I’ve been working lately in a command line application called Bard which is a music manager for your local music collection. Bard does an acoustic fingerprinting of your songs (using acoustid) and stores all song metadata in a sqlite database. With this, you can do queries and find song duplicates easily even if the songs are not correctly tagged. I’ll talk in another post more about Bard and its features, but here I wanted to talk about the algorithm to find song duplicates and how I optimized it to run around 8000 times faster.

The algorithm

To find out if two songs are similar, you have to compare their acoustic fingerprints. That seems easy (and in fact, it is), but it’s not as straightforward as it seems. A fingerprint (as acoustid calculates it) is not just a number, but an array of numbers, or better said, an array of bits, so you can’t just compare the numbers themselves, but you have to compare the bits in those numbers. If all bits are exactly the same, the songs are considered the same, if 99% of bits are the same then that means there’s a 99% chance it’s the same tune, maybe differing because of encoding issues (like one song being encoded as mp3 with 192 kbits/s and the other with 128 kbits/s).

But there are more things to have in mind when comparing songs. Sometimes they have different silence lengths at the beginning or end, so the bits that we compare are not correctly aligned and they don’t match as they are calculated, but could match if we shifted one of the fingerprints a bit.

This means that to compare two songs, we don’t just have to compare the two fingerprints, but then we have to simulate increasing/decreasing silence lengths at the beginning of a song by shifting its fingerprint and calculate the match level for each shift to see if we improve/worsen the similarity percentage. Right now, Bard shiftes the array by 100 positions in one direction and then another 100 positions in the other direction, this means that for each song we have to compare the two fingerprints 200 times.

Then, if we want to compare all of the songs in a collection to find duplicates, we need to compare the songs with ID 1 and 2, then we need to compare the song with ID 3 with IDs 1 and 2, and in general, each song with all previous ones. This means for a collection with 1000 songs we need to compare 1000*1001/2 = 500500 songs (or 100100000 fingerprints).

The initial python implementation

Bard is written in python, so my first implementation used a python list to store the array of integers from the fingerprint. For each iteration in which I have to shift the array numbers I prepend a 0 to one fingerprint array and then iterate over them comparing each element. To do this comparison, I xor the two elements and then use a standard good known algorithm to count the bits which are set in a integer:

def count_bits_set(i): i = i – ((i >> 1) & 0x55555555) i = (i & 0x33333333) + ((i >> 2) & 0x33333333) return (((i + (i >> 4) & 0xF0F0F0F) * 0x1010101) & 0xffffffff) >> 24

Let’s use the speed of this implementation as a reference and call it 1x.

First improvement

As a first improvement I tried replacing that bit counting algorithm with gmpy.popcount which was faster and also improved the algorithm by introducing a canceling threshold. This new algorithm stops comparing two fingerprints as soon as it’s mathematically impossible to have a match over the canceling threshold. So for example, if we are iterating the fingerprints and we calculate that even if all remaining bits would match we wouldn’t get at least a 55% match between songs, we just return “different songs” (but we still need to shift songs and try again, just in case).

With these improvements (commit) the comparisons ran at nearly an exact 2x speed.

Enter C++17

At that time, I thought that this code wouldn’t scale nicely with a large music collection, so I thought Bard needed a much better implementation. Modifying memory is slow and C/C++ allows for much fine grained low-level optimizations, but I didn’t want to rewrite the application in C++ so I used Boost.Python to implement just this algorithm in C++ and call it from the python application. I should say that I found really easy to integrate methods in C++ with Python and I absolutely recommend Boost.Python .

With the new implementation in C++ (commit) I used STL’s vector to store the fingerprints and I added the maximum offsets in advance so I didn’t need to modify the vector elements during the algorithm and I access elements by simulating the shifting offsets. I also use STL’s map to store all fingerprints indexed on a song ID. Finally, I also added another important optimization which is using the CPU’s instructions to calculate bits set by using gcc’s __builtin_popcount.

The best part of this algorithm is that during the comparison algorithm itself, no fingerprint is copied or modified, which translated in a speed of 126.47x . At this point I started calculating another measure: songs compared per second (remember we’re doing 200 fingerprints comparison for each pair of songs). This algorithm gave an average speed of 580 songs/second. Or put another way, to compare our example collection of 1000 songs, this would take 14 min 22 sec (note that we can calculate the original implementation in Python would take approximately 1 day, 6 hours, 16 minutes and 57 seconds).

First try to parallelize the algorithm

I use an i7 CPU to run Bard and I always thought it was a pity that it only used one CPU. Since the algorithm that compares two songs doesn’t modify their data anymore, I thought it might be interesting to parallelize it to allow it to run in all 8 cores at the same time and just coalesce the result of each independent iterations. So I wondered how to do it and noticed that when I compare each song with all previous ones, this is done using a for loop that iterates over a std::map containing all songs that are already processed. Wouldn’t it be nice to have a for-each loop implementation that runs each iteration on a different thread? Well, there is! std::for_each in C++17 allows to specify an ExecutionPolicy with which you can tell it to run the iterations in different threads. Now the bad news: This part of the standard is not completely supported by gcc yet.

So I searched for a for_each implementation and found this stackoverflow question which included one. The problem is that the question mentions the implementation was copied from the C++ Concurrency in Action book and I’m not sure of the license of that code, so I can’t just copy it into Bard. But I can make some tests with it just for measurements purposes.

This increased the speed to 1897x or ~8700 songs/second (1000 songs would be processed in 57 seconds). Impressive, isn’t it? Well… keep reading 🙂

Second parallelization try

So I needed to find a parallelized for_each version I could use. Fortunately I kept looking and found out that gcc includes an experimental parallel implementation of some algorithms in the C++ standard library which includes __gnu_parallel::for_each (there are more parallelized algorithms documented in that page). You just need to link to the openmp library.

So I ran to change the code to use it and hit a problem: I used __gnu_parallel::for_each but every time I tested, it only ran sequentially! It took me a while to find out what was happening, but after reading the gcc implementation of __gnu_parallel::for_each I noticed it required a random access iterator, but I’m iterating on a std::map and maps have a bidirectional iterator, not a random-access one.

So I changed the code (commit) to first copy the fingerprints from the std::map<int, std::vector<int>> to a std::vector<std::pair<int,std::vector<int>>> and with just that, the same __gnu_parallel::for_each line ran using a pool of 8 threads.

The gcc implementation proved to be faster than the implementation in the stackoverflow question, with a speed of 2442x , ~11200 songs/second and 44 seconds.

The obvious but important improvement I forgot about

While looking at the compiler build Bard I noticed I wasn’t using compiler flags to optimize for speed! So I tested adding -Ofast -march=native -mtune=native -funroll-loops to the compiler (commit). Just that. Guess what happened…

The speed raised to a very nice 6552x, ~30050 songs/second and 16 seconds.

The Tumbleweed improvement I got for free

I’m running openSUSE Tumbleweed in the system I use to develop which as you probably know, is a (very nice) rolling release distribution. One day, while doing these tests, Tumbleweed updated the compiler from gcc 7.3 to using gcc 8.1 by default. So I thought that deserved another measurements.

Just changing the compiler to the newer version increased the speed to 7714x, 35380 songs/second and 14 seconds.

The final optimization

An obvious improvement I didn’t do yet was replacing the map with a vector so I don’t have to convert it before each for_each call. Also, vectors allow to reserve space in advance, and since I know the final size the vector will have at the end of the whole algorithm, I changed to code to use reserve wisely.

This commit gave the last increase of speed, to 7998x, 36680 songs/second and would fully process a music collection of 1000 songs in just 13 seconds.

Conclusion

Just some notes I think are important to keep in mind from this experience: