// SPDX-License-Identifier: MIT
pragma solidity >=0.6.2;
import './SafeMath.sol';
/**
* @title Math Library
* @notice A collection of functions to perform math operations
*/
library Math {
using SafeMath for uint256;
enum Rounding {
Down, // Toward negative infinity
Up, // Toward infinity
Zero // Toward zero
}
/**
* @dev Returns the largest of two numbers.
*/
function max(uint256 a, uint256 b) internal pure returns (uint256) {
return a > b ? a : b;
}
/**
* @dev Returns the smallest of two numbers.
*/
function min(uint256 a, uint256 b) internal pure returns (uint256) {
return a < b ? a : b;
}
/**
* @dev Returns the average of two numbers. The result is rounded towards
* zero.
*/
function average(uint256 a, uint256 b) internal pure returns (uint256) {
// (a + b) / 2 can overflow.
return (a & b) + (a ^ b) / 2;
}
/**
* @dev Calculates the weighted average of two values pondering each of these
* values based on configured weights. The contribution of each value N is
* weightN/(weightA + weightB).
* @param valueA The amount for value A
* @param weightA The weight to use for value A
* @param valueB The amount for value B
* @param weightB The weight to use for value B
*/
function weightedAverage(
uint256 valueA,
uint256 weightA,
uint256 valueB,
uint256 weightB
) internal pure returns (uint256) {
return
valueA.mul(weightA).add(valueB.mul(weightB)).div(
weightA.add(weightB)
);
}
/**
* @dev Returns the difference between two numbers or zero if negative.
*/
function diffOrZero(uint256 x, uint256 y) internal pure returns (uint256) {
return (x > y) ? x.sub(y) : E0;
}
/**
* @dev Returns the ceiling of the division of two numbers.
*
* This differs from standard division with `/` in that it rounds up instead
* of rounding down.
*/
function ceilDiv(uint256 a, uint256 b) internal pure returns (uint256) {
// (a + b - 1) / b can overflow on addition, so we distribute.
return a == 0 ? 0 : (a - 1) / b + 1;
}
/**
* @dev Return the log in base 10, rounded down, of a positive value.
* Returns 0 if given 0.
*/
function log10(uint256 value) internal pure returns (uint256) {
uint256 result = 0;
unchecked {
if (value >= 10 ** 64) {
value /= 10 ** 64;
result += 64;
}
if (value >= 10 ** 32) {
value /= 10 ** 32;
result += 32;
}
if (value >= 10 ** 16) {
value /= 10 ** 16;
result += 16;
}
if (value >= 10 ** 8) {
value /= 10 ** 8;
result += 8;
}
if (value >= 10 ** 4) {
value /= 10 ** 4;
result += 4;
}
if (value >= 10 ** 2) {
value /= 10 ** 2;
result += 2;
}
if (value >= 10 ** 1) {
result += 1;
}
}
return result;
}
/**
* @dev Return the log in base 10, following the selected rounding direction, of a positive value.
* Returns 0 if given 0.
*/
function log10(
uint256 value,
Rounding rounding
) internal pure returns (uint256) {
unchecked {
uint256 result = log10(value);
return
result +
(rounding == Rounding.Up && 10 ** result < value ? 1 : 0);
}
}
/**
* @dev Return the log in base 256, rounded down, of a positive value.
* Returns 0 if given 0.
*
* Adding one to the result gives the number of pairs of hex symbols needed to represent `value` as a hex string.
*/
function log256(uint256 value) internal pure returns (uint256) {
uint256 result = 0;
unchecked {
if (value >> 128 > 0) {
value >>= 128;
result += 16;
}
if (value >> 64 > 0) {
value >>= 64;
result += 8;
}
if (value >> 32 > 0) {
value >>= 32;
result += 4;
}
if (value >> 16 > 0) {
value >>= 16;
result += 2;
}
if (value >> 8 > 0) {
result += 1;
}
}
return result;
}
/**
* @dev Return the log in base 10, following the selected rounding direction, of a positive value.
* Returns 0 if given 0.
*/
function log256(
uint256 value,
Rounding rounding
) internal pure returns (uint256) {
unchecked {
uint256 result = log256(value);
return
result +
(rounding == Rounding.Up && 1 << (result * 8) < value ? 1 : 0);
}
}
}
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