Let’s (Not) Illustrate Dragon Age Origins

So I’ve been spending the past few months playing through Dragon Age Origins and looking for good screen shots I could pixelate as part of my long and futile quest to learn how to art. And while this was kind of fun I eventually came to the realization I was spending more time playing and writing about the game than I was practicing my art skills. That sort of defeated the whole purpose of the exercise so I gave up and came up with a new plan.

But it’s not like I didn’t get any practice done, so here are some of my “better” (as in least worst) efforts.

A tragically cheerful Fault, unaware she’s about to be thrust into yet another cursed world full of things that want to kill her.

Of course there are giant spiders. Can’t call yourself an RPG without giant spiders.

This is so low resolution it’s probably hard to tell who it’s supposed to be but I still kind of like how “meh” that expression turned out.

Alistair’s perpetual smirk increases his aggro by 5% and helps explain why he makes such a great tank.

I failed to capture Morrigan’s trademark scornful frown and instead made her look like she’s trying to remember whether or not she forgot to turn the oven off before leaving home.

I was aiming for “being a refugee is awful” but seem to have wound up with “WHEEE, camping is fun!”.

 

 

Let’s Program A Compression Algorithm Part 6: In Which We Consider How Professional Compression Algorithms Function

Now that we’ve got a working little ASCII compressor it’s time to talk about how “real” compression algorithms work.

Now honestly I should probably just drop a couple wiki links to Huffman_Coding and DEFLATE but presumably you’re here on my blog because you specifically want to hear me talk about computer science so here we go!

Let’s start by refreshing our memories on how we approached the problem of compression.

We started by discovering that normal ASCII text assigns a full 8-bits to every possible letter. We then did some research and found that some ASCII letters are much more common than others. That let us invent a new standard that squished common letters into 4-bits while expanding less common letters into 9-bits. This overall resulted in files that were 20-30% smaller than their plan ASCII equivalents.

So how would a professional approach the same problem?

Believe it or not they would do more or less the same thing. Professional tools achieve their impressive 80%+ compression standards using the same basic approach we did: Find unusually common data patterns and then replace them with much smaller compressed place holders. The professional tools are just much much smarter about how they find and compress these patterns than we were.

How much smarter? Let’s find out by comparing and contrasting what we did against what better compression tools do.

 

Our OK Idea: We designed our compression patterns based around our knowledge of average letter frequencies in the English language. While this worked OK there was the problem that not every text file follows the average English pattern. A report about zigzagging zebras is going to have a ton of z’s and g’s while a C++ code file is going to have lots of brackets and semi-colons. Our average English compression strategy won’t work very well on files like that.

Their Better Idea: Professional tools don’t use a single universal encoding scheme but instead create a unique encoding for every file based on their individual symbol frequency. So if a particular text file has a ton of “z”s or parenthesis or brackets it will get its own custom code that compresses those letters. This lack of a universal standard does mean that each compressed file has to start with a dictionary explaining the specific compression pattern used for that file but the space saved by using an optimized compression pattern for each file more than makes up for the space taken up by the dictionary.

 

Our OK Idea: We not only used the same compression codes for every single file, we used the same compression codes throughout every file. This was easy to program but could be sub-optimal on longer files. If a book starts out talking about zigzagging zebras but later focuses on electric eels then one half of the book might compress better than the other.

Their Better Idea: Many compressional algorithms split files into multiple segments and then compress them individually before gluing them together into an output file. This way each segment can have its own optimized compression pattern. So if one half of a file had a lot of “z”s but no “l”s it could get a compression pattern focused on “z”s. If the second half of the file switched things around and had lots of “l”s but almost no “z”s the algorithm could then switch to a new compression pattern that shrunk down the “l”s and did nothing with “z”s. Of course this means each compressed file has to have multiple dictionaries explaining the specific compression pattern and length of each file segment but once again the space you save in better compression outweighs the space you lose from the extra dictionaries.

 

Our OK Idea: Our compression code focused only on ASCII text files. This made it easy to design and test our project but also severely limits it’s utility.

Their Better Idea: Admittedly some professional tools also only focus on one file type. For example, PNG only compresses image files. But many other professional compression tools work by looking for repeated bit patterns of any sort and length. This lets them compress any file made of bits which is, well, all of them. Sure, not every file compresses particularly well but at least there are no files you plain can’t run the algorithm on.

 

Our OK Idea: Our compression code worked by replacing common 8-bit letter patterns with smaller 4-bit patterns. This means that even in a best case scenario (a file containing only our eight compressible common letters) we could only shrink a file down to 50%.

Their Better Idea: Professional tools don’t restrict themselves to only looking for common 8-bit patterns but can instead find repeated patterns of any length. This can lead to massive compression by finding things like commonly used 256-bit patterns that can be replaced with two or three bit placeholders for 99% compression. Of course not every file is going to have conveniently repeated large bit sequences but being able to recognize these opportunities when they do happen opens up a lot of possibilities.

 

So there you have it. The main difference between professional compression algorithms and our toy is that professional programs spend a lot more time upfront analyzing their target files in order to figure out an ideal compression strategy for that specific file. This obviously is going to lead to better results than our naive “one size fits all” approach.

But figuring out the ideal compression strategy for a specific file or type of file is often easier said than done! To go much deeper into that we’d have to start seriously digging into information theory and various bits of complex math and that’s way beyond the scope of this blog. But if this little project piqued your interest I’d definitely encourage you to take some time and study up on it a bit yourself.

 

BONUS PROJECT FOR ENTERPRISING PROGRAMMERS

Hopefully this article has given you a few ideas on how our little toy compressor could be improved. And while you probably don’t want to try anything as drastic as implementing a full Huffman style algorithm I think there are a lot of relatively simple improvements you could experiment with.

For example, what if you got rid the hard coded set of “English’s eight most common symbols” and instead had your algorithm begin compression by doing a simple ASCII letter count to figure out the eight most common symbols for your specific target file? You could then have your algorithm assign compression short codes to those eight symbols which should probably lead to results at least a few percentage points smaller than our one size fits all prototypes

Of course, in order to decompress these files you’ll have to start your file with a list of which short codes map to which letters. You could do this with some sort of pair syntax (ex: {0000:z,0001:l,0010:p}) or maybe just have the first eight bytes in a compressed file always be the eight symbols from your compression map.

And with that we’re pretty much done talking about compression, but speaking of improvements reminds me that my Lisp code is still slow as cold tar. So if you have any interest in Lisp at all I’d like to encourage you to tune in again next week as we analyze and speed up our code and maybe even talk a little about that “functional programming”.

Let’s Program A Compression Algorithm Part 5: In Which Compressed Files Are Decompressed And The Project Completed

A program that can only compress data is like a packing company that insists on hot gluing your boxes shut: Everything may look nice and neat and tidy but you’re going to be in a real pickle when you want to actually start using your stuff again.

Fortunately writing a decompression function will be pretty easy; after all it’s mostly just the function we already wrote but backwards.

What we want to accomplish boils down to:

1) Read our compressed file and turn it into a list of bits

2) See if the file starts with a 0 or a 1

3) If it starts with a 0 look up a byte value in our short-list table. Add this to output.

4) If it starts with a 1 discard the 1 and turn the next 8 bits into a byte. Add this to output.

5) Discard the bits we just used and then repeat our steps until we see our termination sequence

Step one needs almost no work at all. Our previously written file-to-compressed-bitlist can already read a file bit by bit and then output a bitlist. The only problem is that it creates that bitlist by translating raw bytes into compressing bit sequences. Since we are now reading compressed data we just want the raw bits and bytes which we can get by replacing the call to compress-byte with a call to byte-to-8-bit-list.

I suppose we’ll also have to chop off the final bit of code where we append our termination sequence to the file too. Instead we’ll just return the list we make.

This leads to our new file-to-bitlist function:

(defun file-to-bitlist (filename)
    (let ((bitlist '())
            (in (open filename :element-type '(unsigned-byte 8))))
        (when in
            (loop for testbyte = (read-byte in nil)
                while testbyte do (setf bitlist (append bitlist (byte-to-8-bit-list testbyte))))
        (close in))
        bitlist))

Now that we have our file in an easy to read and manipulate bit format we can assemble our function for decompressing it.

Our decompression function needs to scan through the bit list and identify our special compressed codes. There are three types of codes we need to look for: Our 4 -bit short codes (that always start with 0), our 9-bit expanded codes (that always start with 1) and our termination code (which starts with a 1 and then has eight 0s).

We can take care of that easily enough with two nested if statements. Have some pseudo-code

if (bitlist starts with 0)
{
   do 4-bit shortcode logic
}
else{ //If bit list does not start with 0 it must start with 1
   if(bitlist starts with termination code)
   {
      finish up and close file
   }
   else //If it starts with 1 and is not the termination code it’s an expanded ASCII letter
   {
      do 9-bit expanded code logic.
   }
}

Simple enough. First we check if the next bit is a zero, which means we have a 4-bit shortcode we need to decompress. If the next bit isn’t zero it has to be a 1, which means it’s either a long code or our termination signal. We test for the termination signal first (otherwise we could never stop) and if we don’t find it we know we have a 9-bit expanded code that needs to be made normal.

To do this in Lisp we have to remember that every if statement has a sort of built in else.

(if (true/false)
   (do when true)
   (do when false))

So we can translate our pseudo-code into pseudo-lisp to get this:

(if (= 0 (first bitlist))
    (do short code logic here)
    (if (equals (subsequence bitlist 0 9) ‘(1 0 0 0 0 0 0 0 0))
        (finish things up here)
        (do expanded code logic here)))

Now we just need to wrap that up in a loop and fill in the logic bits and we’re home free.

Let’s look at the logic bits first. Our short code logic requires a few steps:

1) Look up the normal byte value of our 4-bit short code in our handy *list-to-byte-compression-hash*

2) Write that byte to output

3) Remove the 4-bits we just read from the bitlist so we don’t accidentally process them again

(progn (write-byte 
           (gethash (subseq bitlist 0 4) 
           *list-to-byte-compression-hash*) 
            out)
       (setf bitlist (subseq bitlist 4)))

The logic for our expanded code is very similar

1) Ignore the leading 1 and turn the next 8-bits into a byte

2) Write that byte to output

3) Remove the 9-bits we just read from the bitlist so we don’t accidentally process them again

(progn (write-byte (8-bit-list-to-byte (subseq bitlist 1 9)) out)
       (setf bitlist (subseq bitlist 9)))

For the termination sequence logic all we have to do is break out of our loop so we can close the file. To do that first we’re going to need to design our loop. Easiest approach is probably to have a loop that just runs as long as some variable, let’s name it “decompressing” is true. We can then just set that variable to false (nil in Lisp) when we see our termination sequence.

(loop while decompressing do stuff)
(setf decompressing nil)

Toss it all together along with some basic file input and output and we get this handy decompression function:

(defun white-rabbit-decompress-file (input-filename output-filename)
    (let ((bitlist (file-to-bitlist input-filename))
            (decompressing 1)
            (out (open output-filename :direction :output :element-type '(unsigned-byte 8))))
            (when out
                (loop while decompressing do                                             
                        (if (= 0 (first bitlist))
                            (progn (write-byte (gethash (subseq bitlist 0 4) *list-to-byte-compression-hash*) out)
                                    (setf bitlist (subseq bitlist 4)))
                            (if (equal (subseq bitlist 0 9) '(1 0 0 0 0 0 0 0 0))
                                    (setf decompressing nil)                                    
                                    (progn (write-byte (8-bit-list-to-byte (subseq bitlist 1 9)) out)
                                    (setf bitlist (subseq bitlist 9)))))))
            (close out)))

Like most Lips code this is extremely information dense and seems to have way too many nested parenthesis but since we built the individual parts separately it shouldn’t be too hard to follow along with what’s happening here.

Now we can load up our code and run things like:

[87]> (white-rabbit-decompress-file “compresseddrinkme” “decompresseddrinkme.txt”)

T

[88]> (white-rabbit-decompress-file “compressed1stparagraph” “decompressedfirstparagraph.txt”)

T

You should get decompressed files that match the original file you compressed. Nifty!

Whelp… that’s that. An ASCII based compression, decompression program in only a little more than a hundred lines of lisp. Of course, for a professional tool you’d want to add another few hundred lines of error checking and handling and UI and whatnot but the core here works.

So where do we go from here?

Well, first I’d like to spend at least one post talking about how “real” compression algorithms work. After that we can spend a week or two geeking out about how to make to improve our Lisp and make this application faster. I mean, it would be nice if we could handle at least handle the entirety of Alice in Wonderland within a few minutes rather the small eternity it would take with our prototype code as it exists.

Let’s Program A Compression Algorithm Part 4: In Which Byte Compression Code Is Applied To An Entire File

Now that we have a working compression function all that’s left is to grab a file, read it byte by byte, compress the bytes and then output them into a new file. Easy peasy!

Let’s start with reading a file byte by byte. This is one particular topic that depends heavily on your language, so if you’re not using Lisp you’re on your own for this step. What you’re looking for is a way to read a file one byte at a time, which might be tricky since by default most languages try to read text files one line at a time. In general you need to use some specific function or argument to force things into byte mode.

For example, compare these two Lisp functions, both run on a file called “drinkme.txt” which contains nothing but the words “drink me”:

(defun normal-read-test (filename)
    (let ((in (open filename)))
        (when in
            (loop for line = (read-line in nil)
                while line do (print line))
        (close in))))

(defun byte-read-test (filename)
    (let ((in (open filename :element-type '(unsigned-byte 8))))
        (when in
            (loop for testbyte = (read-byte in nil)
                while testbyte do (print testbyte))
        (close in))))

 

[2]> (normal-read-test “drinkme.txt”)

“drink me”

T

[3]> (byte-read-test “drinkme.txt”)

100

114

105

110

107

32

109

101

10

T

Notice that in order to get actual bytes we not only had to use “read-byte” instead of “read-line”, we also had to open the file with the :element type ‘(unsinged-byte) modifier. Your language probably has similar options.

Hopefully, one way or another, you now know how to grab all the bytes in the file you want to compress. With that in place we can use the compress-byte function we wrote last time to change a file into a series of compressed bit lists.

(defun file-to-compressed-bit-lists (filename)
    (let ((bit-lists '())
            (in (open filename :element-type '(unsigned-byte 8))))
        (when in
            (loop for testbyte = (read-byte in nil)
                while testbyte do (setf bit-lists (append bit-lists (list (compress-byte testbyte)))))
        (close in))
        bit-lists))

[35]> (file-to-compressed-bit-lists “drinkme.txt”)

((1 0 1 1 0 0 1 0 0) (1 0 1 1 1 0 0 1 0) (0 1 0 1) (0 1 1 0)

(1 0 1 1 0 1 0 1 1) (0 0 0 0) (1 0 1 1 0 1 1 0 1) (0 0 0 1)

(1 0 0 0 0 1 0 1 0) )

Well whaddaya know, that’s the exact same compression we calculated by hand in part 2. Good sign our code probably did things right!

Lisp trivia: append adds the items of one list to another list. So to add a single list to a list of lists you actually have to wrap that list inside another list, making it a one item list whose item happens to be a list. Otherwise we’d get something like ((0 0 1 1) (1 0 1 0) 1 0 0 1) instead of ((0 0 1 1) (1 0 1 0) (1 0 0 1)).

Trivia aside, now all that’s left is to write our new compressed data back to file.

Unfortunately our compressed data is the wrong “shape” for normal file output code.

Modern computer software is more or less designed around the idea that the smallest unit of data any sane person would ever want to work with is an entire 8-bit byte. This is almost always the correct assumption for something like 99% of computer programs and is the reason programming language come shipped with libraries for reading and writing bytes.

But sometimes you need to work outside of byte land. We certainly do. Our short letters are 4-bits long and our expanded letters are 9-bits long. Neither of those will work with standard byte-based file IO.

Still makes more sense than the tax code

So our data is the wrong shape. Whatever shall we do?

The obvious solution is to make it the right shape and the easiest way to do this is to take our compressed sequence of 4-bit and 9-bit letters, glue them together and then split them apart at new 8-bit boundaries. As long as the end result has the same string of 0s and 1s it doesn’t really matter how they’re grouped.

So a compressed letter list like this

0001 0011 111110100 0000 101101101 0001

Becomes a bit list like this

0001001111111010000001011011010001

Which we can then turn into

00010011 11111010 00000101 10110100 01

Now we have four easy to read and write bytes plus two dangling bits. Let’s fix that by adding in some extra 0s for padding.

00010011 11111010 00000101 10110100 01000000

Looking good. Well, mostly. Those padded zeros might be a problem when we try to decompress the file. The program is going to look at those and think there’s an extra 4-bit letter there at the end.

A quick fix for this would be to have every compressed file end with a specific bit sequence. Then when the decompresser sees that sequence it knows it can stop because everything after that point is just padding.

But what symbol should we use? It can’t be one of our 4-bit codes because we need those for making the compression work. How about a really uncommon ASCII character instead? For instance, 00000000 is “null” and shouldn’t ever appear in a normal text file. That means we can use the 9-bit 100000000 code to mean “end of the compressed text” without worrying about accidentally conflicting with a real 100000000 from the text.

So our new terminated compressed message looks like:

0001 0011 111110100 0000 101101101 0001 100000000

And when cut into bytes and padded out it looks like this (termination sequence underlined and padding comes after the |)

00010011 11111010 00000101 10110100 01100000 000|00000

Some of you probably noticed that between the termination sequence and the padding our supposedly compressed message is now just as long as it would have been had we just saved it as six normal byte characters. This is because our example was so short. Adding an extra byte to the end of a five byte message is obviously a huge change, but when we start working with actual multi-kilobyte text files the impact of padding and termination will be negligible.

Negligible is kind of a funny word when your write it down. I think it’s the two “g”s. gligib. egligibl. Weird, right?

Back to the subject at hand, let’s write some code for doing an actual compression.

Now my first idea was to take the bit lists from our function, strip them out of their lists and then dump them all into a new list. But as I mentioned in the trivia section I actually had to go to quite a bit of work to get the function to create a list of lists instead of one big list of bits. So I can actually just remove a few list calls from our existing function and create a new one that naturally returns one big list of bits. A final append to add our (1 0 0 0 0 0 0 0 0) termination symbol and it’s done!

(defun file-to-compressed-bitlist (filename)
    (let ((bit-lists '())
            (in (open filename :element-type '(unsigned-byte 8))))
        (when in
            (loop for testbyte = (read-byte in nil)
                while testbyte do (setf bit-lists (append bit-lists (compress-byte testbyte))))
        (close in))
        (append bit-lists '(1 0 0 0 0 0 0 0 0))))

[39]> (file-to-bitlist “drinkme.txt”)

(1 0 1 1 0 0 1 0 0 1 0 1 1 1 0 0 1 0 0 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 0 0 0

1 0 1 1 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0)

Now to pad it out and make sure it’s evenly divisible into 8-bit bytes.

We can figure out how many dangling bits there are like this:

[49]> (mod (length (file-to-bitlist “drinkme.txt”)) 8)

6

If there are 6 extra bits then we need 8 – 6 = 2 bits of padding to fill it out to an even byte length. We can generate this padding like this:

[58]> (loop repeat 2 collect 0)

(0 0)

So if we mix that all into one big function:

(defun compress-terminate-and-pad-file (filename)
    (let* ((bitlist (file-to-compressed-bitlist filename))
             (padding (loop repeat (- 8 (mod (length bitlist) 8)) collect 0)))
                (append bitlist padding)))

[70]> (compress-terminate-and-pad-file “drinkme.txt”)

(1 0 1 1 0 0 1 0 0 1 0 1 1 1 0 0 1 0 0 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 0 0 0

1 0 1 1 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0)

[71]> (length (compress-terminate-and-pad-file “drinkme.txt”))

72

For the finishing touch we pop open a byte output file, read through our fully prepared list 8-bits at a time and VOILA we have file compression.

(defun white-rabbit-compress-file (input-filename output-filename)
    (let ((bitlist (compress-terminate-and-pad-file input-filename))
            (out (open output-filename :direction :output :element-type '(unsigned-byte 8))))
            (when out
                (loop while (> (length bitlist) 0) do                     
                    (write-byte (8-bit-list-to-byte (subseq bitlist 0 8)) out)
                    (setf bitlist (subseq bitlist 8))))
            (close out)))

Nothing strange here. As long as there are bits left in the bitlist we take the first eight bits, convert them into a byte, write that byte to file and then drop those bits from the list (by setting the list equal to a subsequence starting at place 8 and continuing to the end of the list). Loop and repeat until the entire file is done.

Now let’s give it a whirl. Run a command like (white-rabbit-compress-file “drinkme.txt” “compresseddrinkme.txt”) and then look at the compressed file with some sort of hex editor. You will find, once again, the exact same sequence of ones and zeros we calculated by hand.

But turning a 9 byte file into a different 9 byte file isn’t much of a compression, so instead let’s grab the entire first paragraph from “Alice in Wonderland” and save it to a file called “1stparagraph.txt”.

Alice was beginning to get very tired of sitting by her sister on the bank, and of having nothing to do: once or twice she had peeped into the book her sister was reading, but it had no pictures or conversations in it, ‘and what is the use of a book,’ thought Alice ‘without pictures or conversations?’

Run that through our compression and then look at the file sizes of the original versus the compressed. For me the original text file was 303 bytes, but the compressed version was only 216.

Compression achieved.

One word of warning though: This is a horribly slow and inefficient Lisp program that will crawl to a halt on any file more than a few kilobytes in length. There are several easy ways to speed it up but I’m not going to talk about those until the end of this LP because 1) Speed doesn’t matter during proof of concept 2) Optimizing Lisp code isn’t the main focus of this project so let’s leave it until last for the handful of people who care.

So now that we have all happily agreed to not mention how horrible this particular implementation is we can move on to part two of the project: Decompressing the files we just compressed. After all, if you can’t decompress your files you might as well just delete them and achieve 100% compression.

Let’s Program A Compression Algorithm Part 3: In Which A General Compression Algorithm Becomes Working Lisp Code

Last time we invented and tested a super-simple compression algorithm that revolves around replacing the eight most common symbols in the English language with tiny 4-bit codes instead of their normal 8-bit representations (at the cost of replacing everything else with bigger 9-bit versions). We even did some examples by hand.

But this is a coding blog, so it’s time to write some actual code. When it comes to language choice our only real requirement is that the language be capable or working directly with bits and bytes and files and since pretty much every language ever has no problem doing that we’re open to choose whatever we want.

I’m personally going to choose Lisp and be keeping all my code in a file named “wrc.lisp” for “White Rabbit Compression”. You, of course, can follow along in whatever language you want. In fact, that would probably be the most educational approach to this series.

Anyways, like we talked about in the design phase, this project will mostly focus on processing lists of bits in batches of 8, 4 and 9. That means we’re going to need a convenient data structure for holding these lists.

Fortunately Lisp is built entirely around list processing and has some very powerful built in tools for creating and managing lists of numbers, so I will be representing our binary fragments as a plain old list of integers which will just so happen to always be either a 0 or a 1.

For those of you not in Lisp I bet your language has it’s own list structures. Could be a vector, a queue, a linked list, whatever. Anything that lets you add new stuff to the end and pull old stuff off the front will be fine.

Now the efficiency buffs in the audience might have noticed that we’re wasting space by using entire integers to keep track of mere bits. Shouldn’t we be using something else, like a bit vector?

Probably! But this is just the proof of concept first pass so doing things the easy way is more important than doing things the best way. If it turns out the program is too slow or memory hungry then we’ll revisit this decision.

With that in mind our first attempt at letter bit lists is going to look something like this:

; An 8-bit ASCII letter
(list 0 1 0 0 0 0 0 1)

;One of our 4 bit compressed letters
(list 0 0 1 1)

;One of our 9 bit labeled ASCII letters
(list 1 0 1 0 0 0 0 0 1)

Next up let’s write some helper functions that can turn real 8-bit bytes into our custom bit lists or turn our bit lists back into bytes.

(defun 8-bit-list-to-byte (bitlist)
    (+     (* 128 (first bitlist))
        (* 64 (second bitlist))
        (* 32 (third bitlist))
        (* 16 (fourth bitlist))
        (* 8 (fifth bitlist))
        (* 4 (sixth bitlist))
        (* 2 (seventh bitlist))
        (* 1 (eighth bitlist))))
        
(defun byte-to-8-bit-list (byte)
    (let ((bitlist nil))
        (if (>= byte 128)
            (progn
                (push 1 bitlist)
                (setf byte (- byte 128)))
            (push 0 bitlist))
        (if (>= byte 64)
            (progn
                (push 1 bitlist)
                (setf byte (- byte 64)))
            (push 0 bitlist))
        (if (>= byte 32)
            (progn
                (push 1 bitlist)
                (setf byte (- byte 32)))
            (push 0 bitlist))
        (if (>= byte 16)
            (progn
                (push 1 bitlist)
                (setf byte (- byte 16)))
            (push 0 bitlist))
        (if (>= byte 8)
            (progn
                (push 1 bitlist)
                (setf byte (- byte 8)))
            (push 0 bitlist))
        (if (>= byte 4)
            (progn
                (push 1 bitlist)
                (setf byte (- byte 4)))
            (push 0 bitlist))
        (if (>= byte 2)
            (progn
                (push 1 bitlist)
                (setf byte (- byte 2)))
            (push 0 bitlist))
        (if (>= byte 1)
            (progn
                (push 1 bitlist)
                (setf byte (- byte 1)))
            (push 0 bitlist))
        (nreverse bitlist)))

 

The logic here is pretty simple although the Lisp syntax can be a bit weird. I think 8-bit-list-to-byte is self-explanatory but byte-to-8-bit-list might need some explaining. The basic idea is that every bit in a byte has a specific value: 128, 64, 32, 16, 8, 4, 2 or 1. Because of how binary works any number greater than 128 must have the first bit set, any number smaller than 128 but larger than 64 must have the second bit set and so on.

So we can turn a byte into a list by first checking if the number is bigger than 128. If not we put a 0 into our list and move on. But if it is we put a 1 into our list and then subtract 128 before working with the remainder of the number. Then the next if statement checks if the numbe ris bigger than 64 and so on. The only Lispy trick here is that Lisp if statements by default can only contain two lines of logic: the first for when the if is true and the second when the if is false. Since we want to run two lines of logic when things are true we wrap them in a progn, which just lumps multiple lines of code into one unit.

Clear as mud? Let’s move on then.

With those generic helpers out of the way let’s move on to writing the core of our compressor: A function that can accept a byte and then transform it into either a 4-bit short code or a 9-bit extended code.

The first thing we’ll want is a single place in the code where we can keep the “official” list of which letters translate to which short codes. It’s important we have only one copy of this list because later on we might find out we need to change it and updating one list is a lot easier than hunting through our code for half a dozen different lists.

(defparameter *compression-map*
   '((160 (0 0 0 0)) 
     (101 (0 0 0 1))
     (116 (0 0 1 0))
     (97  (0 0 1 1))
     (111 (0 1 0 0))
     (105 (0 1 0 1))
     (110 (0 1 1 0))
     (115 (0 1 1 1))))

Here I’m using the ‘ shortcut to create a list of lists since (list (list 160 (list 0 0 0 0))…) would get really tiring to type really fast. Syntax aside the first item in each of the eight items in our list is the ASCII code for the letter we want to compress and the second item is the bit list we want it to compress to.

Now that we’ve gor our compression map in whatever format you prefer all we need is an easy way to get the data we need out of that map. During compression we want to be able to take a byte and find out it’s short code and during decompression we want to take a short-code and find out which byte it used to be.

Off the top of my head there are a few ways to do this. One would be to just loop through the entire list every time we want to do a lookup, stopping when we find an item that starts with the byte we want or ends with the list we want (or returning false if we don’t find anything). The whole list is only eight items long so this isn’t as wasteful as it might sound.

An easier solution (depending on your language) might be to use our master list to create a pair of hash tables or dictionaries. As you probably know these are one way lookup structures that link “keys” to “values”. Give the hash a key and it will very efficiently tell you whether or not it has stored a value for it and what that value is; perfect for our needs. The only trick is that since they are only one way and we want to both compress and decompress our data we’ll actually need two hashes that mirror each other. One would use the bytes as keys and reference the bit-lists. The other would use the bit-lists as keys and reference the bytes.

I think I’ll go with the hash approach since they are a more universal language feature than Lisp’s particular approach to list parsing.

Hash tables seem pretty weird until you understand how they work internally.

To translate my universal compression mapping into a pair of usable hash tables I’m going to first create the hash tables as global variables and then I’m going to use a simple Lisp loop to step through every pair in the compression map. During each step of the loop we will insert the data from one pair into each hash.

(defparameter *byte-to-list-compression-hash* (make-hash-table))
(defparameter *list-to-byte-compression-hash* (make-hash-table :test 'equal))

(loop
    for compression-pair in *compression-map*
    do    (setf 
            (gethash (car compression-pair) *byte-to-list-compression-hash*) 
            (cadr compression-pair))
        (setf 
            (gethash (cadr compression-pair) *list-to-byte-compression-hash*) 
            (car compression-pair)))

 

A little Lisp trivia here for anybody following along in my language of choice:

1) The :test keyword lets you tell a hash how to compare keys. The default value works great with bytes but not so great with lists so I use :test ‘equal to give the *list-to-byte-compression-hash* a more list friendly compartor.

2) To pull data out of or put data into a hash you use the gethash function. The fist argument is a key value, the second argument is the hash you want to use. I tend to get this backwards a lot :-(

3) “car” and “cdr” and combinitions like “cadar” are all old fashioned keywords for grabbing different parts of lists. I could have just as easily used chains of “first” and “second” but what’s the fun in that?

Lisp aside, we now have an official compression map and two easy to search hashes for doing compression lookups and decompression reverse lookups. Let’s put them to good use by actually writing a compression function!

The compression function should take an ASCII byte and check if it’s in the compression map. If it is it will return the proper 4-bit short code. If it isn’t in the map it should transform it to an 8-bit list, glue on a leading 1 and then return the new 9-bit list.

(defun compress-byte (byte-to-compress)
    (let ((short-code (gethash byte-to-compress *byte-to-list-compression-hash*)))
        (if short-code 
            short-code 
            (append '(1) (byte-to-8-bit-list byte-to-compress)))))

Nothing all that clever here. We take the byte-to-compress and lookup whatever value it has in the *byte-to-list-compression-hash*. We then use let to store that result in a local short-code variable. We then us a simple if statment to see whether short-code has an actual value (meaning we found a compression) or if it is empty (meaning that byte doesn’t compress). If it has a compressed value we just return it. Otherwise we take the original byte-to-compress, turn it into a bit list, glue a 1 to the front and return it.

Let’s see it all in action:

[1]> (load “wrc.lisp”)

;; Loading file wrc.lisp …

;; Loaded file wrc.lisp

T

[2]> (compress-byte 111)

(0 1 0 0)

[3]> (compress-byte 82)

(1 0 1 0 1 0 0 1 0)

Cool. It successfully found 111 (“o”) in our compression map and shrunk it from eight bytes down to four. It also noticed that 82 (“R”) was not in our map and so returned the full 8-bits with a ninth “1” marker glued to the front.

Next time we’ll start looking into how to use this function to compress and save an actual file.

Let’s Illustrate Morrowind: Index

Once upon a time a certain programmer had the incorrect idea that it might be fun to learn how to draw by keeping an illustrated journal of video game adventures. One victim of his doodles was Morrowind, famous open world fantasy RPG and ancestor to blockbuster hit Skyrim.

Let’s Illustrate Morrowind: Final Thoughts

So I finally “finished” Morrowind, which is to say I got near the end but got so frustrated with some of the end-game quests that I decided to sequence break and see if I could beat one of the final bosses early.

At least I think it was a final boss. Having never beaten the game means I can only sort of guess what was going to happen. Honestly in the future I should probably avoid doing Let’s Illustrates of games I havn’t finished at least once before.

Anyways, it’s time for final thoughts:

Thoughts On The Game

I can certainly see why a lot of people say Mororwind was their favorite Elder Scrolls game. The setting is unique, the sense of freedom is great and the story is one of the best written open world plots I’ve ever seen.

What made the plot so great?

Well, first off there was the simple fact that it was properly paced for an open world game. The game knew you probably wanted to do side quests and so the main story had regularly scheduled moments of down time where you were encouraged to go off and side quest for a bit. It’s a simple thing but for some reason most open world games just can’t pull it off. Even Bethesda itself seems to have trouble duplicating it and instead gives us things like Skyrim’s “Dragon’s are attacking and we have to stop them ASAP” or Fallout 4’s “Your baby has been kidnapped please rescue them ASAP”.

Beyond that the story also did a great job of making use of such advanced writing techniques as Foreshadowing and Ambiguouty.

For instance, one of my favorite moments in the game was when you first hear about the seven trials of the Neverine and realize that those are all things your character will have to go though. The trials are too vague to really let you know what you’re in for but you still get this lovely sense of doom. And then when you start accomplishing stuff it’s fun to look back and realize that “Oh! That’s what the third trial was talking about”.

I also like the fact that whether you are a reborn hero or just a spy pretending to be a reborn hero was never really clarified, at least not at any point in the game I played. Sure, you hear a lot about prophecy and fate but for all you know that’s just a few Deadra lords playing games or a few scribes being hopeful.

ON THE OTHER HAND: I think we have to admit that the rough gameplay made the story hard to enjoy. I mean, I was so tired of walking back and forth across the ashlands that I bailed out 80% of the way through the story.

So overall I’m glad I played it and it would be really nice if Elder Scrolls 6 were to have a Morrowind style scenario but with Skyrim style gameplay.

Thoughts On The Gimmick

A no armor, weapons or consumable run of an Elder Scrolls game is less intimidating than you might think given how much magic is readily available and how easy it is to regain HP and MP through rest even without items.

What did surprise me was the fact that Fault somehow turned into a melee focused wizard instead of the fireball chunking sorcerer I originally had in mind. I guess that’s what I get for obsessing about having optimal HP instead of actually thinking about how to be a good spell caster.

On the other hand being a transforming hero certainly gave the playthrough a unique feel and resulted in some funny mental images.

On the other other hand combat in Morrowind is tedious enough without having to cast the same armor and weapon summoning spells at the start of every single fight. So I can’t really recommend the power ranger build to anyone.

Thoughts On My Art

My first Let’s Illustrate was just to get me in the habit of regularly practicing art by basically putting my online reputation at risk if I didn’t. This second Let’s Illustrate was then theoretically supposed to focus on developing actual talent by picking a single artistic style and focusing on getting good at it.

Unfortunatley I instead spent most of this series jumping from one style to another like a kid in a candy store. Let’s try a cartoon style! No, comics! Maybe something more Japanese! And so on and so forth.

That said I did finally decide to commit myself to pixel art, for several reasons:

1) It requires and teaches many of the same skills as traditional art (perspective, proportion, shading) while being more forgiving of small mistakes.

2) You can easily adjust the difficulty of a piece by increasing or decreasing the resolution.

3) There are some good smartphone apps for pixel art, letting me slip in a few minutes of practice here and there instead of having to dedicate a solid hour to sitting at my computer with a drawing tablet.

Some time in the future I’d still like to improve my actual sketching skills but for the forseeable future I’m going to restrict myself to pure pixelated Let’s Illustrates until I reach a level where I can produce the sort of stuff I wouldn’t be embarassed to see in an actual SNES game.

As for when I’ll be kicking off the next series, I’ve already started playing and illustrating but want a bigger buffer of saved up posts before anything goes live. Might take a month or two. I know that’s Ages in Internet time but I hope your interest doesn’t Fade while you wait.

Let’s Program A Compression Algorithm Part 2: In Which A General Idea Becomes A Specific Algorithm

Last time we talked about Alice in Wonderland and the deep cruelty of stores that play the same handful of movie trailers on endless loop.

More importantly we also talked about how computers use compression to shrink files down for easier storage and faster transfer. Without good compression algorithms the Internet would crawl to a halt and half the electronics you use on a daily basis wouldn’t exist. For instance, without compression a 2 hour HD movie would be over 300 GB; good luck fitting that all on one disc!

To better understand this vital computer science breakthrough we’re going to be writing our own ASCII text compression program.

Disclaimer: It’s not going to be a very good compression program. Like all of my let’s programs the goal here is education and not the creation of usable code. We’re going to be skipping out on all the security and error checking issues a professional compressor would include and our end goal is a modest 20% reduction in file size compared to the 75%+ reduction well known tools like Zip can pull off.

Now that your expectations have been properly lowered let’s talk about the structure of text files. After all, we can’t compress them if we don’t know what they’re supposed to look like or how they work.

The ASCII text standard is a set of 256 symbols that includes all 26 letters of the English language in both upper and lower case as well as all standard punctuation, some useful computer symbols (like newline) and a bunch of random symbols and proto-emoticons that seem like they were included mostly to fill up space.

The fact that there are 256 symbols is very important because 256 is exactly how high you can count using a single 8-bit computer byte. That means you can store one letter in one byte by simply using binary counting to mark down where the letter is in the ASCII chart.

For example, the capital letter “A” is in spot 65 of the ASCII chart. 65 in binary is 01000001. So to store the letter “A” in our computer we would grab a byte worth of space on our hard drive and fill it with the electronic pattern 01000001.

An ASCII text file is just a bunch of these 8-bit character bytes all in a row. If you want to save a 120 character long text you need a 120-byte long ASCII file. If you want to save a 5,000 character short story you need a roughly 5 kilobyte ASCII file.

Ok, cool. Now we know what an ASCII file’s guts look like. Time to start looking for patterns we can use for compression.

Patterns… patterns… here’s one!

The ASCII files we’ll be working with are all based on the English alphabet, and in English not all letters are used evenly. Things like “s”, “e”, and “a” get used all the time while poor little letters like “x” and “z” hardly ever see the light of day. And don’t forget “ ”! You might not think of the blank space as a letter but just imagine tryingtowritewithoutit.

So some letters are much more common than others but ASCII stores them all in identical 8-bit bytes anyways. What if we were to change that? What if we stored the most common letters in smaller spaces, like 4-bit nibbles*?

The biggest challenge here is figuring out a way to let the computer know when it should expect a nibble instead of a byte. In normal ASCII every letter is eight bits long which makes it easy for the computer to figure out where one letter ends and the next begins.

But since we’re going to have letters of different lengths we need some way to point out to the computer what to expect. A sort of virtual name-tag to say “I’m a 4-bit letter” or “I’m a normal 8-bit letter”.

Here’s a simple idea: Our short 4-bit letters will always start with a 0, on the other hand our 8-bit ASCII letters will always start with a 1.

This solution does have some drawbacks. If the first bit of our 4-bit letters is always 0 that means we only have three bits left for encoding the actual letter. Three bits is only enough to count up to eight so that means we will only be able to compress eight letters.

A bigger problem comes from the 8-bit ASCII letters. They need their full 8-bits to work properly so the only way to mark them with a leading 1 is by gluing it to the front and turning them into 9-bit letters. So while our common letters had their size cut in half our uncommon letters are actually getting bigger. Hopefully we’ll still come out ahead but it might be close.

It’s amazing how many problems are caused by people trying to apply averages to things that ought not be averaged

Anyways, it sounds like we’re going to have eight different shortcut codes to work with. What letters should we use them for? Well, according to Wikipedia the eight most common letters in the English language are, in order: E, T, A, O, I, N, S, H. So that’s probably a good bet if we want as much compression as possible.

But Wikipedia doesn’t count the blank space as a letter. However because it’s so common in text it’s definitely something we want to compress. Let’s add it to the front of the list and drop “H”. That means the letters we will be compressing are “ ”, E, T, A, O, I, N, S.

Or more accurately “ ”, e, t, a, o , i, n, s. Remember that in ASCII upper and lower case letters are coded differently so we have to choose which we want. Since lowercase letters are more common than uppercase it makes sense to focus on them.

Now that we have our eight compression targets all we have to do is assign them one of our short codes, all of which are just the number 0 followed by some binary. Let’s go with this:

“ ” = 0000

“e” = 0001

“t” = 0010

“a” = 0011

“o” = 0100

“i” = 0101

“n” = 0110

“s” = 0111

Also remember that any letter not on this list will actually be expanded by putting a “1” in front of it’s binary representation.

One Makes You Smaller

Whew! That was a lot of abstract thinking but believe it or not we now have a complete compression algorithm. And just to prove it we’re going to do a compression by hand.

But what should we practice on? Well, our theme is “Wonderland” and I seem to recall that Alice was able to shrink herself by fooling around with a bottle labeled “drink me”. In ASCII that looks like this:

d r i n k m e
01100100 01110010 01101001 01101110 01101011 00100000 01101101 01100101

Eight bits times eight letter means 64 bits total. But if we replace the space, ‘i’, ‘e’, and ‘n’ with our 4-bit shortcuts while adding a 1 flag in front of the remaining 8-bit (soon to be 9-bit) letters we get

d r i n k m e
101100100 101110010 0101 0110 101101011 0000 101101101 0001

Which is 9*4 + 4*4 bits long for a total of only 52 bits. So we saved ourselves 12 bits, which is almost 20% less space than the original. Not bad.

One Makes You Grow Taller

Of course, taking text and compressing it is pretty useless unless we also know how to take compressed text and expand it back into normal readable ASCII. So please take a look at the following bit sequence and see if you can figure out what it used to say:

0001001111111010000001011011010001

I don’t want anybody accidentally looking ahead so let’s push the answer down a page or so with some another random comic.

Information theory jokes are funny, right?

So the first thing to do here is to take that big messy data stream and split it into individual letters. Remember that according to our rules the length of each letter is determined by whether it starts with a 0 or a 1. The 0s are 4-bit letters and the 1s are 9-bit letters.

So here we go. 0001001111111010000001011011010001 starts with 0 so the first letter must be four bits long: 0001

After removing those four bits we’re left with 001111111010000001011011010001, which also starts with a 0 meaning our next letter is also four bits long: 0011

Removing those four letters leaves us with 11111010000001011011010001. Since that starts with a 1 that means our next letter is 9 bits long: 111110100

By doing this again and again we finally get these six letters:

0001 0011 111110100 0000 101101101 0001

Now that we have our individual letters it’s time to turn them into, well, letters. But the kind of letters people can read.

For the four bit letters we just reference the list of short codes we made up. Scroll up in the likely event that you neglected to commit them to long term memory.

0001 0011 111110100 0000 101101101 0001
e a ? ? e

For the nine bit letters we need to remove the leading 1 and then look up the remaining eight bit code in the official ASCII chart. For instance 111110100 becomes 11110100 which is the code for “t”.

0001 0011 111110100 0000 101101101 0001
e a t m e

And there we go, the compressed binary has successfully been turned back into human readable data.

I Don’t Like Pretending To Be A Compression Algorithm

Doing these examples by hand was a great way to prove our proposed compression algorithm actually works but I don’t think any of us want to to try and compress an entire book or even an entire email by hand. It would be much better to teach the computer how to do this all for us. Which is exactly what we’re going to start working on next time.

After all, this is a Let’s Program, not a Let’s Spend A Small Eternity Doing Mathematical Busywork.

* Yes, nibble is the actual official term for half a byte. Programmers are weird like that.

Let’s Illustrate Morrowind Part 46: It’s Over When I Say It’s Over

So Azura is willing to back Fault’s claim of Neverine status but the prophecy won’t be fulfilled until the majority of the dark elves have also been convinced. This requires becoming the leader of all four ashlander tribes as well as receiving top honors from three of the great houses in the city of Vivec.

In more practical terms this requires doing dozens of side quests that require trecking across Morrowind’s quick-travel-less wasteland again and again and again. And while some of the quests can be rather clever I honestly only get about halfway through before rebelling. There has to be a better way to save the world than yet another volcano hiking trip!

Let’s see here…

If I remember the plot correctly a lot of Morrowind’s problems stem from the fact that their trio of god kings are slowly going insane. So theoretically if we can just deal with them the day will be saved, right?

The easiest immortal troublemaker to find is Vivec, who lives in the city named after him and hides out in a giant temple secured by a max difficulty lock. Fortunately Fault has just enough mana to cast a max level unlocking spell letting her into the godling’s main chamber with ease.

Once inside she’s immediately blown up by a max level fireball. But if you manage to dodge enough of them Vivec will eventually run out of mana and resort to trying to punch to you death instead. And as Fault well knows punching things to death is next to impossible meaning that it becomes relatively easy to whittle down Vivec’s health bit by bit, running away to regain stamina whenever you’ve been punched so hard it looks like you’re close to passing out.

Finally the mad god falls, but Fault’s victory is interrupted by a popup informing her that the threads of fate have been broken and that the world is likely doomed. Or in other words, we just broke the plot and can no longer win the game.

That has to have been worth a ton of XP

Now you could argue that this is a bad thing and that the game should prevent you from breaking it, which is why Oblivion and Skyrim actually make certain characters unkillable until after their part in the game’s plot is over or make certain doors impossible to open without the story’s permission.

But I like that Morrowind trusts me as a player enough to let me go off the rails and end the game the way I want to. Vivec is hard to kill but not impossible and he is protected by a door that is hard to open but not actually impassable. And while the game warns you that you might want to consider reloading an earlier save so you can still finish the plot there’s nothing actually preventing you from just continuing playing in your now messed up world as long as you want.

So while neither the plot or this Let’s Illustrate have anywhere else they can go from here I like to imagine that Fault, having defeated Vivec, goes on to have an epic battle against the other two kings of Morrowind. With them dead the ghost wall will undoubtedly fall, leaving nothing but Fault between Morrowind and the plagues of Dagoth Ur.

But you know what? I think the odds are in Fault’s favor.

Let’s Illustrate Morrowind Part 45: This Week In The Polls…

Through the power of wiki Fault finally opens the doors to Azura’s shrine.

Inside the shrine Azura herself rewards us the sign of the star and moon, which turns out to be a magic ring we will never actually put on. She also commands us to go forth and fulfill the fourth and fifth trials by uniting all the ashland tribes and becoming champion of at least four of the great houses. After that we have to cast down some false gods and confront the plague demon at which point we presumably win the game.

As a final bit of neatness Azura summons up the ghosts of some of the most famous past failed candidates for the Nevarine. They give us some simple advice, tell their stories and then give Fault a bunch of nifty artifacts which she obviously will never use. Still, it’s the thought that counts, right?

Fault then trecks all the way back to the Ashland camp to get advice on how to unite the four tribes. Apparently if we can both convince them we’re the Neverine and that Dagoth Ur represents an immediate threat they will gladly name us joint warchief.

At first I’m a little afraid our favorite ashlander chief is going to stonewall us with yet another “prove our worth” quest but he seems to have finally warmed up to Fault and recognizes her as the Neverine (but only after politely warning her that naming herself the head of a heritacle cult will probably mess up any temple or political related sidequests she’s on so she should think carefully before saying yes). He also gives us a list of the other three tribes we need to convince and even marks them on our map. All of them live along the grassy east cost which should be a nice break from all this volcanic cliff racer righting.

So… one tribe down. Three to go.

Looks like it’s time to find a new campaign manager…