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Counting the reads, writes and wrapped calls a function performs at several input sizes shows how its work grows as the input gets larger. It does not show how long the function takes to run. That distinction is the core of countfn, a Python and JavaScript package that Seth Wheeler, a software engineer and graduate student, described in an article published September 27, 2026. The method answers a scaling question: if the input doubles, does the work double, grow by a factor of four, or grow more slowly than that?
What countfn measures
countfn runs a function over a ladder of input sizes and counts selected operations at each rung. It then fits those counts to a growth class. The package counts three channels:
- Reads: subscripting or iterating over the wrapped input sequence.
- Writes: assignments into the wrapped sequence.
- Calls: invocations of a callable that has been explicitly wrapped.
Calls are counted only when the author wraps a callable, so an unwrapped helper contributes nothing to the total. Comparisons are handled the same way. Wheeler notes that comparison protocol events differ between Python and JavaScript, so countfn does not try to observe them directly. Instead, the user wraps the comparator, and each comparison becomes a counted call in both languages. The three channels were chosen so that they mean the same thing in each implementation.
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The API takes four inputs: the function under test, a list of input sizes, a builder that produces an input of a given size, and a trial count. A typical run follows this sequence:
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- Write a builder that returns a fresh input of size n, seeded so the run is repeatable.
- Wrap the comparator, if the function uses one, so that comparisons are counted as calls.
- Pass the function, the size ladder, the builder and the trial count to countfn.
- Read the report. For each channel it prints the count at each rung and the growth class the fit selects, or
UNDETERMINEDif it cannot choose one.
In the article’s binary-search example, the report shows reads: log n. Writes are reported as undetermined because the function performed no writes, so there was nothing to fit.
A worked example: insertion sort
Wheeler reports the same insertion-sort run in both languages with seed 17 and input size 64. The figures below come from his article and are examples he chose to show, not independently reproduced benchmarks.
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| Measure | Reported value | Qualification |
|---|---|---|
| Reads at size 64, seed 17 | 3,812 | Identical in the Python and JavaScript implementations, per the author. |
| Writes at size 64, seed 17 | 1,848 | Identical in both implementations, per the author. |
| Comparison fit (wrapped comparator) | 0.2559 ± 0.003006 · n² | Wheeler describes this as the textbook n²/4 relation. The ± term is the author’s stated uncertainty for this fit. |
The comparison fit is a useful illustration of what the tool gives back. It states a coefficient and a growth order, not a runtime. Multiplying it out at a given n yields a count of comparisons, and nothing more.
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countfn can return UNDETERMINED instead of a growth class. Wheeler presents this as deliberate. A refusal means the counts do not justify one class under the tool’s criteria. It is not a failed measurement. There are three situations that produce it.
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Exact counts with zero error
When a count depends only on input size, every rung has a standard error of zero. The fitting step therefore has no measured noise against which to judge whether two candidate classes are separated. The report then prints UNDETERMINED [exact] and still shows the full count ladder, so the numbers remain usable even though the label is withheld.
A user can declare a tolerance to force a fit. The report then has to make clear that the error bars were declared rather than measured. Declared tolerance should not be read as evidence of run-to-run noise.
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Counts that have not settled
Some algorithms need a longer ladder before their normalized counts stop moving. Wheeler’s merge-sort example shows reads divided by n log n rising from 2.755 to 2.861 across a ladder whose largest input is 32 times its smallest. The count is still drifting, so countfn reports that rather than assigning the nearest class.
Two classes that a finite ladder cannot separate
If two candidate classes both settle but remain hard to tell apart, the tool declines to break the tie. The article uses n and n log n to show the problem. Over one ladder those two curves differ by a factor of 1.3, and at the top rung of 2048 they differ by a factor of 1.8. Whether a pair of classes is separable depends on the range of sizes tested, so a longer or wider ladder can resolve a case that a short one cannot.
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Counting versus timing
Wheeler’s central claim is a division of labor. In his words: “It answers how the work grows, which is the question a timing answers badly; it does not answer how long the work takes, which is the question a timing answers well. Use both.” The table sets out where each approach is strong.
| Question | Operation counting (countfn) | Elapsed-time measurement |
|---|---|---|
| What it observes | Volume of selected operations (reads, writes, wrapped calls) | Actual wall-clock duration |
| Sensitivity to machine load | Counts are presented by the author as stable across runs | Timings vary with load and hardware, which can blur growth patterns |
| Typical blind spot | Work outside the wrapped objects is not counted; cache behavior is invisible | Can obscure how the work scales when noise is large relative to the signal |
| Question it answers well | How the work grows with input size | How long the work takes |
Two algorithms with the same read count can still differ in elapsed time because of cache behavior. When runtime or cache effects matter for the decision, Wheeler recommends measuring both.
Limits to keep in view
- The wrapper sees only what it wraps. Wheeler calls this the sharpest limit: “The instrument only sees the object it wrapped.” An out-of-place algorithm that builds and works on a separate structure can do substantial work that is never counted. The optional
probeparameter can instrument those working structures, but only if the user passes them in. - Counts are not runtime. A count tells you how much selected work occurs, not how long it takes on a given machine.
- Declared tolerances are not measurements. Where counts are exact, a tolerance has to be stated by the user and reported as such.
- A finite ladder limits separability. The n versus n log n example shows that the tested range decides whether two growth classes can be told apart.
The verification behind these examples is the author’s own. Wheeler’s article reports that the test suite caught 15 applied source mutations. No independent reproduction of the insertion-sort counts, the merge-sort drift or the package behavior has been published, so treat the figures above as the author’s results.
Installing countfn
The package is distributed for both ecosystems under the same name:
- Python:
pip install countfn - JavaScript:
npm install countfn
The article does not establish the current published version, the repository’s maintenance status or whether the package is still actively released. Check the registry page for the version you plan to use before building a workflow around it.
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