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//!This implements the constraints of the Cairo gates
//!
//! Cairo programs can have the following assembly-like instructions:
//! - Memory access: \[x\]
//! - Assert equal: <`left_hand_op`> = <`right_hand_op`>
//! · val
//! · \[reg1 + off_op1\]
//! · \[reg0 + off_op0\] +|* \[reg1 + off_op1\]
//! · \[reg0 + off_op0\] +|* val
//! · \[\[reg0 + off_op0\] + off_op1\]
//! - Jumps
//! · jmp abs <`address`> // unconditional absolute jump
//! · jmp rel <`offset`> // unconditional relative jump
//! · jmp rel <`offset`> if <`op`> != 0 // conditional jump
//! - Functions
//! · call abs <`address`> // calls a function (absolute location)
//! · call rel <`offset`> // calls a function (relative location)
//! · ret // returns to execution after the call
//! - Increments
//! · ap += <`op`>
//! · ap++
//!
//! A Cairo program runs across a number of state transitions.
//! Each state transition has the following structure:
//!
//! * Has access to a read-only memory
//! * Input: 3 types of registers
//! - pc (= program counter): address of current instruction
//! - ap (= allocation pointer): first free memory address
//! - fp (= frame pointer): beginning of stack (for function arguments)
//! * Output:
//! - `next_pc`: address of next instruction
//! - `next_ap`: address of next free memory slot
//! - `next_fp`: pointer to stack (can remain the same as fp)
//!
//!Cairo words are field elements of characteristic > 2^64
//!Cairo instructions are stored as words (63 or 64 bits - actual instruction or immediate value)
//!Instructions with immediate values are stored in 2 words
//!- The first word stores instruction
//!- The second word stores the value
//!Words of instructions consist of
//!* 3 signed offsets of 16 bits each, in the range [-2^15,2^15) biased representation
//! - `off_dst` (= offset from destination address): used to compute address of assignment
//! - `off_op0` (= offset from first operand): used to compute address of first operand in instruction
//! - `off_op1` (= offset from second operand): used to compute address of second operand in instruction
//!* 15 bits of flags divided into 7 groups
//! When multiple bits, at most one can be 1 and the rest must be 0
//! - `dst_reg` \[0\] = fDST_REG : indicates what pointer `off_dst` refers to ( 0 => ap , 1 => fp )
//! - `op0_reg` \[1\] = fOP0_REG : indicates what pointer `off_op0` refers to ( 0 => ap , 1 => fp )
//! - `op1_src` \[2..4\] : encodes the type of second operand
//! · 0: indicates `off_op1` is b in the double indexing \[\[ point + a \] + b \]
//! · 1: indicates `off_op1` is an immediate value = `fOP1_VAL` = 1
//! · 2: indicates offset `off_op1` relative to fp = `fOP1_FP` = 1
//! · 4: indicates offset `off_op1` relative to ap = `fOP1_AP` = 1
//! - `res_logic` \[5..6\]: defines (if any) arithmetic operation in right part
//! · 0: right part is single operand
//! · 1: right part is addition = `fRES_ADD` = 1
//! · 2: right part is multiplication = `fRES_MUL` = 1
//! - `pc_update` \[7..9\]: defines the type of update for the pc
//! · 0 = regular increase by size of current instruction
//! · 1 = absolute jump to res address = `fPC_ABS_JMP` = 1
//! · 2 = relative jump of step res = `fPC_REL_JMP` = 1
//! · 4 = conditional jump (jnz) with step in op1 = `fPC_JNZ` = 1
//! - `ap_update` \[10..11\]: defines the type of update for the ap
//! · 0: means the new ap is the same, same free position
//! · 1: means there is an ap+=<`op`> instruction = `fAP_INC` = 1
//! · 2: means there is an ap++ instruction = `fAP_ADD1` = 1
//! - opcode \[12..14\]: encodes type of assembly instruction
//! · 0: jumps or increments instruction
//! · 1: call instruction = `fOPC_CALL` = 1
//! · 2: return instruction = `fOPC_RET` = 1
//! · 4: assert equal instruction (assignment to value or check equality) = `fOPC_ASSEQ` = 1
//!* in little-endian form = leftmost least significant bit
//!
//!The transition function uses 4 auxiliary values:
//!- dst: left part of instruction, destination
//!- op0: content of first operand of right part
//!- op1: content of second operand of right part
//!- res: result of the operation in the right part
use crate::{
alphas::Alphas,
circuits::{
argument::{Argument, ArgumentEnv, ArgumentType},
berkeley_columns::{BerkeleyChallengeTerm, BerkeleyChallenges, Column, E},
constraints::ConstraintSystem,
expr::{self, constraints::ExprOps, Cache},
gate::{CircuitGate, GateType},
wires::{GateWires, Wire, COLUMNS},
},
curve::KimchiCurve,
proof::ProofEvaluations,
};
use ark_ff::{FftField, Field, PrimeField};
use log::error;
use std::{array, marker::PhantomData};
use turshi::{
runner::{CairoInstruction, CairoProgram, Pointers},
word::{FlagBits, Offsets},
};
const NUM_FLAGS: usize = 16;
pub const CIRCUIT_GATE_COUNT: usize = 4;
// GATE-RELATED
impl<F: PrimeField> CircuitGate<F> {
/// This function creates a `CairoClaim` gate
pub fn create_cairo_claim(wires: GateWires) -> Self {
CircuitGate::new(GateType::CairoClaim, wires, vec![])
}
/// This function creates a `CairoInstruction` gate
pub fn create_cairo_instruction(wires: GateWires) -> Self {
CircuitGate::new(GateType::CairoInstruction, wires, vec![])
}
/// This function creates a `CairoFlags` gate
pub fn create_cairo_flags(wires: GateWires) -> Self {
CircuitGate::new(GateType::CairoFlags, wires, vec![])
}
/// This function creates a `CairoTransition` gate
pub fn create_cairo_transition(wires: GateWires) -> Self {
CircuitGate::new(GateType::CairoTransition, wires, vec![])
}
/// Gadget generator of the whole cairo circuits from an absolute row and number of instructions
/// Returns a vector of gates, and the next available row after the gadget
pub fn create_cairo_gadget(
// the absolute row in the circuit
row: usize,
// number of instructions
num: usize,
) -> (Vec<Self>, usize) {
// 0: 1 row for final check CairoClaim gate
// 4i+1: 1 row per instruction for CairoInstruction gate
// 4i+2: 1 row per instruction for Flags argument
// 4i+3: 1 row per instruction for CairoTransition gate
// 4i+4: 1 row per instruction for Cairo Auxiliary gate
// ...
// 4n-3: 1 row for last instruction
// 4n-2: 1 row for Auxiliary argument (no constraints)
let mut gates: Vec<CircuitGate<F>> = Vec::new();
if num > 0 {
let claim_gate = Wire::for_row(row);
gates.push(CircuitGate::create_cairo_claim(claim_gate));
}
let last = num - 1;
for i in 0..last {
let ins_gate = Wire::for_row(row + 4 * i + 1);
let flg_gate = Wire::for_row(row + 4 * i + 2);
let tra_gate = Wire::for_row(row + 4 * i + 3);
let aux_gate = Wire::for_row(row + 4 * i + 4);
gates.push(CircuitGate::create_cairo_instruction(ins_gate));
gates.push(CircuitGate::create_cairo_flags(flg_gate));
gates.push(CircuitGate::create_cairo_transition(tra_gate));
gates.push(CircuitGate::zero(aux_gate));
}
// next available row after the full
let next = row + 4 * last + 3;
// the final instruction
let ins_gate = Wire::for_row(next - 2);
let aux_gate = Wire::for_row(next - 1);
gates.push(CircuitGate::create_cairo_instruction(ins_gate));
gates.push(CircuitGate::zero(aux_gate));
(gates, next)
}
/// verifies that the Cairo gate constraints are solved by the witness depending on its type
///
/// # Errors
///
/// Will give error if `constraint evaluation` is invalid.
///
/// # Panics
///
/// Will panic if `constraint linearization` fails.
pub fn verify_cairo_gate<G: KimchiCurve<ScalarField = F>>(
&self,
row: usize,
witness: &[Vec<F>; COLUMNS],
cs: &ConstraintSystem<F>,
) -> Result<(), String> {
// assignments
let curr: [F; COLUMNS] = array::from_fn(|i| witness[i][row]);
let mut next: [F; COLUMNS] = array::from_fn(|_| F::zero());
if self.typ != GateType::Zero {
next = array::from_fn(|i| witness[i][row + 1]);
}
// column polynomials
let polys = {
let mut h = std::collections::HashSet::new();
for i in 0..COLUMNS {
h.insert(Column::Witness(i)); // column witness polynomials
}
// gate selector polynomials
h.insert(Column::Index(GateType::CairoClaim));
h.insert(Column::Index(GateType::CairoInstruction));
h.insert(Column::Index(GateType::CairoFlags));
h.insert(Column::Index(GateType::CairoTransition));
h
};
// assign powers of alpha to these gates
let mut alphas = Alphas::<F>::default();
alphas.register(ArgumentType::Gate(self.typ), Instruction::<F>::CONSTRAINTS);
// Get constraints for this circuit gate
let constraints =
circuit_gate_combined_constraints(self.typ, &alphas, &mut Cache::default());
// Linearize
let linearized = constraints.linearize(polys).unwrap();
// Setup proof evaluations
let rng = &mut o1_utils::tests::make_test_rng(None);
let evals = ProofEvaluations::dummy_with_witness_evaluations(curr, next);
// Setup circuit constants
let constants = expr::Constants {
endo_coefficient: cs.endo,
mds: &G::sponge_params().mds,
zk_rows: 3,
};
let challenges = BerkeleyChallenges {
alpha: F::rand(rng),
beta: F::rand(rng),
gamma: F::rand(rng),
joint_combiner: F::zero(),
};
let pt = F::rand(rng);
// Evaluate constraints
match linearized
.constant_term
.evaluate_(cs.domain.d1, pt, &evals, &constants, &challenges)
{
Ok(x) => {
if x == F::zero() {
Ok(())
} else {
Err(format!("Invalid {:?} constraint", self.typ))
}
}
Err(x) => {
error!("{x:?}");
Err(format!("Failed to evaluate {:?} constraint", self.typ))
}
}
}
}
pub mod witness {
use super::*;
/// Returns the witness of an execution of a Cairo program in `CircuitGate` format
pub fn cairo_witness<F: Field>(prog: &CairoProgram<F>) -> [Vec<F>; COLUMNS] {
// 0: 1 row for final check CairoClaim gate
// 4i+1: 1 row per instruction for CairoInstruction gate
// 4i+2: 1 row per instruction for Flags argument
// 4i+3: 1 row per instruction for CairoTransition gate
// 4i+4: 1 row per instruction for Auxiliary gate (Zero)
// ...
// 4n-3: 1 row for last instruction
// 4n-2: 1 row for Auxiliary argument (no constraints)
let n = prog.trace().len();
let rows = 4 * n - 1;
let mut table: Vec<[F; COLUMNS]> = Vec::new();
table.resize(rows, [F::zero(); COLUMNS]);
for (i, inst) in prog.trace().iter().enumerate() {
if i == 0 {
let claim_wit = claim_witness(prog);
table[i] = claim_wit;
}
let ins_wit = instruction_witness(inst);
let flg_wit = flag_witness(inst);
table[4 * i + 1] = ins_wit;
table[4 * i + 2] = flg_wit;
if i != n - 1 {
// all but last instruction
let tra_wit = transition_witness(inst, &prog.trace()[i + 1]);
let aux_wit = auxiliary_witness(&prog.trace()[i + 1]);
table[4 * i + 3] = tra_wit;
table[4 * i + 4] = aux_wit;
}
}
let mut witness: [Vec<F>; COLUMNS] = Default::default();
for col in 0..COLUMNS {
// initialize column with zeroes
witness[col].resize(table.len(), F::zero());
for (row, wit) in table.iter().enumerate() {
witness[col][row] = wit[col];
}
}
witness
}
fn claim_witness<F: Field>(prog: &CairoProgram<F>) -> [F; COLUMNS] {
let last = prog.trace().len() - 1;
[
prog.ini().pc(), // initial pc from public input
prog.ini().ap(), // initial ap from public input
prog.fin().pc(), // final pc from public input
prog.fin().ap(), // final ap from public input
prog.trace()[last].pc(), // real last pc
prog.trace()[last].ap(), // real last ap
F::zero(),
F::zero(),
F::zero(),
F::zero(),
F::zero(),
F::zero(),
F::zero(),
F::zero(),
F::zero(),
]
}
fn instruction_witness<F: Field>(inst: &CairoInstruction<F>) -> [F; COLUMNS] {
[
inst.pc(),
inst.ap(),
inst.fp(),
inst.size(),
inst.res(),
inst.dst(),
inst.op1(),
inst.op0(),
inst.off_dst(),
inst.off_op1(),
inst.off_op0(),
inst.adr_dst(),
inst.adr_op1(),
inst.adr_op0(),
inst.instr(),
]
}
fn flag_witness<F: Field>(inst: &CairoInstruction<F>) -> [F; COLUMNS] {
[
inst.f_dst_fp(),
inst.f_op0_fp(),
inst.f_op1_val(),
inst.f_op1_fp(),
inst.f_op1_ap(),
inst.f_res_add(),
inst.f_res_mul(),
inst.f_pc_abs(),
inst.f_pc_rel(),
inst.f_pc_jnz(),
inst.f_ap_add(),
inst.f_ap_one(),
inst.f_opc_call(),
inst.f_opc_ret(),
inst.f_opc_aeq(),
]
}
fn transition_witness<F: Field>(
curr: &CairoInstruction<F>,
next: &CairoInstruction<F>,
) -> [F; COLUMNS] {
[
curr.pc(),
curr.ap(),
curr.fp(),
curr.size(),
curr.res(),
curr.dst(),
curr.op1(),
next.pc(),
next.ap(),
next.fp(),
F::zero(),
F::zero(),
F::zero(),
F::zero(),
F::zero(),
]
}
fn auxiliary_witness<F: Field>(next: &CairoInstruction<F>) -> [F; COLUMNS] {
[
next.pc(),
next.ap(),
next.fp(),
F::zero(),
F::zero(),
F::zero(),
F::zero(),
F::zero(),
F::zero(),
F::zero(),
F::zero(),
F::zero(),
F::zero(),
F::zero(),
F::zero(),
]
}
}
pub mod testing {
use super::*;
/// verifies that the Cairo gate constraints are solved by the witness depending on its type
///
/// # Errors
///
/// Will give error if `gate` is not `Cairo`-related gate or `zero` gate.
pub fn ensure_cairo_gate<F: PrimeField>(
gate: &CircuitGate<F>,
row: usize,
witness: &[Vec<F>; COLUMNS],
//_cs: &ConstraintSystem<F>,
) -> Result<(), String> {
// assignments
let this: [F; COLUMNS] = array::from_fn(|i| witness[i][row]);
match gate.typ {
GateType::CairoClaim => {
let next: [F; COLUMNS] = array::from_fn(|i| witness[i][row + 1]);
ensure_claim(&this, &next) // CircuitGate::ensure_transition(&this),
}
GateType::CairoInstruction => {
let next: [F; COLUMNS] = array::from_fn(|i| witness[i][row + 1]);
ensure_instruction(&this, &next)
}
GateType::CairoFlags => {
let next: [F; COLUMNS] = array::from_fn(|i| witness[i][row + 1]);
ensure_flags(&this, &next)
}
GateType::CairoTransition => {
let next: [F; COLUMNS] = array::from_fn(|i| witness[i][row + 1]);
ensure_transition(&this, &next)
}
GateType::Zero => Ok(()),
_ => Err(
"Incorrect GateType: expected CairoInstruction, CairoFlags, CairoTransition, or CairoClaim"
.to_string(),
),
}
}
fn ensure_instruction<F: FftField>(vars: &[F], flags: &[F]) -> Result<(), String> {
let pc = vars[0];
let ap = vars[1];
let fp = vars[2];
let size = vars[3];
let res = vars[4];
let dst = vars[5];
let op1 = vars[6];
let op0 = vars[7];
let off_dst = vars[8];
let off_op1 = vars[9];
let off_op0 = vars[10];
let adr_dst = vars[11];
let adr_op1 = vars[12];
let adr_op0 = vars[13];
let instr = vars[14];
let f_dst_fp = flags[0];
let f_op0_fp = flags[1];
let f_op1_val = flags[2];
let f_op1_fp = flags[3];
let f_op1_ap = flags[4];
let f_res_add = flags[5];
let f_res_mul = flags[6];
let f_pc_abs = flags[7];
let f_pc_rel = flags[8];
let f_pc_jnz = flags[9];
let f_ap_inc = flags[10];
let f_ap_one = flags[11];
let f_opc_call = flags[12];
let f_opc_ret = flags[13];
let f_opc_aeq = flags[14];
let zero = F::zero();
let one = F::one();
// FLAGS RELATED
// check last flag is a zero
// f15 == 0
//ensure_eq!(zero, f15, "last flag is nonzero");
// check booleanity of flags
// fi * (1-fi) == 0 for i=[0..15)
for &flag in flags.iter().take(NUM_FLAGS - 1) {
ensure_eq!(zero, flag * (one - flag), "non-boolean flags");
}
// well formness of instruction
let shape = {
let shift = F::from(2u32.pow(15)); // 2^15;
let pow16 = shift.double(); // 2^16
let dst_sft = off_dst + shift;
let op0_sft = off_op0 + shift;
let op1_sft = off_op1 + shift;
// recompose instruction as: flags[14..0] | op1_sft | op0_sft | dst_sft
let mut aux = flags[14];
for i in (0..14).rev() {
aux = aux * F::from(2u32) + flags[i];
}
// complete with "flags" * 2^48 + op1_sft * 2^32 + op0_sft * 2^16 + dst_sft
((aux * pow16 + op1_sft) * pow16 + op0_sft) * pow16 + dst_sft
};
ensure_eq!(
zero,
instr - shape,
"wrong decomposition of the instruction"
);
// check no two flags of same set are nonzero
let op1_set = f_op1_ap + f_op1_fp + f_op1_val;
let res_set = f_res_mul + f_res_add;
let pc_set = f_pc_jnz + f_pc_rel + f_pc_abs;
let ap_set = f_ap_one + f_ap_inc;
let opcode_set = f_opc_aeq + f_opc_ret + f_opc_call;
ensure_eq!(
zero,
op1_set * (one - op1_set),
"invalid format of `op1_src`"
);
ensure_eq!(
zero,
res_set * (one - res_set),
"invalid format of `res_log`"
);
ensure_eq!(zero, pc_set * (one - pc_set), "invalid format of `pc_up`");
ensure_eq!(zero, ap_set * (one - ap_set), "invalid format of `ap_up`");
ensure_eq!(
zero,
opcode_set * (one - opcode_set),
"invalid format of `opcode`"
);
// OPERANDS RELATED
// * Destination address
// if dst_reg = 0 : dst_dir = ap + off_dst
// if dst_reg = 1 : dst_dir = fp + off_dst
ensure_eq!(
adr_dst,
f_dst_fp * fp + (one - f_dst_fp) * ap + off_dst,
"invalid destination address"
);
// * First operand address
// if op0_reg = 0 : op0_dir = ap + off_dst
// if op0_reg = 1 : op0_dir = fp + off_dst
ensure_eq!(
adr_op0,
f_op0_fp * fp + (one - f_op0_fp) * ap + off_op0,
"invalid first operand address"
);
// * Second operand address
ensure_eq!(
adr_op1, // op1_dir = ..
(f_op1_ap * ap // if op1_src == 4 : ap
+ f_op1_fp * fp // if op1_src == 2 : fp
+ f_op1_val * pc // if op1_src == 1 : pc
+ (one - f_op1_fp - f_op1_ap - f_op1_val) * op0 // if op1_src == 0 : op0
+ off_op1), // + off_op1
"invalid second operand address"
);
// OPERATIONS RELATED
// * Check value of result
ensure_eq!(
(one - f_pc_jnz) * res, // if pc_up != 4 : res = .. // no res in conditional jumps
f_res_mul * op0 * op1 // if res_log = 2 : op0 * op1
+ f_res_add * (op0 + op1) // if res_log = 1 : op0 + op1
+ (one - f_res_add - f_res_mul) * op1, // if res_log = 0 : op1
"invalid result"
);
// * Check storage of current fp for a call instruction
ensure_eq!(
zero,
f_opc_call * (dst - fp),
"current fp after call not stored"
); // if opcode = 1 : dst = fp
// * Check storage of next instruction after a call instruction
ensure_eq!(
zero,
f_opc_call * (op0 - (pc + size)),
"next instruction after call not stored"
); // if opcode = 1 : op0 = pc + size
// * Check destination = result after assert-equal
ensure_eq!(zero, f_opc_aeq * (dst - res), "false assert equal"); // if opcode = 4 : dst = res
Ok(())
}
fn ensure_flags<F: FftField>(curr: &[F], next: &[F]) -> Result<(), String> {
let f_pc_abs = curr[7];
let f_pc_rel = curr[8];
let f_pc_jnz = curr[9];
let f_ap_inc = curr[10];
let f_ap_one = curr[11];
let f_opc_call = curr[12];
let f_opc_ret = curr[13];
let pc = next[0];
let ap = next[1];
let fp = next[2];
let size = next[3];
let res = next[4];
let dst = next[5];
let op1 = next[6];
let pcup = next[7];
let apup = next[8];
let fpup = next[9];
let zero = F::zero();
let one = F::one();
let two = F::from(2u16);
// REGISTERS RELATED
// * Check next allocation pointer
ensure_eq!(
apup, // next_ap =
ap // ap +
+ f_ap_inc * res // if ap_up == 1 : res
+ f_ap_one // if ap_up == 2 : 1
+ f_opc_call.double(), // if opcode == 1 : 2
"wrong ap update"
);
// * Check next frame pointer
ensure_eq!(
fpup, // next_fp =
f_opc_call * (ap + two) // if opcode == 1 : ap + 2
+ f_opc_ret * dst // if opcode == 2 : dst
+ (one - f_opc_call - f_opc_ret) * fp, // if opcode == 4 or 0 : fp
"wrong fp update"
);
// * Check next program counter
ensure_eq!(
zero,
f_pc_jnz * (dst * res - one) * (pcup - (pc + size)), // <=> pc_up = 4 and dst = 0 : next_pc = pc + size // no jump
"wrong pc update"
);
ensure_eq!(
zero,
f_pc_jnz * dst * (pcup - (pc + op1)) // <=> pc_up = 4 and dst != 0 : next_pc = pc + op1 // condition holds
+ (one - f_pc_jnz) * pcup // <=> pc_up = {0,1,2} : next_pc = ... // not a conditional jump
- (one - f_pc_abs - f_pc_rel - f_pc_jnz) * (pc + size) // <=> pc_up = 0 : next_pc = pc + size // common case
- f_pc_abs * res // <=> pc_up = 1 : next_pc = res // absolute jump
- f_pc_rel * (pc + res), // <=> pc_up = 2 : next_pc = pc + res // relative jump
"wrong pc update"
);
Ok(())
}
fn ensure_transition<F: FftField>(curr: &[F], next: &[F]) -> Result<(), String> {
let pcup = curr[7];
let apup = curr[8];
let fpup = curr[9];
let next_pc = next[0];
let next_ap = next[1];
let next_fp = next[2];
// REGISTERS RELATED
// * Check next allocation pointer
ensure_eq!(next_ap, apup, "wrong next allocation pointer");
// * Check next frame pointer
ensure_eq!(next_fp, fpup, "wrong next frame pointer");
// * Check next program counter
ensure_eq!(next_pc, pcup, "wrong next program counter");
Ok(())
}
fn ensure_claim<F: FftField>(claim: &[F], next: &[F]) -> Result<(), String> {
let pc_ini = claim[0];
let ap_ini = claim[1];
let pc_fin = claim[2];
let ap_fin = claim[3];
let pc_n = claim[4];
let ap_n = claim[5];
let pc0 = next[0];
let ap0 = next[1];
let fp0 = next[2];
// * Check initial pc, ap, fp and final pc, ap
ensure_eq!(F::zero(), pc0 - pc_ini, "wrong initial pc");
ensure_eq!(F::zero(), ap0 - ap_ini, "wrong initial ap");
ensure_eq!(F::zero(), fp0 - ap_ini, "wrong initial fp");
ensure_eq!(F::zero(), pc_n - pc_fin, "wrong final pc");
ensure_eq!(F::zero(), ap_n - ap_fin, "wrong final ap");
Ok(())
}
}
//~ The Kimchi 15 columns could be:
//~ GateType Claim Instruction Zero | (Flags+Transition+Aux)
//~ row -> 0 4i+1 4i+2 4i+3 4n-2
//~ ---------------------------------------------------------------------------------
//~ 0 · ® pc_ini pc fDST_FP © pc © next_pc
//~ 1 · ® ap_ini ap fOP0_FP © ap © next_ap
//~ c 2 · ® pc_fin fp fOP1_VAL © fp © next_fp
//~ o 3 · ® ap_fin size fOP1_FP © size
//~ l 4 · © pc\[n-1\] res fOP1_AP © res
//~ | 5 · © ap\[n-1\] dst fRES_ADD © dst
//~ v 6 · op1 fRES_MUL © op1
//~ 7 op0 fPC_ABS pcup
//~ 8 off_dst fPC_REL apup
//~ 9 off_op1 fPC_JNZ fpup
//~ 10 off_op0 fAP_ADD
//~ 11 adr_dst fAP_ONE
//~ 12 adr_op1 fOPC_CALL
//~ 13 adr_op0 fOPC_RET
//~ 14 instr
// CONSTRAINTS-RELATED
/// Returns the expression corresponding to the literal "2"
fn two<F: Field, T: ExprOps<F, BerkeleyChallengeTerm>>() -> T {
T::literal(2u64.into()) // 2
}
/// Combines the constraints for the Cairo gates depending on its type
///
/// # Panics
///
/// Will panic if the `typ` is not `Cairo`-related gate type or `zero` gate type.
pub fn circuit_gate_combined_constraints<F: PrimeField>(
typ: GateType,
alphas: &Alphas<F>,
cache: &mut Cache,
) -> E<F> {
match typ {
GateType::CairoClaim => Claim::combined_constraints(alphas, cache),
GateType::CairoInstruction => Instruction::combined_constraints(alphas, cache),
GateType::CairoFlags => Flags::combined_constraints(alphas, cache),
GateType::CairoTransition => Transition::combined_constraints(alphas, cache),
GateType::Zero => E::literal(F::zero()),
_ => panic!("invalid gate type"),
}
}
pub struct Claim<F>(PhantomData<F>);
impl<F> Argument<F> for Claim<F>
where
F: PrimeField,
{
const ARGUMENT_TYPE: ArgumentType = ArgumentType::Gate(GateType::CairoClaim);
const CONSTRAINTS: u32 = 5;
/// Generates the constraints for the Cairo initial claim and first memory checks
/// Accesses Curr and Next rows
fn constraint_checks<T: ExprOps<F, BerkeleyChallengeTerm>>(
env: &ArgumentEnv<F, T>,
_cache: &mut Cache,
) -> Vec<T> {
let pc_ini = env.witness_curr(0); // copy from public input
let ap_ini = env.witness_curr(1); // copy from public input
let pc_fin = env.witness_curr(2); // copy from public input
let ap_fin = env.witness_curr(3); // copy from public input
let pc_n = env.witness_curr(4); // copy from public input
let ap_n = env.witness_curr(5); // copy from public input
// load address / value pairs from next row
let pc0 = env.witness_next(0);
let ap0 = env.witness_next(1);
let fp0 = env.witness_next(2);
// Initial claim
let mut constraints: Vec<T> = vec![ap0 - ap_ini.clone()]; // ap0 = ini_ap
constraints.push(fp0 - ap_ini); // fp0 = ini_ap
constraints.push(pc0 - pc_ini); // pc0 = ini_pc
// Final claim
constraints.push(ap_n - ap_fin);
constraints.push(pc_n - pc_fin);
constraints
}
}
pub struct Instruction<F>(PhantomData<F>);
impl<F> Argument<F> for Instruction<F>
where
F: PrimeField,
{
const ARGUMENT_TYPE: ArgumentType = ArgumentType::Gate(GateType::CairoInstruction);
const CONSTRAINTS: u32 = 28;
/// Generates the constraints for the Cairo instruction
/// Accesses Curr and Next rows
fn constraint_checks<T: ExprOps<F, BerkeleyChallengeTerm>>(
env: &ArgumentEnv<F, T>,
cache: &mut Cache,
) -> Vec<T> {
// load all variables of the witness corresponding to Cairoinstruction gates
let pc = env.witness_curr(0);
let ap = env.witness_curr(1);
let fp = env.witness_curr(2);
let size = env.witness_curr(3);
let res = env.witness_curr(4);
let dst = env.witness_curr(5);
let op1 = env.witness_curr(6);
let op0 = env.witness_curr(7);
let off_dst = env.witness_curr(8);
let off_op1 = env.witness_curr(9);
let off_op0 = env.witness_curr(10);
let adr_dst = env.witness_curr(11);
let adr_op1 = env.witness_curr(12);
let adr_op0 = env.witness_curr(13);
let instr = env.witness_curr(14);
// Load flags from the following row
let f_dst_fp = env.witness_next(0);
let f_op0_fp = env.witness_next(1);
let f_op1_val = env.witness_next(2);
let f_op1_fp = env.witness_next(3);
let f_op1_ap = env.witness_next(4);
let f_res_add = env.witness_next(5);
let f_res_mul = env.witness_next(6);
let f_pc_abs = env.witness_next(7);
let f_pc_rel = env.witness_next(8);
let f_pc_jnz = env.witness_next(9);
let f_ap_add = env.witness_next(10);
let f_ap_one = env.witness_next(11);
let f_opc_call = env.witness_next(12);
let f_opc_ret = env.witness_next(13);
let f_opc_aeq = env.witness_next(14);
// collect flags in its natural ordering
let flags: Vec<T> = (0..NUM_FLAGS - 1).map(|i| env.witness_next(i)).collect();
// LIST OF CONSTRAINTS
// -------------------
let mut constraints: Vec<T> = vec![];
// INSTRUCTIONS RELATED
// * Check last flag is always zero is redundant with wellformness check
// * Check booleanity of all flags
// fi * (1-fi) == 0 for i=[0..15)
for flag in flags.iter().take(NUM_FLAGS - 1) {
constraints.push(flag.clone() * (T::one() - flag.clone()));
}
// * Check no two flagbits of the same flagset are nonzero
// TODO(querolita): perhaps these are redundant considering all of the logics below
let op1_src = cache.cache(f_op1_ap.clone() + f_op1_fp.clone() + f_op1_val.clone());
let res_log = cache.cache(f_res_mul.clone() + f_res_add.clone());
let pc_up = cache.cache(f_pc_jnz.clone() + f_pc_rel + f_pc_abs);
let ap_up = cache.cache(f_ap_one + f_ap_add);
let opcode = cache.cache(f_opc_aeq.clone() + f_opc_ret + f_opc_call.clone());
constraints.push(op1_src.clone() * (T::one() - op1_src));
constraints.push(res_log.clone() * (T::one() - res_log));
constraints.push(pc_up.clone() * (T::one() - pc_up));
constraints.push(ap_up.clone() * (T::one() - ap_up));
constraints.push(opcode.clone() * (T::one() - opcode));
// * Shape of instruction
let shape = {
let shift: T = cache.cache(two::<F, T>().pow(15)); // 2^15;
let double_shift = shift.double();
let pow16 = cache.cache(double_shift); // 2^16
let dst_sft = off_dst.clone() + shift.clone();
let op0_sft = off_op0.clone() + shift.clone();
let op1_sft = off_op1.clone() + shift;
// recompose instruction as: flags[14..0] | op1_sft | op0_sft | dst_sft
let mut aux: T = flags[14].clone();
for i in (0..14).rev() {
aux = aux * two() + flags[i].clone();
}
// complete with "flags" * 2^48 + op1_sft * 2^32 + op0_sft * 2^16 + dst_sft
aux = ((aux * pow16.clone() + op1_sft) * pow16.clone() + op0_sft) * pow16 + dst_sft;
aux
};
constraints.push(instr - shape);
// OPERANDS RELATED
// * Destination address
// if dst_fp = 0 : dst_dir = ap + off_dst
// if dst_fp = 1 : dst_dir = fp + off_dst
constraints.push(
f_dst_fp.clone() * fp.clone() + (T::one() - f_dst_fp) * ap.clone() + off_dst - adr_dst,
);
// * First operand address
// if op0_fp = 0 : op0_dir = ap + off_dst
// if op0_fp = 1 : op0_dir = fp + off_dst
constraints.push(
f_op0_fp.clone() * fp.clone() + (T::one() - f_op0_fp) * ap.clone() + off_op0 - adr_op0,
);
// * Second operand address
constraints.push(
adr_op1 // op1_dir = ..
- (f_op1_ap.clone() * ap // if op1_src == 4 : ap
+ f_op1_fp.clone() * fp.clone() // if op1_src == 2 : fp
+ f_op1_val.clone() * pc.clone() // if op1_src == 1 : pc
+ (T::one() - f_op1_fp - f_op1_ap - f_op1_val) * op0.clone() // if op1_src == 0 : op0
+ off_op1), // + off_op1
);
// OPERATIONS-RELATED
// * Check value of result
constraints.push(
(T::one() - f_pc_jnz) * res.clone() // if pc_up != 4 : res = .. // no res in conditional jumps
- (f_res_mul.clone() * op0.clone() * op1.clone() // if res_log = 2 : op0 * op1
+ f_res_add.clone() * (op0.clone() + op1.clone()) // if res_log = 1 : op0 + op1
+ (T::one() - f_res_add - f_res_mul) * op1), // if res_log = 0 : op1
);
// * Check storage of current fp for a call instruction
// <=> assert_eq!(dst, fp);
constraints.push(f_opc_call.clone() * (dst.clone() - fp)); // if opcode = 1 : dst = fp
// * Check storage of next instruction after a call instruction
// <=> assert_eq!(op0, pc + size); // checks [ap+1] contains instruction after call
constraints.push(f_opc_call * (op0 - (pc + size))); // if opcode = 1 : op0 = pc + size
// * Check destination = result after assert-equal
// <=> assert_eq!(res, dst);
constraints.push(f_opc_aeq * (dst - res)); // if opcode = 4 : dst = res
constraints
}
}
pub struct Flags<F>(PhantomData<F>);
impl<F> Argument<F> for Flags<F>
where
F: PrimeField,
{
const ARGUMENT_TYPE: ArgumentType = ArgumentType::Gate(GateType::CairoFlags);
const CONSTRAINTS: u32 = 4;
/// Generates the constraints for the Cairo flags
/// Accesses Curr and Next rows
fn constraint_checks<T: ExprOps<F, BerkeleyChallengeTerm>>(
env: &ArgumentEnv<F, T>,
_cache: &mut Cache,
) -> Vec<T> {
// Load current row
let f_pc_abs = env.witness_curr(7);
let f_pc_rel = env.witness_curr(8);
let f_pc_jnz = env.witness_curr(9);
let f_ap_add = env.witness_curr(10);
let f_ap_one = env.witness_curr(11);
let f_opc_call = env.witness_curr(12);
let f_opc_ret = env.witness_curr(13);
// Load next row
let pc = env.witness_next(0);
let ap = env.witness_next(1);
let fp = env.witness_next(2);
let size = env.witness_next(3);
let res = env.witness_next(4);
let dst = env.witness_next(5);
let op1 = env.witness_next(6);
let pcup = env.witness_next(7);
let apup = env.witness_next(8);
let fpup = env.witness_next(9);
// REGISTERS-RELATED
// * Check next allocation pointer
// next_ap =
// ap +
// if ap_up == 1 : res
// if ap_up == 2 : 1
// if opcode == 1 : 2
let mut constraints: Vec<T> =
vec![apup - (ap.clone() + f_ap_add * res.clone() + f_ap_one + f_opc_call.double())];
// * Check next frame pointer
constraints.push(
fpup // next_fp =
- (f_opc_call.clone() * (ap + two()) // if opcode == 1 : ap + 2
+ f_opc_ret.clone() * dst.clone() // if opcode == 2 : dst
+ (T::one() - f_opc_call - f_opc_ret) * fp ), // if opcode == 4 or 0 : fp
);
// * Check next program counter (pc update)
constraints.push(
f_pc_jnz.clone()
* (dst.clone() * res.clone() - T::one())
* (pcup.clone() - (pc.clone() + size.clone())),
); // <=> pc_up = 4 and dst = 0 : next_pc = pc + size // no jump
constraints.push(
f_pc_jnz.clone() * dst * (pcup.clone() - (pc.clone() + op1)) // <=> pc_up = 4 and dst != 0 : next_pc = pc + op1 // condition holds
+ (T::one() - f_pc_jnz.clone()) * pcup // <=> pc_up = {0,1,2} : next_pc = ... // not a conditional jump
- (T::one() - f_pc_abs.clone() - f_pc_rel.clone() - f_pc_jnz) * (pc.clone() + size) // <=> pc_up = 0 : next_pc = pc + size // common case
- f_pc_abs * res.clone() // <=> pc_up = 1 : next_pc = res // absolute jump
- f_pc_rel * (pc + res), // <=> pc_up = 2 : next_pc = pc + res // relative jump
);
constraints
}
}
pub struct Transition<F>(PhantomData<F>);
impl<F> Argument<F> for Transition<F>
where
F: PrimeField,
{
const ARGUMENT_TYPE: ArgumentType = ArgumentType::Gate(GateType::CairoTransition);
const CONSTRAINTS: u32 = 3;
/// Generates the constraints for the Cairo transition
/// Accesses Curr and Next rows (Next only first 3 entries)
fn constraint_checks<T: ExprOps<F, BerkeleyChallengeTerm>>(
env: &ArgumentEnv<F, T>,
_cache: &mut Cache,
) -> Vec<T> {
// load computed updated registers
let pcup = env.witness_curr(7);
let apup = env.witness_curr(8);
let fpup = env.witness_curr(9);
// load next registers
let next_pc = env.witness_next(0);
let next_ap = env.witness_next(1);
let next_fp = env.witness_next(2);
// * Check equality (like a copy constraint)
let constraints: Vec<T> = vec![next_pc - pcup, next_ap - apup, next_fp - fpup];
constraints
}
}