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/*
-----------------------------------------------------------------
FILE INFORMATION
-----------------------------------------------------------------
file: SafeDecimalMath.sol
version: 2.0
author: Kevin Brown
Gavin Conway
date: 2018-10-18
-----------------------------------------------------------------
MODULE DESCRIPTION
-----------------------------------------------------------------
A library providing safe mathematical operations for division and
multiplication with the capability to round or truncate the results
to the nearest increment. Operations can return a standard precision
or high precision decimal. High precision decimals are useful for
example when attempting to calculate percentages or fractions
accurately.
-----------------------------------------------------------------
*/
pragma solidity 0.4.25;
import "openzeppelin-solidity/contracts/math/SafeMath.sol";
/**
* @title Safely manipulate unsigned fixed-point decimals at a given precision level.
* @dev Functions accepting uints in this contract and derived contracts
* are taken to be such fixed point decimals of a specified precision (either standard
* or high).
*/
library SafeDecimalMath {
using SafeMath for uint;
/* Number of decimal places in the representations. */
uint8 public constant decimals = 18;
uint8 public constant highPrecisionDecimals = 27;
/* The number representing 1.0. */
uint public constant UNIT = 10 ** uint(decimals);
/* The number representing 1.0 for higher fidelity numbers. */
uint public constant PRECISE_UNIT = 10 ** uint(highPrecisionDecimals);
uint private constant UNIT_TO_HIGH_PRECISION_CONVERSION_FACTOR = 10 ** uint(highPrecisionDecimals - decimals);
/**
* @return Provides an interface to UNIT.
*/
function unit()
external
pure
returns (uint)
{
return UNIT;
}
/**
* @return Provides an interface to PRECISE_UNIT.
*/
function preciseUnit()
external
pure
returns (uint)
{
return PRECISE_UNIT;
}
/**
* @return The result of multiplying x and y, interpreting the operands as fixed-point
* decimals.
*
* @dev A unit factor is divided out after the product of x and y is evaluated,
* so that product must be less than 2**256. As this is an integer division,
* the internal division always rounds down. This helps save on gas. Rounding
* is more expensive on gas.
*/
function multiplyDecimal(uint x, uint y)
internal
pure
returns (uint)
{
/* Divide by UNIT to remove the extra factor introduced by the product. */
return x.mul(y) / UNIT;
}
/**
* @return The result of safely multiplying x and y, interpreting the operands
* as fixed-point decimals of the specified precision unit.
*
* @dev The operands should be in the form of a the specified unit factor which will be
* divided out after the product of x and y is evaluated, so that product must be
* less than 2**256.
*
* Unlike multiplyDecimal, this function rounds the result to the nearest increment.
* Rounding is useful when you need to retain fidelity for small decimal numbers
* (eg. small fractions or percentages).
*/
function _multiplyDecimalRound(uint x, uint y, uint precisionUnit)
private
pure
returns (uint)
{
/* Divide by UNIT to remove the extra factor introduced by the product. */
uint quotientTimesTen = x.mul(y) / (precisionUnit / 10);
if (quotientTimesTen % 10 >= 5) {
quotientTimesTen += 10;
}
return quotientTimesTen / 10;
}
/**
* @return The result of safely multiplying x and y, interpreting the operands
* as fixed-point decimals of a precise unit.
*
* @dev The operands should be in the precise unit factor which will be
* divided out after the product of x and y is evaluated, so that product must be
* less than 2**256.
*
* Unlike multiplyDecimal, this function rounds the result to the nearest increment.
* Rounding is useful when you need to retain fidelity for small decimal numbers
* (eg. small fractions or percentages).
*/
function multiplyDecimalRoundPrecise(uint x, uint y)
internal
pure
returns (uint)
{
return _multiplyDecimalRound(x, y, PRECISE_UNIT);
}
/**
* @return The result of safely multiplying x and y, interpreting the operands
* as fixed-point decimals of a standard unit.
*
* @dev The operands should be in the standard unit factor which will be
* divided out after the product of x and y is evaluated, so that product must be
* less than 2**256.
*
* Unlike multiplyDecimal, this function rounds the result to the nearest increment.
* Rounding is useful when you need to retain fidelity for small decimal numbers
* (eg. small fractions or percentages).
*/
function multiplyDecimalRound(uint x, uint y)
internal
pure
returns (uint)
{
return _multiplyDecimalRound(x, y, UNIT);
}
/**
* @return The result of safely dividing x and y. The return value is a high
* precision decimal.
*
* @dev y is divided after the product of x and the standard precision unit
* is evaluated, so the product of x and UNIT must be less than 2**256. As
* this is an integer division, the result is always rounded down.
* This helps save on gas. Rounding is more expensive on gas.
*/
function divideDecimal(uint x, uint y)
internal
pure
returns (uint)
{
/* Reintroduce the UNIT factor that will be divided out by y. */
return x.mul(UNIT).div(y);
}
/**
* @return The result of safely dividing x and y. The return value is as a rounded
* decimal in the precision unit specified in the parameter.
*
* @dev y is divided after the product of x and the specified precision unit
* is evaluated, so the product of x and the specified precision unit must
* be less than 2**256. The result is rounded to the nearest increment.
*/
function _divideDecimalRound(uint x, uint y, uint precisionUnit)
private
pure
returns (uint)
{
uint resultTimesTen = x.mul(precisionUnit * 10).div(y);
if (resultTimesTen % 10 >= 5) {
resultTimesTen += 10;
}
return resultTimesTen / 10;
}
/**
* @return The result of safely dividing x and y. The return value is as a rounded
* standard precision decimal.
*
* @dev y is divided after the product of x and the standard precision unit
* is evaluated, so the product of x and the standard precision unit must
* be less than 2**256. The result is rounded to the nearest increment.
*/
function divideDecimalRound(uint x, uint y)
internal
pure
returns (uint)
{
return _divideDecimalRound(x, y, UNIT);
}
/**
* @return The result of safely dividing x and y. The return value is as a rounded
* high precision decimal.
*
* @dev y is divided after the product of x and the high precision unit
* is evaluated, so the product of x and the high precision unit must
* be less than 2**256. The result is rounded to the nearest increment.
*/
function divideDecimalRoundPrecise(uint x, uint y)
internal
pure
returns (uint)
{
return _divideDecimalRound(x, y, PRECISE_UNIT);
}
/**
* @dev Convert a standard decimal representation to a high precision one.
*/
function decimalToPreciseDecimal(uint i)
internal
pure
returns (uint)
{
return i.mul(UNIT_TO_HIGH_PRECISION_CONVERSION_FACTOR);
}
/**
* @dev Convert a high precision decimal to a standard decimal representation.
*/
function preciseDecimalToDecimal(uint i)
internal
pure
returns (uint)
{
uint quotientTimesTen = i / (UNIT_TO_HIGH_PRECISION_CONVERSION_FACTOR / 10);
if (quotientTimesTen % 10 >= 5) {
quotientTimesTen += 10;
}
return quotientTimesTen / 10;
}
}
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