Re: IEEE754
 From: Roman Töngi <roman.toengi@xxxxxxxxxx>
 Date: Thu, 23 Aug 2007 18:08:15 +0200
Boudewijn Dijkstra wrote:
Op Thu, 23 Aug 2007 12:45:52 +0200 schreef Roman Töngi <roman.toengi@xxxxxxxxxx>:From the IEEEspecification for double format.IEEE754 Arithmetic:
Most real numbers can't be stored exactly on the computer, but there can
be stated the range within which a machine number lies.
For the following example, I assume double precision and the round mode in effect to be 'round to nearest' and that the number lies within the
normalized range:
Definitions:
x := real number
round(x) := correctly rounded normalized number
eps := machine epsilon (2^(52) for double precision)
abs(x) := absolute value of x
That is:
round(x) = x*(1 + delta)
with delta:
abs(delta) <= 1/2*eps (round to nearest)
i.d. abs(delta) <= 2^(53) (double precision)
abs(delta) corresponds to the relative rounding error.
Now I can state the range including round(x):

x*(12(53)) <= round(x) <= x*(1+2^(53))

Is this the correct range according to my assumptions?
Yes, but your assumptions are invalid. How did you arrive at a machine epsilon of 2^(52)?
.
 FollowUps:
 Re: IEEE754
 From: Boudewijn Dijkstra
 Re: IEEE754
 References:
 IEEE754
 From: Roman Töngi
 Re: IEEE754
 From: Boudewijn Dijkstra
 IEEE754
 Prev by Date: Re: Are there books about C data structures?
 Next by Date: Bitfields vs integral promotions
 Previous by thread: Re: IEEE754
 Next by thread: Re: IEEE754
 Index(es):
Relevant Pages
