Thread Subject: realmin not actually the lowest ??

>> realmax
ans =
    1.797693134862316e+308

>> realmin
ans =
    2.225073858507201e-308

>> 1/realmax
ans =
    5.562684646268004e-309

If realmin is actually O(10^-308), then how did I just make a number smaller than that ??

The documentation for realmin says that realmin is the smallest positive normalized (whatever the heck this means) floating point number on my computer.

On Aug 10, 1:50 pm, "Juliette Salexa" <juliette.physic...@gmail.com>
wrote:
> >> realmax
>
> ans =
>     1.797693134862316e+308
>
> >> realmin
>
> ans =
>     2.225073858507201e-308
>
> >> 1/realmax
>
> ans =
>     5.562684646268004e-309
>
> If realmin is actually O(10^-308), then how did I just make a number smaller than that ??
>
> The documentation for realmin says that realmin is the smallest positive normalized (whatever the heck this means) floating point number on my computer.

But you didn't finish the quote:
Anything smaller underflows or is an IEEE
    "denormal".

Now, let me ask you something that is equally as important:
How many angels can dance on the head of a pin?

It depends on the size of the angels! There's no need for sarcasm.. I'm working with extremely small numbers and need very high accuracy.

I looked up what denormal/subnormal numbers are and what normalized means.
Thanks for the clarification.

"Juliette Salexa" <juliette.physicist@gmail.com> wrote in message
news:h5nucc$3dc$1@fred.mathworks.com...
>>> realmax
> ans =
> 1.797693134862316e+308
>
>>> realmin
> ans =
> 2.225073858507201e-308
>
>>> 1/realmax
> ans =
> 5.562684646268004e-309
>
> If realmin is actually O(10^-308), then how did I just make a number
> smaller than that ??

Easily. Note that REALMIN is NOT the smallest positive number, and the
documentation doesn't say it is.

http://www.mathworks.com/access/helpdesk/help/techdoc/ref/realmin.html

> The documentation for realmin says that realmin is the smallest positive
> normalized (whatever the heck this means) floating point number on my
> computer.

That's correct. The word "normalized" is extremely important for the
definition of REALMIN. There are smaller positive _non-normalized_ floating
point numbers, commonly referred to as denormal numbers.

http://en.wikipedia.org/wiki/Denormal

Basically, instead of having an assumed (but not stored) leading binary
digit of 1 (i.e. the mantissa is between 1 and 2), the assumed leading digit
of a denormal number is 0 (the mantissa is between 0 and 1.)

Cleve talks about denormal numbers around the end of page 2 of his Cleve's
Corner article about floating-point arithmetic.

http://www.mathworks.com/company/newsletters/news_notes/pdf/Fall96Cleve.pdf

--
Steve Lord
slord@mathworks.com

Thanks a lot Steven Lord,

TideMan's response motivated me to read up on denormal/subnormal numbers and normalized numbers.

So basically, the lowest number we can get is realnum/(9.999... *10^15) , but there will be truncation errors in its calculation, so only the first digit is really true.

On Aug 10, 2:22 pm, "Juliette Salexa" <juliette.physic...@gmail.com>
wrote:
> It depends on the size of the angels! There's no need for sarcasm.. I'm working with extremely small numbers and need very high accuracy.
>
> I looked up what denormal/subnormal numbers are and what normalized means.
> Thanks for the clarification.

Huh!!
As per earlier posts, your next post will be that Matlab desperately
needs a 300 digit capacity because:
realmax*(1/realmax) - 1
is not identically zero