8  Generating and exporting/importing the raw data

The raw data behind everything that follows is produced by the counting routines of the previous chapter and stored as CSV files, so that the expensive computation is done once rather than on every run. The generation lives in src/euclid_analysis/frequencies.py, and the saving and loading in src/euclid_analysis/dataio.py.

The one-dimensional data is a single call to heilbronn over \(a = 1, \ldots, 10^4\). On the machine used here that took about 201 seconds, some three and a half minutes.

The two-dimensional data is a single call to euclid_alg_frequencies over all pairs \(0 < b < a < N\), with \(N\) running up to just past \(10^5\) in steps of \(1000\). This is the expensive part: it covers almost five billion pairs, and it took about 17,600 seconds, close to five hours. That is the kind of run one wants to do exactly once, which is why the data is generated, saved, and simply loaded from then on.

The two-dimensional run yields three tables: the frequencies of each gcd value, and the frequencies of each step-count \(T(a,b)\) in a coprime-restricted and an unrestricted version. The one-dimensional run yields the coprime-restricted and unrestricted step-count tables. tabulate turns each into a pandas DataFrame and save_meta_dict writes it to CSV; the five files are registered by name (A, B, C, H1, H) in DATASETS, under DATA_DIR.

Reading the data back is a single call to load_meta_dict, or load_dataset, which looks a file up by its registered name. The CSV round-trip would otherwise leave the dictionary keys as strings and scatter the tables with empty cells; the loader casts the keys back to integers and drops the zero entries, so what comes back matches what was saved. From there, basic_stats and dists produce the relative-frequency distributions and summary statistics used in the next chapter.