Why Not Return A Function? July 2nd, 2009
Patrick Stein

This morning, I was catching up on the RSS feeds I follow. I noticed an interesting snippet of code in the Abstract Heresies journal for the Discrete-time Fourier Transform. Here is his snippet of code:

(define (dtft samples)
  (lambda (omega)
    (sum 0 (vector-length samples)
        (lambda (n)
          (* (vector-ref samples n)
             (make-polar 1.0 (* omega n)))))))

My first thought was That’s way too short. Then, I started reading through it. My next thought was, maybe I don’t understand scheme at all. Then, my next thought was, I do understand this code, it just didn’t do things the way I expected.

Here, I believe is a decent translation of the above into Common Lisp:

(defun dtft (samples)
  #'(lambda (omega)
      (loop for nn from 0 below (length samples)
           summing (let ((angle (* omega nn)))
                     (* (aref samples nn)
                        (complex (cos angle) (sin angle)))))))

Now, what I find most interesting here is that most implementations you’ll find for the DTFT (Discrete-Time Fourier Transform) take an array of samples and a wavelength, and returns a result. This, instead, returns a function which you can call with a wavelength omega. It returns an evaluator. This is an interesting pattern that I will have to try to keep in mind. I have used it in some places before. But, I am sure there are other places that I should have used it, and missed. This is one where I would have missed.

Usage for the above would go something like:

(let ((dd (dtft samples)))
  (dd angle1)
  (dd angle2)

For those not into Lisp either (who are you?), here is a rough translation into C++.

#include <cmath>
#include <complex>

class DTFT {
  unsigned int len;
  double* samples;

  DTFT( double* _samples, unsigned int _len ) {
    this->len = _len;
    this->samples = new double[ this->len ];
    for ( unsigned int ii=0; ii < this->len; ++ii ) {
      this->samples[ ii ] = _samples[ ii ];

  ~DTFT( void ) {
    delete[] this->samples;

  std::complex< double > operator () ( double omega ) const {
    std::complex< double > sum( 0.0, 0.0 );
    for ( unsigned int ii=0; ii < this->len; ++ii ) {
      sum += this->samples[ ii ] * std::polar( 1.0, omega );
    return sum;

With usage like:

DTFT dd( samples, 1024 );
dd( angle1 );
dd( angle2 );

So, six lines of Scheme or Lisp. Twenty-five lines of C++ including explicit definition of a class to act as a pseudo-closure, explicit copying and management of the samples buffer, etc. I suppose, a more direct translation would have used a std::vector to hold the samples and would have just kept a pointer to the buffer. That would have shaved off six or seven lines and the whole len and _len variables.

To CLOS or not to CLOS June 29th, 2009
Patrick Stein

I am working on some Lisp code. I am trying to mimic the basic structure of a large C++ project. I think the way the C++ project is structured is a good fit for the tasks involved.

Most of the C++ stuff is done with classes. Most of the methods of those classes are virtual methods. Many of the methods will be called multiple times every hundredth of a second. Very few of the virtual methods ever get overridden by subclasses.

So, I got to thinking. Does it make sense for me to use CLOS stuff at all for most of this? Would it be significantly faster to use (defstruct …) and (defun …) instead of (defclass …) and (defgeneric …)?

My gut instinct was: Yes. My first set of test code didn’t bear that out. For both the classes and the structs, I used (MAKE-INSTANCE …) to allocate and (WITH-SLOTS …) to access. When doing so, the classes with generic functions took about 1.5 seconds for 10,000,000 iterations under SBCL while the structs with non-generic functions took about 2.2 seconds.

For the next iteration of testing, I decided to use accessors instead of slots. I had the following defined:

(defclass base-class ()
  ((slot-one :initform (random 1.0f0) :type single-float
             :accessor class-slot-one)
   (slot-two :initform (random 1.0f0) :type single-float
             :accessor class-slot-two)))

(defclass sub-class (base-class)
  ((slot-three :initform (random 1.0f0) :type single-float
               :accessor class-slot-three)
   (slot-four  :initform (random 1.0f0) :type single-float
               :accessor class-slot-four)))

(defstruct (base-struct)
  (slot-one (random 1.0f0) :type single-float)
  (slot-two (random 1.0f0) :type single-float))

(defstruct (sub-struct (:include base-struct))
  (slot-three (random 1.0f0) :type single-float)
  (slot-four (random 1.0f0) :type single-float))

I then switched from using calls like (slot-value instance ‘slot-three) in my functions to using calls like (class-slot-three instance) or (sub-struct-slot-three instance). Now, 10,000,000 iterations took 2.6 seconds for the classes and 0.3 seconds for the structs in SBCL. In Clozure (64-bit), 10,000,000 iterations with classes and with method-dispatch and with accessors took 11.0 seconds, with classess and without method-dispatch but with accessors took 6.1 seconds, and with structs and without method-dispatch and with accessors took 0.4 seconds.

There is much more that I can explore to tune this code. But, for now, I think the answer is fairly easy. I am going to use structs, functions, and accessors for as many cases as I can. Here is the generic-function, class, struct test code with accessors. The first loop uses classes and generic functions. The second loop uses classes and regular functions. The third loop uses structs and regular functions.

How I Know I Don’t Know Enough About Lisp Macros June 19th, 2009
Patrick Stein

I have a pretty good grasp on macros in Lisp, C/C++, TeX, m4, and nroff. Lisp macros are, far and away, the most powerful in that set. In fact, Lisp macros get a bad rap by sharing a name with macros in those other languages. Still, I often hit the same wall when trying to write a Lisp macro so I know that there’s more I have to learn.

A Quick Look at Macros

First, let’s review macros for a moment to make sure we’re all on the same page. The C/C++ macros are the simplest to understand so we’ll start there. The C and C++ compilers run in two stages. First, the C preprocessor runs to expand all of your macros. Then, the compiler runs to actually compile your code. In C and C++, macros are declared using the #define command to the preprocessor. For example, you might do something like the following:
Read the rest of this entry ⇒

Programming When Clarity Counts May 5th, 2009
Patrick Stein

In my previous post, I wrote some code in Perl because I wanted the code to be clear and obvious. Wait? What? Who uses Perl when they want clarity?


I admit: I was surprised myself. Seriously, I tried several other languages first. Let’s just focus on the first loop here. Here’s the Perl again for reference:

my $total = 0.0;
foreach my $item ( @list_of_items ) {
    $total += weight( $item );

Objective C

The actual code that I was attempting to explain was in Objective C with the NeXTStep foundation classes. I couldn’t imagine that anyone would want to try to understand it:

double total = 0.0;
NSEnumerator* ee = [itemList objectEnumerator];
Item* item;
while ( ( item = (Item*)[ee nextObject] ) != nil ) {
    total += [item weight];


My first attempt for the article was to write it in C using an array of items.

double total = 0.0;
unsigned int ii;
for ( ii = 0; ii < itemCount; ++ii ) {
    total += weight( itemArray[ ii ] );

That’s not too terrible. There is, however, a great deal of syntax and code devoted to handling the array including an extra variable to track its length. Beyond that, the loop counter is of little use to someone trying to understand the concept.


My next go was C++. My hope was that iterators would make the looping less painful. C++ iterators, however, are the very model of pain.

double total = 0.0;
std::list< Item* >::const_iterator it;
for ( it = itemList.begin(); it != itemList.end(); ++it ) {
    total += weight( *it );

This requires the reader to wade through a syntactic thicket to get the iterator into the picture at all. It also requires a certain comfort with pointers that one wouldn’t have coming from another language.


My next attempt was Java. I hate Java. It may not be terrible for this code with the new looping constructs that came in Java 1.5. Alas, I quit coding it before I made it through this first loop.


Of course, I wanted to code this in Lisp:

(let ((total (reduce #'+ list-of-items :key #'weight)))

That would be perfectly clear to someone who has used Lisp or Scheme. Alas, not everyone has.

So… Perl…

If you want to write the Perl code, you have to understand the difference between scalars and arrays. To read the code, however, you don’t have to grok that distinction to see what’s going on. I didn’t try it in Python. Maybe it would be clear to a wider audience. I may have to try it next time.

Sapir-Whorf with Programming Languages February 12th, 2009
Patrick Stein

I’ve been coding in Objective-C for a month or so now. It is interesting (in a Sapir-Whorf sort of way), how the language changes the way that I code. Switching from Objective-C to Lisp made me notice something that I hadn’t really noticed when moving from C++/Java/Perl to Lisp.

In Lisp, I will pull something out into a separate function if it makes the current function more self-contained, more one idea. In C++, I will only pull something out into a separate function if I need the same functionality in multiple places.

Actually, it’s even worse than that in C++. For stuff that is less than six or so lines, I might maintain it in several functions. Or, if I’m using some Literate Programming tool, I will just use the same chunk in multiple places. The notable exception in C++ is when I want to use something as a loop conditional, I may bother to break it out into its
own function:

while ( incrementCounter( cntr, min, max, dimensions ) ) {
    // body of loop here

In C++ or Objective-C, I might do something like this:

// some portion of my function

unsigned int choice = random() % length;
void* currentChoice = options[ choice ];
    // yes, I know I can memcpy(), but that's not as obvious
for ( unsigned int ii=choice+1; ii < length; ++ii ) {
    options[ ii-1 ] = options[ ii ];

// some code using currentChoice

In Lisp, I would never consider keeping that code inline. I would put it in another function right away.

This, this is one of the things I meant when I said Lisp is just plain fun. It’s easy to make a new function. I can just do it. I don’t have to fret too much over the name. I don’t have to fret too much over the argument
list. I don’t have to pre-declare it in this header file with the same signature as that implementation file. I
don’t have to pretend its a method when it’s really just a function. I can return multiple values if I need to do so. I don’t have to worry much about which compilation units will need to see this to compile.

Part of the maze generation code that I wrote in Objective-C needs to track walls. I don’t need the same structure during generation that I will use once it’s generated. So, I have a Wall class declared. It feels wrong to declare it right in the header file for the Maze. It feels silly to break it out into its own header file. What I should be doing is making a separate MazeFactory and have its implementation include the declaration of this Wall class. But, that is such overkill here. I just want the darn maze.

In Lisp, I would just be done with no feelings of guilt at all.