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/*
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.
/// @param numerator Numerator.
/// @param denominator Denominator.
/// @param target Value to calculate partial of.
/// @return Partial value of target.
function getPartialAmount(
uint256 numerator,
uint256 denominator,
uint256 target
)
internal
pure
returns (uint256 partialAmount)
{
partialAmount = safeDiv(
safeMul(numerator, target),
denominator
);
return partialAmount;
}
/// @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 isRoundingError(
uint256 numerator,
uint256 denominator,
uint256 target
)
internal
pure
returns (bool isError)
{
// 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. We want the relative rounding error to be strictly less
// than 0.1%.
// Let's call `numerator * target % denominator` the remainder.
// The ideal value is `numerator * target / denominator`.
// The absolute error is `remainder / denominator`.
// 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;
}
}
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