> But there's a useful rule of thumb: you need about twice the amount of working precision as your final result. Since double precision has a 53-bit mantissa (~

> But there's a useful rule of thumb: you need about twice the amount of working precision as your final result. Since double precision has a 53-bit mantissa (~16 decimal digits), that means if you need only 8 or fewer decimal digits, you're completely fine with double precision. This doesn't seem right, or at least it's not very general. The more operations you do, the more rounding errors you have, and each operation has the potential to magnify earlier errors. In solving ill-conditioned problems (which are not uncommon) the errors can easily be magnified so much that they're bigger than your signal, even with relatively small and simple situations.