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Diffstat (limited to 'contracts/core/contracts/protocol/Exchange/libs/LibMath.sol')
| -rw-r--r-- | contracts/core/contracts/protocol/Exchange/libs/LibMath.sol | 253 |
1 files changed, 253 insertions, 0 deletions
diff --git a/contracts/core/contracts/protocol/Exchange/libs/LibMath.sol b/contracts/core/contracts/protocol/Exchange/libs/LibMath.sol new file mode 100644 index 000000000..c0b85ea10 --- /dev/null +++ b/contracts/core/contracts/protocol/Exchange/libs/LibMath.sol @@ -0,0 +1,253 @@ +/* + + Copyright 2018 ZeroEx Intl. + + Licensed under the Apache License, Version 2.0 (the "License"); + you may not use this file except in compliance with the License. + You may obtain a copy of the License at + + http://www.apache.org/licenses/LICENSE-2.0 + + Unless required by applicable law or agreed to in writing, software + distributed under the License is distributed on an "AS IS" BASIS, + WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + See the License for the specific language governing permissions and + limitations under the License. + +*/ + +pragma solidity 0.4.24; + +import "../../../utils/SafeMath/SafeMath.sol"; + + +contract LibMath is + SafeMath +{ + /// @dev Calculates partial value given a numerator and denominator rounded down. + /// Reverts if rounding error is >= 0.1% + /// @param numerator Numerator. + /// @param denominator Denominator. + /// @param target Value to calculate partial of. + /// @return Partial value of target rounded down. + function safeGetPartialAmountFloor( + uint256 numerator, + uint256 denominator, + uint256 target + ) + internal + pure + returns (uint256 partialAmount) + { + require( + denominator > 0, + "DIVISION_BY_ZERO" + ); + + require( + !isRoundingErrorFloor( + numerator, + denominator, + target + ), + "ROUNDING_ERROR" + ); + + partialAmount = safeDiv( + safeMul(numerator, target), + denominator + ); + return partialAmount; + } + + /// @dev Calculates partial value given a numerator and denominator rounded down. + /// Reverts if rounding error is >= 0.1% + /// @param numerator Numerator. + /// @param denominator Denominator. + /// @param target Value to calculate partial of. + /// @return Partial value of target rounded up. + function safeGetPartialAmountCeil( + uint256 numerator, + uint256 denominator, + uint256 target + ) + internal + pure + returns (uint256 partialAmount) + { + require( + denominator > 0, + "DIVISION_BY_ZERO" + ); + + require( + !isRoundingErrorCeil( + numerator, + denominator, + target + ), + "ROUNDING_ERROR" + ); + + // 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 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 down. + function getPartialAmountFloor( + uint256 numerator, + uint256 denominator, + uint256 target + ) + internal + pure + returns (uint256 partialAmount) + { + require( + denominator > 0, + "DIVISION_BY_ZERO" + ); + + partialAmount = safeDiv( + safeMul(numerator, target), + denominator + ); + return partialAmount; + } + + /// @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 isRoundingErrorFloor( + uint256 numerator, + uint256 denominator, + uint256 target + ) + internal + pure + returns (bool isError) + { + 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; + } + + // 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" + ); + + // 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 + ); + remainder = safeSub(denominator, remainder) % denominator; + isError = safeMul(1000, remainder) >= safeMul(numerator, target); + return isError; + } +} |