diff --git a/spec/heaphash_spec.cr b/spec/heaphash_spec.cr
new file mode 100644
index 0000000..e955635
--- /dev/null
+++ b/spec/heaphash_spec.cr
@@ -0,0 +1,65 @@
+require "./spec_helper"
+
+describe HeapHash do
+  describe "#[]" do
+    hh = HeapHash(String, Int32).new
+
+    it "correctly assigns new keys" do
+      hh["a"] = 5
+      hh["b"] = 3
+      hh["c"] = 10
+      hh["a"].should eq(5)
+      hh["b"].should eq(3)
+      hh["c"].should eq(10)
+      hh.size.should eq(3)
+    end
+
+    it "correctly updates the value of a key" do
+      hh["a"] = 0
+      hh["a"].should eq(0)
+      hh.size.should eq(3)
+    end
+
+    it "returns nil for non-existent keys" do
+      hh["?"]?.should be_nil
+    end
+
+    it "throws for non-existent keys" do
+      expect_raises(KeyError) do
+        hh["?"]
+      end
+    end
+  end
+
+  describe "#pop" do
+    it "pops keys in the right oder" do
+      hh = HeapHash(String, Int32).new
+      expect_raises(IndexError) do
+        hh.pop
+      end
+
+      hh["last"] = 1
+      hh["first"] = 10
+      hh["medium"] = 5
+
+      hh.pop.should eq({"first", 10})
+      hh.pop.should eq({"medium", 5})
+      hh.pop.should eq({"last", 1})
+    end
+  end
+
+  describe "#delete" do
+    it "doesn't break the heap property" do
+      hh = HeapHash(String, Int32).new
+
+      hh["last"] = 1
+      hh["first"] = 10
+      hh["medium"] = 5
+      
+      popped = hh.delete "last"
+      popped.should eq({"last", 1})
+      hh.pop.should eq({"first", 10})
+      hh.pop.should eq({"medium", 5})
+    end
+  end
+end
diff --git a/spec/util_spec.cr b/spec/util_spec.cr
index 2097efa..1fd2142 100644
--- a/spec/util_spec.cr
+++ b/spec/util_spec.cr
@@ -27,3 +27,67 @@ describe Array do
     end
   end
 end
+
+describe Tuple do
+  describe "#add" do
+    it "works for pairs" do
+      {1,2}.add({2,3}).should eq({3,5})
+    end
+
+    it "works for triples" do
+      {1,2,3}.add({3,4,5}).should eq({4, 6, 8})
+    end
+  end
+
+  describe "#neg" do
+    it "works for pairs" do
+      {1,2}.neg.should eq({-1,-2})
+    end
+
+    it "works for triples" do
+      {1,2,3}.neg.should eq({-1, -2, -3})
+    end
+  end
+
+  describe "#dot" do
+    it "works for pairs" do
+      {1,2}.dot({2,3}).should eq(8)
+    end
+
+    it "works for triples" do
+      {1,2,3}.dot({2,3,4}).should eq(20)
+    end
+  end
+
+  describe "#reduce_fraction" do
+    it "works with nonzero numbers" do
+      [{1, 3}, {2, 6}, {3, 9}].each(&.reduce_fraction.should eq({1,3}))
+    end
+
+    it "works when the denominator is zero" do
+      # This is technically not a fraction, but it helps to have
+      # consistent behavior
+      {5, 0}.reduce_fraction.should eq({1,0})
+    end
+
+    it "works when the numerator is zero" do
+      {0, 5}.reduce_fraction.should eq({0, 1})
+    end
+  end
+end
+
+describe Number do
+  describe "#signum" do
+    it "works properly for positive numbers" do
+      [1,2,3,4,5].each(&.signum.should eq(1))
+    end
+
+    it "works properly for negative numbers" do
+      [-1,-2,-3,-4].each(&.signum.should eq(-1))
+    end
+
+    it "works properly for zero" do
+      0.signum.should eq(0)
+    end
+  end
+end