Re: Possreps and numeric types

Date: Thu, 29 Mar 2007 20:36:39 GMT
Message-ID: <rrVOh.17061\$PV3.175756_at_ursa-nb00s0.nbnet.nb.ca>

Gene Wirchenko wrote:
>
>

```>>Gene Wirchenko wrote:
>>
>>
>>>
>>>
>>>>Gene Wirchenko wrote:
>>>>
>>>>
>>>>>
>>>>>
>>>>>>Gene Wirchenko wrote:
>>>>>>
>>>>>>
>>>>>>>
>>>>>>>[snip]
>>>>>>>
>>>>>>>
>>>>>>>>I admit I used epsilon somewhat sloppily and not necessarily with the
>>>>>>>>exact meaning used when discussing a particular floating-point
>>>>>>>>implementation. I used it to mean the distance to the representable

>
>  ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

```
>
```>>>>>>>>predecessor or successor of any representable rational value.

>
>        ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

```
>
```>>>>>>>   That is incorrect.  It is per
>>>>>>>        http://en.wikipedia.org/wiki/Machine_epsilon
>>>>>>>In a floating-point system, epsilon is the smallest number such that

>
>  ^^^^^^^^^^^^^^^^^^^^^^^^^

>
>>>>>>>        1 + epsilon > 1

>
>                ^^^^^^^^^^^^^^^

```
>
```>>>>>>>[snip]
>>>>>>
>>>>>>When you say the above is incorrect, are you saying I was not using
>>>>>>epsilon sloppily? Or are you saying I didn't use it to mean the distance
>>>>>>to the representable predecessor or successor of any representable
>>>>>>rational value?
>>>>>
>>>>>    The definition of epsilon.
>>>>
>>>>Other than the "scaled by the exponent" bit, what exactly is the
>>>>difference? ie. If I subtracted one from the other, what answer would I get?
>>>
>>>     If I am understanding you, other than that difference, none.  The
>>
>>I really don't understand your objection. I noted I used the term
>>sloppily and not as defined for floating point when I was discussing
>>rational representations. Using the only definition I gave for the
>>floating point version, the difference would be zero. The definitions
>>are equivalent only stated differently.

>
>      No.  The definition that I gave is in terms of 1, not just any

```
> representatable value.

I guess I will just roll my eyes and move along. Received on Thu Mar 29 2007 - 22:36:39 CEST

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