[Decompose] why can't use mod or >> in circuit?

[Demian101]

👋🏻👋🏻👋🏻

In my struggle coding life, I frequently encounter the need to understand and implement right shift operations, as in the examples '1111 >> 3 = 1' or '1101 >> 2 = 3'.

However, in the context of Halo2 and its decompose circuit : , I'm puzzled about a specific line of code:

z = (z - chunk) * Assigned::from(F::from(1u64 << LOOKUP_NUM_BITS)).invert();

In this case, why isn't the right shift operator ('>>') used instead? I mean

z = (z - chunk) >> F::from(1u64 << LOOKUP_NUM_BITS)

is much more clear, right ?

Additionally, why can't we simply use the modulo operator ('%') to achieve bit shifting?

---

My core problem is :

I know some finite field operations may not work in circuits, what is the rule?

I know we can use multiplication, addition,

But I don't know when I can use left shift, right shift, modular operation

[dajuguan]

Because << is not overloaded in Finite Field, actually only Add, AddAssign, Mul, MulAssign, Neg, Sub, SubAssign are overloaded in the Field trait. Ref: https://github.com/zkcrypto/ff/blob/e853770f4843e47cd5e07330140b5bd1cdfc9f11/src/lib.rs#L41