Using Lush with Gnuplot

I had not been using Lush for about a year and yesterday I wanted to write a few lines of code to recreate a plot from a linear algebra textbook. This is the sort of thing that people turn to Matlab for: write a few lines of code to generate some data, call plot once or twice, done. When I am on the top of my game I can do the same with Lush, it would not take me more than ten minutes.


The plot in question shows the roots of Wilkinson's polynomial in the complex plane and illustrates that polynomial root finding is an ill-conditioned problem. The thicker black dots are the known roots of the polynomial and the many little red dots are the roots returned by a polynomial root finder after perturbing the polynomial's coefficients slightly. More precisely, the program randomly perturbed the coefficients, called the root finder and plotted the roots in red. Repeating this 100 times you get a plot like the one above.

The point of the plot is that the exact location of the roots as a function of the polynomial coefficients is very sensitive for this polynomial. Perturbing the coefficients cause changes in the roots' locations many orders of magnitude larger than the changes in the coefficients.

The point of this blog post, on the other hand, is to show how easy it is to generate that plot in Lush. Here is the function that created the plot (the complete script is in Lush's demos directory).

(defun wilkinson-demo (&optional (n-pertubations 100))
  (let* ((p *p-wilkinson*)
     (n ($n *p-wilkinson*))
     (s ($> [@ 1e-10] n-pertubations n))
     (coeffs (* ($< p n-pertubations) (+ 1 (rand s))))
     (plotter (new Gnuplot 'interactive ())) )
    (plot
      (title "Roots of Wilkinson's polynomial")
      (points (++> *roots-wilkinson* [0]) (lc 'black) (pt 7) (ps 1))
      (do ((c coeffs))
        (points (poly-solve c) (lc 'red) (pt 7) (ps 0.2)) ))
    plotter))

Just a few lines, nice. But yesterday it took me more than half a day to get this done. Not because I forgot so many things about the language, but because I had not fully rebuilt everything I needed after upgrading my laptop a few months back: The gnuplot installed on Ubuntu simply did not work with Lush and I had to figure out/remember why.

Long story short, if you want to use gnuplot with Lush (you do), then you need to build it yourself. That is, download the sources, install all the development packages for the dependencies that make gnuplot most powerful and pleasant to use (libreadline, wxWidgets, cairo, pango, libgd), and build it.

I installed the most recent version 4.4. and the gnuplot demos in Lush all worked fine.

The mm_manage call

I have been away working on my thesis and on Lush 2 for the last few months. The garbage collector got quite a bit faster since and I made changes to the API. The most recent change was the introduction of the mm_manage call.

mm_manage(const void *p);

With mm_manage you hand to MM a pointer to memory that you allocated with a C library function (malloc, calloc, stdrup, etc.). MM then will take care of it and free the memory for you when it is no longer referenced.

This call makes MM more useful in situations where you get objects from calls into third-party code that uses the C library functions for memory allocation. Of course, you may use mm_manage only for memory objects that are leafs in the dependency graph that MM oversees, and mm_manage assigns those the memory type mt_blob. (The type mt_blob is a predefined, unsized memory type for things that don't contain further memory references).

What if a library does return something more complicated than a blob? For instance, the OpenCV API contains functions like cvFindContours that builds up a complicated data structure, which you need to hold on to and traverse and query with other OpenCV functions. While the address to the data structure created by cvFindContours is, to an OpenCV user, an address to something opaque and pretty much a blob conceptually, you may not simply call free with this address (and therefore you cannot give it to mm_manage).

However, for every call that builds an object, OpenCV has a counterpart, a destructor function, which releases the object. With a little bit more work the mechanism behind mm_manage may be extended to deal with such objects as well. What is needed is a variant mm_manage_foreign, which not only takes a pointer, but, in addition, a custom free function that MM will call instead of free when the object becomes unreachable:

typedef void free_func_t(void *p);
mm_manage_foreign(const void *p, free_func_t *f);

MM would tag those foreign addresses with a special memory type mt_foreign instead of mt_blob and maintain a mapping from foreign pointers to their respective free functions. And mm_manage will then be equivalent to

mm_manage_foreign(p, free);

End of SoC

It has almost been a month since my last post, and Google Summer of Code has come to an end. Although I have not achieved all my milestones, this project is nevertheless a success. The Lush interpreter is now powered by the new memory manager module and the result of my SoC work is the basis for "Lush 2", the next major Lush release (see https://lush.svn.sourceforge.net/svnroot/lush/).

The garbage collector is faster now than a few weeks ago thanks to using a bitmap to record the state of the small object heap. Not maintaining free lists at all but using the bitmap for finding unused memory in the small object heap might give further improvements, albeit small ones. I will try it out some time, after describing the work in a brief tech report.

Debugging and Tuning

Friday last week I had a major break-through: I saw the shell again after more than four weeks. Debugging was exactly as much fun as everybody says it is. It's particular frustrating if you spend five hours from not having any clue what part of the system might be causing a crash over narrowing it down to a small number of hypotheses to finding a really stupid mistake that you can't believe you are responsible for. Gdb is a close friend now.

For testing the interpreter I was basically using the startup procedure. When the interpreter starts up it reads in and parses a bunch of source files with definitions. So there surely are a couple of more bugs that this "test" did not expose. Before I try running other programs to tease out more bugs, though, I will spend a little more time on performance tuning. Having to wait a minute or two until the interpreter got to a point where it broke while parsing the standard files was an annoyance while debugging last week (and besides, that performance is unacceptable).

Three items are on my performance tuning to-do list for now:

• Do some profiling and try to speed up the hot spots in the MM code
  
• Implement asynchronous collect (so far there's only synchronous)
• Implement a smarter collection trigger policy

On Designing Interfaces

I talked a little bit about ATs in an earlier post. To summarize, ATs serve three different roles in the original Lush interpreter, namely

1. As generic, unique identifiers for Lisp objects
   
2. As carriers of runtime type information
3. As carriers of information for memory management (reference counts)
   

In the branch that I am currently working on, the third point is no longer true and ATs serve only the first two purposes. In this posting I want to talk about the first purpose.

There are many type-generic functions in the interpreter that may work with many or all kinds of objects (creating a string representation, writing an object to a file, computing a hash code, etc.). Many other functions work with objects of particulars type only (open a file given a name (string), slicing an array, arithmetic functions, etc.). And a third kind of function are found in the class structure of Lisp objects. They are type specific versions of functions that should work with all objects (dispose, creating a string representation, listeval, etc.).

The natural signature of type-generic functions include an AT argument pointing to the object in question. They may be implemented as dispatchers to type-specific functions of the third kind. Function signatures for the second kind may or may not include an AT.

When you look at the original Lush interpreter implementation you will find that functions of the second and third kind do have generic signatures as well. The ones of the second kind typically do a runtime type-check, the ones of the third do not. I consider this bad design. If a function works with arguments of a particular type only, then the signature should say so and the implementation should not waste (run)time doing type checks. This is one kind of changes that I have been making since I started hacking Lush, and there's still a lot of work to be done on overhauling internal interfaces.

Yesterday I was churning through the dispose functions, which are functions of the third kind. Objects with non-trivial dispose functions need a finalizer to invoke the dispose function. Lush also has a function delete to explicitly destroy a Lisp object, no matter if it is still referenced or not. Delete calls an object's dispose function and then modifies the AT to make it look like a NIL. So a dispose needs to be idempotent since it may be called twice (once by delete and a second time by the finalizer).

Since I was going to look at all dispose functions I decided to change their signatures from generic to type specific along the way. When I got to dispose for OO objects, I hit a snag: This dispose invokes a user-defined destructor (if one has been defined), and at that point, I need to know the object's AT because the destructor is a Lisp function and evaluate has a generic signature. After making dispose type-specific, however, I don't have the object's AT anymore.

That led me to wonder if maybe I was wrong and there is some value in having all signatures generic. Anyway, I fixed it by adding a "back pointer" to the OO object structure (a pointer that points back to the AT referencing the object), which is not nice. Perhaps the dispose interface still isn't quite right?