Improve efficiency of Range Check

[enricobottazzi]

The biggest cost center of the circuit implementation revolves around calling the range_check function.

According to the design of halo2-lib it is not possible to fill up a lookup table with the desired values and perform the lookup. For example I want to constraint a polynomial to be in the range [0, 5] the only way to do that is to:

• load a lookup table with using 3 as lookup_bits
• perform a lookup that the value exist in the lookup table
• check that the value is less than 6.

A more immediate approach would be to load the lookup table with values from 0 to 5 and just perform a lookup that the value exist in this lookup table. Unfortunately, halo2-lib doesn't allow that out of the box.