diff --git a/random/mersennetwister.js b/random/mersennetwister.js
index bbd8611..67e0422 100644
--- a/random/mersennetwister.js
+++ b/random/mersennetwister.js
@@ -77,10 +77,10 @@ function MersenneTwister()
     y = y ^ ((y << 15) & 0xefc60000);
     y = y ^ (y >>> 18);
 
-    return y;
+    return y >>> 0;
   };
 
   this.real2 = function () {
     return this.int32() * (1.0 / 4294967296.0);
-  }
+  };
 }
diff --git a/random/random.js b/random/random.js
index 623175a..d7d93e4 100644
--- a/random/random.js
+++ b/random/random.js
@@ -9,18 +9,23 @@ var random = {
     this.twister.seed(seed);
   },
   number: function (limit) {
-    // Returns an integer in [0, limit]. Uniform distribution.
+    // Returns an integer in [0, limit). Uniform distribution.
     if (limit == 0) {
       return limit;
     }
     if (limit == null || limit === undefined) {
       limit = 0xffffffff;
     }
-    return (this.twister.int32() >>> 0) % limit;
+    let x = (0x100000000 / limit) >>> 0,
+        y = (x * limit) >>> 0, r;
+    do {
+      r = this.twister.int32();
+    } while(y && r >= y);
+    return (r / x) >>> 0;
   },
   float: function () {
-    // Returns a float in [0, 1]. Uniform distribution.
-    return this.twister.real2() >>> 0;
+    // Returns a float in [0, 1). Uniform distribution.
+    return this.twister.real2();
   },
   range: function (start, limit) {
     // Returns an integer in [start, limit]. Uniform distribution.
@@ -28,16 +33,16 @@ var random = {
       Utils.traceback();
       throw new TypeError("random.range() received a non number type: '" + start + "', '" + limit + "')");
     }
-    return random.number(limit - start + 1) + start;
+    return this.number(limit - start + 1) + start;
   },
   ludOneTo: function(limit) {
     // Returns a float in [1, limit]. The logarithm has uniform distribution.
-    return Math.exp(random.float() * Math.log(limit));
+    return Math.exp(this.float() * Math.log(limit));
   },
   item: function (list) {
     if (!(list instanceof Array || (typeof list != "string" && "length" in list))) {
       Utils.traceback();
-      throw new TypeError("random.item() received a non array type: '" + list + "'");
+      throw new TypeError("this.item() received a non array type: '" + list + "'");
     }
     return list[this.number(list.length)];
   },
@@ -106,13 +111,13 @@ var random = {
     return a;
   },
   use: function (obj) {
-    return random.bool() ? obj : "";
+    return this.bool() ? obj : "";
   },
   shuffle: function (arr) {
     let len = arr.length;
     let i = len;
     while (i--) {
-      let p = random.number(i + 1);
+      let p = this.number(i + 1);
       let t = arr[i];
       arr[i] = arr[p];
       arr[p] = t;
@@ -120,7 +125,7 @@ var random = {
   },
   shuffled: function (arr) {
     let newArray = arr.slice();
-    random.shuffle(newArray);
+    this.shuffle(newArray);
     return newArray;
   },
   subset: function (list, limit) {
diff --git a/tests/random/mersennetwister.js b/tests/random/mersennetwister.js
index 7f5a772..180bc43 100644
--- a/tests/random/mersennetwister.js
+++ b/tests/random/mersennetwister.js
@@ -1,23 +1,29 @@
-/* XXX: translate some of the dieharder tests here? */
-
-QUnit.test("MersenneTwister test distribution", function(assert) {
+QUnit.test("MersenneTwister test uniform distribution", function(assert) {
+  const N = Math.pow(2, 17), expected = N * 1.35;
   let mt = new MersenneTwister();
   mt.seed(new Date().getTime());
-  for (let i = 0; i < 100; ++i) {
-    let a = [], again = false;
-    for (let j = 0; j < 10; ++j) {
-      a[j] = mt.int32();
-    }
-    a.sort();
-    for (let j = 0; j < (a.length - 1); ++j) {
-      if (a[j] === a[j+1]) {
-        again = true;
-      }
-    }
-    if (!again) {
-      assert.ok(true, "no dupes in 10 entries");
-      return;
-    }
+  let data = new Uint32Array(N);
+  for (let i = 0; i < data.length; ++i) {
+    data[i] = mt.int32();
+  }
+  for (let sh = 0; sh <= 24; ++sh) {
+    let bins = new Uint32Array(256);
+    for (let b of data) {
+      ++bins[(b >>> sh) & 0xFF];
+    }
+    let variance = bins.reduce(function(a, v){ return a + Math.pow(v - N / bins.length, 2); }, 0);
+    assert.ok(variance < expected, "Expecting variance to be under " + expected + ", got " + variance);
   }
-  assert.ok(false, "could not get unique entries");
+});
+
+QUnit.test("MersenneTwister test float distribution", function(assert) {
+  const N = Math.pow(2, 17), expected = N * 1.3;
+  let mt = new MersenneTwister();
+  mt.seed(new Date().getTime());
+  let bins = new Uint32Array(512);
+  for (let i = 0; i < N; ++i) {
+    ++bins[(mt.real2() * bins.length) >>> 0];
+  }
+  let variance = bins.reduce(function(a, v){ return a + Math.pow(v - N / bins.length, 2); }, 0);
+  assert.ok(variance < expected, "Expecting variance to be under " + expected + ", got " + variance);
 });
diff --git a/tests/random/random.js b/tests/random/random.js
index 96f3491..d8d9a9c 100644
--- a/tests/random/random.js
+++ b/tests/random/random.js
@@ -11,23 +11,110 @@ QUnit.test("random.init() with provided seed", function(assert) {
 });
 */
 
+QUnit.test("random.init() is required", function(assert) {
+  assert.throws(random.number, /undefined/, "twister is uninitialized");
+  random.init(1);
+  random.number();
+});
+
+QUnit.test("random.number() corner cases", function(assert) {
+  random.init(new Date().getTime());
+  let sum = 0;
+  for (let i = 0; i < 100; ++i)
+    sum += random.number(0);
+  assert.equal(sum, 0);
+  for (let i = 0; i < 100; ++i)
+    sum += random.number(1);
+  assert.equal(sum, 0);
+  let bins = new Uint32Array(2);
+  for (let i = 0; i < 100; ++i)
+    ++bins[random.number(2)];
+  assert.equal(bins[0] + bins[1], 100);
+  assert.ok(bins[0] > 20);
+  sum = 0;
+  for (let i = 0; i < 12; ++i)
+    sum |= random.number();
+  assert.equal(sum>>>0, 0xFFFFFFFF);
+});
+
+QUnit.test("random.float() uniform distribution", function(assert) {
+  const N = Math.pow(2, 17), expected = N * 2;
+  random.init(new Date().getTime());
+  let bins = new Uint32Array(512), tmp;
+  for (let i = 0; i < N; ++i) {
+    tmp = (random.float() * bins.length) >>> 0;
+    if (tmp >= bins.length) throw "random.float() >= 1.0";
+    ++bins[tmp];
+  }
+  let variance = bins.reduce(function(a, v){ return a + Math.pow(v - N / bins.length, 2); }, 0);
+  assert.ok(variance < expected, "Expecting variance to be under " + expected + ", got " + variance);
+});
+
+QUnit.test("random.range() uniform distribution", function(assert) {
+  const N = 10000, expected = N * 2;
+  let bins = new Uint32Array(50), tmp;
+  random.init(new Date().getTime());
+  for (let i = 0; i < N; ++i) {
+    tmp = random.range(0, bins.length - 1);
+    if (tmp >= bins.length) throw "random.range() > upper bound";
+    ++bins[tmp];
+  }
+  let variance = bins.reduce(function(a, v){ return a + Math.pow(v - N / bins.length, 2); }, 0);
+  assert.ok(variance < expected, "Expecting variance to be under " + expected + ", got " + variance);
+});
+
 QUnit.test("random.range() PRNG reproducibility", function(assert) {
   let seed, result1, result2;
   seed = new Date().getTime();
-  random.init(seed);
-  result1 = random.range(1, 20);
-  random.init(seed);
-  result2 = random.range(1, 20);
-  assert.equal(result1, result2, "both results are the same")
+  for (let t = 0; t < 50; ++t) {
+    random.init(seed);
+    result1 = random.range(1, 20);
+    for (let i = 0; i < 5; ++i) {
+      random.init(seed);
+      result2 = random.range(1, 20);
+      assert.equal(result1, result2, "both results are the same")
+    }
+    seed = random.number();
+  }
 });
 
 QUnit.test("random.choose() with equal distribution", function(assert) {
-  let foo = 0, bar = 0;
+  const N = 10000, expected = N * 3;
+  let bins = new Uint32Array(3), tmp;
   random.init(new Date().getTime());
-  for (let i = 0; i < 100; ++i) {
-    let tmp = random.choose([[1, 'foo'], [1, 'bar']]);
-    if (tmp == "foo") { foo += 1; }
-    if (tmp == "bar") { bar += 1; }
+  for (let i = 0; i < N; ++i) {
+    tmp = random.choose([[1, 0], [1, 1], [1, 2]]);
+    if (tmp >= bins.length) throw "random.choose() > upper bound";
+    ++bins[tmp];
   }
-  assert.ok(bar > 0 && foo > 0, "both objects were chosen")
+  let variance = Math.pow(bins[0] - N / 3, 2) + Math.pow(bins[1] - N / 3, 2) + Math.pow(bins[2] - N / 3, 2);
+  assert.ok(variance < expected, "Expecting variance to be under " + expected + ", got " + variance + " (" + bins + ")");
 });
+
+QUnit.test("random.choose() with unequal distribution", function(assert) {
+  const N = 10000, expected = N * 3;
+  let bins = new Uint32Array(3), tmp;
+  random.init(new Date().getTime());
+  for (let i = 0; i < N; ++i) {
+    tmp = random.choose([[1, 0], [2, 1], [1, 2]]);
+    if (tmp >= bins.length) throw "random.choose() > upper bound";
+    ++bins[tmp];
+  }
+  let variance = Math.pow(bins[0] - N / 4, 2) + Math.pow(bins[1] - N / 2, 2) + Math.pow(bins[2] - N / 4, 2);
+  assert.ok(variance < expected, "Expecting variance to be under " + expected + ", got " + variance + " (" + bins + ")");
+});
+
+/*
+ludOneTo(limit)
+item(list)
+key(obj)
+bool()
+pick(obj)
+chance(limit)
+weighted(wa)
+use(obj)
+shuffle(arr)
+shuffled(arr)
+subset(list, limit)
+choose(list, flat=true)
+*/