diff --git a/Int64.js b/Int64.js
index d394c4a..f870a2a 100644
--- a/Int64.js
+++ b/Int64.js
@@ -235,6 +235,13 @@ Int64.prototype = {
    * @param {Int64} other  Other Int64 to compare.
    */
   compare: function(other) {
+
+    // If sign bits differ ...
+    if ((this.buffer[this.offset] & 0x80) != (other.buffer[other.offset] & 0x80)) {
+      return other.buffer[other.offset] - this.buffer[this.offset];
+    }
+
+    // otherwise, compare bytes lexicographically
     for (var i = 0; i < 8; i++) {
       if (this.buffer[this.offset+i] !== other.buffer[other.offset+i]) {
         return this.buffer[this.offset+i] - other.buffer[other.offset+i];
@@ -243,6 +250,15 @@ Int64.prototype = {
     return 0;
   },
 
+  /**
+   * Returns a boolean indicating if this integer is equal to other.
+   *
+   * @param {Int64} other  Other Int64 to compare.
+   */
+  equals: function(other) {
+    return this.compare(other) === 0;
+  },
+
   /**
    * Pretty output in console.log
    */
diff --git a/test.js b/test.js
index 1187364..cdf4303 100644
--- a/test.js
+++ b/test.js
@@ -81,3 +81,40 @@ exports.testBufferOffsets = function(test) {
 
   test.done();
 };
+
+exports.testInstanceOf = function(test) {
+  var x = new Int64();
+  assert(x instanceof Int64, 'Variable is not instance of Int64');
+  var y = {};
+  assert(!(y instanceof Int64), 'Object is an instance of Int64');
+  test.done();
+};
+
+exports.testCompare = function(test) {
+  var intMin = new Int64(2147483648, 0);
+  var intMinPlusOne = new Int64(2147483648, 1);
+  var zero = new Int64(0, 0);
+  var intMaxMinusOne = new Int64(2147483647, 4294967294);
+  var intMax = new Int64(2147483647, 4294967295);
+  assert(intMin.compare(intMinPlusOne) < 0, "INT64_MIN is not less than INT64_MIN+1");
+  assert(intMin.compare(zero) < 0, "INT64_MIN is not less than 0");
+  assert(intMin.compare(zero) < intMax, "INT64_MIN is not less than INT64_MAX");
+  assert(intMax.compare(intMaxMinusOne) > 0, "INT64_MAX is not greater than INT64_MAX-1");
+  assert(intMax.compare(zero) > 0, "INT64_MAX is not greater than 0");
+  assert(intMax.compare(intMin) > 0, "INT64_MAX is not greater than INT_MIN");
+  test.done();
+};
+
+exports.testEquals = function(test) {
+  var intMin = new Int64(2147483648, 0);
+  var zero = new Int64(0, 0);
+  var intMax = new Int64(2147483647, 4294967295);
+  assert(intMin.equals(intMin), "INT64_MIN !== INT64_MIN");
+  assert(intMax.equals(intMax), "INT64_MAX !== INT64_MAX");
+  assert(zero.equals(zero), "0 !== 0");
+  assert(!intMin.equals(zero), "INT64_MIN === 0");
+  assert(!intMin.equals(intMax), "INT64_MIN === INT64_MAX");
+  assert(!intMax.equals(zero), "INT64_MAX === 0");
+  assert(!intMax.equals(intMin), "INT64_MAX === INT64_MIN");
+  test.done();
+};