converge to zero via underflow <p><strong>please ignore this post, I misread algorithm, so the question is not relevant. However, I cannot close post anymore</strong>. Please vote to close</p> <p>I have been using certain algorithm from numerical recipes, which converges to zero via underflow:</p> <pre><code>// all types are the same floating type sum = 0 for (i in 0,N) sum += abs(V[i]); </code></pre> <p>my question, how does it happen? how does sum of small positive floating-point numbers converge to underflow/zero?</p> <p>is there some condition where <code>0 + f = 0 , f &gt; 0</code>?</p> <p>algorithm in question is Jacoby, <a href="http://www.mpi-hd.mpg.de/astrophysik/HEA/internal/Numerical_Recipes/f11-1.pdf" rel="nofollow noreferrer">http://www.mpi-hd.mpg.de/astrophysik/HEA/internal/Numerical_Recipes/f11-1.pdf</a>, page 460. It is quite possible I misunderstand how the convergence is achieved, if so, please correct me.</p> <p>thank you</p>