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fix: various fixes
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@MathisGD
MathisGD committed Nov 4, 2023
1 parent 6e99116 commit aaaa332
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Showing 3 changed files with 30 additions and 26 deletions.
37 changes: 21 additions & 16 deletions src/SpeedJumpIrm.sol
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Original file line number Diff line number Diff line change
Expand Up @@ -105,7 +105,7 @@ contract AdaptativeCurveIrm is IIrm {
return avgBorrowRate;
}

/// @dev Returns err, endBorrowRate and avgBorrowRate.
/// @dev Returns avgBorrowRate and newRateAtTarget.
/// @dev Assumes that the inputs `marketParams` and `id` match.
function _borrowRate(Id id, Market memory market) private view returns (uint256, uint256) {
uint256 utilization =
Expand All @@ -116,44 +116,49 @@ contract AdaptativeCurveIrm is IIrm {
int256 err = (int256(utilization) - int256(TARGET_UTILIZATION)).wDivDown(int256(errNormFactor));

// Safe "unchecked" cast because ADJUSTMENT_SPEED <= type(int256).max.
int256 speed = int256(ADJUSTMENT_SPEED).wMulDown(err);
int256 speed = ADJUSTMENT_SPEED.wMulDown(err);

uint256 prevRateAtTarget = rateAtTarget[id];
uint256 elapsed = (prevRateAtTarget > 0) ? block.timestamp - market.lastUpdate : 0;
uint256 startRateAtTarget = rateAtTarget[id];
uint256 elapsed = (startRateAtTarget > 0) ? block.timestamp - market.lastUpdate : 0;
// Safe "unchecked" cast because elapsed <= block.timestamp.
int256 linearVariation = speed * int256(elapsed);
uint256 variationMultiplier = MathLib.wExp(linearVariation);
// newRateAtTarget is bounded between MIN_RATE_AT_TARGET and MAX_RATE_AT_TARGET.
uint256 newRateAtTarget = (prevRateAtTarget > 0)
? prevRateAtTarget.wMulDown(variationMultiplier).bound(MIN_RATE_AT_TARGET, MAX_RATE_AT_TARGET)
// endRateAtTarget is bounded between MIN_RATE_AT_TARGET and MAX_RATE_AT_TARGET.
uint256 endRateAtTarget = (startRateAtTarget > 0)
? startRateAtTarget.wMulDown(variationMultiplier).bound(MIN_RATE_AT_TARGET, MAX_RATE_AT_TARGET)
: INITIAL_RATE_AT_TARGET;
uint256 endBorrowRate = _curve(newRateAtTarget, err);
uint256 endBorrowRate = _curve(endRateAtTarget, err);

uint256 startBorrowRate = _curve(prevRateAtTarget, err);
// Then we compute the average rate over the period (this is what Morpho needs to accrue the interest).
// NB: startBorrowRate is defined below.
// avgBorrowRate = 1 / elapsed * ∫ startBorrowRate * exp(speed * t) dt between 0 and elapsed
// = startBorrowRate * (exp(linearVariation) - 1) / linearVariation
// = (endBorrowRate - startBorrowRate) / linearVariation
// And avgBorrowRate ~ startBorrowRate ~ endBorrowRate for linearVariation around zero.
// Also, when it is the first interaction (rateAtTarget == 0).
uint256 avgBorrowRate;
if (linearVariation == 0 || prevRateAtTarget == 0) {
if (linearVariation == 0 || startRateAtTarget == 0) {
avgBorrowRate = endBorrowRate;
} else {
// Safe "unchecked" cast to uint256 because linearVariation < 0 <=> endBorrowRate <= startBorrowRate.
uint256 startBorrowRate = _curve(startRateAtTarget, err);
// Safe "unchecked" cast to uint256 because linearVariation < 0 <=> variationMultiplier <= 1.
// <=> endBorrowRate <= startBorrowRate.
avgBorrowRate = uint256((int256(endBorrowRate) - int256(startBorrowRate)).wDivDown(linearVariation));
}

return (avgBorrowRate, newRateAtTarget);
return (avgBorrowRate, endRateAtTarget);
}

/// @dev Returns the rate for a given `_rateAtTarget` and an `err`.
/// The formula of the curve is the following:
/// r = ((1-1/C)*err + 1) * rateAtTarget if err < 0
/// ((C-1)*err + 1) * rateAtTarget else.
function _curve(uint256 _rateAtTarget, int256 err) private view returns (uint256) {
// Safe "unchecked" cast because err >= -1 (in WAD).
if (err < 0) {
return uint256((WAD_INT - WAD_INT.wDivDown(int256(CURVE_STEEPNESS))).wMulDown(err) + WAD_INT).wMulDown(
_rateAtTarget
);
return uint256((WAD - WAD.wDivDown(CURVE_STEEPNESS)).wMulDown(err) + WAD_INT).wMulDown(_rateAtTarget);
} else {
return uint256((CURVE_STEEPNESS - WAD).wMulDown(err) + WAD_INT).wMulDown(_rateAtTarget);
}
return uint256((int256(CURVE_STEEPNESS) - WAD_INT).wMulDown(err) + WAD_INT).wMulDown(_rateAtTarget);
}
}
8 changes: 4 additions & 4 deletions src/libraries/MathLib.sol
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Original file line number Diff line number Diff line change
Expand Up @@ -14,7 +14,6 @@ library MathLib {
using MathLib for uint128;
using MathLib for uint256;
using {wDivDown} for int256;
using {wMulDown} for int256;

/// @dev ln(2).
int256 private constant LN2_INT = 0.693147180559945309 ether;
Expand All @@ -37,16 +36,17 @@ library MathLib {

// Compute e^r with a 2nd-order Taylor polynomial.
// Safe unchecked because |r| < 1, expR < 2 and the sum is positive.
uint256 expR = uint256(WAD_INT + r + r.wMulDown(r) / 2);
uint256 expR = uint256(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;
function wMulDown(uint256 a, int256 b) internal pure returns (int256) {
require(a <= uint256(type(int256).max));
return int256(a) * b / WAD_INT;
}

function wDivDown(int256 a, int256 b) internal pure returns (int256) {
Expand Down
11 changes: 5 additions & 6 deletions test/SpeedJumpIrmTest.sol
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Original file line number Diff line number Diff line change
Expand Up @@ -186,7 +186,7 @@ contract AdaptativeCurveIrmTest is Test {

function _expectedRateAtTarget(Id id, Market memory market) internal view returns (uint256) {
uint256 rateAtTarget = irm.rateAtTarget(id);
int256 speed = int256(ADJUSTMENT_SPEED).wMulDown(_err(market));
int256 speed = ADJUSTMENT_SPEED.wMulDown(_err(market));
uint256 elapsed = (rateAtTarget > 0) ? block.timestamp - market.lastUpdate : 0;
int256 linearVariation = speed * int256(elapsed);
uint256 variationMultiplier = MathLib.wExp(linearVariation);
Expand All @@ -198,7 +198,7 @@ contract AdaptativeCurveIrmTest is Test {
function _expectedAvgRate(Id id, Market memory market) internal view returns (uint256) {
uint256 rateAtTarget = irm.rateAtTarget(id);
int256 err = _err(market);
int256 speed = int256(ADJUSTMENT_SPEED).wMulDown(err);
int256 speed = ADJUSTMENT_SPEED.wMulDown(err);
uint256 elapsed = (rateAtTarget > 0) ? block.timestamp - market.lastUpdate : 0;
int256 linearVariation = speed * int256(elapsed);
uint256 newRateAtTarget = _expectedRateAtTarget(id, market);
Expand All @@ -218,11 +218,10 @@ contract AdaptativeCurveIrmTest is Test {
function _curve(uint256 rateAtTarget, int256 err) internal pure returns (uint256) {
// Safe "unchecked" cast because err >= -1 (in WAD).
if (err < 0) {
return uint256((WAD_INT - WAD_INT.wDivDown(int256(CURVE_STEEPNESS))).wMulDown(err) + WAD_INT).wMulDown(
rateAtTarget
);
return uint256((WAD - WAD.wDivDown(CURVE_STEEPNESS)).wMulDown(err) + WAD_INT).wMulDown(rateAtTarget);
} else {
return uint256((CURVE_STEEPNESS - WAD).wMulDown(err) + WAD_INT).wMulDown(rateAtTarget);
}
return uint256((int256(CURVE_STEEPNESS) - WAD_INT).wMulDown(err) + WAD_INT).wMulDown(rateAtTarget);
}

function _err(Market memory market) internal pure returns (int256) {
Expand Down

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