Building an API Library

Bitwise Operators (aka Bits, Bits, Bits Part II)

Did you know that Mata supports bitwise operators?  Well, it actually doesn't – in the typical sense.  But that won't stop us from making it work.  You see, Mata can handle data extremely well, and with a little finesse, can be forced to do things it wasn't really made to do.  Yes it's going to be slow, and yes it's probably not very useful to the average user, but let me try to convince you how great using Mata really is!

For those who don't know, Mata is a lower level language than Stata – many of Stata's complex functions are actually written in Mata because it's really quite fast.  Mata mimics a lot of C's syntax, but also simplifies things so you don't feel like you have to explicitly declare everything.  In previous posts we've exploited the power of the - inbase() - function and we will make ample use of that today.

Say we have a text file containing the word "Chunk".  While we see a word, the computer sees numbers which correspond to each letter – otherwise known as ASCII.  Mata's - ascii() - function can help us find this representation:

This is a simple way of converting our text into numbers, but how about into bytes?  Typically, bytes are displayed in base 16:

But now we want to see each bit.  Remember, I'm not a computer scientist, so you can trust me when I say this really isn't all that bad for those of you who haven't been exposed to this stuff.  Just know that each of these bytes contains 8 bits.  Each bit can either be on or off (1 or 0) which means that there’s a total possible bit combination of 2^8 = 256 per byte.  Let's look at what Stata shows us when we look at everything in base 2:

Notice, I added a zero and a one at the end of the text string "chunk" for illustrative purposes.  Why are these values not 0 and 1 respectively?  That’s because the digits are also ASCII characters (digits 48 and 49).  We can get the values of zero and one by using the - char() - function.  For fun, we'll also look at values two and three as well.

​Well, because there are technically 8 bits per byte, we need to pad each output with zeros so that the total length is 8 bits.  For example: the value "3" can be written as "11" in base 2, but is the same "00000011" so that we can imagine all 8 bits.  We can easily accomplish this in matrix form.

Notice the use of the colon operator?  It's by far one of my favorite operands (not that I have that many) because it does the same operation on each element of the matrix, which makes the overall statement extremely succinct!  The statement above just says: "Give me some zeros, exactly 8 minus how every many numbers we had, and append the original statement to the end to make sure every element has exactly 8 digits."

We should probably make this into a function, since we’ll use it a lot.  So let's make the size of the padding an input as well.

mata:
string matrix padbit(string matrix x, real scalar padnum)
{
        string matrix y
        y = "0" :* (padnum :- strlen(x)) :+ x
        return (y)
}
end
mata: padbit(chunk, 8)

Logical Operators

And, Or, Not, Xor – These are easy to implement.  You can think of these functions as truth tables if you want, but really, you're just comparing each bit to the respective bit of another byte. 

For example: I have two bytes (they need to be of the same length): 00111100 and 10101010.  If I were to use the And operator, for the result to be true (1), the first bit of Byte 1 must be the same number as the corresponding bit in Byte 2 (=).  The following illustration helps demonstrate this idea:

The Or operator implies that either bit could be a 1 for the output to be true:

Not works with only one byte and says to flip all the bits (make all 1's 0's and all 0's 1's):

Finally, Xor (the exclusive or) states that Byte 1 and Byte 2 must have opposite values to be true.  So if the first bit of Byte 1 is a zero, the first bit of Byte 2 has to be the opposite for the outcome to be true:

Had enough logic yet?  I certainly have... so I won’t go into any of the functions anymore, but I’ll make these available for you to download so you won't have to worry about the logistics:

bitwise-mata-functions.do
File Size:	2 kb
File Type:	do

Download File

---

Shifts and Rotations

The second thing we need to handle when dealing with bitwise operations are methods to move the bits.  There are two main ways to shuffle bits around: the shift and the rotation.  While they both move the position of the bits, a shift actually destroys bits and replaces trailing values with zeros, whereas the rotation just moves the shifted value to the opposite side of the bit.  Therefore, we can think of the shift as a way to destroy information and a rotate as a way of hiding information.  Let’s see this in action:

Note: this animation was made using - twoway scatteri -

It's interesting to follow, though not all that interesting if it doesn't have a practical application.  If you're like "honestly, I don’t know nothing about bit functions", I'll say - well I've got the one you.  How about a way to easily encrypt your files so that you can hide your sensitive stuff in plain sight?  First find a file and read it in:

// Read in File to Copy
fh  = fopen("Building an API Library.docx", "r")
eof = _fseek(fh, 0, 1)
fseek(fh, 0, -1)
x = fread(fh, eof)
fclose(fh)

​Convert the file characters to the ASCII decimal value then convert this number into the base 2 representation (don't forget to pad the bits).  From here, we can use our bitwise operations before converting this number back to base 10 and finally back to characters:

// Run Bitwise Not
y = padbit(inbase(2, ascii(x)), 8)
for (i=1; i<=cols(y); i++) {
        y[i] = bitnot(y[i])
}
y = char(frombase(2, y))

​Lastly, write your newly altered file using Mata.  This is obviously very basic, but a great way to hamper nosy coworkers.

// Write the Results to File
fh = fopen("Copy.docx", "w")
fwrite(fh, y)
fclose(fh)

​But really, we're doing this with the ultimate goal of gaining access to Twitter data using Twitter's API.  This is just step one of a three part series and if you're lost so far. there's plenty of time to see the motivation for this post in the next step.  I promise it gets more interesting, yet I hope I've shown some of Mata's potential and how you can easily bring in the concepts to your own do-files.