Signed SafeMath (#1559)

* signed safe math

* fix lint errors

* refactor overflow checks and add descriptions

* remove incorrect description

* add test for reversed arguments in multiplication test

* fix power operator

* improve multiplication test descriptions

* Update SafeMath.test.js

* add feature to changelog

CHANGELOG.md

@@ -9,6 +9,7 @@
  * `ERC20`: `transferFrom` and `_burnFrom ` now emit `Approval` events, to represent the token's state comprehensively through events. ([#1524](https://github.com/OpenZeppelin/openzeppelin-solidity/pull/1524))
  * `ERC721`: added `_burn(uint256 tokenId)`, replacing the similar deprecated function (see below). ([#1550](https://github.com/OpenZeppelin/openzeppelin-solidity/pull/1550))
  * `ERC721`: added `_tokensOfOwner(address owner)`, allowing to internally retrieve the array of an account's owned tokens. ([#1522](https://github.com/OpenZeppelin/openzeppelin-solidity/pull/1522))
+ * `SafeMath`: added overflow-safe operations for signed integers (`int256`). ([#1559](https://github.com/OpenZeppelin/openzeppelin-solidity/pull/1559))
 
 ### Improvements:
  * The compiler version required by `Array` was behind the rest of the libray so it was updated to `v0.4.24`. ([#1553](https://github.com/OpenZeppelin/openzeppelin-solidity/pull/1553))

contracts/math/SafeMath.sol

@@ -5,8 +5,10 @@ pragma solidity ^0.4.24;
  * @dev Math operations with safety checks that revert on error
  */
 library SafeMath {
+    int256 constant private INT256_MIN = -2**255;
+
     /**
-    * @dev Multiplies two numbers, reverts on overflow.
+    * @dev Multiplies two unsigned integers, reverts on overflow.
     */
     function mul(uint256 a, uint256 b) internal pure returns (uint256) {
         // Gas optimization: this is cheaper than requiring 'a' not being zero, but the
@@ -23,7 +25,26 @@ library SafeMath {
     }
 
     /**
-    * @dev Integer division of two numbers truncating the quotient, reverts on division by zero.
+    * @dev Multiplies two signed integers, reverts on overflow.
+    */
+    function mul(int256 a, int256 b) internal pure returns (int256) {
+        // Gas optimization: this is cheaper than requiring 'a' not being zero, but the
+        // benefit is lost if 'b' is also tested.
+        // See: https://github.com/OpenZeppelin/openzeppelin-solidity/pull/522
+        if (a == 0) {
+            return 0;
+        }
+
+        require(!(a == -1 && b == INT256_MIN)); // This is the only case of overflow not detected by the check below
+
+        int256 c = a * b;
+        require(c / a == b);
+
+        return c;
+    }
+
+    /**
+    * @dev Integer division of two unsigned integers truncating the quotient, reverts on division by zero.
     */
     function div(uint256 a, uint256 b) internal pure returns (uint256) {
         // Solidity only automatically asserts when dividing by 0
@@ -35,7 +56,19 @@ library SafeMath {
     }
 
     /**
-    * @dev Subtracts two numbers, reverts on overflow (i.e. if subtrahend is greater than minuend).
+    * @dev Integer division of two signed integers truncating the quotient, reverts on division by zero.
+    */
+    function div(int256 a, int256 b) internal pure returns (int256) {
+        require(b != 0); // Solidity only automatically asserts when dividing by 0
+        require(!(b == -1 && a == INT256_MIN)); // This is the only case of overflow
+
+        int256 c = a / b;
+
+        return c;
+    }
+
+    /**
+    * @dev Subtracts two unsigned integers, reverts on overflow (i.e. if subtrahend is greater than minuend).
     */
     function sub(uint256 a, uint256 b) internal pure returns (uint256) {
         require(b <= a);
@@ -45,7 +78,17 @@ library SafeMath {
     }
 
     /**
-    * @dev Adds two numbers, reverts on overflow.
+    * @dev Subtracts two signed integers, reverts on overflow.
+    */
+    function sub(int256 a, int256 b) internal pure returns (int256) {
+        int256 c = a - b;
+        require((b >= 0 && c <= a) || (b < 0 && c > a));
+
+        return c;
+    }
+
+    /**
+    * @dev Adds two unsigned integers, reverts on overflow.
     */
     function add(uint256 a, uint256 b) internal pure returns (uint256) {
         uint256 c = a + b;
@@ -55,7 +98,17 @@ library SafeMath {
     }
 
     /**
-    * @dev Divides two numbers and returns the remainder (unsigned integer modulo),
+    * @dev Adds two signed integers, reverts on overflow.
+    */
+    function add(int256 a, int256 b) internal pure returns (int256) {
+        int256 c = a + b;
+        require((b >= 0 && c >= a) || (b < 0 && c < a));
+
+        return c;
+    }
+
+    /**
+    * @dev Divides two unsigned integers and returns the remainder (unsigned integer modulo),
     * reverts when dividing by zero.
     */
     function mod(uint256 a, uint256 b) internal pure returns (uint256) {

contracts/mocks/SafeMathMock.sol

@@ -1,25 +1,43 @@
 pragma solidity ^0.4.24;
 
+
 import "../math/SafeMath.sol";
 
+
 contract SafeMathMock {
-    function mul(uint256 a, uint256 b) public pure returns (uint256) {
+    function mulUints(uint256 a, uint256 b) public pure returns (uint256) {
         return SafeMath.mul(a, b);
     }
 
-    function div(uint256 a, uint256 b) public pure returns (uint256) {
+    function mulInts(int256 a, int256 b) public pure returns (int256) {
+        return SafeMath.mul(a, b);
+    }
+
+    function divUints(uint256 a, uint256 b) public pure returns (uint256) {
         return SafeMath.div(a, b);
     }
 
-    function sub(uint256 a, uint256 b) public pure returns (uint256) {
+    function divInts(int256 a, int256 b) public pure returns (int256) {
+        return SafeMath.div(a, b);
+    }
+
+    function subUints(uint256 a, uint256 b) public pure returns (uint256) {
         return SafeMath.sub(a, b);
     }
 
-    function add(uint256 a, uint256 b) public pure returns (uint256) {
+    function subInts(int256 a, int256 b) public pure returns (int256) {
+        return SafeMath.sub(a, b);
+    }
+
+    function addUints(uint256 a, uint256 b) public pure returns (uint256) {
         return SafeMath.add(a, b);
     }
 
-    function mod(uint256 a, uint256 b) public pure returns (uint256) {
+    function addInts(int256 a, int256 b) public pure returns (int256) {
+        return SafeMath.add(a, b);
+    }
+
+    function modUints(uint256 a, uint256 b) public pure returns (uint256) {
         return SafeMath.mod(a, b);
     }
 }

test/helpers/constants.js

@@ -3,4 +3,6 @@ const BigNumber = web3.BigNumber;
 module.exports = {
   ZERO_ADDRESS: '0x0000000000000000000000000000000000000000',
   MAX_UINT256: new BigNumber(2).pow(256).minus(1),
+  MAX_INT256: new BigNumber(2).pow(255).minus(1),
+  MIN_INT256: new BigNumber(2).pow(255).times(-1),
 };

test/math/SafeMath.test.js

@@ -1,5 +1,5 @@
 const shouldFail = require('../helpers/shouldFail');
-const { MAX_UINT256 } = require('../helpers/constants');
+const { MAX_UINT256, MIN_INT256, MAX_INT256 } = require('../helpers/constants');
 
 const SafeMathMock = artifacts.require('SafeMathMock');
 
@@ -10,19 +10,20 @@ contract('SafeMath', function () {
     this.safeMath = await SafeMathMock.new();
   });
 
+  describe('unsigned', function () {
     describe('add', function () {
       it('adds correctly', async function () {
         const a = new BigNumber(5678);
         const b = new BigNumber(1234);
 
-      (await this.safeMath.add(a, b)).should.be.bignumber.equal(a.plus(b));
+        (await this.safeMath.addUints(a, b)).should.be.bignumber.equal(a.plus(b));
       });
 
-    it('throws a revert error on addition overflow', async function () {
+      it('reverts on addition overflow', async function () {
         const a = MAX_UINT256;
         const b = new BigNumber(1);
 
-      await shouldFail.reverting(this.safeMath.add(a, b));
+        await shouldFail.reverting(this.safeMath.addUints(a, b));
       });
     });
 
@@ -31,14 +32,14 @@ contract('SafeMath', function () {
         const a = new BigNumber(5678);
         const b = new BigNumber(1234);
 
-      (await this.safeMath.sub(a, b)).should.be.bignumber.equal(a.minus(b));
+        (await this.safeMath.subUints(a, b)).should.be.bignumber.equal(a.minus(b));
       });
 
-    it('throws a revert error if subtraction result would be negative', async function () {
+      it('reverts if subtraction result would be negative', async function () {
         const a = new BigNumber(1234);
         const b = new BigNumber(5678);
 
-      await shouldFail.reverting(this.safeMath.sub(a, b));
+        await shouldFail.reverting(this.safeMath.subUints(a, b));
       });
     });
 
@@ -47,28 +48,28 @@ contract('SafeMath', function () {
         const a = new BigNumber(1234);
         const b = new BigNumber(5678);
 
-      (await this.safeMath.mul(a, b)).should.be.bignumber.equal(a.times(b));
+        (await this.safeMath.mulUints(a, b)).should.be.bignumber.equal(a.times(b));
       });
 
       it('handles a zero product correctly (first number as zero)', async function () {
         const a = new BigNumber(0);
         const b = new BigNumber(5678);
 
-      (await this.safeMath.mul(a, b)).should.be.bignumber.equal(a.times(b));
+        (await this.safeMath.mulUints(a, b)).should.be.bignumber.equal(a.times(b));
       });
 
       it('handles a zero product correctly (second number as zero)', async function () {
         const a = new BigNumber(5678);
         const b = new BigNumber(0);
 
-      (await this.safeMath.mul(a, b)).should.be.bignumber.equal(a.times(b));
+        (await this.safeMath.mulUints(a, b)).should.be.bignumber.equal(a.times(b));
       });
 
-    it('throws a revert error on multiplication overflow', async function () {
+      it('reverts on multiplication overflow', async function () {
         const a = MAX_UINT256;
         const b = new BigNumber(2);
 
-      await shouldFail.reverting(this.safeMath.mul(a, b));
+        await shouldFail.reverting(this.safeMath.mulUints(a, b));
       });
     });
 
@@ -77,28 +78,28 @@ contract('SafeMath', function () {
         const a = new BigNumber(5678);
         const b = new BigNumber(5678);
 
-      (await this.safeMath.div(a, b)).should.be.bignumber.equal(a.div(b));
+        (await this.safeMath.divUints(a, b)).should.be.bignumber.equal(a.div(b));
       });
 
       it('divides zero correctly', async function () {
         const a = new BigNumber(0);
         const b = new BigNumber(5678);
 
-      (await this.safeMath.div(a, b)).should.be.bignumber.equal(0);
+        (await this.safeMath.divUints(a, b)).should.be.bignumber.equal(0);
       });
 
       it('returns complete number result on non-even division', async function () {
         const a = new BigNumber(7000);
         const b = new BigNumber(5678);
 
-      (await this.safeMath.div(a, b)).should.be.bignumber.equal(1);
+        (await this.safeMath.divUints(a, b)).should.be.bignumber.equal(1);
       });
 
-    it('throws a revert error on zero division', async function () {
+      it('reverts on zero division', async function () {
         const a = new BigNumber(5678);
         const b = new BigNumber(0);
 
-      await shouldFail.reverting(this.safeMath.div(a, b));
+        await shouldFail.reverting(this.safeMath.divUints(a, b));
       });
     });
 
@@ -108,28 +109,28 @@ contract('SafeMath', function () {
           const a = new BigNumber(284);
           const b = new BigNumber(5678);
 
-        (await this.safeMath.mod(a, b)).should.be.bignumber.equal(a.mod(b));
+          (await this.safeMath.modUints(a, b)).should.be.bignumber.equal(a.mod(b));
         });
 
         it('when the dividend is equal to the divisor', async function () {
           const a = new BigNumber(5678);
           const b = new BigNumber(5678);
 
-        (await this.safeMath.mod(a, b)).should.be.bignumber.equal(a.mod(b));
+          (await this.safeMath.modUints(a, b)).should.be.bignumber.equal(a.mod(b));
         });
 
         it('when the dividend is larger than the divisor', async function () {
           const a = new BigNumber(7000);
           const b = new BigNumber(5678);
 
-        (await this.safeMath.mod(a, b)).should.be.bignumber.equal(a.mod(b));
+          (await this.safeMath.modUints(a, b)).should.be.bignumber.equal(a.mod(b));
         });
 
         it('when the dividend is a multiple of the divisor', async function () {
           const a = new BigNumber(17034); // 17034 == 5678 * 3
           const b = new BigNumber(5678);
 
-        (await this.safeMath.mod(a, b)).should.be.bignumber.equal(a.mod(b));
+          (await this.safeMath.modUints(a, b)).should.be.bignumber.equal(a.mod(b));
         });
       });
 
@@ -137,7 +138,136 @@ contract('SafeMath', function () {
         const a = new BigNumber(5678);
         const b = new BigNumber(0);
 
-      await shouldFail.reverting(this.safeMath.mod(a, b));
+        await shouldFail.reverting(this.safeMath.modUints(a, b));
+      });
+    });
+  });
+
+  describe('signed', function () {
+    describe('add', function () {
+      it('adds correctly if it does not overflow and the result is positve', async function () {
+        const a = new BigNumber(1234);
+        const b = new BigNumber(5678);
+
+        (await this.safeMath.addUints(a, b)).should.be.bignumber.equal(a.plus(b));
+      });
+
+      it('adds correctly if it does not overflow and the result is negative', async function () {
+        const a = MAX_INT256;
+        const b = MIN_INT256;
+
+        const result = await this.safeMath.addInts(a, b);
+        result.should.be.bignumber.equal(a.plus(b));
+      });
+
+      it('reverts on positive addition overflow', async function () {
+        const a = MAX_INT256;
+        const b = new BigNumber(1);
+
+        await shouldFail.reverting(this.safeMath.addInts(a, b));
+      });
+
+      it('reverts on negative addition overflow', async function () {
+        const a = MIN_INT256;
+        const b = new BigNumber(-1);
+
+        await shouldFail.reverting(this.safeMath.addInts(a, b));
+      });
+    });
+
+    describe('sub', function () {
+      it('subtracts correctly if it does not overflow and the result is positive', async function () {
+        const a = new BigNumber(5678);
+        const b = new BigNumber(1234);
+
+        const result = await this.safeMath.subInts(a, b);
+        result.should.be.bignumber.equal(a.minus(b));
+      });
+
+      it('subtracts correctly if it does not overflow and the result is negative', async function () {
+        const a = new BigNumber(1234);
+        const b = new BigNumber(5678);
+
+        const result = await this.safeMath.subInts(a, b);
+        result.should.be.bignumber.equal(a.minus(b));
+      });
+
+      it('reverts on positive subtraction overflow', async function () {
+        const a = MAX_INT256;
+        const b = new BigNumber(-1);
+
+        await shouldFail.reverting(this.safeMath.subInts(a, b));
+      });
+
+      it('reverts on negative subtraction overflow', async function () {
+        const a = MIN_INT256;
+        const b = new BigNumber(1);
+
+        await shouldFail.reverting(this.safeMath.subInts(a, b));
+      });
+    });
+
+    describe('mul', function () {
+      it('multiplies correctly', async function () {
+        const a = new BigNumber(5678);
+        const b = new BigNumber(-1234);
+
+        const result = await this.safeMath.mulInts(a, b);
+        result.should.be.bignumber.equal(a.times(b));
+      });
+
+      it('handles a zero product correctly', async function () {
+        const a = new BigNumber(0);
+        const b = new BigNumber(5678);
+
+        const result = await this.safeMath.mulInts(a, b);
+        result.should.be.bignumber.equal(a.times(b));
+      });
+
+      it('reverts on multiplication overflow, positive operands', async function () {
+        const a = MAX_INT256;
+        const b = new BigNumber(2);
+
+        await shouldFail.reverting(this.safeMath.mulInts(a, b));
+      });
+
+      it('reverts when minimum integer is multiplied by -1', async function () {
+        const a = MIN_INT256;
+        const b = new BigNumber(-1);
+
+        await shouldFail.reverting(this.safeMath.mulInts(a, b));
+      });
+
+      it('reverts when -1 is multiplied by minimum integer', async function () {
+        const a = new BigNumber(-1);
+        const b = MIN_INT256;
+
+        await shouldFail.reverting(this.safeMath.mulInts(a, b));
+      });
+    });
+
+    describe('div', function () {
+      it('divides correctly', async function () {
+        const a = new BigNumber(-5678);
+        const b = new BigNumber(5678);
+
+        const result = await this.safeMath.divInts(a, b);
+        result.should.be.bignumber.equal(a.div(b));
+      });
+
+      it('reverts on zero division', async function () {
+        const a = new BigNumber(-5678);
+        const b = new BigNumber(0);
+
+        await shouldFail.reverting(this.safeMath.divInts(a, b));
+      });
+
+      it('reverts on overflow, negative second', async function () {
+        const a = new BigNumber(MIN_INT256);
+        const b = new BigNumber(-1);
+
+        await shouldFail.reverting(this.safeMath.divInts(a, b));
+      });
     });
   });
 });