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//! This module represents a run of a Cairo program as a series of consecutive
//! execution steps, each of which define the execution logic of Cairo instructions
use crate::{
flags::*,
memory::CairoMemory,
word::{CairoWord, FlagBits, FlagSets, Offsets},
};
use ark_ff::Field;
/// A structure to store program counter, allocation pointer and frame pointer
#[derive(Clone, Copy)]
pub struct CairoState<F> {
/// Program counter: points to address in memory
pc: F,
/// Allocation pointer: points to first free space in memory
ap: F,
/// Frame pointer: points to the beginning of the stack in memory (for arguments)
fp: F,
}
/// This trait contains functions to obtain the Cairo pointers (program counter, allocation pointer and frame pointer)
pub trait Pointers<F> {
/// Returns the program counter
fn pc(&self) -> F;
/// Returns the allocation pointer
fn ap(&self) -> F;
/// Returns the frame pointer
fn fp(&self) -> F;
}
impl<F: Field> CairoState<F> {
/// Creates a new triple of pointers
pub fn new(pc: F, ap: F, fp: F) -> Self {
CairoState { pc, ap, fp }
}
}
impl<F: Field> Pointers<F> for CairoState<F> {
fn pc(&self) -> F {
self.pc
}
fn ap(&self) -> F {
self.ap
}
fn fp(&self) -> F {
self.fp
}
}
#[derive(Clone, Copy)]
/// A structure to store auxiliary variables throughout computation
pub struct CairoContext<F> {
/// Destination
dst: Option<F>,
/// First operand
op0: Option<F>,
/// Second operand
op1: Option<F>,
/// Result
res: Option<F>,
/// Destination address
adr_dst: F,
/// First operand address
adr_op0: F,
/// Second operand address
adr_op1: F,
/// Size of the instruction
size: F,
}
impl<F: Field> Default for CairoContext<F> {
/// This function creates an instance of a default [CairoContext] struct
fn default() -> Self {
Self {
dst: None,
op0: None,
op1: None,
res: None,
adr_dst: F::zero(),
adr_op0: F::zero(),
adr_op1: F::zero(),
size: F::zero(),
}
}
}
#[derive(Clone, Copy)]
/// This structure stores all the needed information relative to an instruction at a given step of computation
pub struct CairoInstruction<F> {
/// instruction word
word: CairoWord<F>,
/// pointers
ptrs: CairoState<F>,
/// auxiliary variables
vars: CairoContext<F>,
}
impl<F: Field> CairoInstruction<F> {
/// Creates a [CairoInstruction]
pub fn new(word: CairoWord<F>, ptrs: CairoState<F>, vars: CairoContext<F>) -> Self {
Self { word, ptrs, vars }
}
/// Returns the field element corresponding to the [CairoInstruction]
pub fn instr(&self) -> F {
self.word.word()
}
/// Returns the size of the instruction
pub fn size(&self) -> F {
self.vars.size
}
/// Returns the result of the instruction
pub fn res(&self) -> F {
self.vars.res.expect("None res")
}
/// Returns the destination of the instruction
pub fn dst(&self) -> F {
self.vars.dst.expect("None dst")
}
/// Returns the first operand of the instruction
pub fn op0(&self) -> F {
self.vars.op0.expect("None op0")
}
/// Returns the second operand of the instruction
pub fn op1(&self) -> F {
self.vars.op1.expect("None op1")
}
/// Returns the destination address of the instruction
pub fn adr_dst(&self) -> F {
self.vars.adr_dst
}
/// Returns the first operand address of the instruction
pub fn adr_op0(&self) -> F {
self.vars.adr_op0
}
/// Returns the second operand address of the instruction
pub fn adr_op1(&self) -> F {
self.vars.adr_op1
}
}
impl<F: Field> Pointers<F> for CairoInstruction<F> {
fn pc(&self) -> F {
self.ptrs.pc // Returns the current program counter
}
fn ap(&self) -> F {
self.ptrs.ap //Returns the current allocation pointer
}
fn fp(&self) -> F {
self.ptrs.fp // Returns the current program counter
}
}
impl<F: Field> Offsets<F> for CairoInstruction<F> {
fn off_dst(&self) -> F {
self.word.off_dst()
}
fn off_op0(&self) -> F {
self.word.off_op0()
}
fn off_op1(&self) -> F {
self.word.off_op1()
}
}
impl<F: Field> FlagBits<F> for CairoInstruction<F> {
fn f_dst_fp(&self) -> F {
self.word.f_dst_fp()
}
fn f_op0_fp(&self) -> F {
self.word.f_op0_fp()
}
fn f_op1_val(&self) -> F {
self.word.f_op1_val()
}
fn f_op1_fp(&self) -> F {
self.word.f_op1_fp()
}
fn f_op1_ap(&self) -> F {
self.word.f_op1_ap()
}
fn f_res_add(&self) -> F {
self.word.f_res_add()
}
fn f_res_mul(&self) -> F {
self.word.f_res_mul()
}
fn f_pc_abs(&self) -> F {
self.word.f_pc_abs()
}
fn f_pc_rel(&self) -> F {
self.word.f_pc_rel()
}
fn f_pc_jnz(&self) -> F {
self.word.f_pc_jnz()
}
fn f_ap_add(&self) -> F {
self.word.f_ap_add()
}
fn f_ap_one(&self) -> F {
self.word.f_ap_one()
}
fn f_opc_call(&self) -> F {
self.word.f_opc_call()
}
fn f_opc_ret(&self) -> F {
self.word.f_opc_ret()
}
fn f_opc_aeq(&self) -> F {
self.word.f_opc_aeq()
}
fn f15(&self) -> F {
self.word.f15()
}
}
/// A data structure to store a current step of Cairo computation
pub struct CairoStep<'a, F> {
/// state of the computation
pub mem: &'a mut CairoMemory<F>,
// comment instr for efficiency
/// current pointers
pub curr: CairoState<F>,
/// (if any) next pointers
pub next: Option<CairoState<F>>,
/// state auxiliary variables
pub vars: CairoContext<F>,
}
impl<'a, F: Field> CairoStep<'a, F> {
/// Creates a new Cairo execution step from a step index, a Cairo word, and current pointers
pub fn new(mem: &mut CairoMemory<F>, ptrs: CairoState<F>) -> CairoStep<F> {
CairoStep {
mem,
curr: ptrs,
next: None,
vars: CairoContext::default(),
}
}
/// Executes a Cairo step from the current registers
pub fn execute(&mut self) -> CairoInstruction<F> {
// This order is important in order to allocate the memory in time
self.set_op0();
self.set_op1();
self.set_res();
self.set_dst();
// If the Option<> is not a guarantee for continuation of the program, we may be removing this
let next_pc = self.next_pc();
let (next_ap, next_fp) = self.next_apfp();
self.next = Some(CairoState::new(
next_pc.expect("Empty next program counter"),
next_ap.expect("Empty next allocation pointer"),
next_fp.expect("Empty next frame pointer"),
));
CairoInstruction::new(self.instr(), self.curr, self.vars)
}
/// This function returns the current word instruction being executed
pub fn instr(&mut self) -> CairoWord<F> {
CairoWord::new(self.mem.read(self.curr.pc).expect("pc points to None cell"))
}
/// This function computes the first operand address
pub fn set_op0(&mut self) {
let reg = match self.instr().op0_reg() {
/*0*/ OP0_AP => self.curr.ap, // reads first word from allocated memory
/*1*/ _ => self.curr.fp, // reads first word from input stack
}; // no more values than 0 and 1 because op0_reg is one bit
self.vars.adr_op0 = reg + self.instr().off_op0();
self.vars.op0 = self.mem.read(self.vars.adr_op0);
}
/// This function computes the second operand address and content and the instruction size
/// Panics if the flagset `OP1_SRC` has more than 1 nonzero bit
pub fn set_op1(&mut self) {
let (reg, size) = match self.instr().op1_src() {
/*0*/
OP1_DBL => (self.vars.op0.expect("None op0 for OP1_DBL"), F::one()), // double indexing, op0 should be positive for address
/*1*/
OP1_VAL => (self.curr.pc, F::from(2u32)), // off_op1 will be 1 and then op1 contains an immediate value
/*2*/ OP1_FP => (self.curr.fp, F::one()),
/*4*/ OP1_AP => (self.curr.ap, F::one()),
_ => panic!("Invalid op1_src flagset"),
};
self.vars.size = size;
self.vars.adr_op1 = reg + self.instr().off_op1(); // apply second offset to corresponding register
self.vars.op1 = self.mem.read(self.vars.adr_op1);
}
/// This function computes the value of the result of the arithmetic operation
/// Panics if a `jnz` instruction is used with an invalid format
/// or if the flagset `RES_LOG` has more than 1 nonzero bit
pub fn set_res(&mut self) {
if self.instr().pc_up() == PC_JNZ {
/*4*/
// jnz instruction
if self.instr().res_log() == RES_ONE /*0*/
&& self.instr().opcode() == OPC_JMP_INC /*0*/
&& self.instr().ap_up() != AP_ADD
/* not 1*/
{
self.vars.res = Some(F::zero()); // "unused"
} else {
panic!("Invalid JNZ instruction");
}
} else if self.instr().pc_up() == PC_SIZ /*0*/
|| self.instr().pc_up() == PC_ABS /*1*/
|| self.instr().pc_up() == PC_REL
/*2*/
{
// rest of types of updates
// common increase || absolute jump || relative jump
match self.instr().res_log() {
/*0*/
RES_ONE => self.vars.res = self.vars.op1, // right part is single operand
/*1*/
RES_ADD => {
self.vars.res = Some(
self.vars.op0.expect("None op0 after RES_ADD")
+ self.vars.op1.expect("None op1 after RES_ADD"),
)
} // right part is addition
/*2*/
RES_MUL => {
self.vars.res = Some(
self.vars.op0.expect("None op0 after RES_MUL")
* self.vars.op1.expect("None op1 after RES_MUL"),
)
} // right part is multiplication
_ => panic!("Invalid res_log flagset"),
}
} else {
// multiple bits take value 1
panic!("Invalid pc_up flagset");
}
}
/// This function computes the destination address
pub fn set_dst(&mut self) {
let reg = match self.instr().dst_reg() {
/*0*/ DST_AP => self.curr.ap, // read from stack
/*1*/ _ => self.curr.fp, // read from parameters
}; // no more values than 0 and 1 because op0_reg is one bit
self.vars.adr_dst = reg + self.instr().off_dst();
self.vars.dst = self.mem.read(self.vars.adr_dst);
}
/// This function computes the next program counter
/// Panics if the flagset `PC_UP` has more than 1 nonzero bit
pub fn next_pc(&mut self) -> Option<F> {
match self.instr().pc_up() {
/*0*/
PC_SIZ => Some(self.curr.pc + self.vars.size), // common case, next instruction is right after the current one
/*1*/
PC_ABS => Some(self.vars.res.expect("None res after PC_ABS")), // absolute jump, next instruction is in res,
/*2*/
PC_REL => Some(self.curr.pc + self.vars.res.expect("None res after PC_REL")), // relative jump, go to some address relative to pc
/*4*/
PC_JNZ => {
// conditional relative jump (jnz)
if self.vars.dst == Some(F::zero()) {
Some(self.curr.pc + self.vars.size) // if condition false, common case
} else {
// if condition true, relative jump with second operand
Some(self.curr.pc + self.vars.op1.expect("None op1 after PC_JNZ"))
}
}
_ => panic!("Invalid pc_up flagset"),
}
}
/// This function computes the next values of the allocation and frame pointers
/// Panics if in a `call` instruction the flagset [AP_UP] is incorrect
/// or if in any other instruction the flagset AP_UP has more than 1 nonzero bit
/// or if the flagset `OPCODE` has more than 1 nonzero bit
fn next_apfp(&mut self) -> (Option<F>, Option<F>) {
let (next_ap, next_fp);
// The following branches don't include the assertions. That is done in the verification.
if self.instr().opcode() == OPC_CALL {
/*1*/
// "call" instruction
self.mem.write(self.curr.ap, self.curr.fp); // Save current fp
self.vars.dst = self.mem.read(self.curr.ap); // update dst content
self.mem
.write(self.curr.ap + F::one(), self.curr.pc + self.vars.size); // Save next instruction
self.vars.op0 = self.mem.read(self.curr.ap + F::one()); //update op0 content
// Update fp
next_fp = Some(self.curr.ap + F::from(2u32)); // pointer for next frame is after current fp and instruction after call
// Update ap
match self.instr().ap_up() {
/*0*/
AP_Z2 => next_ap = Some(self.curr.ap + F::from(2u32)), // two words were written so advance 2 positions
_ => panic!("ap increment in call instruction"), // ap increments not allowed in call instructions
};
} else if self.instr().opcode() == OPC_JMP_INC /*0*/
|| self.instr().opcode() == OPC_RET /*2*/
|| self.instr().opcode() == OPC_AEQ
/*4*/
{
// rest of types of instruction
// jumps and increments || return || assert equal
match self.instr().ap_up() {
/*0*/ AP_Z2 => next_ap = Some(self.curr.ap), // no modification on ap
/*1*/
AP_ADD => {
// ap += <op> should be larger than current ap
next_ap = Some(self.curr.ap + self.vars.res.expect("None res after AP_ADD"))
}
/*2*/ AP_ONE => next_ap = Some(self.curr.ap + F::one()), // ap++
_ => panic!("Invalid ap_up flagset"),
}
match self.instr().opcode() {
/*0*/
OPC_JMP_INC => next_fp = Some(self.curr.fp), // no modification on fp
/*2*/
OPC_RET => next_fp = Some(self.vars.dst.expect("None dst after OPC_RET")), // ret sets fp to previous fp that was in [ap-2]
/*4*/
OPC_AEQ => {
// The following conditional is a fix that is not explained in the whitepaper
// The goal is to distinguish two types of ASSERT_EQUAL where one checks that
// dst = res , but in order for this to be true, one sometimes needs to write
// the res in mem(adr_dst) and sometimes write dst in mem(res_dir). The only
// case where res can be None is when res = op1 and thus res_dir = adr_op1
if self.vars.res.is_none() {
// res = dst
self.mem.write(
self.vars.adr_op1,
self.vars.dst.expect("None dst after OPC_AEQ"),
);
// update the value of the variable as well
self.vars.op1 = self.mem.read(self.vars.adr_op1);
self.vars.res = self.mem.read(self.vars.adr_op1);
} else {
// dst = res
self.mem.write(
self.vars.adr_dst,
self.vars.res.expect("None res after OPC_AEQ"),
);
// update the value of the variable as well
self.vars.dst = self.mem.read(self.vars.adr_dst);
}
next_fp = Some(self.curr.fp); // no modification on fp
}
_ => {
panic!("This case must never happen")
}
}
} else {
panic!("Invalid opcode flagset");
}
(next_ap, next_fp)
}
}
/// This struct stores the needed information to run a program
pub struct CairoProgram<'a, F> {
/// total number of steps
pub steps: F,
/// full execution memory
pub mem: &'a mut CairoMemory<F>,
/// initial computation registers
pub ini: CairoState<F>,
/// final computation pointers
pub fin: CairoState<F>,
/// execution trace as a vector of [CairoInstruction]
pub trace: Vec<CairoInstruction<F>>,
}
impl<'a, F: Field> CairoProgram<'a, F> {
/// Creates a Cairo execution from the public information (memory and initial pointers)
pub fn new(mem: &mut CairoMemory<F>, pc: u64) -> CairoProgram<F> {
let ap = mem.len();
let mut prog = CairoProgram {
steps: F::zero(),
mem,
ini: CairoState::new(F::from(pc), F::from(ap), F::from(ap)),
fin: CairoState::new(F::zero(), F::zero(), F::zero()),
trace: Vec::new(),
};
prog.execute();
prog
}
/// Outputs the total number of steps of the execution carried out by the runner
pub fn steps(&self) -> F {
self.steps
}
/// Outputs the initial value of the pointers after the execution carried out by the runner
pub fn ini(&self) -> CairoState<F> {
self.ini
}
/// Outputs the final value of the pointers after the execution carried out by the runner
pub fn fin(&self) -> CairoState<F> {
self.fin
}
/// Returns a reference to the set of instructions
pub fn trace(&self) -> &Vec<CairoInstruction<F>> {
&self.trace
}
/// This function simulates an execution of the Cairo program received as input.
/// It generates the full memory stack and the execution trace
fn execute(&mut self) {
// set finishing flag to false, as it just started
let mut end = false;
// saves local copy of the initial (claimed) pointers of the program
let mut curr = self.ini;
let mut next = self.ini;
// first timestamp
let mut n: u64 = 0;
// keep executing steps until the end is reached
while !end {
// create current step of computation
let mut step = CairoStep::new(self.mem, next);
// save current value of the pointers
curr = step.curr;
// execute current step and increase time counter
let instr = step.execute();
self.trace.push(instr);
n += 1;
match step.next {
None => end = true, // if find no next pointers, end
_ => {
// if there are next pointers
end = false;
// update next value of pointers
next = step.next.expect("Empty next pointers");
if curr.ap <= next.pc {
// if reading from unallocated memory, end
end = true;
}
}
}
}
self.steps = F::from(n);
self.fin = CairoState::new(curr.pc, curr.ap, curr.fp);
}
}