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BSIP: 0035
Title: Mitigate Rounding Issue On Order Matching
Author: Abit More <https://github.com/abitmore>
Status: Accepted
Type: Protocol
Created: 2018-02-19
Discussion: https://github.com/bitshares/bitshares-core/issues/132,
            https://github.com/bitshares/bitshares-core/issues/184,
            https://github.com/bitshares/bitshares-core/issues/342
Replaces: -
Worker: 1.14.96

Abstract

Under some circumstances, when two orders get matched, due to rounding, one order may be paying more than enough, even paying something but receiving nothing. This looks unfair.

This BSIP proposes an overall mechanism to mitigate rounding issue when matching orders and avoid something-for-nothing issue completely.

This BSIP also sets two principles for order matching:

never pay more than enough, and
something-for-nothing shouldn't happen.

Motivation

There are mechanisms in the system to try to avoid something-for-nothing issue, however, not all scenarios are well-handled, see bitshares-core issue #184 for example.

Other than that, rounding issue occurs frequently and has led to a lot of confusion among market participants, see bitshares-core issue #342 for example.

Rationale

Amounts, Prices and Rounding

Amounts in the system are integers with per-asset fixed precisions. The minimum positive amount of an asset is called one Satoshi.

Prices in the system are rational numbers, which are expressed as base_amount / quote_amount (precisions are omitted here).

To calculate how much amount of asset B is equivalent to some amount of asset A, need to calculate amount_of_a * a_to_b_price which is amount_of_a * b_amount_in_price / a_amount_in_price. The accurate result of this formula is a rational number. To convert it to the final result which is an amount, which is an integer, may need to round.

Order Matching

An order means someone is willing to give out some amount of asset X expecting to get some amount of asset Y. The ratio between the two assets is the price of the order. The price can be expressed as either x_amount / y_amount or y_amount / x_amount, when we know which amount in the price is of which asset, the two expressions are equivalent. The amount of asset X is known and fixed.

In a market, E.G. the X:Y market, some people are selling X for Y, some people are selling Y for X (or say buying X with Y). Orders are classified by type (buy or sell), then ordered by price. For each type, the order offering the best price is on the top. So, in every market there may be a top buy order and a top sell order, name them highest bid and lowest ask, so there is a highest bid price (in terms of asset X amount / asset Y amount), and a lowest ask price (in terms of asset X amount / asset Y amount as well).

When the highest bid price is higher or equal to the lowest ask price, the two top orders can be matched with each other.

The Match Price

In a continuous trading market, orders are placed one by one, when comparing every two orders, it's deterministic that one order is placed earlier than the other.

In BitShares, it doesn't mean that the transaction that contains the first order is signed before the transaction contains the second, but means that the first order is processed earlier than the second in the witness node that produced the block that contains the second order.

When two orders get matched, the one placed earlier is maker, the other one is taker. Say, the maker provides an offer, the taker accept the offer. So, when calculating who will get how much, we use the maker order's price, aka maker price, as the match price.

The Need for Compromise

When matching two orders, due to rounding, usually we're unable to completely satisfy both parties.

Here is an example mentioned in the 4th comment of bitshares-core issue #132:

Alice's order: Sell CORE at $3 / 8, balance 1000000 CORE Bob's order: Buy CORE at $19 / 50, balance $10

Both assets have precision of 1, i.e. the order balances are 1000000 CORE-satoshis and 10 USD-satoshis repectively.

Alice is selling at $3/8 CORE = $0.375 / CORE and Bob is buying at $19 / 50 CORE = $0.38, so based on the price, Alice and Bob should match.

Bob's $10 / $0.38 ~ 26.3. So 26.3 is the fewest CORE he is willing to accept (assuming that the meaning of "price" is "the least favorable exchange rate a party is willing to accept in trade"). Combined with the design restriction that satoshis are indivisible, in practice this means Bob will only accept 27 or more CORE for his $10.

But $10 / 27 gives a price smaller than $0.370 and $0.371, which is smaller than Alice's sale price of $0.375. So neither party can fill this offer.

We need to come to a compromise.

The Possible Solutions

There are some possible solutions listed in the 5th comment of bitshares-core issue #132:

(a) Fill someone at a less favorable exchange rate than the price they specified in their order. Downside: This violates the above definition of price; i.e. if a user enters a price intending the system to never sell below that price in any circumstance, the system will not always behave in a way which fulfills that user intent.
(b) Keep both orders on the books. Downside: This complicates the matching algorithm, as now Alice might be able to match an order behind Bob's order. Naive implementation would have potentially unbounded matching complexity; a more clever implementation might be possible but would require substantial design and testing effort.
(c) Cancel an order. This is complicated by the fact that an order such as a margin call cannot be cancelled. Downside: When there are margin calls happening, it seems perverse to delete a large order that's willing to fill them just because the lead margin call happens to fall in a narrow window which causes a rounding issue. Also, orders cancelled by this mechanism cannot be refunded. Otherwise an attacker who wants to consume a lot of memory on all nodes could create a large number of orders, then trigger this case to cancel them all, getting their investment in deferred cancellation fees back without paying the cancel op's per-order fee as intended.
(d) Require all orders to use the same denominator. Altcoin exchanges and many real-world markets like the stock market solve this problem by specifying one asset as the denominator asset, specifying a "tick" which is the smallest unit of price precision, and requiring all prices to conform. Downside: Complicates the implementation of flipped market UI, may require re-working part of market GUI, reduces user flexibility, new asset fields required to specify precision, if n assets exist then O(n^2) markets could exist and we need to figure out how to determine the precision requirement for all of them.

The Chosen Solution

Current code actually implemented (a) in the first place: when matching two orders, if there is a rounding issue, the order with smaller volume will be filled at a less favorable price. It's the least bad compromise since it has the most efficiency (highest traded volume while not hard to implement) among the solutions.

The algorithm can be described as follows (sample code is here):

Assuming the maker order is selling amount X of asset A, with price maker_price = maker_b_amount / maker_a_amount; assuming the taker is buying asset A with amount Y of asset B, with price taker_price = taker_b_amount / taker_a_amount. Anyway, since the two orders will be matched at maker price, the taker price doesn't matter here as long as it's higher than or equal to maker price. Note: currently all limit orders are implemented as sell limit orders, so in the example, the taker order can only specify amount of asset B but not amount of asset A.

Now compare X * maker_price with Y. To be accurate (avoid rounding), compare X' = X * maker_b_amount with Y' = Y * maker_a_amount.

The best scenario is when X' == Y', which means both orders can be completely filled at maker_price.
If X' < Y', it means the maker order can be completely filled but the taker order can't, aka the maker order is smaller. In this case, maker pay amount X of asset A to taker, taker pay amount Y" = round_down( X' / maker_a_amount ) of asset B to maker. Note: due to rounded down, it's possible that Y" is smaller than the rational number X * maker_price, which means Y" / X may be lower than maker_price, that said, the maker order may has been filled at a less favorable price.
If X' > Y', it means the taker order can be completely filled but the maker order can't, aka the taker order is smaller. In this case, taker pay amount Y of asset B to maker, maker pay amount X" = round_down( Y' / maker_b_amount ) of asset A to taker. Note: due to rounded down, it's possible that X" is smaller than the rational number Y / taker_price, which means Y / X" may be higher than taker_price, that said, the taker order may has been filled at a less favorable price.

Issues With The Chosen Solution

The Something-for-nothing Issue

When filling a small order at a less favorable price, the receiving amount is often rounded down to zero, thus causes the something-for-nothing issue. Current code tried to solve the issue by cancelling the smaller order when it would receive nothing, but only applied this rule in a few senarios (the processed parties won't be paying something for nothing):

when matching two limit orders, processed the maker
when matching a limit order with a call order, processed the call order
when matching a settle order with a call order, processed the call order
when globally settling, processed the call order

Other senarios that need to be processed as well (these to-be-processed parties may be paying something for nothing in current system):

when matching two limit orders, process the taker
when matching a limit order with a call order, process the limit order
when matching a force settle order with a call order, process the settle order
when globally settling, process the settlement fund
when force settling after an asset has been globally settled, paying the force settle order from global settlement fund, process the settle order

The Broader Rounding Issue

Something-for-nothing is only a subset of rounding issues, it's the most extreme one. There are much more scenarios that one of the matched parties would be paying more than enough, although they're not paying something for nothing overall. Some scenarios are discussed in bitshares-core issue #342.

Take a scenario similar to the one described in the 4th comment of bitshare-core issue #132 as an example:

Alice's order: Sell CORE at $3 / 80 = $0.0375, balance 50 CORE
Bob's order: Buy CORE at $19 / 500 = $0.038, balance $100

Current system would process them as follows:

If Alice's order is maker, use $3 / 80 as match price; since Alice's order is smaller, round in favor of Bob's order, so Alice will pay the whole 50 CORE and get round_down(50 CORE * $3 / 80 CORE) = round_down($1.6) = $1, the effective price would be $1 / 50 = $0.02;
If Bob's order is maker, use $19 / 500 as match price; since Alice's order is smaller, round in favor of Bob's order, so Alice will pay the whole 50 CORE and get round_down(50 CORE * $19 / 500 CORE = round_down($1.9) = $1, the effective price would still be $1 / 50 = $0.02.

Both results are far from Alice's desired price $0.0375. Actually, according to Bob's desired price, paying round_up($1 * 500 CORE / $19) = 27 CORE would be enough, then the effective price would be $1 / 27 = $0.037, which is still below Alice's desired price $0.0375, but much closer than $0.02.

The Improved Solution Proposed By This BSIP

The detailed rules proposed by this BSIP with new rules highlighted:

match in favor of taker, or say, match at maker price;
round the receiving amounts according to rules below.
- When matching two limit orders, round down the receiving amount of the smaller order,
  - if the smaller order would get nothing, cancel it;
  - otherwise, calculate the amount that the smaller order would pay as round_up(receiving_amount * match_price).
  - After filled both orders, for each remaining order (with a positive amount remaining), check the remaining amount, if the amount is too small so the order would receive nothing on next match, cancel the order.
- When matching a limit order with a call order,
  - if the call order is receiving the whole debt amount, which means it's smaller and the short position will be closed after the match, round up its paying amount; otherwise, round down its paying amount.
  - In the latter case,
    - if the limit order would receive nothing, cancel it (it's smaller, so safe to cancel);
    - otherwise, calculate the amount that the limit order would pay as round_up(receiving_amount * match_price). After filled both orders, if the limit order still exists, the remaining amount might be too small, so cancel it.
- When matching a settle order with a call order,
  - if the call order is receiving the whole debt amount, which means it's smaller and the short position will be closed after the match, round up its paying amount; otherwise, round down its paying amount.
  - In the latter case,
    - if the settle order would receive nothing,
      - if the settle order would be completely filled, cancel it;
      - otherwise, it means both orders won't be completely filled, which may due to hitting maximum_force_settlement_volume, in this case, don't fill any of the two orders, and stop matching for this asset at this block;
    - otherwise (if the settle order would not receive nothing), calculate the amount that the settle order would pay as round_up(receiving_amount * match_price). After filled both orders, if the settle order still exists, match the settle order with the call order again. In the new match, either the settle order will be cancelled due to too small, or we will stop matching due to hitting maximum_force_settlement_volume.
  - That said, only round up the collateral amount paid by the call order when it is completely filled, so if the call order still exist after the match, its collateral ratio won't be lower than before, which means we won't trigger a black swan event, nor need to check whether a black swan event would be triggered.
- When globally settling, in favor of global settlement fund, round up collateral amount.
- When paying a settle order from global settlement fund, for predition markets, there would be no rounding issue, also no need to deal with something-for-nothing issue; for other assets, apply rules below:
  - if the settling amount is equal to total supply of that asset, pay the whole remaining settlement fund to the settle order;
  - otherwise, in favor of global settlement fund since its volume is bigger, round down collateral amount. If the settle order would receive nothing, raise an exception (aka let the operation fail). Otherwise, calculate the amount that the settle order would pay as round_up(receiving_amount * match_price); after filled the order, if there is still some amount remaining in the order, return it to the owner.

Examples Of The Improved Solution

Example 1

Take the example mentioned in the 4th comment of bitshares-core issue #132:

Alice's order: Sell CORE at $3 / 8 = $0.375, balance 1000000 CORE
Bob's order: Buy CORE at $19 / 50 = $0.38, balance $10

Process:

If both orders are limit orders
- If Alice's order is maker, use $3 / 8 as match price; since Bob's order is smaller, round in favor of Alice's order, so Bob will get round_down($10 * 8 CORE / $3) = round_down(26.67 CORE) = 26 CORE, and Alice will get round_up(26 CORE * $3 / 8 CORE) = round_up($9.75) = $10, the effective price would be $10 / 26 CORE = $0.3846.
- If Bob's order is maker, use $19 / 50 as match price; since Bob's order is smaller, round in favor of Alice's order, so Bob will get round_down($10 * 50 CORE / $19 = round_down(26.32 CORE) = 26 CORE, and Alice will get round_up(26 CORE * $19 / 50 CORE) = round_up($9.88) = $10, the effective price would still be $10 / 26 CORE = $0.3846.
If Alice's order is a call order, since it's bigger, round in favor of it, we will get same results.

Example 2

If we change the example to this:

Alice's order: Buy CORE at 3 CORE / $8 = 0.375, balance $1000000
Bob's order: Sell CORE at 19 CORE / $50 = 0.38, balance 10 CORE

Process:

If both orders are limit orders, we get similar results as above.
If Bob's order is a call order, it should have a debt amount which is an integer, for example $26, then
- Alice would get
  - round_up(26 * 3 / 8) = round_up(9.75) = 10 CORE as a maker, or
  - round_up(26 * 19 / 50) = round_up(9.88) = 10 CORE as a taker.
- Bob would get the full debt amount which is $26.
If Bob's order is a call order, but the debt amount is a bit high, for example $27, then Alice would get
- round_up(27 * 3 / 8) = round_up(10.125) = 11 CORE as a maker, or
- round_up(27 * 19 / 50) = round_up(10.26) = 11 CORE as a taker.
However, since the collateral is only 10 CORE, this match will fail and trigger a black swan event.

Example 3

If we change the example to that one used above:

Alice's order: Sell CORE at $3 / 80 = $0.0375, balance 50 CORE
Bob's order: Buy CORE at $19 / 500 = $0.038, balance $100

Assuming both orders are limit orders, they'll be processed as follows:

If Alice's order is maker, use $3 / 80 as match price; since Alice's order is smaller, round in favor of Bob's order, so Alice will get round_down(50 CORE * $3 / 80 CORE) = round_down($1.6) = $1, and Bob will get round_up($1 * 80 CORE / $3) = round_up($26.67) = $27, the effective price would be $1 / 27 = $0.037;
If Bob's order is maker, use $19 / 500 as match price; since Alice's order is smaller, round in favor of Bob's order, so Alice will get round_down(50 CORE * $19 / 500 CORE = round_down($1.9) = $1, and Bob will get round_up($1 * 500 CORE / $19) = round_up($26.3) = $27, the effective price would also be $1 / 27 = $0.037.

Specifications

When Matching Two Limit Orders

Handling Something-For-Nothing Issue

In match( const limit_order_object&, OrderType ... ) function of database class, after calculated usd_receives which is for the taker, check if it is zero. If the answer is true, skip filling and see the order is filled, return 1, so the order will be cancelled later.

Handling Rounding Issue

In match( const limit_order_object&, OrderType ... ) function of database class, after calculated receives for the smaller order, if it isn't zero, calculate pays for it as round_up(receives * match_price).

If the smaller order is taker, after filled, even if there is still some amount remaining in the order, see it as completely filled and set the lowest bit of return value to 1.

If the smaller order is maker, since it will be culled when filling, no need to change the logic.

When Matching A Limit Order With A Call Order

In check_call_orders(...) function of database class, if the call order is smaller, round up order_receives, otherwise round down order_receives.

In the latter case,

if order_receives is zero, skip filling and cancel the limit order.
otherwise, calculate order_pays as round_up(order_receives * match_price), then the limit order will be either completely filled, or culled due to too small after partially filled.

When Matching A Settle Order With A Call Order

In match( const call_order_object&, ... ) function of database class, if the call order is smaller, round up call_pays, otherwise round down call_pays.

In the latter case, check if call_pays is zero.

If the answer is true,
- if call_receives is equal to settle.balance, call cancel_order(...) with parameter set to settle, then return a zero-amount collateral asset object;
- otherwise, return a zero-amount collateral asset object directly.
Otherwise, calculate call_receives as round_up(call_pays * match_price), then fill both orders normally. If the settle order still exists after the match, it will be processed again later but with different condition.

After returned, need to check the amount of returned asset at where calling the match(...) function, specifically, clear_expired_orders() function of database class. If the returned amount is 0, break out of the while loop. If the settle order is still there and the returned amount is 0, label that processing of this asset has completed. Also, in the outer loop, need to check the label, if found it's completed, process next asset.

When Globally Settling

In global_settle_asset(...) function of database class, round up pays.

When Paying A Settle Order From Global Settlement Fund

In do_apply(...) function of asset_settle_evaluator class, after calculated settled_amount and adjusted it according to the "total supply" rule, check if it's zero.

If the answer is true, and the asset is not a prediction market, throw a fc::exception.

If the answer is false, and the asset is not a prediction market, and op.amount.amount is not equal to mia_dyn.current_supply, calculate pays as round_up(settled_amount * bitasset.settlement_price), then, only deduct pays from total supply, and refund op.amount.amount - pays to the user.

Discussion

There is an argument suggests when matching call orders, we should always round in favour of the call. If a settlement receives 0 collateral as a result, that's acceptable, because the settlement price is unknown at the time when settlement is requested, so no guarantee is violated (within the range of rounding errors). This should keep the collateral > 0 as long as there is outstanding debt. A counter-argument supports rounding up to 1 Satoshi since rounding down to zero may break the promise of "every smart coin is backed by something".

There is an argument says breaking the min_to_receive limit is a no-go, because that's why it's called a "limit order". A counter-argument says slightly breaking the limit is the least bad compromise.

Summary for Shareholders

[to be added if any]

Copyright

This document is placed in the public domain.

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