Using a table of logarithms

My favorite quote from Richard Feynman is his remark that “nearly everything is really interesting if you go into it deeply enough.” This post will look at something that seems utterly trivial—looking up numbers in a table—and show that there’s much more to it when you dig a little deeper.

More than just looking up numbers

Before calculators were common, function values would be looked up in a table. For example, here is a piece of a table of logarithms from Abramowitz and Stegun, affectionately known as A&S.

But you wouldn’t just “look up” logarithm values. If you needed to know the value of a logarithm at a point where it is explicitly tabulated, then yes, you’d simply look it up. If you wanted to know the log of 1.754, then there it is in the table. But what if, for example, you wanted to know the log of 1.7543?

Notice that function values are given to 15 significant figures but input values are only given to four significant figures. If you wanted 15 sig figs in your output, presumably you’d want to specify your input to 15 sig figs as well. Or maybe you only needed 10 figures of precision, in which case you could ignore the rightmost column of decimal places in the table, but you still can’t directly specify input values to 10 figures.

Lagrange interpolation

If you go to the bottom of the column of A&S in the image above, you see this:

What’s the meaning of the mysterious square bracket expression? It’s telling you that for the input values in the range of this column, i.e. between 1.750 and 1.800, the error using linear interpolation will be less than 4 × 10−8, and that if you want full precision, i.e. 15 sig figs, then you’ll need to use Lagrange interpolation with 5 points.

So going back to the example of wanting to know the value of log(1,7543), we could calculate it using

0.7 × log(1.754) + 0.3 × log(1.755)

and expect the error to be less than 4 × 10−8.

We can confirm this with a little Python code.

>>> from math import log
>>> exact = log(1.7543)
>>> approx = 0.7*log(1.754) + 0.3*log(1.755)
>>> exact - approx

Python uses double precision arithmetic, which is accurate to between 15 and 16 figures—more on that here—and so the function calls above are essentially the same as the tabulated values.

Now suppose we want the value of x = 1.75430123456789. The hint in square brackets says we should use Lagrange interpolation at five points, centered at the nearest tabulated value to x. That is, we’ll use the values of log at 1.752, 1.753, 1.754, 1.755, and 1.756 to compute the value of log(x).

Here’s the Lagrange interpolation formula, given in A&S as equation 25.2.15.

We illustrate this with the following Python code.

def interpolate(fs, p, h):
    s = (p**2 - 1)*p*(p-2)*fs[0]/24
    s -= (p - 1)*p*(p**2 - 4)*fs[1]/6
    s += (p**2 - 1)*(p**2 - 4)*fs[2]/4
    s -= (p + 1)*p*(p**2 - 4)*fs[3]/6
    s += (p**2 - 1)*p*(p + 2)*fs[4]/24
    return s

xs = np.linspace(1.752, 1.756, 5)
fs = np.log(xs)
h = 0.001
x = 1.75430123456789
p = (x - 1.754)/h

print(interpolate(fs, p, h))

This prints


confirming that the interpolated value is indeed accurate to 15 figures.

Lagrange interpolation takes a lot of work to carry out by hand, and so sometimes you might use other techniques, such as transforming your calculation into one for which a Taylor series approximation converges quickly. In any case, sophisticated use of numerical tables was not simply a matter of looking things up.

Contemporary applications

A book of numerical tables enables you to do calculations without a computer. More than that, understanding how to do calculations without a computer helps you program calculations with a computer. Computers have to evaluate functions somehow, and one way is interpolating tabulated values.

For example, you could think of a digital image as a numerical table, the values of some ideal analog image sampled at discrete points. The screenshots above are interpolated: the HTML specifies the width to be less than that of the original screenshots,. You’re not seeing the original image; you’re seeing a new image that your computer has created for you using interpolation.

Interpolation is a kind of compression. A&S would be 100 billion times larger if it tabulated functions at 15 figure inputs. Instead, it tabulated functions for 4 figure inputs and gives you a recipe (Lagrange interpolation) for evaluating the functions at 15 figure inputs if you desire. This is a very common pattern. An SVG image, for example, does not tell you pixel values, but gives you equations for calculating pixel values at whatever scale is needed.

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Duct tape value creation

Excerpt from from John Carmack’s review of the book Bullshit Jobs.

He talks about how software developers bemoan duct taping systems together, and would rather work on core technologies. He thinks it is some tragic failure, that if only wise system design was employed, you wouldn’t be doing all the duct taping.


Every expansion in capabilities opens up the opportunity to duct tape it to new areas, and this is where a lot of value creation happens. Eventually, when a sufficient amount of duct tape is found in an area, it is an opportunity for systemic redesigns, but you don’t wait for that before grabbing newly visible low hanging fruit!

The realistic alternative to duct tape and other aesthetically disappointing code is often no code.

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One-liner to troubleshoot LaTeX references

In LaTeX, sections are labeled with commands like \label{foo} and referenced like \ref{foo}. Referring to sections by labels rather than hard-coded numbers allows references to automatically update when sections are inserted, deleted, or rearranged.

For every reference there ought to be a label. A label without a corresponding reference is fine, though it might be a mistake. If you have a reference with no corresponding label, and one label without a reference, there’s a good chance the reference is a typo variation on the unreferenced label.

We’ll build up a one-liner for comparing labels and references. We’ll use grep to find patterns that look like labels by searching for label{ followed by any string of letters up to but not including a closing brace. We don’t want the label{ part, just what follows it, so we’ll use look-behind syntax, to exclude it from the match.

Here’s our regular expression:


We’re using Perl-style look-behind syntax, so we’ll need to give grep the -P option. Also, we only want the match itself, not matching lines, so we’ll also using the -o option. This will print all the labels:

    grep -oP '(?<=label{)[^}]+' foo.tex

The regex for finding references is the same with label replaced with ref.

To compare the list of labels and the list of references, we’ll use the comm command. For more on comm, see Set theory at the command line.

We could save the labels to a file, save the references to a file, and run comm on the two files. But we’re more interested in the differences between the two lists than the two lists, so we could pass both as streams to comm using the <(...) syntax. Finally, comm assumes its inputs are sorted so we pipe the output of both grep commands to sort.

Here’s our one-liner

    comm -12 <(grep -oP '(?<=label{)[^}]+' foo.tex | sort) 
             <(grep -oP '(?<=ref{)[^}]+' foo.tex | sort)

This will produce three sections of output: labels which are not references, references which not labels, and labels that are also references.

If you just want to see references that don’t refer to a label, give comm the option -13. This suppresses the first and third sections of output, leaving only the second section, references that are not labels.

You can also add a -u option (u for unique) to the calls to sort to suppress multiple instances of the same label or same reference.

Choosing a Computer Language for a Project

Julia. Scala. Lua. TypeScript. Haskell. Go. Dart. Various computer languages new and old are sometimes proposed as better alternatives to mainstream languages. But compared to mainstream choices like Python, C, C++ and Java (cf. Tiobe Index)—are they worth using?

Certainly it depends a lot on the planned use: is it a one-off small project, or a large industrial-scale software application?

Yet even a one-off project can quickly grow to production-scale, with accompanying growing pains. Startups sometimes face a growth crisis when the nascent code base becomes unwieldy and must be refactored or fully rewritten (or you could do what Facebook/Meta did and just write a new compiler to make your existing code base run better).

The scope of different types of software projects and their requirements is so incredibly diverse that any single viewpoint from experience runs a risk of being myopic and thus inaccurate for other kinds of projects. With this caveat, I’ll share some of my own experience from observing projects for many dozens of production-scale software applications written for leadership-scale high performance computing systems. These are generally on a scale of 20,000 to 500,000 lines of code and often require support of mathematical and scientific libraries and middleware for build support, parallelism, visualization, I/O, data management and machine learning.

Here are some of the main issues regarding choice of programming languages and compilers for these codes:

1. Language and compiler sustainability. While the lifetime of computing systems is measured in years, the lifetime of an application code base can sometimes be measured in decades. Is the language it is written in likely to survive and be well-supported long into the future? For example, Fortran, though still used and frequently supported, is is a less common language thus requiring special effort from vendors, with fewer developer resources than more popular languages. Is there a diversity of multiple compilers from different providers to mitigate risk? A single provider means a single point of failure, a high risk; what happens if the supplier loses funding? Are the language and compilers likely to be adaptable for future computer hardware trends (though sometimes this is hard to predict)? Is there a large customer base to help ensure future support? Similarly, is there an adequate pool of available programmers deeply skilled in the language? Does the language have a well-featured standard library ecosystem and good support for third-party libraries and frameworks? Is there good tool support (debuggers, profilers, build tools)?

2. Related to this is the question of language governance. How are decisions about future updates to the language made? Is there broad participation from the user community and responsiveness to their needs? I’ve known members of the C++ language committee; from my limited experience they seem very reasonable and thoughtful about future directions of the language. On the other hand, some standards have introduced features that scarcely anyone ever uses—a waste of time and more clutter for the standard.

3. Productivity. It is said that programmer productivity is limited by the ability of a few lines of code to express high level abstractions that can do a lot with minimal syntax. Does the language permit this? Does the language standard make sense (coherent, cohesive) and follow the principle of least surprise? At the same time, the language should not engulf what might better be handled modularly by a library. For example, a matrix-matrix product that is bound up with the language might be highly productive for simple cases but have difficulty supporting the many variants of matrix-matrix product provided for example by the NVIDIA CUTLASS library. Also, in-language support for CUDA GPU operations, for example, would make it hard for the language not to lag behind in support of the frequent new releases of CUDA.

4. Strategic advantage. The 10X improvement rule states that an innovation is only worth adopting if it offers 10X improvement compared to existing practice according to some metric . If switching to a given new language doesn’t bring significant improvement, it may not be worth doing. This is particularly true if there is an existing code base of some size. A related question is whether the new language offers an incremental transition path for an existing code to the new language (in many cases this is difficult or impossible).

5. Performance (execution speed). Does the language allow one to get down to bare-metal performance rather than going through costly abstractions or an interpreter layer? Are the features of the underlying hardware exposed for the user to access? Is performance predictable? Can one get a sense of the performance of each line of code just by inspection, or is this occluded by abstractions or a complex compilation process? Is the use of just-in-time compilation or garbage collection unpredictable, which could be a problem for parallel computing wherein unexpected “hangs” can be caused by one process unexpectedly performing one of these operations? Do the compiler developers provide good support for effective and accurate code optimization options? Have results from standardized non-cherry-picked benchmarks been published (kernel benchmarks, proxy apps, full applications)?

Early adopters provide a vibrant “early alert” system for new language and tool developments that are useful for small projects and may be broadly impactful. Python was recognized early in the scientific computing community for its potential complementary use with standard languages for large scientific computations. When it comes to planning large-scale software projects, however, a range of factors based on project requirements must be considered to ensure highest likelihood of success.


More is less

When I first started using Unix, I used a program called “more” to read files. The name makes sense because each time you press the space bar, more will show you more of your file, one screen at a time.

Now everyone uses less, and more is all but forgotten.

Daniel Halbert wrote more in 1978. Mark Nudelman a similar program with more functionality in 1984 which he named less. The name was a pun on the aphorism “less is more” [1]. Soon less completely replaced more.

I’m curious why I ever used more, since less had taken over before I touched Unix. One possibility is that someone who was accustomed to more showed me that command. Another possibility is that I learned it from reading The Unix Programming Environment which came out in November 1983. It includes more but not less.

My laptop contains executables for more and less in /usr/bin. The command

    diff less more

returns nothing, indicating that the binaries are identical: less literally is more.

My desktop has distinct binaries for less and more. The more binary is much smaller, and so I assume it is limited to the original functionality of more, more or less.

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[1] I don’t know who coined the phrase “less is more,” but it is associated with architect Ludwig Mies van der Rohe (1886–1969) who often quoted it. He did not apply the principle to is own name, however. He was born Ludwig Mies and later appended van der Rohe.

Distance from a point to a line

Eric Lengyel’s new book Projective Geometric Algebra Illuminated arrived yesterday and I’m enjoying reading it. Imagine if someone started with ideas like dot products, cross products, and determinants that you might see in your first year of college, then thought deeply about those things for years. That’s kinda what the book is.

Early in the book is the example of finding the distance from a point q to a line of the form p + tv.

If you define u = q − p then a straightforward derivation shows that the distance d from q to the line is given by

d = \sqrt{{\bold u}^2 - \frac{({\bold u}\cdot {\bold v})^2}{{\bold v}^2}}

But as the author explains, it is better to calculate d by

d = \sqrt{\frac{({\bold u}\times {\bold v})^2}{{\bold v}^2}}

Why is that? The two expressions are algebraically equal, but the latter is better suited for numerical calculation.

The cardinal rule of numerical calculation is to avoid subtracting nearly equal floating point numbers. If two numbers agree to b bits, you may lose up to b bits of significance when computing their difference.

If u and v are vectors with large magnitude, but q is close to the line, then the first equation subtracts two large, nearly equal numbers under the square root.

The second equation involves subtraction too, but it’s less obvious. This is a common theme in numerical computing. Imagine this dialog.

[Student produces first equation.]

Mentor: Avoid subtracting nearly equal numbers.

[Student produces section equation.]

Student: OK, did it.

Mentor: That’s much better, though it could still have problems.

Where is there a subtraction in the second equation? We started with a subtraction in defining u. More subtly, the definition of cross product involves subtractions. But these subtractions involve smaller numbers than the first formula, because the first formula subtracts squared values. Eric Lengyel points this out in his book.

None of this may matter in practice, until it does matter, which is a common pattern in numerical computing. You implement something like the first formula, something that can be derived directly. You implicitly have in mind vectors whose magnitude is comparable to d and this guides your choice of unit tests, which all pass.

Some time goes by and a colleague tells you your code is failing. Impossible! You checked your derivation by hand and in Mathematica. Your unit tests all pass. Must be your colleague’s fault. But it’s not. Your code would be correct in infinite precision, but in an actual computer it fails on inputs that violate your implicit assumptions.

This can be frustrating, but it can also be fun. Implementing equations from a freshman textbook accurately, efficiently, and robustly is not a freshman-level exercise.

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Experiences with Thread Programming in Microsoft Windows

Lately I’ve been helping a colleague to add worker threads to his GUI-based Windows application.

Thread programming can be tricky. Here are a few things I’ve learned along the way.

Performance. This app does compute-intensive work. It is helpful to offload this very compute-heavy work to a worker thread. Doing this frees the main thread to service GUI requests better.

Thread libraries. Windows has multiple thread libraries, for example Microsoft Foundation Class library threads and C++ standard library threads. It is hazardous to use different thread libraries in the same app. In the extreme case, different thread libraries, such as GOMP  vs. LOMP, used in resp. the GCC and LLVM compiler families, have different threading runtimes which keep track of threads in different ways. Mixing them in the same code can cause hazardous silent errors.

Memory fences are a thing. Different threads can run on different processor cores and hold variables in different respective L1 caches that are not flushed (this to maintain high performance). An update to a variable by one thread is not guaranteed to be visible to other threads without special measures. For example, one could safely transfer information using ::PostMessage coupled with a handler function on the receiver thread. Or one could send a signal using an MFC CEvent on one thread and read its Lock on the other. Also, a thread launch implicitly does a memory fence, so that, at least then, the new thread is guaranteed to correctly see the state of all memory locations.

GUI access should be done from the master thread only, not a worker thread. Doing so can result in deadlock. A worker thread can instead ::PostMessage to ask the master thread to do a GUI action.

Thread launch. By default AfxBeginThread returns a thread handle which MFC takes care of deleting when no longer needed. If you want to manage the life cycle of the handle yourself, you can do something like:

myWorkerThreadHandle = AfxBeginThread(myFunc, myParams,
myWorkerThreadHandle->m_bAutoDelete = false;

Joint use of a shared library like the DAO database library has hazards. One should beware of using the library to allocate something in one thread and deallocating in another, as this will likely allocate in a thread-local heap or stack instead of a shared thread-safe heap, this resulting in a crash.

Initialization. One should call CoInitializeEx(NULL, COINIT_APARTMENTTHREADED) and AfxDaoInit() (if using DAO) at thread initialization on both master and worker threads, and correspondingly CoUninitialize() and AfxDaoTerm() at completion of the thread.

Monitoring of thread state can be done with
WaitForSingleObject(myWorkerThreadHandle->m_hThread, 0) to determine if the thread has completed or WaitForSingleObject(myWorkerThreadHandle->m_hThread, INFINITE) for a blocking wait until completion.

Race conditions are always a risk but can be avoided by careful reasoning about execution. Someone once said up to 90% of code errors can be found by desk checking [1]. Race conditions are notoriously hard to debug, partly because they can occur nondeterministically. There are tools for trying to find race condition errors, though I’ve never tried them.

So far I find no rigorous specification of the MFC threading model online that touches on all these concerns. Hopefully this post is useful to someone else working through these issues.


[1] Dasso, Aristides., Funes, Ana. Verification, Validation and Testing in Software Engineering. United Kingdom: Idea Group Pub., 2007, p. 163.

Archiving data on paper

This is a guest post by Ondřej Čertík. Ondřej formerly worked at Los Alamos National Labs and now works for GSI Technologies. He is known in the Python community for starting the SymPy project and in the Fortran community for starting LFortran. — John


Ondřej Čertík

I finally got to experiment a bit with archiving data on a regular A4 or US Letter page using a regular printer and a phone camera to read it. It’s been bothering me for about 10 years. What is the maximum data size that we can store on the paper and reliably retrieve?

My setup

It seems it is limited by my camera, not my printer. This image stores 30KB of data. I printed it, took a photo with my iPhone, and then decoded and unpacked it using tar and bzip2. It correctly unpacks into 360KB of C++ files, 6305 lines.

I am using the Twibright Optar software.

It uses Golay codes (used by Voyager) that can fix 3 bad bits in each 24-bit code word (which contains 12-bit payload, and 12-bit parity bits). If there are 4 bad bits, the errors are detected, but cannot be corrected. In my experiment, there were 6 codewords which had 3 bad bits, and no codewords with more bad bits, so there was no data loss. It seems most of the bad bits were in the area where my phone cast a shadow on the paper, so possibly retaking the picture in broad daylight might help.

Bad bits

Here are the stats from the optar code:

7305 bits bad from 483840, bit error rate 1.5098%.

49.1855% black dirt, 50.8145% white dirt and 0 (0%) irreparable. Golay stats
0 bad bits      13164
1 bad bit       6693
2 bad bits      297
3 bad bits      6
4 bad bits      0
total codewords 20160

The original setup can store 200KB of data. I tried it, it seems to print fine. But it’s really tiny, and my iPhone camera can’t read it well enough, so nothing is recovered. So I used larger pixels. The 30KB is what I was able to store and retrieve and from the stats above, it seems this is the limit.

Other possibilities

Competing products, such as this one only store 3-4KB/page, so my experiment above is 10x that.

One idea is to use a different error correction scheme. The Golay above only uses 50% to store data. If we could use 75% to store data, that gives us 50% more capacity.

Another idea to improve is to use colors, with 8 colors we get 3x larger capacity, with 16 colors we get 4x more. That would give us around 100KB/page with colors. Can we do better?

Comparison with other storage techniques

I think the closest to compare is floppy disks. The 5¼-inch floppy disk that I used as a kid could store 180 KB single side, 360KB both sides. The 3½-inch floppy disk could store 720 KB single side or 1.44MB both sides. We can also print on both sides of the paper, so let’s just compare single side for both:

  • Optar original (requires a good scanner): 200 KB
  • My experiment above (iPhone): 30 KB
  • Estimate with 8 colors: 120 KB
  • 5¼-inch floppy disk: 180 KB
  • 3½-inch floppy disk: 720 KB

It seems that the 5¼-inch floppy disk is a good target.


One application is to store this at the end of a book, so that you don’t need to distribute CDs or floppy disks (as used to be the habit), but you just put 10-20 pages to the appendix, this should be possible to decode even 100 years from now quite reliably.

Another application is just archiving any projects that I care about. I still have some floppy disks in my parents’ attic, and I am quite sure they are completely unreadable by now. While I also have some printouts on paper from the same era 30 years ago, and they are perfectly readable.

I think the requirement to use a regular iPhone is good (mine is a few years old, perhaps the newest one can do better?). If we allow scanners, then of course we can do better, but not many people have a high quality scanner at home, and there is no limit to it: GitHub’s Arctic Vault uses microfilm and high quality scanner. I want something that can be put into a book, or article on paper, something that anyone can decode with any phone, and that doesn’t require any special treatment to store.

What’s the Best Code Editor?

Emacs, vi, TextEdit, nano, Sublime, Notepad, Wordpad, Visual Studio, Eclipse, etc., etc.—everyone’s got a favorite.

I used Visual Studio previously and liked the integrated debugger. Recently I started using VS again and found the code editing windows rather cluttered. Thankfully you can tone this down, if you can locate the right options.

Eclipse for Java has instantaneous checking for syntax errors. I have mixed feelings on this. Perhaps you could type a little more code before getting a glaring error message?

Concerning IDEs (integrated development environments) like this—I’ve met people who think that a full GUI-based IDE is the only way to go. Maybe so. However , there’s another view.

You’d think if anyone would know how to write code quickly, accurately and effectively, it would be world-class competitive programmers. They’re the best, right?

One of the very top people is Gennady Korotkevich. He’s won many international competitions.

What does he use? Far Manager, a text-based user interface tool with a mere two panels and command prompt. It’s based on 1980s pre-GUI file manager methodologies that were implemented under DOS.

It reminds me of a conversation I had with our admin when I was in grad school. I asked, “Why do you use vi instead of MS Word for editing documents?” Answer: “I like vi because it’s faster—your fingers never need to leave the keyboard.”

Admittedly, not all developer workflows would necessarily find this approach optimal. But still it makes you think. Sometimes the conventional answer is not the best one.

Do you have a favorite code editor? Please let us know in the comments.

Natural one-liners

I learned to use Unix in college—this was before Linux—but it felt a little mysterious. Clearly it was developed by really smart people, but what were the problems that motivated their design choices?

Some of these are widely repeated. For example, commands have terse names because you may have to transmit commands over a glacial 300 baud network connection.

OK, but why are there so many tools for munging text files, for example? That’s great if your job requires munging text files, but what about everything else. What I didn’t realize at the time was that nearly everything involves munging text files, or can be turned into a problem involving munging text files.

Working with data at the command line

There’s an old joke that Unix is user friendly, it’s just picky about who its friends are. I’d rephrase to say Unix makes more sense when you’re doing the kind of work the Unix developers were doing.

I was writing programs when I learned Unix, so some things about Unix made sense at the time. But I didn’t see the motivation for many of the standard command line tools until I started analyzing datasets years later. I thought awk was cool—it was the first scripting language I encountered—but it wasn’t until years later that I realized awk is essentially a command line spreadsheet. It was written for manipulating tabular data stored in text files.

Mythological scripts

Unix one-liners are impressive, but they can seem like a rabbit out of a hat. How would anyone think to do that?

When you develop your own one liners, one piece at a time, they seem much more natural. You get a feel for how the impressive one-liners you see on display were developed incrementally. They almost certainly did not pop into the world fully formed like Athena springing from the head of Zeus.

Example: Voter registration data

Here’s an example. I was looking at Washington state voter registration data. There’s a file 20240201_VRDB_Extract.txt. What’s in there?

The first line of a data file often contains column headers. Looking at just the first few lines of a file is a perennial task, so there’s a tool for that: head. By default it shows the first 10 lines of a file. We just want to see the first line, and there’s an option for that: -n 1.

> head -n 1 20240201_VRDB_Extract.txt


Inserting line breaks

OK, those look like column headers, but they’re hard to read. It would be nice if we could replace all the pipe characters used as field separators with line breaks. There’s a command for that too. The sed tool let’s you, among other things, replace one string with another. The tiny sed program


does just what we want. It may look cryptic, but it’s very straight forward. The “s” stands for substitute. The program s/foo/bar/ substitutes the first instance of foo with bar. If you want to replace all instances, you tack on a “g” on the end for “global.”

Eliminating temporary files

We could save our list of column headings to a file, and then run sed on the output, but that creates an unnecessary temporary file. If you do this very much, you get a lot of temporary files cluttering your working area, say with names like temp1 and temp2. Then after a while you start to forget what you named each intermediary file.

It would be nice if you could connect your processing steps together without having to create intermediary files. And that’s just what pipes do. So instead of saving our list of column headers to a file, we pipe it through to sed.

> head -n 1 20240201_VRDB_Extract.txt | sed 's/|/\n/g'


Scrolling and searching

This is much better. But it produces more output than you may be able to see in your terminal. You could see the list, one terminal window at a time, by piping the output to less.

> head -n 1 20240201_VRDB_Extract.txt | sed 's/|/\n/g' | less

This file only has 33 columns, but it’s not uncommon for a data file to have hundreds of columns. Suppose there were more columns than you wanted to scan through, and you wanted to know whether one of the columns contained a zip code. You could do that by piping the output through grep to look for “zip.”

> head -n 1 20240201_VRDB_Extract.txt | sed 's/|/\n/g' | grep -i zip

There are no column headings containing “zip”, but there are a couple containing “Zip.” Adding -i (for case insensitive) finds the zip code columns.


Our modest little one-liner now has three segments separated by pipes. It might look impressive to someone new to working this way, but it’s really just stringing common commands together in a common way.

A famous one-liner

When you see a more complicated one-liner like

tr -cs A-Za-z '
' |
tr A-Z a-z |
sort |
uniq -c |
sort -rn |
sed ${1}q

you can imagine how it grew incrementally. Incidentally, the one-liner above is somewhat famous. You can find the story behind it here.

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