Recognizing the slow parts of your program is the single most important task when it comes to speeding up your code. Luckily, in most cases, the code that causes the application to slow down is a very small fraction of the program. By locating those critical sections, you can focus on the parts that need improvement without wasting time in micro-optimization.
Profiling is the technique that allows us to pinpoint the most resource-intensive spots in an application. A profiler is a program that runs an application and monitors how long each function takes to execute, thus detecting the functions in which your application spends most of its time.
Python provides several tools to help us find these bottlenecks and measure important performance metrics. In this chapter, we will learn how to use the standard cProfile
module and the line_profiler
third-party package. We will also learn how to profile an application's memory consumption through the memory_profiler
tool. Another useful tool that we will cover is KCachegrind, which can be used to graphically display the data produced by various profilers.
Benchmarks are small scripts used to assess the total execution time of your application. We will learn how to write benchmarks and how to accurately time your programs.
The list of topics we will cover in this chapter is as follows:
- General principles of high performance programming
- Writing tests and benchmarks
- The Unix
time
command - The Python
timeit
module - Testing and benchmarking with
pytest
- Profiling your application
- The
cProfile
standard tool - Interpreting profiling results with KCachegrind
line_profiler
andmemory_profiler
tools- Disassembling Python code through the
dis
module
When designing a performance-intensive program, the very first step is to write your code without bothering with small optimizations:
"Premature optimization is the root of all evil."
- Donald Knuth
In the early development stages, the design of the program can change quickly and may require large rewrites and reorganizations of the code base. By testing different prototypes without the burden of optimization, you are free to devote your time and energy to ensure that the program produces correct results and that the design is flexible. After all, who needs an application that runs fast but gives the wrong answer?
The mantras that you should remember when optimizing your code are as follows:
- Make it run: We have to get the software in a working state, and ensure that it produces the correct results. This exploratory phase serves to better understand the application and to spot major design issues in the early stages.
- Make it right: We want to ensure that the design of the program is solid. Refactoring should be done before attempting any performance optimization. This really helps separate the application into independent and cohesive units that are easier to maintain.
- Make it fast: Once our program is working and is well structured, we can focus on performance optimization. We may also want to optimize memory usage if that constitutes an issue.
In this section, we will write and profile a particle simulator test application. The simulator is a program that takes some particles and simulates their movement over time according to a set of laws that we impose. These particles can be abstract entities or correspond to physical objects, for example, billiard balls moving on a table, molecules in gas, stars moving through space, smoke particles, fluids in a chamber, and so on.
Computer simulations are useful in fields such as Physics, Chemistry, Astronomy, and many other disciplines. The applications used to simulate systems are particularly performance-intensive and scientists and engineers spend an inordinate amount of time optimizing these codes. In order to study realistic systems, it is often necessary to simulate a very high number of bodies and every small increase in performance counts.
In our first example, we will simulate a system containing particles that constantly rotate around a central point at various speeds, just like the hands of a clock.
The necessary information to run our simulation will be the starting positions of the particles, the speed, and the rotation direction. From these elements, we have to calculate the position of the particle in the next instant of time. An example system is shown in the following figure. The origin of the system is the (0, 0)
point, the position is indicated by the x, y vector and the velocity is indicated by the vx, vy vector:
The basic feature of a circular motion is that the particles always move perpendicular to the direction connecting the particle and the center. To move the particle, we simply change the position by taking a series of very small steps (which correspond to advancing the system for a small interval of time) in the direction of motion, as shown in the following figure:
We will start by designing the application in an object-oriented way. According to our requirements, it is natural to have a generic Particle
class that stores the particle positions, x
and y
, and their angular velocity, ang_vel
:
class Particle: def __init__(self, x, y, ang_vel): self.x = x self.y = y self.ang_vel = ang_vel
Note that we accept positive and negative numbers for all the parameters (the sign of ang_vel
will simply determine the direction of rotation).
Another class, called ParticleSimulator
, will encapsulate the laws of motion and will be responsible for changing the positions of the particles over time. The __init__
method will store a list of Particle
instances and the evolve
method will change the particle positions according to our laws.
We want the particles to rotate around the position corresponding to the x=0
and y=0
coordinates, at a constant speed. The direction of the particles will always be perpendicular to the direction from the center (refer to the first figure of this chapter). To find the direction of the movement along the x and y axes (corresponding to the Python v_x
and v_y
variables), it is sufficient to use these formulae:
v_x = -y / (x**2 + y**2)**0.5 v_y = x / (x**2 + y**2)**0.5
If we let one of our particles move, after a certain time t, it will reach another position following a circular path. We can approximate a circular trajectory by dividing the time interval, t, into tiny time steps, dt, where the particle moves in a straight line tangentially to the circle. The final result is just an approximation of a circular motion. In order to avoid a strong divergence, such as the one illustrated in the following figure, it is necessary to take very small time steps:
In a more schematic way, we have to carry out the following steps to calculate the particle position at time t:
- Calculate the direction of motion (
v_x
andv_y
). - Calculate the displacement (
d_x
andd_y
), which is the product of time step, angular velocity, and direction of motion. - Repeat steps 1 and 2 for enough times to cover the total time t.
The following code shows the full ParticleSimulator
implementation:
class ParticleSimulator: def __init__(self, particles): self.particles = particles def evolve(self, dt): timestep = 0.00001 nsteps = int(dt/timestep) for i in range(nsteps): for p in self.particles: # 1. calculate the direction norm = (p.x**2 + p.y**2)**0.5 v_x = -p.y/norm v_y = p.x/norm # 2. calculate the displacement d_x = timestep * p.ang_vel * v_x d_y = timestep * p.ang_vel * v_y p.x += d_x p.y += d_y # 3. repeat for all the time steps
We can use the matplotlib
library to visualize our particles. This library is not included in the Python standard library, and it can be easily installed using the pip install matplotlib
command.
Note
Alternatively, you can use the Anaconda Python distribution (https://store.continuum.io/cshop/anaconda/) that includes matplotlib
and most of the other third-party packages used in this book. Anaconda is free and is available for Linux, Windows, and Mac.
To make an interactive visualization, we will use the matplotlib.pyplot.plot
function to display the particles as points and the matplotlib.animation.FuncAnimation
class to animate the evolution of the particles over time.
The visualize
function takes a particle ParticleSimulator
instance as an argument and displays the trajectory in an animated plot. The steps necessary to display the particle trajectory using the matplotlib
tools are as follows:
- Set up the axes and use the
plot
function to display the particles.plot
takes a list of x and y coordinates. - Write an initialization function,
init
, and a function,animate
, that updates the x and y coordinates using theline.set_data
method. - Create a
FuncAnimation
instance by passing theinit
andanimate
functions plus theinterval
parameters, which specify the update interval, andblit
, which improves the update rate of the image. - Run the animation with
plt.show()
:
from matplotlib import pyplot as plt from matplotlib import animation def visualize(simulator): X = [p.x for p in simulator.particles] Y = [p.y for p in simulator.particles] fig = plt.figure() ax = plt.subplot(111, aspect='equal') line, = ax.plot(X, Y, 'ro') # Axis limits plt.xlim(-1, 1) plt.ylim(-1, 1) # It will be run when the animation starts def init(): line.set_data([], []) return line, # The comma is important! def animate(i): # We let the particle evolve for 0.01 time units simulator.evolve(0.01) X = [p.x for p in simulator.particles] Y = [p.y for p in simulator.particles] line.set_data(X, Y) return line, # Call the animate function each 10 ms anim = animation.FuncAnimation(fig, animate, init_func=init, blit=True, interval=10) plt.show()
To test things out, we define a small function, test_visualize
, that animates a system of three particles rotating in different directions. Note that the third particle completes a round three times faster than the others:
def test_visualize(): particles = [Particle(0.3, 0.5, 1), Particle(0.0, -0.5, -1), Particle(-0.1, -0.4, 3)] simulator = ParticleSimulator(particles) visualize(simulator) if __name__ == '__main__': test_visualize()
The test_visualize
function is helpful to graphically understand the system time evolution. In the following section, we will write more test functions to properly verify program correctness and measure performance.
Now that we have a working simulator, we can start measuring our performance and tune-up our code so that the simulator can handle as many particles as possible. As a first step, we will write a test and a benchmark.
We need a test that checks whether the results produced by the simulation are correct or not. Optimizing a program commonly requires employing multiple strategies; as we rewrite our code multiple times, bugs may easily be introduced. A solid test suite ensures that the implementation is correct at every iteration so that we are free to go wild and try different things with the confidence that, if the test suite passes, the code will still work as expected.
Our test will take three particles, simulate them for 0.1 time units, and compare the results with those from a reference implementation. A good way to organize your tests is using a separate function for each different aspect (or unit) of your application. Since our current functionality is included in the evolve
method, our function will be named test_evolve
. The following code shows the test_evolve
implementation. Note that, in this case, we compare floating point numbers up to a certain precision through the fequal
function:
def test_evolve(): particles = [Particle( 0.3, 0.5, +1), Particle( 0.0, -0.5, -1), Particle(-0.1, -0.4, +3)] simulator = ParticleSimulator(particles) simulator.evolve(0.1) p0, p1, p2 = particles def fequal(a, b, eps=1e-5): return abs(a - b) < eps assert fequal(p0.x, 0.210269) assert fequal(p0.y, 0.543863) assert fequal(p1.x, -0.099334) assert fequal(p1.y, -0.490034) assert fequal(p2.x, 0.191358) assert fequal(p2.y, -0.365227) if __name__ == '__main__': test_evolve()
A test ensures the correctness of our functionality but gives little information about its running time. A benchmark is a simple and representative use case that can be run to assess the running time of an application. Benchmarks are very useful to keep score of how fast our program is with each new version that we implement.
We can write a representative benchmark by instantiating a thousand Particle
objects with random coordinates and angular velocity, and feed them to a ParticleSimulator
class. We then let the system evolve for 0.1 time units:
from random import uniform def benchmark(): particles = [Particle(uniform(-1.0, 1.0), uniform(-1.0, 1.0), uniform(-1.0, 1.0)) for i in range(1000)] simulator = ParticleSimulator(particles) simulator.evolve(0.1) if __name__ == '__main__': benchmark()
A very simple way to time a benchmark is through the Unix time
command. Using the time
command, as follows, you can easily measure the execution time of an arbitrary process:
$ time python simul.py real 0m1.051s user 0m1.022s sys 0m0.028s
Note
The time
command is not available for Windows. To install Unix tools, such as time
, on Windows you can use the cygwin
shell, downloadable from the official website (http://www.cygwin.com/). Alternatively, you can use similar PowerShell commands, such as Measure-Command
(https://msdn.microsoft.com/en-us/powershell/reference/5.1/microsoft.powershell.utility/measure-command), to measure execution time.
By default, time
displays three metrics:
Note that sometimes user
+ sys
might be greater than real
, as multiple processors may work in parallel.
Note
time
also offers richer formatting options. For an overview, you can explore its manual (using the man time
command). If you want a summary of all the metrics available, you can use the -v
option.
The Unix time
command is one of the simplest and more direct ways to benchmark a program. For an accurate measurement, the benchmark should be designed to have a long enough execution time (in the order of seconds) so that the setup and tear-down of the process is small compared to the execution time of the application. The user
metric is suitable as a monitor for the CPU performance, while the real
metric also includes the time spent in other processes while waiting for I/O operations.
Another convenient way to time Python scripts is the timeit
module. This module runs a snippet of code in a loop for n times and measures the total execution times. Then, it repeats the same operation r times (by default, the value of r is 3
) and records the time of the best run. Due to this timing scheme, timeit
is an appropriate tool to accurately time small statements in isolation.
The timeit
module can be used as a Python package, from the command line or from IPython.
IPython is a Python shell design that improves the interactivity of the Python interpreter. It boosts tab completion and many utilities to time, profile, and debug your code. We will use this shell to try out snippets throughout the book. The IPython shell accepts magic commands--statements that start with a %
symbol--that enhance the shell with special behaviors. Commands that start with %%
are called cell magics, which can be applied on multi-line snippets (termed as cells).
IPython is available on most Linux distributions through pip
and is included in Anaconda.
Note
You can use IPython as a regular Python shell (ipython
), but it is also available in a Qt-based version (ipython qtconsole
) and as a powerful browser-based interface (jupyter notebook
).
In IPython and command-line interfaces, it is possible to specify the number of loops or repetitions with the -n
and -r
options. If not specified, they will be automatically inferred by timeit
. When invoking timeit
from the command line, you can also pass some setup code, through the -s
option, which will execute before the benchmark. In the following snippet, the IPython command line and Python module version of timeit
are demonstrated:
# IPython Interface $ ipython In [1]: from simul import benchmark In [2]: %timeit benchmark() 1 loops, best of 3: 782 ms per loop # Command Line Interface $ python -m timeit -s 'from simul import benchmark' 'benchmark()' 10 loops, best of 3: 826 msec per loop # Python Interface # put this function into the simul.py script import timeit result = timeit.timeit('benchmark()', setup='from __main__ import benchmark', number=10) # result is the time (in seconds) to run the whole loop result = timeit.repeat('benchmark()', setup='from __main__ import benchmark', number=10, repeat=3) # result is a list containing the time of each repetition (repeat=3 in this case)
Note that while the command line and IPython interfaces automatically infer a reasonable number of loops n
, the Python interface requires you to explicitly specify a value through the number
argument.
The Unix time
command is a versatile tool that can be used to assess the running time of small programs on a variety of platforms. For larger Python applications and libraries, a more comprehensive solution that deals with both testing and benchmarking is pytest
, in combination with its pytest-benchmark
plugin.
In this section, we will write a simple benchmark for our application using the pytest
testing framework. For the interested reader, the pytest
documentation, which can be found at http://doc.pytest.org/en/latest/, is the best resource to learn more about the framework and its uses.
Note
You can install pytest
from the console using the pip install pytest
command. The benchmarking plugin can be installed, similarly, by issuing the pip install pytest-benchmark
command.
A testing framework is a set of tools that simplifies writing, executing, and debugging tests and provides rich reports and summaries of the test results. When using the pytest
framework, it is recommended to place tests separately from the application code. In the following example, we create the test_simul.py
file, which contains the test_evolve
function:
from simul import Particle, ParticleSimulator def test_evolve(): particles = [Particle( 0.3, 0.5, +1), Particle( 0.0, -0.5, -1), Particle(-0.1, -0.4, +3)] simulator = ParticleSimulator(particles) simulator.evolve(0.1) p0, p1, p2 = particles def fequal(a, b, eps=1e-5): return abs(a - b) < eps assert fequal(p0.x, 0.210269) assert fequal(p0.y, 0.543863) assert fequal(p1.x, -0.099334) assert fequal(p1.y, -0.490034) assert fequal(p2.x, 0.191358) assert fequal(p2.y, -0.365227)
The pytest
executable can be used from the command line to discover and run tests contained in Python modules. To execute a specific test, we can use the pytest path/to/module.py::function_name
syntax. To execute test_evolve
, we can type the following command in a console to obtain simple but informative output:
$ pytest test_simul.py::test_evolve platform linux -- Python 3.5.2, pytest-3.0.5, py-1.4.32, pluggy-0.4.0 rootdir: /home/gabriele/workspace/hiperf/chapter1, inifile: plugins: collected 2 items test_simul.py . =========================== 1 passed in 0.43 seconds ===========================
Once we have a test in place, it is possible for you to execute your test as a benchmark using the pytest-benchmark
plugin. If we change our test
function so that it accepts an argument named benchmark
, the pytest
framework will automatically pass the benchmark
resource as an argument (in pytest
terminology, these resources are called fixtures). The benchmark resource can be called by passing the function that we intend to benchmark as the first argument, followed by the additional arguments. In the following snippet, we illustrate the edits necessary to benchmark the ParticleSimulator.evolve
function:
from simul import Particle, ParticleSimulator
def test_evolve(benchmark):
# ... previous code
benchmark(simulator.evolve, 0.1)
To run the benchmark, it is sufficient to rerun the pytest test_simul.py::test_evolve
command. The resulting output will contain detailed timing information regarding the test_evolve
function, as shown:
For each test collected, pytest-benchmark
will execute the benchmark function several times and provide a statistic summary of its running time. The output shown earlier is very interesting as it shows how running times vary between runs.
In this example, the benchmark in test_evolve
was run 34
times (column Rounds
), its timings ranged between 29
and 41
ms (Min
and Max
), and the Average
and Median
times were fairly similar at about 30
ms, which is actually very close to the best timing obtained. This example demonstrates how there can be substantial performance variability between runs, and that when taking timings with one-shot tools such as time
, it is a good idea to run the program multiple times and record a representative value, such as the minimum or the median.
pytest-benchmark
has many more features and options that can be used to take accurate timings and analyze the results. For more information, consult the documentation at http://pytest-benchmark.readthedocs.io/en/stable/usage.html.
After assessing the correctness and timing the execution time of the program, we are ready to identify the parts of the code that need to be tuned for performance. Those parts are typically quite small compared to the size of the program.
Two profiling modules are available through the Python standard library:
- The
profile
module: This module is written in pure Python and adds a significant overhead to the program execution. Its presence in the standard library is because of its vast platform support and because it is easier to extend. - The
cProfile
module: This is the main profiling module, with an interface equivalent toprofile
. It is written in C, has a small overhead, and is suitable as a general purpose profiler.
The cProfile
module can be used in three different ways:
- From the command line
- As a Python module
- With IPython
cProfile
does not require any change in the source code and can be executed directly on an existing Python script or function. You can use cProfile
from the command line in this way:
$ python -m cProfile simul.py
This will print a long output containing several profiling metrics of all of the functions called in the application. You can use the -s
option to sort the output by a specific metric. In the following snippet ,the output is sorted by the tottime
metric, which will be described here:
$ python -m cProfile -s tottime simul.py
The data produced by cProfile
can be saved in an output file by passing the -o
option. The format that cProfile
uses is readable by the stats
module and other tools. The usage of the -o
option is as follows:
$ python -m cProfile -o prof.out simul.py
The usage of cProfile as a Python module requires invoking the cProfile.run
function in the following way:
from simul import benchmark import cProfile cProfile.run("benchmark()")
You can also wrap a section of code between method calls of a cProfile.Profile
object, as shown:
from simul import benchmark import cProfile pr = cProfile.Profile() pr.enable() benchmark() pr.disable() pr.print_stats()
cProfile
can also be used interactively with IPython. The %prun
magic command lets you profile an individual function call, as illustrated:
The cProfile
output is divided into five columns:
ncalls
: The number of times the function was called.tottime
: The total time spent in the function without taking into account the calls to other functions.cumtime
: The time in the function including other function calls.percall
: The time spent for a single call of the function--it can be obtained by dividing the total or cumulative time by the number of calls.filename:lineno
: The filename and corresponding line numbers. This information is not available when calling C extensions modules.
The most important metric is tottime
, the actual time spent in the function body excluding subcalls, which tell us exactly where the bottleneck is.
Unsurprisingly, the largest portion of time is spent in the evolve
function. We can imagine that the loop is the section of the code that needs performance tuning.cProfile
only provides information at the function level and does not tell us which specific statements are responsible for the bottleneck. Fortunately, as we will see in the next section, the line_profiler
tool is capable of providing line-by-line information of the time spent in the function.
Analyzing the cProfile
text output can be daunting for big programs with a lot of calls and subcalls. Some visual tools aid the task by improving navigation with an interactive, graphical interface.
KCachegrind is a Graphical User Interface (GUI) useful to analyze the profiling output emitted by cProfile
.
Note
KCachegrind is available in the Ubuntu 16.04 official repositories. The Qt port, QCacheGrind, can be downloaded for Windows from http://sourceforge.net/projects/qcachegrindwin/. Mac users can compile QCacheGrind using Mac Ports (http://www.macports.org/) by following the instructions present in the blog post at http://blogs.perl.org/users/rurban/2013/04/install-kachegrind-on-macosx-with-ports.html.
KCachegrind can't directly read the output files produced by cProfile
. Luckily, the pyprof2calltree
third-party Python module is able to convert the cProfile
output file into a format readable by KCachegrind.
Note
You can install pyprof2calltree
from the Python Package Index using the command pip install pyprof2calltree
.
To best show the KCachegrind features, we will use another example with a more diversified structure. We define a recursive
function, factorial
, and two other functions that use factorial
, named taylor_exp
and taylor_sin
. They represent the polynomial coefficients of the Taylor approximations of exp(x)
and sin(x)
:
def factorial(n): if n == 0: return 1.0 else: return n * factorial(n-1) def taylor_exp(n): return [1.0/factorial(i) for i in range(n)] def taylor_sin(n): res = [] for i in range(n): if i % 2 == 1: res.append((-1)**((i-1)/2)/float(factorial(i))) else: res.append(0.0) return res def benchmark(): taylor_exp(500) taylor_sin(500) if __name__ == '__main__': benchmark()
To access profile information, we first need to generate the cProfile
output file:
$ python -m cProfile -o prof.out taylor.py
Then, we can convert the output file with pyprof2calltree
and launch KCachegrind:
$ pyprof2calltree -i prof.out -o prof.calltree $ kcachegrind prof.calltree # or qcachegrind prof.calltree
The output is shown in the following screenshot:
The preceding screenshot shows the KCachegrind user interface. On the left, we have an output fairly similar to cProfile
. The actual column names are slightly different: Incl.
translates to cProfile
module's cumtime
and Self
translates to tottime
. The values are given in percentages by clicking on the Relative
button on the menu bar. By clicking on the column headers, you can sort them by the corresponding property.
On the top right, a click on the Callee Map
tab will display a diagram of the function costs. In the diagram, the time percentage spent by the function is proportional to the area of the rectangle. Rectangles can contain sub-rectangles that represent subcalls to other functions. In this case, we can easily see that there are two rectangles for the factorial
function. The one on the left corresponds to the calls made by taylor_exp
and the one on the right to the calls made by taylor_sin
.
On the bottom right, you can display another diagram, the call graph, by clicking on the Call Graph
tab. A call graph is a graphical representation of the calling relationship between the functions; each square represents a function and the arrows imply a calling relationship. For example, taylor_exp
calls factorial
500
times, and taylor_sin
calls factorial 250
times. KCachegrind also detects recursive calls: factorial
calls itself 187250
times.
You can navigate to the Call Graph
or the Caller Map
tab by double-clicking on the rectangles; the interface will update accordingly, showing that the timing properties are relative to the selected function. For example, double-clicking on taylor_exp
will cause the graph to change, showing only the contribution of taylor_exp
to the total cost.
Note
Gprof2Dot (https://github.com/jrfonseca/gprof2dot) is another popular tool used to produce call graphs. Starting from output files produced by one of the supported profilers, it will generate a .dot
diagram representing the call graph.
Now that we know which function we have to optimize, we can use the line_profiler
module that provides information on how time is spent in a line-by-line fashion. This is very useful in situations where it's difficult to determine which statements are costly. The line_profiler
module is a third-party module that is available on the Python Package Index and can be installed by following the instructions at https://github.com/rkern/line_profiler.
In order to use line_profiler
, we need to apply a @profile
decorator to the functions we intend to monitor. Note that you don't have to import the profile
function from another module as it gets injected in the global namespace when running the kernprof.py
profiling script. To produce profiling output for our program, we need to add the @profile
decorator to the evolve
function:
@profile def evolve(self, dt): # code
The kernprof.py
script will produce an output file and will print the result of the profiling on the standard output. We should run the script with two options:
-l
to use theline_profiler
function-v
to immediately print the results on screen
The usage of kernprof.py
is illustrated in the following line of code:
$ kernprof.py -l -v simul.py
It is also possible to run the profiler in an IPython shell for interactive editing. You should first load the line_profiler
extension that will provide the lprun
magic command. Using that command, you can avoid adding the @profile
decorator:
The output is quite intuitive and is divided into six columns:
Line #
: The number of the line that was runHits
: The number of times that line was runTime
: The execution time of the line in microseconds (Time
)Per Hit
: Time/hits% Time
: Fraction of the total time spent executing that lineLine Contents
: The content of the line
By looking at the percentage column, we can get a pretty good idea of where the time is spent. In this case, there are a few statements in the for
loop body with a cost of around 10-20 percent each.
Now that we have identified where exactly our application is spending most of its time, we can make some changes and assess the change in performance.
There are different ways to tune up our pure Python code. The way that produces the most remarkable results is to improve the algorithms used. In this case, instead of calculating the velocity and adding small steps, it will be more efficient (and correct as it is not an approximation) to express the equations of motion in terms of radius, r
, and angle, alpha
, (instead of x
and y
), and then calculate the points on a circle using the following equation:
x = r * cos(alpha) y = r * sin(alpha)
Another way lies in minimizing the number of instructions. For example, we can precalculate the timestep * p.ang_vel
factor that doesn't change with time. We can exchange the loop order (first we iterate on particles, then we iterate on time steps) and put the calculation of the factor outside the loop on the particles.
The line-by-line profiling also showed that even simple assignment operations can take a considerable amount of time. For example, the following statement takes more than 10 percent of the total time:
v_x = (-p.y)/norm
We can improve the performance of the loop by reducing the number of assignment operations performed. To do that, we can avoid intermediate variables by rewriting the expression into a single, slightly more complex statement (note that the right-hand side gets evaluated completely before being assigned to the variables):
p.x, p.y = p.x - t_x_ang*p.y/norm, p.y + t_x_ang * p.x/norm
This leads to the following code:
def evolve_fast(self, dt): timestep = 0.00001 nsteps = int(dt/timestep) # Loop order is changed for p in self.particles: t_x_ang = timestep * p.ang_vel for i in range(nsteps): norm = (p.x**2 + p.y**2)**0.5 p.x, p.y = (p.x - t_x_ang * p.y/norm, p.y + t_x_ang * p.x/norm)
After applying the changes, we should verify that the result is still the same by running our test. We can then compare the execution times using our benchmark:
$ time python simul.py # Performance Tuned real 0m0.756s user 0m0.714s sys 0m0.036s $ time python simul.py # Original real 0m0.863s user 0m0.831s sys 0m0.028s
As you can see, we obtained only a modest increment in speed by making a pure Python micro-optimization.
Sometimes it's not easy to estimate how many operations a Python statement will take. In this section, we will dig into the Python internals to estimate the performance of individual statements. In the CPython interpreter, Python code is first converted to an intermediate representation, the bytecode, and then executed by the Python interpreter.
To inspect how the code is converted to bytecode, we can use the dis
Python module (dis
stands for disassemble). Its usage is really simple; all that is needed is to call the dis.dis
function on the ParticleSimulator.evolve
method:
import dis from simul import ParticleSimulator dis.dis(ParticleSimulator.evolve)
This will print, for each line in the function, a list of bytecode instructions. For example, the v_x = (-p.y)/norm
statement is expanded in the following set of instructions:
29 85 LOAD_FAST 5 (p) 88 LOAD_ATTR 4 (y) 91 UNARY_NEGATIVE 92 LOAD_FAST 6 (norm) 95 BINARY_TRUE_DIVIDE 96 STORE_FAST 7 (v_x)
LOAD_FAST
loads a reference of the p
variable onto the stack and LOAD_ATTR
loads the y
attribute of the item present on top of the stack. The other instructions, UNARY_NEGATIVE
and BINARY_TRUE_DIVIDE
, simply do arithmetic operations on top-of-stack items. Finally, the result is stored in v_x
(STORE_FAST
).
By analyzing the dis
output, we can see that the first version of the loop produces 51
bytecode instructions while the second gets converted into 35
instructions.
The dis
module helps discover how the statements get converted and serves mainly as an exploration and learning tool of the Python bytecode representation.
To improve our performance even further, we can keep trying to figure out other approaches to reduce the amount of instructions. It's clear, however, that this approach is ultimately limited by the speed of the Python interpreter and it is probably not the right tool for the job. In the following chapters, we will see how to speed up interpreter-limited calculations by executing fast specialized versions written in a lower level language (such as C or Fortran).
In some cases, high memory usage constitutes an issue. For example, if we want to handle a huge number of particles, we will incur a memory overhead due to the creation of many Particle
instances.
The memory_profiler
module summarizes, in a way similar to line_profiler
, the memory usage of the process.
Note
The memory_profiler
package is also available on the Python Package Index. You should also install the psutil
module (https://github.com/giampaolo/psutil) as an optional dependency that will make memory_profiler
considerably faster.
Just like line_profiler
, memory_profiler
also requires the instrumentation of the source code by placing a @profile
decorator on the function we intend to monitor. In our case, we want to analyze the benchmark
function.
We can slightly change benchmark
to instantiate a considerable amount (100000
) of Particle
instances and decrease the simulation time:
def benchmark_memory(): particles = [Particle(uniform(-1.0, 1.0), uniform(-1.0, 1.0), uniform(-1.0, 1.0)) for i in range(100000)] simulator = ParticleSimulator(particles) simulator.evolve(0.001)
We can use memory_profiler
from an IPython shell through the %mprun
magic command as shown in the following screenshot:
Note
It is possible to run memory_profiler
from the shell using the mprof run
command after adding the @profile
decorator.
From the Increment
column, we can see that 100,000 Particle
objects take 23.7 MiB
of memory.
Note
1 MiB (mebibyte) is equivalent to 1,048,576 bytes. It is different from 1 MB (megabyte), which is equivalent to 1,000,000 bytes.
We can use __slots__
on the Particle
class to reduce its memory footprint. This feature saves some memory by avoiding storing the variables of the instance in an internal dictionary. This strategy, however, has a drawback--it prevents the addition of attributes other than the ones specified in __slots__
:
class Particle: __slots__ = ('x', 'y', 'ang_vel') def __init__(self, x, y, ang_vel): self.x = x self.y = y self.ang_vel = ang_vel
We can now rerun our benchmark to assess the change in memory consumption, the result is displayed in the following screenshot:
By rewriting the Particle
class using __slots__
, we can save about 10 MiB
of memory.
In this chapter, we introduced the basic principles of optimization and applied those principles to a test application. When optimizing, the first thing to do is test and identify the bottlenecks in the application. We saw how to write and time a benchmark using the time
Unix command, the Python timeit
module, and the full-fledged pytest-benchmark
package. We learned how to profile our application using cProfile
, line_profiler
, and memory_profiler
, and how to analyze and navigate the profiling data graphically with KCachegrind.
In the next chapter, we will explore how to improve performance using algorithms and data structures available in the Python standard library. We will cover scaling, sample usage of several data structures, and learn techniques such as caching and memoization.