1 files changed, 108 insertions, 14 deletions

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;
     }
 }