fix(protocol): refine EIP-1559 basefee calculation and gas excess adjustment in TaikoL2

packages/protocol/contract_layout.md

@@ -35,10 +35,10 @@
 | __gap           | uint256[49]                 | 202  | 0      | 1568  | contracts/L2/TaikoL2.sol:TaikoL2 |
 | l2Hashes        | mapping(uint256 => bytes32) | 251  | 0      | 32    | contracts/L2/TaikoL2.sol:TaikoL2 |
 | publicInputHash | bytes32                     | 252  | 0      | 32    | contracts/L2/TaikoL2.sol:TaikoL2 |
-| gasExcess       | uint64                      | 253  | 0      | 8     | contracts/L2/TaikoL2.sol:TaikoL2 |
+| parentGasExcess | uint64                      | 253  | 0      | 8     | contracts/L2/TaikoL2.sol:TaikoL2 |
 | lastSyncedBlock | uint64                      | 253  | 8      | 8     | contracts/L2/TaikoL2.sol:TaikoL2 |
 | parentTimestamp | uint64                      | 253  | 16     | 8     | contracts/L2/TaikoL2.sol:TaikoL2 |
-| __deprecated2   | uint64                      | 253  | 24     | 8     | contracts/L2/TaikoL2.sol:TaikoL2 |
+| parentGasTarget | uint64                      | 253  | 24     | 8     | contracts/L2/TaikoL2.sol:TaikoL2 |
 | l1ChainId       | uint64                      | 254  | 0      | 8     | contracts/L2/TaikoL2.sol:TaikoL2 |
 | __gap           | uint256[46]                 | 255  | 0      | 1472  | contracts/L2/TaikoL2.sol:TaikoL2 |
 

packages/protocol/contracts/L1/TaikoData.sol

@@ -41,7 +41,7 @@ library TaikoData {
         // ---------------------------------------------------------------------
         uint8 basefeeAdjustmentQuotient;
         uint8 basefeeSharingPctg;
-        uint32 gasTargetPerL1Block;
+        uint32 gasIssuancePerSecond;
         // ---------------------------------------------------------------------
         // Group 6: Others
         // ---------------------------------------------------------------------
@@ -126,7 +126,7 @@ library TaikoData {
         uint8 blobIndex;
         uint8 basefeeAdjustmentQuotient;
         uint8 basefeeSharingPctg;
-        uint32 gasTargetPerL1Block;
+        uint32 gasIssuancePerSecond;
     }
 
     /// @dev Struct representing transition to be proven.

packages/protocol/contracts/L1/TaikoL1.sol

@@ -287,7 +287,7 @@ contract TaikoL1 is EssentialContract, ITaikoL1, TaikoEvents {
             maxAnchorHeightOffset: 64,
             basefeeAdjustmentQuotient: 8,
             basefeeSharingPctg: 75,
-            gasTargetPerL1Block: 60_000_000,
+            gasIssuancePerSecond: 5_000_000,
             ontakeForkHeight: 374_400 // = 7200 * 52
          });
     }

packages/protocol/contracts/L1/libs/LibData.sol

@@ -78,7 +78,7 @@ library LibData {
             blobIndex: 0,
             basefeeAdjustmentQuotient: 0,
             basefeeSharingPctg: 0,
-            gasTargetPerL1Block: 0
+            gasIssuancePerSecond: 0
         });
     }
 }

packages/protocol/contracts/L1/libs/LibProposing.sol

@@ -176,7 +176,7 @@ library LibProposing {
                 blobIndex: local.params.blobIndex,
                 basefeeAdjustmentQuotient: _config.basefeeAdjustmentQuotient,
                 basefeeSharingPctg: _config.basefeeSharingPctg,
-                gasTargetPerL1Block: _config.gasTargetPerL1Block
+                gasIssuancePerSecond: _config.gasIssuancePerSecond
             });
         }
 

packages/protocol/contracts/L2/Lib1559Math.sol

@@ -15,8 +15,7 @@ library Lib1559Math {
     error EIP1559_INVALID_PARAMS();
 
     function calc1559BaseFee(
-        uint32 _gasTarget,
-        uint8 _adjustmentQuotient,
+        uint256 _gasTarget,
         uint64 _gasExcess,
         uint64 _gasIssuance,
         uint32 _parentGasUsed
@@ -35,42 +34,50 @@ library Lib1559Math {
         // bonding curve, regardless the actual amount of gas used by this
         // block, however, this block's gas used will affect the next
         // block's base fee.
-        basefee_ = basefee(gasExcess_, uint256(_adjustmentQuotient) * _gasTarget);
-
-        // Always make sure basefee is nonzero, this is required by the node.
-        if (basefee_ == 0) basefee_ = 1;
+        basefee_ = basefee(gasExcess_, _gasTarget);
     }
 
-    /// @dev eth_qty(excess_gas_issued) / (TARGET * ADJUSTMENT_QUOTIENT)
-    /// @param _gasExcess The gas excess value
-    /// @param _adjustmentFactor The product of gasTarget and adjustmentQuotient
-    function basefee(
-        uint256 _gasExcess,
-        uint256 _adjustmentFactor
+    /// @dev Returns the new gas excess that will keep the basefee the same.
+    /// `_newGasTarget * ln(_newGasTarget / _target) + _gasExcess * _newGasTarget / _target`
+    function adjustExcess(
+        uint64 _gasExcess,
+        uint64 _gasTarget,
+        uint64 _newGasTarget
     )
         internal
         pure
-        returns (uint256)
+        returns (uint64)
     {
-        if (_adjustmentFactor == 0) {
-            revert EIP1559_INVALID_PARAMS();
+        if (_gasTarget == 0) revert EIP1559_INVALID_PARAMS();
+
+        uint256 f = LibFixedPointMath.SCALING_FACTOR;
+        uint256 ratio = f * _newGasTarget / _gasTarget;
+        if (ratio > uint256(type(int256).max)) revert EIP1559_INVALID_PARAMS();
+
+        int256 lnRatio = LibFixedPointMath.ln(int256(ratio)); // may be negative
+
+        uint256 newGasExcess;
+        assembly {
+            newGasExcess := sdiv(add(mul(lnRatio, _newGasTarget), mul(ratio, _gasExcess)), f)
         }
-        return _ethQty(_gasExcess, _adjustmentFactor) / LibFixedPointMath.SCALING_FACTOR;
+
+        return uint64(newGasExcess.min(type(uint64).max));
     }
 
-    /// @dev exp(gas_qty / TARGET / ADJUSTMENT_QUOTIENT)
-    function _ethQty(
-        uint256 _gasExcess,
-        uint256 _adjustmentFactor
-    )
-        private
-        pure
-        returns (uint256)
-    {
-        uint256 input = _gasExcess * LibFixedPointMath.SCALING_FACTOR / _adjustmentFactor;
+    /// @dev exp(_gasExcess / _gasTarget) / _gasTarget
+    function basefee(uint256 _gasExcess, uint256 _gasTarget) internal pure returns (uint256) {
+        uint256 fee = ethQty(_gasExcess, _gasTarget) / _gasTarget;
+        return fee == 0 ? 1 : fee;
+    }
+
+    /// @dev exp(_gasExcess / _gasTarget)
+    function ethQty(uint256 _gasExcess, uint256 _gasTarget) internal pure returns (uint256) {
+        if (_gasTarget == 0) revert EIP1559_INVALID_PARAMS();
+
+        uint256 input = LibFixedPointMath.SCALING_FACTOR * _gasExcess / _gasTarget;
         if (input > LibFixedPointMath.MAX_EXP_INPUT) {
             input = LibFixedPointMath.MAX_EXP_INPUT;
         }
-        return uint256(LibFixedPointMath.exp(int256(input)));
+        return uint256(LibFixedPointMath.exp(int256(input))) / LibFixedPointMath.SCALING_FACTOR;
     }
 }

packages/protocol/contracts/L2/TaikoL2.sol

@@ -35,12 +35,12 @@ contract TaikoL2 is EssentialContract {
 
     /// @notice The gas excess value used to calculate the base fee.
     /// @dev Slot 3.
-    uint64 public gasExcess;
+    uint64 public parentGasExcess;
 
     /// @notice The last synced L1 block height.
     uint64 public lastSyncedBlock;
     uint64 private parentTimestamp;
-    uint64 private __deprecated2; // was __currentBlockTimestamp
+    uint64 private parentGasTarget;
 
     /// @notice The L1's chain ID.
     uint64 public l1ChainId;
@@ -49,8 +49,8 @@ contract TaikoL2 is EssentialContract {
 
     /// @notice Emitted when the latest L1 block details are anchored to L2.
     /// @param parentHash The hash of the parent block.
-    /// @param gasExcess The gas excess value used to calculate the base fee.
-    event Anchored(bytes32 parentHash, uint64 gasExcess);
+    /// @param parentGasExcess The gas excess value used to calculate the base fee.
+    event Anchored(bytes32 parentHash, uint64 parentGasExcess);
 
     error L2_BASEFEE_MISMATCH();
     error L2_FORK_ERROR();
@@ -65,12 +65,12 @@ contract TaikoL2 is EssentialContract {
     /// @param _owner The owner of this contract. msg.sender will be used if this value is zero.
     /// @param _rollupAddressManager The address of the {AddressManager} contract.
     /// @param _l1ChainId The ID of the base layer.
-    /// @param _gasExcess The initial gasExcess.
+    /// @param _initialGasExcess The initial parentGasExcess.
     function init(
         address _owner,
         address _rollupAddressManager,
         uint64 _l1ChainId,
-        uint64 _gasExcess
+        uint64 _initialGasExcess
     )
         external
         initializer
@@ -95,11 +95,21 @@ contract TaikoL2 is EssentialContract {
         }
 
         l1ChainId = _l1ChainId;
-        gasExcess = _gasExcess;
-        parentTimestamp = uint64(block.timestamp);
+        parentGasExcess = _initialGasExcess;
         (publicInputHash,) = _calcPublicInputHash(block.number);
     }
 
+    /// @dev Reinitialize some state variables.
+    /// We may want to init the basefee to a default value using one of the following values.
+    /// - _initialGasExcess = 274*5_000_000 => basefee =0.01 gwei
+    /// - _initialGasExcess = 282*5_000_000 => basefee =0.05 gwei
+    /// - _initialGasExcess = 288*5_000_000 => basefee =0.1 gwei
+    function init2(uint64 _initialGasExcess) external onlyOwner reinitializer(2) {
+        parentGasExcess = _initialGasExcess;
+        parentTimestamp = uint64(block.timestamp);
+        parentGasTarget = 0;
+    }
+
     /// @notice Anchors the latest L1 block details to L2 for cross-layer
     /// message verification.
     /// @dev This function can be called freely as the golden touch private key is publicly known,
@@ -134,7 +144,7 @@ contract TaikoL2 is EssentialContract {
         uint64 _anchorBlockId,
         bytes32 _anchorStateRoot,
         uint32 _parentGasUsed,
-        uint32 _gasTargetPerL1Block,
+        uint32 _gasIssuancePerSecond,
         uint8 _basefeeAdjustmentQuotient
     )
         external
@@ -145,7 +155,7 @@ contract TaikoL2 is EssentialContract {
             _anchorBlockId,
             _anchorStateRoot,
             _parentGasUsed,
-            _gasTargetPerL1Block,
+            _gasIssuancePerSecond,
             _basefeeAdjustmentQuotient
         );
     }
@@ -177,21 +187,20 @@ contract TaikoL2 is EssentialContract {
     /// @param _anchorBlockId The synced L1 height in the next Taiko block
     /// @param _parentGasUsed Gas used in the parent block.
     /// @return basefee_ The calculated EIP-1559 base fee per gas.
-    /// @return gasExcess_ The new gasExcess value.
+    /// @return parentGasExcess_ The new parentGasExcess value.
     function getBasefee(
         uint64 _anchorBlockId,
         uint32 _parentGasUsed
     )
         public
         view
-        returns (uint256 basefee_, uint64 gasExcess_)
+        returns (uint256 basefee_, uint64 parentGasExcess_)
     {
         LibL2Config.Config memory config = getConfig();
 
-        (basefee_, gasExcess_) = Lib1559Math.calc1559BaseFee(
-            config.gasTargetPerL1Block,
-            config.basefeeAdjustmentQuotient,
-            gasExcess,
+        (basefee_, parentGasExcess_) = Lib1559Math.calc1559BaseFee(
+            uint256(config.gasTargetPerL1Block) * config.basefeeAdjustmentQuotient,
+            parentGasExcess,
             uint64(_anchorBlockId - lastSyncedBlock) * config.gasTargetPerL1Block,
             _parentGasUsed
         );
@@ -225,29 +234,28 @@ contract TaikoL2 is EssentialContract {
 
     /// @notice Calculates the basefee and the new gas excess value based on parent gas used and gas
     /// excess.
-    /// @param _gasTargetPerL1Block The gas target for L2 based on each L1 block.
+    /// @param _gasIssuancePerSecond The gas target for L2 per second.
     /// @param _blocktime The time between this block and the parent block.
     /// @param _adjustmentQuotient The gas adjustment quotient.
-    /// @param _gasExcess The current gas excess value.
+    /// @param _parentGasExcess The current gas excess value.
     /// @param _parentGasUsed Total gas used by the parent block.
     /// @return basefee_ Next block's base fee.
-    /// @return gasExcess_ The new gas excess value.
+    /// @return parentGasExcess_ The new gas excess value.
     function calculateBaseFee(
-        uint32 _gasTargetPerL1Block,
+        uint32 _gasIssuancePerSecond,
         uint64 _blocktime,
         uint8 _adjustmentQuotient,
-        uint64 _gasExcess,
+        uint64 _parentGasExcess,
         uint32 _parentGasUsed
     )
         public
         pure
-        returns (uint256 basefee_, uint64 gasExcess_)
+        returns (uint256 basefee_, uint64 parentGasExcess_)
     {
         return Lib1559Math.calc1559BaseFee(
-            _gasTargetPerL1Block,
-            _adjustmentQuotient,
-            _gasExcess,
-            _blocktime * _gasTargetPerL1Block / 12,
+            uint256(_gasIssuancePerSecond) * _adjustmentQuotient,
+            _parentGasExcess,
+            _blocktime * _gasIssuancePerSecond,
             _parentGasUsed
         );
     }
@@ -256,7 +264,7 @@ contract TaikoL2 is EssentialContract {
         uint64 _anchorBlockId,
         bytes32 _anchorStateRoot,
         uint32 _parentGasUsed,
-        uint32 _gasTargetPerL1Block,
+        uint32 _gasIssuancePerSecond,
         uint8 _basefeeAdjustmentQuotient
     )
         private
@@ -276,16 +284,26 @@ contract TaikoL2 is EssentialContract {
             _calcPublicInputHash(parentId);
         if (publicInputHash != currentPublicInputHash) revert L2_PUBLIC_INPUT_HASH_MISMATCH();
 
+        // Check if the gas settings has changed
+        bool postFork = block.number >= ontakeForkHeight();
+        uint64 newGasTarget = uint64(_gasIssuancePerSecond) * _basefeeAdjustmentQuotient;
+        if (postFork && newGasTarget != parentGasTarget) {
+            // adjust parentGasExcess to keep the basefee unchanged. Note that due to math
+            // calculation precision, the basefee may change slightly.
+            parentGasExcess =
+                Lib1559Math.adjustExcess(parentGasExcess, parentGasTarget, newGasTarget);
+        }
+
         // Verify the base fee per gas is correct
-        (uint256 basefee, uint64 newGasExcess) = block.number < ontakeForkHeight()
-            ? getBasefee(_anchorBlockId, _parentGasUsed)
-            : calculateBaseFee(
-                _gasTargetPerL1Block,
+        (uint256 basefee, uint64 newGasExcess) = postFork
+            ? calculateBaseFee(
+                _gasIssuancePerSecond,
                 uint64(block.timestamp - parentTimestamp),
                 _basefeeAdjustmentQuotient,
-                gasExcess,
+                parentGasExcess,
                 _parentGasUsed
-            );
+            )
+            : getBasefee(_anchorBlockId, _parentGasUsed);
 
         if (!skipFeeCheck() && block.basefee != basefee) revert L2_BASEFEE_MISMATCH();
 
@@ -300,13 +318,13 @@ contract TaikoL2 is EssentialContract {
         }
 
         // Update state variables
-
         bytes32 parentHash = blockhash(parentId);
         l2Hashes[parentId] = parentHash;
 
         publicInputHash = newPublicInputHash;
-        gasExcess = newGasExcess;
+        parentGasExcess = newGasExcess;
         parentTimestamp = uint64(block.timestamp);
+        parentGasTarget = newGasTarget;
 
         emit Anchored(parentHash, newGasExcess);
     }

packages/protocol/contracts/hekla/HeklaTaikoL1.sol

@@ -22,7 +22,7 @@ contract HeklaTaikoL1 is TaikoL1 {
             maxAnchorHeightOffset: 64,
             basefeeAdjustmentQuotient: 8,
             basefeeSharingPctg: 75,
-            gasTargetPerL1Block: 60_000_000,
+            gasIssuancePerSecond: 5_000_000,
             ontakeForkHeight: 720_000 // = 7200 * 100
          });
     }

packages/protocol/contracts/mainnet/MainnetTaikoL1.sol

@@ -32,7 +32,7 @@ contract MainnetTaikoL1 is TaikoL1 {
             maxAnchorHeightOffset: 64,
             basefeeAdjustmentQuotient: 8,
             basefeeSharingPctg: 75,
-            gasTargetPerL1Block: 60_000_000,
+            gasIssuancePerSecond: 5_000_000,
             ontakeForkHeight: 374_400 // = 7200 * 52
          });
     }