feat: replace bitwise ANDs used for truncation with Instruction::Truncate

[TomAFrench]

…

Description

Problem*

Resolves

Summary*

It's common for us to have new Noir developers to perform bitwise operations in order to truncate a value before they cast to a smaller type, leading to programs such as the below:

fn main(num: u72) -> pub [u8; 8] {
    let mut out: [u8; 8] = [0; 8];
    for i in 0..8 {
        out[i] = (num >> (56 - (i * 8)) as u72 & 0xff) as u8;
    }

    out
}

This is expensive and unnecessary as we perform truncation on casts anyway. This PR then adds an optimisation which converts any bitwise AND of the form lhs & 0xff into an equivalent truncation instruction.

Before
acir fn main f0 {
  b0(v0: u72):
    v277 = div v0, u72 2⁵⁶
    v278 = and v277, u72 255
    v279 = truncate v278 to 8 bits, max_bit_size: 72
    v280 = cast v279 as u8
    v281 = div v0, u72 2⁴⁸
    v282 = and v281, u72 255
    v283 = truncate v282 to 8 bits, max_bit_size: 72
    v284 = cast v283 as u8
    v285 = div v0, u72 2⁴⁰
    v286 = and v285, u72 255
    v287 = truncate v286 to 8 bits, max_bit_size: 72
    v288 = cast v287 as u8
    v289 = div v0, u72 2³²
    v290 = and v289, u72 255
    v291 = truncate v290 to 8 bits, max_bit_size: 72
    v292 = cast v291 as u8
    v293 = div v0, u72 2²⁴
    v294 = and v293, u72 255
    v295 = truncate v294 to 8 bits, max_bit_size: 72
    v296 = cast v295 as u8
    v297 = div v0, u72 2¹⁶
    v298 = and v297, u72 255
    v299 = truncate v298 to 8 bits, max_bit_size: 72
    v300 = cast v299 as u8
    v301 = div v0, u72 2⁸
    v302 = and v301, u72 255
    v303 = truncate v302 to 8 bits, max_bit_size: 72
    v304 = cast v303 as u8
    v305 = and v0, u72 255
    v306 = truncate v305 to 8 bits, max_bit_size: 72
    v307 = cast v306 as u8
    return [v280, v284, v288, v292, v296, v300, v304, v307]
}

+--------------+----------------------+
| ACIR Opcodes | Backend Circuit Size |
+--------------+----------------------+
| 70           | 5617                 |
+--------------+----------------------+
After
acir fn main f0 {
  b0(v0: u72):
    v242 = div v0, u72 2⁵⁶
    v243 = truncate v242 to 8 bits, max_bit_size: 72
    v244 = cast v243 as u8
    v245 = div v0, u72 2⁴⁸
    v246 = truncate v245 to 8 bits, max_bit_size: 72
    v247 = cast v246 as u8
    v248 = div v0, u72 2⁴⁰
    v249 = truncate v248 to 8 bits, max_bit_size: 72
    v250 = cast v249 as u8
    v251 = div v0, u72 2³²
    v252 = truncate v251 to 8 bits, max_bit_size: 72
    v253 = cast v252 as u8
    v254 = div v0, u72 2²⁴
    v255 = truncate v254 to 8 bits, max_bit_size: 72
    v256 = cast v255 as u8
    v257 = div v0, u72 2¹⁶
    v258 = truncate v257 to 8 bits, max_bit_size: 72
    v259 = cast v258 as u8
    v260 = div v0, u72 2⁸
    v261 = truncate v260 to 8 bits, max_bit_size: 72
    v262 = cast v261 as u8
    v263 = truncate v0 to 8 bits, max_bit_size: 72
    v264 = cast v263 as u8
    return [v244, v247, v250, v253, v256, v259, v262, v264]
}

+--------------+----------------------+
| ACIR Opcodes | Backend Circuit Size |
+--------------+----------------------+
| 61           | 3801                 |
+--------------+----------------------+

The ANDs then completely disappear as the truncation instructions they get converted into are merged into the existing truncations.

Additional Context

Documentation*

Check one:

• No documentation needed.
• Documentation included in this PR.
• [Exceptional Case] Documentation to be submitted in a separate PR.

PR Checklist*

• I have tested the changes locally.
• I have formatted the changes with Prettier and/or cargo fmt on default settings.

[github-actions]

Changes to circuit sizes

Generated at commit: 40f8b6073fa578c0e0b499b2c16cc3afadff60cc, compared to commit: fc32703ca05e2da15c781d88c96e7e29ce80ad95

🧾 Summary (10% most significant diffs)

Program	ACIR opcodes (+/-)	%	Circuit size (+/-)	%
regression	+8 ❌	+3.17%	-890 ✅	-21.61%

---

Full diff report 👇

Program	ACIR opcodes (+/-)	%	Circuit size (+/-)	%
regression	260 (+8)	+3.17%	3,228 (-890)	-21.61%