u001b[36mnorm\u001b[39m keyword argument when comparing numeric\n",
"\u001b[39m\u001b[1m │\u001b[22m (non-array) arguments requires Julia 1.6 or later.\n",
"\n",
"\u001b[1m Examples\u001b[22m\n",
"\u001b[1m ≡≡≡≡≡≡≡≡≡≡\u001b[22m\n",
"\n",
"\u001b[36m julia> isapprox(0.1, 0.15; atol=0.05)\u001b[39m\n",
"\u001b[36m true\u001b[39m\n",
"\u001b[36m \u001b[39m\n",
"\u001b[36m julia> isapprox(0.1, 0.15; rtol=0.34)\u001b[39m\n",
"\u001b[36m true\u001b[39m\n",
"\u001b[36m \u001b[39m\n",
"\u001b[36m julia> isapprox(0.1, 0.15; rtol=0.33)\u001b[39m\n",
"\u001b[36m false\u001b[39m\n",
"\u001b[36m \u001b[39m\n",
"\u001b[36m julia> 0.1 + 1e-10 ≈ 0.1\u001b[39m\n",
"\u001b[36m true\u001b[39m\n",
"\u001b[36m \u001b[39m\n",
"\u001b[36m julia> 1e-10 ≈ 0\u001b[39m\n",
"\u001b[36m false\u001b[39m\n",
"\u001b[36m \u001b[39m\n",
"\u001b[36m julia> isapprox(1e-10, 0, atol=1e-8)\u001b[39m\n",
"\u001b[36m true\u001b[39m\n",
"\u001b[36m \u001b[39m\n",
"\u001b[36m julia> isapprox([10.0^9, 1.0], [10.0^9, 2.0]) # using `norm`\u001b[39m\n",
"\u001b[36m true\u001b[39m\n",
"\n",
" ────────────────────────────────────────────────────────────────────────────\n",
"\n",
"\u001b[36m isapprox(x; kwargs...) / ≈(x; kwargs...)\u001b[39m\n",
"\n",
" Create a function that compares its argument to \u001b[36mx\u001b[39m using \u001b[36m≈\u001b[39m, i.e. a function\n",
" equivalent to \u001b[36my -> y ≈ x\u001b[39m.\n",
"\n",
" The keyword arguments supported here are the same as those in the 2-argument\n",
" \u001b[36misapprox\u001b[39m.\n",
"\n",
"\u001b[39m\u001b[1m │ \u001b[22m\u001b[39m\u001b[1mJulia 1.5\u001b[22m\n",
"\u001b[39m\u001b[1m │\u001b[22m\n",
"\u001b[39m\u001b[1m │\u001b[22m This method requires Julia 1.5 or later.\n",
"\n",
" ────────────────────────────────────────────────────────────────────────────\n",
"\n",
"\u001b[36m isapprox(x::FixedPoint, y::FixedPoint; rtol=0, atol=max(eps(x), eps(y)))\u001b[39m\n",
"\n",
" For FixedPoint numbers, the default criterion is that \u001b[36mx\u001b[39m and \u001b[36my\u001b[39m differ by no\n",
" more than \u001b[36meps\u001b[39m, the separation between adjacent fixed-point numbers.\n",
"\n",
" ────────────────────────────────────────────────────────────────────────────\n",
"\n",
"\u001b[36m isapprox(df1::AbstractDataFrame, df2::AbstractDataFrame;\u001b[39m\n",
"\u001b[36m rtol::Real=atol>0 ? 0 : √eps, atol::Real=0,\u001b[39m\n",
"\u001b[36m nans::Bool=false, norm::Function=norm)\u001b[39m\n",
"\n",
" Inexact equality comparison. \u001b[36mdf1\u001b[39m and \u001b[36mdf2\u001b[39m must have the same size and column\n",
" names. Return \u001b[36mtrue\u001b[39m if \u001b[36misapprox\u001b[39m with given keyword arguments applied to all\n",
" pairs of columns stored in \u001b[36mdf1\u001b[39m and \u001b[36mdf2\u001b[39m returns \u001b[36mtrue\u001b[39m."
]
},
"execution_count": 70,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"?isapprox"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can now benchmark the C code directly from Julia:"
]
},
{
"cell_type": "code",
"execution_count": 71,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"BenchmarkTools.Trial: 527 samples with 1 evaluation.\n",
" Range \u001b[90m(\u001b[39m\u001b[36m\u001b[1mmin\u001b[22m\u001b[39m … \u001b[35mmax\u001b[39m\u001b[90m): \u001b[39m\u001b[36m\u001b[1m9.188 ms\u001b[22m\u001b[39m … \u001b[35m 13.331 ms\u001b[39m \u001b[90m┊\u001b[39m GC \u001b[90m(\u001b[39mmin … max\u001b[90m): \u001b[39m0.00% … 0.00%\n",
" Time \u001b[90m(\u001b[39m\u001b[34m\u001b[1mmedian\u001b[22m\u001b[39m\u001b[90m): \u001b[39m\u001b[34m\u001b[1m9.367 ms \u001b[22m\u001b[39m\u001b[90m┊\u001b[39m GC \u001b[90m(\u001b[39mmedian\u001b[90m): \u001b[39m0.00%\n",
" Time \u001b[90m(\u001b[39m\u001b[32m\u001b[1mmean\u001b[22m\u001b[39m ± \u001b[32mσ\u001b[39m\u001b[90m): \u001b[39m\u001b[32m\u001b[1m9.472 ms\u001b[22m\u001b[39m ± \u001b[32m467.701 μs\u001b[39m \u001b[90m┊\u001b[39m GC \u001b[90m(\u001b[39mmean ± σ\u001b[90m): \u001b[39m0.00% ± 0.00%\n",
"\n",
" \u001b[39m▃\u001b[39m▇\u001b[39m█\u001b[34m█\u001b[39m\u001b[39m▇\u001b[39m▅\u001b[32m▄\u001b[39m\u001b[39m▂\u001b[39m▃\u001b[39m▂\u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \n",
" \u001b[39m█\u001b[39m█\u001b[39m█\u001b[34m█\u001b[39m\u001b[39m█\u001b[39m█\u001b[32m█\u001b[39m\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m▇\u001b[39m▆\u001b[39m▅\u001b[39m▇\u001b[39m▄\u001b[39m▁\u001b[39m▆\u001b[39m▅\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▄\u001b[39m▄\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▄\u001b[39m▁\u001b[39m▁\u001b[39m▄\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▄\u001b[39m▄\u001b[39m▁\u001b[39m▄\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▄\u001b[39m▄\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▄\u001b[39m \u001b[39m▇\n",
" 9.19 ms\u001b[90m \u001b[39m\u001b[90mHistogram: \u001b[39m\u001b[90m\u001b[1mlog(\u001b[22m\u001b[39m\u001b[90mfrequency\u001b[39m\u001b[90m\u001b[1m)\u001b[22m\u001b[39m\u001b[90m by time\u001b[39m 12.2 ms \u001b[0m\u001b[1m<\u001b[22m\n",
"\n",
" Memory estimate\u001b[90m: \u001b[39m\u001b[33m0 bytes\u001b[39m, allocs estimate\u001b[90m: \u001b[39m\u001b[33m0\u001b[39m."
]
},
"execution_count": 71,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"c_bench = @benchmark c_sum($a)"
]
},
{
"cell_type": "code",
"execution_count": 72,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"C: Fastest time was 9.18846 msec\n"
]
}
],
"source": [
"println(\"C: Fastest time was $(minimum(c_bench.times) / 1e6) msec\")"
]
},
{
"cell_type": "code",
"execution_count": 73,
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
"text/plain": [
"Dict{Any, Any} with 1 entry:\n",
" \"C\" => 9.18846"
]
},
"execution_count": 73,
"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": 74,
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
"text/plain": [
"Plots.GRBackend()"
]
},
"execution_count": 74,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"using Plots\n",
"gr()"
]
},
{
"cell_type": "code",
"execution_count": 75,
"metadata": {},
"outputs": [
{
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},
"execution_count": 75,
"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": 76,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"WARNING: redefinition of constant Clib_fastmath. This may fail, cause incorrect answers, or produce other errors.\n"
]
},
{
"data": {
"text/plain": [
"c_sum_fastmath (generic function with 1 method)"
]
},
"execution_count": 76,
"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": 77,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"BenchmarkTools.Trial: 812 samples with 1 evaluation.\n",
" Range \u001b[90m(\u001b[39m\u001b[36m\u001b[1mmin\u001b[22m\u001b[39m … \u001b[35mmax\u001b[39m\u001b[90m): \u001b[39m\u001b[36m\u001b[1m5.542 ms\u001b[22m\u001b[39m … \u001b[35m 11.767 ms\u001b[39m \u001b[90m┊\u001b[39m GC \u001b[90m(\u001b[39mmin … max\u001b[90m): \u001b[39m0.00% … 0.00%\n",
" Time \u001b[90m(\u001b[39m\u001b[34m\u001b[1mmedian\u001b[22m\u001b[39m\u001b[90m): \u001b[39m\u001b[34m\u001b[1m5.948 ms \u001b[22m\u001b[39m\u001b[90m┊\u001b[39m GC \u001b[90m(\u001b[39mmedian\u001b[90m): \u001b[39m0.00%\n",
" Time \u001b[90m(\u001b[39m\u001b[32m\u001b[1mmean\u001b[22m\u001b[39m ± \u001b[32mσ\u001b[39m\u001b[90m): \u001b[39m\u001b[32m\u001b[1m6.134 ms\u001b[22m\u001b[39m ± \u001b[32m564.309 μs\u001b[39m \u001b[90m┊\u001b[39m GC \u001b[90m(\u001b[39mmean ± σ\u001b[90m): \u001b[39m0.00% ± 0.00%\n",
"\n",
" \u001b[39m \u001b[39m \u001b[39m \u001b[39m▂\u001b[39m \u001b[39m \u001b[39m \u001b[39m▄\u001b[39m█\u001b[34m▅\u001b[39m\u001b[39m▂\u001b[39m \u001b[39m \u001b[39m \u001b[32m \u001b[39m\u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \n",
" \u001b[39m▃\u001b[39m▂\u001b[39m▇\u001b[39m█\u001b[39m▇\u001b[39m▇\u001b[39m▇\u001b[39m█\u001b[39m█\u001b[34m█\u001b[39m\u001b[39m█\u001b[39m█\u001b[39m▇\u001b[39m▅\u001b[32m▃\u001b[39m\u001b[39m▄\u001b[39m▃\u001b[39m▃\u001b[39m▄\u001b[39m▄\u001b[39m▃\u001b[39m▄\u001b[39m▃\u001b[39m▂\u001b[39m▃\u001b[39m▃\u001b[39m▄\u001b[39m▃\u001b[39m▂\u001b[39m▂\u001b[39m▃\u001b[39m▃\u001b[39m▃\u001b[39m▂\u001b[39m▂\u001b[39m▂\u001b[39m▃\u001b[39m▂\u001b[39m▂\u001b[39m▂\u001b[39m▂\u001b[39m▃\u001b[39m▂\u001b[39m▂\u001b[39m▂\u001b[39m▂\u001b[39m▂\u001b[39m▂\u001b[39m▂\u001b[39m▂\u001b[39m▂\u001b[39m▁\u001b[39m▂\u001b[39m▁\u001b[39m▂\u001b[39m▂\u001b[39m▂\u001b[39m▂\u001b[39m▂\u001b[39m \u001b[39m▃\n",
" 5.54 ms\u001b[90m Histogram: frequency by time\u001b[39m 8.12 ms \u001b[0m\u001b[1m<\u001b[22m\n",
"\n",
" Memory estimate\u001b[90m: \u001b[39m\u001b[33m16 bytes\u001b[39m, allocs estimate\u001b[90m: \u001b[39m\u001b[33m1\u001b[39m."
]
},
"execution_count": 77,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"c_fastmath_bench = @benchmark $c_sum_fastmath($a)"
]
},
{
"cell_type": "code",
"execution_count": 78,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"5.542088"
]
},
"execution_count": 78,
"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": 79,
"metadata": {
"scrolled": true
},
"outputs": [],
"source": [
"#using Pkg; Pkg.add(\"PyCall\")\n",
"using PyCall"
]
},
{
"cell_type": "code",
"execution_count": 80,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"PyObject <built-in function sum>"
]
},
"execution_count": 80,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# get the Python built-in \"sum\" function:\n",
"pysum = pybuiltin(\"sum\")"
]
},
{
"cell_type": "code",
"execution_count": 81,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"4.998784559011017e6"
]
},
"execution_count": 81,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pysum(a)"
]
},
{
"cell_type": "code",
"execution_count": 82,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"true"
]
},
"execution_count": 82,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pysum(a) ≈ sum(a)"
]
},
{
"cell_type": "code",
"execution_count": 83,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"BenchmarkTools.Trial: 3 samples with 1 evaluation.\n",
" Range \u001b[90m(\u001b[39m\u001b[36m\u001b[1mmin\u001b[22m\u001b[39m … \u001b[35mmax\u001b[39m\u001b[90m): \u001b[39m\u001b[36m\u001b[1m1.681 s\u001b[22m\u001b[39m … \u001b[35m 1.866 s\u001b[39m \u001b[90m┊\u001b[39m GC \u001b[90m(\u001b[39mmin … max\u001b[90m): \u001b[39m0.00% … 0.00%\n",
" Time \u001b[90m(\u001b[39m\u001b[34m\u001b[1mmedian\u001b[22m\u001b[39m\u001b[90m): \u001b[39m\u001b[34m\u001b[1m1.820 s \u001b[22m\u001b[39m\u001b[90m┊\u001b[39m GC \u001b[90m(\u001b[39mmedian\u001b[90m): \u001b[39m0.00%\n",
" Time \u001b[90m(\u001b[39m\u001b[32m\u001b[1mmean\u001b[22m\u001b[39m ± \u001b[32mσ\u001b[39m\u001b[90m): \u001b[39m\u001b[32m\u001b[1m1.789 s\u001b[22m\u001b[39m ± \u001b[32m96.528 ms\u001b[39m \u001b[90m┊\u001b[39m GC \u001b[90m(\u001b[39mmean ± σ\u001b[90m): \u001b[39m0.00% ± 0.00%\n",
"\n",
" \u001b[34m█\u001b[39m\u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[32m \u001b[39m\u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m█\u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m█\u001b[39m \u001b[39m \n",
" \u001b[34m█\u001b[39m\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[32m▁\u001b[39m\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m█\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m█\u001b[39m \u001b[39m▁\n",
" 1.68 s\u001b[90m Histogram: frequency by time\u001b[39m 1.87 s \u001b[0m\u001b[1m<\u001b[22m\n",
"\n",
" Memory estimate\u001b[90m: \u001b[39m\u001b[33m240 bytes\u001b[39m, allocs estimate\u001b[90m: \u001b[39m\u001b[33m6\u001b[39m."
]
},
"execution_count": 83,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"py_list_bench = @benchmark $pysum($a)"
]
},
{
"cell_type": "code",
"execution_count": 84,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Dict{Any, Any} with 3 entries:\n",
" \"C\" => 9.18846\n",
" \"Python built-in\" => 1680.52\n",
" \"C -ffast-math\" => 5.54209"
]
},
"execution_count": 84,
"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": 85,
"metadata": {},
"outputs": [],
"source": [
"#using Pkg; Pkg.add(\"Conda\")\n",
"using Conda"
]
},
{
"cell_type": "code",
"execution_count": 86,
"metadata": {},
"outputs": [],
"source": [
"#Conda.add(\"numpy\")"
]
},
{
"cell_type": "code",
"execution_count": 87,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"BenchmarkTools.Trial: 963 samples with 1 evaluation.\n",
" Range \u001b[90m(\u001b[39m\u001b[36m\u001b[1mmin\u001b[22m\u001b[39m … \u001b[35mmax\u001b[39m\u001b[90m): \u001b[39m\u001b[36m\u001b[1m4.393 ms\u001b[22m\u001b[39m … \u001b[35m 8.287 ms\u001b[39m \u001b[90m┊\u001b[39m GC \u001b[90m(\u001b[39mmin … max\u001b[90m): \u001b[39m0.00% … 0.00%\n",
" Time \u001b[90m(\u001b[39m\u001b[34m\u001b[1mmedian\u001b[22m\u001b[39m\u001b[90m): \u001b[39m\u001b[34m\u001b[1m5.027 ms \u001b[22m\u001b[39m\u001b[90m┊\u001b[39m GC \u001b[90m(\u001b[39mmedian\u001b[90m): \u001b[39m0.00%\n",
" Time \u001b[90m(\u001b[39m\u001b[32m\u001b[1mmean\u001b[22m\u001b[39m ± \u001b[32mσ\u001b[39m\u001b[90m): \u001b[39m\u001b[32m\u001b[1m5.170 ms\u001b[22m\u001b[39m ± \u001b[32m459.198 μs\u001b[39m \u001b[90m┊\u001b[39m GC \u001b[90m(\u001b[39mmean ± σ\u001b[90m): \u001b[39m0.00% ± 0.00%\n",
"\n",
" \u001b[39m \u001b[39m▁\u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m▅\u001b[39m▆\u001b[39m█\u001b[39m█\u001b[39m▆\u001b[34m▆\u001b[39m\u001b[39m▆\u001b[39m▆\u001b[32m▅\u001b[39m\u001b[39m▄\u001b[39m▄\u001b[39m▃\u001b[39m▂\u001b[39m▁\u001b[39m \u001b[39m▂\u001b[39m \u001b[39m▁\u001b[39m▁\u001b[39m \u001b[39m▁\u001b[39m \u001b[39m \u001b[39m \u001b[39m▁\u001b[39m \u001b[39m \u001b[39m▁\u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m▁\n",
" \u001b[39m▇\u001b[39m█\u001b[39m▇\u001b[39m▄\u001b[39m▁\u001b[39m▅\u001b[39m▆\u001b[39m▄\u001b[39m▅\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[34m█\u001b[39m\u001b[39m█\u001b[39m█\u001b[32m█\u001b[39m\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m▇\u001b[39m█\u001b[39m▇\u001b[39m█\u001b[39m█\u001b[39m▇\u001b[39m█\u001b[39m▇\u001b[39m█\u001b[39m▆\u001b[39m█\u001b[39m█\u001b[39m▄\u001b[39m█\u001b[39m▅\u001b[39m▆\u001b[39m▆\u001b[39m▅\u001b[39m▇\u001b[39m▅\u001b[39m▆\u001b[39m▆\u001b[39m▁\u001b[39m▆\u001b[39m▅\u001b[39m▅\u001b[39m▄\u001b[39m▄\u001b[39m▆\u001b[39m▄\u001b[39m▆\u001b[39m▄\u001b[39m▄\u001b[39m▄\u001b[39m▄\u001b[39m▅\u001b[39m \u001b[39m█\n",
" 4.39 ms\u001b[90m \u001b[39m\u001b[90mHistogram: \u001b[39m\u001b[90m\u001b[1mlog(\u001b[22m\u001b[39m\u001b[90mfrequency\u001b[39m\u001b[90m\u001b[1m)\u001b[22m\u001b[39m\u001b[90m by time\u001b[39m 7.01 ms \u001b[0m\u001b[1m<\u001b[22m\n",
"\n",
" Memory estimate\u001b[90m: \u001b[39m\u001b[33m240 bytes\u001b[39m, allocs estimate\u001b[90m: \u001b[39m\u001b[33m6\u001b[39m."
]
},
"execution_count": 87,
"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": 88,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"4.998784559011253e6"
]
},
"execution_count": 88,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"numpy_sum(a)"
]
},
{
"cell_type": "code",
"execution_count": 89,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"true"
]
},
"execution_count": 89,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"numpy_sum(a) ≈ sum(a)"
]
},
{
"cell_type": "code",
"execution_count": 90,
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
"text/plain": [
"Dict{Any, Any} with 4 entries:\n",
" \"C\" => 9.18846\n",
" \"Python numpy\" => 4.3934\n",
" \"Python built-in\" => 1680.52\n",
" \"C -ffast-math\" => 5.54209"
]
},
"execution_count": 90,
"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": 91,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"PyObject <function py_sum at 0x7f243c581af0>"
]
},
"execution_count": 91,
"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": 92,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"BenchmarkTools.Trial: 3 samples with 1 evaluation.\n",
" Range \u001b[90m(\u001b[39m\u001b[36m\u001b[1mmin\u001b[22m\u001b[39m … \u001b[35mmax\u001b[39m\u001b[90m): \u001b[39m\u001b[36m\u001b[1m1.683 s\u001b[22m\u001b[39m … \u001b[35m 1.876 s\u001b[39m \u001b[90m┊\u001b[39m GC \u001b[90m(\u001b[39mmin … max\u001b[90m): \u001b[39m0.00% … 0.00%\n",
" Time \u001b[90m(\u001b[39m\u001b[34m\u001b[1mmedian\u001b[22m\u001b[39m\u001b[90m): \u001b[39m\u001b[34m\u001b[1m1.831 s \u001b[22m\u001b[39m\u001b[90m┊\u001b[39m GC \u001b[90m(\u001b[39mmedian\u001b[90m): \u001b[39m0.00%\n",
" Time \u001b[90m(\u001b[39m\u001b[32m\u001b[1mmean\u001b[22m\u001b[39m ± \u001b[32mσ\u001b[39m\u001b[90m): \u001b[39m\u001b[32m\u001b[1m1.797 s\u001b[22m\u001b[39m ± \u001b[32m100.946 ms\u001b[39m \u001b[90m┊\u001b[39m GC \u001b[90m(\u001b[39mmean ± σ\u001b[90m): \u001b[39m0.00% ± 0.00%\n",
"\n",
" \u001b[34m█\u001b[39m\u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[32m \u001b[39m\u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m█\u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m█\u001b[39m \u001b[39m \n",
" \u001b[34m█\u001b[39m\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[32m▁\u001b[39m\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m█\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m█\u001b[39m \u001b[39m▁\n",
" 1.68 s\u001b[90m Histogram: frequency by time\u001b[39m 1.88 s \u001b[0m\u001b[1m<\u001b[22m\n",
"\n",
" Memory estimate\u001b[90m: \u001b[39m\u001b[33m240 bytes\u001b[39m, allocs estimate\u001b[90m: \u001b[39m\u001b[33m6\u001b[39m."
]
},
"execution_count": 92,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"py_hand = @benchmark $sum_py($a)"
]
},
{
"cell_type": "code",
"execution_count": 93,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"4.998784559011017e6"
]
},
"execution_count": 93,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"sum_py(a)"
]
},
{
"cell_type": "code",
"execution_count": 94,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"true"
]
},
"execution_count": 94,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"sum_py(a) ≈ sum(a)"
]
},
{
"cell_type": "code",
"execution_count": 95,
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
"text/plain": [
"Dict{Any, Any} with 5 entries:\n",
" \"C\" => 9.18846\n",
" \"Python numpy\" => 4.3934\n",
" \"Python hand-written\" => 1683.29\n",
" \"Python built-in\" => 1680.52\n",
" \"C -ffast-math\" => 5.54209"
]
},
"execution_count": 95,
"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": 96,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"sum(a::<b>AbstractArray</b>; <i>dims, kw...</i>) in Base at <a href=\"https://github.com/JuliaLang/julia/tree/3bf9d1773144bc4943232dc2ffaac307a700853d/base/reducedim.jl#L889\" target=\"_blank\">reducedim.jl:889</a>"
],
"text/plain": [
"sum(a::AbstractArray; dims, kw...) in Base at reducedim.jl:889"
]
},
"execution_count": 96,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"@which sum(a)"
]
},
{
"cell_type": "code",
"execution_count": 97,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"BenchmarkTools.Trial: 1060 samples with 1 evaluation.\n",
" Range \u001b[90m(\u001b[39m\u001b[36m\u001b[1mmin\u001b[22m\u001b[39m … \u001b[35mmax\u001b[39m\u001b[90m): \u001b[39m\u001b[36m\u001b[1m4.132 ms\u001b[22m\u001b[39m … \u001b[35m 8.876 ms\u001b[39m \u001b[90m┊\u001b[39m GC \u001b[90m(\u001b[39mmin … max\u001b[90m): \u001b[39m0.00% … 0.00%\n",
" Time \u001b[90m(\u001b[39m\u001b[34m\u001b[1mmedian\u001b[22m\u001b[39m\u001b[90m): \u001b[39m\u001b[34m\u001b[1m4.557 ms \u001b[22m\u001b[39m\u001b[90m┊\u001b[39m GC \u001b[90m(\u001b[39mmedian\u001b[90m): \u001b[39m0.00%\n",
" Time \u001b[90m(\u001b[39m\u001b[32m\u001b[1mmean\u001b[22m\u001b[39m ± \u001b[32mσ\u001b[39m\u001b[90m): \u001b[39m\u001b[32m\u001b[1m4.697 ms\u001b[22m\u001b[39m ± \u001b[32m413.209 μs\u001b[39m \u001b[90m┊\u001b[39m GC \u001b[90m(\u001b[39mmean ± σ\u001b[90m): \u001b[39m0.00% ± 0.00%\n",
"\n",
" \u001b[39m \u001b[39m▁\u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m▃\u001b[39m█\u001b[34m█\u001b[39m\u001b[39m▅\u001b[39m▃\u001b[39m▂\u001b[32m \u001b[39m\u001b[39m▁\u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \n",
" \u001b[39m▇\u001b[39m█\u001b[39m▇\u001b[39m▅\u001b[39m▅\u001b[39m▅\u001b[39m▅\u001b[39m▅\u001b[39m█\u001b[39m█\u001b[39m█\u001b[34m█\u001b[39m\u001b[39m█\u001b[39m█\u001b[39m█\u001b[32m█\u001b[39m\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m▇\u001b[39m▇\u001b[39m▇\u001b[39m█\u001b[39m▇\u001b[39m█\u001b[39m▆\u001b[39m▆\u001b[39m█\u001b[39m▅\u001b[39m█\u001b[39m▇\u001b[39m▄\u001b[39m▆\u001b[39m▅\u001b[39m▅\u001b[39m▅\u001b[39m▆\u001b[39m▆\u001b[39m▅\u001b[39m▆\u001b[39m▅\u001b[39m▄\u001b[39m▅\u001b[39m▆\u001b[39m▅\u001b[39m▅\u001b[39m▅\u001b[39m█\u001b[39m▄\u001b[39m▁\u001b[39m▅\u001b[39m▄\u001b[39m▄\u001b[39m▄\u001b[39m▄\u001b[39m▁\u001b[39m▁\u001b[39m▆\u001b[39m \u001b[39m█\n",
" 4.13 ms\u001b[90m \u001b[39m\u001b[90mHistogram: \u001b[39m\u001b[90m\u001b[1mlog(\u001b[22m\u001b[39m\u001b[90mfrequency\u001b[39m\u001b[90m\u001b[1m)\u001b[22m\u001b[39m\u001b[90m by time\u001b[39m 6.32 ms \u001b[0m\u001b[1m<\u001b[22m\n",
"\n",
" Memory estimate\u001b[90m: \u001b[39m\u001b[33m0 bytes\u001b[39m, allocs estimate\u001b[90m: \u001b[39m\u001b[33m0\u001b[39m."
]
},
"execution_count": 97,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"j_bench = @benchmark sum($a)"
]
},
{
"cell_type": "code",
"execution_count": 98,
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
"text/plain": [
"Dict{Any, Any} with 6 entries:\n",
" \"C\" => 9.18846\n",
" \"Python numpy\" => 4.3934\n",
" \"Python hand-written\" => 1683.29\n",
" \"Python built-in\" => 1680.52\n",
" \"Julia built-in\" => 4.13181\n",
" \"C -ffast-math\" => 5.54209"
]
},
"execution_count": 98,
"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": 99,
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
"text/plain": [
"mysum (generic function with 1 method)"
]
},
"execution_count": 99,
"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": 100,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"BenchmarkTools.Trial: 468 samples with 1 evaluation.\n",
" Range \u001b[90m(\u001b[39m\u001b[36m\u001b[1mmin\u001b[22m\u001b[39m … \u001b[35mmax\u001b[39m\u001b[90m): \u001b[39m\u001b[36m\u001b[1m 9.278 ms\u001b[22m\u001b[39m … \u001b[35m19.230 ms\u001b[39m \u001b[90m┊\u001b[39m GC \u001b[90m(\u001b[39mmin … max\u001b[90m): \u001b[39m0.00% … 0.00%\n",
" Time \u001b[90m(\u001b[39m\u001b[34m\u001b[1mmedian\u001b[22m\u001b[39m\u001b[90m): \u001b[39m\u001b[34m\u001b[1m10.088 ms \u001b[22m\u001b[39m\u001b[90m┊\u001b[39m GC \u001b[90m(\u001b[39mmedian\u001b[90m): \u001b[39m0.00%\n",
" Time \u001b[90m(\u001b[39m\u001b[32m\u001b[1mmean\u001b[22m\u001b[39m ± \u001b[32mσ\u001b[39m\u001b[90m): \u001b[39m\u001b[32m\u001b[1m10.657 ms\u001b[22m\u001b[39m ± \u001b[32m 1.394 ms\u001b[39m \u001b[90m┊\u001b[39m GC \u001b[90m(\u001b[39mmean ± σ\u001b[90m): \u001b[39m0.00% ± 0.00%\n",
"\n",
" \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m▆\u001b[39m█\u001b[34m▅\u001b[39m\u001b[39m▃\u001b[39m▂\u001b[39m▂\u001b[32m▁\u001b[39m\u001b[39m▁\u001b[39m▂\u001b[39m \u001b[39m▁\u001b[39m \u001b[39m▁\u001b[39m \u001b[39m▁\u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \n",
" \u001b[39m▅\u001b[39m▁\u001b[39m▅\u001b[39m▇\u001b[39m█\u001b[39m█\u001b[34m█\u001b[39m\u001b[39m█\u001b[39m█\u001b[39m█\u001b[32m█\u001b[39m\u001b[39m█\u001b[39m█\u001b[39m▇\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m▄\u001b[39m█\u001b[39m▅\u001b[39m▇\u001b[39m▅\u001b[39m▇\u001b[39m▄\u001b[39m▄\u001b[39m▅\u001b[39m▆\u001b[39m▅\u001b[39m▄\u001b[39m▁\u001b[39m▅\u001b[39m▆\u001b[39m▅\u001b[39m▅\u001b[39m▁\u001b[39m▄\u001b[39m▄\u001b[39m▁\u001b[39m▄\u001b[39m▁\u001b[39m▄\u001b[39m▄\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▄\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▄\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▅\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▄\u001b[39m \u001b[39m▇\n",
" 9.28 ms\u001b[90m \u001b[39m\u001b[90mHistogram: \u001b[39m\u001b[90m\u001b[1mlog(\u001b[22m\u001b[39m\u001b[90mfrequency\u001b[39m\u001b[90m\u001b[1m)\u001b[22m\u001b[39m\u001b[90m by time\u001b[39m 17.3 ms \u001b[0m\u001b[1m<\u001b[22m\n",
"\n",
" Memory estimate\u001b[90m: \u001b[39m\u001b[33m0 bytes\u001b[39m, allocs estimate\u001b[90m: \u001b[39m\u001b[33m0\u001b[39m."
]
},
"execution_count": 100,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"j_bench_hand = @benchmark mysum($a)"
]
},
{
"cell_type": "code",
"execution_count": 101,
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
"text/plain": [
"Dict{Any, Any} with 7 entries:\n",
" \"C\" => 9.18846\n",
" \"Python numpy\" => 4.3934\n",
" \"Julia hand-written\" => 9.27795\n",
" \"Python hand-written\" => 1683.29\n",
" \"Python built-in\" => 1680.52\n",
" \"Julia built-in\" => 4.13181\n",
" \"C -ffast-math\" => 5.54209"
]
},
"execution_count": 101,
"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": 102,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"mysum_simd (generic function with 1 method)"
]
},
"execution_count": 102,
"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": 103,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"BenchmarkTools.Trial: 1140 samples with 1 evaluation.\n",
" Range \u001b[90m(\u001b[39m\u001b[36m\u001b[1mmin\u001b[22m\u001b[39m … \u001b[35mmax\u001b[39m\u001b[90m): \u001b[39m\u001b[36m\u001b[1m3.950 ms\u001b[22m\u001b[39m … \u001b[35m 21.844 ms\u001b[39m \u001b[90m┊\u001b[39m GC \u001b[90m(\u001b[39mmin … max\u001b[90m): \u001b[39m0.00% … 0.00%\n",
" Time \u001b[90m(\u001b[39m\u001b[34m\u001b[1mmedian\u001b[22m\u001b[39m\u001b[90m): \u001b[39m\u001b[34m\u001b[1m4.092 ms \u001b[22m\u001b[39m\u001b[90m┊\u001b[39m GC \u001b[90m(\u001b[39mmedian\u001b[90m): \u001b[39m0.00%\n",
" Time \u001b[90m(\u001b[39m\u001b[32m\u001b[1mmean\u001b[22m\u001b[39m ± \u001b[32mσ\u001b[39m\u001b[90m): \u001b[39m\u001b[32m\u001b[1m4.365 ms\u001b[22m\u001b[39m ± \u001b[32m904.188 μs\u001b[39m \u001b[90m┊\u001b[39m GC \u001b[90m(\u001b[39mmean ± σ\u001b[90m): \u001b[39m0.00% ± 0.00%\n",
"\n",
" \u001b[39m \u001b[39m▃\u001b[39m█\u001b[39m█\u001b[34m▅\u001b[39m\u001b[39m▃\u001b[39m▂\u001b[39m▁\u001b[39m \u001b[39m \u001b[39m \u001b[39m▁\u001b[32m▁\u001b[39m\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▂\u001b[39m▁\u001b[39m▁\u001b[39m \u001b[39m▂\u001b[39m \u001b[39m▂\u001b[39m▁\u001b[39m▂\u001b[39m▂\u001b[39m \u001b[39m▁\u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \n",
" \u001b[39m▇\u001b[39m█\u001b[39m█\u001b[39m█\u001b[34m█\u001b[39m\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m▇\u001b[39m█\u001b[39m█\u001b[32m█\u001b[39m\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m▆\u001b[39m█\u001b[39m█\u001b[39m▇\u001b[39m▆\u001b[39m▆\u001b[39m█\u001b[39m▅\u001b[39m▄\u001b[39m▅\u001b[39m▆\u001b[39m▅\u001b[39m▆\u001b[39m▄\u001b[39m▆\u001b[39m▅\u001b[39m▅\u001b[39m▅\u001b[39m▅\u001b[39m▁\u001b[39m▁\u001b[39m▆\u001b[39m▁\u001b[39m▅\u001b[39m▅\u001b[39m▁\u001b[39m▄\u001b[39m▁\u001b[39m▄\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▄\u001b[39m \u001b[39m█\n",
" 3.95 ms\u001b[90m \u001b[39m\u001b[90mHistogram: \u001b[39m\u001b[90m\u001b[1mlog(\u001b[22m\u001b[39m\u001b[90mfrequency\u001b[39m\u001b[90m\u001b[1m)\u001b[22m\u001b[39m\u001b[90m by time\u001b[39m 6.03 ms \u001b[0m\u001b[1m<\u001b[22m\n",
"\n",
" Memory estimate\u001b[90m: \u001b[39m\u001b[33m0 bytes\u001b[39m, allocs estimate\u001b[90m: \u001b[39m\u001b[33m0\u001b[39m."
]
},
"execution_count": 103,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"j_bench_hand_simd = @benchmark mysum_simd($a)"
]
},
{
"cell_type": "code",
"execution_count": 104,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"4.998784559011221e6"
]
},
"execution_count": 104,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"mysum_simd(a)"
]
},
{
"cell_type": "code",
"execution_count": 105,
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
"text/plain": [
"Dict{Any, Any} with 8 entries:\n",
" \"Julia hand-written simd\" => 3.95038\n",
" \"C\" => 9.18846\n",
" \"Python numpy\" => 4.3934\n",
" \"Julia hand-written\" => 9.27795\n",
" \"Python hand-written\" => 1683.29\n",
" \"Python built-in\" => 1680.52\n",
" \"Julia built-in\" => 4.13181\n",
" \"C -ffast-math\" => 5.54209"
]
},
"execution_count": 105,
"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": [
"# 9. Using R"
]
},
{
"cell_type": "code",
"execution_count": 106,
"metadata": {},
"outputs": [],
"source": [
"#Pkg.add(\"RCall\")\n",
"using RCall"
]
},
{
"cell_type": "code",
"execution_count": 107,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"BenchmarkTools.Trial: 51 samples with 1 evaluation.\n",
" Range \u001b[90m(\u001b[39m\u001b[36m\u001b[1mmin\u001b[22m\u001b[39m … \u001b[35mmax\u001b[39m\u001b[90m): \u001b[39m\u001b[36m\u001b[1m54.146 ms\u001b[22m\u001b[39m … \u001b[35m167.534 ms\u001b[39m \u001b[90m┊\u001b[39m GC \u001b[90m(\u001b[39mmin … max\u001b[90m): \u001b[39m0.00% … 0.00%\n",
" Time \u001b[90m(\u001b[39m\u001b[34m\u001b[1mmedian\u001b[22m\u001b[39m\u001b[90m): \u001b[39m\u001b[34m\u001b[1m95.011 ms \u001b[22m\u001b[39m\u001b[90m┊\u001b[39m GC \u001b[90m(\u001b[39mmedian\u001b[90m): \u001b[39m0.00%\n",
" Time \u001b[90m(\u001b[39m\u001b[32m\u001b[1mmean\u001b[22m\u001b[39m ± \u001b[32mσ\u001b[39m\u001b[90m): \u001b[39m\u001b[32m\u001b[1m99.729 ms\u001b[22m\u001b[39m ± \u001b[32m 19.300 ms\u001b[39m \u001b[90m┊\u001b[39m GC \u001b[90m(\u001b[39mmean ± σ\u001b[90m): \u001b[39m0.00% ± 0.00%\n",
"\n",
" \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m▄\u001b[39m \u001b[39m▁\u001b[39m▁\u001b[39m█\u001b[34m▃\u001b[39m\u001b[39m▁\u001b[39m \u001b[32m \u001b[39m\u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \n",
" \u001b[39m▄\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▄\u001b[39m▇\u001b[39m█\u001b[39m▄\u001b[39m█\u001b[39m█\u001b[39m█\u001b[34m█\u001b[39m\u001b[39m█\u001b[39m▆\u001b[32m▄\u001b[39m\u001b[39m▆\u001b[39m▆\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▄\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▄\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▄\u001b[39m▁\u001b[39m▄\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▄\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▄\u001b[39m \u001b[39m▁\n",
" 54.1 ms\u001b[90m Histogram: frequency by time\u001b[39m 157 ms \u001b[0m\u001b[1m<\u001b[22m\n",
"\n",
" Memory estimate\u001b[90m: \u001b[39m\u001b[33m160 bytes\u001b[39m, allocs estimate\u001b[90m: \u001b[39m\u001b[33m8\u001b[39m."
]
},
"execution_count": 107,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"@rimport base as rbase\n",
"rbench = @benchmark rbase.sum(a)"
]
},
{
"cell_type": "code",
"execution_count": 108,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"RObject{RealSxp}\n",
"[1] 4998785\n"
]
},
"execution_count": 108,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"rbase.sum(a)"
]
},
{
"cell_type": "code",
"execution_count": 109,
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
"text/plain": [
"54.14556"
]
},
"execution_count": 109,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"d[\"R base sum\"] = minimum(rbench.times) / 1e6"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# 10. R, hand-written"
]
},
{
"cell_type": "code",
"execution_count": 110,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"RObject{ClosSxp}\n",
"function (x) \n",
"{\n",
" sum1 <- 0\n",
" for (n in x) {\n",
" sum1 <- sum1 + n\n",
" }\n",
" return(sum1)\n",
"}\n"
]
},
"execution_count": 110,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"R\"\"\"\n",
"r_sum <- function(x) {\n",
" sum1 <- 0\n",
" for (n in x) {\n",
" sum1 <- sum1 + n\n",
" }\n",
" return(sum1)\n",
"}\n",
"\"\"\"\n",
"sum_r = R\"r_sum\""
]
},
{
"cell_type": "code",
"execution_count": 111,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"RObject{RealSxp}\n",
"[1] 4998785\n"
]
},
"execution_count": 111,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"sum_r(a)"
]
},
{
"cell_type": "code",
"execution_count": 112,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"BenchmarkTools.Trial: 12 samples with 1 evaluation.\n",
" Range \u001b[90m(\u001b[39m\u001b[36m\u001b[1mmin\u001b[22m\u001b[39m … \u001b[35mmax\u001b[39m\u001b[90m): \u001b[39m\u001b[36m\u001b[1m339.174 ms\u001b[22m\u001b[39m … \u001b[35m519.857 ms\u001b[39m \u001b[90m┊\u001b[39m GC \u001b[90m(\u001b[39mmin … max\u001b[90m): \u001b[39m0.00% … 0.00%\n",
" Time \u001b[90m(\u001b[39m\u001b[34m\u001b[1mmedian\u001b[22m\u001b[39m\u001b[90m): \u001b[39m\u001b[34m\u001b[1m452.910 ms \u001b[22m\u001b[39m\u001b[90m┊\u001b[39m GC \u001b[90m(\u001b[39mmedian\u001b[90m): \u001b[39m0.00%\n",
" Time \u001b[90m(\u001b[39m\u001b[32m\u001b[1mmean\u001b[22m\u001b[39m ± \u001b[32mσ\u001b[39m\u001b[90m): \u001b[39m\u001b[32m\u001b[1m433.554 ms\u001b[22m\u001b[39m ± \u001b[32m 67.763 ms\u001b[39m \u001b[90m┊\u001b[39m GC \u001b[90m(\u001b[39mmean ± σ\u001b[90m): \u001b[39m0.00% ± 0.00%\n",
"\n",
" \u001b[39m█\u001b[39m \u001b[39m█\u001b[39m \u001b[39m█\u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m█\u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m█\u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[32m \u001b[39m\u001b[39m \u001b[39m \u001b[39m \u001b[39m█\u001b[34m \u001b[39m\u001b[39m \u001b[39m█\u001b[39m \u001b[39m \u001b[39m \u001b[39m█\u001b[39m \u001b[39m█\u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m█\u001b[39m \u001b[39m█\u001b[39m \u001b[39m█\u001b[39m \u001b[39m \n",
" \u001b[39m█\u001b[39m▁\u001b[39m█\u001b[39m▁\u001b[39m█\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m█\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m█\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[32m▁\u001b[39m\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m█\u001b[34m▁\u001b[39m\u001b[39m▁\u001b[39m█\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m█\u001b[39m▁\u001b[39m█\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m█\u001b[39m▁\u001b[39m█\u001b[39m▁\u001b[39m█\u001b[39m \u001b[39m▁\n",
" 339 ms\u001b[90m Histogram: frequency by time\u001b[39m 520 ms \u001b[0m\u001b[1m<\u001b[22m\n",
"\n",
" Memory estimate\u001b[90m: \u001b[39m\u001b[33m160 bytes\u001b[39m, allocs estimate\u001b[90m: \u001b[39m\u001b[33m8\u001b[39m."
]
},
"execution_count": 112,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"rbench2 = @benchmark sum_r(a)"
]
},
{
"cell_type": "code",
"execution_count": 113,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"339.173887"
]
},
"execution_count": 113,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"d[\"R, hand written\"] = minimum(rbench2.times) / 1e6"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Summary"
]
},
{
"cell_type": "code",
"execution_count": 114,
"metadata": {
"scrolled": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Julia hand-written simd.....4.0\n",
"Julia built-in..............4.1\n",
"Python numpy................4.4\n",
"C -ffast-math...............5.5\n",
"C...........................9.2\n",
"Julia hand-written..........9.3\n",
"R base sum.................54.1\n",
"R, hand written...........339.2\n",
"Python built-in..........1680.5\n",
"Python hand-written......1683.3\n"
]
}
],
"source": [
"for (key, value) in sort(collect(d), by=last)\n",
" println(rpad(key, 25, \".\"), lpad(round(value; digits=1), 6, \".\"))\n",
"end"
]
}
],
"metadata": {
"anaconda-cloud": {},
"kernelspec": {
"display_name": "Julia 1.7.0",
"language": "julia",
"name": "julia-1.7"
},
"language_info": {
"file_extension": ".jl",
"mimetype": "application/julia",
"name": "julia",
"version": "1.7.0"
},
"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": 4
}
Raw
README.md
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