Jonathan Kirwan wrote:

On Fri, 27 Jun 2003 17:58:50 GMT, Jonathan Kirwan
wrote:

Hmm. Are you *THE* Jack Crenshaw? The "Let's Build A Compiler"
and "Math Toolkit for Real-Time Programming" Jack _W._ Crenshaw?

Actually, I think I've answered my own question, here. You
really *are* that Jack.

Grin! Yep, I really am.

What clues me in is your use of "phantom" he

mantissa -- 23 bits + phantom bit in bit 24.

The same term used on page 50 in "Math toolkit..."

In my own experience, even that predating the Intel 8087 or the
IEEE standardization, it was called a "hidden bit" notation. I
don't know where "phantom" comes from, as my own reading managed
to completely miss it.

So, a hearty "Hello" from me!

Hello. Re the term, phantom bit: I've been using that term since I can
remember -- and that's
a looooonnnngggg time. Then again, I still sometimes catch myself
saying "cycles" or "kilocycles,"
or "B+". I first heard the term in 1975. Not sure when it became
Politically Incorrect. Maybe
someone objected to the implied occult nature of the term, "phantom"?
Who knows?
but as far as I'm concerned the term "hidden bit" is a
Johnny-come-lately on the scene.

Back to the point. I want to thank you and everyone else who responded
(except the guy who said
"stop it") for helping to straighten out my warped brain.

It's nice that you have my book. Thanks for buying it. As a matter of
fact, I first ran across this
"peculiarity" three years ago, when I was writing it. I needed to
twiddle the components of the
floating-point number -- separate the exponent from mantissa -- to write
the fp_hack structure for
the square root algorithm. I looked at the formats for float, double,
and long double, and found the
second two formats easy enough to grok. But when I looked at the format
for floats, I sort of went,
"Gag!" and quickly decided to use doubles for the book.

It's funny how an idea, once formed, can persist. Lo those many years
ago, I didn't have a lot of time
to think about it -- had to get the chapter done. I just managed to
convince myself that the format
used this peculiar convention, what with base-4 exponents, and all. I
had no more need of it at the time,
so never went back and revisited the impression. It's persisted ever
since.

All of the folks who responded are absolutely right. Once I got my head
screwed on straight, it was
quite obvious that the format has no mysteries. It is indeed the IEEE
754 format, plain and simple.
The thing that had me confused was the exponents: 3f8, 400, 408, etc.
With one bit for the sign and
eight for the exponent, it's perfectly obvious that the exponent has to
bleed down one bit into the next
lower hex digit. That's what I was seeing, but somehow in my haste, I
didn't recognize it as such, and
formed this "theory" that it was using a base-4 exponent.

Wanna hear the funny part? After tinkering with it for awhile, I worked
out the rules for my imagined
format, that worked just fine. At work, I've got a Mathcad file that
takes the hex number, shifts it
two bits at a time, diddles the "phantom" bit, and produces the right
results. I can go from integer to
float and back nicely, using this cockamamie scheme.

Needless to say, the conversion is a whole lot easier if one uses the
real format! My Mathcad file just
got a lot shorter.

Thanks again to everyone who responded, and my apologies for bothering
y'all with this imaginary problem.

Jack