diff --git a/stdlib/datatypes.h b/stdlib/datatypes.h
index 5dddaa0..31a9963 100644
--- a/stdlib/datatypes.h
+++ b/stdlib/datatypes.h
@@ -53,6 +53,7 @@ typedef struct {
 
 typedef struct table_s {
     Array_t entries;
+    uint64_t hash;
     bucket_info_t *bucket_info;
     struct table_s *fallback;
 } Table_t;
diff --git a/stdlib/tables.c b/stdlib/tables.c
index df42ef6..dea7a45 100644
--- a/stdlib/tables.c
+++ b/stdlib/tables.c
@@ -228,6 +228,8 @@ public void *Table$reserve(Table_t *t, const void *key, const void *value, const
     if (!t || !key) return NULL;
     hshow(t);
 
+    t->hash = 0;
+
     int64_t key_size = type->TableInfo.key->size,
             value_size = type->TableInfo.value->size;
     if (!t->bucket_info || t->bucket_info->count == 0) {
@@ -334,6 +336,8 @@ public void Table$remove(Table_t *t, const void *key, const TypeInfo_t *type)
   found_it:;
     assert(bucket->occupied);
 
+    t->hash = 0;
+
     // Always remove the last entry. If we need to remove some other entry,
     // swap the other entry into the last position and then remove the last
     // entry. This disturbs the ordering of the table, but keeps removal O(1)
@@ -405,14 +409,27 @@ PUREFUNC public bool Table$equal(const void *vx, const void *vy, const TypeInfo_
     if (vx == vy) return true;
     Table_t *x = (Table_t*)vx, *y = (Table_t*)vy;
 
+    if (x->hash && y->hash && x->hash != y->hash)
+        return false;
+
     assert(type->tag == TableInfo);
-    if (Table$length(*x) != Table$length(*y))
+    if (x->entries.length != y->entries.length)
         return false;
     
     if ((x->fallback != NULL) != (y->fallback != NULL))
         return false;
 
-    return (Table$compare(x, y, type) == 0);
+    const TypeInfo_t *value_type = type->TableInfo.value;
+    size_t offset = value_offset(type);
+    for (int64_t i = 0; i < x->entries.length; i++) {
+        void *x_key = x->entries.data + i*x->entries.stride;
+        void *y_value = Table$get_raw(*y, x_key, type);
+        if (!y_value) return false;
+        void *x_value = x_key + offset;
+        if (!generic_equal(y_value, x_value, value_type))
+            return false;
+    }
+    return true;
 }
 
 PUREFUNC public int32_t Table$compare(const void *vx, const void *vy, const TypeInfo_t *type)
@@ -422,20 +439,90 @@ PUREFUNC public int32_t Table$compare(const void *vx, const void *vy, const Type
     Table_t *x = (Table_t*)vx, *y = (Table_t*)vy;
     assert(type->tag == TableInfo);
     auto table = type->TableInfo;
-    if (x->entries.length == 0)
-        return 0;
-    else if (x->entries.length != y->entries.length)
-        return (x->entries.length > y->entries.length) - (x->entries.length < y->entries.length);
 
+    // Sort empty tables before non-empty tables:
+    if (x->entries.length == 0 || y->entries.length == 0)
+        return ((x->entries.length > 0) - (y->entries.length > 0));
+
+    // Table comparison rules:
+    // - If two tables have different keys, then compare as if comparing a
+    // sorted array of the keys of the two tables:
+    //    `x.keys:sorted() <> y.keys:sorted()`
+    // - Otherwise, compare as if comparing arrays of values for the sorted key
+    // arrays:
+    //    `[x[k] for k in x.keys:sorted()] <> [y[k] for k in y.keys:sorted()]`
+    // 
+    // We can do this in _linear_ time if we find the smallest `k` such that
+    // `x[k] != y[k]`, as well as the largest key in `x` and `y`.
+
+    void *mismatched_key = NULL, *max_x_key = NULL;
     for (int64_t i = 0; i < x->entries.length; i++) {
-        void *x_key = x->entries.data + x->entries.stride * i;
-        void *y_key = y->entries.data + y->entries.stride * i;
-        int32_t diff = generic_compare(x_key, y_key, table.key);
-        if (diff != 0) return diff;
-        void *x_value = x_key + value_offset(type);
-        void *y_value = y_key + value_offset(type);
-        diff = generic_compare(x_value, y_value, table.value);
-        if (diff != 0) return diff;
+        void *key = x->entries.data + x->entries.stride * i;
+        if (max_x_key == NULL || generic_compare(key, max_x_key, table.key) > 0)
+            max_x_key = key;
+
+        void *x_value = key + value_offset(type);
+        void *y_value = Table$get_raw(*y, key, type);
+
+        if (!y_value || (table.value->size > 0 && !generic_equal(x_value, y_value, table.value))) {
+            if (mismatched_key == NULL || generic_compare(key, mismatched_key, table.key) < 0) 
+                mismatched_key = key;
+        }
+    }
+
+    // If the keys are not all equal, we gotta check to see if there exists a
+    // `y[k]` such that `k` is smaller than all keys that `x` has and `y` doesn't:
+    void *max_y_key = NULL;
+    for (int64_t i = 0; i < y->entries.length; i++) {
+        void *key = y->entries.data + y->entries.stride * i;
+        if (max_y_key == NULL || generic_compare(key, max_y_key, table.key) > 0)
+            max_y_key = key;
+
+        void *y_value = key + value_offset(type);
+        void *x_value = Table$get_raw(*x, key, type);
+        if (!x_value || !generic_equal(x_value, y_value, table.value)) {
+            if (mismatched_key == NULL || generic_compare(key, mismatched_key, table.key) < 0) 
+                mismatched_key = key;
+        }
+    }
+
+    if (mismatched_key) {
+        void *x_value = Table$get_raw(*x, mismatched_key, type);
+        void *y_value = Table$get_raw(*y, mismatched_key, type);
+        if (x_value && y_value) {
+            return generic_compare(x_value, y_value, table.value);
+        } else if (y_value) {
+            // The smallest mismatched key is in Y, but not X.
+            // In this case, we should judge if the key is smaller than *any*
+            // key in X or if it's bigger than *every* key in X.
+            // Example 1:
+            //     x={10, 20, 30} > y={10, 20, 25, 30}
+            // The smallest mismatched key is `25`, and we know that `x` is
+            // larger than `y` because `30 > 25`.
+            // Example 2:
+            //     x={10, 20, 30} > y={10, 20, 30, 999}
+            // The smallest mismatched key is `999`, and we know that `x` is
+            // smaller than `y` because `30 < 999`.
+            return max_x_key ? generic_compare(max_x_key, mismatched_key, table.key) : -1;
+        } else {
+            assert(x_value);
+            // The smallest mismatched key is in X, but not Y. The same logic
+            // above applies, but reversed.
+            return max_y_key ? -generic_compare(max_y_key, mismatched_key, table.key) : 1;
+        }
+    }
+
+    assert(x->entries.length == y->entries.length);
+
+    // Assuming keys are the same, compare values:
+    if (table.value->size > 0) {
+        for (int64_t i = 0; i < x->entries.length; i++) {
+            void *key = x->entries.data + x->entries.stride * i;
+            void *x_value = key + value_offset(type);
+            void *y_value = Table$get_raw(*y, key, type);
+            int32_t diff = generic_compare(x_value, y_value, table.value);
+            if (diff != 0) return diff;
+        }
     }
 
     if (!x->fallback != !y->fallback) {
@@ -451,16 +538,39 @@ PUREFUNC public uint64_t Table$hash(const void *obj, const TypeInfo_t *type)
 {
     assert(type->tag == TableInfo);
     Table_t *t = (Table_t*)obj;
+    if (t->hash != 0)
+        return t->hash;
+
     // Table hashes are computed as:
-    // hash(hash(t.keys), hash(t.values), hash(t.fallback), hash(t.default))
+    // hash(t.length, (xor: t.keys), (xor: t.values), t.fallback)
     // Where fallback and default hash to zero if absent
     auto table = type->TableInfo;
-    uint64_t components[] = {
-        Array$hash(&t->entries, Array$info(table.key)),
-        Array$hash(&t->entries + value_offset(type), Array$info(table.value)),
-        t->fallback ? Table$hash(t->fallback, type) : 0,
+    uint64_t keys_hash = 0, values_hash = 0;
+    size_t offset = value_offset(type);
+    if (table.value->size > 0) {
+        for (int64_t i = 0; i < t->entries.length; i++) {
+            keys_hash ^= generic_hash(t->entries.data + i*t->entries.stride, table.key);
+            values_hash ^= generic_hash(t->entries.data + i*t->entries.stride + offset, table.value);
+        }
+    } else {
+        for (int64_t i = 0; i < t->entries.length; i++)
+            keys_hash ^= generic_hash(t->entries.data + i*t->entries.stride, table.key);
+    }
+
+    struct {
+        int64_t length;
+        uint64_t keys_hash, values_hash;
+        Table_t *fallback;
+    } components = {
+        t->entries.length,
+        keys_hash,
+        values_hash,
+        t->fallback,
     };
-    return siphash24((void*)&components, sizeof(components));
+    t->hash = siphash24((void*)&components, sizeof(components));
+    if unlikely (t->hash == 0)
+        t->hash = 1234567;
+    return t->hash;
 }
 
 public Text_t Table$as_text(const void *obj, bool colorize, const TypeInfo_t *type)
diff --git a/test/tables.tm b/test/tables.tm
index e67c712..6abbbe3 100644
--- a/test/tables.tm
+++ b/test/tables.tm
@@ -88,3 +88,18 @@ func main():
 		>> t4
 		= &{"one":999, "two":222}
 
+	do:
+		>> {1:1, 2:2} == {2:2, 1:1}
+		= yes
+		>> {1:1, 2:2} == {1:1, 2:999}
+		= no
+
+		>> {1:1, 2:2} <> {2:2, 1:1}
+		= 0
+		>> [{:Int:Int}, {0:0}, {99:99}, {1:1, 2:2, 3:3}, {1:1, 99:99, 3:3}, {1:1, 2:-99, 3:3}, {1:1, 99:-99, 3:4}]:sorted()
+		= [{}, {0:0}, {1:1, 2:-99, 3:3}, {1:1, 2:2, 3:3}, {1:1, 99:99, 3:3}, {1:1, 99:-99, 3:4}, {99:99}]
+
+		>> [{:Int}, {1}, {2}, {99}, {0, 3}, {1, 2}, {99}]:sorted()
+		= [{}, {0, 3}, {1}, {1, 2}, {2}, {99}, {99}]
+
+