tasm_lib/list/multiset_equality_digests.rs
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use triton_vm::prelude::*;
use crate::data_type::DataType;
use crate::hashing::algebraic_hasher::hash_varlen::HashVarlen;
use crate::library::Library;
use crate::list::length::Length;
use crate::traits::basic_snippet::BasicSnippet;
/// Determine whether two lists are equal up to permutation.
///
/// The lists are given as lists of digests. This function uses hashing
/// to compute a challenge indeterminate, and then computes a running
/// products for both lists. In the future, the implementation of
/// function may be replaced by one that uses Triton VM's native
/// support for permutation checks instead of Fiat-Shamir and running
/// products.
#[derive(Debug, Default, Copy, Clone, Eq, PartialEq, Hash)]
pub struct MultisetEqualityDigests;
impl BasicSnippet for MultisetEqualityDigests {
fn inputs(&self) -> Vec<(DataType, String)> {
vec![
(DataType::List(Box::new(DataType::Digest)), "a".to_owned()),
(DataType::List(Box::new(DataType::Digest)), "b".to_owned()),
]
}
fn outputs(&self) -> Vec<(DataType, String)> {
vec![(DataType::Bool, "equal_multisets".to_owned())]
}
fn entrypoint(&self) -> String {
"tasmlib_list_multiset_equality_digests".to_owned()
}
fn code(&self, library: &mut Library) -> Vec<LabelledInstruction> {
let entrypoint = self.entrypoint();
let length_snippet = library.import(Box::new(Length::new(DataType::Digest)));
let hash_varlen = library.import(Box::new(HashVarlen));
let early_abort_label = format!("{entrypoint}_early_abort");
let continue_label = format!("{entrypoint}_continue");
let running_product_label = format!("{entrypoint}_running_product");
let running_product_loop_label = format!("{entrypoint}_running_product_loop");
triton_asm!(
// BEFORE: _ *list_a *list_b
// AFTER: _ list_a==list_b (as multisets, or up to permutation)
{entrypoint}:
// read lengths of lists
dup 1 dup 1 // _ *list_a *list_b *list_a *list_b
call {length_snippet} // _ *list_a *list_b *list_a len_b
swap 1 // _ *list_a *list_b len_b *list_a
call {length_snippet} // _ *list_a *list_b len_b len_a
// equate lengths and return early if possible
dup 1 // _ *list_a *list_b len_b len_a len_b
eq // _ *list_a *list_b len_b (len_a==len_b)
push 0 eq // _ *list_a *list_b len_b (len_a!=len_b)
// early return if lengths mismatch
// otherwise continue
push 1 swap 1 // _ *list_a *list_b len_b 1 (len_a!=len_b)
skiz call {early_abort_label}
skiz call {continue_label}
// _ (list_a == list_b) (as multisets, or up to permutation)
return
{early_abort_label}:
// _ *list_a *list_b len_b 1
pop 4
// push return value (false)
push 0 // _ 0
// ensure `else` branch is not taken
push 0
return
{continue_label}:
// _ *list_a *list_b len
// hash list_a
dup 2 // _ *list_a *list_b len *list_a
push 1 add // _ *list_a *list_b len *list_a[0]
dup 1 // _ *list_a *list_b len *list_a[0] len
push {Digest::LEN} mul // _ *list_a *list_b len *list_a[0] (len*{Digest::LEN})
call {hash_varlen} // _ *list_a *list_b len da4 da3 da2 da1 da0
// hash list_b
dup 6 // _ *list_a *list_b len da4 da3 da2 da1 da0 *list_b
push 1 add // _ *list_a *list_b len *list_b[0]
dup 6 // _ *list_a *list_b len da4 da3 da2 da1 da0 *list_b[0] len
push {Digest::LEN} mul // _ *list_a *list_b len da4 da3 da2 da1 da0 *list_b[0] (len*{Digest::LEN})
call {hash_varlen} // _ *list_a *list_b len da4 da3 da2 da1 da0 db4 db3 db2 db1 db0
// hash together
hash
// _ *list_a *list_b len d4 d3 d2 d1 d0
// Get 2nd challenge
push 0
push 0
push 0
push 0
push 0
dup 9
dup 9
dup 9
dup 9
dup 9
// _ *list_a *list_b len d4 d3 d2 d1 d0 0 0 0 0 0 d4 d3 d2 d1 d0
hash
// _ *list_a *list_b len d4 d3 d2 d1 d0 e4 e3 e2 e1 e0
pop 4
hint _x0: XFieldElement = stack[3..6]
hint x1: XFieldElement = stack[0..3]
// _ *list_a *list_b len d4 d3 d2 d1 d0 e4
// _ *list_a *list_b len [-x0] [x1] <- rename
call {running_product_label} // _ *list_a *list_b len [-x0] [x1] [rpb]
dup 11 // _ *list_a *list_b len [-x0] [x1] [rpb] *list_a
dup 10 // _ *list_a *list_b len [-x0] [x1] [rpb] *list_a len
dup 10 dup 10 dup 10 // _ *list_a *list_b len [-x0] [x1] [rpb] *list_a len [-x0]
dup 10 dup 10 dup 10 // _ *list_a *list_b len [-x0] [x1] [rpb] *list_a len [-x0] [x1]
call {running_product_label} // _ *list_a *list_b len [-x0] [x1] [rpb] *list_a len [-x0] [x1] [rpa]
// test equality
dup 11 // _ *list_a *list_b len [-x0] [x1] rpb2 rpb1 rpb0 *list_a len [-x0] [x1] rpa2 rpa1 rpa0 rpb0
eq // _ *list_a *list_b len [-x0] [x1] rpb2 rpb1 rpb0 *list_a len [-x0] [x1] rpa2 rpa1 rpa0==rpb0
swap 1 // _ *list_a *list_b len [-x0] [x1] rpb2 rpb1 rpb0 *list_a len [-x0] [x1] rpa2 rpa0==rpb0 rpa1
dup 12 // _ *list_a *list_b len [-x0] [x1] rpb2 rpb1 rpb0 *list_a len [-x0] [x1] rpa2 rpa0==rpb0 rpa1 rpb1
eq mul // _ *list_a *list_b len [-x0] [x1] rpb2 rpb1 rpb0 *list_a len [-x0] [x1] rpa2 rpa0==rpb0&&rpa1==rpb1
swap 1 // _ *list_a *list_b len [-x0] [x1] rpb2 rpb1 rpb0 *list_a len [-x0] [x1] rpa0==rpb0&&rpa1==rpb1 rpa2
dup 12 // _ *list_a *list_b len [-x0] [x1] rpb2 rpb1 rpb0 *list_a len [-x0] [x1] rpa0==rpb0&&rpa1==rpb1 rpa2 rpb2
eq mul // _ *list_a *list_b len [-x0] [x1] rpb2 rpb1 rpb0 *list_a len [-x0] [x1] rpa0==rpb0&&rpa1==rpb1&&rpa2==rpb2
// clean up and return
swap 14 // _ rpa0==rpb0&&rpa1==rpb1 rpa2 rpb2 *list_b len [-indeterminate] rpb2 rpb1 rpb0 *list_a len [-indeterminate] list_a
pop 5 pop 5 pop 4
// _ *list_a *list_b len [-x0] (rpa == rpb)
swap 6
pop 5
pop 1
// _ (rpa0==rpb0&&rpa1==rpb1)
return
// BEFORE: _ *list len [-x0] [x1]
// AFTER: _ *list len [-x0] [x1] rp2 rp1 rp0
{running_product_label}:
// initialize loop
dup 7 // _ *list len [-x0] [x1] *list
push 1 add // _ *list len [-x0] [x1] addr
dup 7 // _ *list len [-x0] [x1] addr itrs_left
push 0 push 0 push 1 // _ *list len [-x0] [x1] addr itrs_left [rp]
call {running_product_loop_label}
// _ *list len [-x0] [x1] addr* 0 [rp]
// clean up and return
swap 2
swap 4
pop 1
swap 2
pop 1
// _ *list len [-x0] [x1] [rp]
return
// INVARIANT: _ *list len [-x0] [x1] addr itrs_left [rp]
{running_product_loop_label}:
hint running_prod: XFieldElement = stack[0..3]
hint itrs_left = stack[3]
// test termination condition
dup 3 // _ *list len [-x0] [x1] addr itrs_left [rp] itrs_left
push 0 eq // _ *list len [-x0] [x1] addr itrs_left [rp] itrs_left==0
skiz return // _ *list len [-x0] [x1] addr itrs_left [rp]
// read two first words
dup 4 push {Digest::LEN - 1} add read_mem 2
// _ *list len [-x0] [x1] addr itrs_left [rp] m4 m3 (addr + 2)
swap 7
pop 1
// _ *list len [-x0] [x1] (addr + 2) itrs_left [rp] m4 m3
push 0
dup 10
dup 10
dup 10
// _ *list len [-x0] [x1] (addr + 2) itrs_left [rp] m4 m3 0 [x1]
xx_mul
// _ *list len [-x0] [x1] (addr + 2) itrs_left [rp] m4' m3' µ
// Read last three words
dup 7
read_mem 3
push {Digest::LEN + 1} add
swap 11
pop 1
// _ *list len [-x0] [x1] (addr + 5) itrs_left [rp] m4' m3' µ m2 m1 m0
xx_add
// _ *list len [-x0] [x1] (addr + 5) itrs_left [rp] [m']
// itrs_left -= 1
swap 6 push -1 add swap 6 // _ *list len [-x0] [x1] addr' itrs_left' [rp] [m']
// add x0
dup 13 dup 13 dup 13 // _ *list len [-x0] [x1] addr' itrs_left' [rp] [m'] [-x0]
xx_add // _ *list len [-x0] [x1] addr' itrs_left' [rp] [m' - x0]
// multiply into running product
xx_mul // _ *list len [-x0] [x1] addr' itrs_left' [rp']
recurse
)
}
}
#[cfg(test)]
mod tests {
use std::collections::HashMap;
use itertools::Itertools;
use num::One;
use rand::random;
use rand::rngs::StdRng;
use rand::Rng;
use rand::SeedableRng;
use tip5::Digest;
use twenty_first::math::other::random_elements;
use super::*;
use crate::empty_stack;
use crate::rust_shadowing_helper_functions;
use crate::rust_shadowing_helper_functions::list::load_list_with_copy_elements;
use crate::snippet_bencher::BenchmarkCase;
use crate::traits::function::Function;
use crate::traits::function::FunctionInitialState;
use crate::traits::function::ShadowedFunction;
use crate::traits::rust_shadow::RustShadow;
#[test]
fn prop_test() {
ShadowedFunction::new(MultisetEqualityDigests).test();
}
impl Function for MultisetEqualityDigests {
fn rust_shadow(
&self,
stack: &mut Vec<BFieldElement>,
memory: &mut HashMap<BFieldElement, BFieldElement>,
) {
let list_b_pointer = stack.pop().unwrap();
let list_a_pointer = stack.pop().unwrap();
let a: Vec<[BFieldElement; Digest::LEN]> =
load_list_with_copy_elements(list_a_pointer, memory);
let mut a = a.into_iter().map(Digest::new).collect_vec();
a.sort_unstable();
let b: Vec<[BFieldElement; Digest::LEN]> =
load_list_with_copy_elements(list_b_pointer, memory);
let mut b = b.into_iter().map(Digest::new).collect_vec();
b.sort_unstable();
// equate and push result to stack
let result = a == b;
stack.push(BFieldElement::new(result as u64));
}
fn pseudorandom_initial_state(
&self,
seed: [u8; 32],
bench_case: Option<BenchmarkCase>,
) -> FunctionInitialState {
match bench_case {
Some(BenchmarkCase::CommonCase) => self.random_equal_lists(2),
Some(BenchmarkCase::WorstCase) => self.random_equal_lists(100),
None => {
let mut rng: StdRng = SeedableRng::from_seed(seed);
let length = rng.gen_range(1..50);
let index = rng.gen_range(0..length);
let digest_word_index = rng.gen_range(0..Digest::LEN);
let another_length = length + rng.gen_range(1..10);
match rng.gen_range(0..=3) {
0 => self.random_equal_lists(length),
1 => self.random_unequal_lists(length),
2 => self.random_unequal_length_lists(length, another_length),
3 => {
self.random_lists_one_element_flipped(length, index, digest_word_index)
}
_ => unreachable!(),
}
}
}
}
fn corner_case_initial_states(&self) -> Vec<FunctionInitialState> {
let short_equal_multisets = (0..15).map(|i| self.random_equal_lists(i)).collect_vec();
let short_unequal_multisets =
(0..15).map(|i| self.random_unequal_lists(i)).collect_vec();
let mut short_lists_one_element_flipped = vec![];
for length in 1..7 {
for manipulated_element in 0..length {
for manipulated_word in 0..Digest::LEN {
short_lists_one_element_flipped.push(
self.random_lists_one_element_flipped(
length,
manipulated_element,
manipulated_word,
),
);
}
}
}
let unequal_lengths = vec![
self.random_unequal_length_lists(0, 5),
self.random_unequal_length_lists(0, 1),
self.random_unequal_length_lists(1, 0),
self.random_unequal_length_lists(5, 0),
self.random_unequal_length_lists(1, 2),
self.random_unequal_length_lists(2, 1),
self.random_unequal_length_lists(10, 17),
self.random_unequal_length_lists(21, 0),
];
[
short_equal_multisets,
short_unequal_multisets,
short_lists_one_element_flipped,
unequal_lengths,
]
.concat()
}
}
impl MultisetEqualityDigests {
fn random_equal_lists(&self, length: usize) -> FunctionInitialState {
let list_a: Vec<Digest> = random_elements(length);
let mut list_b = list_a.clone();
list_b.sort();
let pointer_a: BFieldElement = random();
let pointer_b: BFieldElement =
BFieldElement::new(pointer_a.value() + random::<u32>() as u64);
let mut memory: HashMap<BFieldElement, BFieldElement> = HashMap::new();
rust_shadowing_helper_functions::list::list_insert(pointer_a, list_a, &mut memory);
rust_shadowing_helper_functions::list::list_insert(pointer_b, list_b, &mut memory);
let stack = [empty_stack(), vec![pointer_a, pointer_b]].concat();
FunctionInitialState { stack, memory }
}
fn random_unequal_lists(&self, length: usize) -> FunctionInitialState {
let list_a: Vec<Digest> = random_elements(length);
let list_b: Vec<Digest> = random_elements(length);
let pointer_a: BFieldElement = random();
let pointer_b: BFieldElement =
BFieldElement::new(pointer_a.value() + random::<u32>() as u64);
let mut memory: HashMap<BFieldElement, BFieldElement> = HashMap::new();
rust_shadowing_helper_functions::list::list_insert(pointer_a, list_a, &mut memory);
rust_shadowing_helper_functions::list::list_insert(pointer_b, list_b, &mut memory);
let stack = [empty_stack(), vec![pointer_a, pointer_b]].concat();
FunctionInitialState { stack, memory }
}
fn random_unequal_length_lists(
&self,
length_a: usize,
length_b: usize,
) -> FunctionInitialState {
let list_a: Vec<Digest> = random_elements(length_a);
let list_b: Vec<Digest> = random_elements(length_b);
let pointer_a: BFieldElement = random();
let pointer_b: BFieldElement =
BFieldElement::new(pointer_a.value() + random::<u32>() as u64);
let mut memory: HashMap<BFieldElement, BFieldElement> = HashMap::new();
rust_shadowing_helper_functions::list::list_insert(pointer_a, list_a, &mut memory);
rust_shadowing_helper_functions::list::list_insert(pointer_b, list_b, &mut memory);
let stack = [empty_stack(), vec![pointer_a, pointer_b]].concat();
FunctionInitialState { stack, memory }
}
fn random_lists_one_element_flipped(
&self,
length: usize,
manipulated_index: usize,
manipulated_digest_word_index: usize,
) -> FunctionInitialState {
assert!(manipulated_index < length);
assert!(manipulated_digest_word_index < Digest::LEN);
let list_a: Vec<Digest> = random_elements(length);
let mut list_b = list_a.clone();
list_b.sort();
list_b[manipulated_index].0[manipulated_digest_word_index] += BFieldElement::one();
let pointer_a: BFieldElement = random();
let pointer_b: BFieldElement =
BFieldElement::new(pointer_a.value() + random::<u32>() as u64);
let mut memory: HashMap<BFieldElement, BFieldElement> = HashMap::new();
rust_shadowing_helper_functions::list::list_insert(pointer_a, list_a, &mut memory);
rust_shadowing_helper_functions::list::list_insert(pointer_b, list_b, &mut memory);
let stack = [empty_stack(), vec![pointer_a, pointer_b]].concat();
FunctionInitialState { stack, memory }
}
}
}
#[cfg(test)]
mod benches {
use super::*;
use crate::traits::function::ShadowedFunction;
use crate::traits::rust_shadow::RustShadow;
#[test]
fn multiset_eq_digests_benchmark() {
ShadowedFunction::new(MultisetEqualityDigests).bench();
}
}