From f15693af1d13c06492d0a32464f4fe65865ff461 Mon Sep 17 00:00:00 2001
From: Greg Hysen <greg.hysen@gmail.com>
Date: Thu, 23 May 2019 17:26:04 -0700
Subject: [PATCH] Much simplified cobb douglas implementation

---
 .../staking/contracts/src/libs/LibMath.sol    | 45 +++++++++++++------
 contracts/staking/test/core_test.ts           | 18 +++-----
 2 files changed, 39 insertions(+), 24 deletions(-)

diff --git a/contracts/staking/contracts/src/libs/LibMath.sol b/contracts/staking/contracts/src/libs/LibMath.sol
index 356549bcb0..2637447d43 100644
--- a/contracts/staking/contracts/src/libs/LibMath.sol
+++ b/contracts/staking/contracts/src/libs/LibMath.sol
@@ -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);
     }
 }
diff --git a/contracts/staking/test/core_test.ts b/contracts/staking/test/core_test.ts
index 7846844417..d3d4bab3b0 100644
--- a/contracts/staking/test/core_test.ts
+++ b/contracts/staking/test/core_test.ts
@@ -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);
         });
     });