Dappsys

Safe, simple, flexible building-blocks for smart-contract systems.

Auth

ds-auth ds-guard ds-roles

Token

ds-token ds-vault

Oracle

ds-cache ds-value

Util

ds-exec ds-math ds-note ds-proxy ds-stop ds-thing

Gov

ds-multisig

DSMath

Safe Arithmetic

DS-Math provides arithmetic functions for the common numerical primitive types of Solidity. You can safely add, subtract, multiply, and divide uint numbers without fear of integer overflow. You can also find the minimum and maximum of two numbers.

Additionally, this package provides arithmetic functions for new two higher level numerical concepts called wad (18 decimals) and ray (27 decimals). These are used to represent fixed-point decimal numbers.

A wad is a decimal number with 18 digits of precision and a ray is a decimal number with 27 digits of precision. These functions are necessary to account for the difference between how integer arithmetic behaves normally, and how decimal arithmetic should actually work. A brief example using wmul, which returns the product of a wad and another number:

1.1 * 2.2 == 2.42

//Regular integer arithmetic adds orders of magnitude:

110 * 220 == 24200

// Wad arithmetic does not add orders of magnitude:

wmul(1.1 ether, 2.2 ether) == 2.42 ether

Naming Convention

The standard functions are the uint set, so their function names are not prefixed: add, sub, mul, min, and max. There is no div function, as divide-by-zero checking is built into the Solidity compiler.

The int functions have an i prefix: imin, and imax.

Wad functions have a w prefix: wmul, wdiv.

Ray functions have a r prefix: rmul, rdiv, rpow.

API Reference

add

Return x + y or an exception in case of uint overflow.

sub

Return x - y or an exception in case of uint overflow.

mul

Return x * y or an exception in case of uint overflow.

min

Return the smaller number of x and y.

max

Return the larger number of x and y.

imin

Return the smaller number of x and y.

imax

Return the larger number of x and y.

wmul

Multiply two Wads and return a new Wad with the correct level of precision. A Wad is a decimal number with 18 digits of precision that is being represented as an integer.

wdiv

Divide two Wads and return a new Wad with the correct level of precision. A Wad is a decimal number with 18 digits of precision that is being represented as an integer.

rmul

Multiply two Rays and return a new Ray with the correct level of precision. A Ray is a decimal number with 27 digits of precision that is being represented as an integer.

rdiv

Divide two Rays and return a new Ray with the correct level of precision. A Ray is a decimal number with 27 digits of precision that is being represented as an integer.

rpow

Raise a Ray to the n^th power and return a new Ray with the correct level of precision. A Ray is a decimal number with 27 digits of precision that is being represented as an integer.

  /// 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 ^0.4.13;

contract DSMath {
    function add(uint x, uint y) internal pure returns (uint z) {
        require((z = x + y) >= x);
    }
    function sub(uint x, uint y) internal pure returns (uint z) {
        require((z = x - y) <= x);
    }
    function mul(uint x, uint y) internal pure returns (uint z) {
        require(y == 0 || (z = x * y) / y == x);
    }

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

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

    function wmul(uint x, uint y) internal pure returns (uint z) {
        z = add(mul(x, y), WAD / 2) / WAD;
    }
    function rmul(uint x, uint y) internal pure returns (uint z) {
        z = add(mul(x, y), RAY / 2) / RAY;
    }
    function wdiv(uint x, uint y) internal pure returns (uint z) {
        z = add(mul(x, WAD), y / 2) / y;
    }
    function rdiv(uint x, uint y) internal 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) internal 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);
            }
        }
    }
}