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3 changes: 2 additions & 1 deletion contracts/Nargo.toml
Original file line number Diff line number Diff line change
@@ -1,4 +1,5 @@
[workspace]
members = [
"proof_of_password"
"proof_of_password",
"amm"
]
9 changes: 9 additions & 0 deletions contracts/amm/Nargo.toml
Original file line number Diff line number Diff line change
@@ -0,0 +1,9 @@
[package]
name = "amm_contract"
authors = [""]
type = "contract"

[dependencies]
aztec = { git = "https://github.com/AztecProtocol/aztec-packages/", tag = "v4.2.0-aztecnr-rc.2", directory = "noir-projects/aztec-nr/aztec" }
token = { git = "https://github.com/AztecProtocol/aztec-packages/", tag = "v4.2.0-aztecnr-rc.2", directory = "noir-projects/noir-contracts/contracts/app/token_contract" }
uint_note = { git = "https://github.com/AztecProtocol/aztec-packages/", tag = "v4.2.0-aztecnr-rc.2", directory = "noir-projects/aztec-nr/uint-note" }
11 changes: 11 additions & 0 deletions contracts/amm/src/config.nr
Original file line number Diff line number Diff line change
@@ -0,0 +1,11 @@
use aztec::protocol::{address::AztecAddress, traits::{Deserialize, Packable, Serialize}};
use std::meta::derive;

/// We store the tokens of the pool in a struct such that to load it from PublicImmutable asserts only a single
/// merkle proof.
#[derive(Deserialize, Eq, Packable, Serialize)]
pub struct Config {
pub token0: AztecAddress,
pub token1: AztecAddress,
pub liquidity_token: AztecAddress,
}
96 changes: 96 additions & 0 deletions contracts/amm/src/lib.nr
Original file line number Diff line number Diff line change
@@ -0,0 +1,96 @@
/// Given an input amount of an asset and pair balances, returns the maximum output amount of the other asset.
pub fn get_amount_out(amount_in: u128, balance_in: u128, balance_out: u128) -> u128 {
assert(amount_in > 0 as u128, "INSUFFICIENT_INPUT_AMOUNT");
assert((balance_in > 0 as u128) & (balance_out > 0 as u128), "INSUFFICIENT_LIQUIDITY");

// The expression below is:
// (amount_in * 997 * balance_out) / (balance_in * 10000 + amount_in * 997)
// which is equivalent to:
// balance_out * ((amount_in * 0.997) / (balance_in + amount_in * 0.997))
// resulting in an implicit 0.3% fee on the amount in, as the fee tokens are not taken into consideration.

let amount_in_with_fee = amount_in * 997 as u128;
let numerator = amount_in_with_fee * balance_out;
let denominator = balance_in * 1000 as u128 + amount_in_with_fee;
numerator / denominator
}

/// Given an output amount of an asset and pair balances, returns a required input amount of the other asset.
pub fn get_amount_in(amount_out: u128, balance_in: u128, balance_out: u128) -> u128 {
assert(amount_out > 0 as u128, "INSUFFICIENT_OUTPUT_AMOUNT");
assert((balance_in > 0 as u128) & (balance_out > 0 as u128), "INSUFFICIENT_LIQUIDITY");

// The expression below is:
// (balance_in * amount_out * 1000) / (balance_out - amount_out * 997) + 1
// which is equivalent to:
// balance_in * (amount_out / (balance_in + amount_in)) * 1/0.997 + 1
// resulting in an implicit 0.3% fee on the amount in, as the fee tokens are not taken into consideration. The +1
// at the end ensures the rounding error favors the pool.

let numerator = balance_in * amount_out * 1000 as u128;
let denominator = (balance_out - amount_out) * 997 as u128;
(numerator / denominator) + 1 as u128
}

/// Given the desired amounts and balances of token0 and token1 returns the optimal amount of token0 and token1 to be added to the pool.
pub fn get_amounts_to_add(
amount0_max: u128,
amount1_max: u128,
amount0_min: u128,
amount1_min: u128,
balance0: u128,
balance1: u128,
) -> (u128, u128) {
// When adding tokens, both balances must grow by the same ratio, which means that their spot price is unchanged.
// Since any swaps would affect these ratios, liquidity providers supply a range of minimum and maximum balances
// they are willing to supply for each token (which translates to minimum and maximum relative prices of the
// tokens, preventing loss of value outside of this range due to e.g. front-running).

if (balance0 == 0 as u128) | (balance1 == 0 as u128) {
// The token balances should only be zero when initializing the pool. In this scenario there is no prior ratio
// to follow so we simply transfer the full maximum balance - it is up to the caller to make sure that the ratio
// they've chosen results in a a reasonable spot price.
(amount0_max, amount1_max)
} else {
// There is a huge number of amount combinations that respect the minimum and maximum for each token, but we'll
// only consider the two scenarios in which one of the amounts is the maximum amount.

// First we calculate the token1 amount that'd need to be supplied if we used the maximum amount for token0.
let amount1_equivalent = get_equivalent_amount(amount0_max, balance0, balance1);
if (amount1_equivalent <= amount1_max) {
assert(amount1_equivalent >= amount1_min, "AMOUNT_1_BELOW_MINIMUM");
(amount0_max, amount1_equivalent)
} else {
// If the max amount for token0 results in a token1 amount larger than the maximum, then we try with the
// maximum token1 amount, hoping that it'll result in a token0 amount larger than the minimum.
let amount0_equivalent = get_equivalent_amount(amount1_max, balance1, balance0);
// This should never happen, as it'd imply that the maximum is lower than the minimum.
assert(amount0_equivalent <= amount0_max);

assert(amount0_equivalent >= amount0_min, "AMOUNT_0_BELOW_MINIMUM");
(amount0_equivalent, amount1_max)
}
}
}

/// Returns the amount of tokens to return to a liquidity provider when they remove liquidity from the pool.
pub fn get_amounts_on_remove(
to_burn: u128,
total_supply: u128,
balance0: u128,
balance1: u128,
) -> (u128, u128) {
// Since the liquidity token tracks ownership of the pool, the liquidity provider gets a proportional share of each
// token.
(to_burn * balance0 / total_supply, to_burn * balance1 / total_supply)
}

/// Given some amount of an asset and pair balances, returns an equivalent amount of the other asset. Tokens should be
/// added and removed from the Pool respecting this ratio.
fn get_equivalent_amount(amount0: u128, balance0: u128, balance1: u128) -> u128 {
assert((balance0 > 0 as u128) & (balance1 > 0 as u128), "INSUFFICIENT_LIQUIDITY");

// This is essentially the Rule of Three, since we're computing proportional ratios. Note we divide at the end to
// avoid introducing too much error due to truncation.
(amount0 * balance1) / balance0
}
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