Tuesday, August 28, 2012


A Forward Reference

Having had a couple of responses to the last post, I couldn't help but revisit the code. There's not much to report, but since I've had some feedback from a few people who are new to Clojure I thought that there were a couple of things that I could mention.

First, (and you can see this in the comments to the previous post) I wrote my original code in a REPL and pasted it into the blog. Unfortunately, this caused me to miss a forward reference to the parse-t function. On my first iteration of the code, I wasn't trying to parse all the data types, to the map of parsers didn't need to recurse into the parse-t function. However, when I updated the map, the  parse-t function had been fully defined, so the references worked just fine.


That brings me to my second and third points: testing and Leiningen. As is often the case, I found the issues by writing and running tests. Setting up an environment for tests can be annoying for some systems, particularly for such a simple function. However, using Leiningen makes it very easy. The entire project was built using Leiningen, and was set up with the simple command:
  lein new tnetstrings.
I'll get on to Leiningen in a moment, but for now I'll stick with the tests.

Clojure tests are easy to set up and use. They are based on a DSL built out of a set of macros that are defined in clojure.test. The two main macros are deftest and is. deftest is used to define a test in the same way that defn is used to define a function, sans a parameter definition. In fact, a test is a function, and can be called directly (it takes no parameters). This is very useful to run an individual test from a REPL.

The other main macro is called "is" and is simply used to assert the truth of something. This macro is used inside a test.

My tests for tnetstrings are very simple:

(ns tnetstrings.test.core
  (:use [tnetstrings.core :only [parse-t]]

(deftest test-single
  (is (= ["hello" ""] (parse-t "5:hello,")))
  (is (= [42 ""] (parse-t "2:42#")))
  (is (= [3.14 ""] (parse-t "4:3.14^")))
  (is (= [true ""] (parse-t "4:true!")))
  (is (= [nil ""] (parse-t "0:~"))))

(deftest test-compound
  (is (= [["hello" 42] ""] (parse-t "13:5:hello,2:42#]")))
  (is (= [{"hello" 42} ""] (parse-t "13:5:hello,2:42#}")))
  (is (= [{"pi" 3.14, "hello" 42} ""] (parse-t "25:5:hello,2:42#2:pi,4:3.14^}"))))

Note that I've brought in the tnetstrings.core namespace (my source code), and only referenced the parse-t function. I always try to list the specific functions I want in a use clause, though I'm not usually so particular when writing test code. You'll also see clojure.test. As mentioned, this is necessary for the deftest and is macros. It is worth pointing out that both of these use clauses were automatically generated for me by Leiningen, along with a the first deftest.

I could have created a convenience function that just extracted the first element out of the returned tuple, thereby making the tests more concise. However, I intentionally tested the entire tuple, to ensure that nothing was being left at the end. I ought to create a string with some garbage at the end as well, to see that being returned, but the array and map tests have this built in... and I was being lazy.

Something else that caught me out was that when I parse a floating point number, I did it with java.lang.Float/parseFloat. This worked fine, but by default Clojure uses double values instead, and all floating point literals are parsed this way. Consequently the tests around "4:3.14^" failed with messages like:

expected: (= [3.14 ""] (parse-t "4:3.14^"))
  actual: (not (= [3.14 ""] [3.14 ""]))

What isn't being shown here is that the two values of 3.14 have different types (float vs. double). Since Clojure prefers double, I changed the parser to use java.lang.Double/parseDouble and the problem was fixed.


For anyone unfamiliar with Leiningen, here is a brief rundown of what it does. By running the new command Leiningen sets up a directory structure and a number of stub files for a project. By default, two of these directories are src/ and test. Under src/ you'll find a stub source file (complete with namespace definition) for the main source code, and under test/ you'll find a stub test file, again with the namespace defined, and with clojure.test already brought in for you. In my case, these two files were:

  • src/tnetstrings/core.clj
  • test/tnetstrings/test/core.clj

To get running, all you have to do is put your code into the src/ file, and put your tests into the test/ file. Once this is done, you use the command:
  lein test
to run the tests. Clojure gets compiled as it is run, so any problems in syntax and grammar can be found this way as well.

However, one of the biggest advantages to using this build environment, is the ease of bringing in libraries. Using Leiningen can be similar to using Maven, without much of the pain, and indeed, Leiningen even offers a pom command to generate a Maven POM file. It automatically downloads packages from both Clojars and Maven repositories, so this feature alone makes it valuable.

Leiningen is configured with a file called project.clj which is autogenerated when a project is created. This file is relatively easy to configure for simple things, so rather than delving into it here, I'll let anyone new to the system go the project page and sample file to learn more about it.

project.clj also works for some not-so-simple setups, but it gets more and more difficult the fancier it gets. It's relatively easy to update the source path, test path, etc, to mimic Maven directory structures, which can be useful, since the Maven structure allows different file types (e.g. Java sources, resources) to be stored in different directories. But since I always want this, it's annoying that I always have to manually configure it.

I'm also in the process of copying Alex Hall's setup for pre-compiling Antlr parser definitions so that I can do the same with Beaver. Again, it's great that I can do this with Leiningen, but it's annoying to do so. I shouldn't be too harsh though, as the way that extensions are done look more like they are derived from the flexibility of Clojure than Leiningen itself.

Wednesday, August 22, 2012

Clojure DC

Tonight was the first night for Clojure DC, which is a meetup group for Clojure users. It's a bit of a hike for me to get up there, but I dread getting too isolated from other professionals, so I decided it was worth making the trip despite the distance and traffic. Luckily, I was not disappointed.

Although I was late (have you ever tried to cross the 14th Street Bridge at 6pm? Ugh) not much had happened beyond som pizza consumption. The organizers, Matt and Chris, had a great venue to work with, and did a good job of getting the ball rolling.

After introductions all around, Matt and Chris gave a description of what they're hoping to do with the group, prompted us with ideas for future meetings, and asked for feedback. They suggested perhaps doing some Clojure Koans, and in that spirit they provided new users with an introduction to writing Clojure code (not an intro to Clojure, but an intro to writing code), by embarking on a function to parse tnetstrings. I'd never heard of these, but they're a similar concept to JSON, only the encoding and parsing is even simpler.

This part of the presentation was fun, since Matt and Chris had a banter that was reminiscent of Daniel Friedman and William Byrd presenting miniKanren at Clojure/Conj last year. While writing the code they asked for feedback, and I was pleased to learn a few things from some of the more experienced developers who'd shown up (notably, Relevance employee Craig Andera, and ex-Clojure.core developer, and co-author of my favorite Clojure book, Michael Fogus). For instance, while I knew that maps operate as functions where they look up an argument in themselves, I did not know that they can optionally accept a "not-found" parameter like clojure.core/get does. I've always used "get" to handle this in the past, and it's nice to know I can skip it.

While watching what was going on, I decided that a regex would work nicely. So I ended up giving it a go myself. The organizers stopped after parsing a string and a number, but I ended up doing the lot, including maps and arrays. Interestingly, I decided I needed to return a tuple, and after I finished I perused the reference Python implementation and discovered that this returned the same tuple. Always nice to know when you're on the right track. :-)

Anyway, my attempt looked like:

(ns tnetstrings.core)

(def type-map {\, identity
               \# #(Integer/parseInt %)
               \^ #(Float/parseFloat %)
               \! #(Boolean/parseBoolean %)
               \~ (constantly nil)
               \} (fn [m] (loop [mp {} remainder m]
                            (if (empty? remainder)
                              (let [[k r] (parse-t remainder)
                                    [v r] (parse-t r)]
                                (recur (assoc mp k v) r)))))
               \] (fn [m] (loop [array [] remainder m]
                            (if (empty? remainder)
                              (let [[a r] (parse-t remainder)]
                                (recur (conj array a) r)))))})

(defn parse-t [msg]
  (if-let [[header len] (re-find #"([0-9]+):" msg)]
    (let [head-length (count header)
          data-length (Integer/parseInt len)
          end (+ data-length head-length)
          parser (type-map (nth msg end) identity)]
      [(parser (.substring msg head-length end)) (.substring msg (inc end))])))

There are lots of long names in here, but I wasn't trying to play "golf". The main reason I liked this was because of the if-let I introduced. It isn't perfect, but if the data doesn't start out correctly, then the function just returns nil without blowing up.

While this worked, it was bothering me that both the array and the map forms looked so similar. I thought about this in the car on the way home, and I recalled the handy equivalence:

(= (assoc m k v) (conj m [k v]))

So with this in hand, I had another go when I got home:

(ns tnetstrings.core)

(defn embedded [s f]
  (fn [m] (loop [data s remainder m]
            (if (empty? remainder)
              (let [[d r] (f remainder)]
                (recur (conj data d) r))))))

(def type-map {\, identity
               \# #(Integer/parseInt %)
               \^ #(Float/parseFloat %)
               \! #(Boolean/parseBoolean %)
               \~ (constantly nil)
               \} (embedded {} (fn [m] (let [[k r] (parse-t m)
                                             [v r] (parse-t r)]
                                         [[k v] r])))
               \] (embedded [] (fn [m] (let [[a r] (parse-t m)]
                                         [a r])))})

(defn parse-t [msg]
  (if-let [[header len] (re-find #"([0-9]+):" msg)]
    (let [head-length (count header)
          data-length (Integer/parseInt len)
          end (+ data-length head-length)
          parser (type-map (nth msg end) identity)]
      [(parser (.substring msg head-length end)) (.substring msg (inc end))])))

So now each of the embedded structures is based on a function returned from "embedded". This contains the general structure of:

  • Seeing if there is anything left to parse.
  • If not, then return the already parsed data.
  • If so, then parse it, and add the parsed data to the structure before repeating on the remaining string to be parsed.
In the case of the array, just one element is parsed by re-entering the main parsing function. The result is just the returned data. In the case of the map, the result is a key/value tuple, obtained by re-entering the parsing function twice. By wrapping the key/value like this we not only get to return it as a single "value", but it's also in the form required for the conj function that is used on the provided data structure (vector or map).

The result looks a little noisy (lots of brackets and parentheses), but I think it abstracts out the operations much better. Exercises like this are designed to help you think about problems the right way, so I think it was a great little exercise.

Other than this code, I also got the chance to chat with a few people, which was the whole point of the trip. It's getting late, so I won't go into those conversations now, but I was pleased to hear that many of them will be going to Clojure/Conj this year.

Tuesday, May 22, 2012

Clojure Lessons

Recently I've been working with Java code in a Spring framework. I'm not a big fan of Spring, since the bean approach means that everything has a similar public face, which means that the data types don't document the system very well. The bean approach also means that most types can be plugged into most places (kind of like Lego), but just because something can be connected doesn't mean it will do anything meaningful. It can make for a confusing system. As a result, I'm not really have much fun at work.

To get myself motivated again, I thought I'd try something fun and render a Mandelbrot set. I know these are easy, but it's something I've never done for myself. I also thought it might be fun to do something with graphics on the JVM, since I'm always working on server-side code. Turned out that it was fun, keeping me up much later than I ought to have been. Being tired tonight I may end up rambling a bit. It may also be why I've decided to spell "colour" the way I grew up with, rather than the US way (except in code. After all, I have to use the Color class, and it's just too obtuse to have two different spellings in the same program).

To get my feet wet, I started with a simple Java application, with a plan to move it into Clojure. My approach gave me a class called Complex that can do the basic arithmetic (trivial to write, but surprising that it's not already there), and an abstract class called Drawing that does all of the Window management and just expects the implementing class to implement paint(Graphics). With that done it was easy to write a pair of functions:

  • coord2Math to convert a canvas coordinate into a complex number.
  • mandelbrotColor to calculate a colour for a given complex number (using a logarithmic scale, since linear shows too many discontinuities in colour).
Drawing this onto a graphical context is easy in Java:
for (int x = 0; x < gWidth; x++) {
  for (int y = 0; y < gHeight; y++) {
    g.setColor(mandelbrotColor(coord2Math(x, y)));
    plot(g, x, y);

(plot(Graphics,int,int) is a simple function that draws one pixel at the given location).

A small image (300x200 pixels) on this MacBookPro takes ~360ms. A big one (1397x856) took ~11500ms. Room for improvement, but it'll do. So with a working Java implementation in hand, I turned to writing the same thing in Clojure.

Clojure Graphics

Initially I tried extending my Drawing class using proxy, with a plan of moving to an implementation completely in Clojure. However, after getting it working that way I realized that doing the entire thing in Clojure wasn't going to take much at all, so I did that straight away. The resulting code is reasonably simple and boilerplate:

(def window-name "Mandelbrot")
(def draw-fn)

(defn new-drawing-obj []
  (proxy [JPanel] []
    (paint [^Graphics graphics-context]
      (let [width (proxy-super getWidth)
            height (proxy-super getHeight)]
        (draw-fn graphics-context width height)))))

(defn show-window []
  (let [^JPanel drawing-obj (new-drawing-obj)
        frame (JFrame. window-name)]
    (.setPreferredSize drawing-obj (Dimension. default-width default-height))
    (.add (.getContentPane frame) drawing-obj)
    (doto frame
      (.setDefaultCloseOperation JFrame/EXIT_ON_CLOSE)
      (.setBackground Color/WHITE)
      (.setVisible true))))

(defn start-window []
  (SwingUtilities/invokeLater #(show-window)))

Calling start-window sets off a thread that will run the event loop and then call the show-window function. That function uses new-drawing-obj to create a proxy object that handles the paint event. Then it sets the size of panel, puts it into a frame (the main window), and sets up the frame for display.

The only thing that seems worth noting from a Clojure perspective is the proxy object returned by new-drawing-obj. This is simple extension of java.swing.JPanel that implements the paint(Graphics) method of that class. Almost every part of the drawing can be done in an external function (draw-fn here), but the width and height are obtained by calling getWidth() and getHeight() on the JPanel object. That object isn't directly available to the draw-fn function, nor is it available through a name like "this". The object is returned from the proxy function, but that's out of scope for the paint method to access it. The only reasonable way to access methods that are inherited in the proxy is with the proxy-super function (I can think of some unreasonable ways as well, like setting a reference to the proxy, and using this reference in paint. But we won't talk about that kind of abuse).

While I haven't shown it here, I also wanted to close my window by pressing the "q" key. This takes just a couple of lines of code, whereby a proxy for KeyListener is created, and then added to the frame via (.addKeyListener the-key-listener-proxy). Compared to the equivalent code in Java, it's strikingly terse.


The Java code for rendering used a pair of nested loops to generate coordinates, and then calculated the colour for each coordinate as it went. However, this imperative style of coding is something to explicitly avoid in any kind of functional programming. So the question for me at this point, was how should I think about the problem?

Each time the mandelbrotColor was to be called, it is mapping a coordinate to a colour. This gave me my first hint. I needed to map coordinates to colours. This implies calling map on a seq of coordinates, and ending up with a seq of colours. (Actually, not a seq, but rather a reducible collection). However, what order are the colours in? Row-by-row? That would work, but it would involve keeping a count of the offset while working over the seq, which seems onerous, particular when the required coordinates were available when the colour was calculated in the first place. So why not include the coordinates in the seq with the colour? Not only does that simplify processing, it makes the rendering of this map stateless, since any element of the seq could be rendered independently of any other.

Coordinates can be created as pairs of integers using a comprehension:

  (for [x (range width) y (range height)] [x y])

and the calculation can be done by mapping on a function that unpacks x and y and returns a triple of these two coordinates along with the calculated colour. I'll rename x and y to "a" and "b" in the mapping function to avoid ambiguity:

  (map (fn [[a b] [a b (mandelbrot-color (coord-2-math a b))])
       (for [x (range width) y (range height)] [x y]))

So now we have a sequence of coordinates and colours, but how do these get turned into an image? Again, the form of the problem provides the solution. We have a sequence (of tuples), and we want to reduce it into a single value (an image). Reductions like this are done using reduce. The first parameter for the reduction function will be the image, the second will be the next tuple to draw, and the result will be a new image with the tuple drawn in it. The reduce function isn't really supposed to mutate its first parameter, but we don't want to keep the original image without the pixel to be drawn, so it works for us here. The result is the following reduction function (type hint provided to avoid reflection on the graphical context):

  (defn plot [^Graphics g [x y c]]
    (.setColor g c)
    (.fillRect g x y 1 1)

Note that the original graphics context is returned, since this is the "new" value that plot has created (i.e. the image with the pixel added to it). Also, note that the second parameter is a 3 element tuple, which is just unpacked into x y and c.

So now the entire render process can be given as:

(reduce plot g
  (map (fn [[a b] [a b (mandelbrot-color (coord-2-math a b))])
       (for [x (range width) y (range height)] [x y])))

This works just fine, but there were performance issues, which was the part of this process that was most interesting. The full screen render (1397x856) took ~682 seconds (up from the 11.5 seconds it took Java). Obviously there were a few things to be fixed. There is still more to do, but I'll share what I came across so far.


The first thing that @objcmdo suggested was to look for reflection. I planned on doing that, but thought I'd continue cleaning the program up first. The Complex class was still written in Java, so I embarked on rewriting that in Clojure.

The easiest way to do this was to implement a protocol that describes the actions (plus, minus, times, divide, absolute value), and to then define a record (of real/imaginary) that extends the protocol. It would have been nicer than the equivalent Java, but for one thing. Java allows method overloading based on parameter types, which means that a method like plus can be defined differently depending on whether it receives a double value, or another Complex number. My understanding is that Clojure only overloads functions based on the parameter count, meaning that different function names are required to redefine the same operation for different types. So for instance, the plus functions were written in Java as:

  public final Complex plus(Complex that) {
    return new Complex(real + that.real, imaginary + that.imaginary);

  public final Complex plus(double that) {
    return new Complex(real + that, imaginary);
But in Clojure I had to give them different names:
  (plus [this {that-real :real, that-imaginary :imaginary}]
        (Complex. (+ real that-real) (+ imaginary that-imaginary)))
  (plus-dbl [this that] (Complex. (+ real that) imaginary))

Not a big deal, but code like math manipulation looks prettier when function overloading is available.

It may be worth pointing out that I used the names of the operations (like "plus") instead of the symbolic operators ("+"). While the issue of function overloading would have made this awkward (+dbl is no clearer than plus-dbl) it has the bigger problem of clashing with functions of the same name in clojure.core. Some namespaces do this (the * character is a popular one to reuse), but I don't like it. You have to explicitly reject it from your current namespace, and then you need to refer to it by its full name if you do happen to need it. Given that Complex needs to manipulate internal numbers, then these original operators are needed.

So I created my protocol containing all the operators, defined a Complex record to implement it, and then I replaced all use of the original Java Complex class. Once I was finished I ran it again just to make sure that I hadn't broken anything.

To my great surprise, the full screen render went from 682 seconds down to 112 seconds. Protocols are an efficient mechanism, but they shouldn't be that good. At that point I realised that I hadn't used type hints around the Complex class, and that as a consequence the Clojure code had to perform reflection on the complex numbers. Just as @objcmdo had suggested.

Wondering what other reflection I may have missed, I tried enabling the *warn-on-reflection* flag in the repl, but no warnings were forthcoming. I suspect that this was being subverted by the fact that the code is all being run by a thread that belongs to the Swing runtime. I tried adding some other type hints, but nothing I added had any effect, meaning that the Clojure compiler was already able to figure out the types involved (or else it just wasn't in a critical piece of code).

Composable Abstractions

The next thing I wondered about was the map/reduce part of the algorithm. While it made for elegant programming, it was creating unnecessary tuples at every step of the way. Could these be having an impact?

Once you have a nice list comprehension, it's tough to break it out into an imperative-style loop. Aside from ruining the elegance of the original construct, once you've seen your way through to viewing a problem in such clear terms, it's difficult to reconceptualize it as a series of steps. Even when you do, how do you make Clojure work against itself?

Creating a loop without burning through resources can be done easily with tail recursion. Clojure doesn't do this automatically (since the JVM does not provide for it), but it can be emulated well with loop/recur. Since I want to loop between 0 (inclusive) and the width/height (exclusive), I decremented the upper limits for convenience. Also, the plot function is no longer constraint to just 2 arguments, so I changed the definition to accept all 4 arguments directly, thereby eliminating the need to construct that 3-tuple:

(let [dwidth (dec width)
                 dheight (dec height)]
  (loop [x 0 y 0]
    (let [[next-x next-y] (if (= x dwidth)
                              (if (= y dheight)
                                  [-1 -1]      ;; signal to terminate
                                  [0 (inc y)])
                              [(inc x) y])]
      (plot g x y (mandelbrotColor (coord-2-math x y)))
      (if (= -1 next-x)
        :end    ;; anything can be returned here
        (recur next-x next-y)))))

My word, that's ugly. The let that assigns next-x and next-y has a nasty nested if construct that increments x and resets it at the end of each row. It also returns a flag (could be any invalid number, such as the keyword :end) to indicate that the loop should be terminated. The loop itself terminates by testing for the termination value and returning a value that will be ignored.

But it all works as intended. Now instead of creating a tuple for every coordinate, it simply iterates through each coordinate and plots the point directly, just as the Java code did. So what's the performance difference here?

So far, the numbers I've provided are rounded to the nearest second. Repeated runs have usually taken a similar amount of time to the ones that I've reported here. However, there is always some jitter, sometimes by several seconds. Because of this, I was unable to see any difference whatsoever between using map/reduce on a for comprehension, versus using loop/recur.

That's an interesting result, since it shows that the Clojure compiler and JVM are indeed as clever as we're told, when we see that better abstractions are just as efficient as the direct approach. It's all well and good for a language to make it easy to write powerful constructs, but being able to perform more elegant code just as efficiently as more direct, imperative code that a language is really offering useful power.

Aside from the obvious clarity issues, the composability of the for/map/reduce makes an enormous difference. Because each element in the range being mapped is completely independent, we are free to use the pmap function instead of map. The documentation claims that this function is,

"Only useful for computationally intensive functions where the time of f dominates the coordination overhead."

Yup. That's us.

So how much does this change make for us? Using map on the current code, a full screen render takes 112 seconds. Changing map to pmap improves it to 75 seconds. That's a 33% improvement with no work, simply because the correct abstraction was applied. That's a very powerful abstraction.

Future Work

(Hmmm, that makes this sound like an academic paper. Should I be drawing charts?)

The final result is still a long way short of the 11.5 seconds the naïve Java code renders at. The single threaded version is particularly bad, taking about 10 times as long. I don't expect Clojure to be as fast as Java, but a factor of 10 suggests that there are some obvious things that I've missed, most likely related to reflection. If I can get it down to the same order of magnitude as the Java code, then using pmap could make the Clojure version faster due to being multi-threaded. Of course, Java can be multi-threaded as well, but the effort and infrastructure for doing this would be significant.