🌚 Computer Science After Dark

⚡️ The computers are fast, but you don't know it

Humans have a shit sense of measurement, especially for quantities that they can't biologically perceive. For example, you intuitively know how much more heavy a 10kg object is than a 1kg object.

For such quantities, your sense of measurement can improve if you have some way to translate them into signals that the brain is familiar with. For example, have you seen these videos?

  1. Universe Size Comparision 3D
  2. Measuring Jeff Bezos' Wealth in Rice

The second is my favorite. I eat one cup of rice every day. So I measure Jeff's wealth not just visually but also with my stomach.

Very recently, I did a few optimizations on a piece of code, which helped me intuitively understand how fast a computer can really go. Thought I'd share [2].

What are we optimizing?

The function looks something like this:

# note that this is a reduced form of the actual function
def aggregate(input_df):
    weights = initialize_weights(len(input_df)) 

    # input_df contains three columns timestamp, score & id
    output_df = group_by_id(input_df) 

    # sorting happens within group
    output_df = sort_by_time(output_df) 
    output_df = sort_by_score(output_df, desc=True)

    # ranking happens within the group
    output_df = rank_within_id(output_df)

    # adds column `results`
    output_df = multiply_weights(output_df, weights) 
    results = results_sum_in_each_group(output_df)

    return results # is a list

This is a score aggregation function that's used by one of our Machine Learning (ML) services. This function is crucial to getting the model to work. Note that the output of this function needs to be computed in less than 500ms for it to even make it to production (where we need to do between 400-800 calls to this function under 500ms). I was asked to optimize it.

Okay let's measure how this function performs for a 1000 calls (assume each input will have 10 items max)

Base

Took ~8 seconds to do 1000 calls. Not good at all :( Well, I wanted to try for 1 million calls but it just takes over 20 minutes to do so. Let's see how we can do better:

Optimization 1: Writing the algorithm without Pandas 🐼 + trivial algorithm improvements

Python's "Pandas" library is great for playing around with the data but it's horrible for production. If you find yourself using it in a production system then it's time to grow up [1]. I replaced Pandas with simple python lists and implemented the algorithm manually to do the group-by and sort.

Also, the function for calculating weights was being re-initialized in every call, and all it did was initialize the same sequence of weights for some size of the array. This was a bonus and I pre-computed weights.

Here is how the function looked:

WEIGHTS = initialize_weights(99999) 
def aggregate_efficient(input_lists):
    global WEIGHTS

    # input_lists contain 2 lists
    output_lists = algorithm_wizardry(input_lists) 

    # add column `results`
    output_lists = multiply_weights(output_lists, WEIGHTS) 
    results = results_sum_in_each_group(output_lists)

    return results # is a list

aggregate_efficient(ip_list)

And this is how long it takes for 1 million calls:

Post optimization

So from 20 minutes, we have come down to 12 seconds! That's roughly a 9900% increase in speed.

This is enough for the function to go to production. But why stop here?

Optimization 2: Cythonizing our functions

One of the simplest tricks to speed up a python function is to simply write it in Cython. Here is how to do it:

  1. Create your .pyx function

The more cdef you can put here the better the optimization

def aggregate_efficient_cyth(double[:] score_array, 
                        double[:] time_array, 
                        double[:] weights): 

    results = algorithm_wizardry(score_array, 
                                 time_array, weights)
    return results
  1. Define your setup.py file

We add some compiler flags to make it go fast. Some say -O3 flag is dangerous but that's how we roll

from distutils.core import setup
from Cython.Build import cythonize
from distutils.extension import Extension
from Cython.Distutils import build_ext


ext_modules = [
        Extension("agg_cython",
            ["agg_cython.pyx"],
            libraries=["m"],
            extra_compile_args = ["-O3", "-ffast-math", "-march=native", "-fopenmp" ],
            extra_link_args=['-fopenmp'],
            language="c++")
        ]
setup(name="agg_cyth_pure",cmdclass = {'build_ext': build_ext}, ext_modules=ext_modules,)

And this is how it performs for 1 million calls:

Cython

~6.59 seconds i.e. ~82% increase in the speed. We managed to almost half the time of the previous optimization :) This is awesome!

We will not stop here. Let's go nuts

Optimization 3: Writing your function in pure C++

This is where the fun starts. This is one of the most important skills that I've been able to add to my tech inventory (thanks Rags ), and if performance really matters to you then this will help you:

  1. Implement the function in pure C++
#include "agg_cyth_fast.hpp"

using namespace std;

double agg_efficient(double score_array[], 
                    long time_array[],
                    double weight_lookup[],
                    int N){

    vector<double> results = algorithm_wizardry(score_array,
                                   time_array, weight_lookup, N);
    return results;
}
  1. Prepare your header file
#ifndef AGG_H
#define AGG_H

#include <iostream>
#include <map>
#include <vector>
#include <algorithm>

double agg_efficient(double[], long[], double[], int);
#endif
  1. Write a .pyx file to talk to C++
import numpy as np
from math import exp 
from libc.math cimport exp as c_exp
from cython.parallel import prange
cimport cython


cdef extern from "agg_cyth_fast.hpp" nogil:
    double agg_efficient(double[], long[], double[], int)

def agg_efficient_fs(double[:] score_array, 
                      long[:] time_array,  
                       double[:] weight_lookup):
    cdef int N = len(time_array)
    cdef double Y;
    Y = agg_efficient(&score_array[0], 
                      &time_array[0], 
                       &weight_lookup[0], N);
    return Y

Finally, we use a similar setup.py file as the previous optimization and build our function. This is effectively going to let us pass Python objects to a pure C++ function.

This is how it performs for 1 million calls: Pure CPP

It's crazy how fast pure C++ can be. We have sped up [3] the computation by ~119%! 🎉

We are not done yet. The .pyx file in this section has some code hidden but someone with a keen observation might have guessed the next optimization by looking at the imports.

Optimization 4: Time to banish the Global Interpreter Lock (GIL)

Python has this annoying thing called GIL, which won't let your multi-threaded python code run faster than a single-threaded one.

If you really want to bully your computer, why do it on a single core?

We now, use prange to simply parallelize our computations.

Simply add this to the .pyx file:

@cython.boundscheck(False)
@cython.wraparound(False)
def agg_efficient_fs_batch(double[:,:] score_array, 
                            long[:,:] time_array, 
                            double[:] weight_lookup):
    cdef int M = len(score_array)
    cdef double[:] Y = np.zeros(M)
    cdef int i, N
    for i in prange(M, nogil=True):
        N = len(time_array[i])
        Y[i] = agg_efficient(&score_array[i][0], 
                             &time_array[i][0], 
                             &weight_lookup[0], N);
    return Y

This is how much it takes the same 1 million calls in parallel on a 4 core machine: PrangeCyth

That's an approximate ~237% increase in speed over the last optimization.

To Summarize, for 1 million calls:

Optimization Time Taken Speedup Over Original
None 1200s -
Remove Pandas + Algo improvement 12s ~9900%
Cythonize Function 6.59s ~18109.4%
Pure C++ Implementation 3s ~33326.2%
Parallel C++ on 4 cores 890ms ~134731%
Parallel C++ on 32 cores 201ms ~596915%

I guess this is how fast computers can be

Follow me on Twitter if you want to bully your computer into going fast

If this helped you, consider buying me a coffee!

Footnotes:

[1] Please don't get me wrong. Pandas is pretty fast for a typical dataset but it's not the processing that slows down pandas in my case. It's the creation of Pandas objects itself which can be slow. If you wanted to do a group by + sort on 1 million rows then Pandas will be faster than pure Python. But, if your service needs to respond in less than 500ms, then you will feel the effect of each line of Pandas code (or any abstraction overhead).

[2] Wow, this hit the front page on Hackernews. Check out the discussion for some further enlightenment

[3] Consistent & correct language (reduced time vs increase speed)

[4] Best Book on algorithms: The Algorithm Design Manual

#machine-learning #python #algorithms #ml #cython #optimization #c #numpy #pandas

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