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Balancer Stable Math: calculate_invariant_v2 #368

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merged 8 commits into from
Jul 19, 2022
Merged

Balancer Stable Math: calculate_invariant_v2 #368

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ffa7996
update stable math implementation
bh2smith Jul 14, 2022
a648fc3
fix operational error
bh2smith Jul 16, 2022
7df8657
remove unnecessary use of rounded div
bh2smith Jul 16, 2022
8a1785e
fix test
bh2smith Jul 18, 2022
47d8280
rewire calculate invariant to support both implementations
bh2smith Jul 18, 2022
8e76a2d
cargo fmt --all
bh2smith Jul 18, 2022
fd8de16
Merge branch 'main' into stable-math-update
bh2smith Jul 19, 2022
52499f6
remove old invariant calculation
bh2smith Jul 19, 2022
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30 changes: 0 additions & 30 deletions crates/shared/src/sources/balancer_v2/swap/math.rs
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Original file line number Diff line number Diff line change
Expand Up @@ -41,40 +41,10 @@ impl BalU256 for U256 {
}
}

pub fn rounded_div(numerator: U256, denominator: U256, round_up: bool) -> Result<U256, Error> {
if round_up {
numerator.bdiv_up(denominator)
} else {
numerator.bdiv_down(denominator)
}
}

#[cfg(test)]
mod tests {
use super::*;

#[test]
fn rounded_div_ok() {
assert_eq!(rounded_div(1.into(), 2.into(), true).unwrap(), 1.into());
assert_eq!(rounded_div(1.into(), 2.into(), false).unwrap(), 0.into());
}

#[test]
fn rounded_div_err() {
assert_eq!(
rounded_div(1.into(), 0.into(), true)
.unwrap_err()
.to_string(),
"BAL#004: ZeroDivision"
);
assert_eq!(
rounded_div(1.into(), 0.into(), false)
.unwrap_err()
.to_string(),
"BAL#004: ZeroDivision"
);
}

#[test]
fn bmul_tests() {
let zero = U256::zero();
Expand Down
93 changes: 35 additions & 58 deletions crates/shared/src/sources/balancer_v2/swap/stable_math.rs
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Original file line number Diff line number Diff line change
Expand Up @@ -5,23 +5,16 @@
//! https://github.com/balancer-labs/balancer-v2-monorepo/blob/stable-deployment/pkg/pool-stable/contracts/StableMath.sol

use super::error::Error;
use crate::sources::balancer_v2::swap::{
fixed_point::Bfp,
math::{rounded_div, BalU256},
};
use crate::sources::balancer_v2::swap::{fixed_point::Bfp, math::BalU256};
use ethcontract::U256;
use lazy_static::lazy_static;

lazy_static! {
static ref AMP_PRECISION: U256 = U256::from(1000);
}

/// https://github.com/balancer-labs/balancer-v2-monorepo/blob/ad1442113b26ec22081c2047e2ec95355a7f12ba/pkg/pool-stable/contracts/StableMath.sol#L49-L105
fn calculate_invariant(
amplification_parameter: U256,
balances: &[Bfp],
round_up: bool,
) -> Result<U256, Error> {
/// https://github.com/balancer-labs/balancer-v2-monorepo/blob/9eb7e44a4e9ebbadfe3c6242a086118298cadc9f/pkg/pool-stable-phantom/contracts/StableMath.sol#L57-L119
fn calculate_invariant(amplification_parameter: U256, balances: &[Bfp]) -> Result<U256, Error> {
let mut sum = U256::zero();
let num_tokens_usize = balances.len();
for balance_i in balances.iter() {
Expand All @@ -36,50 +29,33 @@ fn calculate_invariant(
let amp_times_total = amplification_parameter.bmul(num_tokens)?;
for _ in 0..255 {
// If balances were empty, we would have returned on sum.is_zero()
let mut p_d = balances[0].as_uint256().bmul(num_tokens)?;
for balance in &balances[1..] {
// P_D = Math.div(Math.mul(Math.mul(P_D, balances[j]), numTokens), invariant, roundUp);
p_d = rounded_div(
p_d.bmul(balance.as_uint256())?.bmul(num_tokens)?,
invariant,
round_up,
)?
let mut d_p = invariant;
for balance in balances {
// (d_p * invariant) / (balance * numTokens)
d_p = d_p
.bmul(invariant)?
.bdiv_down(balance.as_uint256().bmul(num_tokens)?)?;
}
let prev_invariant = invariant;

invariant = rounded_div(
// invariant = Math.div(
// Math.mul(Math.mul(numTokens, invariant), invariant).add(
// Math.div(Math.mul(Math.mul(ampTimesTotal, sum), P_D), _AMP_PRECISION, roundUp)
// ),
num_tokens
.bmul(invariant)?
.bmul(invariant)?
.badd(rounded_div(
amp_times_total.bmul(sum)?.bmul(p_d)?,
*AMP_PRECISION,
round_up,
)?)?,
// Math.mul(numTokens + 1, invariant).add(
// // No need to use checked arithmetic for the amp precision, the amp is guaranteed to be at least 1
// Math.div(Math.mul(ampTimesTotal - _AMP_PRECISION, P_D), _AMP_PRECISION, !roundUp)
// ),
(num_tokens.badd(1.into())?)
.bmul(invariant)?
.badd(rounded_div(
(amp_times_total.bsub(*AMP_PRECISION)?).bmul(p_d)?,
*AMP_PRECISION,
!round_up,
)?)?,
round_up,
)?;

// ((ampTimesTotal * sum) / AMP_PRECISION + D_P * numTokens) * invariant
let numerator = amp_times_total
.bmul(sum)?
.bdiv_down(*AMP_PRECISION)?
.badd(d_p.bmul(num_tokens)?)?
.bmul(invariant)?;
// ((ampTimesTotal - _AMP_PRECISION) * invariant) / _AMP_PRECISION + (numTokens + 1) * D_P
let denominator = amp_times_total
.bsub(*AMP_PRECISION)?
.bmul(invariant)?
.bdiv_down(*AMP_PRECISION)?
.badd(num_tokens.badd(1.into())?.bmul(d_p)?)?;
invariant = numerator.bdiv_down(denominator)?;
match convergence_criteria(invariant, prev_invariant) {
None => continue,
Some(invariant) => return Ok(invariant),
}
}

Err(Error::StableInvariantDidntConverge)
}

Expand All @@ -95,7 +71,7 @@ pub fn calc_out_given_in(
if token_index_out >= balances.len() || token_index_in >= balances.len() {
return Err(Error::InvalidToken);
}
let invariant = calculate_invariant(amplification_parameter, balances, true)?;
let invariant = calculate_invariant(amplification_parameter, balances)?;
balances[token_index_in] = balances[token_index_in].add(token_amount_in)?;

let final_balance_out = get_token_balance_given_invariant_and_all_other_balances(
Expand Down Expand Up @@ -127,7 +103,7 @@ pub fn calc_in_given_out(
if token_index_out >= balances.len() || token_index_in >= balances.len() {
return Err(Error::InvalidToken);
}
let invariant = calculate_invariant(amplification_parameter, balances, true)?;
let invariant = calculate_invariant(amplification_parameter, balances)?;
balances[token_index_out] = balances[token_index_out].sub(token_amount_out)?;

let final_balance_in = get_token_balance_given_invariant_and_all_other_balances(
Expand Down Expand Up @@ -356,32 +332,33 @@ mod tests {
let amp = 100.;
let amplification_parameter = U256::from_f64_lossy(amp * AMP_PRECISION.to_f64_lossy());
let balances = vec![Bfp::from(10), Bfp::from(12)];
let result = calculate_invariant(amplification_parameter, &balances, true).unwrap();
let max_relative_error = 0.001;
let expected = calculate_analytic_invariant_two_tokens(
balances[0].to_f64_lossy(),
balances[1].to_f64_lossy(),
amp,
);
let max_relative_error = 0.001;
let result = calculate_invariant(amplification_parameter, &balances).unwrap();
assert!((result.to_f64_lossy() / 1e18 - expected)
.abs()
.le(&max_relative_error));
}

#[test]
fn invariant_two_tokens_err() {
fn invariant_converges_at_extreme_values() {
let amp = 5000.;
let balances: Vec<Bfp> = vec!["0.00001", "1200000", "300"]
.iter()
.map(|x| Bfp::from_str(x).unwrap())
.collect();
let amplification_parameter = U256::from_f64_lossy(amp * AMP_PRECISION.to_f64_lossy());
assert_eq!(
calculate_invariant(amplification_parameter, balances.as_slice(), true)
.unwrap_err()
.to_string(),
"BAL#321: StableInvariantDidntConverge"
);
let result = calculate_invariant(amplification_parameter, balances.as_slice()).unwrap();
let float_balances = balances.iter().map(|x| x.to_f64_lossy()).collect();
let expected = calculate_invariant_approx(float_balances, amp);
let max_relative_error = 0.001;
assert!((result.to_f64_lossy() / 1e18 - expected)
.abs()
.le(&max_relative_error));
}

#[test]
Expand All @@ -390,9 +367,9 @@ mod tests {
let amplification_parameter = U256::from_f64_lossy(amp * AMP_PRECISION.to_f64_lossy());
let balances = vec![Bfp::from(10), Bfp::from(12), Bfp::from(14)];
let float_balances = balances.iter().map(|x| x.to_f64_lossy()).collect();
let result = calculate_invariant(amplification_parameter, &balances, true).unwrap();
let expected = calculate_invariant_approx(float_balances, amp);
let max_relative_error = 0.001;
let result = calculate_invariant(amplification_parameter, &balances).unwrap();
assert!((result.to_f64_lossy() / 1e18 - expected)
.abs()
.le(&max_relative_error));
Expand Down