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return early linear adaptation zero #88

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merged 3 commits into from
Nov 16, 2023
Merged

return early linear adaptation zero #88

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500a957
feat: return early
MathisGD Nov 16, 2023
af5e27e
Merge branch 'feat/riemann-avg' into feat/return-early-linearAdaptati…
MathisGD Nov 16, 2023
1387436
docs: format doc
MathisGD Nov 16, 2023
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49 changes: 27 additions & 22 deletions src/SpeedJumpIrm.sol
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Original file line number Diff line number Diff line change
Expand Up @@ -137,29 +137,34 @@ contract AdaptiveCurveIrm is IIrm {
int256 elapsed = int256(block.timestamp - market.lastUpdate);
int256 linearAdaptation = speed * elapsed;

// Formula of the average rate that should be returned to Morpho Blue:
// avg = 1/T ∫_0^T curve(startRateAtTarget * exp(speed * x), err) dx
// The integral is approximated with a Riemann sum (steps of length T/N). To underestimate the rate, a left
// Riemann (a=0, b=N-1) is done when the rate goes up (err>0) and a right Riemann (a=1, b=N) is done when
// the rate goes down (err<0).
// avg ~= 1/T Σ_i=a^b curve(startRateAtTarget * exp(speed * T/N * i), err) * T / N
// ~= Σ_i=a^b curve(startRateAtTarget * exp(linearAdaptation/N * i), err) / N
// curve is linear in startRateAtTarget, so:
// ~= curve(Σ_i=a^b startRateAtTarget * exp(linearAdaptation/N * i), err) / N
// ~= curve(Σ_i=a^b startRateAtTarget * exp(linearAdaptation/N * i) / N, err)
int256 sumRateAtTarget;
int256 step = linearAdaptation / N_STEPS;
// Compute the terms 1 to N_STEPS - 1.
for (int256 k = 1; k < N_STEPS; k++) {
sumRateAtTarget += _newRateAtTarget(startRateAtTarget, step * k);
if (linearAdaptation == 0) {
// If linearAdaptation == 0, avgRateAtTarget = endRateAtTarget = startRateAtTarget;
return (uint256(_curve(startRateAtTarget, err)), startRateAtTarget);
} else {
// Formula of the average rate that should be returned to Morpho Blue:
// avg = 1/T ∫_0^T curve(startRateAtTarget * exp(speed * x), err) dx
// The integral is approximated with a Riemann sum (steps of length T/N). To underestimate the rate, a
// left Riemann (a=0, b=N-1) is done when the rate goes up (err>0) and a right Riemann (a=1, b=N) is
// done when the rate goes down (err<0).
// avg ~= 1/T Σ_i=a^b curve(startRateAtTarget * exp(speed * T/N * i), err) * T / N
// ~= Σ_i=a^b curve(startRateAtTarget * exp(linearAdaptation/N * i), err) / N
// curve is linear in startRateAtTarget, so:
// ~= curve(Σ_i=a^b startRateAtTarget * exp(linearAdaptation/N * i), err) / N
// ~= curve(Σ_i=a^b startRateAtTarget * exp(linearAdaptation/N * i) / N, err)
int256 sumRateAtTarget;
int256 step = linearAdaptation / N_STEPS;
// Compute the terms 1 to N_STEPS - 1.
for (int256 k = 1; k < N_STEPS; k++) {
sumRateAtTarget += _newRateAtTarget(startRateAtTarget, step * k);
}
int256 endRateAtTarget = _newRateAtTarget(startRateAtTarget, linearAdaptation);
// Add the term 0 for a left Riemann or the term N_STEPS for a right Riemann.
sumRateAtTarget += err < 0 ? endRateAtTarget : startRateAtTarget;
int256 avgRateAtTarget = sumRateAtTarget / N_STEPS;

// Safe "unchecked" cast because avgRateAtTarget >= 0.
return (uint256(_curve(avgRateAtTarget, err)), endRateAtTarget);
}
int256 endRateAtTarget = _newRateAtTarget(startRateAtTarget, linearAdaptation);
// Add the term 0 for a left Riemann or the term N_STEPS for a right Riemann.
sumRateAtTarget += err < 0 ? endRateAtTarget : startRateAtTarget;
int256 avgRateAtTarget = sumRateAtTarget / N_STEPS;

// Safe "unchecked" cast because avgRateAtTarget >= 0.
return (uint256(_curve(avgRateAtTarget, err)), endRateAtTarget);
}
}

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