Friday, June 01, 2012

Compression of the lyrics of "Never gonna give you up" using the Bentley/McIlroy algorithm

There's a fun StackExchange post about the smallest program to output the lyrics to Never gonna give you up making the rounds today.  I'm not entering the competition, but I thought it would be interesting to look at from a compression perspective.  I've been working a lot with the Bentley/McIlroy algorithm for long string compression and this is a good example to illustrate its output.

Here are the original lyrics (1871 bytes):
We're no strangers to love
You know the rules and so do I
A full commitment's what I'm thinking of
You wouldn't get this from any other guy
I just wanna tell you how I'm feeling
Gotta make you understand
Never gonna give you up
Never gonna let you down
Never gonna run around and desert you
Never gonna make you cry
Never gonna say goodbye
Never gonna tell a lie and hurt you
We've known each other for so long
Your heart's been aching but
You're too shy to say it
Inside we both know what's been going on
We know the game and we're gonna play it
And if you ask me how I'm feeling
Don't tell me you're too blind to see
Never gonna give you up
Never gonna let you down
Never gonna run around and desert you
Never gonna make you cry
Never gonna say goodbye
Never gonna tell a lie and hurt you
Never gonna give you up
Never gonna let you down
Never gonna run around and desert you
Never gonna make you cry
Never gonna say goodbye
Never gonna tell a lie and hurt you
(Ooh, give you up)
(Ooh, give you up)
(Ooh)
Never gonna give, never gonna give
(Give you up)
(Ooh)
Never gonna give, never gonna give
(Give you up)
We've know each other for so long
Your heart's been aching but
You're too shy to say it
Inside we both know what's been going on
We know the game and we're gonna play it
I just wanna tell you how I'm feeling
Gotta make you understand
Never gonna give you up
Never gonna let you down
Never gonna run around and desert you
Never gonna make you cry
Never gonna say goodbye
Never gonna tell a lie and hurt you
Never gonna give you up
Never gonna let you down
Never gonna run around and desert you
Never gonna make you cry
Never gonna say goodbye
Never gonna tell a lie and hurt you
Never gonna give you up
Never gonna let you down
Never gonna run around and desert you
Never gonna make you cry
Never gonna say goodbye
Never gonna tell a lie and hurt you
And here's the compressed version (note that the actual compressed file is a 611 byte binary file, here I've altered it for readability).  You see either the text itself, or a reference to preceding text (which has potentially been expanded first).  The references are in the form where p is the position (counting from zero at the start of the decompressed text) and n the number of characters: it means 'copy n characters from position p to here'.
We're no strangers to love
You know the rules and so do I
A full commitment's what I'm thinking of
You wouldn't get this from any other guy
I just wanna tell you how I'm feeling
Gotta make you understand
Never gonna give you up<204,13>let you down<204,13>run around<45,5>desert you<20
4,13><184,9>cry<204,13>say goodbye<204,13>tell a lie<45,5>hu<285,7>
We've<30,5>n each<129,7>for so long
Your heart's been aching but
You're too shy to say it
Inside we both<30,6>wha<422,9>going on
We<30,10>game<45,5>we're<210,7>play it
And if you ask me<161,17>Don't tell m<220,5>'re too blind to see
<340,13><217,161><229,12><634,161>(Ooh,<633,12>)<967,24>)<340,13>give, n<230,11>
give
(G<635,10><1004,57><377,11><389,160><139,239><229,12><634,333>
The first <204,13> is the reference back to "Never gonna " which is used many times.  The <45,5> is a reference to the first instance of " and ".  Notice how "Never gonna make you cry" is made up from a reference to "Never gonna " and then "make you ".
But it's towards the end where large blocks of text are repeated in the lyrics that the reference scheme really comes into its own.   The end references are to large repeated blocks, but notice how those blocks themselves first have to be decompressed in the early parts of the lyrics.
On this short text we get a compression to 33% of the original size.  But gzip still wins getting the text down to 402 bytes (22%).  Bentley/McIlroy works better with longer blocks of text where there's repetition of long strings over long distances.

If you enjoyed this blog post, you might enjoy my travel book for people interested in science and technology: The Geek Atlas. Signed copies of The Geek Atlas are available.

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