Orderbook

The system mints pegged assets (stablecoins) using an orderbook, using over-collateralized staked ETH.

Orders

The system is a central limit orderbook, with the addition of the Limit Short order type. Orders specify a price (ETH) and an amount. Market orders don't remain on the OB if there is no match.

• Limit Bid + Market Bid (createBid())
• Limit Ask + Market Ask (createAsk())
• Limit Short (no Market Short) (createLimitShort())

Note: Orders have a minimum ETH amount (price * amount): if (eth < minBidEth (or minAskEth)) revert Errors.OrderUnderMinimumSize(). This prevents small orders from clogging up the Orderbook.

This minimum check is done for incoming Orders as well as existing ones, so new orders cannot be smaller than a certain amount, and matched limit orders are removed from the OB if the remaining amount is too small.

Order Struct

To keep gas down, struct packing is employed. Order is 2 slots.

• ercAmount: uint88 is a max of 300m. Don't expect orders higher than this. Can also just make multiple orders instead.
• price: uint80 is max of 1.2m. This would be the price of the asset in terms of ETH, so it's reasonable to expect an order to never pass anything higher.
• id, prevId, nextId: Order id uses uint16 (65536). Because order ids are reuseable, it's not expected to have that many on the orderbook at once without matching.
• orderType: The Order type as of most the recent action.
• creationTime: Timestamp of when an order is created in seconds.
• addr: The user's address.
• prevOrderType: The Order type before the most recent action. (Example: Re-using a matched id for a LimitBid shows the orderType is LimitBid, while the prevOrderType is Matched; likewise for a previously Cancelled Order).
• shortOrderCR (Short): This is only the CR accounting for what is provided by shorter. shortOrderCR + 1x CR from the bidder on match equals the initialCR
• shortRecordId (Short): Corresponding shortRecord id if the Short order isn't fully matched (it overwrites the same shortRecord position rather than create a new one)

// 2 slots
struct Order {
      // SLOT 1: 88 + 80 + 16 + 16 + 16 + 8 + 32 = 256
      uint88 ercAmount; // max 300m erc
      uint80 price; // max 1.2m eth
      // max orders 65k, with id re-use
      uint16 prevId;
      uint16 id;
      uint16 nextId;
      O orderType;
      // @dev diff against contract creation timestamp to prevent overflow in 2106
      uint32 creationTime; // seconds
      // SLOT 2: 160 + 8 + 16 + 8 = 192 (64 unused)
      address addr; // 160
      O prevOrderType;
      // @dev storing as 170 with 2 decimals -> 1.70 ether
      uint16 shortOrderCR; // @dev CR from the shorter only used for limit short
      uint8 shortRecordId; // @dev only used for LimitShort
      uint64 filler;
    }

Short Orders

The system's "sell" side also includes shorters.

When a bid and short Order match, it will create/modify a debt position called a shortRecord. This idea is similar to a Collateral Debt Position (CDP) in MakerDAO or Trove in Liquity.

The difference is that the shorter doesn't gain the stable asset, rather the bidder gains it. However, the shorter does get the bidder's collateral as a part of their shorter position, and thus the yield since the collateral is staked.

User	Brings	Receives	Claim to Yield
Bidder	dETH	stable asset	None
Shorter	dETH x shortOrderCR	shortRecord	Yes

Notes:

• The bidder doesn't receive the stable asset in the wallet until they withdraw, it's virtually accounted for to save gas if they make multiple trades before they want to withdraw.
• The shorter provides a multiplied amount of dETH because the position needs to be over-collateralized, starting from a limit set by the system.
• The shorter doesn't receive any stable asset. They get a debt position that receives the yield from their collateral, which also includes the bidder's portion.

The collateral used in both the bid and short order is combined to virtually "mint" an asset (the stable asset isn't actually minted until the user withdraws to save on gas). In the case of USD, it would mint a pegged asset to USD.

• 1 CR = 100% collateral ratio, meaning the shortRecord is fully collateralized at a given oracle price.

            collateral
CR = -----------------------
     debt * getOraclePrice()

• Short orders are required to be over-collateralized (above 1 CR), unlike a bid or ask. The minimum ratio that is required for a short Order is at least initialCR, which is saved to each Order. (ex: if (ethEscrowed < shortEth * initialCR) revert).
• The system allows the shorter to specify the CR so that it fits between initialCR < CR < MAX CR.

Note: Short orders can be made at any limit price, but shortRecords are to be created at or above oracle price due to the constraint that assets should be minted at or above oracle price.

In the example below, assume the current oracle price is 10.5. Bids are sorted from highest to lowest in price and asks are sorted lowest to highest. The shorts under 10 aren't matched against bids even though the highest bid is 10. This is because shorts can't be matched below the oracle price of 10.5. This nuance is specific for shorts. If instead a new ask comes in below 10, it would be matched like normal.

Bids	Asks	Shorts
10	13	12
9	12	11
8	11	9
7	11	8
6	10.6	7

Note: When there is an incoming bid, the system prioritizes limit asks over limit shorts. If there are asks and shorts of the same price, the bid will match with the ask first.

Multiple ShortRecords

Other systems have one 1 CDP, Vault, or Trove per address. Because of the orderbook model, multiple shortRecord positions are allowed. This can be useful if you want the flexibility of multiple positions, but also makes it difficult to manage if you don't want to track each CR.

The combineShorts function allows you to specify which of your shorts you want to combine. It will merge positions by weighting each position.

Shorter Yield

Shorters have an incentive to match on the Orderbook because while the bidder gets the minted asset (USD), the shorter gets the bidder's collateral, thus it's portion of staking yield.

Example:

• Setup: ETH/USD is $2000, so USD/ETH is 0.0005. initialCR = 2.
• Bidder places a bid order of $1 at price 0.0005 eth.
• Shorter places a short order at the same parameters (but they must a multiple of initialCR dETH).
• When they match, the bidder gets $1 of dUSD. The shorter gets a shortRecord position worth price * amount * (initialCR + 1) of collateral which is 0.0005 * 1 * (2 + 1) = 0.0015 dETH.

The +1 is what gives the shorter extra yield for matching against a bid order, which results in 1 / initialCR extra yield.

If initialCR is 2, shorters are providing 2x as much dETH as the bidder (1x dETH). Thus a shorter is getting 3x yield vs 2x on their own, which is 1/2 or 50% more.

shortRecord

shortRecord is also 2 slots.

• collateral: uint88 is a max of 300m. collateral is denominated in ETH.
• ercDebt: uint88 to match Order.ercAmount.
• dethYieldRate: Tracks the current yield rate for this shortRecord, which is updated with distributeYield.
• status: uint8 enum to show whether a short is partially filled (meaning there is still a corresponding short order that isn't completely filled on the orderbook), filled, or closed.
• id, prevId, nextId: id, uses uint8 (255). Similar to order id but because this is per address, doesn't need to be so large.
• ercDebtRate: uint64 is a max of 18x. Tracks if a penalty needs to be applied across all shortRecords if the system isn't able to handle the debt.
• updatedAt: uint32 holds seconds. This tracks the last time a shortRecord was modified (created, increaseCollateral, etc) to determine yield eligibility as a defense against exploitative flash loans.
• ercDebtFee: uint88 is a max of 300m. This separately tracks the fee (already accounted for in ercDebt), so it's not compounded.

// 2 slots
// @dev dethYieldRate should match Vault
struct ShortRecord {
  // SLOT 1: 88 + 88 + 80 = 256
  uint88 collateral; // price * ercAmount * initialCR
  uint88 ercDebt; // same as Order.ercAmount
  uint80 dethYieldRate;
  // SLOT 2: 88 + 80 + 32 + 8 + 8 + 8 + 8 = 216 (24 remaining)
  SR status;
  uint8 prevId;
  uint8 id;
  uint8 nextId;
  uint80 ercDebtRate; // socialized penalty rate
  uint32 updatedAt; // seconds
  uint88 ercDebtFee;
  uint24 filler1;
}

A shortRecord saves the debt position a shorter creates when a short Order is matched. So a matched short Order will create a shortRecord.

Note: Unlike other systems, each user can have multiple shortRecords tracked in a mapping.

mapping(
  address asset
    => mapping(address account => mapping(uint16 id => DataTypes.ShortRecord))
  ) shortRecords;

The shortRecord saves the amount of debt the user owes in ercDebt, as well as the current collateral.

Short functions:

• increaseCollateral(): add more to the position by taking from your ethEscrowed.
• decreaseCollateral(): remove collateral from position, which increases your ethEscrowed.
• combineShorts(): uses a weighted average to combine multiple ShortRecords into one, as it's easier to manage fewer positions. Having fewer positions lowers the gas costs of getting yield, which loops over each shortRecord.
• exitShort(): a user can decrease their ercDebt, and potentially leave the position entirely to get back the underlying collateral.

Events

Events are emitted when a shortRecord is created and removed to track the list of addresses that should be liquidatable.

• ShortRecordCreated when a shortRecord by a user is created at index i.
• ShortRecordDeleted when a shortRecord by a user is deleted at index i.

These events can be used by an indexer service to determine a list of shorters and thus a list of shortRecords that are liquidatable. There should be a query that gives back a sorted list of positions by CR, from lowest to highest. This could be used by a front-end to liquidate positions or by bots.

Ordered Linked List

For this limit orderbook, a mapping is used to represent a doubly-linked list with a HEAD:

mapping(address asset => mapping(uint16 id => DataTypes.Order))

The DataTypes.Order struct contains a prevId and nextId to maintain the link between orders. This makes it possible to cancel/match orders (cancelBid(),cancelAsk(),cancelShort()) and sort them by price. Using prevIdand nextId also allows the recycling of order ids that have been previously cancelled/matched. By linking the cancelled/matched order struct to the HEAD of the linked list, a queue of re-usable order ids (that are currently inactive) is stored. This provides substantial gas savings by avoiding re-initializing a new Order struct each time a new order is made. See below in section (Re-using Orders).

The system uses the Constants.HEAD id as the starting point to iterate through the orders. To iterate through the orders, you can start at HEAD and get id.nextId until id is back at TAIL.

Note: TAIL and HEAD are both constants with the value of 1. The difference in nomenclature is simply for readability.

Since matching multiple orders requires more gas than matching one order of the same amount, the system also requires a minimum ETH amount to be used in a new order. This way, the orderbook isn't filled with super low order amounts. If an incoming limit order is matched and has a leftover amount, the remaining won't be placed on the orderbook if it is under the same minimum ETH amount.

Order Hints

Since the linked list of orders needs to be sorted, inserting a new limit order can be expensive. The contract needs to loop to find the right place to add an order starting from HEAD. The farther away the order's price is from HEAD, the more gas is required. This means doing an SLOAD on each order until the incoming order finds its proper place.

A hintId is used to lower gas costs by providing the contract the place in the list that a new limit order is supposed to be in. The contract verifies that the incoming order is correct, which is done by checking that the incoming order price is in between the hint price and the next price.

• for a ask or short: hintOrder.price >= order.price >= nextOrder.price
• for a bid: hintOrder.price <= order.price <= nextOrder.price

This verification also checks against a user providing an invalid hint like a non-existent order, or an order that is cancelled/matched via findOrderHintId().

The hintId will be exact if the orderbook doesn't change between the snapshot in time when an order is placed by a user and when it's executed. But it's possible the orderbook will have changed depending on how much a user pays in gas, MEV, etc.

HEAD <-> ..NEWLY_CREATED_ORDERS.. <-> HINT_ID <-> ..NEWLY_CREATED_ORDERS..

A hintId could turn out to be offset/incorrect in a few ways:

• if the hintId is not cancelled/matched/re-used but is no longer exact, as orders were added in-between the hint and the incoming order.
  • Loop from hintId.
• if the hintId is matched, cancelled, or cancelled and re-used.
  • There might not be a reasonable id to guess to start looping from. By providing multiple hints instead of just one, the other hints can be used for verification.
• if the hintId was matched and re-used.
  • It's likely that the incoming order would also be matched, or at least be placed close to the start of HEAD. Loop from HEAD.

The system checks whether the hint was cancelled/matched and re-used by checking the creationTime of the order. If the creationTime is different than the creationTime provided, then it implies the order was re-used.

Matching Bids to Shorts

Because the system allows for short orders to be placed under the oracle price, but not "matched", this system can behave differently than a normal orderbook. Usually an orderbook loops through its orders starting from the start of the Linked List (namely HEAD). But, in this case it would need to start from the first short order that is at or above oracle price, startingShortId.

This becomes an issue when the oracle price changes, given the cost of looping through orders to find where to start matching. To solve for this, another hint specific to shorts (shortHintId) is incorporated to determine where to start matching shorts based on the current oracle price.

Because the oracle price can change to be anything, the startingShortId is dynamic and changes according to that oracle price. There isn't a guaranteed way for a call to provide an exact hint of where the starting short would be because it wouldn't have access to a price not determined yet. Instead, some leeway is allowed by checking that the provided startingShortId price is within 0.5% of the actual oracle price at that moment. If it's below the oracle price, or over 0.5% of the oracle price, the transaction will fail.

This is very different from a normal orderbook that always matches from HEAD.

If startingShortId is valid within that range but is not exact, the orderbook will match downwards until it hits the true startingShortId. Once it hits that, the system will match back upwards and will behave like a normal orderbook again. This is to allow the next order to set the new oracle price within some reasonable range of values when the oracle price needs to change (freshness).

The issue is that an order can stay in the mempool for an indeterminate period of time. As a result, the state of the orderbook could be completely different from when the transaction was made, like a snapshot in time.

A bidder has an incentive to pass in a lower price oracle hint, so they can match at a lower price. Since the matching algorithm prioritizes limit asks over shorts, the incoming bid will match against all ask orders under the startingShortId price before going to the shorts.

Example using prices:

Short orders linked list

   id: HEAD    1         2           3          4          5
price:  N/A  $1000 .. $1000.5 .. $1009.999 .. $1010 .. $1010.001

Scenario: the oracle price is actually $1000, and the startingShortId is supposed to be id == 1. A user can pass in a different startingShortId, such as id == 2, because the price of that order ($1000.5) is within +1.0% of $1000 (basically between $1000-$1010). This means id == 3 or id == 4 is also a valid hint, but id == 5 wouldn't be.

If id == 4, then assuming the order was large enough, it would attempt to match down from 4 until it hits id == 1. If it doesn't finish and the oracle is still the same, the next order would continue to match downward until it hits the correct startingShortId of id == 1, and then continue to match upward as normal until the order is completely filled.

Re-using Orders

Context: EIP-2929: Gas cost increases for state access opcodes and EIP-3529: Reduction in refunds. Refunds were used before to incentivize clearing storage, but the use of gas tokens lead to EIP-3529. State expiry is a new proposal to handle storage bloat.

• A zero to non-zero SSTORE costs 20k + 2100 per slot.
• A non-zero to non-zero SSTORE costs 5k per slot. Re-using an order means modifying the order, so it would cost 10k.

The OrderBook normally goes from HEAD <-> ... id .. <-> TAIL.

• -> represents id.nextId
• <- represents id.prevId
• <-> represents both directions

In the scenario where ID is an order that is cancelled/matched, the link between PREV (id.prevId) and NEXT (id.nextId) is set.

BEFORE: HEAD <- > .. <- HEAD <-> .. PREV <-> ID <-> NEXT
 AFTER: HEAD <- > .. <- HEAD <-> .. PREV <--------> NEXT

ID itself can be deleted, but there could be a benefit to re-using old storage slots if possible. In the case of this kind of linked list, re-using old orders can make the creation of new ones cheaper.

HEAD.prevId is unused, and just points to HEAD. When an Order is either cancelled/matched, it's moved on the side of HEAD.prevId rather than being deleted.

The area to the left of HEAD is untouched by the matching algorithm, making it an ideal place to store this data

This just requires a few extra operations on match.

• id.prevId = HEAD.prevId; // 5k
• HEAD.prevId = id; // 5k
• id.order = CANCELLED; // 5k

This will cost 15k gas to set each cancel/match, as opposed to deleting the order.

In the example below, ID1 and ID2 are cancelled/matched sequentially. The most recent cancelled/matched ID is placed immediately before HEAD and any prior IDs get pushed back towards the left.

BEFORE: HEAD <------------------- HEAD <-> (ID1) <-> (ID2) <-> (ID3) <-> NEXT <-> TAIL
AFTER1: HEAD <- [ID1] <---------- HEAD <-----------> (ID2) <-> (ID3) <-> NEXT <-> TAIL
AFTER2: HEAD <- [ID1] <- [ID2] <- HEAD <---------------------> (ID3) <-> NEXT <-> TAIL

When a new order comes in, check that HEAD.prevId != HEAD. If true, it means the new order can use it, otherwise it should make a new order.

Continuing the example above, a new order would re-use the last cancelled/matched ID, which is ID2.

BEFORE: HEAD <- [ID1] <- [ID2] <- HEAD <---------------------> (ID3) <-----------> NEXT <-> TAIL
AFTER1: HEAD <- [ID1] <---------- HEAD <---------------------> (ID3) <-> (ID2) <-> NEXT <-> TAIL

Normally a new order id is generated for a new order. Id is a uint16, giving a maximum capacity of ~65,000. That value should never be hit if ids are re-used. It is also the case that the greater the depth that the orderbook is able to grow, the more orders that can be re-used in the future.

In summary, the gas savings from re-using ids (if an order is 2 slots) are as follows:

• it's 20k + 20k = 40k for a new order.
• it's 5k + 5k = 10k for a reused order.
• This should save 40k - 10k = 30k on all new orders over time.

Cancelling Spam Orders

While re-using ids greatly reduces the chance of hitting the ~65,000 limit, there is always a risk of adversarial attack that attempts to prevent market operations. Specifically, attackers might try to spam the network with small orders. To mitigate this, the DAO is allowed to cancel the last order in a given orderbook via cancelOrderFarFromOracle().

To prevent abuse, there are heavy restrictions in place:

1. This can only be called when the order id > 65,000. Rational market participants are expected to place orders that have reasonable likelihood to be matched, so it is unlikely that order ids ever reach this level.
2. The DAO cannot cancel more than 1000 orders.

Given the restrictions, it is unlikely that this function is ever called. However, its existence will effectively deter attackers from attempting to spam the network. Combined with the fact that each order requires a minimum ETH amount, it will be uneconomical for an attacker.