# Multi precision

Last updated

Last updated

This document explains the multi-precision option for bit-width assignment for integers.

The multi-precision option enables the frontend to use the smallest bit-width possible for each operation in Fully Homomorphic Encryption (FHE), improving computation efficiency.

Bit-width and encoding differences

Each integer in the circuit has a certain bit-width, which is determined by the input-set. These bit-widths are visible when graphs are printed, for example:

However, adding integers with different bit-widths (for example, 3-bit and 4-bit numbers) directly isn't possible due to differences in encoding, as shown below:

When you add a 3-bit number and a 4-bit number, the result is a 5-bit number with a different encoding:

Bit-width assignment with graph processing

To address these encoding differences, a graph processing step called bit-width assignment is performed. This step updates the graph's bit-widths to ensure compatibility with Fully Homomorphic Encryption (FHE).

After this step, the graph might look like this:

Encoding flexibility with Table Lookup

Most operations cannot change the encoding, requiring the input and output bit-widths to remain the same. However, the table lookup operation can change the encoding. For example, consider the following graph:

This graph represents the computation `(x**2) + y`

where `x`

is 2-bits and `y`

is 5-bits. Without the ability to change encodings, all bit-widths would need to be adjusted to 6-bits. However, since the encoding can change, bit-widths are assigned more efficiently:

In this case, `x`

remains a 2-bit integer, but the Table Lookup result and `y`

are set to 6-bits to allow for the addition.

Enabling and disabling multi-precision

This approach to bit-width assignment is known as multi-precision and is enabled by default. To disable multi-precision and enforce a single precision across the circuit, use the `single_precision=True`

configuration option.