Exactness

One of the most common operations in Concrete is Table Lookups (TLUs). TLUs are performed with an FHE operation called Programmable Bootstrapping (PBS). PBS's have a certain probability of error, which, when triggered, result in inaccurate results.

Let's say you have the table:

lut = [0, 1, 4, 9, 16, 25, 36, 49, 64]

And you perform a Table Lookup using 4. The result you should get is lut[4] = 16, but because of the possibility of error, you could get any other value in the table.

The probability of this error can be configured through the p_error and global_p_error configuration options. The difference between these two options is that, p_error is for individual TLUs but global_p_error is for the whole circuit.

If you set p_error to 0.01, for example, it means every TLU in the circuit will have a 99% chance of being exact with a 1% probability of error. If you have a single TLU in the circuit, global_p_error would be 1% as well. But if you have 2 TLUs for example, global_p_error would be almost 2% (1 - (0.99 * 0.99)).

However, if you set global_p_error to 0.01, the whole circuit will have 1% probability of error, no matter how many Table Lookups are included.

If you set both of them, both will be satisfied. Essentially, the stricter one will be used.

By default, both p_error and global_p_error is set to None, which results in a global_p_error of 1 / 100_000 being used.

Feel free to play with these configuration options to pick the one best suited for your needs! See How to Configure to learn how you can set a custom p_error and/or global_p_error.

Configuring either of those variables impacts computation time (compilation, keys generation, circuit execution) and space requirements (size of the keys on disk and in memory). Lower error probabilities would result in longer computation times and larger space requirements.