Velocity Reviews > IEEE-754

# IEEE-754

Peter J. Holzer
Guest
Posts: n/a

 08-28-2007
On 2007-08-28 07:42, Boudewijn Dijkstra <(E-Mail Removed)> wrote:
> Op Mon, 27 Aug 2007 15:52:30 +0200 schreef Peter J. Holzer
><(E-Mail Removed)>:
>> On 2007-08-27 07:24, Boudewijn Dijkstra <(E-Mail Removed)> wrote:
>>> Exactly. The epsilon will be proportional to the exponent.

>>
>> And now read the OP again.

>
> You're beyond me now. The OP was talking about a constant epsilon for the
> whole range of numbers within the normalized range.

Yes, but that epsilon was always multiplied by the number:

| round(x) = x*(1 + delta)
^ here
|
| 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*(1-2(-53)) <= round(x) <= x*(1+2^(-53))
^ here ^ here
| -----------------------------------------

This is afaik the normal use of eps. See for example
http://en.wikipedia.org/wiki/Machine_epsilon.

> Or did you read something else between lines?

No, I just read the lines.

hp

--
_ | Peter J. Holzer | I know I'd be respectful of a pirate
|_|_) | Sysadmin WSR | with an emu on his shoulder.
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Boudewijn Dijkstra
Guest
Posts: n/a

 08-29-2007
Op Tue, 28 Aug 2007 13:59:18 +0200 schreef CBFalconer
<(E-Mail Removed)>:
> Boudewijn Dijkstra wrote:
>> schreef Peter J. Holzer <(E-Mail Removed)>:
>>> Boudewijn Dijkstra <(E-Mail Removed)> wrote:
>>>
>>>> Exactly. The epsilon will be proportional to the exponent.
>>>
>>> And now read the OP again.

>>
>> You're beyond me now. The OP was talking about a constant epsilon
>> for the whole range of numbers within the normalized range. Or
>> did you read something else between lines?

>
> You are the first I have noted to consider 'proportional' to denote
> a constant.

You could note that, but it'd be more correct to note that I wasn't
denoting a constant, but an entity identified by the OP as a constant.

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Boudewijn Dijkstra
Guest
Posts: n/a

 08-29-2007
Op Wed, 29 Aug 2007 00:45:30 +0200 schreef Peter J. Holzer
<(E-Mail Removed)>:
> On 2007-08-28 07:42, Boudewijn Dijkstra <(E-Mail Removed)> wrote:
>> Op Mon, 27 Aug 2007 15:52:30 +0200 schreef Peter J. Holzer
>> <(E-Mail Removed)>:
>>> On 2007-08-27 07:24, Boudewijn Dijkstra <(E-Mail Removed)> wrote:
>>>> Exactly. The epsilon will be proportional to the exponent.
>>>
>>> And now read the OP again.

>>
>> You're beyond me now. The OP was talking about a constant epsilon for
>> the whole range of numbers within the normalized range.

>
> Yes, but that epsilon was always multiplied by the number:
>
> | round(x) = x*(1 + delta)
> ^ here

Yes, you're right. I was being incredibly thick (which doesn't usually
happen (for this long)).

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