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

[contracts] Add getPartialAmountCeil and isRoundingErrorCeil

18 files changed, 392 insertions, 115 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
diff --git a/packages/contracts/test/exchange/internal.ts b/packages/contracts/test/exchange/internal.ts
index 67d1d2d2c..2521665c2 100644
--- a/packages/contracts/test/exchange/internal.ts
+++ b/packages/contracts/test/exchange/internal.ts
@@ -1,6 +1,7 @@
 import { BlockchainLifecycle } from '@0xproject/dev-utils';
 import { Order, RevertReason, SignedOrder } from '@0xproject/types';
 import { BigNumber } from '@0xproject/utils';
+import * as chai from 'chai';
 import * as _ from 'lodash';
 
 import { TestExchangeInternalsContract } from '../../generated_contract_wrappers/test_exchange_internals';
@@ -16,6 +17,8 @@ import { FillResults } from '../utils/types';
 import { provider, txDefaults, web3Wrapper } from '../utils/web3_wrapper';
 
 chaiSetup.configure();
+const expect = chai.expect;
+
 const blockchainLifecycle = new BlockchainLifecycle(web3Wrapper);
 
 const MAX_UINT256 = new BigNumber(2).pow(256).minus(1);
@@ -43,26 +46,11 @@ const emptySignedOrder: SignedOrder = {
 
 const overflowErrorForCall = new Error(RevertReason.Uint256Overflow);
 
-async function referenceGetPartialAmountAsync(
-    numerator: BigNumber,
-    denominator: BigNumber,
-    target: BigNumber,
-): Promise<BigNumber> {
-    const invalidOpcodeErrorForCall = new Error(await getInvalidOpcodeErrorMessageForCallAsync());
-    const product = numerator.mul(target);
-    if (product.greaterThan(MAX_UINT256)) {
-        throw overflowErrorForCall;
-    }
-    if (denominator.eq(0)) {
-        throw invalidOpcodeErrorForCall;
-    }
-    return product.dividedToIntegerBy(denominator);
-}
-
 describe('Exchange core internal functions', () => {
     let testExchange: TestExchangeInternalsContract;
     let invalidOpcodeErrorForCall: Error | undefined;
     let overflowErrorForSendTransaction: Error | undefined;
+    let divisionByZeroErrorForCall: Error | undefined;
 
     before(async () => {
         await blockchainLifecycle.startAsync();
@@ -79,11 +67,29 @@ describe('Exchange core internal functions', () => {
         overflowErrorForSendTransaction = new Error(
             await getRevertReasonOrErrorMessageForSendTransactionAsync(RevertReason.Uint256Overflow),
         );
+        divisionByZeroErrorForCall = new Error(
+            await getRevertReasonOrErrorMessageForSendTransactionAsync(RevertReason.DivisionByZero),
+        );
         invalidOpcodeErrorForCall = new Error(await getInvalidOpcodeErrorMessageForCallAsync());
     });
     // Note(albrow): Don't forget to add beforeEach and afterEach calls to reset
     // the blockchain state for any tests which modify it!
 
+    async function referenceGetPartialAmountFloorAsync(
+        numerator: BigNumber,
+        denominator: BigNumber,
+        target: BigNumber,
+    ): Promise<BigNumber> {
+        if (denominator.eq(0)) {
+            throw divisionByZeroErrorForCall;
+        }
+        const product = numerator.mul(target);
+        if (product.greaterThan(MAX_UINT256)) {
+            throw overflowErrorForCall;
+        }
+        return product.dividedToIntegerBy(denominator);
+    }
+
     describe('addFillResults', async () => {
         function makeFillResults(value: BigNumber): FillResults {
             return {
@@ -159,18 +165,18 @@ describe('Exchange core internal functions', () => {
             // implementation or the Solidity implementation of
             // calculateFillResults.
             return {
-                makerAssetFilledAmount: await referenceGetPartialAmountAsync(
+                makerAssetFilledAmount: await referenceGetPartialAmountFloorAsync(
                     takerAssetFilledAmount,
                     orderTakerAssetAmount,
                     otherAmount,
                 ),
                 takerAssetFilledAmount,
-                makerFeePaid: await referenceGetPartialAmountAsync(
+                makerFeePaid: await referenceGetPartialAmountFloorAsync(
                     takerAssetFilledAmount,
                     orderTakerAssetAmount,
                     otherAmount,
                 ),
-                takerFeePaid: await referenceGetPartialAmountAsync(
+                takerFeePaid: await referenceGetPartialAmountFloorAsync(
                     takerAssetFilledAmount,
                     orderTakerAssetAmount,
                     otherAmount,
@@ -193,18 +199,55 @@ describe('Exchange core internal functions', () => {
         );
     });
 
-    describe('getPartialAmount', async () => {
-        async function testGetPartialAmountAsync(
+    describe('getPartialAmountFloor', async () => {
+        async function testGetPartialAmountFloorAsync(
             numerator: BigNumber,
             denominator: BigNumber,
             target: BigNumber,
         ): Promise<BigNumber> {
-            return testExchange.publicGetPartialAmount.callAsync(numerator, denominator, target);
+            return testExchange.publicGetPartialAmountFloor.callAsync(numerator, denominator, target);
         }
         await testCombinatoriallyWithReferenceFuncAsync(
             'getPartialAmount',
-            referenceGetPartialAmountAsync,
-            testGetPartialAmountAsync,
+            referenceGetPartialAmountFloorAsync,
+            testGetPartialAmountFloorAsync,
+            [uint256Values, uint256Values, uint256Values],
+        );
+    });
+
+    describe('getPartialAmountCeil', async () => {
+        async function referenceGetPartialAmountCeilAsync(
+            numerator: BigNumber,
+            denominator: BigNumber,
+            target: BigNumber,
+        ): Promise<BigNumber> {
+            if (denominator.eq(0)) {
+                throw divisionByZeroErrorForCall;
+            }
+            const product = numerator.mul(target);
+            const offset = product.add(denominator.sub(1));
+            if (offset.greaterThan(MAX_UINT256)) {
+                throw overflowErrorForCall;
+            }
+            const result = offset.dividedToIntegerBy(denominator);
+            if (product.mod(denominator).eq(0)) {
+                expect(result.mul(denominator)).to.be.bignumber.eq(product);
+            } else {
+                expect(result.mul(denominator)).to.be.bignumber.gt(product);
+            }
+            return result;
+        }
+        async function testGetPartialAmountCeilAsync(
+            numerator: BigNumber,
+            denominator: BigNumber,
+            target: BigNumber,
+        ): Promise<BigNumber> {
+            return testExchange.publicGetPartialAmountCeil.callAsync(numerator, denominator, target);
+        }
+        await testCombinatoriallyWithReferenceFuncAsync(
+            'getPartialAmountCeil',
+            referenceGetPartialAmountCeilAsync,
+            testGetPartialAmountCeilAsync,
             [uint256Values, uint256Values, uint256Values],
         );
     });
@@ -215,33 +258,33 @@ describe('Exchange core internal functions', () => {
             denominator: BigNumber,
             target: BigNumber,
         ): Promise<boolean> {
-            const product = numerator.mul(target);
             if (denominator.eq(0)) {
-                throw invalidOpcodeErrorForCall;
+                throw divisionByZeroErrorForCall;
             }
-            const remainder = product.mod(denominator);
-            if (remainder.eq(0)) {
+            if (numerator.eq(0)) {
+                return false;
+            }
+            if (target.eq(0)) {
                 return false;
             }
+            const product = numerator.mul(target);
+            const remainder = product.mod(denominator);
+            const remainderTimes1000 = remainder.mul('1000');
+            const isError = remainderTimes1000.gt(product);
             if (product.greaterThan(MAX_UINT256)) {
                 throw overflowErrorForCall;
             }
-            if (product.eq(0)) {
-                throw invalidOpcodeErrorForCall;
-            }
-            const remainderTimes1000000 = remainder.mul('1000000');
-            if (remainderTimes1000000.greaterThan(MAX_UINT256)) {
+            if (remainderTimes1000.greaterThan(MAX_UINT256)) {
                 throw overflowErrorForCall;
             }
-            const errPercentageTimes1000000 = remainderTimes1000000.dividedToIntegerBy(product);
-            return errPercentageTimes1000000.greaterThan('1000');
+            return isError;
         }
         async function testIsRoundingErrorAsync(
             numerator: BigNumber,
             denominator: BigNumber,
             target: BigNumber,
         ): Promise<boolean> {
-            return testExchange.publicIsRoundingError.callAsync(numerator, denominator, target);
+            return testExchange.publicIsRoundingErrorFloor.callAsync(numerator, denominator, target);
         }
         await testCombinatoriallyWithReferenceFuncAsync(
             'isRoundingError',
@@ -251,6 +294,49 @@ describe('Exchange core internal functions', () => {
         );
     });
 
+    describe('isRoundingErrorCeil', async () => {
+        async function referenceIsRoundingErrorAsync(
+            numerator: BigNumber,
+            denominator: BigNumber,
+            target: BigNumber,
+        ): Promise<boolean> {
+            if (denominator.eq(0)) {
+                throw divisionByZeroErrorForCall;
+            }
+            if (numerator.eq(0)) {
+                return false;
+            }
+            if (target.eq(0)) {
+                return false;
+            }
+            const product = numerator.mul(target);
+            const remainder = product.mod(denominator);
+            const error = denominator.sub(remainder).mod(denominator);
+            const errorTimes1000 = error.mul('1000');
+            const isError = errorTimes1000.gt(product);
+            if (product.greaterThan(MAX_UINT256)) {
+                throw overflowErrorForCall;
+            }
+            if (errorTimes1000.greaterThan(MAX_UINT256)) {
+                throw overflowErrorForCall;
+            }
+            return isError;
+        }
+        async function testIsRoundingErrorCeilAsync(
+            numerator: BigNumber,
+            denominator: BigNumber,
+            target: BigNumber,
+        ): Promise<boolean> {
+            return testExchange.publicIsRoundingErrorCeil.callAsync(numerator, denominator, target);
+        }
+        await testCombinatoriallyWithReferenceFuncAsync(
+            'isRoundingErrorCeil',
+            referenceIsRoundingErrorAsync,
+            testIsRoundingErrorCeilAsync,
+            [uint256Values, uint256Values, uint256Values],
+        );
+    });
+
     describe('updateFilledState', async () => {
         // Note(albrow): Since updateFilledState modifies the state by calling
         // sendTransaction, we must reset the state after each test.
diff --git a/packages/contracts/test/exchange/libs.ts b/packages/contracts/test/exchange/libs.ts
index 6c3305d1d..37234489e 100644
--- a/packages/contracts/test/exchange/libs.ts
+++ b/packages/contracts/test/exchange/libs.ts
@@ -71,29 +71,57 @@ describe('Exchange libs', () => {
     // combinatorial tests in test/exchange/internal. They test specific edge
     // cases that are not covered by the combinatorial tests.
     describe('LibMath', () => {
-        it('should return false if there is a rounding error of 0.1%', async () => {
-            const numerator = new BigNumber(20);
-            const denominator = new BigNumber(999);
-            const target = new BigNumber(50);
-            // rounding error = ((20*50/999) - floor(20*50/999)) / (20*50/999) = 0.1%
-            const isRoundingError = await libs.publicIsRoundingError.callAsync(numerator, denominator, target);
-            expect(isRoundingError).to.be.false();
-        });
-        it('should return false if there is a rounding of 0.09%', async () => {
-            const numerator = new BigNumber(20);
-            const denominator = new BigNumber(9991);
-            const target = new BigNumber(500);
-            // rounding error = ((20*500/9991) - floor(20*500/9991)) / (20*500/9991) = 0.09%
-            const isRoundingError = await libs.publicIsRoundingError.callAsync(numerator, denominator, target);
-            expect(isRoundingError).to.be.false();
+        describe('isRoundingError', () => {
+            it('should return true if there is a rounding error of 0.1%', async () => {
+                const numerator = new BigNumber(20);
+                const denominator = new BigNumber(999);
+                const target = new BigNumber(50);
+                // rounding error = ((20*50/999) - floor(20*50/999)) / (20*50/999) = 0.1%
+                const isRoundingError = await libs.publicIsRoundingErrorFloor.callAsync(numerator, denominator, target);
+                expect(isRoundingError).to.be.true();
+            });
+            it('should return false if there is a rounding of 0.09%', async () => {
+                const numerator = new BigNumber(20);
+                const denominator = new BigNumber(9991);
+                const target = new BigNumber(500);
+                // rounding error = ((20*500/9991) - floor(20*500/9991)) / (20*500/9991) = 0.09%
+                const isRoundingError = await libs.publicIsRoundingErrorFloor.callAsync(numerator, denominator, target);
+                expect(isRoundingError).to.be.false();
+            });
+            it('should return true if there is a rounding error of 0.11%', async () => {
+                const numerator = new BigNumber(20);
+                const denominator = new BigNumber(9989);
+                const target = new BigNumber(500);
+                // rounding error = ((20*500/9989) - floor(20*500/9989)) / (20*500/9989) = 0.011%
+                const isRoundingError = await libs.publicIsRoundingErrorFloor.callAsync(numerator, denominator, target);
+                expect(isRoundingError).to.be.true();
+            });
         });
-        it('should return true if there is a rounding error of 0.11%', async () => {
-            const numerator = new BigNumber(20);
-            const denominator = new BigNumber(9989);
-            const target = new BigNumber(500);
-            // rounding error = ((20*500/9989) - floor(20*500/9989)) / (20*500/9989) = 0.011%
-            const isRoundingError = await libs.publicIsRoundingError.callAsync(numerator, denominator, target);
-            expect(isRoundingError).to.be.true();
+        describe('isRoundingErrorCeil', () => {
+            it('should return true if there is a rounding error of 0.1%', async () => {
+                const numerator = new BigNumber(20);
+                const denominator = new BigNumber(1001);
+                const target = new BigNumber(50);
+                // rounding error = (ceil(20*50/1001) - (20*50/1001)) / (20*50/1001) = 0.1%
+                const isRoundingError = await libs.publicIsRoundingErrorCeil.callAsync(numerator, denominator, target);
+                expect(isRoundingError).to.be.true();
+            });
+            it('should return false if there is a rounding of 0.09%', async () => {
+                const numerator = new BigNumber(20);
+                const denominator = new BigNumber(10009);
+                const target = new BigNumber(500);
+                // rounding error = (ceil(20*500/10009) - (20*500/10009)) / (20*500/10009) = 0.09%
+                const isRoundingError = await libs.publicIsRoundingErrorCeil.callAsync(numerator, denominator, target);
+                expect(isRoundingError).to.be.false();
+            });
+            it('should return true if there is a rounding error of 0.11%', async () => {
+                const numerator = new BigNumber(20);
+                const denominator = new BigNumber(10011);
+                const target = new BigNumber(500);
+                // rounding error = (ceil(20*500/10011) - (20*500/10011)) / (20*500/10011) = 0.11%
+                const isRoundingError = await libs.publicIsRoundingErrorCeil.callAsync(numerator, denominator, target);
+                expect(isRoundingError).to.be.true();
+            });
         });
     });
 
diff --git a/packages/contracts/test/utils/fill_order_combinatorial_utils.ts b/packages/contracts/test/utils/fill_order_combinatorial_utils.ts
index a9318571c..92d0f4003 100644
--- a/packages/contracts/test/utils/fill_order_combinatorial_utils.ts
+++ b/packages/contracts/test/utils/fill_order_combinatorial_utils.ts
@@ -467,17 +467,17 @@ export class FillOrderCombinatorialUtils {
             ? remainingTakerAmountToFill
             : alreadyFilledTakerAmount.add(takerAssetFillAmount);
 
-        const expFilledMakerAmount = orderUtils.getPartialAmount(
+        const expFilledMakerAmount = orderUtils.getPartialAmountFloor(
             expFilledTakerAmount,
             signedOrder.takerAssetAmount,
             signedOrder.makerAssetAmount,
         );
-        const expMakerFeePaid = orderUtils.getPartialAmount(
+        const expMakerFeePaid = orderUtils.getPartialAmountFloor(
             expFilledTakerAmount,
             signedOrder.takerAssetAmount,
             signedOrder.makerFee,
         );
-        const expTakerFeePaid = orderUtils.getPartialAmount(
+        const expTakerFeePaid = orderUtils.getPartialAmountFloor(
             expFilledTakerAmount,
             signedOrder.takerAssetAmount,
             signedOrder.takerFee,
@@ -668,7 +668,7 @@ export class FillOrderCombinatorialUtils {
         signedOrder: SignedOrder,
         takerAssetFillAmount: BigNumber,
     ): Promise<void> {
-        const makerAssetFillAmount = orderUtils.getPartialAmount(
+        const makerAssetFillAmount = orderUtils.getPartialAmountFloor(
             takerAssetFillAmount,
             signedOrder.takerAssetAmount,
             signedOrder.makerAssetAmount,
@@ -705,7 +705,7 @@ export class FillOrderCombinatorialUtils {
                 );
         }
 
-        const makerFee = orderUtils.getPartialAmount(
+        const makerFee = orderUtils.getPartialAmountFloor(
             takerAssetFillAmount,
             signedOrder.takerAssetAmount,
             signedOrder.makerFee,
@@ -829,7 +829,7 @@ export class FillOrderCombinatorialUtils {
                 );
         }
 
-        const takerFee = orderUtils.getPartialAmount(
+        const takerFee = orderUtils.getPartialAmountFloor(
             takerAssetFillAmount,
             signedOrder.takerAssetAmount,
             signedOrder.takerFee,
diff --git a/packages/contracts/test/utils/order_utils.ts b/packages/contracts/test/utils/order_utils.ts
index 019f6e74b..444e27c44 100644
--- a/packages/contracts/test/utils/order_utils.ts
+++ b/packages/contracts/test/utils/order_utils.ts
@@ -5,7 +5,7 @@ import { constants } from './constants';
 import { CancelOrder, MatchOrder } from './types';
 
 export const orderUtils = {
-    getPartialAmount(numerator: BigNumber, denominator: BigNumber, target: BigNumber): BigNumber {
+    getPartialAmountFloor(numerator: BigNumber, denominator: BigNumber, target: BigNumber): BigNumber {
         const partialAmount = numerator
             .mul(target)
             .div(denominator)
diff --git a/packages/order-utils/src/order_state_utils.ts b/packages/order-utils/src/order_state_utils.ts
index a0e24acf0..8398776aa 100644
--- a/packages/order-utils/src/order_state_utils.ts
+++ b/packages/order-utils/src/order_state_utils.ts
@@ -81,7 +81,7 @@ export class OrderStateUtils {
         const remainingTakerAssetAmount = signedOrder.takerAssetAmount.minus(
             sidedOrderRelevantState.filledTakerAssetAmount,
         );
-        const isRoundingError = OrderValidationUtils.isRoundingError(
+        const isRoundingError = OrderValidationUtils.isRoundingErrorFloor(
             remainingTakerAssetAmount,
             signedOrder.takerAssetAmount,
             signedOrder.makerAssetAmount,
@@ -191,7 +191,7 @@ export class OrderStateUtils {
         );
         const remainingFillableTakerAssetAmountGivenMakersStatus = signedOrder.makerAssetAmount.eq(0)
             ? new BigNumber(0)
-            : utils.getPartialAmount(
+            : utils.getPartialAmountFloor(
                   orderRelevantMakerState.remainingFillableAssetAmount,
                   signedOrder.makerAssetAmount,
                   signedOrder.takerAssetAmount,
diff --git a/packages/order-utils/src/order_validation_utils.ts b/packages/order-utils/src/order_validation_utils.ts
index 972e6f6d6..8227fb07c 100644
--- a/packages/order-utils/src/order_validation_utils.ts
+++ b/packages/order-utils/src/order_validation_utils.ts
@@ -24,7 +24,7 @@ export class OrderValidationUtils {
      * @param denominator Denominator value.  When used to check an order, pass in `order.takerAssetAmount`
      * @param target Target value. When used to check an order, pass in `order.makerAssetAmount`
      */
-    public static isRoundingError(numerator: BigNumber, denominator: BigNumber, target: BigNumber): boolean {
+    public static isRoundingErrorFloor(numerator: BigNumber, denominator: BigNumber, target: BigNumber): boolean {
         // Solidity's mulmod() in JS
         // Source: https://solidity.readthedocs.io/en/latest/units-and-global-variables.html#mathematical-and-cryptographic-functions
         if (denominator.eq(0)) {
@@ -58,7 +58,7 @@ export class OrderValidationUtils {
         zrxAssetData: string,
     ): Promise<void> {
         try {
-            const fillMakerTokenAmount = utils.getPartialAmount(
+            const fillMakerTokenAmount = utils.getPartialAmountFloor(
                 fillTakerAssetAmount,
                 signedOrder.takerAssetAmount,
                 signedOrder.makerAssetAmount,
@@ -79,7 +79,7 @@ export class OrderValidationUtils {
                 TradeSide.Taker,
                 TransferType.Trade,
             );
-            const makerFeeAmount = utils.getPartialAmount(
+            const makerFeeAmount = utils.getPartialAmountFloor(
                 fillTakerAssetAmount,
                 signedOrder.takerAssetAmount,
                 signedOrder.makerFee,
@@ -92,7 +92,7 @@ export class OrderValidationUtils {
                 TradeSide.Maker,
                 TransferType.Fee,
             );
-            const takerFeeAmount = utils.getPartialAmount(
+            const takerFeeAmount = utils.getPartialAmountFloor(
                 fillTakerAssetAmount,
                 signedOrder.takerAssetAmount,
                 signedOrder.takerFee,
@@ -218,7 +218,7 @@ export class OrderValidationUtils {
             zrxAssetData,
         );
 
-        const wouldRoundingErrorOccur = OrderValidationUtils.isRoundingError(
+        const wouldRoundingErrorOccur = OrderValidationUtils.isRoundingErrorFloor(
             desiredFillTakerTokenAmount,
             signedOrder.takerAssetAmount,
             signedOrder.makerAssetAmount,
diff --git a/packages/order-utils/src/utils.ts b/packages/order-utils/src/utils.ts
index 7aaaf0609..0ff05e8ed 100644
--- a/packages/order-utils/src/utils.ts
+++ b/packages/order-utils/src/utils.ts
@@ -12,7 +12,7 @@ export const utils = {
         const milisecondsInSecond = 1000;
         return new BigNumber(Date.now() / milisecondsInSecond).round();
     },
-    getPartialAmount(numerator: BigNumber, denominator: BigNumber, target: BigNumber): BigNumber {
+    getPartialAmountFloor(numerator: BigNumber, denominator: BigNumber, target: BigNumber): BigNumber {
         const fillMakerTokenAmount = numerator
             .mul(target)
             .div(denominator)
diff --git a/packages/order-utils/test/order_validation_utils_test.ts b/packages/order-utils/test/order_validation_utils_test.ts
index d3ff867d7..d3133c0a6 100644
--- a/packages/order-utils/test/order_validation_utils_test.ts
+++ b/packages/order-utils/test/order_validation_utils_test.ts
@@ -16,7 +16,7 @@ describe('OrderValidationUtils', () => {
             const denominator = new BigNumber(999);
             const target = new BigNumber(50);
             // rounding error = ((20*50/999) - floor(20*50/999)) / (20*50/999) = 0.1%
-            const isRoundingError = OrderValidationUtils.isRoundingError(numerator, denominator, target);
+            const isRoundingError = OrderValidationUtils.isRoundingErrorFloor(numerator, denominator, target);
             expect(isRoundingError).to.be.false();
         });
 
@@ -25,7 +25,7 @@ describe('OrderValidationUtils', () => {
             const denominator = new BigNumber(9991);
             const target = new BigNumber(500);
             // rounding error = ((20*500/9991) - floor(20*500/9991)) / (20*500/9991) = 0.09%
-            const isRoundingError = OrderValidationUtils.isRoundingError(numerator, denominator, target);
+            const isRoundingError = OrderValidationUtils.isRoundingErrorFloor(numerator, denominator, target);
             expect(isRoundingError).to.be.false();
         });
 
@@ -34,7 +34,7 @@ describe('OrderValidationUtils', () => {
             const denominator = new BigNumber(9989);
             const target = new BigNumber(500);
             // rounding error = ((20*500/9989) - floor(20*500/9989)) / (20*500/9989) = 0.011%
-            const isRoundingError = OrderValidationUtils.isRoundingError(numerator, denominator, target);
+            const isRoundingError = OrderValidationUtils.isRoundingErrorFloor(numerator, denominator, target);
             expect(isRoundingError).to.be.true();
         });
 
@@ -43,7 +43,7 @@ describe('OrderValidationUtils', () => {
             const denominator = new BigNumber(7);
             const target = new BigNumber(10);
             // rounding error = ((3*10/7) - floor(3*10/7)) / (3*10/7) = 6.67%
-            const isRoundingError = OrderValidationUtils.isRoundingError(numerator, denominator, target);
+            const isRoundingError = OrderValidationUtils.isRoundingErrorFloor(numerator, denominator, target);
             expect(isRoundingError).to.be.true();
         });
 
@@ -52,7 +52,7 @@ describe('OrderValidationUtils', () => {
             const denominator = new BigNumber(2);
             const target = new BigNumber(10);
 
-            const isRoundingError = OrderValidationUtils.isRoundingError(numerator, denominator, target);
+            const isRoundingError = OrderValidationUtils.isRoundingErrorFloor(numerator, denominator, target);
             expect(isRoundingError).to.be.false();
         });
 
@@ -63,7 +63,7 @@ describe('OrderValidationUtils', () => {
             const target = new BigNumber(105762562);
             // rounding error = ((76564*105762562/676373677) - floor(76564*105762562/676373677)) /
             // (76564*105762562/676373677) = 0.0007%
-            const isRoundingError = OrderValidationUtils.isRoundingError(numerator, denominator, target);
+            const isRoundingError = OrderValidationUtils.isRoundingErrorFloor(numerator, denominator, target);
             expect(isRoundingError).to.be.false();
         });
     });
diff --git a/packages/types/src/index.ts b/packages/types/src/index.ts
index 4375fc631..f07d7f756 100644
--- a/packages/types/src/index.ts
+++ b/packages/types/src/index.ts
@@ -172,6 +172,7 @@ export enum RevertReason {
     InvalidSender = 'INVALID_SENDER',
     InvalidOrderSignature = 'INVALID_ORDER_SIGNATURE',
     InvalidTakerAmount = 'INVALID_TAKER_AMOUNT',
+    DivisionByZero = 'DIVISION_BY_ZERO',
     RoundingError = 'ROUNDING_ERROR',
     InvalidSignature = 'INVALID_SIGNATURE',
     SignatureIllegal = 'SIGNATURE_ILLEGAL',