PMMPricing library
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mingda
237
contracts/lib/PMMPricing.sol
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237
contracts/lib/PMMPricing.sol
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/*
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Copyright 2020 DODO ZOO.
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SPDX-License-Identifier: Apache-2.0
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*/
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pragma solidity 0.6.9;
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pragma experimental ABIEncoderV2;
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import {SafeMath} from "../lib/SafeMath.sol";
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import {DecimalMath} from "../lib/DecimalMath.sol";
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import {DODOMath} from "../lib/DODOMath.sol";
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/**
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* @title Pricing
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* @author DODO Breeder
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*
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* @notice DODO Pricing model
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*/
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enum RState {ONE, ABOVE_ONE, BELOW_ONE}
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struct PMMState {
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uint256 i;
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uint256 K;
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uint256 B;
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uint256 Q;
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uint256 B0;
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uint256 Q0;
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RState R;
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}
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library PMMPricing {
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using SafeMath for uint256;
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function sellBaseToken(PMMState memory state, uint256 payBaseAmount)
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public
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pure
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returns (uint256 receiveQuoteAmount, RState newR)
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{
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if (state.R == RState.ONE) {
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// case 1: R=1
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// R falls below one
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receiveQuoteAmount = _ROneSellBaseToken(state, payBaseAmount);
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newR = RState.BELOW_ONE;
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} else if (state.R == RState.ABOVE_ONE) {
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uint256 backToOnePayBase = state.B0.sub(state.B);
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uint256 backToOneReceiveQuote = state.Q.sub(state.Q0);
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// case 2: R>1
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// complex case, R status depends on trading amount
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if (payBaseAmount < backToOnePayBase) {
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// case 2.1: R status do not change
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receiveQuoteAmount = _RAboveSellBaseToken(state, payBaseAmount);
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newR = RState.ABOVE_ONE;
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if (receiveQuoteAmount > backToOneReceiveQuote) {
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// [Important corner case!] may enter this branch when some precision problem happens. And consequently contribute to negative spare quote amount
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// to make sure spare quote>=0, mannually set receiveQuote=backToOneReceiveQuote
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receiveQuoteAmount = backToOneReceiveQuote;
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}
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} else if (payBaseAmount == backToOnePayBase) {
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// case 2.2: R status changes to ONE
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receiveQuoteAmount = backToOneReceiveQuote;
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newR = RState.ONE;
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} else {
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// case 2.3: R status changes to BELOW_ONE
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receiveQuoteAmount = backToOneReceiveQuote.add(
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_ROneSellBaseToken(state, payBaseAmount.sub(backToOnePayBase))
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);
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newR = RState.BELOW_ONE;
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}
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} else {
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// state.R == RState.BELOW_ONE
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// case 3: R<1
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receiveQuoteAmount = _RBelowSellBaseToken(state, payBaseAmount);
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newR = RState.BELOW_ONE;
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}
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return (receiveQuoteAmount, newR);
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}
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function sellQuoteToken(PMMState memory state, uint256 payQuoteAmount)
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public
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pure
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returns (uint256 receiveBaseAmount, RState newR)
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{
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if (state.R == RState.ONE) {
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receiveBaseAmount = _ROneSellQuoteToken(state, payQuoteAmount);
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newR = RState.ABOVE_ONE;
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} else if (state.R == RState.ABOVE_ONE) {
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receiveBaseAmount = _RAboveSellQuoteToken(state, payQuoteAmount);
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newR = RState.ABOVE_ONE;
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} else {
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uint256 backToOnePayQuote = state.Q0.sub(state.Q);
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uint256 backToOneReceiveBase = state.B.sub(state.B0);
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if (payQuoteAmount < backToOnePayQuote) {
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receiveBaseAmount = _RBelowSellQuoteToken(state, payQuoteAmount);
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newR = RState.BELOW_ONE;
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if (receiveBaseAmount > backToOneReceiveBase) {
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receiveBaseAmount = backToOneReceiveBase;
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}
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} else if (payQuoteAmount == backToOnePayQuote) {
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receiveBaseAmount = backToOneReceiveBase;
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newR = RState.ONE;
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} else {
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receiveBaseAmount = backToOneReceiveBase.add(
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_ROneSellQuoteToken(state, payQuoteAmount.sub(backToOnePayQuote))
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);
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newR = RState.ABOVE_ONE;
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}
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}
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return (receiveBaseAmount, newR);
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}
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// ============ R = 1 cases ============
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function _ROneSellBaseToken(PMMState memory state, uint256 payBaseAmount)
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internal
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pure
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returns (uint256 receiveQuoteToken)
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{
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// in theory Q2 <= targetQuoteTokenAmount
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// however when amount is close to 0, precision problems may cause Q2 > targetQuoteTokenAmount
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return
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DODOMath._SolveQuadraticFunctionForTrade(
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state.Q0,
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state.Q0,
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DecimalMath.mulFloor(state.i, payBaseAmount),
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false,
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state.K
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);
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}
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function _ROneSellQuoteToken(PMMState memory state, uint256 payQuoteAmount)
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internal
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pure
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returns (uint256 receiveBaseToken)
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{
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return
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DODOMath._SolveQuadraticFunctionForTrade(
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state.B0,
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state.B0,
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DecimalMath.divFloor(payQuoteAmount, state.i),
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false,
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state.K
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);
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}
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// ============ R < 1 cases ============
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function _RBelowSellQuoteToken(PMMState memory state, uint256 payQuoteAmount)
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internal
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pure
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returns (uint256 receiveBaseToken)
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{
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return
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DODOMath._GeneralIntegrate(
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state.Q0,
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state.Q.add(payQuoteAmount),
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state.Q,
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DecimalMath.divFloor(DecimalMath.ONE, state.i),
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state.K
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);
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}
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function _RBelowSellBaseToken(PMMState memory state, uint256 payBaseAmount)
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internal
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pure
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returns (uint256 receiveQuoteToken)
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{
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return
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DODOMath._SolveQuadraticFunctionForTrade(
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state.Q0,
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state.Q,
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DecimalMath.mul(state.i, payBaseAmount),
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false,
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state.K
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);
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}
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// ============ R > 1 cases ============
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function _RAboveSellBaseToken(PMMState memory state, uint256 payBaseAmount)
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internal
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pure
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returns (uint256 receiveQuoteToken)
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{
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return
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DODOMath._GeneralIntegrate(
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state.B0,
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state.B.add(payBaseAmount),
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state.B,
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state.i,
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state.K
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);
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}
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function _RAboveSellQuoteToken(PMMState memory state, uint256 payQuoteAmount)
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internal
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pure
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returns (uint256 receiveBaseToken)
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{
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return
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DODOMath._SolveQuadraticFunctionForTrade(
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state.B0,
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state.B,
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DecimalMath.divFloor(payQuoteAmount, state.i),
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false,
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state.i
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);
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}
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// ============ Helper functions ============
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function adjustedTarget(PMMState memory state) public pure {
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if (state.R == RState.BELOW_ONE) {
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uint256 fairAmount = DecimalMath.mulFloor(state.B.sub(state.B0), state.i);
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state.Q0 = DODOMath._SolveQuadraticFunctionForTarget(state.B, state.K, fairAmount);
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} else if (state.R == RState.ABOVE_ONE) {
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uint256 fairAmount = DecimalMath.divFloor(state.Q.sub(state.Q0), state.i);
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state.B0 = DODOMath._SolveQuadraticFunctionForTarget(state.Q, state.K, fairAmount);
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}
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}
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function getMidPrice(PMMState memory state) public pure returns (uint256 midPrice) {
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if (state.R == RState.BELOW_ONE) {
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uint256 R = DecimalMath.divFloor(state.Q0.mul(state.Q0).div(state.Q), state.Q);
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R = DecimalMath.ONE.sub(state.K).add(DecimalMath.mul(state.K, R));
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return DecimalMath.divFloor(state.i, R);
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} else {
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uint256 R = DecimalMath.divFloor(state.B0.mul(state.B0).div(state.B), state.B);
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R = DecimalMath.ONE.sub(state.K).add(DecimalMath.mul(state.K, R));
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return DecimalMath.mul(state.i, R);
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}
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}
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}
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