Merge pull request #1003 from 0xProject/feature/contracts/roundup

[contracts] Add getPartialAmountCeil and isRoundingErrorCeil

9 files changed, 198 insertions, 36 deletions

diff --git a/packages/contracts/src/2.0.0/extensions/Forwarder/MixinExchangeWrapper.sol b/packages/contracts/src/2.0.0/extensions/Forwarder/MixinExchangeWrapper.sol
index 218713d3c..a7ff400b9 100644
--- a/packages/contracts/src/2.0.0/extensions/Forwarder/MixinExchangeWrapper.sol
+++ b/packages/contracts/src/2.0.0/extensions/Forwarder/MixinExchangeWrapper.sol
@@ -163,7 +163,7 @@ contract MixinExchangeWrapper is
 
             // Convert the remaining amount of makerAsset to buy into remaining amount
             // of takerAsset to sell, assuming entire amount can be sold in the current order
-            uint256 remainingTakerAssetFillAmount = getPartialAmount(
+            uint256 remainingTakerAssetFillAmount = getPartialAmountFloor(
                 orders[i].takerAssetAmount,
                 orders[i].makerAssetAmount,
                 remainingMakerAssetFillAmount
@@ -231,7 +231,7 @@ contract MixinExchangeWrapper is
 
             // Convert the remaining amount of ZRX to buy into remaining amount
             // of WETH to sell, assuming entire amount can be sold in the current order.
-            uint256 remainingWethSellAmount = getPartialAmount(
+            uint256 remainingWethSellAmount = getPartialAmountFloor(
                 orders[i].takerAssetAmount,
                 safeSub(orders[i].makerAssetAmount, orders[i].takerFee),  // our exchange rate after fees 
                 remainingZrxBuyAmount
diff --git a/packages/contracts/src/2.0.0/extensions/Forwarder/MixinForwarderCore.sol b/packages/contracts/src/2.0.0/extensions/Forwarder/MixinForwarderCore.sol
index 42cec4d36..14f191879 100644
--- a/packages/contracts/src/2.0.0/extensions/Forwarder/MixinForwarderCore.sol
+++ b/packages/contracts/src/2.0.0/extensions/Forwarder/MixinForwarderCore.sol
@@ -87,7 +87,7 @@ contract MixinForwarderCore is
         uint256 makerAssetAmountPurchased;
         if (orders[0].makerAssetData.equals(ZRX_ASSET_DATA)) {
             // Calculate amount of WETH that won't be spent on ETH fees.
-            wethSellAmount = getPartialAmount(
+            wethSellAmount = getPartialAmountFloor(
                 PERCENTAGE_DENOMINATOR,
                 safeAdd(PERCENTAGE_DENOMINATOR, feePercentage),
                 msg.value
@@ -103,7 +103,7 @@ contract MixinForwarderCore is
             makerAssetAmountPurchased = safeSub(orderFillResults.makerAssetFilledAmount, orderFillResults.takerFeePaid);
         } else {
             // 5% of WETH is reserved for filling feeOrders and paying feeRecipient.
-            wethSellAmount = getPartialAmount(
+            wethSellAmount = getPartialAmountFloor(
                 MAX_WETH_FILL_PERCENTAGE,
                 PERCENTAGE_DENOMINATOR,
                 msg.value
diff --git a/packages/contracts/src/2.0.0/extensions/Forwarder/MixinWeth.sol b/packages/contracts/src/2.0.0/extensions/Forwarder/MixinWeth.sol
index 93e85e599..5863b522d 100644
--- a/packages/contracts/src/2.0.0/extensions/Forwarder/MixinWeth.sol
+++ b/packages/contracts/src/2.0.0/extensions/Forwarder/MixinWeth.sol
@@ -82,7 +82,7 @@ contract MixinWeth is
         uint256 wethRemaining = safeSub(msg.value, wethSold);
 
         // Calculate ETH fee to pay to feeRecipient.
-        uint256 ethFee = getPartialAmount(
+        uint256 ethFee = getPartialAmountFloor(
             feePercentage,
             PERCENTAGE_DENOMINATOR,
             wethSoldExcludingFeeOrders
diff --git a/packages/contracts/src/2.0.0/protocol/Exchange/MixinExchangeCore.sol b/packages/contracts/src/2.0.0/protocol/Exchange/MixinExchangeCore.sol
index ab5c6e507..f3a0591b2 100644
--- a/packages/contracts/src/2.0.0/protocol/Exchange/MixinExchangeCore.sol
+++ b/packages/contracts/src/2.0.0/protocol/Exchange/MixinExchangeCore.sol
@@ -320,7 +320,7 @@ contract MixinExchangeCore is
 
         // Validate fill order rounding
         require(
-            !isRoundingError(
+            !isRoundingErrorFloor(
                 takerAssetFilledAmount,
                 order.takerAssetAmount,
                 order.makerAssetAmount
@@ -376,17 +376,17 @@ contract MixinExchangeCore is
     {
         // Compute proportional transfer amounts
         fillResults.takerAssetFilledAmount = takerAssetFilledAmount;
-        fillResults.makerAssetFilledAmount = getPartialAmount(
+        fillResults.makerAssetFilledAmount = getPartialAmountFloor(
             takerAssetFilledAmount,
             order.takerAssetAmount,
             order.makerAssetAmount
         );
-        fillResults.makerFeePaid = getPartialAmount(
+        fillResults.makerFeePaid = getPartialAmountFloor(
             takerAssetFilledAmount,
             order.takerAssetAmount,
             order.makerFee
         );
-        fillResults.takerFeePaid = getPartialAmount(
+        fillResults.takerFeePaid = getPartialAmountFloor(
             takerAssetFilledAmount,
             order.takerAssetAmount,
             order.takerFee
diff --git a/packages/contracts/src/2.0.0/protocol/Exchange/MixinMatchOrders.sol b/packages/contracts/src/2.0.0/protocol/Exchange/MixinMatchOrders.sol
index 56b309a1b..20f4b1c33 100644
--- a/packages/contracts/src/2.0.0/protocol/Exchange/MixinMatchOrders.sol
+++ b/packages/contracts/src/2.0.0/protocol/Exchange/MixinMatchOrders.sol
@@ -183,7 +183,7 @@ contract MixinMatchOrders is
             leftTakerAssetFilledAmount = leftTakerAssetAmountRemaining;
 
             // The right order receives an amount proportional to how much was spent.
-            rightTakerAssetFilledAmount = getPartialAmount(
+            rightTakerAssetFilledAmount = getPartialAmountFloor(
                 rightOrder.takerAssetAmount,
                 rightOrder.makerAssetAmount,
                 leftTakerAssetFilledAmount
@@ -193,7 +193,7 @@ contract MixinMatchOrders is
             rightTakerAssetFilledAmount = rightTakerAssetAmountRemaining;
 
             // The left order receives an amount proportional to how much was spent.
-            leftTakerAssetFilledAmount = getPartialAmount(
+            leftTakerAssetFilledAmount = getPartialAmountFloor(
                 rightOrder.makerAssetAmount,
                 rightOrder.takerAssetAmount,
                 rightTakerAssetFilledAmount
diff --git a/packages/contracts/src/2.0.0/protocol/Exchange/MixinWrapperFunctions.sol b/packages/contracts/src/2.0.0/protocol/Exchange/MixinWrapperFunctions.sol
index 86194f461..1b77cfbcb 100644
--- a/packages/contracts/src/2.0.0/protocol/Exchange/MixinWrapperFunctions.sol
+++ b/packages/contracts/src/2.0.0/protocol/Exchange/MixinWrapperFunctions.sol
@@ -298,7 +298,7 @@ contract MixinWrapperFunctions is
 
             // Convert the remaining amount of makerAsset to buy into remaining amount
             // of takerAsset to sell, assuming entire amount can be sold in the current order
-            uint256 remainingTakerAssetFillAmount = getPartialAmount(
+            uint256 remainingTakerAssetFillAmount = getPartialAmountFloor(
                 orders[i].takerAssetAmount,
                 orders[i].makerAssetAmount,
                 remainingMakerAssetFillAmount
@@ -350,7 +350,7 @@ contract MixinWrapperFunctions is
 
             // Convert the remaining amount of makerAsset to buy into remaining amount
             // of takerAsset to sell, assuming entire amount can be sold in the current order
-            uint256 remainingTakerAssetFillAmount = getPartialAmount(
+            uint256 remainingTakerAssetFillAmount = getPartialAmountFloor(
                 orders[i].takerAssetAmount,
                 orders[i].makerAssetAmount,
                 remainingMakerAssetFillAmount
diff --git a/packages/contracts/src/2.0.0/protocol/Exchange/libs/LibMath.sol b/packages/contracts/src/2.0.0/protocol/Exchange/libs/LibMath.sol
index fa09da6ac..0e0fba5d2 100644
--- a/packages/contracts/src/2.0.0/protocol/Exchange/libs/LibMath.sol
+++ b/packages/contracts/src/2.0.0/protocol/Exchange/libs/LibMath.sol
@@ -25,12 +25,12 @@ contract LibMath is
     SafeMath
 {
 
-    /// @dev Calculates partial value given a numerator and denominator.
+    /// @dev Calculates partial value given a numerator and denominator rounded down.
     /// @param numerator Numerator.
     /// @param denominator Denominator.
     /// @param target Value to calculate partial of.
-    /// @return Partial value of target.
-    function getPartialAmount(
+    /// @return Partial value of target rounded down.
+    function getPartialAmountFloor(
         uint256 numerator,
         uint256 denominator,
         uint256 target
@@ -39,19 +39,56 @@ contract LibMath is
         pure
         returns (uint256 partialAmount)
     {
+        require(
+            denominator > 0,
+            "DIVISION_BY_ZERO"
+        );
+        
         partialAmount = safeDiv(
             safeMul(numerator, target),
             denominator
         );
         return partialAmount;
     }
-
-    /// @dev Checks if rounding error > 0.1%.
+    
+    /// @dev Calculates partial value given a numerator and denominator rounded down.
+    /// @param numerator Numerator.
+    /// @param denominator Denominator.
+    /// @param target Value to calculate partial of.
+    /// @return Partial value of target rounded up.
+    function getPartialAmountCeil(
+        uint256 numerator,
+        uint256 denominator,
+        uint256 target
+    )
+        internal
+        pure
+        returns (uint256 partialAmount)
+    {
+        require(
+            denominator > 0,
+            "DIVISION_BY_ZERO"
+        );
+        
+        // safeDiv computes `floor(a / b)`. We use the identity (a, b integer):
+        //       ceil(a / b) = floor((a + b - 1) / b)
+        // To implement `ceil(a / b)` using safeDiv.
+        partialAmount = safeDiv(
+            safeAdd(
+                safeMul(numerator, target),
+                safeSub(denominator, 1)
+            ),
+            denominator
+        );
+        return partialAmount;
+    }
+    
+    /// @dev Checks if rounding error >= 0.1% when rounding down.
     /// @param numerator Numerator.
     /// @param denominator Denominator.
     /// @param target Value to multiply with numerator/denominator.
     /// @return Rounding error is present.
-    function isRoundingError(
+    function isRoundingErrorFloor(
         uint256 numerator,
         uint256 denominator,
         uint256 target
@@ -60,16 +97,73 @@ contract LibMath is
         pure
         returns (bool isError)
     {
-        uint256 remainder = mulmod(target, numerator, denominator);
-        if (remainder == 0) {
-            return false; // No rounding error.
+        require(
+            denominator > 0,
+            "DIVISION_BY_ZERO"
+        );
+        
+        // The absolute rounding error is the difference between the rounded
+        // value and the ideal value. The relative rounding error is the
+        // absolute rounding error divided by the absolute value of the
+        // ideal value. This is undefined when the ideal value is zero.
+        //
+        // The ideal value is `numerator * target / denominator`.
+        // Let's call `numerator * target % denominator` the remainder.
+        // The absolute error is `remainder / denominator`.
+        //
+        // When the ideal value is zero, we require the absolute error to
+        // be zero. Fortunately, this is always the case. The ideal value is
+        // zero iff `numerator == 0` and/or `target == 0`. In this case the
+        // remainder and absolute error are also zero. 
+        if (target == 0 || numerator == 0) {
+            return false;
         }
-
-        uint256 errPercentageTimes1000000 = safeDiv(
-            safeMul(remainder, 1000000),
-            safeMul(numerator, target)
+        
+        // Otherwise, we want the relative rounding error to be strictly
+        // less than 0.1%.
+        // The relative error is `remainder / (numerator * target)`.
+        // We want the relative error less than 1 / 1000:
+        //        remainder / (numerator * denominator)  <  1 / 1000
+        // or equivalently:
+        //        1000 * remainder  <  numerator * target
+        // so we have a rounding error iff:
+        //        1000 * remainder  >=  numerator * target
+        uint256 remainder = mulmod(target, numerator, denominator);
+        isError = safeMul(1000, remainder) >= safeMul(numerator, target);
+        return isError;
+    }
+    
+    /// @dev Checks if rounding error >= 0.1% when rounding up.
+    /// @param numerator Numerator.
+    /// @param denominator Denominator.
+    /// @param target Value to multiply with numerator/denominator.
+    /// @return Rounding error is present.
+    function isRoundingErrorCeil(
+        uint256 numerator,
+        uint256 denominator,
+        uint256 target
+    )
+        internal
+        pure
+        returns (bool isError)
+    {
+        require(
+            denominator > 0,
+            "DIVISION_BY_ZERO"
         );
-        isError = errPercentageTimes1000000 > 1000;
+        
+        // See the comments in `isRoundingError`.
+        if (target == 0 || numerator == 0) {
+            // When either is zero, the ideal value and rounded value are zero
+            // and there is no rounding error. (Although the relative error
+            // is undefined.)
+            return false;
+        }
+        // Compute remainder as before
+        uint256 remainder = mulmod(target, numerator, denominator);
+        // TODO: safeMod
+        remainder = safeSub(denominator, remainder) % denominator;
+        isError = safeMul(1000, remainder) >= safeMul(numerator, target);
         return isError;
     }
 }
diff --git a/packages/contracts/src/2.0.0/test/TestExchangeInternals/TestExchangeInternals.sol b/packages/contracts/src/2.0.0/test/TestExchangeInternals/TestExchangeInternals.sol
index d9cec9edc..da9313e02 100644
--- a/packages/contracts/src/2.0.0/test/TestExchangeInternals/TestExchangeInternals.sol
+++ b/packages/contracts/src/2.0.0/test/TestExchangeInternals/TestExchangeInternals.sol
@@ -67,7 +67,7 @@ contract TestExchangeInternals is
     /// @param denominator Denominator.
     /// @param target Value to calculate partial of.
     /// @return Partial value of target.
-    function publicGetPartialAmount(
+    function publicGetPartialAmountFloor(
         uint256 numerator,
         uint256 denominator,
         uint256 target
@@ -76,15 +76,49 @@ contract TestExchangeInternals is
         pure
         returns (uint256 partialAmount)
     {
-        return getPartialAmount(numerator, denominator, target);
+        return getPartialAmountFloor(numerator, denominator, target);
     }
 
-    /// @dev Checks if rounding error > 0.1%.
+    /// @dev Calculates partial value given a numerator and denominator.
+    /// @param numerator Numerator.
+    /// @param denominator Denominator.
+    /// @param target Value to calculate partial of.
+    /// @return Partial value of target.
+    function publicGetPartialAmountCeil(
+        uint256 numerator,
+        uint256 denominator,
+        uint256 target
+    )
+        public
+        pure
+        returns (uint256 partialAmount)
+    {
+        return getPartialAmountCeil(numerator, denominator, target);
+    }
+
+    /// @dev Checks if rounding error >= 0.1%.
+    /// @param numerator Numerator.
+    /// @param denominator Denominator.
+    /// @param target Value to multiply with numerator/denominator.
+    /// @return Rounding error is present.
+    function publicIsRoundingErrorFloor(
+        uint256 numerator,
+        uint256 denominator,
+        uint256 target
+    )
+        public
+        pure
+        returns (bool isError)
+    {
+        return isRoundingErrorFloor(numerator, denominator, target);
+    }
+
+    /// @dev Checks if rounding error >= 0.1%.
     /// @param numerator Numerator.
     /// @param denominator Denominator.
     /// @param target Value to multiply with numerator/denominator.
     /// @return Rounding error is present.
-    function publicIsRoundingError(
+    function publicIsRoundingErrorCeil(
         uint256 numerator,
         uint256 denominator,
         uint256 target
@@ -93,7 +127,7 @@ contract TestExchangeInternals is
         pure
         returns (bool isError)
     {
-        return isRoundingError(numerator, denominator, target);
+        return isRoundingErrorCeil(numerator, denominator, target);
     }
  
     /// @dev Updates state with results of a fill order.
diff --git a/packages/contracts/src/2.0.0/test/TestLibs/TestLibs.sol b/packages/contracts/src/2.0.0/test/TestLibs/TestLibs.sol
index 4a99dd9c1..c8c58545f 100644
--- a/packages/contracts/src/2.0.0/test/TestLibs/TestLibs.sol
+++ b/packages/contracts/src/2.0.0/test/TestLibs/TestLibs.sol
@@ -49,7 +49,7 @@ contract TestLibs is
         return fillOrderCalldata;
     }
 
-    function publicGetPartialAmount(
+    function publicGetPartialAmountFloor(
         uint256 numerator,
         uint256 denominator,
         uint256 target
@@ -58,7 +58,7 @@ contract TestLibs is
         pure
         returns (uint256 partialAmount)
     {
-        partialAmount = getPartialAmount(
+        partialAmount = getPartialAmountFloor(
             numerator,
             denominator,
             target
@@ -66,7 +66,41 @@ contract TestLibs is
         return partialAmount;
     }
 
-    function publicIsRoundingError(
+    function publicGetPartialAmountCeil(
+        uint256 numerator,
+        uint256 denominator,
+        uint256 target
+    )
+        public
+        pure
+        returns (uint256 partialAmount)
+    {
+        partialAmount = getPartialAmountCeil(
+            numerator,
+            denominator,
+            target
+        );
+        return partialAmount;
+    }
+
+    function publicIsRoundingErrorFloor(
+        uint256 numerator,
+        uint256 denominator,
+        uint256 target
+    )
+        public
+        pure
+        returns (bool isError)
+    {
+        isError = isRoundingErrorFloor(
+            numerator,
+            denominator,
+            target
+        );
+        return isError;
+    }
+
+    function publicIsRoundingErrorCeil(
         uint256 numerator,
         uint256 denominator,
         uint256 target
@@ -75,7 +109,7 @@ contract TestLibs is
         pure
         returns (bool isError)
     {
-        isError = isRoundingError(
+        isError = isRoundingErrorCeil(
             numerator,
             denominator,
             target