add hint helper functions to Liquity resolver

contracts/protocols/mainnet/liquity.sol

@@ -30,13 +30,53 @@ interface PoolLike {
   function getETH() external view returns (uint);
 }
 
-contract DSMath {
+interface HintHelpersLike {
+  function computeNominalCR(uint _coll, uint _debt) external pure returns (uint);
+  function computeCR(uint _coll, uint _debt, uint _price) external pure returns (uint);
+  function getApproxHint(uint _CR, uint _numTrials, uint _inputRandomSeed) external view returns (
+    address hintAddress,
+    uint diff,
+    uint latestRandomSeed
+  );
+  function getRedemptionHints(uint _LUSDamount, uint _price, uint _maxIterations) external view returns (
+    address firstHint,
+    uint partialRedemptionHintNICR,
+    uint truncatedLUSDamount
+  );
+}
+
+interface SortedTrovesLike {
+  function getSize() external view returns (uint256);
+  function findInsertPosition(uint256 _ICR, address _prevId, address _nextId) external view returns (address, address);
+}
+
+contract Math {
+  /* DSMath add */
   function add(uint x, uint y) internal pure returns (uint z) {
     require((z = x + y) >= x, "math-not-safe");
   }
+  
+  /* DSMath mul */
+  function mul(uint x, uint y) internal pure returns (uint z) {
+        require(y == 0 || (z = x * y) / y == x, "math-not-safe");
+    }
+
+  /* Uniswap V2 sqrt */
+  function sqrt(uint y) internal pure returns (uint z) {
+    if (y > 3) {
+      z = y;
+      uint x = y / 2 + 1;
+      while (x < z) {
+        z = x;
+        x = (y / x + x) / 2;
+      }
+    } else if (y != 0) {
+      z = 1;
+      }
+    }
 }
 
-contract Helpers is DSMath {
+contract Helpers is Math {
   TroveManagerLike internal constant troveManager =
     TroveManagerLike(0xA39739EF8b0231DbFA0DcdA07d7e29faAbCf4bb2);
 
@@ -52,6 +92,12 @@ contract Helpers is DSMath {
   PoolLike internal constant defaultPool =
     PoolLike(0x896a3F03176f05CFbb4f006BfCd8723F2B0D741C);
 
+  HintHelpersLike internal constant hintHelpers =
+    HintHelpersLike(0xE84251b93D9524E0d2e621Ba7dc7cb3579F997C0);
+  
+  SortedTrovesLike internal constant sortedTroves =
+    SortedTrovesLike(0x8FdD3fbFEb32b28fb73555518f8b361bCeA741A6);
+  
   struct Trove {
     uint collateral;
     uint debt;
@@ -120,6 +166,30 @@ contract Resolver is Helpers {
     bool isInRecoveryMode = troveManager.checkRecoveryMode(oracleEthPrice);
     return System(borrowFee, ethTvl, tcr, isInRecoveryMode);
   }
+
+  function getTrovePositionHints(uint collateral, uint debt, uint searchIterations) external view returns (
+    address upperHint,
+    address lowerHint
+  ) {
+    // See: https://github.com/liquity/dev#supplying-hints-to-trove-operations
+    uint nominalCr = hintHelpers.computeNominalCR(collateral, debt);
+    searchIterations = searchIterations == 0 ? mul(10, sqrt(sortedTroves.getSize())) : searchIterations;
+    (address hintAddress, ,) = hintHelpers.getApproxHint(nominalCr, searchIterations, 3);
+    return sortedTroves.findInsertPosition(nominalCr, hintAddress, hintAddress);
+  }
+
+  function getRedemptionPositionHints(uint amount, uint oracleEthPrice, uint searchIterations) external view returns (
+    uint partialHintNicr,
+    address firstHint,
+    address upperHint,
+    address lowerHint
+  ) {
+    // See: https://github.com/liquity/dev#hints-for-redeemcollateral
+    (firstHint, partialHintNicr, ) = hintHelpers.getRedemptionHints(amount, oracleEthPrice, 0);
+    searchIterations = searchIterations == 0 ? mul(10, sqrt(sortedTroves.getSize())) : searchIterations;
+    (address hintAddress, ,) = hintHelpers.getApproxHint(partialHintNicr, searchIterations, 3);
+    (upperHint, lowerHint) = sortedTroves.findInsertPosition(partialHintNicr, hintAddress, hintAddress);
+  }
 }
 
 contract InstaLiquityResolver is Resolver {

test/liquity.js

@@ -112,6 +112,45 @@ describe("InstaLiquityResolver", () => {
       expect(systemState).to.eql(expectedSystemState);
     });
   });
+
+  describe("getTrovePositionHints()", () => {
+    it("returns the upper and lower address of Troves nearest to the given Trove", async () => {
+      const collateral = hre.ethers.utils.parseEther("10");
+      const debt = hre.ethers.utils.parseUnits("5000", 18);
+      const searchIterations = 10;
+      const [upperHint, lowerHint] = await liquity.getTrovePositionHints(
+        collateral,
+        debt,
+        searchIterations
+      );
+
+      expect(upperHint).eq("0xbf9a4eCC4151f28C03100bA2C0555a3D3e439e69");
+      expect(lowerHint).eq("0xa4FC81A7AB93360543eb1e814D0127f466012CED");
+    });
+  });
+
+  describe("getRedemptionPositionHints()", () => {
+    it("returns the upper and lower address of the range of Troves to be redeemed against the given amount", async () => {
+      const amount = hre.ethers.utils.parseUnits("10000", 18); // 10,000 LUSD
+      const oracleEthPrice = await liquityPriceOracle.callStatic.fetchPrice();
+      const searchIterations = 10;
+      const [
+        partialRedemptionHintNicr,
+        firstHint,
+        upperHint,
+        lowerHint,
+      ] = await liquity.getRedemptionPositionHints(
+        amount,
+        oracleEthPrice,
+        searchIterations
+      );
+
+      expect(partialRedemptionHintNicr).eq("69529933762909647");
+      expect(firstHint).eq("0xc16aDd8bA17ab81B27e930Da8a67848120565d8c");
+      expect(upperHint).eq("0x66882C005188F0F4d95825ED7A7F78ed3055f167");
+      expect(lowerHint).eq("0x0C22C11a8ed4C23ffD19629283548B1692b58e92");
+    });
+  });
 });
 
 const resetHardhatBlockNumber = async (blockNumber) => {