> True, but a good hex editor will offer a mode to interpret the data as IEEE
> floating point.

true, just like hex workshop. after all, its up to programs/machines to
read the binary/hexadecimal stuff, and since my hex editor can
interpret floats and doubles both in little-endian and big-endian, i
have no reason to complain :)

"glen herrmannsfeldt" <gah@ugcs.caltech.edu> wrote in message
news:ge2dncQrXdNNMD_fRVn-jQ@comcast.com...
> Michel Rouzic wrote:
>
> >>Not so much hidden as assumed. The way floating-point numbers are
> >>normalized, the most significant bit of the mantissa is always 1.* That
> >>being the case, there's no need to waste space representing it; just
> >>assume it's there.
>
> > oh yeah, i remeber that, i learnt that at school. and damn, i got bad
> > memories from trying to write by hand IEEE floats in binary, in
> > architecture tests and all that. yeah, that hidden bit makes me think
> > that it's definitly a smart way to represent floats.
>
> Before I ever heard of hidden bits I learned to read S/360 floating
> point from hex dumps.  There are six, 14, or 28 hex digits, and an
> exponent giving the position of the hexadecimal point.  Very easy.
>
> Reading IEEE floats from a hex dump is much harder.

True, but a good hex editor will offer a mode to interpret the data as IEEE
floating point.

glen herrmannsfeldt <gah@ugcs.caltech.edu> writes:
> Michel Rouzic wrote:
> 
> >>Not so much hidden as assumed. The way floating-point numbers are
> >>normalized, the most significant bit of the mantissa is always 1.* That
> >>being the case, there's no need to waste space representing it; just
> >>assume it's there.
> 
> > oh yeah, i remeber that, i learnt that at school. and damn, i got bad
> > memories from trying to write by hand IEEE floats in binary, in
> > architecture tests and all that. yeah, that hidden bit makes me think
> > that it's definitly a smart way to represent floats.
> 
> Before I ever heard of hidden bits I learned to read S/360 floating 
> point from hex dumps.  There are six, 14, or 28 hex digits, and an 
> exponent giving the position of the hexadecimal point.  Very easy.
> 
> Reading IEEE floats from a hex dump is much harder.

Talking about reading memory dumps says something about
your age.  :-)

Mentioning hex dumps further categorizes your history as
does your frequent postings to the PL/I newsgroup.

Michel Rouzic wrote:

>>Not so much hidden as assumed. The way floating-point numbers are
>>normalized, the most significant bit of the mantissa is always 1.* That
>>being the case, there's no need to waste space representing it; just
>>assume it's there.

> oh yeah, i remeber that, i learnt that at school. and damn, i got bad
> memories from trying to write by hand IEEE floats in binary, in
> architecture tests and all that. yeah, that hidden bit makes me think
> that it's definitly a smart way to represent floats.

Before I ever heard of hidden bits I learned to read S/360 floating 
point from hex dumps.  There are six, 14, or 28 hex digits, and an 
exponent giving the position of the hexadecimal point.  Very easy.

Reading IEEE floats from a hex dump is much harder.

-- glen

Michel Rouzic wrote:
>>Not so much hidden as assumed. The way floating-point numbers are
>>normalized, the most significant bit of the mantissa is always 1.* That
>>being the case, there's no need to waste space representing it; just
>>assume it's there.
>>
>>Jerry
>>__________________________________
>>* Decimal floats are represented as x.y*10^n, binary floats, as x.y*2^n,
>>where x is a single non-zero digit. In decimal, x can be 1, 2, ... 9. In
>>binary, it is always 1 and can be assumed.
>>--
>>Engineering is the art of making what you want from things you can get.
>>�����������������������������������������������������������������������
> 
> 
> oh yeah, i remeber that, i learnt that at school. and damn, i got bad
> memories from trying to write by hand IEEE floats in binary, in
> architecture tests and all that. yeah, that hidden bit makes me think
> that it's definitly a smart way to represent floats.

Smart for general-purpose use, or when you need (or don't know you don't 
need) the extra precision. Dumb when you know you don't.

Jerry
-- 
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������

> Not so much hidden as assumed. The way floating-point numbers are
> normalized, the most significant bit of the mantissa is always 1.* That
> being the case, there's no need to waste space representing it; just
> assume it's there.
>
> Jerry
> __________________________________
> * Decimal floats are represented as x.y*10^n, binary floats, as x.y*2^n,
> where x is a single non-zero digit. In decimal, x can be 1, 2, ... 9. In
> binary, it is always 1 and can be assumed.
> --
> Engineering is the art of making what you want from things you can get.
> =AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=
=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=
=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF

oh yeah, i remeber that, i learnt that at school. and damn, i got bad
memories from trying to write by hand IEEE floats in binary, in
architecture tests and all that. yeah, that hidden bit makes me think
that it's definitly a smart way to represent floats.

in article 1117888476.783826.31940@g49g2000cwa.googlegroups.com, Michel
Rouzic at Michel0528@yahoo.fr wrote on 06/04/2005 08:34:

>> I'm thinking of the things like the "hidden
>> bit" which increases your precision by ~6dB for "free" and denormals.
> 
> hidden bit? what is that?

there's a nice webpage (probably dozens of them) on the subject at

      http://stevehollasch.com/cgindex/coding/ieeefloat.html   .

go to "The Mantissa".

-- 

r b-j                  rbj@audioimagination.com

"Imagination is more important than knowledge."

Michel Rouzic wrote:
>>I'm thinking of the things like the "hidden
>>bit" which increases your precision by ~6dB for "free" and denormals.
> 
> 
> hidden bit? what is that?

Not so much hidden as assumed. The way floating-point numbers are 
normalized, the most significant bit of the mantissa is always 1.* That 
being the case, there's no need to waste space representing it; just 
assume it's there.

Jerry
__________________________________
* Decimal floats are represented as x.y*10^n, binary floats, as x.y*2^n, 
where x is a single non-zero digit. In decimal, x can be 1, 2, ... 9. In 
binary, it is always 1 and can be assumed.
-- 
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������

> I'm thinking of the things like the "hidden
> bit" which increases your precision by ~6dB for "free" and denormals.

hidden bit? what is that?

"robert bristow-johnson" <rbj@audioimagination.com> wrote in message
news:BEC63948.7EE5%rbj@audioimagination.com...
> in article 11a1bf2ta619674@corp.supernews.com, Jon Harris at
> jon_harrisTIGER@hotmail.com wrote on 06/03/2005 15:23:
>
> > "Michel Rouzic" <Michel0528@yahoo.fr> wrote in message
> > news:1117819203.135271.290510@g44g2000cwa.googlegroups.com...
> >>
> >> maybe, but the only silly thing about IEEE floating point
> >> representation is the question people can ask because if you understand
> >> it good (and im sure you do) you realize that there is no better way to
> >> represent floats (unless there's a smarter way i havent heard of)
> >
> > Even though some of the features of IEEE floating point make designing
> > hardware to use it more complicated, those same features make it a pretty
nice
> > way to represent floating point values.  I'm thinking of the things like the
> > "hidden bit" which increases your precision by ~6dB for "free" and
denormals.
>
> it's also a bitch to deal with in software (a floating-point library running
> on an integer machine), largely for the same reasons.  i've complained about
> this some years ago here on comp.dsp .  i have to admit now, that although i
> then hated the "hidden 1 MSB", it's probably a good thing they put it in.
> but it *is* ugly.

Yep, it's a double-edged sword:  nice for the user, but more difficult to
implement in either hardware or software emulation.  When I was in college, a
lab problem we had in our microprocessor design class was to write IEEE
floating-point addition and multiplication routines (in assembler) on a Motorola
integer chip (68000 family maybe?).  It was surprisingly difficult and took
quite a bit of code for such seemingly simple tasks.