On Friday, 21 February 2014 at 05:21:53 UTC, Frustrated wrote:
I think though adding a "repeating" bit would make it even more
accurate so that repeating decimals within the bounds of maximum
bits used could be represented perfectly. e.g., 1/3 = 0.3333...
could be represented perfectly with such a bit and sliding fp
type. With proper cpu support one could have 0.3333... * 3 = 1
exactly.
By having two extra bits one could represent constants to any
degree of accuracy. e.g., the last bit says the value represents
the ith constant in some list. This would allow very common
irrational constants to be used: e, pi, sqrt(2), etc...
Unfortunately maths (real world maths) isn't made by "common"
constants. More, such a "repeating bit" should become a
"repeating counter", since you usually get a certain number of
repeating digits, not just a single one.
For floating points, the 3rd last bit could represent a
repeating
decimal or they could be used in the constants for common
repeating decimals. (since chances are, repeated calculations
would not produce repeating decimals)
Things like those are cool and might have their application (I'm
thinking mostly at message passing via TCP/IP), but have no real
use in scientific computation. If you want good precision, you
might as well be better off with bignum numbers.
