Refactor CreateAuctionsFromDeposit (#589)

* refactor CreateAuctionsFromDeposit to complete exhibits 7 & 8 by
removing auction slices and simplify usage of largest remainder method

x/cdp/keeper/auctions.go

@@ -30,36 +30,80 @@ func (k Keeper) AuctionCollateral(ctx sdk.Context, deposits types.Deposits, debt
 // CreateAuctionsFromDeposit creates auctions from the input deposit
 func (k Keeper) CreateAuctionsFromDeposit(
 	ctx sdk.Context, collateral sdk.Coin, returnAddr sdk.AccAddress, debt, auctionSize sdk.Int,
-	principalDenom string) (err error) {
+	principalDenom string) error {
 
-	// the number of auctions to start with lot = auctionSize
+	// number of auctions of auctionSize
-	wholeAuctions := collateral.Amount.Quo(auctionSize)
+	numberOfAuctions := collateral.Amount.Quo(auctionSize)
-	// remaining collateral (< lot) to auction
+	debtPerAuction := debt.Mul(auctionSize).Quo(collateral.Amount)
-	partialAuctionAmount := collateral.Amount.Mod(auctionSize)
-	auctionLots := []sdk.Int{}
 
-	for i := int64(0); i < wholeAuctions.Int64(); i++ {
+	// last auction for remaining collateral (collateral < auctionSize)
-		auctionLots = append(auctionLots, auctionSize)
+	lastAuctionCollateral := collateral.Amount.Mod(auctionSize)
+	lastAuctionDebt := debt.Mul(lastAuctionCollateral).Quo(collateral.Amount)
+
+	// amount of debt that has not been allocated due to
+	// rounding error (unallocated debt is less than numberOfAuctions + 1)
+	unallocatedDebt := debt.Sub(numberOfAuctions.Mul(debtPerAuction).Add(lastAuctionDebt))
+
+	// rounding error for whole and last auctions in units of collateral
+	// higher value means a larger truncation
+	wholeAuctionError := debt.Mul(auctionSize).Mod(collateral.Amount)
+	lastAuctionError := debt.Mul(lastAuctionCollateral).Mod(collateral.Amount)
+
+	// if last auction has larger rounding error, then allocate one debt to last auction first
+	// follows the largest remainder method https://en.wikipedia.org/wiki/Largest_remainder_method
+	if lastAuctionError.GT(wholeAuctionError) {
+		lastAuctionDebt = lastAuctionDebt.Add(sdk.OneInt())
+		unallocatedDebt = unallocatedDebt.Sub(sdk.OneInt())
 	}
-	if partialAuctionAmount.IsPositive() {
+
-		auctionLots = append(auctionLots, partialAuctionAmount)
-	}
-	// use the auction lots as weights to split the debt into buckets,
-	// where each bucket represents how much debt that auction will attempt to cover
-	debtAmounts := splitIntIntoWeightedBuckets(debt, auctionLots)
 	debtDenom := k.GetDebtDenom(ctx)
-	for i, debtAmount := range debtAmounts {
+	numAuctions := numberOfAuctions.Int64()
+
+	// create whole auctions
+	for i := int64(0); i < numAuctions; i++ {
+		debtAmount := debtPerAuction
+
+		// distribute unallocated debt left over starting with first auction created
+		if unallocatedDebt.IsPositive() {
+			debtAmount = debtAmount.Add(sdk.OneInt())
+			unallocatedDebt = unallocatedDebt.Sub(sdk.OneInt())
+		}
+
 		penalty := k.ApplyLiquidationPenalty(ctx, collateral.Denom, debtAmount)
+
 		_, err := k.auctionKeeper.StartCollateralAuction(
-			ctx, types.LiquidatorMacc, sdk.NewCoin(collateral.Denom, auctionLots[i]),
+			ctx, types.LiquidatorMacc, sdk.NewCoin(collateral.Denom, auctionSize),
 			sdk.NewCoin(principalDenom, debtAmount.Add(penalty)), []sdk.AccAddress{returnAddr},
-			[]sdk.Int{auctionLots[i]}, sdk.NewCoin(debtDenom, debtAmount),
+			[]sdk.Int{auctionSize}, sdk.NewCoin(debtDenom, debtAmount),
 		)
+
 		if err != nil {
 			return err
 		}
 	}
+
+	// skip last auction if there is no collateral left to auction
+	if !lastAuctionCollateral.IsPositive() {
 		return nil
+	}
+
+	// if the last auction had a larger rounding error than whole auctions,
+	// then unallocatedDebt will be zero since we will have already distributed
+	// all of the unallocated debt
+	if unallocatedDebt.IsPositive() {
+		lastAuctionDebt = lastAuctionDebt.Add(sdk.OneInt())
+		unallocatedDebt = unallocatedDebt.Sub(sdk.OneInt())
+	}
+
+	penalty := k.ApplyLiquidationPenalty(ctx, collateral.Denom, lastAuctionDebt)
+
+	_, err := k.auctionKeeper.StartCollateralAuction(
+		ctx, types.LiquidatorMacc, sdk.NewCoin(collateral.Denom, lastAuctionCollateral),
+		sdk.NewCoin(principalDenom, lastAuctionDebt.Add(penalty)), []sdk.AccAddress{returnAddr},
+		[]sdk.Int{lastAuctionCollateral}, sdk.NewCoin(debtDenom, lastAuctionDebt),
+	)
+
+	return err
 }
 
 // NetSurplusAndDebt burns surplus and debt coins equal to the minimum of surplus and debt balances held by the liquidator module account

x/cdp/keeper/math.go

@@ -1,81 +0,0 @@
-package keeper
-
-import (
-	"sort"
-
-	sdk "github.com/cosmos/cosmos-sdk/types"
-)
-
-// splitIntIntoWeightedBuckets divides an initial +ve integer among several buckets in proportion to the buckets' weights
-// It uses the largest remainder method: https://en.wikipedia.org/wiki/Largest_remainder_method
-// See also: https://stackoverflow.com/questions/13483430/how-to-make-rounded-percentages-add-up-to-100
-// note - copied from auction, tests are located there.
-func splitIntIntoWeightedBuckets(amount sdk.Int, buckets []sdk.Int) []sdk.Int {
-	// Limit input to +ve numbers as algorithm hasn't been scoped to work with -ve numbers.
-	if amount.IsNegative() {
-		panic("negative amount")
-	}
-	if len(buckets) < 1 {
-		panic("no buckets")
-	}
-	for _, bucket := range buckets {
-		if bucket.IsNegative() {
-			panic("negative bucket")
-		}
-	}
-
-	// 1) Split the amount by weights, recording whole number part and remainder
-
-	totalWeights := totalInts(buckets...)
-	if !totalWeights.IsPositive() {
-		panic("total weights must sum to > 0")
-	}
-
-	quotients := make([]quoRem, len(buckets))
-	for i := range buckets {
-		// amount * ( weight/total_weight )
-		q := amount.Mul(buckets[i]).Quo(totalWeights)
-		r := amount.Mul(buckets[i]).Mod(totalWeights)
-		quotients[i] = quoRem{index: i, quo: q, rem: r}
-	}
-
-	// 2) Calculate total left over from remainders, and apportion it to buckets with the highest remainder (to minimize error)
-
-	// sort by decreasing remainder order
-	sort.Slice(quotients, func(i, j int) bool {
-		return quotients[i].rem.GT(quotients[j].rem)
-	})
-
-	// calculate total left over from remainders
-	allocated := sdk.ZeroInt()
-	for _, qr := range quotients {
-		allocated = allocated.Add(qr.quo)
-	}
-	leftToAllocate := amount.Sub(allocated)
-
-	// apportion according to largest remainder
-	results := make([]sdk.Int, len(quotients))
-	for _, qr := range quotients {
-		results[qr.index] = qr.quo
-		if !leftToAllocate.IsZero() {
-			results[qr.index] = results[qr.index].Add(sdk.OneInt())
-			leftToAllocate = leftToAllocate.Sub(sdk.OneInt())
-		}
-	}
-	return results
-}
-
-type quoRem struct {
-	index int
-	quo   sdk.Int
-	rem   sdk.Int
-}
-
-// totalInts adds together sdk.Ints
-func totalInts(is ...sdk.Int) sdk.Int {
-	total := sdk.ZeroInt()
-	for _, i := range is {
-		total = total.Add(i)
-	}
-	return total
-}