23 KiB
BSIP: 0035
Title: Mitigate Rounding Issue On Order Matching
Author: Abit More <https://github.com/abitmore>
Status: Accepted
Type: Protocol
Created: 20180219
Discussion: https://github.com/bitshares/bitsharescore/issues/132,
https://github.com/bitshares/bitsharescore/issues/184,
https://github.com/bitshares/bitsharescore/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 somethingfornothing issue completely.
This BSIP also sets two principles for order matching:
 never pay more than enough, and
 somethingfornothing shouldn't happen.
Motivation
There are mechanisms in the system to try to avoid somethingfornothing issue, however, not all scenarios are wellhandled, see bitsharescore issue #184 for example.
Other than that, rounding issue occurs frequently and has led to a lot of confusion among market participants, see bitsharescore issue #342 for example.
Rationale
Amounts, Prices and Rounding
Amounts in the system are integers with perasset 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 bitsharescore 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 COREsatoshis and 10 USDsatoshis 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 bitsharescore 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 perorder fee as intended.

(d) Require all orders to use the same denominator. Altcoin exchanges and many realworld 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 reworking part of market GUI, reduces user flexibility, new asset fields required to specify precision, if
n
assets exist thenO(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 atmaker_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 amountX
of asset A to taker, taker pay amountY" = round_down( X' / maker_a_amount )
of asset B to maker. Note: due to rounded down, it's possible thatY"
is smaller than the rational numberX * maker_price
, which meansY" / X
may be lower thanmaker_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 amountY
of asset B to maker, maker pay amountX" = round_down( Y' / maker_b_amount )
of asset A to taker. Note: due to rounded down, it's possible thatX"
is smaller than the rational numberY / taker_price
, which meansY / X"
may be higher thantaker_price
, that said, the taker order may has been filled at a less favorable price.
Issues With The Chosen Solution
The Somethingfornothing Issue
When filling a small order at a less favorable price, the receiving amount is often rounded down to zero, thus causes the somethingfornothing 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 tobeprocessed 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
Somethingfornothing 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 bitsharescore issue #342.
Take a scenario similar to the one described in the 4th comment of bitsharecore issue #132 as an example:
 Alice's order: Sell CORE at
$3 / 80 = $0.0375
, balance50 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 whole50 CORE
and getround_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 whole50 CORE
and getround_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 hittingmaximum_force_settlement_volume
.
 if the settle order would receive nothing,
 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 somethingfornothing 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 bitsharescore issue #132:
 Alice's order: Sell CORE at
$3 / 8 = $0.375
, balance1000000 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 getround_down($10 * 8 CORE / $3) = round_down(26.67 CORE) = 26 CORE
, and Alice will getround_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 getround_down($10 * 50 CORE / $19 = round_down(26.32 CORE) = 26 CORE
, and Alice will getround_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 maker, use
 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
, balance10 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, orround_up(26 * 19 / 50) = round_up(9.88) = 10 CORE
as a taker.
 Bob would get the full debt amount which is
$26
.
 Alice would get

If Bob's order is a call order, but the debt amount is a bit high, for example
$27
, then Alice would getround_up(27 * 3 / 8) = round_up(10.125) = 11 CORE
as a maker, orround_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
, balance50 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 getround_down(50 CORE * $3 / 80 CORE) = round_down($1.6) = $1
, and Bob will getround_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 getround_down(50 CORE * $19 / 500 CORE = round_down($1.9) = $1
, and Bob will getround_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 SomethingForNothing 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
asround_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 tosettle.balance
, callcancel_order(...)
with parameter set tosettle
, then return a zeroamount collateral asset object;  otherwise, return a zeroamount collateral asset object directly.
 if
 Otherwise, calculate
call_receives
asround_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 counterargument 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 nogo,
because that's why it's called a "limit order". A counterargument 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.