fix(constructor): add parameter bounds & extract constants / wExp

src/SpeedJumpIrm.sol → src/AdaptiveCurveIrm.sol

@@ -6,6 +6,8 @@ import {IIrm} from "../lib/morpho-blue/src/interfaces/IIrm.sol";
 import {UtilsLib} from "./libraries/UtilsLib.sol";
 import {ErrorsLib} from "./libraries/ErrorsLib.sol";
 import {MathLib, WAD_INT as WAD} from "./libraries/MathLib.sol";
+import {ExpLib} from "./libraries/adaptive-curve/ExpLib.sol";
+import {ConstantsLib} from "./libraries/adaptive-curve/ConstantsLib.sol";
 import {MarketParamsLib} from "../lib/morpho-blue/src/libraries/MarketParamsLib.sol";
 import {Id, MarketParams, Market} from "../lib/morpho-blue/src/interfaces/IMorpho.sol";
 import {MathLib as MorphoMathLib} from "../lib/morpho-blue/src/libraries/MathLib.sol";
@@ -25,25 +27,25 @@ contract AdaptiveCurveIrm is IIrm {
     /// @notice Emitted when a borrow rate is updated.
     event BorrowRateUpdate(Id indexed id, uint256 avgBorrowRate, uint256 rateAtTarget);
 
-    /* CONSTANTS */
+    /* IMMUTABLES */
 
-    /// @notice Maximum rate at target per second (scaled by WAD) (1B% APR).
-    int256 public constant MAX_RATE_AT_TARGET = int256(0.01e9 ether) / 365 days;
-    /// @notice Mininimum rate at target per second (scaled by WAD) (0.1% APR).
-    int256 public constant MIN_RATE_AT_TARGET = int256(0.001 ether) / 365 days;
     /// @notice Address of Morpho.
     address public immutable MORPHO;
+
     /// @notice Curve steepness (scaled by WAD).
-    /// @dev Verified to be greater than 1 at construction.
+    /// @dev Verified to be inside the expected range at construction.
     int256 public immutable CURVE_STEEPNESS;
+
     /// @notice Adjustment speed (scaled by WAD).
     /// @dev The speed is per second, so the rate moves at a speed of ADJUSTMENT_SPEED * err each second (while being
-    /// continuously compounded). A typical value for the ADJUSTMENT_SPEED would be 10 ethers / 365 days.
-    /// @dev Verified to be non-negative at construction.
+    /// continuously compounded). A typical value for the ADJUSTMENT_SPEED would be 10 ether / 365 days.
+    /// @dev Verified to be inside the expected range at construction.
     int256 public immutable ADJUSTMENT_SPEED;
+
     /// @notice Target utilization (scaled by WAD).
     /// @dev Verified to be strictly between 0 and 1 at construction.
     int256 public immutable TARGET_UTILIZATION;
+
     /// @notice Initial rate at target per second (scaled by WAD).
     /// @dev Verified to be between MIN_RATE_AT_TARGET and MAX_RATE_AT_TARGET at contruction.
     int256 public immutable INITIAL_RATE_AT_TARGET;
@@ -71,11 +73,13 @@ contract AdaptiveCurveIrm is IIrm {
     ) {
         require(morpho != address(0), ErrorsLib.ZERO_ADDRESS);
         require(curveSteepness >= WAD, ErrorsLib.INPUT_TOO_SMALL);
+        require(curveSteepness <= ConstantsLib.MAX_CURVE_STEEPNESS, ErrorsLib.INPUT_TOO_LARGE);
         require(adjustmentSpeed >= 0, ErrorsLib.INPUT_TOO_SMALL);
+        require(adjustmentSpeed <= ConstantsLib.MAX_ADJUSTMENT_SPEED, ErrorsLib.INPUT_TOO_LARGE);
         require(targetUtilization < WAD, ErrorsLib.INPUT_TOO_LARGE);
         require(targetUtilization > 0, ErrorsLib.ZERO_INPUT);
-        require(initialRateAtTarget >= MIN_RATE_AT_TARGET, ErrorsLib.INPUT_TOO_SMALL);
-        require(initialRateAtTarget <= MAX_RATE_AT_TARGET, ErrorsLib.INPUT_TOO_LARGE);
+        require(initialRateAtTarget >= ConstantsLib.MIN_RATE_AT_TARGET, ErrorsLib.INPUT_TOO_SMALL);
+        require(initialRateAtTarget <= ConstantsLib.MAX_RATE_AT_TARGET, ErrorsLib.INPUT_TOO_LARGE);
 
         MORPHO = morpho;
         CURVE_STEEPNESS = curveSteepness;
@@ -179,6 +183,8 @@ contract AdaptiveCurveIrm is IIrm {
     /// The formula is: max(min(startRateAtTarget * exp(linearAdaptation), maxRateAtTarget), minRateAtTarget).
     function _newRateAtTarget(int256 startRateAtTarget, int256 linearAdaptation) private pure returns (int256) {
         // Non negative because MIN_RATE_AT_TARGET > 0.
-        return startRateAtTarget.wMulDown(MathLib.wExp(linearAdaptation)).bound(MIN_RATE_AT_TARGET, MAX_RATE_AT_TARGET);
+        return startRateAtTarget.wMulDown(ExpLib.wExp(linearAdaptation)).bound(
+            ConstantsLib.MIN_RATE_AT_TARGET, ConstantsLib.MAX_RATE_AT_TARGET
+        );
     }
 }

src/libraries/MathLib.sol

@@ -8,51 +8,8 @@ int256 constant WAD_INT = int256(WAD);
 /// @title MathLib
 /// @author Morpho Labs
 /// @custom:contact security@morpho.org
-/// @notice Library to manage fixed-point arithmetic and approximate the exponential function.
+/// @notice Library to manage fixed-point arithmetic on signed integers.
 library MathLib {
-    using MathLib for uint128;
-    using MathLib for uint256;
-    using {wDivDown} for int256;
-
-    /// @dev ln(2).
-    int256 internal constant LN_2_INT = 0.693147180559945309 ether;
-
-    /// @dev ln(1e-18).
-    int256 internal constant LN_WEI_INT = -41.446531673892822312 ether;
-
-    /// @dev Above this bound, `wExp` is clipped to avoid overflowing when multiplied with 1 ether.
-    /// @dev This upper bound corresponds to: ln(type(int256).max / 1e36) (scaled by WAD, floored).
-    int256 internal constant WEXP_UPPER_BOUND = 93.859467695000404319 ether;
-
-    /// @dev The value of wExp(`WEXP_UPPER_BOUND`).
-    int256 internal constant WEXP_UPPER_VALUE = 57716089161558943862588783571184261698504.523000224082296832 ether;
-
-    /// @dev Returns an approximation of exp.
-    function wExp(int256 x) internal pure returns (int256) {
-        unchecked {
-            // If x < ln(1e-18) then exp(x) < 1e-18 so it is rounded to zero.
-            if (x < LN_WEI_INT) return 0;
-            // `wExp` is clipped to avoid overflowing when multiplied with 1 ether.
-            if (x >= WEXP_UPPER_BOUND) return WEXP_UPPER_VALUE;
-
-            // Decompose x as x = q * ln(2) + r with q an integer and -ln(2)/2 <= r <= ln(2)/2.
-            // q = x / ln(2) rounded half toward zero.
-            int256 roundingAdjustment = (x < 0) ? -(LN_2_INT / 2) : (LN_2_INT / 2);
-            // Safe unchecked because x is bounded.
-            int256 q = (x + roundingAdjustment) / LN_2_INT;
-            // Safe unchecked because |q * ln(2) - x| <= ln(2)/2.
-            int256 r = x - q * LN_2_INT;
-
-            // Compute e^r with a 2nd-order Taylor polynomial.
-            // Safe unchecked because |r| < 1e18.
-            int256 expR = WAD_INT + r + (r * r) / WAD_INT / 2;
-
-            // Return e^x = 2^q * e^r.
-            if (q >= 0) return expR << uint256(q);
-            else return expR >> uint256(-q);
-        }
-    }
-
     function wMulDown(int256 a, int256 b) internal pure returns (int256) {
         return a * b / WAD_INT;
     }

src/libraries/adaptive-curve/ConstantsLib.sol

@@ -0,0 +1,19 @@
+// SPDX-License-Identifier: MIT
+pragma solidity ^0.8.0;
+
+/// @title ConstantsLib
+/// @author Morpho Labs
+/// @custom:contact security@morpho.org
+library ConstantsLib {
+    /// @notice Maximum rate at target per second (scaled by WAD) (1B% APR).
+    int256 internal constant MAX_RATE_AT_TARGET = int256(0.01e9 ether) / 365 days;
+
+    /// @notice Mininimum rate at target per second (scaled by WAD) (0.1% APR).
+    int256 internal constant MIN_RATE_AT_TARGET = int256(0.001 ether) / 365 days;
+
+    /// @notice Maximum curve steepness allowed (scaled by WAD).
+    int256 internal constant MAX_CURVE_STEEPNESS = 100 ether;
+
+    /// @notice Maximum adjustment speed allowed (scaled by WAD).
+    int256 internal constant MAX_ADJUSTMENT_SPEED = int256(1_000 ether) / 365 days;
+}

src/libraries/adaptive-curve/ExpLib.sol

@@ -0,0 +1,49 @@
+// SPDX-License-Identifier: MIT
+pragma solidity ^0.8.0;
+
+import {WAD_INT} from "../MathLib.sol";
+
+/// @title ExpLib
+/// @author Morpho Labs
+/// @custom:contact security@morpho.org
+/// @notice Library to approximate the exponential function.
+library ExpLib {
+    /// @dev ln(2).
+    int256 internal constant LN_2_INT = 0.693147180559945309 ether;
+
+    /// @dev ln(1e-18).
+    int256 internal constant LN_WEI_INT = -41.446531673892822312 ether;
+
+    /// @dev Above this bound, `wExp` is clipped to avoid overflowing when multiplied with 1 ether.
+    /// @dev This upper bound corresponds to: ln(type(int256).max / 1e36) (scaled by WAD, floored).
+    int256 internal constant WEXP_UPPER_BOUND = 93.859467695000404319 ether;
+
+    /// @dev The value of wExp(`WEXP_UPPER_BOUND`).
+    int256 internal constant WEXP_UPPER_VALUE = 57716089161558943949701069502944508345128.422502756744429568 ether;
+
+    /// @dev Returns an approximation of exp.
+    function wExp(int256 x) internal pure returns (int256) {
+        unchecked {
+            // If x < ln(1e-18) then exp(x) < 1e-18 so it is rounded to zero.
+            if (x < LN_WEI_INT) return 0;
+            // `wExp` is clipped to avoid overflowing when multiplied with 1 ether.
+            if (x >= WEXP_UPPER_BOUND) return WEXP_UPPER_VALUE;
+
+            // Decompose x as x = q * ln(2) + r with q an integer and -ln(2)/2 <= r <= ln(2)/2.
+            // q = x / ln(2) rounded half toward zero.
+            int256 roundingAdjustment = (x < 0) ? -(LN_2_INT / 2) : (LN_2_INT / 2);
+            // Safe unchecked because x is bounded.
+            int256 q = (x + roundingAdjustment) / LN_2_INT;
+            // Safe unchecked because |q * ln(2) - x| <= ln(2)/2.
+            int256 r = x - q * LN_2_INT;
+
+            // Compute e^r with a 2nd-order Taylor polynomial.
+            // Safe unchecked because |r| < 1e18.
+            int256 expR = WAD_INT + r + (r * r) / WAD_INT / 2;
+
+            // Return e^x = 2^q * e^r.
+            if (q >= 0) return expR << uint256(q);
+            else return expR >> uint256(-q);
+        }
+    }
+}

test/SpeedJumpIrmTest.sol → test/AdaptiveCurveIrmTest.sol

@@ -1,12 +1,11 @@
 // SPDX-License-Identifier: MIT
 pragma solidity ^0.8.0;
 
-import "../src/SpeedJumpIrm.sol";
+import "../src/AdaptiveCurveIrm.sol";
 
 import "../lib/forge-std/src/Test.sol";
 
 contract AdaptiveCurveIrmTest is Test {
-    using MathLib for int256;
     using MathLib for int256;
     using MathLib for uint256;
     using UtilsLib for int256;
@@ -216,10 +215,6 @@ contract AdaptiveCurveIrmTest is Test {
         assertApproxEqRel(irm.rateAtTarget(marketParams.id()), expectedRateAtTarget, 0.001 ether, "rateAtTarget");
     }
 
-    function testWExpWMulDownMaxRate() public view {
-        MathLib.wExp(MathLib.WEXP_UPPER_BOUND).wMulDown(irm.MAX_RATE_AT_TARGET());
-    }
-
     /* HANDLERS */
 
     function handleBorrowRate(uint256 totalSupplyAssets, uint256 totalBorrowAssets, uint256 elapsed) external {
@@ -243,17 +238,25 @@ contract AdaptiveCurveIrmTest is Test {
         market.totalBorrowAssets = 9 ether;
         market.totalSupplyAssets = 10 ether;
 
-        assertGe(irm.borrowRateView(marketParams, market), uint256(irm.MIN_RATE_AT_TARGET().wDivDown(CURVE_STEEPNESS)));
-        assertGe(irm.borrowRate(marketParams, market), uint256(irm.MIN_RATE_AT_TARGET().wDivDown(CURVE_STEEPNESS)));
+        assertGe(
+            irm.borrowRateView(marketParams, market), uint256(ConstantsLib.MIN_RATE_AT_TARGET.wDivDown(CURVE_STEEPNESS))
+        );
+        assertGe(
+            irm.borrowRate(marketParams, market), uint256(ConstantsLib.MIN_RATE_AT_TARGET.wDivDown(CURVE_STEEPNESS))
+        );
     }
 
     function invariantLeMaxRateAtTarget() public {
         Market memory market;
         market.totalBorrowAssets = 9 ether;
         market.totalSupplyAssets = 10 ether;
 
-        assertLe(irm.borrowRateView(marketParams, market), uint256(irm.MAX_RATE_AT_TARGET().wMulDown(CURVE_STEEPNESS)));
-        assertLe(irm.borrowRate(marketParams, market), uint256(irm.MAX_RATE_AT_TARGET().wMulDown(CURVE_STEEPNESS)));
+        assertLe(
+            irm.borrowRateView(marketParams, market), uint256(ConstantsLib.MAX_RATE_AT_TARGET.wMulDown(CURVE_STEEPNESS))
+        );
+        assertLe(
+            irm.borrowRate(marketParams, market), uint256(ConstantsLib.MAX_RATE_AT_TARGET.wMulDown(CURVE_STEEPNESS))
+        );
     }
 
     /* HELPERS */
@@ -263,9 +266,11 @@ contract AdaptiveCurveIrmTest is Test {
         int256 speed = ADJUSTMENT_SPEED.wMulDown(_err(market));
         uint256 elapsed = (rateAtTarget > 0) ? block.timestamp - market.lastUpdate : 0;
         int256 linearAdaptation = speed * int256(elapsed);
-        int256 adaptationMultiplier = MathLib.wExp(linearAdaptation);
+        int256 adaptationMultiplier = ExpLib.wExp(linearAdaptation);
         return (rateAtTarget > 0)
-            ? rateAtTarget.wMulDown(adaptationMultiplier).bound(irm.MIN_RATE_AT_TARGET(), irm.MAX_RATE_AT_TARGET())
+            ? rateAtTarget.wMulDown(adaptationMultiplier).bound(
+                ConstantsLib.MIN_RATE_AT_TARGET, ConstantsLib.MAX_RATE_AT_TARGET
+            )
             : INITIAL_RATE_AT_TARGET;
     }
 

test/ExpLibTest.sol

@@ -0,0 +1,88 @@
+// SPDX-License-Identifier: MIT
+pragma solidity ^0.8.0;
+
+import {MathLib, WAD_INT} from "../src/libraries/MathLib.sol";
+import {ConstantsLib} from "../src/libraries/adaptive-curve/ConstantsLib.sol";
+import {ExpLib} from "../src/libraries/adaptive-curve/ExpLib.sol";
+import {wadExp} from "../lib/solmate/src/utils/SignedWadMath.sol";
+import {MathLib as MorphoMathLib} from "../lib/morpho-blue/src/libraries/MathLib.sol";
+
+import "../lib/forge-std/src/Test.sol";
+
+contract ExpLibTest is Test {
+    using MathLib for int256;
+    using MorphoMathLib for uint256;
+
+    /// @dev ln(1e-9) truncated at 2 decimal places.
+    int256 internal constant LN_GWEI_INT = -20.72 ether;
+
+    function testWExp(int256 x) public {
+        // Bounded to have sub-1% relative error.
+        x = bound(x, LN_GWEI_INT, ExpLib.WEXP_UPPER_BOUND);
+
+        assertApproxEqRel(ExpLib.wExp(x), wadExp(x), 0.01 ether);
+    }
+
+    function testWExpSmall(int256 x) public {
+        x = bound(x, ExpLib.LN_WEI_INT, LN_GWEI_INT);
+
+        assertApproxEqAbs(ExpLib.wExp(x), 0, 1e10);
+    }
+
+    function testWExpTooSmall(int256 x) public {
+        x = bound(x, type(int256).min, ExpLib.LN_WEI_INT);
+
+        assertEq(ExpLib.wExp(x), 0);
+    }
+
+    function testWExpTooLarge(int256 x) public {
+        x = bound(x, ExpLib.WEXP_UPPER_BOUND, type(int256).max);
+
+        assertEq(ExpLib.wExp(x), ExpLib.WEXP_UPPER_VALUE);
+    }
+
+    function testWExpDoesNotLeadToOverflow() public {
+        assertGt(ExpLib.WEXP_UPPER_VALUE * 1e18, 0);
+    }
+
+    function testWExpContinuousUpperBound() public {
+        assertApproxEqRel(ExpLib.wExp(ExpLib.WEXP_UPPER_BOUND - 1), ExpLib.WEXP_UPPER_VALUE, 1e-10 ether);
+        assertEq(_wExpUnbounded(ExpLib.WEXP_UPPER_BOUND), ExpLib.WEXP_UPPER_VALUE);
+    }
+
+    function testWExpPositive(int256 x) public {
+        x = bound(x, 0, type(int256).max);
+
+        assertGe(ExpLib.wExp(x), 1e18);
+    }
+
+    function testWExpNegative(int256 x) public {
+        x = bound(x, type(int256).min, 0);
+
+        assertLe(ExpLib.wExp(x), 1e18);
+    }
+
+    function testWExpWMulDownMaxRate() public pure {
+        ExpLib.wExp(ExpLib.WEXP_UPPER_BOUND).wMulDown(ConstantsLib.MAX_RATE_AT_TARGET);
+    }
+
+    function _wExpUnbounded(int256 x) internal pure returns (int256) {
+        unchecked {
+            // Decompose x as x = q * ln(2) + r with q an integer and -ln(2)/2 <= r <= ln(2)/2.
+            // q = x / ln(2) rounded half toward zero.
+            int256 roundingAdjustment = (x < 0) ? -(ExpLib.LN_2_INT / 2) : (ExpLib.LN_2_INT / 2);
+            // Safe unchecked because x is bounded.
+            int256 q = (x + roundingAdjustment) / ExpLib.LN_2_INT;
+            // Safe unchecked because |q * ln(2) - x| <= ln(2)/2.
+            int256 r = x - q * ExpLib.LN_2_INT;
+
+            // Compute e^r with a 2nd-order Taylor polynomial.
+            // Safe unchecked because |r| < 1e18.
+            int256 expR = WAD_INT + r + (r * r) / WAD_INT / 2;
+
+            // Return e^x = 2^q * e^r.
+            if (q >= 0) return expR << uint256(q);
+            else return expR >> uint256(-q);
+        }
+    }
+}