halo2arith implements various standart like plonk arithmetic gates for halo2 backend. MainGateInstructions trait has many primitives such as arithemtic operations, assignments, assertions and branching instructions.
Currently one four width gate and one five width gate are available with following expressions:
a * s_a + b * s_b + a * b * s_mul + c * s_c + d * s_d + s_constanta * s_a + b * s_b + a * b * s_mul_ab + c * s_c + d * s_d + c * d * s_mul_cd + s_constant
Range gate utilizes witness columns in the main gate. So it's a custom gate only with some selector column contributions. Range gates basically combines upto 5 limbs of a value where limbs are tested against tables. For example for 55 bit value range gate combines three 17 bit limbs and one 4 bit limb. In that case we have two tables one commits to values in [0, 2^17) and the other to [0, 2^4).
Upto 4 limbs range proof takes only single row with 5 limbs it will be two rows.