tasm_lib/arithmetic/u128/safe_mul.rs
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use std::collections::HashMap;
use triton_vm::prelude::*;
use crate::prelude::*;
use crate::traits::basic_snippet::Reviewer;
use crate::traits::basic_snippet::SignOffFingerprint;
/// Multiply two `u128`s and crash on overflow.
///
/// ### Behavior
///
/// ```text
/// BEFORE: _ [right: u128] [left: u128]
/// AFTER: _ [left · right: u128]
/// ```
///
/// ### Preconditions
///
/// - all input arguments are properly [`BFieldCodec`] encoded
/// - the product of `left` and `right` is less than or equal to [`u128::MAX`]
///
/// ### Postconditions
///
/// - the output is the product of the input
/// - the output is properly [`BFieldCodec`] encoded
#[derive(Debug, Default, Copy, Clone, Eq, PartialEq, Hash)]
pub struct SafeMul;
impl BasicSnippet for SafeMul {
fn inputs(&self) -> Vec<(DataType, String)> {
["right", "left"]
.map(|side| (DataType::U128, side.to_string()))
.to_vec()
}
fn outputs(&self) -> Vec<(DataType, String)> {
vec![(DataType::U128, "product".to_string())]
}
fn entrypoint(&self) -> String {
"tasmlib_arithmetic_u128_safe_mul".to_string()
}
fn code(&self, _: &mut Library) -> Vec<LabelledInstruction> {
triton_asm!(
// BEFORE: _ r_3 r_2 r_1 r_0 l_3 l_2 l_1 l_0
// AFTER: _ p_3 p_2 p_1 p_0
{self.entrypoint()}:
/*
* p_0 is low limb, c_0 high limb of
* l_0·r_0
*
* p_1 is low limb, c_1 high limb of
* (l_1·r_0)_lo + (l_0·r_1)_lo
* + c_0
*
* p_2 is low limb, c_2 high limb of
* (l_1·r_0)_hi + (l_0·r_1)_hi
* + (l_2·r_0)_lo + (l_1·r_1)_lo + (l_0·r_2)_lo
* + c_1
*
* p_3 is low limb, c_3 high limb of
* (l_2·r_0)_hi + (l_1·r_1)_hi + (l_0·r_2)_hi
* + (l_3·r_0)_lo + (l_2·r_1)_lo + (l_1·r_2)_lo + (l_0·r_3)_lo
* + c_2
*
* All remaining limb combinations (l_3·r_1, l_3·r_2, l_3·r_3 l_2·r_2,
* l_2·r_3, and l_1·r_3) as well as c_3 must be 0.
*/
/* p_0 */
dup 0 dup 5 mul split
// _ r_3 r_2 r_1 r_0 l_3 l_2 l_1 l_0 c_0 p_0
place 9
// _ p_0 r_3 r_2 r_1 r_0 l_3 l_2 l_1 l_0 c_0
/* p_1 */
dup 2 dup 6 mul split
// _ p_0 r_3 r_2 r_1 r_0 l_3 l_2 l_1 l_0 c_0 (l_1·r_0)_hi (l_1·r_0)_lo
dup 3 dup 9 mul split
// _ p_0 r_3 r_2 r_1 r_0 l_3 l_2 l_1 l_0 c_0 (l_1·r_0)_hi (l_1·r_0)_lo (l_0·r_1)_hi (l_0·r_1)_lo
// ^^^ ^^^^^^^^^^^^ ^^^^^^^^^^^^
pick 2 pick 4
add add
split
// _ p_0 r_3 r_2 r_1 r_0 l_3 l_2 l_1 l_0 (l_1·r_0)_hi (l_0·r_1)_hi c_1 p_1
place 12
// _ p_1 p_0 r_3 r_2 r_1 r_0 l_3 l_2 l_1 l_0 (l_1·r_0)_hi (l_0·r_1)_hi c_1
/* p_2 */
add add
// _ p_1 p_0 r_3 r_2 r_1 r_0 l_3 l_2 l_1 l_0 p_2_wip
dup 3 dup 6 mul split
// _ p_1 p_0 r_3 r_2 r_1 r_0 l_3 l_2 l_1 l_0 p_2_wip (l_2·r_0)_hi (l_2·r_0)_lo
dup 4 dup 9 mul split
// _ p_1 p_0 r_3 r_2 r_1 r_0 l_3 l_2 l_1 l_0 p_2_wip (l_2·r_0)_hi (l_2·r_0)_lo (l_1·r_1)_hi (l_1·r_1)_lo
dup 5 dup 12 mul split
// _ p_1 p_0 r_3 r_2 r_1 r_0 l_3 l_2 l_1 l_0 p_2_wip (l_2·r_0)_hi (l_2·r_0)_lo (l_1·r_1)_hi (l_1·r_1)_lo (l_0·r_2)_hi (l_0·r_2)_lo
// ^^^^^^^ ^^^^^^^^^^^^ ^^^^^^^^^^^^ ^^^^^^^^^^^^
pick 2 pick 4 pick 6
add add add
split
// _ p_1 p_0 r_3 r_2 r_1 r_0 l_3 l_2 l_1 l_0 (l_2·r_0)_hi (l_1·r_1)_hi (l_0·r_2)_hi c_2 p_2
place 14
// _ p_2 p_1 p_0 r_3 r_2 r_1 r_0 l_3 l_2 l_1 l_0 (l_2·r_0)_hi (l_1·r_1)_hi (l_0·r_2)_hi c_2
/* p_3 */
add add add
// _ p_2 p_1 p_0 r_3 r_2 r_1 r_0 l_3 l_2 l_1 l_0 p_3_wip
dup 4 pick 6 mul split
// _ p_2 p_1 p_0 r_3 r_2 r_1 l_3 l_2 l_1 l_0 p_3_wip (l_3·r_0)_hi (l_3·r_0)_lo
dup 5 dup 8 mul split
// _ p_2 p_1 p_0 r_3 r_2 r_1 l_3 l_2 l_1 l_0 p_3_wip (l_3·r_0)_hi (l_3·r_0)_lo (l_2·r_1)_hi (l_2·r_1)_lo
dup 6 dup 11 mul split
// _ p_2 p_1 p_0 r_3 r_2 r_1 l_3 l_2 l_1 l_0 p_3_wip (l_3·r_0)_hi (l_3·r_0)_lo (l_2·r_1)_hi (l_2·r_1)_lo (l_1·r_2)_hi (l_1·r_2)_lo
pick 7 dup 13 mul split
// _ p_2 p_1 p_0 r_3 r_2 r_1 l_3 l_2 l_1 p_3_wip (l_3·r_0)_hi (l_3·r_0)_lo (l_2·r_1)_hi (l_2·r_1)_lo (l_1·r_2)_hi (l_1·r_2)_lo (l_0·l_3)_hi (l_0·l_3)_lo
// ^^^^^^^ ^^^^^^^^^^^^ ^^^^^^^^^^^^ ^^^^^^^^^^^^ ^^^^^^^^^^^^
pick 2 pick 4 pick 6 pick 8
add add add add
split
// _ p_2 p_1 p_0 r_3 r_2 r_1 l_3 l_2 l_1 (l_3·r_0)_hi (l_2·r_1)_hi (l_1·r_2)_hi (l_0·l_3)_hi c_3 p_3
place 14
// _ [p; 4] r_3 r_2 r_1 l_3 l_2 l_1 (l_3·r_0)_hi (l_2·r_1)_hi (l_1·r_2)_hi (l_0·l_3)_hi c_3
/* overflow checks
*
* Carry c_3 and the high limbs still on stack are guaranteed to be smaller than
* 2^32 since they resulted from instruction `split`. The sum of those 5 elements
* cannot “wrap around” `BFieldElement::P`.
*/
add add add add
push 0 eq assert error_id 500
// _ [p; 4] r_3 r_2 r_1 l_3 l_2 l_1
/* l_3·r_1 */
dup 2 pick 4 mul
push 0 eq assert error_id 501
// _ [p; 4] r_3 r_2 l_3 l_2 l_1
/* l_2·r_2 */
dup 1 dup 4 mul
push 0 eq assert error_id 502
// _ [p; 4] r_3 r_2 l_3 l_2 l_1
/* l_1·r_3 */
dup 4 mul
push 0 eq assert error_id 503
// _ [p; 4] r_3 r_2 l_3 l_2
/* l_3·r_2 */
dup 1 pick 3 mul
push 0 eq assert error_id 504
// _ [p; 4] r_3 l_3 l_2
/* l_2·r_3 */
dup 2 mul
push 0 eq assert error_id 505
// _ [p; 4] r_3 l_3
/* l_3·r_3 */
mul
push 0 eq assert error_id 506
// _ [p; 4]
return
)
}
fn sign_offs(&self) -> HashMap<Reviewer, SignOffFingerprint> {
let mut sign_offs = HashMap::new();
sign_offs.insert(Reviewer("ferdinand"), 0x6a6ab0928dd2f0e4.into());
sign_offs
}
}
#[cfg(test)]
mod tests {
use super::*;
use crate::test_prelude::*;
use rand::rngs::StdRng;
impl SafeMul {
fn test_assertion_failure(&self, left: u128, right: u128, error_ids: &[i128]) {
test_assertion_failure(
&ShadowedClosure::new(Self),
InitVmState::with_stack(self.set_up_test_stack((right, left))),
error_ids,
);
}
}
impl Closure for SafeMul {
type Args = (u128, u128);
fn rust_shadow(&self, stack: &mut Vec<BFieldElement>) {
let (right, left) = pop_encodable::<Self::Args>(stack);
let product = left.checked_mul(right).unwrap();
push_encodable(stack, &product);
}
fn pseudorandom_args(
&self,
seed: [u8; 32],
bench_case: Option<BenchmarkCase>,
) -> Self::Args {
let Some(bench_case) = bench_case else {
let mut rng = StdRng::from_seed(seed);
let left = rng.random_range(1..=u128::MAX);
let right = rng.random_range(0..=u128::MAX / left);
return (right, left);
};
match bench_case {
BenchmarkCase::CommonCase => (1 << 63, (1 << 45) - 1),
BenchmarkCase::WorstCase => (1 << 63, (1 << 63) - 1),
}
}
fn corner_case_args(&self) -> Vec<Self::Args> {
const LEFT_NOISE: u128 = 0xfd4e_3f84_8677_df6b_da64_b83c_8267_c72d;
const RIGHT_NOISE: u128 = 0x538e_e051_c430_3e7a_0a29_a45a_5efb_67fa;
(0..u128::BITS)
.cartesian_product(0..u128::BITS)
.map(|(l, r)| {
let left = (1 << l) | ((1 << l) - 1) & LEFT_NOISE;
let right = (1 << r) | ((1 << r) - 1) & RIGHT_NOISE;
(right, left)
})
.filter(|&(right, left)| left.checked_mul(right).is_some())
.step_by(5) // test performance is atrocious otherwise
.chain([(0, 0)])
.collect()
}
}
#[test]
fn rust_shadow() {
ShadowedClosure::new(SafeMul).test();
}
#[test]
fn overflow_crashes_vm() {
SafeMul.test_assertion_failure(1 << 127, 1 << 1, &[500]);
SafeMul.test_assertion_failure(1 << 96, 1 << 32, &[501]);
SafeMul.test_assertion_failure(1 << 64, 1 << 64, &[502]);
SafeMul.test_assertion_failure(1 << 32, 1 << 96, &[503]);
SafeMul.test_assertion_failure(1 << 96, 1 << 64, &[504]);
SafeMul.test_assertion_failure(1 << 64, 1 << 96, &[505]);
SafeMul.test_assertion_failure(1 << 96, 1 << 96, &[506]);
for i in 1..64 {
let left = u128::MAX >> i;
let right = (1 << i) + 1;
SafeMul.test_assertion_failure(left, right, &[500]);
SafeMul.test_assertion_failure(right, left, &[500]);
}
for i in 1..128 {
let left = 1 << i;
let right = 1 << (128 - i);
SafeMul.test_assertion_failure(left, right, &[500, 501, 502, 503]);
}
}
#[proptest(cases = 1_000)]
fn arbitrary_overflow_crashes_vm(
#[strategy(2_u128..)] left: u128,
#[strategy(u128::MAX / #left + 1..)] right: u128,
) {
SafeMul.test_assertion_failure(left, right, &[500, 501, 502, 503, 504, 505, 506]);
}
}
#[cfg(test)]
mod benches {
use super::*;
use crate::test_prelude::*;
#[test]
fn benchmark() {
ShadowedClosure::new(SafeMul).bench();
}
}