How to use TDD correctly to implement a numerical method?

Question

I am trying to use Test Driven Development to implement my signal processing library. But I have a little doubt: Assume I am trying to implement a sine method (I'm not):

1. Write the test (pseudo-code)

   assertEqual(0, sine(0))
   

2. Write the first implementation

   function sine(radians)
       return 0
   

3. Second test

   assertEqual(1, sine(pi))
   

At this point, should I:

1. implement a smart code that will work for pi and other values, or
2. implement the dumbest code that will work only for 0 and pi?

If you choose the second option, when can I jump to the first option? I will have to do it eventually...

Answer 1

Note that (in NUnit) you can also do

Assert.That(2.1 + 1.2, Is.EqualTo(3.3).Within(0.0005);

when you're dealing with floating-point equality.

One piece of advice I remember reading was to try to refactor out the magic numbers from your implementations.