nothings/gist:06ac1d8ea61635d09e0f

## gistfile1.txt
Thinking about this some more: the decimal expansion of the halfway point between two numbers is always going to be either

  ...xyz000000

or

  ...xyz500000

We don't want to deal with the 5s if we can avoid it. Say the longest decimal expansion of a binary float is N digits (it's somewhere around 770, haven't calculated it exactly). Then the halfway point is gonna be all zeros after N+1 decimal digits, guaranteed.

To round, we just need to know if we're *exactly* on the edge between two numbers (in which case we might need to employ a tie breaker like round to nearest even) or slightly higher - in effect, is the number "1234.50000" or "1234.50000+"?

So we read at least N+1 digits exactly (LuaJIT just reads up to 800, which is definitely enough for doubles); beyond that, we just need to know if any of the following digits is nonzero (we have the '+') or not.
	Thinking about this some more: the decimal expansion of the halfway point between two numbers is always going to be either

	...xyz000000

	or

	...xyz500000

	We don't want to deal with the 5s if we can avoid it. Say the longest decimal expansion of a binary float is N digits (it's somewhere around 770, haven't calculated it exactly). Then the halfway point is gonna be all zeros after N+1 decimal digits, guaranteed.

	To round, we just need to know if we're exactly on the edge between two numbers (in which case we might need to employ a tie breaker like round to nearest even) or slightly higher - in effect, is the number "1234.50000" or "1234.50000+"?

	So we read at least N+1 digits exactly (LuaJIT just reads up to 800, which is definitely enough for doubles); beyond that, we just need to know if any of the following digits is nonzero (we have the '+') or not.