lcw: Estimate the number of lines in a file.
==============================================
lcw is like ``wc -l`` but faster, less precise, and equally accurate. ::

    usage: lcw [-h] [--sample-size N] [--page-size PAGE_SIZE] [--pattern PATTERN]
               [--regex]
               file [file ...]

    Estimate how many lines are in a file.

    positional arguments:
      file

    optional arguments:
      -h, --help            show this help message and exit
      --sample-size N, -n N
                            How many pages to count (default: 1000)
      --page-size PAGE_SIZE, -p PAGE_SIZE
                            Size of an observation (default: 16384)
      --pattern PATTERN, -e PATTERN
                            The pattern to match (default: b'\n')
      --regex, -r           Use regular expressions (statistically unsound)
                            (default: False)

Speed
--------
It's faster than ``wc -l`` on big files. ::

    $ wc -c big-file.csv
     1071895374 big-file.csv

    $ time lcw big-file.csv
    2386238 ± 22903 lines (99% confidence)

    real    0m0.172s
    user    0m0.140s
    sys     0m0.027s

    $ time wc -l big-file.csv
     2388430 big-file.csv

    real    0m1.379s
    user    0m1.170s
    sys     0m0.197s

Math
------
lcw uses elementary statistics to perform unbiased estimates of the
number of lines in a file. It takes a random sample of "pages" within
the file and counts how many newlines are in each page.

It multiplies the average count by the number of pages in the file
in order to get its best guess at the number of lines in the file
(the maximum likelihood estimate) and then computes a 99% normal
confidence interval, applying a finite population correction for the
estimate the standard deviation of sample totals.

Tuning
--------
It is best to use the page size that your storage medium uses;
modern storage media read entire pages at once, so using a page size
that is too small will be bad for performance.

The sample size is set with ``-n``, and typical rules of thumb say
that this should be at least 20 for the confidence level to be valid.
The page size is set with ``-p`` and should be something like
2048, 4096, 8192, or 16384.

Matching things other than newline
-----------------------------------
You can count occurrences of a string other than newline; specify
the string with ``-e``. It will be interpreted as a regular expression
if you pass ``-r``. The statistical estimates do not account for the
variable length of regular expression matches, so you are better off
using plain strings if you care about accuracy.

Future work
--------------
I have been thinking about how to quickly sample from lots of files.
Things like lcw can help us with samples within files, but it can be
could be part of a broader survey plan, with cluster sampling or
stratification on directories or filenames and with multistage sampling,
using pilot tests to estimate the costs of the sampling of different
files.

lcw presently uses a simple random sample. Because data in text files
often vary with their position within the file, (Later lines often
correspond to later dates.) systematic sampling would be appropriate.

Or, does this already exist so I don't have to write it?
