Gelato-automations/contracts/vendor/DSMath.sol

// "SPDX-License-Identifier: AGPL-3.0-or-later"
/// math.sol -- mixin for inline numerical wizardry

// This program is free software: you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.

// This program is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU General Public License for more details.

// You should have received a copy of the GNU General Public License
// along with this program.  If not, see <http://www.gnu.org/licenses/>.

pragma solidity 0.7.4;

function add(uint x, uint y) pure returns (uint z) {
    require((z = x + y) >= x, "ds-math-add-overflow");
}
function sub(uint x, uint y) pure returns (uint z) {
    require((z = x - y) <= x, "ds-math-sub-underflow");
}
function mul(uint x, uint y) pure returns (uint z) {
    require(y == 0 || (z = x * y) / y == x, "ds-math-mul-overflow");
}

function min(uint x, uint y) pure returns (uint z) {
    return x <= y ? x : y;
}
function max(uint x, uint y) pure returns (uint z) {
    return x >= y ? x : y;
}
function imin(int x, int y) pure returns (int z) {
    return x <= y ? x : y;
}
function imax(int x, int y) pure returns (int z) {
    return x >= y ? x : y;
}

uint constant WAD = 10 ** 18;
uint constant RAY = 10 ** 27;

//rounds to zero if x*y < WAD / 2
function wmul(uint x, uint y) pure returns (uint z) {
    z = add(mul(x, y), WAD / 2) / WAD;
}
//rounds to zero if x*y < WAD / 2
function rmul(uint x, uint y) pure returns (uint z) {
    z = add(mul(x, y), RAY / 2) / RAY;
}
//rounds to zero if x*y < WAD / 2
function wdiv(uint x, uint y) pure returns (uint z) {
    z = add(mul(x, WAD), y / 2) / y;
}
//rounds to zero if x*y < RAY / 2
function rdiv(uint x, uint y) pure returns (uint z) {
    z = add(mul(x, RAY), y / 2) / y;
}

// This famous algorithm is called "exponentiation by squaring"
// and calculates x^n with x as fixed-point and n as regular unsigned.
//
// It's O(log n), instead of O(n) for naive repeated multiplication.
//
// These facts are why it works:
//
//  If n is even, then x^n = (x^2)^(n/2).
//  If n is odd,  then x^n = x * x^(n-1),
//   and applying the equation for even x gives
//    x^n = x * (x^2)^((n-1) / 2).
//
//  Also, EVM division is flooring and
//    floor[(n-1) / 2] = floor[n / 2].
//
function rpow(uint x, uint n) pure returns (uint z) {
    z = n % 2 != 0 ? x : RAY;

    for (n /= 2; n != 0; n /= 2) {
        x = rmul(x, x);

        if (n % 2 != 0) {
            z = rmul(z, x);
        }
    }
}