367 lines
12 KiB
TypeScript
367 lines
12 KiB
TypeScript
import { BigNumber } from 'bignumber.js';
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export const RStatusOne = 0;
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export const RStatusAboveOne = 1;
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export const RStatusBelowOne = 2;
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export class DODOHelper {
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// unstable
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public B!: BigNumber; // DODO._BASE_BALANCE_() / 10^baseDecimals
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public Q!: BigNumber; // DODO._QUOTE_BALANCE_() / 10^quoteDecimals
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public B0!: BigNumber; // DODO._TARGET_BASE_TOKEN_AMOUNT_() / 10^baseDecimals
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public Q0!: BigNumber; // DODO._TARGET_QUOTE_TOKEN_AMOUNT_() / 10^quoteDecimals
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public RStatus!: number; // DODO._R_STATUS_()
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public OraclePrice!: BigNumber; // DODO.getOraclePrice() / 10^(18-baseDecimals+quoteDecimals)
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// stable
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public k!: BigNumber; // DODO._K_()/10^18
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public mtFeeRate!: BigNumber; // DODO._MT_FEE_RATE_()/10^18
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public lpFeeRate!: BigNumber; // DODO._LP_FEE_RATE_()/10^18
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constructor(pairDetail:any) {
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this.B = pairDetail.B
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this.Q = pairDetail.Q
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this.B0 = pairDetail.B0
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this.Q0 = pairDetail.Q0
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this.RStatus = pairDetail.RStatus
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this.OraclePrice = pairDetail.OraclePrice
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this.k = pairDetail.k
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this.mtFeeRate = pairDetail.mtFeeRate
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this.lpFeeRate = pairDetail.lpFeeRate
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}
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// return mid price
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public getMidPrice(): BigNumber {
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if (this.RStatus === RStatusOne) {
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return this.OraclePrice;
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}
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if (this.RStatus === RStatusAboveOne) {
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let R = this.B0.div(this.B);
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R = R.multipliedBy(R)
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.multipliedBy(this.k)
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.minus(this.k)
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.plus(new BigNumber(1));
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return this.OraclePrice.multipliedBy(R);
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}
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if (this.RStatus === RStatusBelowOne) {
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let R = this.Q0.div(this.Q);
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R = R.multipliedBy(R)
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.multipliedBy(this.k)
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.minus(this.k)
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.plus(new BigNumber(1));
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return this.OraclePrice.div(R);
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}
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return this.OraclePrice;
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}
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// return the targetBase and targetQuote assuming system balanced
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public getExpectedTarget(): { base: BigNumber; quote: BigNumber } {
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let baseTarget: BigNumber;
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let quoteTarget: BigNumber;
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baseTarget = this.B0;
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quoteTarget = this.Q0;
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if (this.RStatus === RStatusOne) {
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baseTarget = this.B0;
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quoteTarget = this.Q0;
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}
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if (this.RStatus === RStatusAboveOne) {
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quoteTarget = this.Q0;
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baseTarget = solveQuadraticFunctionForTarget(this.B, this.k, this.Q.minus(this.Q0).div(this.OraclePrice));
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}
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if (this.RStatus === RStatusBelowOne) {
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baseTarget = this.B0;
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quoteTarget = solveQuadraticFunctionForTarget(
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this.Q,
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this.k,
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this.B.minus(this.B0).multipliedBy(this.OraclePrice)
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);
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}
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return {
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base: baseTarget,
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quote: quoteTarget
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};
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}
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// return paid quote amount (fee deducted)
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public queryBuyBase(amount: BigNumber) {
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let mtFee = amount.multipliedBy(this.mtFeeRate);
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let lpFee = amount.multipliedBy(this.lpFeeRate);
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amount = amount.plus(mtFee).plus(lpFee);
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let target = this.getExpectedTarget();
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let quote = new BigNumber(0);
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if (this.RStatus === RStatusOne) {
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quote = this.ROneBuyBase(amount, target.base);
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} else if (this.RStatus === RStatusAboveOne) {
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quote = this.RAboveBuyBase(amount, target.base);
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} else {
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let backOneBase = this.B.minus(target.base);
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let backOneQuote = target.quote.minus(this.Q);
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if (amount.isLessThanOrEqualTo(backOneBase)) {
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quote = this.RBelowBuyBase(amount, target.quote);
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} else {
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quote = backOneQuote.plus(this.ROneBuyBase(amount.minus(backOneBase), target.base));
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}
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}
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return quote
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}
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// return received quote amount (fee deducted)
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public querySellBase(amount: BigNumber) {
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let result: BigNumber;
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let target = this.getExpectedTarget();
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if (this.RStatus === RStatusOne) {
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result = this.ROneSellBase(amount, target.quote);
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} else if (this.RStatus === RStatusBelowOne) {
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result = this.RBelowSellBase(amount, target.quote);
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} else {
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let backOneBase = target.base.minus(this.B);
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let backOneQuote = this.Q.minus(target.quote);
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if (amount.isLessThanOrEqualTo(backOneBase)) {
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result = this.RAboveSellBase(amount, target.base);
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} else {
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result = backOneQuote.plus(this.ROneSellBase(amount.minus(backOneBase), target.quote));
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}
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}
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let mtFee = result.multipliedBy(this.mtFeeRate);
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let lpFee = result.multipliedBy(this.lpFeeRate);
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const quote = result.minus(mtFee).minus(lpFee);
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return quote
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}
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// return paid base amount (fee deducted)
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public queryBuyQuote(amount: BigNumber): BigNumber {
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let mtFee = amount.multipliedBy(this.mtFeeRate);
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let lpFee = amount.multipliedBy(this.lpFeeRate);
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amount = amount.plus(mtFee).plus(lpFee);
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let target = this.getExpectedTarget();
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if (this.RStatus === RStatusOne) {
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return this.ROneBuyQuote(amount, target.quote);
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} else if (this.RStatus === RStatusBelowOne) {
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return this.RBelowBuyQuote(amount, target.quote);
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} else {
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let backOneBase = target.base.minus(this.B);
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let backOneQuote = this.Q.minus(target.quote);
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if (amount.isLessThanOrEqualTo(backOneQuote)) {
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return this.RAboveBuyQuote(amount, target.base);
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} else {
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return backOneBase.plus(this.ROneBuyQuote(amount.minus(backOneQuote), target.quote));
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}
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}
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}
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// return received base amount (fee deducted)
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public querySellQuote(amount: BigNumber): BigNumber {
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let result: BigNumber;
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let target = this.getExpectedTarget();
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if (this.RStatus === RStatusOne) {
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result = this.ROneSellQuote(amount, target.base);
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} else if (this.RStatus === RStatusAboveOne) {
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result = this.RAboveSellQuote(amount, target.base);
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} else {
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let backOneBase = this.B.minus(target.base);
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let backOneQuote = target.quote.minus(this.Q);
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if (amount.isLessThanOrEqualTo(backOneQuote)) {
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result = this.RBelowSellQuote(amount, target.quote);
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} else {
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result = backOneBase.plus(this.ROneSellQuote(amount.minus(backOneQuote), target.base));
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}
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}
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let mtFee = result.multipliedBy(this.mtFeeRate);
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let lpFee = result.multipliedBy(this.lpFeeRate);
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return result.minus(mtFee).minus(lpFee);
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}
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public getWithdrawBasePenalty(amount: BigNumber): BigNumber {
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if (this.RStatus === RStatusAboveOne) {
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let baseTarget = solveQuadraticFunctionForTarget(this.B, this.k, this.Q.minus(this.Q0).div(this.OraclePrice));
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let baseTargetWithdraw = solveQuadraticFunctionForTarget(
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this.B.minus(amount),
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this.k,
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this.Q.minus(this.Q0).div(this.OraclePrice)
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);
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let penalty = baseTarget.minus(baseTargetWithdraw).minus(amount);
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return penalty;
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} else {
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return new BigNumber(0);
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}
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}
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public getWithdrawQuotePenalty(amount: BigNumber): BigNumber {
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if (this.RStatus === RStatusBelowOne) {
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let quoteTarget = solveQuadraticFunctionForTarget(
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this.Q,
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this.k,
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this.B.minus(this.B0).multipliedBy(this.OraclePrice)
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);
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let quoteTargetWithdraw = solveQuadraticFunctionForTarget(
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this.Q.minus(amount),
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this.k,
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this.B.minus(this.B0).multipliedBy(this.OraclePrice)
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);
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let penalty = quoteTarget.minus(quoteTargetWithdraw).minus(amount);
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return penalty;
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} else {
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return new BigNumber(0);
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}
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}
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// =========== helper ROne ===========
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public ROneBuyBase(amount: BigNumber, targetBase: BigNumber): BigNumber {
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if (amount.isGreaterThanOrEqualTo(targetBase)) {
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throw new Error('ROne Buy Base Amount Exceed Limitation');
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}
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return integrate(targetBase, targetBase, targetBase.minus(amount), this.OraclePrice, this.k);
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}
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public ROneBuyQuote(amount: BigNumber, targetQuote: BigNumber): BigNumber {
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if (amount.isGreaterThanOrEqualTo(targetQuote)) {
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throw new Error('ROne Buy Quote Amount Exceed Limitation');
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}
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return integrate(
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targetQuote,
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targetQuote,
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targetQuote.minus(amount),
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new BigNumber(1).div(this.OraclePrice),
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this.k
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);
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}
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public ROneSellBase(amount: BigNumber, targetQuote: BigNumber): BigNumber {
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let newQ = solveQuadraticFunctionForTrade(targetQuote, targetQuote, this.OraclePrice, amount.negated(), this.k);
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return targetQuote.minus(newQ);
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}
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public ROneSellQuote(amount: BigNumber, targetBase: BigNumber): BigNumber {
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let newB = solveQuadraticFunctionForTrade(
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targetBase,
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targetBase,
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new BigNumber(1).div(this.OraclePrice),
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amount.negated(),
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this.k
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);
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return targetBase.minus(newB);
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}
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// =========== helper RAbove ===========
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public RAboveBuyBase(amount: BigNumber, targetBase: BigNumber): BigNumber {
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if (amount.isGreaterThanOrEqualTo(this.B)) {
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throw new Error('RAbove Buy Base Amount Exceed Limitation');
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}
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return integrate(targetBase, this.B, this.B.minus(amount), this.OraclePrice, this.k);
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}
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public RAboveSellBase(amount: BigNumber, targetBase: BigNumber): BigNumber {
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if (amount.plus(this.B).isGreaterThan(targetBase)) {
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throw new Error('RAbove Sell Base Amount Exceed Limitation');
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}
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return integrate(targetBase, this.B.plus(amount), this.B, this.OraclePrice, this.k);
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}
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public RAboveBuyQuote(amount: BigNumber, targetBase: BigNumber): BigNumber {
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let newB = solveQuadraticFunctionForTrade(
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targetBase,
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this.B,
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new BigNumber(1).div(this.OraclePrice),
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amount,
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this.k
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);
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return newB.minus(this.B);
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}
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public RAboveSellQuote(amount: BigNumber, targetBase: BigNumber): BigNumber {
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let newB = solveQuadraticFunctionForTrade(
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targetBase,
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this.B,
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new BigNumber(1).div(this.OraclePrice),
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amount.negated(),
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this.k
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);
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return this.B.minus(newB);
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}
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// =========== helper RBelow ===========
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public RBelowBuyQuote(amount: BigNumber, targetQuote: BigNumber): BigNumber {
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if (amount.isGreaterThanOrEqualTo(this.Q)) {
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throw new Error('RBelow Buy Quote Amount Exceed Limitation');
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}
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return integrate(targetQuote, this.Q, this.Q.minus(amount), new BigNumber(1).div(this.OraclePrice), this.k);
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}
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public RBelowSellQuote(amount: BigNumber, targetQuote: BigNumber): BigNumber {
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if (amount.plus(this.Q).isGreaterThan(targetQuote)) {
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throw new Error('RBelow Sell Quote Amount Exceed Limitation');
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}
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return integrate(targetQuote, this.Q.plus(amount), this.Q, new BigNumber(1).div(this.OraclePrice), this.k);
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}
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public RBelowBuyBase(amount: BigNumber, targetQuote: BigNumber): BigNumber {
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let newQ = solveQuadraticFunctionForTrade(targetQuote, this.Q, this.OraclePrice, amount, this.k);
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return newQ.minus(this.Q);
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}
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public RBelowSellBase(amount: BigNumber, targetQuote: BigNumber): BigNumber {
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let newQ = solveQuadraticFunctionForTrade(targetQuote, this.Q, this.OraclePrice, amount.negated(), this.k);
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return this.Q.minus(newQ);
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}
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}
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export const integrate = (V0: BigNumber, V1: BigNumber, V2: BigNumber, i: BigNumber, k: BigNumber): BigNumber => {
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let fairAmount = i.multipliedBy(V1.minus(V2));
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let penalty = V0.multipliedBy(V0)
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.div(V1)
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.div(V2)
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.multipliedBy(k);
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return fairAmount.multipliedBy(new BigNumber(1).minus(k).plus(penalty));
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};
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export const solveQuadraticFunctionForTrade = (
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V0: BigNumber,
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V1: BigNumber,
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i: BigNumber,
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delta: BigNumber,
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k: BigNumber
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): BigNumber => {
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// -b = (1-k)V1-kV0^2/V1+i*delta
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let minusB = new BigNumber(1).minus(k).multipliedBy(V1);
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minusB = minusB.minus(
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k
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.multipliedBy(V0)
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.multipliedBy(V0)
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.div(V1)
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);
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minusB = minusB.plus(i.multipliedBy(delta));
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// sqrt(b*b+4(1-k)kQ0*Q0)
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let squareRoot = new BigNumber(4)
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.multipliedBy(new BigNumber(1).minus(k))
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.multipliedBy(k)
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.multipliedBy(V0)
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.multipliedBy(V0);
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squareRoot = minusB
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.multipliedBy(minusB)
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.plus(squareRoot)
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.sqrt();
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// 2(1-k)
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let denominator = new BigNumber(2).multipliedBy(new BigNumber(1).minus(k));
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return minusB.plus(squareRoot).div(denominator);
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};
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export const solveQuadraticFunctionForTarget = (V1: BigNumber, k: BigNumber, fairAmount: BigNumber): BigNumber => {
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// V0 = V1+V1*(sqrt-1)/2k
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let sqrt = new BigNumber(4)
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.multipliedBy(k)
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.multipliedBy(fairAmount)
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.div(V1);
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sqrt = new BigNumber(1).plus(sqrt).sqrt();
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let premium = sqrt.minus(new BigNumber(1)).div(k.multipliedBy(new BigNumber(2)));
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return V1.multipliedBy(new BigNumber(1).plus(premium));
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};
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