Problem: Scale

* The Wikipedia articles are a bit dense; feel free to skim or skip!

This course’s philosophy on academic honesty is best stated as "be reasonable." The course recognizes that interactions with classmates and others can facilitate mastery of the course’s material. However, there remains a line between enlisting the help of another and submitting the work of another. This policy characterizes both sides of that line.

The essence of all work that you submit to this course must be your own. Collaboration on problems is not permitted (unless explicitly stated otherwise) except to the extent that you may ask classmates and others for help so long as that help does not reduce to another doing your work for you. Generally speaking, when asking for help, you may show your code or writing to others, but you may not view theirs, so long as you and they respect this policy’s other constraints. Collaboration on quizzes and tests is not permitted at all. Collaboration on the final project is permitted to the extent prescribed by its specification.

Below are rules of thumb that (inexhaustively) characterize acts that the course considers reasonable and not reasonable. If in doubt as to whether some act is reasonable, do not commit it until you solicit and receive approval in writing from your instructor. If a violation of this policy is suspected and confirmed, your instructor reserves the right to impose local sanctions on top of any disciplinary outcome that may include an unsatisfactory or failing grade for work submitted or for the course itself.

Your work on this problem set will be evaluated along four axes primarily.

To obtain a passing grade in this course, all students must ordinarily submit all assigned problems unless granted an exception in writing by the instructor.

Welcome back!

As always, first open a terminal window and execute

to make sure your workspace is up-to-date.

Next, navigate to your ~/workspace directory and create a new directory therein called week12. Navigate inside of that directory, and then execute:

in order to download a ZIP (i.e., compressed version) of a similar problem’s distro. If you then execute

you should see that you now have a file called whodunit.zip in your ~/workspace/week12 directory. Unzip it by executing the below.

If you again execute

you should see that you now also have a whodunit directory. But let’s call it something else instead. Type:

to rename that directory to something else instead! You’re now welcome to delete the original ZIP file with the below.

Now dive into that scale directory by executing the below.

Now execute

and you should see that the directory contains the below.

How fun! A C file, a header file, and four images. Who knows what could be inside those! Let’s get started.

Off we go!

First, some background.

Perhaps the simplest way to represent an image is with a grid of pixels (i.e., dots), each of which can be of a different color. For black-and-white images, we thus need 1 bit per pixel, as 0 could represent black and 1 could represent white, as in the below. (Image adapted from http://www.brackeen.com/vga/bitmaps.html.)

In this sense, then, is an image just a bitmap (i.e., a map of bits). For more colorful images, you simply need more bits per pixel. A file format (like GIF) that supports "8-bit color" uses 8 bits per pixel. A file format (like BMP, JPEG, or PNG) that supports "24-bit color" uses 24 bits per pixel. (BMP actually supports 1-, 4-, 8-, 16-, 24-, and 32-bit color.)

A 24-bit BMP uses 8 bits to signify the amount of red in a pixel’s color, 8 bits to signify the amount of green in a pixel’s color, and 8 bits to signify the amount of blue in a pixel’s color. If you’ve ever heard of RGB color, well, there you have it: red, green, blue.

If the R, G, and B values of some pixel in a BMP are, say, 0xff, 0x00, and 0x00 in hexadecimal, that pixel is purely red, as 0xff (otherwise known as 255 in decimal) implies "a lot of red," while 0x00 and 0x00 imply "no green" and "no blue," respectively. Incidentally, HTML and CSS (languages in which webpages can be written) model colors in this same way. If curious, see http://en.wikipedia.org/wiki/Web_colors for more details.

A file is just a sequence of bits, arranged in some fashion. A 24-bit BMP file, then, is essentially just a sequence of bits, (almost) every 24 of which happen to represent some pixel’s color. But a BMP file also contains some "metadata," information like an image’s height and width. That metadata is stored at the beginning of the file in the form of two data structures generally referred to as "headers" (not to be confused with C’s header files). (Incidentally, these headers have evolved over time. This problem only expects that you support version 4.0 (the latest) of Microsoft’s BMP format, which debuted with Windows 95.) The first of these headers, called BITMAPFILEHEADER, is 14 bytes long. (Recall that 1 byte equals 8 bits.) The second of these headers, called BITMAPINFOHEADER, is 40 bytes long. Immediately following these headers is the actual bitmap: an array of bytes, triples of which represent a pixel’s color. (In 1-, 4-, and 16-bit BMPs, but not 24- or 32-, there’s an additional header right after BITMAPINFOHEADER called RGBQUAD, an array that defines "intensity values" for each of the colors in a device’s palette.) However, BMP stores these triples backwards (i.e., as BGR), with 8 bits for blue, followed by 8 bits for green, followed by 8 bits for red. (Some BMPs also store the entire bitmap backwards, with an image’s top row at the end of the BMP file. But we’ve stored this problem set’s BMPs as described herein, with each bitmap’s top row first and bottom row last.) In other words, were we to convert the 1-bit smiley above to a 24-bit smiley, substituting red for black, a 24-bit BMP would store this bitmap as follows, where 0000ff signifies red and ffffff signifies white; we’ve highlighted in red all instances of 0000ff.

Because we’ve presented these bits from left to right, top to bottom, in 8 columns, you can actually see the red smiley if you take a step back.

To be clear, recall that a hexadecimal digit represents 4 bits. Accordingly, ffffff in hexadecimal actually signifies 111111111111111111111111 in binary.

Okay, stop! Don’t proceed further until you’re sure you understand why 0000ff represents a red pixel in a 24-bit BMP file.

Let’s look at the underlying bytes that compose smiley.bmp using xxd, a command-line "hex editor." Execute:

You should see the below; we’ve highlighted in red all instances of 0000ff.

In the leftmost column above are addresses within the file or, equivalently, offsets from the file’s first byte, all of them given in hex. Note that 00000036 in hexadecimal is 54 in decimal. You’re thus looking at byte 54 onward of smiley.bmp. Recall that a 24-bit BMP’s first 14 + 40 = 54 bytes are filled with metadata. If you really want to see that metadata in addition to the bitmap, execute the command below.

If smiley.bmp actually contained ASCII characters, you’d see them in xxd's rightmost column instead of all of those dots. (Interesting way to maybe hide some information in a file!)

So, smiley.bmp is 8 pixels wide by 8 pixels tall, and it’s a 24-bit BMP (each of whose pixels is represented with 24 ÷ 8 = 3 bytes). Each row (aka "scanline") thus takes up (8 pixels) × (3 bytes per pixel) = 24 bytes, which happens to be a multiple of 4. It turns out that BMPs are stored a bit differently if the number of bytes in a scanline is not, in fact, a multiple of 4. In small.bmp, for instance, is another 24-bit BMP, a green box that’s 3 pixels wide by 3 pixels wide. If you view it with Image Viewer (as by double-clicking it), you’ll see that it resembles the below, albeit much smaller. (Indeed, you might need to zoom in again to see it.)

Each scanline in small.bmp thus takes up (3 pixels) × (3 bytes per pixel) = 9 bytes, which is not a multiple of 4. And so the scanline is "padded" with as many zeroes as it takes to extend the scanline’s length to a multiple of 4. In other words, between 0 and 3 bytes of padding are needed for each scanline in a 24-bit BMP. (Understand why?) In the case of small.bmp, 3 bytes' worth of zeroes are needed, since (3 pixels) × (3 bytes per pixel) + (3 bytes of padding) = 12 bytes, which is indeed a multiple of 4.

To "see" this padding, go ahead and run the below.

Note that we’re using a different value for -c than we did for smiley.bmp so that xxd outputs only 4 columns this time (3 for the green box and 1 for the padding). You should see output like the below; we’ve highlighted in green all instances of 00ff00.

For contrast, let’s use xxd on large.bmp, which looks identical to small.bmp but, at 12 pixels by 12 pixels, is four times as large. Go ahead and execute the below; you may need to widen your window to avoid wrapping.

You should see output like the below; we’ve again highlighted in green all instances of 00ff00

Okay, xxd only showed you the bytes in these BMPs. How do we actually get at them programmatically? Well, in copy.c is a program whose sole purpose in life is to create a copy of a BMP, piece by piece. Of course, you could just use cp for that, but maybe copy.c can help us understand this file format a bit more. Go ahead and compile copy.c into a program called copy using make. (Remember how?) Then execute a command like the below.

If you then execute ls (with the appropriate switch), you should see that smiley.bmp and copy.bmp are indeed the same size. Let’s double-check that they’re actually the same! Execute the below.

If that command tells you nothing, the files are indeed identical. (Note that some programs, like Photoshop, include trailing zeroes at the ends of some BMPs. Our version of copy throws those away, so don’t be too worried if you try to copy a BMP that you’ve downloaded or made only to find that the copy is actually a few bytes smaller than the original.) Feel free to open both files in your IDE (as by double-clicking each) to confirm as much visually. But diff does a byte-by-byte comparison, so its eye is probably sharper than yours!

So how now did that copy get made? It turns out that copy.c relies on bmp.h. Let’s take a look. Open up bmp.h, and you’ll see actual definitions of those headers we’ve mentioned, adapted from Microsoft’s own implementations thereof. In addition, that file defines BYTE, DWORD, LONG, and WORD, data types normally found in the world of Win32 (i.e., Windows) programming. Notice how they’re just aliases for primitives with which you are (hopefully) already familiar. It appears that BITMAPFILEHEADER and BITMAPINFOHEADER make use of these types. This file also defines a struct called RGBTRIPLE that, quite simply, "encapsulates" three bytes: one blue, one green, and one red (the order, recall, in which we expect to find RGB triples actually on disk).

Why are these structs useful? Well, recall that a file is just a sequence of bytes (or, ultimately, bits) on disk. But those bytes are generally ordered in such a way that the first few represent something, the next few represent something else, and so on. "File formats" exist because the world has standardized what bytes mean what. Now, we could just read a file from disk into RAM as one big array of bytes. And we could just remember that the byte at location [i] represents one thing, while the byte at location [j] represents another. But why not give some of those bytes names so that we can retrieve them from memory more easily? That’s precisely what the structs in bmp.h allow us to do. Rather than think of some file as one long sequence of bytes, we can instead think of it as a sequence of `struct`s.

Recall that smiley.bmp is 8 by 8 pixels, and so it should take up 14 + 40 + (8 × 8) × 3 = 246 bytes on disk. (Confirm as much if you’d like using ls.) Here’s what it thus looks like on disk according to Microsoft:

As this figure suggests, order does matter when it comes to structs' members. Byte 57 is rgbtBlue (and not, say, rgbtRed), because rgbtBlue is defined first in RGBTRIPLE. Our use, incidentally, of the attribute called packed ensures that clang does not try to "word-align" members (whereby the address of each member’s first byte is a multiple of 4), lest we end up with "gaps" in our `struct`s that don’t actually exist on disk.

Now go ahead and pull up the URLs to which BITMAPFILEHEADER and BITMAPINFOHEADER are attributed, per the comments in bmp.h. These reference guides will allow you go get some answers to your bitmap-related questions from MSDN (Microsoft Developer Network).

Alright, next challenge! Implement now in scale.c a program called scale that resizes 24-bit uncompressed BMPs by a factor of n. Your program should accept exactly three command-line arguments, per the below usage, whereby the first (n) must be a positive integer less than or equal to 100, the second the name of the file to be resized, and the third the name of the resized version to be written.

With a program like this, we could have created large.bmp out of small.bmp by resizing the latter by a factor of 4 (i.e., by multiplying both its width and its height by 4), per the below.

You’re welcome (and indeed encouraged!) to get started by copying copy.c and naming the copy scale.c (remember how?). But spend some time thinking about what it means to resize a BMP. (You may assume that n times the size of infile will not exceed 2³² - 1.) Decide which of the fields in BITMAPFILEHEADER and BITMAPINFOHEADER you might need to modify. Consider whether or not you’ll need to add or subtract padding to scanlines. And be thankful that we don’t expect you to support fractional n between 0 and 1! (At least, not until and unless you tackle Shrink) But we do expect you to support a value of 1 for n, the result of which should be an outfile with dimensions identical to infile's.

If you’d like to check the correctness of your program with check50, you may execute the below.

If you’d like to play with the staff’s own implementation of scale, you may execute the below.

If you’d like to peek at, e.g., large.bmp's headers (in a more user-friendly way than xxd allows), you may execute the below.

Better yet, if you’d like to compare your outfile’s headers against the staff’s, you might want to execute commands like the below while inside your ~/workspace/week12/scale directory. (Think about what each is doing.)

If you happen to use malloc, be sure to use free so as not to leak memory. Try using valgrind to check for any leaks!

Here’s Zamyla again!

To submit your assignment, please do the following by Sat 12/3 at noon.

This was Scale, your most complex challenge to date!