This week, Twitter upped their single-tweet character limit from 140 to 280, purportedly based on this interesting analysis of tweet lengths published on Twitter's engineering blog. The gist of the analysis is this: English language tweets display a roughly log-normal distribution of character counts, except near the 140-character limit, at which the distribution spikes:

The analysis takes this as evidence that twitter users often "cram" their longer thoughts into the 140 character limit, and suggest that a 280-character limit would more naturally accommodate the distribution of people's desired tweet lengths.

This immediately brought to mind another character limit that many Python programmers face in their day-to-day lives: the 79-character line limit suggested by Python's PEP8 style guide:

Limit all lines to a maximum of 79 characters.

I began to wonder whether popular Python packages (e.g. NumPy, SciPy, Pandas, Scikit-Learn, Matplotlib, AstroPy) display anything similar to what is seen in the distribution of tweet lengths.

Spoiler alert: they do! And the details of the distribution reveal some insights into the programming habits and stylistic conventions of the communities who write them.

To take a look at this, we first need a way to access all the raw lines of code in any Python package.
In a standard system architecture, if you have installed a package you already have the Python source stored in your system.
For example, the `numpy`

source code on my system is stored here:

In [1]:

```
import numpy
numpy.__path__
```

Out[1]:

['/Users/jakevdp/anaconda/lib/python3.6/site-packages/numpy']

`os.walk`

function to write a quick generator function that will iterate over all lines of Python code in a given package:

In [2]:

```
# Python 3.X
import os
def iter_lines(module):
"""Iterate over all lines of Python in module"""
for root, dirs, files in os.walk(module.__path__[0]):
for filename in files:
if filename.endswith('.py'):
with open(os.path.join(root, filename)) as f:
yield from f
```

In [3]:

```
lines = iter_lines(numpy)
len(list(lines))
```

Out[3]:

179615

Given this we can find the lengths of all the lines and plot a histogram:

In [4]:

```
%matplotlib inline
import matplotlib.pyplot as plt
import numpy as np
plt.style.use('seaborn-whitegrid')
```

In [5]:

```
lengths = [len(line) for line in iter_lines(numpy)]
plt.hist(lengths, bins=np.arange(max(lengths)), histtype='step', linewidth=1);
```

In [6]:

```
lengths = [len(line) for line in iter_lines(numpy) if len(line) > 1]
plt.hist(lengths, bins=np.arange(125), histtype='step', linewidth=1);
```

Now this is looking interesting!

In [7]:

```
np.argmax(np.bincount(lengths))
```

Out[7]:

13

We can use a list comprehension to extract all lines of length 13:

In [8]:

```
lines13 = [line for line in iter_lines(numpy) if len(line) == 13]
len(lines13)
```

Out[8]:

3637

`value_counts`

function is useful for this:

In [9]:

```
import pandas as pd
pd.value_counts(lines13).head(10)
```

Out[9]:

--------\n 1349 Examples\n 646 See Also\n 645 try:\n 218 pass\n 62 See also\n 59 return c\n 38 return a\n 22 None\n 20 finally:\n 19 dtype: int64

*unique* lines, by passing the ist through Python's `set`

collection:

In [10]:

```
lengths = [len(line) for line in set(iter_lines(numpy))]
plt.hist(lengths, bins=np.arange(125), histtype='step', linewidth=1);
```

That's a much cleaner distribution!

In order to aid comparison between packages, let's quickly refactor the above histogram code into a function that we can re-use. In addition, we'll add a vertical line at the PEP8's maximum character count:

In [11]:

```
def hist_linelengths(module, ax):
"""Plot a histogram of lengths of unique lines in the given module"""
lengths = [len(line.rstrip('\n')) for line in set(iter_lines(module))]
h = ax.hist(lengths, bins=np.arange(125) + 0.5, histtype='step', linewidth=1.5)
ax.axvline(x=79.5, linestyle=':', color='black')
ax.set(title="{0} {1}".format(module.__name__, module.__version__),
xlim=(1, 100),
ylim=(0, None),
xlabel='characters in line',
ylabel='number of lines')
return h
```

In [12]:

```
import numpy, scipy, matplotlib, pandas, sklearn, astropy
modules = [numpy, scipy, pandas, matplotlib, sklearn, astropy]
fig, ax = plt.subplots(2, 3, figsize=(14, 6), sharex=True)
fig.subplots_adjust(hspace=0.2, wspace=0.2)
for axi, module in zip(ax.flat, modules):
hist_linelengths(module, ax=axi)
for axi in ax[0]:
axi.set_xlabel('')
for axi in ax[:, 1:].flat:
axi.set_ylabel('')
```

The results here are quite interesting: similar to Twitter's tweet length analysis, we see that each of these packages have a somewhat smooth distribution of characters, with a "bump" at or near the 79-character PEP8 limit! Additionally, it is clear that some packages (namely matplotlib, sklearn, and particularly pandas) seem to be quite strict about this limit, while other packages (numpy, scipy, astropy) are a bit more lenient.

But one package stands out: matplotlib displays some noticeable spikes at a few intermediate line lengths; let's take a look at these:

In [13]:

```
lines = set(iter_lines(matplotlib))
counts = np.bincount([len(line) for line in lines])
np.argmax(counts)
```

Out[13]:

29

In [14]:

```
[line for line in lines if len(line) == 29][:10]
```

Out[14]:

[' pick(mouseevent)\n', " if aspect == 'auto':\n", ' for a in alias_list:\n', " 'violet red': '#a50055',\n", ' cache_dir = None\n', " rc('image', cmap='gray')\n", " 'uni2270' : 8816,\n", ' x0t -= delta\n', ' if lolims.any():\n', " 'expanded' : 700,\n"]

We see that many lines seem to be defining some dictionary of keys starting with "uni":

In [15]:

```
[line for line in lines if 'uni203' in line]
```

Out[15]:

[" 'uni2035' : 8245,\n", " 'uni203E' : 8254,\n", " 'uni2033' : 8243,\n", " 'uni2031' : 8241,\n", " 'uni2037' : 8247,\n", " 'uni203B' : 8251,\n", " 'uni2034' : 8244,\n", " 'uni2032' : 8242,\n", " 'uni203C' : 8252,\n", " 'uni2036' : 8246,\n", " 'uni2038' : 8248,\n"]

This turns out to be some auto-generated code mapping unicode strings to numbers. Other spikes in the matplotlib are due to similar artifacts.

There is also the mini-dropoff at line lengths of 70; I've not looked into it, but my suspicion is that might be a remnant of the code style used by matplotlib's creator in the early days of the package.

Following the Twitter character analysis, let's see if we can fit a log-normal distribution to the number of lines with each character count. As a reminder, the log-normal can be parametrized like this:

$$ LogNorm(x; \mu, \sigma) = \frac{1}{x \sigma \sqrt{2\pi}} \exp\left(-\frac{[\log(x) - \mu]^2}{2\sigma^2}\right) $$Here $x$ is the number of counts, $\exp(\mu)$ is the median of the peak of the distribution, and $\sigma^2$ controls the distribution's width.
We can implement this using the `lognorm`

distribution available in scipy:

In [16]:

```
from scipy import stats
def lognorm_model(x, amplitude, mu, sigma):
return amplitude * stats.lognorm.pdf(x, scale=np.exp(mu), s=sigma)
x = np.linspace(0, 100, 1000)
plt.plot(x, lognorm_model(x, 1000, 3.5, 0.7));
```

In [17]:

```
from scipy import optimize
counts, bins, _ = hist_linelengths(numpy, ax=plt.axes())
lengths = 0.5 * (bins[:-1] + bins[1:])
def minfunc(theta, lengths, counts):
return np.sum((counts - lognorm_model(lengths, *theta)) ** 2)
opt = optimize.minimize(minfunc, x0=[10000, 4, 1],
args=(lengths[:50], counts[:50]),
method='Nelder-Mead')
print("optimal parameters:", opt.x)
plt.fill_between(lengths, lognorm_model(lengths, *opt.x), alpha=0.3, color='gray');
```

optimal parameters: [ 9.92126791e+04 3.75476977e+00 5.19760726e-01]

Seems like a reasonable fit! From this, you could argue (as the Twitter engineering team did) that the line lengths might "naturally" follow a log-normal distribution, if it weren't for the artificial imposition of the PEP8 maximum line length.

For convenience, let's create a function that will plot this lognormal fit for any given module:

In [18]:

```
def lognorm_model(x, theta):
amp, mu, sigma = theta
return amp * stats.lognorm.pdf(x, scale=np.exp(mu), s=sigma)
def minfunc(theta, lengths, freqs):
return np.sum((freqs - lognorm_model(lengths, theta)) ** 2)
def lognorm_mode(amp, mu, sigma):
return np.exp(mu - sigma ** 2)
def lognorm_std(amp, mu, sigma):
var = (np.exp(sigma ** 2) - 1) * np.exp(2 * mu + sigma ** 2)
return np.sqrt(var)
```

In [19]:

```
def hist_linelengths_with_fit(module, ax, indices=slice(50)):
counts, bins, _ = hist_linelengths(module, ax)
lengths = 0.5 * (bins[:-1] + bins[1:])
opt = optimize.minimize(minfunc, x0=[1E5, 4, 0.5],
args=(lengths[indices], counts[indices]),
method='Nelder-Mead')
model_counts = lognorm_model(lengths, opt.x)
ax.fill_between(lengths, model_counts, alpha=0.3, color='gray')
# Add text describing mu and sigma
A, mu, sigma = opt.x
mode = np.exp(mu - sigma ** 2)
ax.text(0.22, 0.15, 'mode = {0:.1f}'.format(lognorm_mode(*opt.x)),
transform=ax.transAxes, size=14)
ax.text(0.22, 0.05, 'stdev = {0:.1f}'.format(lognorm_std(*opt.x)),
transform=ax.transAxes, size=14)
return opt.x
```

Now we can compare the models for each package:

In [20]:

```
modules = [numpy, scipy, pandas, matplotlib, sklearn, astropy]
fig, ax = plt.subplots(2, 3, figsize=(14, 6), sharex=True)
fig.subplots_adjust(hspace=0.2, wspace=0.2)
fits = {}
for axi, module in zip(ax.flat, modules):
fits[module.__name__] = hist_linelengths_with_fit(module, ax=axi)
for axi in ax[0]:
axi.set_xlabel('')
for axi in ax[:, 1:].flat:
axi.set_ylabel('')
```

In [21]:

```
ha = {'sklearn': 'right', 'scipy': 'right', 'pandas': 'right'}
va = {'sklearn': 'top'}
for name, fit in sorted(fits.items()):
mode = lognorm_mode(*fit)
std = lognorm_std(*fit)
plt.plot(mode, std, 'ok')
plt.text(mode, std, ' ' + name + ' ', size=14,
ha=ha.get(name, 'left'), va=va.get(name, 'bottom'))
plt.xlabel('mode of model', size=14)
plt.ylabel('std. deviation of model', size=14);
plt.xlim(30, 41);
```

I found it curious that a log-normal distribution fits both tweets and lines of code. Doing some digging, I found some literature on the subject of message lengths on the internet. This study finds that across languages and mediums, comment lengths follow a log-normal distribution quite closely. They propose a mechanism related to the Weber-Fechner law, which suggests a logarithmic scale in degrees of perception. It seems reasonable that lengths of code lines would respond to the same mechanism.

As for the data, I think it's quite interesting what this reveals about each project's commitment to the PEP8 line length. Pandas, Scikit-Learn, and Matplotlib seem to be strongly committed to keeping their lines below 79 characters; by contrast, AstroPy doesn't seem to mind the occasional long line (though it does still display a "cramming" pattern, to use the parlance of the Twitter team's analysis).

Comparing the summary statistics between packages, it is interesting to note the relative similarity of the numpy and scipy packages in terms of distribution of line lengths. This makes a lot of sense, because historically the development team has overlapped strongly between these two packages.

By contrast, scikit-learn tends to have around 10 more characters per line, and a much wider distribution of typical line lengths. I suspect the length of the lines is due to the nature of scikit-learn's code: it has relatively long class names (e.g. `RandomForestClassifier`

) which are used frequently throughout the code. The prevalence of classes also adds a four-space indentation to much of the package.
As for the larger standard deviation, this may be due to the larger pool of contributors: scikit-learn has about twice the total number of contributors as either numpy or scipy.

Pandas is interesting in that it doesn't show the pronounced "cramming" effect seen in the other packages. Long lines seem to be broken-up in a more distributed way, perhaps through assignment of temporary variables rather than through line breaks.

Each package displays a distinct "fingerprint" regarding the lengths of code lines, and the above visualizations suggest that PEP8's restrictions really do affect the way people write code, particularly in packages that use more characters per line, such as Pandas and Scikit-Learn.

Keep in mind that all of this is based on a couple fairly strong assumptions:

- PEP8 aside, the "natural" distribution of line lengths is log-normal
- We can meaningfully extrapolate from the frequency of lines with fewer than 50 characters to find statistics describing this "natural" log-normal distribution.

We *could* follow the lead of the Twitter engineering team, and use this analysis to argue that the PEP8 line length limit should be lifted, so as to not constrain people's "natural" inclinations toward the top end of each distribution. But I think that good arguments can be made, in both the case of PEP8 and Twitter's character limit, that this is too eager an interpretation.

Those controversies aside, it would be interesting to dive a bit deeper into this kind of analysis. I can think of a few interesting question you could ask:

- Where do other Python packages fit on the mode/spread graph?
- Has the coding style in these packages, reflected in line length, evolved over time?
- How do individual contributors behave? Do they tend to have similar habits across packages?
- What do these distributions look like for code written in other languages?

All of these would be interesting to address, but I've spent enough words on this already: I'll leave those questions for another time, or another person. Thanks for reading!