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103 lines
3.2 KiB
103 lines
3.2 KiB
// SPDX-License-Identifier: MIT OR Apache-2.0
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pragma solidity ^0.8.15;
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import "@openzeppelin/contracts-upgradeable/utils/math/SafeMathUpgradeable.sol";
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/**
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* @title SafeMathInt
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* @dev Math operations for int256 with overflow safety checks.
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*/
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library SafeMathInt {
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int256 private constant MIN_INT256 = int256(1) << 255;
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int256 private constant MAX_INT256 = ~(int256(1) << 255);
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/**
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* @dev Multiplies two int256 variables and fails on overflow.
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*/
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function mul(int256 a, int256 b) internal pure returns (int256) {
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int256 c = a * b;
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// Detect overflow when multiplying MIN_INT256 with -1
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require(c != MIN_INT256 || (a & MIN_INT256) != (b & MIN_INT256));
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require((b == 0) || (c / b == a));
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return c;
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}
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/**
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* @dev Division of two int256 variables and fails on overflow.
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*/
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function div(int256 a, int256 b) internal pure returns (int256) {
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// Prevent overflow when dividing MIN_INT256 by -1
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require(b != -1 || a != MIN_INT256);
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// Solidity already throws when dividing by 0.
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return a / b;
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}
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/**
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* @dev Subtracts two int256 variables and fails on overflow.
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*/
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function sub(int256 a, int256 b) internal pure returns (int256) {
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int256 c = a - b;
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require((b >= 0 && c <= a) || (b < 0 && c > a));
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return c;
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}
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/**
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* @dev Adds two int256 variables and fails on overflow.
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*/
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function add(int256 a, int256 b) internal pure returns (int256) {
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int256 c = a + b;
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require((b >= 0 && c >= a) || (b < 0 && c < a));
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return c;
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}
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/**
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* @dev Converts to absolute value, and fails on overflow.
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*/
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function abs(int256 a) internal pure returns (int256) {
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require(a != MIN_INT256);
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return a < 0 ? -a : a;
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}
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/**
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* @dev Computes 2^exp with limited precision where -100 <= exp <= 100 * one
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* @param one 1.0 represented in the same fixed point number format as exp
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* @param exp The power to raise 2 to -100 <= exp <= 100 * one
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* @return 2^exp represented with same number of decimals after the point as one
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*/
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function twoPower(int256 exp, int256 one) internal pure returns (int256) {
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bool reciprocal = false;
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if (exp < 0) {
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reciprocal = true;
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exp = abs(exp);
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}
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// Precomputed values for 2^(1/2^i) in 18 decimals fixed point numbers
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int256[5] memory ks = [
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int256(1414213562373095049),
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1189207115002721067,
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1090507732665257659,
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1044273782427413840,
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1021897148654116678
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];
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int256 whole = div(exp, one);
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require(whole <= 100);
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int256 result = mul(int256(uint256(1) << uint256(whole)), one);
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int256 remaining = sub(exp, mul(whole, one));
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int256 current = div(one, 2);
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for (uint256 i = 0; i < 5; i++) {
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if (remaining >= current) {
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remaining = sub(remaining, current);
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result = div(mul(result, ks[i]), 10**18); // 10**18 to match hardcoded ks values
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}
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current = div(current, 2);
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}
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if (reciprocal) {
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result = div(mul(one, one), result);
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}
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return result;
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}
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}
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