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ExponentialNoError.sol
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ExponentialNoError.sol
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// SPDX-License-Identifier: BSD-3-Clause
pragma solidity ^0.8.10;
/**
* @title Exponential module for storing fixed-precision decimals
* @author Compound
* @notice Exp is a struct which stores decimals with a fixed precision of 18 decimal places.
* Thus, if we wanted to store the 5.1, mantissa would store 5.1e18. That is:
* `Exp({mantissa: 5100000000000000000})`.
*/
contract ExponentialNoError {
uint constant expScale = 1e18;
uint constant doubleScale = 1e36;
uint constant halfExpScale = expScale/2;
uint constant mantissaOne = expScale;
struct Exp {
uint mantissa;
}
struct Double {
uint mantissa;
}
/**
* @dev Truncates the given exp to a whole number value.
* For example, truncate(Exp{mantissa: 15 * expScale}) = 15
*/
function truncate(Exp memory exp) pure internal returns (uint) {
// Note: We are not using careful math here as we're performing a division that cannot fail
return exp.mantissa / expScale;
}
/**
* @dev Multiply an Exp by a scalar, then truncate to return an unsigned integer.
*/
function mul_ScalarTruncate(Exp memory a, uint scalar) pure internal returns (uint) {
Exp memory product = mul_(a, scalar);
return truncate(product);
}
/**
* @dev Multiply an Exp by a scalar, truncate, then add an to an unsigned integer, returning an unsigned integer.
*/
function mul_ScalarTruncateAddUInt(Exp memory a, uint scalar, uint addend) pure internal returns (uint) {
Exp memory product = mul_(a, scalar);
return add_(truncate(product), addend);
}
/**
* @dev Checks if first Exp is less than second Exp.
*/
function lessThanExp(Exp memory left, Exp memory right) pure internal returns (bool) {
return left.mantissa < right.mantissa;
}
/**
* @dev Checks if left Exp <= right Exp.
*/
function lessThanOrEqualExp(Exp memory left, Exp memory right) pure internal returns (bool) {
return left.mantissa <= right.mantissa;
}
/**
* @dev Checks if left Exp > right Exp.
*/
function greaterThanExp(Exp memory left, Exp memory right) pure internal returns (bool) {
return left.mantissa > right.mantissa;
}
/**
* @dev returns true if Exp is exactly zero
*/
function isZeroExp(Exp memory value) pure internal returns (bool) {
return value.mantissa == 0;
}
function safe224(uint n, string memory errorMessage) pure internal returns (uint224) {
require(n < 2**224, errorMessage);
return uint224(n);
}
function safe32(uint n, string memory errorMessage) pure internal returns (uint32) {
require(n < 2**32, errorMessage);
return uint32(n);
}
function add_(Exp memory a, Exp memory b) pure internal returns (Exp memory) {
return Exp({mantissa: add_(a.mantissa, b.mantissa)});
}
function add_(Double memory a, Double memory b) pure internal returns (Double memory) {
return Double({mantissa: add_(a.mantissa, b.mantissa)});
}
function add_(uint a, uint b) pure internal returns (uint) {
return a + b;
}
function sub_(Exp memory a, Exp memory b) pure internal returns (Exp memory) {
return Exp({mantissa: sub_(a.mantissa, b.mantissa)});
}
function sub_(Double memory a, Double memory b) pure internal returns (Double memory) {
return Double({mantissa: sub_(a.mantissa, b.mantissa)});
}
function sub_(uint a, uint b) pure internal returns (uint) {
return a - b;
}
function mul_(Exp memory a, Exp memory b) pure internal returns (Exp memory) {
return Exp({mantissa: mul_(a.mantissa, b.mantissa) / expScale});
}
function mul_(Exp memory a, uint b) pure internal returns (Exp memory) {
return Exp({mantissa: mul_(a.mantissa, b)});
}
function mul_(uint a, Exp memory b) pure internal returns (uint) {
return mul_(a, b.mantissa) / expScale;
}
function mul_(Double memory a, Double memory b) pure internal returns (Double memory) {
return Double({mantissa: mul_(a.mantissa, b.mantissa) / doubleScale});
}
function mul_(Double memory a, uint b) pure internal returns (Double memory) {
return Double({mantissa: mul_(a.mantissa, b)});
}
function mul_(uint a, Double memory b) pure internal returns (uint) {
return mul_(a, b.mantissa) / doubleScale;
}
function mul_(uint a, uint b) pure internal returns (uint) {
return a * b;
}
function div_(Exp memory a, Exp memory b) pure internal returns (Exp memory) {
return Exp({mantissa: div_(mul_(a.mantissa, expScale), b.mantissa)});
}
function div_(Exp memory a, uint b) pure internal returns (Exp memory) {
return Exp({mantissa: div_(a.mantissa, b)});
}
function div_(uint a, Exp memory b) pure internal returns (uint) {
return div_(mul_(a, expScale), b.mantissa);
}
function div_(Double memory a, Double memory b) pure internal returns (Double memory) {
return Double({mantissa: div_(mul_(a.mantissa, doubleScale), b.mantissa)});
}
function div_(Double memory a, uint b) pure internal returns (Double memory) {
return Double({mantissa: div_(a.mantissa, b)});
}
function div_(uint a, Double memory b) pure internal returns (uint) {
return div_(mul_(a, doubleScale), b.mantissa);
}
function div_(uint a, uint b) pure internal returns (uint) {
return a / b;
}
function fraction(uint a, uint b) pure internal returns (Double memory) {
return Double({mantissa: div_(mul_(a, doubleScale), b)});
}
}