On Thursday, July 30, 2015 at 11:08:50 AM UTC-4, Tom Breloff wrote: > > It's better in the sense that you have a reason to try it with a larger > type. You know exactly how much precision you've lost, and so you can > decide to use up to 1024 bits for intermediate calculations if you need to. >
No, it's worse, because you will likely use much more precision than you need. You don't know "exactly how much precision you've lost," you have a (probably) grossly pessimistic estimate of how much precision you've lost. Compared to that, performing the calculation in Float32, then Float64, then (rarely) Float128 (or better, rearrange your calculation to avoid the catastrophic loss of accuracy that is necessitating > double precision) until the answer stops changing to your desired tolerance is vastly more efficient.
