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Much simplified cobb douglas implementation

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This commit is contained in:
Greg Hysen 2019-05-23 17:26:04 -07:00
parent 64e42d18e2
commit f15693af1d
2 changed files with 39 additions and 24 deletions
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45
contracts/staking/contracts/src/libs/LibMath.sol
View File

@ -136,8 +136,35 @@ library LibMath {
return result;
}
function _exp2(uint256 numerator_1, uint256 numerator_2, uint256 denominator, uint256 power)
internal
pure
returns (uint256 result)
{
result = (numerator_1 * numerator_2) / denominator;
for(power = power - 1; power > 0; power -= 1) {
result *= numerator_1;
result /= denominator;
result *= numerator_2;
}
return result;
}
function _exp3(uint256 numerator, uint256 denominator, uint256 power)
internal
pure
returns (uint256 result)
{
result = numerator / denominator;
for(power = power - 1; power > 0; power -= 1) {
result = (result * numerator) / denominator;
}
return result;
}
uint256 constant fixedPointDecimals = 18;
uint256 constant scalar = 10**fixedPointDecimals;
uint256 constant halfScalar = 10**(fixedPointDecimals/2);
// rough implementation of cobb-douglas using the nth root fixed point algorithm above
function _cobbDouglas(
@ -153,18 +180,10 @@ library LibMath {
pure
returns (uint256)
{
require(
alphaDenominator - alphaNumerator <= 10,
"numerator of (1 - alpha) is out of range"
);
uint256 feeRatio = _exp((totalRewards * ownerFees) / totalFees, alphaNumerator);
uint256 rootedFeeRatio = _nthRootFixedPoint(feeRatio, alphaDenominator, fixedPointDecimals);
uint256 inverseAlphaNumerator = alphaDenominator - alphaNumerator;
uint256 stakeRatio = _exp((totalRewards * ownerStake) / totalStake, inverseAlphaNumerator);
uint256 rootedStakeRatio = _nthRootFixedPoint(stakeRatio, alphaDenominator, fixedPointDecimals);
return (rootedFeeRatio * rootedStakeRatio) / scalar;
uint256 lhs = _exp3(_nthRootFixedPoint(ownerFees * totalStake, alphaDenominator, 18),
_nthRootFixedPoint(totalFees * ownerStake, alphaDenominator, 18),
alphaNumerator
);
return lhs * ((totalRewards * ownerStake) / totalStake);
}
}

18
contracts/staking/test/core_test.ts
View File

@ -210,12 +210,13 @@ describe('Staking Core', () => {
const alphaNumerator = new BigNumber(1);
const alphaDenominator = new BigNumber(2);
/*const expectedOwnerReward = totalRewards
const expectedOwnerReward = totalRewards
.times(
(ownerFees.div(totalFees)).squareRoot()
).times(
(ownerStake.div(totalStake)).squareRoot()
).dividedToIntegerBy(1); // 25000000000000000000*/
console.log(`EXPECTED - `, stakingWrapper.toFloatingPoint(expectedOwnerReward, 18));
const ownerReward = await stakingWrapper.cobbDouglas(
totalRewards,
@ -226,8 +227,7 @@ describe('Staking Core', () => {
alphaNumerator,
alphaDenominator
);
console.log(ownerReward);
console.log(stakingWrapper.toFloatingPoint(ownerReward, 18));
console.log(`ACTUAL - `, stakingWrapper.toFloatingPoint(ownerReward, 18));
//expect(ownerReward).to.be.bignumber.equal(expectedOwnerReward);
});
@ -240,12 +240,8 @@ describe('Staking Core', () => {
const alphaNumerator = new BigNumber(1);
const alphaDenominator = new BigNumber(3);
/*const expectedOwnerReward = totalRewards
.times(
(ownerFees.div(totalFees)).squareRoot()
).times(
(ownerStake.div(totalStake)).squareRoot()
).dividedToIntegerBy(1); // 25000000000000000000*/
// https://www.wolframalpha.com/input/?i=57.154398+*+(5.64375%2F29.00679)+%5E+(1%2F3)+*+(56+%2F+10906)+%5E+(1+-+1%2F3)
console.log(`EXPECTED - 0.9857...`);
const ownerReward = await stakingWrapper.cobbDouglas(
totalRewards,
@ -256,8 +252,8 @@ describe('Staking Core', () => {
alphaNumerator,
alphaDenominator
);
console.log(ownerReward);
console.log(stakingWrapper.toFloatingPoint(ownerReward, 18));
//console.log(ownerReward);
console.log(`ACTUAL - `, stakingWrapper.toFloatingPoint(ownerReward, 18));
//expect(ownerReward).to.be.bignumber.equal(expectedOwnerReward);
});
});