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Merge pull request #66 from morpho-org/fix/bound-constructor
fix(constructor): add parameter bounds & extract constants / wExp
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| // SPDX-License-Identifier: MIT | ||
| pragma solidity ^0.8.0; | ||
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| /// @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; | ||
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| /// @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; | ||
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| /// @notice Maximum curve steepness allowed (scaled by WAD). | ||
| int256 internal constant MAX_CURVE_STEEPNESS = 100 ether; | ||
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| /// @notice Maximum adjustment speed allowed (scaled by WAD). | ||
| int256 internal constant MAX_ADJUSTMENT_SPEED = int256(1_000 ether) / 365 days; | ||
| } |
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| // SPDX-License-Identifier: MIT | ||
| pragma solidity ^0.8.0; | ||
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| import {WAD_INT} from "../MathLib.sol"; | ||
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| /// @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; | ||
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| /// @dev ln(1e-18). | ||
| int256 internal constant LN_WEI_INT = -41.446531673892822312 ether; | ||
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| /// @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; | ||
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| /// @dev The value of wExp(`WEXP_UPPER_BOUND`). | ||
| int256 internal constant WEXP_UPPER_VALUE = 57716089161558943949701069502944508345128.422502756744429568 ether; | ||
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| /// @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; | ||
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| // 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; | ||
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| // Compute e^r with a 2nd-order Taylor polynomial. | ||
| // Safe unchecked because |r| < 1e18. | ||
| int256 expR = WAD_INT + r + (r * r) / WAD_INT / 2; | ||
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| // Return e^x = 2^q * e^r. | ||
| if (q >= 0) return expR << uint256(q); | ||
| else return expR >> uint256(-q); | ||
| } | ||
| } | ||
| } |
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| Original file line number | Diff line number | Diff line change |
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| @@ -0,0 +1,88 @@ | ||
| // SPDX-License-Identifier: MIT | ||
| pragma solidity ^0.8.0; | ||
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| 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"; | ||
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| import "../lib/forge-std/src/Test.sol"; | ||
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| contract ExpLibTest is Test { | ||
| using MathLib for int256; | ||
| using MorphoMathLib for uint256; | ||
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| /// @dev ln(1e-9) truncated at 2 decimal places. | ||
| int256 internal constant LN_GWEI_INT = -20.72 ether; | ||
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| function testWExp(int256 x) public { | ||
| // Bounded to have sub-1% relative error. | ||
| x = bound(x, LN_GWEI_INT, ExpLib.WEXP_UPPER_BOUND); | ||
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| assertApproxEqRel(ExpLib.wExp(x), wadExp(x), 0.01 ether); | ||
| } | ||
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| function testWExpSmall(int256 x) public { | ||
| x = bound(x, ExpLib.LN_WEI_INT, LN_GWEI_INT); | ||
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| assertApproxEqAbs(ExpLib.wExp(x), 0, 1e10); | ||
| } | ||
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| function testWExpTooSmall(int256 x) public { | ||
| x = bound(x, type(int256).min, ExpLib.LN_WEI_INT); | ||
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| assertEq(ExpLib.wExp(x), 0); | ||
| } | ||
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| function testWExpTooLarge(int256 x) public { | ||
| x = bound(x, ExpLib.WEXP_UPPER_BOUND, type(int256).max); | ||
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| assertEq(ExpLib.wExp(x), ExpLib.WEXP_UPPER_VALUE); | ||
| } | ||
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| function testWExpDoesNotLeadToOverflow() public { | ||
| assertGt(ExpLib.WEXP_UPPER_VALUE * 1e18, 0); | ||
| } | ||
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| 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); | ||
| } | ||
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| function testWExpPositive(int256 x) public { | ||
| x = bound(x, 0, type(int256).max); | ||
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| assertGe(ExpLib.wExp(x), 1e18); | ||
| } | ||
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| function testWExpNegative(int256 x) public { | ||
| x = bound(x, type(int256).min, 0); | ||
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| assertLe(ExpLib.wExp(x), 1e18); | ||
| } | ||
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| function testWExpWMulDownMaxRate() public pure { | ||
| ExpLib.wExp(ExpLib.WEXP_UPPER_BOUND).wMulDown(ConstantsLib.MAX_RATE_AT_TARGET); | ||
| } | ||
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| 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; | ||
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| // Compute e^r with a 2nd-order Taylor polynomial. | ||
| // Safe unchecked because |r| < 1e18. | ||
| int256 expR = WAD_INT + r + (r * r) / WAD_INT / 2; | ||
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| // Return e^x = 2^q * e^r. | ||
| if (q >= 0) return expR << uint256(q); | ||
| else return expR >> uint256(-q); | ||
| } | ||
| } | ||
| } |
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