将整数转换为笛卡尔坐标的替代/更快方法？

As a fun side-project for myself to help in learning yet another PHP MVC framework, I've been writing Reversi / Othello as a PHP & Ajax application, mostly straightforward stuff. I decided against using a multidimensional array for a number of reasons and instead have a linear array ( in this case 64 elements long ) and a couple methods to convert from the coordinates to integers.As a fun side-project for myself to help in lea