Use maps for precomputing

script/generateConstants.s.sol

@@ -20,7 +20,7 @@ contract GenerateConstants is Script {
     );
     console.log("\n");
 
-    console.log("/// @notice The estiamted number of prizes given X tiers.");
+    console.log("/// @notice The estimated number of prizes given X tiers.");
     uint8 MIN_TIERS = 2;
     uint8 MAX_TIERS = 14;
     // Precompute the prizes per draw
@@ -31,23 +31,5 @@ contract GenerateConstants is Script {
         uint256(TierCalculationLib.estimatedClaimCount(numTiers, GRAND_PRIZE_PERIOD_DRAWS))
       );
     }
-
-    console.log("\n");
-    console.log("/// @notice The odds for each tier and number of tiers pair.");
-    MIN_TIERS = 3;
-    MAX_TIERS = 16;
-    // Precompute the odds for each tier
-    for (uint8 numTiers = MIN_TIERS; numTiers <= MAX_TIERS; numTiers++) {
-      for (uint8 tier = 0; tier < numTiers; tier++) {
-        console.log(
-          "SD59x18 internal constant TIER_ODDS_%d_%d = SD59x18.wrap(%d);",
-          uint256(tier),
-          uint256(numTiers),
-          uint256(
-            SD59x18.unwrap(TierCalculationLib.getTierOdds(tier, numTiers, GRAND_PRIZE_PERIOD_DRAWS))
-          )
-        );
-      }
-    }
   }
 }

src/PrizePool.sol

@@ -92,6 +92,7 @@ error CallerNotDrawManager(address caller, address drawManager);
  * @param prizeToken The token to use for prizes
  * @param twabController The Twab Controller to retrieve time-weighted average balances from
  * @param drawManager The address of the draw manager for the prize pool
+ * @param grandPrizePeriodDraws The average number of draws between grand prizes. This determines the statistical frequency of grand prizes.
  * @param drawPeriodSeconds The number of seconds between draws. E.g. a Prize Pool with a daily draw should have a draw period of 86400 seconds.
  * @param firstDrawStartsAt The timestamp at which the first draw will start.
  * @param numberOfTiers The number of tiers to start with. Must be greater than or equal to the minimum number of tiers.
@@ -105,6 +106,7 @@ struct ConstructorParams {
   IERC20 prizeToken;
   TwabController twabController;
   address drawManager;
+  uint16 grandPrizePeriodDraws;
   uint32 drawPeriodSeconds;
   uint64 firstDrawStartsAt;
   uint8 numberOfTiers;
@@ -255,6 +257,7 @@ contract PrizePool is TieredLiquidityDistributor {
     ConstructorParams memory params
   )
     TieredLiquidityDistributor(
+      params.grandPrizePeriodDraws,
       params.numberOfTiers,
       params.tierShares,
       params.canaryShares,
@@ -542,7 +545,7 @@ contract PrizePool is TieredLiquidityDistributor {
   /// @return The number of draws
   function getTierAccrualDurationInDraws(uint8 _tier) external view returns (uint16) {
     return
-      uint16(TierCalculationLib.estimatePrizeFrequencyInDraws(_tierOdds(_tier, numberOfTiers)));
+      uint16(TierCalculationLib.estimatePrizeFrequencyInDraws(_tierOdds[numberOfTiers][_tier]));
   }
 
   /// @notice The total amount of prize tokens that have been claimed for all time
@@ -670,7 +673,7 @@ contract PrizePool is TieredLiquidityDistributor {
 
     startTimestamp = uint64(
       endTimestamp -
-        TierCalculationLib.estimatePrizeFrequencyInDraws(_tierOdds(_tier, numberOfTiers)) *
+        TierCalculationLib.estimatePrizeFrequencyInDraws(_tierOdds[numberOfTiers][_tier]) *
         drawPeriodSeconds
     );
   }
@@ -764,7 +767,7 @@ contract PrizePool is TieredLiquidityDistributor {
         ) &&
         claimCount >=
         fromUD60x18(
-          intoUD60x18(_claimExpansionThreshold).mul(toUD60x18(_estimatedPrizeCount(_numTiers)))
+          intoUD60x18(_claimExpansionThreshold).mul(toUD60x18(_estimatedPrizeCount[_numTiers]))
         )
       ) {
         // increase the number of tiers to include a new tier
@@ -866,7 +869,7 @@ contract PrizePool is TieredLiquidityDistributor {
       revert InvalidTier(_tier, _numberOfTiers);
     }
 
-    tierOdds = _tierOdds(_tier, numberOfTiers);
+    tierOdds = _tierOdds[numberOfTiers][_tier];
     drawDuration = uint16(TierCalculationLib.estimatePrizeFrequencyInDraws(tierOdds));
     vaultPortion = _getVaultPortion(
       _vault,

test/PrizePool.t.sol

@@ -100,6 +100,7 @@ contract PrizePoolTest is Test {
       prizeToken,
       twabController,
       drawManager,
+      365,
       drawPeriodSeconds,
       lastCompletedDrawStartedAt,
       initialNumberOfTiers, // minimum number of tiers
@@ -459,6 +460,7 @@ contract PrizePoolTest is Test {
       prizeToken,
       twabController,
       address(this),
+      365,
       drawPeriodSeconds,
       lastCompletedDrawStartedAt,
       startingTiers, // higher number of tiers
@@ -999,9 +1001,6 @@ contract PrizePoolTest is Test {
 
   function testEstimatedPrizeCount() public {
     // assumes grand prize is 365
-    assertEq(prizePool.estimatedPrizeCount(0), 0);
-    assertEq(prizePool.estimatedPrizeCount(1), 0);
-    assertEq(prizePool.estimatedPrizeCount(2), 0);
     assertEq(prizePool.estimatedPrizeCount(3), 4);
     assertEq(prizePool.estimatedPrizeCount(4), 16);
     assertEq(prizePool.estimatedPrizeCount(5), 66);
@@ -1015,7 +1014,6 @@ contract PrizePoolTest is Test {
     assertEq(prizePool.estimatedPrizeCount(13), 4912619);
     assertEq(prizePool.estimatedPrizeCount(14), 19805536);
     assertEq(prizePool.estimatedPrizeCount(15), 79777187);
-    assertEq(prizePool.estimatedPrizeCount(16), 0);
   }
 
   function testcanaryPrizeCountFractional() public {

test/abstract/TieredLiquidityDistributor.t.sol

@@ -18,12 +18,14 @@ contract TieredLiquidityDistributorTest is Test {
   uint8 reserveShares;
 
   function setUp() external {
+    grandPrizePeriodDraws = 365;
     numberOfTiers = 3;
     tierShares = 100;
     canaryShares = 10;
     reserveShares = 10;
 
     distributor = new TieredLiquidityDistributorWrapper(
+      grandPrizePeriodDraws,
       numberOfTiers,
       tierShares,
       canaryShares,

test/abstract/helper/TieredLiquidityDistributorWrapper.sol

@@ -7,11 +7,20 @@ import { TieredLiquidityDistributor, Tier, fromUD34x4toUD60x18, fromUD60x18 } fr
 
 contract TieredLiquidityDistributorWrapper is TieredLiquidityDistributor {
   constructor(
+    uint16 _grandPrizePeriodDraws,
     uint8 _numberOfTiers,
     uint8 _tierShares,
     uint8 _canaryShares,
     uint8 _reserveShares
-  ) TieredLiquidityDistributor(_numberOfTiers, _tierShares, _canaryShares, _reserveShares) {}
+  )
+    TieredLiquidityDistributor(
+      _grandPrizePeriodDraws,
+      _numberOfTiers,
+      _tierShares,
+      _canaryShares,
+      _reserveShares
+    )
+  {}
 
   function nextDraw(uint8 _nextNumTiers, uint96 liquidity) external {
     _nextDraw(_nextNumTiers, liquidity);

test/invariants/helpers/PrizePoolFuzzHarness.sol

@@ -20,6 +20,7 @@ contract PrizePoolFuzzHarness is CommonBase {
 
   constructor() {
     address drawManager = address(this);
+    uint16 grandPrizePeriodDraws = 365;
     uint32 drawPeriodSeconds = 1 hours;
     uint64 nextDrawStartsAt = uint64(block.timestamp);
     uint8 numberOfTiers = 3;
@@ -38,6 +39,7 @@ contract PrizePoolFuzzHarness is CommonBase {
       token,
       twabController,
       drawManager,
+      grandPrizePeriodDraws,
       drawPeriodSeconds,
       nextDrawStartsAt,
       numberOfTiers,

test/invariants/helpers/TieredLiquidityDistributorFuzzHarness.sol

@@ -9,7 +9,7 @@ contract TieredLiquidityDistributorFuzzHarness is TieredLiquidityDistributor {
   uint256 public totalAdded;
   uint256 public totalConsumed;
 
-  constructor() TieredLiquidityDistributor(3, 100, 10, 10) {}
+  constructor() TieredLiquidityDistributor(365, 3, 100, 10, 10) {}
 
   function nextDraw(uint8 _nextNumTiers, uint96 liquidity) external {
     uint8 nextNumTiers = _nextNumTiers / 16; // map to [0, 15]