improve signed average formula

contracts/utils/math/SignedMath.sol

@@ -25,13 +25,13 @@ library SignedMath {
      * towards zero.
      */
     function average(int256 a, int256 b) internal pure returns (int256) {
-        if ((b < 0 && a > 0 && -b < a) || (a < 0 && b > 0 && -a < b))
-            return (a / 2) + (b / 2) + (((a % 2 + b % 2) - 1) / 2);
-
-        if ((b < 0 && a > 0 && -b > a) || (a < 0 && b > 0 && -a > b))
-            return (a / 2) + (b / 2) + (((a % 2 + b % 2) + 1) / 2);
-
-        return (a / 2) + (b / 2) + ((a % 2 + b % 2) / 2);
+        // (a + b) / 2 can overflow, and the unsigned formula doesn't simply translate to signed integers
+        int256 base = (a & b) + (a ^ b) / 2;
+        if ((a < 0 && b < 0) || ((a < 0 || b < 0) && (a + b > 0))) {
+            return base + (a ^ b) % 2;
+        } else {
+            return base;
+        }
     }
 
     /**
@@ -45,4 +45,4 @@ library SignedMath {
         int256 r = a % b == 0 ? int256(0) : int256(1);
         return z < 0 ? z - r : z + r;
     }
-}
+}

test/utils/math/SignedMath.test.js

@@ -85,56 +85,63 @@ contract('SignedMath', function (accounts) {
       expect(await this.math.average(a, b)).to.be.bignumber.equal(bnAverage(a, b));
     });
 
+    // eslint-disable-next-line max-len
     it('is correctly calculated with one even number and one odd signed number and even its greater than odd, both in module', async function () {
       const a = new BN('2');
       const b = new BN('-1');
 
       expect(await this.math.average(a, b)).to.be.bignumber.equal(bnAverage(a, b));
     });
 
+    // eslint-disable-next-line max-len
     it('is correctly calculated with one odd number and one even signed number and odd its greater than even, both in module', async function () {
       const a = new BN('3');
       const b = new BN('-2');
 
       expect(await this.math.average(a, b)).to.be.bignumber.equal(bnAverage(a, b));
     });
 
-
+    // eslint-disable-next-line max-len
     it('is correctly calculated with one even number and one odd signed number and odd its greater than even, both in module', async function () {
       const a = new BN('2');
       const b = new BN('-3');
 
       expect(await this.math.average(a, b)).to.be.bignumber.equal(bnAverage(a, b));
     });
 
+    // eslint-disable-next-line max-len
     it('is correctly calculated with one odd number and one even signed number and even its greater than odd, both in module', async function () {
       const a = new BN('3');
       const b = new BN('-4');
 
       expect(await this.math.average(a, b)).to.be.bignumber.equal(bnAverage(a, b));
     });
 
+    // eslint-disable-next-line max-len
     it('is correctly calculated with one even signed number and one odd number and even its greater than odd, both in module', async function () {
       const a = new BN('-2');
       const b = new BN('1');
 
       expect(await this.math.average(a, b)).to.be.bignumber.equal(bnAverage(a, b));
     });
 
+    // eslint-disable-next-line max-len
     it('is correctly calculated with one odd signed number and one even number and odd its greater than even, both in module', async function () {
       const a = new BN('-3');
       const b = new BN('2');
 
       expect(await this.math.average(a, b)).to.be.bignumber.equal(bnAverage(a, b));
     });
 
+    // eslint-disable-next-line max-len
     it('is correctly calculated with one even signed number and one odd number and odd its greater than even, both in module', async function () {
       const a = new BN('-2');
       const b = new BN('3');
 
       expect(await this.math.average(a, b)).to.be.bignumber.equal(bnAverage(a, b));
     });
 
+    // eslint-disable-next-line max-len
     it('is correctly calculated with one odd signed number and one even number and even its greater than odd, both in module', async function () {
       const a = new BN('-3');
       const b = new BN('4');