Multi precision
Each integer in the circuit has a certain bit-width, which is determined by the inputset. These bit-widths can be observed when graphs are printed:
However, it's not possible to add 3-bit and 4-bit numbers together because their encoding is different:
The result of such an addition is a 5-bit number, which also has a different encoding:
Because of these encoding differences, we perform a graph processing step called bit-width assignment, which takes the graph and updates the bit-widths to be compatible with FHE.
After this graph processing step, the graph would look like:
Most operations cannot change the encoding, which means that the input and output bit-widths need to be the same. However, there is an operation which can change the encoding: the table lookup operation.
Let's say you have this graph:
This is the graph for (x**2) + y
where x
is 2-bits and y
is 5-bits. If the table lookup operation wasn't able to change the encoding, we'd need to make everything 6-bits. However, since the encoding can be changed, the bit-widths can be assigned like so:
In this case, we kept x
as 2-bits, but set the table lookup result and y
to be 6-bits, so that the addition can be performed.
This style of bit-width assignment is called multi-precision, and it is enabled by default. To disable it and use a single precision across the circuit, you can use the single_precision=True
configuration option.
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