The nerdiest of the nerds

C is too high level

2009-07-21T22:43:00.001-07:00

I propose that C is too high level of a language for the purposes for which it's used. While it purports to give programmers power over memory layout -- in particular, over heap (via malloc) and stack (via alloca) allocation -- it gives them no control, and does not allow them to describe, how function arguments or struct fields are laid out in memory. Knowing how struct fields are laid out means you can use structs from languages other than C, in a portable way. (Some foreign function interfaces, such as ANSI Common Lisp's CFFI, refuse to allow passing structs by value for this reason.) You can know exactly how much memory to allocate, and bound more tightly from above how much stack space a particular C function call requires.

Given the state of C as it is, what I would like is a domain-specific language for describing binary interfaces, such as struct layout or function call signatures. I would like C compilers to support standard annotations that guarantee particular layouts. Currently this is done in an ad hoc, compiler-specific way -- sometimes by command-line flags ("pack the structs") and sometimes by pragmas or annotations.

The main reason I want standard compiler support for such a minilanguage is for interoperability between C and other languages. I have the misfortune of needing to call into a lot of C libraries from my code, but I don't want to be stuck writing C or C++ (The Language Which Shall Not Be Parsed). Nevertheless, I don't want to tie any other users of my code to a particular C compiler (if the code were just for me, it wouldn't matter so much).

Python win: csv, sqlite3, subprocess, signal

2009-07-01T10:50:00.000-07:00

I've been working these past few months (ugh, months...) on a benchmark-quality implementation of some new parallel shared-memory algorithms. It's a messy, tempermental code that on occasion randomly hangs, but when it works, it often outperforms the competition. Successful output consists of rows of space-delimited data in a plain text format, written to standard output.

I spent a week or so on writing a script driver and output data processor for the benchmark. The effort was both minimal, and paid off handsomely, thanks to some handy Python packages: csv, sqlite3, subprocess, and signal.

The csv ("comma-separated values") package, despite its name, can handle all kinds of text data delimited by some kind of separating character; it reads in the benchmark output with no troubles. sqlite3 is a Python binding to the SQLite library, which is a lightweight database that supports a subset of SQL queries. SQL's SELECT statement can replace pages and pages of potentially bug-ridden loops with a single line of code. I use a cute trick: I read in benchmark output using CSV, and create an SQLite database in memory (so I don't have to worry about keeping files around). Then, I can issue pretty much arbitrary SQL queries in my script. Since I only use one script, which takes command-line arguments to decide whether to run benchmarks or process the results, I don't have to maintain two different scripts if I decide to change the benchmark output format.

The subprocess and signal packages work together to help me deal with the benchmark's occasional flakiness. The latter is a wrapper around the POSIX signalling facility, which lets me set a kind of alarm clock in the Python process. If I don't stop the alarm clock early, it "goes off" by sending Python a signal, interrupting whatever it might be doing at the time. The subprocess package lets me start an instance of the benchmark process and block until it returns. "Block until it returns" means that Python doesn't steal my benchmark's cycles in a busy loop, and the alarm means I can time out the benchmark if it hangs (which it does sometimes). This means I don't burn through valuable processing time if I'm benchmarking on a machine with a batch queue.

I wish the benchmark itself were as easy to write as the driver script was! I've certainly found it immensely productive to use a non-barbaric language, with all kinds of useful libraries, to implement benchmarking driver logic and data processing.

On metadata, shared memory, NUMA, and caches

2009-06-22T12:58:00.000-07:00

Many modern shared-memory multiprocessors improve memory locality by providing each socket (group of processors) in the machine with its own chunk of memory. Each socket can access all the chunks of memory, but accesses to its own chunk are faster (in terms of latency, at least). This design decision is called "nonuniform memory access" (NUMA).

Programming a NUMA machine for performance in scientific kernels looks a lot like programming a distributed-memory machine: one must "distribute" the data among the chunks so as to improve locality. There is a difference, however, in the way one deals with metadata -- the data describing the layout of the data.

In the distributed-memory world, one generally tries to distribute the metadata, because fetching it from another node takes a long time. This means that memory usage increases with the number of processors, regardless of the actual problem size. It also means that programmers have to think harder and debug longer, as distributing metadata correctly (and avoiding bottlenecks) is hard. (Imagine, for example, implementing a reduction tree of arbitrary topology on arbitrary subsets of processors, when you aren't allowed to store a list of all the processors on any one node.)

In the NUMA world, one need not replicate the metadata. Of course one _may_, but metadata access latency is small enough that it's practical to keep one copy of the metadata for all the processors. This is where caches come in: if the metadata is read-only, caches can replicate the relevant parts of the metadata for free (in terms of programming effort). Of course, it would be nice also to have a non-coherent "local store," accessible via direct memory transfers, for the actual data. Once you have the metadata, it's often easy to know what data you want, so it's easier to manage the explicit memory transfers to and from the local store. However, if you only have a local store, you have to store metadata there, and managing that reduces to the distributed-memory case (except more painful, since you have much less memory capacity).

Memory capacity is really the most important difference between the shared-memory NUMA and distributed-memory worlds. Our experience is that on a single shared-memory node, memory capacity cannot scale with the number of processors. This is because DRAM uses too much power. The same power concerns hold, of course, for the distributed-memory world. However, an important use of distributed-memory machines is for their scale-out capacity to solve very large problems, so their architects budget for those power requirements. Architects of single-node shared-memory systems don't have that freedom to expand memory capacity. This, along with the lower latencies between sockets within a single node, makes sharing metadata in the shared-memory world attractive.

It's often easy to delimit sections of a computation in which metadata is only read and never modified. This suggests an architectural feature: using cache coherence to fetch metadata once, but tagging the metadata in cache as read-only, or having a "read-only" section of cache. I'm not a hardware person so I don't know if this is worthwhile, but it's a way to extract locality out of semantic information.

Productivity language for performance-oriented programmers

2009-06-13T18:57:00.000-07:00

Our computer science department last semester offered a graduate seminar course on parallel productivity languages -- that is, programming languages in which it's easy to write parallel code whose performance scales well, even if single-processor performance is not so good (e.g., because the language is interpreted or there is a lot of runtime error checking). Implicit in the word "productivity" is that the target users need not be expert low-level programmers.

According to a professor who helped lead the course, however, most of the class projects ended up being "productivity languages for efficiency-layer programmers." That is, the target users were not non-computer-scientist domain experts, but experienced low-level programmers who want to boost their productivity when optimizing a particular computational kernel. One example was a domain-specific language (DSL) for stencil operations, along with a compiler and autotuner. Users write the stencil operation in a familiar notation, and the system transforms it at runtime (the source language is dynamic) into highly optimized code which performs just about as well as if it were optimized by hand.

The professor's observation resonated, because I'm currently near the end of what turned out to be a long, painful implementation and debugging project. It's a benchmark implementation of a new solver, which itself contains at least three different computational kernels. The project has taught me hard lessons about what bugs consume the most time. What I've found is that working in a language "close to the metal" is not the problem. I'm not afraid to optimize for hardware or operating system features, to allocate and deallocate chunks of memory, or to impose matrix semantics on chunks of raw memory. My frustrations usually come from silly human errors, that result in inscrutable errors which debuggers like gdb and memory analysis tools like Valgrind cannot diagnose. Furthermore, sometimes bugs only manifest with very large problems, that make losing a factor of 10-100x performance to an analysis tool (like Valgrind, which is an amazing tool and perhaps one of the best optimized out there) impractical (or at least annoying).

One source of human errors is conversion between units. The classic example is the loss of the Mars Climate Orbiter in 1999 due to a failure to convert between metric and English units. However, units, or a related kind of semantic information, often come up in pure programming tasks that have little to do with physical measurements. For example, my current project involves a lot of C code that iterates over one kind of data structure, and copies it into a new kind of data structure. A lot of indices fly around, and I usually have to give them suggestive names like "index_old" or "index_new" to indicate whether they "belong" to the old or new data structure. Naming conventions aren't enough to prevent a mismatch, though, and a mistake (like addressing a "new" array with an "old" index) may result in a segfault, smashing the stack, intermittent semantic errors that depend on runtime parameters, or no problems at all. Here, "old" and "new" are a kind of "unit" or semantic restriction: for example, "this index can only be used to address this array, not any other." This kind of language feature seems like it should result in little or no runtime performance hit in many cases.

Another source of human errors is resource scope: who initializes what, when, and who de-initializes it, when. Many HPC codes require careful control of memory allocation and deallocation that often cannot be left to a garbage collector, either because the amounts of memory involved are huge, or because the allocation method is specialized (e.g., optimizations for nonuniform memory access (NUMA) machines). Furthermore, garbage collection doesn't solve all resource management problems: files, pipes, sockets, and the like are often shared by multiple threads. Many languages, such as ANSI Common Lisp and the concurrent JVM-based language Clojure, have a special syntax for managing the scope of objects like files that need to be opened and closed, regardless of whether the operations done during the lifetime of the opened file succeed. Common Lisp has a convention to name such scope management macros "WITH-*", where one replaces the * with the kind of object being managed. Of course, a syntax for scope management assumes that one can statically determine the scope of the object, but many situations and kinds of object fit that pattern.

My current project involves a shared-memory parallel solver written in an SPMD programming model. There's a lot of shared state, and it gets initialized at different times: either before the compute threads are created, during the scope of the threads, or after the threads complete. Sometimes, threads cooperate to initialize an object, and sometimes they let just one compute thread do the work. In general, it's hard for compilers to tell when different threads might be accessing a shared object. However, my choice of the SPMD programming model restricts the implementationenough that the compiler can easily identify whether something happensbefore or after thread creation or completion. It would be nice to have a syntax or some kind of help from the language to manage the different kinds of shared object creation. The runtime could also help out by forbidding multiple initializations, or by "tagging" a shared object as accessible only by a certain thread.

A third source of errors has been imposing structure on raw pointers. For example, a memory allocation returns a chunk of contiguously stored memory, but I have to divide up that chunk in place into multiple nonoverlapping matrices. This is something that Fortran (especially Fortran 2003, if implemented correctly, *ahem*) does much better than C: Fortran always imposes array structure on chunks of memory, and if you've done the mapping right, the runtime can identify indexing errors. C only gives you raw pointers, onto which you have to impose structure. If you mess up, only something like Valgrind may be able to help. However, even Valgrind has no access to the semantic information that a particular chunk of memory is supposed to be an M by N matrix with leading dimension LDA. Having an option to do bounds checking, which does not interfere with or affect parallel performance, but which can be turned off (at build time even) to improve performance on one thread, would be a big help.

When I see new languages proposed for scientific computing, often they have lots of new features -- nested parallelism, data structures suited to scientific things like irregular discretizations, or a full library of parallel primitives.
What I don't see, however, is a new low-level language which can be used to implement those new higher-level languages, or to implement highly optimized library routines. A good low-level language is also important for bridging the gap between declarative optimization approaches (i.e., identifying features of the data or algorithm that enable optimizations without requiring them), and imperative approaches (mandating which optimization or feature to use, so that one can predict and measure performance). Predictable performance makes optimization a science rather than a collection of incantations. Furthermore, if a good low-level imperative language is used as a compilation target of a declarative language, then one can examine the generated code and figure out what the compiler is doing -- or even introspect and alter the implementation strategy at runtime.

C++: Worlds of Pain

2009-06-10T16:35:00.000-07:00

MS's efforts to implement the new C++0x standard in their compiler remind me of the world of pain that is C++ syntax. James Iry jokes that the "language is so complex that programs must be sent to thefuture to be compiled by the Skynet artificial intelligence," but of course programmers do a kind of compilation in their head too, in order to understand and work with the language.

My experience with C++ was typified by looking at Boost's graph library and wondering what the developers were smoking and whether or not I wanted to try some. I took C++ reasonably far in my professional work; I used the STL containers extensively and even dipped into some of the generic algorithms (even with Visual Studio 6's awful C++ templates support, some of them were still useful). However, there were too many ad hoc - seeming rules and conventions and ways to shoot myself in the foot, and name mangling was always an annoyance for me.

C and Fortran: the right balance

2009-04-20T00:21:00.000-07:00

I'm a fan of picking the right programming language for the job, even if it means mixing languages in a project. Sometimes this can lead to pain, especially if I'm using relatively new language features that haven't had enough code coverage to be fully debugged. However, getting the right balance between languages can make one's code concise and elegant.

This weekend, I've been working on rewriting a parallel matrix factorization. I had written most of it in (modern) Fortran, but that made it tricky to interface with C code written by collaborators and others in our research group. However, C's lack of 2-D array notation makes it awkward to write matrix operations. Thankfully the factorization algorithm splits naturally into a series of operations on submatrices. I implemented each of those "local" factorization steps in Fortran, using the ISO_C_BINDING module so that I can call them from C without needing to guess the Fortran compiler's name mangling convention, or needing to make everything a pointer (by default, Fortran calls everything by reference). C code sequences those calls to local factorization steps and does the necessary parallel synchronization. The resulting C is significantly shorter than the Fortran version I had written before, but I still get the benefits of Fortran's concise notation for matrix operations.

Dark secrets of the art: C pointers and Fortran pointers

2009-03-10T22:29:00.000-07:00

Lately, I've been implementing some new numerical algorithms for benchmarking. Normally I would write such things in C rather than Fortran, out of habit and experience. However, since this code calls Fortran routines (specifically, in the BLAS and LAPACK) a lot, I found it less trouble to write it in Fortran, than to try to manage calling C from Fortran. This is because C and Fortran have different linking conventions, and C has no standard interface for calling into Fortran. Different compilers have different standards about translating Fortran subroutine and function names into linker symbols -- sometimes they add one or more underscores, sometimes not. It's deceptively easy if you only use one compiler, such as gcc; developers that aim to build with multiple compilers often discover the differences by accident, and account for them with ad-hoc symbol translation macros (or paper them over by build systems such as GNU Autoconf, that hide the ad-hockery for you). Fortran subroutines and functions also have no idea of "pass by value," so when calling them from C, you have to keep track of which arguments are inputs and which are "outputs," and make sure to copy the output arguments in and out.

These factors have annoyed me enough in the past that for this project, I taught myself enough "modern" Fortran to get by. (I define "modern" as Fortran 90 and newer, or generally, anything with free-form input and colon array slice notation.) However, I have users who code exclusively in C. Fortran >= 2003 has what C does not, though: an ISO standard for interoperability with C. You can give a Fortran routine a C binding, which solves the linker symbol name problem. More importantly, you can get Fortran and C pointers to talk to each other.

Yes, Fortran >= 90 does actually have a pointer type! (It has dynamic memory allocation too, unlike in previous Fortran standards!) Fortran's pointers to arrays are "smarter" than C pointers in some sense: they have a "rank" and a "shape," which means (for instance) that you can compute with a submatrix of a larger matrix, whose elements aren't necessarily contiguous, as if it were just a plain old matrix. The corresponding C code would look much less like linear algebra and much more like the innards of some device driver. The price of Fortran pointers' ease of use is that a Fortran pointer contains more information than just a memory address. You can't just pass a Fortran pointer into C space and expect C to understand it, or vice versa. Fortran 2003 has an ISO_C_BINDING module whose C_F_POINTER subroutine solves this particular problem: it pulls in a C pointer from C space, and associates it to a Fortran pointer along with a rank and shape.

I'm currently using the ISO_C_BINDING module to build a C interface to my Fortran library. It's easy enough that it makes me wonder why many other languages don't come equipped with a language-level C binding!

You might be an LAPACK geek if...

2009-02-14T23:45:00.000-08:00

Here's a quiz modeled after the infamous "purity tests," except that it has nothing to do with goats and everything to do with LAPACK, the most awesome body of Fortran ever created. Score +1 for a yes answer, 0 for a no answer, and add up the points.

n00bs:

1. Have you ever called an LAPACK routine from one of your codes?

2. Do you know what the abbreviation LAPACK stands for?

3. Do you know how to pronounce LAPACK? (No, it's not "la" like "lalala"...)

4. Are you aware that using the reference BLAS implementation is generally a bad idea, and do you know how to seek out a better one?

"Smug LAPACK weenies"

5. Have you ever built the reference LAPACK library from the Fortran, not because you didn't know it was installed but because you (a) wanted the latest version, or (b) it wasn't available on the exotic prototype hardware which you have the misfortune of being asked to use?

6. Have you ever found and reported an actual bug in some LAPACK implementation? (One extra point if you went to the vendor's booth at a conference specifically to report the bug.)

7. Did you learn Fortran specifically to call BLAS or LAPACK routines, because it "seems more natural" than using the CBLAS header files?

8. Do you get the math joke on the cover of the LAPACK Users' Guide?

1337 |-|/\x0rz

9. Can you explain from memory what the first three letters of "DGEQRF" mean?

10. Have you ever contributed to LAPACK code?

11. Are you an author of an LAPACK Working Note?

12. Do you belong to a UC Berkeley or UTK "lapackers" e-mail list?

Beyond the Pale

13. If somebody asks for a banded LU factorization with partial pivoting, can you tell them the LAPACK routine name without looking?

14. Do you own and proudly wear a ScaLAPACK 1.0 T-shirt? (One extra point if you get the math joke on the front.)

15. Have you found a counterexample for convergence of an eigenvalue routine?

Scoring:
1-5: Just starting
6-10: Escape while you can
11-15: Hopeless
>15: I know exactly who you are so you'd better not skew the curve!

Modeling reality with code: Nethack

2009-01-21T12:24:00.000-08:00

One of my secret vices is Nethack, a classic dungeon-crawl game with an ASCII user interface, in the tradition of Rogue and Angband. (The name "nethack" refers to the game's development as a hacking project by people distributed over the Internet, and has nothing to do with the game's content.) Nethack is a great game, despite its ludicrously primitive graphics by modern standards, for the following reasons:

Game play is rich and complex, but intuitive. Rules make sense (especially if you catch the allusions to myth and modern storytelling) and actions have consequences. Almost any object or creature can and will interact with anything else.
Intelligent humor makes the perverse and random ways to suffer and die (almost) bearable.
The game is so challenging that even if I skim the spoilers and play with infinite lives, I can get myself into apparently inextricable situations. Yet, it's still enjoyable without cheats and spoilers.
The display is stripped-down but suggestive. For example, line of sight and memory interact intuitively -- both are combined into one map, which lets you fit more of the map on one screen (unlike, say, a first-person shooter, which keeps the map separate from the view).

Nethack also makes a good motivating example for teaching new programmers how to model reality with code. The game has some elements which are representative of real-life situations:

Agents have limited information, and may even forget things.
Things happen beyond agents' awareness.
Attempted actions may not succeed: luck (which may improve with skill) plays a role. (Nethack, like most games, models luck probabilistically.)
Actions usually change the world state irreversibly.
Object interactions depend on the properties of all the objects involved. (In terms of object-oriented programming, your object system needs mixins.)
Some items and creatures are unique and irreplaceable.

It also has properties which are not representative of reality:

Turn-based: there is no need to manage simultaneous attempts to change the world's state.
Rule-based: interactions are modeled simply, with little resort to a priori physical modeling (e.g., Newton's laws). This means interactions are not usually computationally intensive.
Very simple graphics.

These three properties make Nethack fit into a natural progression of increasingly complex situations to model. The game belongs after explaining object-oriented programming (OOP), but before explaining concurrency. The simple graphics let students concentrate on the algorithmic interactions (and save teaching assistants and graders a lot of trouble writing a GUI framework for them!). These interactions are rich enough to exercise many OOP lessons, such as member and class methods, inheritance, generic (a.k.a. virtual) methods, and object factories (for uniqueness). However, they are not generally computationally expensive, so complicated algorithms are not necessary.

The chosen programming model affects the teaching approach. For example, probabilistic success requires pseudorandom number generation, but if the programming model is functional, the novice's mental model ("rolling a die") differs from the usual stateful implementation. Also, the lessons learned at this stage may require correction when the model is generalized to handle real-time (instead of turn-based) interactions, since multiple agents will need to draw random numbers simultaneously (parallel pseudorandom number generation). In addition, the programming language's version of OOP may make it more or less difficult to explain how to implement object interactions. Some (such as Common Lisp) handle mixins trivially, whereas others (Java, C++) do not. Reliance on "design patterns" to cover the programming language's deficiencies can help students deal with languages used in industry, but may also limit their flexibility with programming languages and models. This doesn't mean a dogmatic insistence on "the one true programming language." It's better to understand the deficiencies of one's chosen language, and learn how to work around them, than not to recognize deficiencies at all.

Nethack offers another useful pedagogical feature: it's well-crafted and balanced. Playing it teaches students that making an application good comes not so much from learning new programming tricks, as from careful and laborious design and testing. "Testing" here means both correctness ("It didn't crash"), which students experience by necessity, as well as user experience testing ("It's fun to play"), which few students experience much in an undergraduate computer science curriculum.

Making LaTeX builds faster

2008-12-06T13:24:00.000-08:00

I do most of my home computing on a first-generation Asus Eee -- with the seven-inch screen and all (though it's hooked up to a big monitor and ergonomic keyboard -- I'd go nuts otherwise!). The little Eee is terrifically portable (only 2.2 lbs, and fits easily with fully open screen on an airplane tray) but is a bit underpowered -- mine has an Intel Celeron processor overclocked to 900 MHz, and presumably the memory bandwidth is much less than that of my workstation at work. I notice especially how underpowered the Eee is when I typeset documents with LaTeX. Of course, making the most of underpowered hardware is a great nerd exercise ;-) so I'm posting some tips about how to do that here.

The first trick I tried was to precompile the document header. This saved a little bit of time but not much. Plus, the binary format of the precompiled preamble is not portable between different versions of the LaTeX toolchain, even when running under the same OS and brand of CPU. I left it in just to save 0.4 or so seconds per document pass.

Precompiling the preamble didn't save much time, so it seemed then that processing the (100-page) document was taking most of the time. This made me think about the TeX build process. Prof. Knuth considered a build an interactive process: TeX runs, gives some warnings about overly long lines (with locations so you can correct them later), and on an error stops with a prompt for interactive editing. This was probably because at the time Knuth developed TeX, building the document was a long computation. One would want to interact with it in midstream to correct errors, rather than breaking off a build, editing, and starting the build over again. This is partly why it's so much trouble to write a good Makefile for TeX documents -- Knuth set the tools to give you a lot of feedback by default, and you're supposed to read the feedback to tell whether you need to let a tool make another pass over the document. On a fast computer, all the informative messages and warnings produced by the TeX toolchain zip by too fast to see. On my Eee, however, they don't -- which made me wonder about the expense of terminal output itself. TeX has an option ("-interaction batchmode") to turn off all the informative output. Using this brought the time for a complete build (pdflatex once, bibtex once, then pdflatex twice) down from 30 seconds to 6 seconds!

Another optimization is taking advantage of the \include and \includeonly comamnds before the document is finished. The \include command generates a .aux file for each included file. If you add all the included files in the \includeonly list once and do a complete build, then you'll generate .aux files for all the included files. This gives LaTeX references and page locations for all the files. Then, you can remove files from the \includeonly list if you're not working on them, and only build the parts of the document in which you're interested. This technique also preserves page numbers, equation numbers, and other reference-related things. I was able to optimize a single pdflatex step down from 3.5 seconds to 2.5 seconds with this technique.

The \include command has a side effect: it adds a page break after the included file. (Presumably this lets LaTeX compute page numbers without needing to regenerate the .aux file.) For shorter documents, I prefer to use \input to add files, because it doesn't create page breaks. Since I'm writing a longer document with chapters and LaTeX inserts a page break at the end of each chapter anyway, I can use \include for "chapter files" and within each chapter file, use \input to include section files. This website recommends solving the page break problem by using \include when editing, and \input when publishing, but for me, using \include for chapters reflects how I work on the document anyway.

LaTeX is missing some features that could make a build go a lot faster. First, building a document doesn't work like building a C library: compilation of individual files isn't independent of the whole build. I have a long document and I've taken the care to break it up into modular files; this helps with revision control, but LaTeX can't exploit this very effectively (other than with the \includeonly trick). Second, LaTeX must pass several times over the same document in order to get references right; in Knuth's time, this probably was meant to save memory, but now it would be nice to use more memory in order to save some passes.

Copying by hand

2008-10-06T12:38:00.000-07:00

A couple weeks ago, I noticed in a BoingBoing post the following quote:

Before literacy, we were mere listeners. We heard stories read to us as a group. After the printing press, we were elevating to individuals, each with our own, acknowledged perspective on what we read.

I made a comment (as "hilbertastronaut"), and I feel like expanding on
it a bit more.

The writer argues that the printing press elevated us (Westerners,
perhaps?) from mere listeners to individuals with opinions. If
anything, the opposite might be true. Back when the only way to
propagate information was to copy it by hand, it was standard practice
to add commentary to the margins of the document. This could include
clarifications or even personal reflections. One sees this in Western
monastic manuscripts as well as Chinese brush paintings (where
standard practice was to indicate receipt of the painting by marking
it with one's personal stamp, and then perhaps write one's thoughts on
the piece in the margin). In contrast, the printing press (and the
Reformation in some sense) gave people the idea of a book as an
official, received text. Written comments have a lesser status than
the printed text. For example, if one buys a used textbook at a
college bookstore, one generally hopes that it hasn't been written on
much. Before the printing press, the commentary could often be equally
or more valuable than the main text itself.

Copying other kinds of information by hand besides text also has
the same effect. For example, when J. S. Bach copied Italian
concerti, he added inner voices and ornamentation, making the concerti
into pieces universally recognized as his own compositions (and
arguably more interesting than the originals!). Bach treated copying
both as an end (to get his hands on other people's music), and as a
means (to improve his compositional skills). Even today, mathematics
teachers consider copying out and working through proofs an important
part of learning mathematics. This is because mathematics, like music
composition, is not about memorization of facts but about developing
one's creative problem-solving ability according to a combination of
rules and aesthetic principles. Copying a proof and understanding
each step is a guided re-creation of the original author's work.
Furthermore, creative mathematical thinkers in this process of
re-creation usually have new things to say, like clarifications or
generalizations, which they "write in the margins" and use in their
research -- just like Bach wrote inner voices and ornamentations "in
the margins" to produce new compositions.

My sophomore high school English teacher handed out red pens on
the first day of class, and exhorted us, even required us to
write in our books with them. At the time, it seemed ridiculous to
ruin books which could be reused for the next class. Pencil
annotations could at least be erased. Now I understand that using a
red pen elevates the status of the handwritten text, to be more
visible and more permanent even than the printed text. It makes the
reader's commentary just as valuable, if not more so, than the
original document. Whether my commentary really was more valuable
than what I read at the time is doubtful, but at least the long-term
lesson of the value of "manual" commentary stuck in my head.

ImageMagick crops your white space!

2008-08-06T09:48:00.000-07:00

ImageMagick is a fabulous command-line tool for image processing. I use it a lot for converting between different image formats, which it does with no fuss whatsoever -- as the following PNG to PDF example illustrates:


$ convert in.png out.pdf

ImageMagick can do much, much more than conversions. Today I learned the following trick from an
e-mail list discussion:


$ convert -trim img.pdf

which trims all the white space from around an image. It's a great trick for inserting Matlab plots into papers! I used to do this by hand with an image editing program like the GIMP; it's great to know that I don't have to fire up such a massive tool in order to accomplish this simple task. (The GIMP is a wonderful program, incidentally, but starting it up just to crop some white space is a task beneath its mighty powers.)

New version of ECL is out

2008-08-05T22:56:00.000-07:00

A new version of Embeddable Common Lisp (ECL) is out!!! I use ECL in my projects to support Lisp as an embedded scripting language in large C-based projects. ECL's chief developer (Juan Jose Garcia Ripoll) is amazingly responsive, which makes the library a pleasure to use. Yay ECL!!!

(Pseudo)random numbers matter

2008-06-30T09:11:00.000-07:00

The newly released LAPACK Working Note #206 gives yet another reason why generating good pseudorandom numbers matters:

In May 2007, a large high performance computer manufacturer ran a twenty-hour long High Performance Linpack benchmark. The run fails with the following output:
|| A x - b ||_oo / ( eps * ||A||_1 * N ) = 9.22e+94 ...... FAILED

What happened was that the benchmark's matrix generator uses a lame linear congruential pseudorandom number generator, which causes generated matrices to have repeated columns for certain unfortunate choices of matrix dimension. This of course makes one wonder why the generator doesn't just make a matrix which is known to be invertible, say, by generating a sufficiently nonzero diagonal matrix and hitting it on both sides with orthogonal transforms until the zeros are filled in. Regardless, the bug meant 20 hours of very expensive, intensely power-consuming supercomputer time were wasted on computing the wrong answer to a problem which at such sizes very few people need to solve. So, random numbers do matter ;-)

Contemplation leads to messes

2008-06-26T10:51:00.000-07:00

I like to make espresso using one of these gadgets. When you press out all the water, it leaves a "puck" of compressed grounds, which you can pop out straight into the garbage or compost just by pushing on the handle. I was looking at the puck this morning and saw some lovely patterns made by different layers of grounds. One thin layer in the puck appeared more compressed than the other layers, but this more compact layer wasn't a straightforward horizontal cross section -- it had a ridged topography like one sees in the sedimentary rock hills around here. It made me wonder about the bulk properties of solid particles, about which I had seen an interesting presentation a few months before, on simulating such materials.

As I was holding the puck in my hand and examining this layer from all angles, the puck suddenly broke into its constituent coffee grounds and made a huge mess all over the floor. I realized then that I had fallen into the nerd's usual trap of neglecting practical matters for the sake of contemplating lovely abstractions ;-)

The horror

2008-06-17T15:27:00.000-07:00

Add "MS Visual" in front to get the full effect.

Securing your laptop from customs officials

2008-05-15T11:34:00.000-07:00

Be sure to read Bruce Schneier's Guardian article on how to secure your laptop from customs officials. Why should you trust them not to steal your credit card numbers, just because they're wearing a badge?

Verifying identity: Existence and uniqueness

2008-05-13T12:02:00.000-07:00

Some friends of mine have been playing an online diplomacy and military simulation game, in which each player represents an independent country. One of the biggest problems in the game is "multis" -- multiple accounts created by one person. The one person uses the multiple nations to magnify his/her power in the game. The rules prohibit this practice, but it can be hard to detect. Restricting each player to use only one IP address is annoying (as it prevents multiple people from using the same computer), but a start. The underlying problem is how to establish uniqueness of identity: Are you the only person who claims to be you?

Another identity problem is that of verification: Are you the person whom you claim to be? This was a problem faced by Daniel Plainview, the protagonist of the 2008 movie There Will Be Blood. Was the man claiming to be his brother Henry actually that person? Daniel is understandably mistrustful. Ultimately the question is resolved accidentally, by the exchange of a bit of personal information -- an oblique reference to an inside joke. When verifying identity, one has to take care not to give away information when asking for it: for example, if you give a bank your social security number, the bank could then use it to masquerade as you. Some recent security research has addressed the question of how to verify identity without giving away a secret. Daniel Plainview's homegrown solution is just as effective: inside jokes rely not only on objective information, but on a particular emotional response which would be very hard for either a machine or an unrelated human to mimic. In that sense, they are even better than CAPTCHAs: They give away very little information and are very difficult for unauthorized agents to solve.

Uniqueness is an easy problem to solve in person, aside from comedy sketches involving twins. This is because human "duplicates" (genetically identical multiple births) are difficult to "make." In contrast, it's very hard to solve remotely and electronically. If you can fake a verification test, then you can break a uniqueness test. So verification and uniqueness go hand-in-hand.

Oftentimes in math, there's a fruitful tension between existence and uniqueness. When one wishes to prove that "there exists a unique object," one generally proves existence and uniqueness separately. (In this context, "uniqueness" means that if such a thing does exist, it must be unique. So uniqueness by itself doesn't necessarily imply existence, nor does existence by itself necessarily imply uniqueness.) I'm curious whether this tension could be helpful in the field of verifying identity. Answering the question "Am I Jane Doe?" is relatively easy, but the question "If I am really Jane Doe as I claim to be, then there is only one such person" doesn't even seem to be the right question to answer. Furthermore, it shouldn't be necessary to reveal your true identity in order to play an online game. Can uniqueness be solved without verification?

2008-05-07T11:07:00.000-07:00

Two new LAPACK Working Notes have been published!

"LAPACK Working Note 199: Regular Full Packed Format for Cholesky's Algorithm: Factorization, Solution and Inversion."

by Fred G. Gustavson, Jerzy Wasniewski, and Jack J. Dongarra

UT-CS-08-614, April 28, 2008.

"LAPACK Working Note 200: Some Issues in Dense Linear Algebra for Multicore and Special Purpose Architectures."

by Marc Baboulin, Jack Dongarra and Stanimire Tomov

UT-CS-08-615, May 6, 2008.

You can download them at the above link.

The Other Blog

2008-05-02T15:52:00.001-07:00

I post on religious, musical, and other matters at my other blog, which you are welcome to visit :-) I just put up a small sermon on the Ascension as the first post. Eventually I'll clean up some older essays for reposting.

Microsoft comes over to play

2008-04-28T21:53:00.000-07:00

Monday and Tuesday this week: a new (three months old!) numerical libraries group from Microsoft came over to speak with us linear algebra hackers and parallel performance tuners. Today we did most of the talking, but we learned something from them: They aren't from MS Research, and they aim to do applied research (not "blue-sky research," as the group's manager put it) with a 2-5 year horizon, and then transition successful, desired prototypes out into a production group. They've been incubating some scientific libraries for about two years, and they want to push it out into a core scientific library (sparse and dense linear algebra for now). Target hardware is single-node multicore -- no network stuff -- and they are especially interested in higher-level interface design for languages like C++, C#, and IronPython, built on both native and managed code. ("Managed code" means heavyweight runtimes like the JVM and .NET -- .NET is a big thing for them in improving programmer productivity, and these runtimes have a growing ecosystem of friendly higher-level languages.) Their group is pretty small now, but they are actively hiring (in case any of you are looking for a job in Redmond-world), and they have some bright folks on their team.

One of our biggest questions was, and probably still is, "why?" -- why wouldn't third-party applications suffice? Then again, one could ask the same of a company like Intel -- why do they need a large in-house group of HPC hackers? However, there's a difference: MS doesn't have the personpower or expertise to contribute as much to, say, ScaLAPACK development as Intel has, nor do they intend to grow their group that much. This team seems to be mainly focused on interface design: how to wrap efficient but hard-to-use scientific codes so that coders in the MS world can exploit them. In that context, my advisor showed one of his favorite slides: three different interfaces to a linear solver (solve Ax = b for the vector x, where b is a known vector and A is a matrix). One is Matlab's: "A \ b". The other two are two possible invocations of ScaLAPACK's parallel linear solver. The second of these has nearly twenty obscurely named arguments relating to the data distribution (it's a parallel distributed-memory routine) and to iterative refinement -- clearly not what you want to give to a 22-year-old n00b fresh out of an undergrad CS curriculum who knows barely enough math to balance a checkbook. Ultimately, MS has to design programmer interfaces for these people, as well as for gurus -- which is something that the gurus often forget.

Another reason perhaps for the "why" is that high-performance, mathematical calculations are a compelling reason to buy new computing hardware and software. There are interesting performance-bound consumer applications being developed, most of which have some kind of math kernel(s) at their core. MS presumably wants to get in on that action, especially as it is starting to lose out on the shrink-wrapped OS-and-Office software market as well as the Web 2.0 / search market.

It's interesting to watch a large, bureaucratic company like Microsoft struggling to evolve. IBM managed this sort of transition pretty well, from what I understand. They still sell mainframes (and supercomputers!), but they also sell services, and maintain a huge and successful research effort on many fronts. MS Research is also a powerhouse, but somehow we don't see the research transitioning into products, or even driving the brand, as it does in IBM's case (think about the Kasparov-defeating chess computer Deep Blue, for example). Maybe it does drive the products, but somehow the marketing has failed to convey this. I kind of feel for them, just like the "Mac guy" feels for the "PC guy" in Apple's ad series: They have to struggle not only to command a new market, but also to reinvent their image and command a brand.

Engineering applications of general relativity?

2008-04-17T17:05:00.000-07:00

The first engineering application of general relativity: GPS. Apparently, global positioning requires accurate time computations, and once you can measure time to sufficient accuracy, you need to account for time dilation due to gravity.

(Originally posted 16 April 2008.)

Preconditioners as eigenvalue clusterers

2008-04-17T17:04:00.001-07:00

At the Copper Mountain Iterative Methods conference this year, I heard a really good explanation of how preconditioners work, from a PhD student at the University of Manchester. (Thanks Richard!) He explained to me that one can think of a Krylov subspace method as polynomial interpolation of the spectrum of the matrix. Each time you do a matrix-vector multiply, you increase the polynomial's degree by one. (This gets more clear if you've seen the proof that conjugate gradients is optimal in the norm induced by the matrix.)

If the matrix's eigenvalues are evenly distributed, it will get harder and harder to interpolate the spectrum, because of the Gibbs phenomenon. In contrast, if one eigenvalue is separated from the others, it's easy to interpolate that part of the spectrum accurately and "pick off" the separated eigenvalue. This is called "deflation." After this point, the Krylov method converges pretty much as if the separated eigenvalue wasn't there. This makes the goal of a good preconditioner clear: It should separate and cluster the eigenvalues (away from the origin), so that the Krylov method can pick off the clusters.

If I may also engage in some speculation, this perhaps also explains one reason why block preconditioners are popular in multiphysics solvers: they group together eigenmodes that are on similar scales, and separate unrelated eigenmodes. Of course, block preconditioning is the mathematical equivalent of encapsulation in the software engineering world: it lets you solve one problem at a time and then stitch together a combined solution out of the components. Mushing together all the subproblems into a single big problem loses the structure, whereas sparse linear algebra is all about exploiting structure.

(Originally posted 16 April 2008.)

Alchemy: pride and wonder

2008-04-17T16:56:00.000-07:00

The website of NOVA, a PBS science program, has a neat article which decodes a page from Isaac Newton's alchemy notebooks, and discusses Newton's interest in alchemy in its historical context. Alchemy is a fascinating subject because it shows the tight links between science, philosophy, and religion at the very beginning of what we consider "modern" science, and also because it illustrates the tension between rationalization (wanting to understand or control the universe by discovering or imposing universal laws that govern it) and wonder (non-rational awe of nature). Newton himself shows both tendencies. The article mentions how he secretly called himself "Jehovah the Holy One," and William Blake depicts both Newton and God bearing the compass to measure and bound Creation. Yet, Newton saw his discoveries as if he were just a child picking up a pretty shell on the beach and barely intuiting the existence of countless more in the ocean before him.

Alchemy's all-encompassing vision arguably failed to persist into its successor sciences. By 1800 or so, Friedrich von Hardenberg (a.k.a. Novalis, a geologist and poet) was already condemning the "Scheidekunst" of the sciences: how they were dissected cadaver-like into subfields, without regard for the living interactions between fields. In some sense, modern physics with quantum mechanics inherited the idea of reaching for a universal theory: "grand unified theory" and "quantum gravity" reveal this desire to explain all interactions at both tiny and grand scales. They also attract their share of superstition and quackery (e.g., the use of "quantum tangling between doctor and patient" to explain how homeopathic medicine supposedly works), just as alchemy did in its time. Yet Novalis' and Newton's pursuit of universal natural philosophy as a spiritual activity shows the importance of non-rational awe, wonder, and curiosity in the sciences. Even such an avowed atheist as Carl Sagan could wax eloquent at the "billions and billions" of stars and speak tenderly of our planet as a "pale blue dot." (I've never heard an atheist write more reverently than he!)

(Originally posted 31March 2008.)

(Re)new(ed) blog

2008-04-17T16:52:00.000-07:00

Welcome to my (re)new(ed) blog!

I deleted my old blog in order to start fresh. This new version will only have "nerdy" posts -- i.e., about the sciences or related recreational interests. I will spawn off different blog(s) for other topics, in particular, about music, religion, and politics.