It shows how young the field of computer science is, that improvements are still being made to such basic algorithms as drawing a straight line on a digital grid. Gill has modified a basic line drawing algorithm attributed to Bresenham. The new algorithm generates more than one pixel per inner loop, thus reducing inner loop overhead. In its simplest form, Gill’s quad-step algorithm generates four pixels per inner loop. A generalization to any number of pixels per inner loop is also described. The quad step algorithm generates straight lines at twice the rate of Bresenham’s algorithm. The tradeoff is an order-of-magnitude increase in code complexity and size. Gill does not consider this increase a problem, because of the larger memory size of modern microprocessors.