In the days before
"Floating Point Units" in computers

floating point computers have been around since the 1950's. I have seen early
60's such machines still in use.

accounting computers used integer arithemtic because the calcs were quicker.

If your coding skills were 0.1% of what you claim you could easily use an
interger machine to get as many decimal places as you wanted. It was commonly
done, by freshmen in college.

Well, I said this would be too complicated for jaxie to understand. Newton's
method converges quickly and can easily be worked to the desired accuracy, just
like the normal method for doing long division.

Sorry jaxie, as for square roots, one math lesson a day is all I'm willing to
give someone incapable of learning. OK, you can just iterate on:
x2 = x1 - (x1^2 - a)/(2 * x1)
A tad more tedious than the method taught in high school, but easier to program.



"JAXAshby" wrote in message
...
jeffies, that is NOT algebraic. Ask your wife to explain the term to you.

a bit of a hint for you jeffies. algebraic would give you precision to as
many
decimals was you might wish to calc with accuracy to the next to last digit
calc'd.

go ahead. tell us how to do that with a pencil and paper. Tell you what.
Tell us how to do square roots *algebraically* with a pencil and paper.

ask your wife to explain square roots.

Well, I wouldn't say its so easy that jaxie can follow, but there are all
sorts
of techniques that have been developed over the years. Computers don't use
"magic" to calculate complex functions, there are often just programmed to
follow algorithms developed many years ago by people like Newton. Jaxie
forgets
that this is what I did for a living.

To compute a 4th root, using Newton's method:

Assume you want to compute x = a^(1/4)
Make a guess at the answer, call it x1. Then compute the next guess, x2, as
follows:
x2 = x1 - (x1^4 - a)/(4 * x1^3)
iterate again as
x3 = x2 - (x2^4 - a)/(4 * x2^3)

When the results get sufficiently close, you have an answer. Often only 3 or
4
iterations are needed. Similar techniques can be used to calculate the roots
of
polynomials.

I used the square root version of this a number of times. In the days before
"Floating Point Units" in computers considerable time savings (a factor of 10
or
more) could be had by adjusting the algorithms to match the input data and
desired accuracy.




"JAXAshby" wrote in message
...
wanna show us how?

]okay group, watch now how jeffies blathers on for days telling us that
what
with his degree in physics and all that he can do it easily. if I say he
can
not he will get all snippy. he couldn't tell us how RDF worked how is he
going
to tell us how to do 4th roots with pencil and paper.]

jeffies? do note the word algebraicly was there. in other words, SWAGing
is
not the answer.

What's so hard about doing 4th roots with pencil and paper?



"JAXAshby" wrote in message
...
bull. there is no intuitive way to calculate the product of those
numbers
in
that way, any more than you can calc a 4th root of a number algabraicly
with a
pencil and paper.

You clearly know little of computer hardware. I'm sure you'll claim now you
sold them for a living, which would make this all the more pathetic. While
hardware floating point units (FPU's) were available it was expensive and not
used by those on a tight budget. The smaller computers I worked on (Data
General Nova's) usually didn't have FPU's so I programmed FP software manually.
Even when they did have FP, it was often much faster to work in integer space.
Further, the early FPU's didn't do trig or roots, they still had to be
programmed manually.

Intel floating point wasn't standard until the mid-90's. (Was it the 386 or 486
where all CPU's had FP?) The graphics package I developed at Lotus in '92 was
done in "fixed point" because it had to run quickly on all Windows machines.

Another problem is that some FPU didn't support the mantissa precision or the
exponent range desired. When DEC came out with the VAX they pushed hard to
place one where I worked, the Smithsonian Astrophysical Observatory. However,
the native FP format only had limited exponent range (10^38?). We insisted on
more range, so they invented a new format with very high range and precision.
At the time, it was the largest VAX installation - I think there was 6 megabytes
of main memory!


"JAXAshby" wrote in message
...
In the days before
"Floating Point Units" in computers

floating point computers have been around since the 1950's. I have seen early
60's such machines still in use.

accounting computers used integer arithemtic because the calcs were quicker.

If your coding skills were 0.1% of what you claim you could easily use an
interger machine to get as many decimal places as you wanted. It was commonly
done, by freshmen in college.

Subject: uffda.
From: (JAXAshby)

JAX, JAx, Jax .... first, you need to learn to think, then you need to learn to
think of possibilities and not be so concerned by doing things only by rote.
(might help you to understand how to take bearings using a magnetic compass).


bull. not even remotely possible. there is no relationship between the
numbers and the product as you claim.

The numbers, when strung together, created the correct total .... or didn't you
realize that? (oops, sorry ....question)



Or ...

... would you like to make mention of the relationship?

see above.


We will wait no more than a few hours.

Hell, the way you reason, it will be next week before you can see a possible
relationship.
Ya know, Jax, I'll bet you're the only one who didn't understand the
possibilities in my first post on this issue.

Shen

jeffies, I knew how to use newton to *****approximate***** square roots using
an ADDING MACHINE several decades ago.

That was not the question.

Go back and read the question AGAIN, this time ask your wife to help you.

Well, I said this would be too complicated for jaxie to understand. Newton's
method converges quickly and can easily be worked to the desired accuracy,
just
like the normal method for doing long division.

Sorry jaxie, as for square roots, one math lesson a day is all I'm willing to
give someone incapable of learning. OK, you can just iterate on:
x2 = x1 - (x1^2 - a)/(2 * x1)
A tad more tedious than the method taught in high school, but easier to
program.



"JAXAshby" wrote in message
...
jeffies, that is NOT algebraic. Ask your wife to explain the term to you.

a bit of a hint for you jeffies. algebraic would give you precision to as
many
decimals was you might wish to calc with accuracy to the next to last digit
calc'd.

go ahead. tell us how to do that with a pencil and paper. Tell you what.
Tell us how to do square roots *algebraically* with a pencil and paper.

ask your wife to explain square roots.

Well, I wouldn't say its so easy that jaxie can follow, but there are all
sorts
of techniques that have been developed over the years. Computers don't
use
"magic" to calculate complex functions, there are often just programmed to
follow algorithms developed many years ago by people like Newton. Jaxie
forgets
that this is what I did for a living.

To compute a 4th root, using Newton's method:

Assume you want to compute x = a^(1/4)
Make a guess at the answer, call it x1. Then compute the next guess, x2,
as
follows:
x2 = x1 - (x1^4 - a)/(4 * x1^3)
iterate again as
x3 = x2 - (x2^4 - a)/(4 * x2^3)

When the results get sufficiently close, you have an answer. Often only 3
or
4
iterations are needed. Similar techniques can be used to calculate the
roots
of
polynomials.

I used the square root version of this a number of times. In the days
before
"Floating Point Units" in computers considerable time savings (a factor of
10
or
more) could be had by adjusting the algorithms to match the input data
and
desired accuracy.




"JAXAshby" wrote in message
...
wanna show us how?

]okay group, watch now how jeffies blathers on for days telling us that
what
with his degree in physics and all that he can do it easily. if I say
he
can
not he will get all snippy. he couldn't tell us how RDF worked how is
he
going
to tell us how to do 4th roots with pencil and paper.]

jeffies? do note the word algebraicly was there. in other words,
SWAGing
is
not the answer.

What's so hard about doing 4th roots with pencil and paper?



"JAXAshby" wrote in message
...
bull. there is no intuitive way to calculate the product of those
numbers
in
that way, any more than you can calc a 4th root of a number
algabraicly
with a
pencil and paper.

jeffies, data general machines were *accounting* machines, so therefore used
integer calc (it is faster).

Intel makes MICROprocessors.

Floating point machines date from the 1950's. Ever hear of Control Data?

[snip a bunch of trivia dating from 35 years later]

Of course I heard of Control data - I once took a class where the final exam
required being able to explain the purpose of every wire on a discrete
transistor CDC computer was for. The computer replaced by the VAX in my
previous post was a CDC Cyber 76.

However, the point is not that SOME computers had FPUs, it was that most
computers DID NOT have FPUs, or they were slow and/or expensive, and thus
software floating point and fixed point math had to be implemented by the
application programmers.

You can claim the DG machines were primarily used for "accounting," and it may
even be so, but I worked in Astronomy and Space Sciences at the Smithsonian
(located at Harvard) and at MIT; I can assure you that in the mid '70s the labs
were filled with DG machines, because they gave the most bang for the buck.
My first "home computer" (in 1980) was an old DG 1200, followed quickly by a DEC
11/23. I still have the faceplate from the Nova.


"JAXAshby" wrote in message
...
jeffies, data general machines were *accounting* machines, so therefore used
integer calc (it is faster).

Intel makes MICROprocessors.

Floating point machines date from the 1950's. Ever hear of Control Data?

[snip a bunch of trivia dating from 35 years later]

so, how come you didn't know that CDC made computers in the 1950's?

btw, you "home" computer was 11/23 in the early 80's?

sure, and you traveled to junior high school on a hydrazine rocket.

btw, how many wires on a "discrete" transitor used on a CDC machine? careful
how you speak, for my brother worked the technical end of CDC for over 30
years.

[snip the junk wherein jeffies tries to cover that even to this moment he
doesn't know even WHAT it means to calculate *algebraicly* the nth root of a
number, something every last person with degree in physics [which jeffies
claims to have] knew thoroughly before the graduated high school]

jeffies, you are hopeless. Even now you don't have a clew that you were set up
with bait a high school kid would have seen from a thousand yards.

"JAXAshby" wrote in message
...
so, how come you didn't know that CDC made computers in the 1950's?

You never asked. Your claim was that all computers had FPUs so it was
unnecessary to code floating point. The fact that some computers had it is
irrelevant. Most did not.

BTW, CDC was founded late in the 50s; I'm not sure they actually shipped a
machine with floating point until the mid '60s.


btw, you "home" computer was 11/23 in the early 80's?

Sure, why not? It only cost a few thousand dollars, used. Besides, my partner
and I had a small company -we didn't rent an office for 2 years. He worked on
the DG at his house, I had the DEC at mine. These were floppy based machines,
without a lot of memory and certainly no FPU. A small disk, like an RL02 (10
meg "top loader") went for around $25,000, much more than the computer. We got
our first in '82 from Apple computer, as payment for porting our software to the
not-yet-released "Lisa," which I guess was our third computer. A Compaq
"luggable" came in 1983, a microVax and a Sun soon followed.

Actually, around 1972 I had at home an IBM 2741 Selectric terminal with a 134.5
baud modem that I could dial into Multics developement system at MIT, but that's
another story.


sure, and you traveled to junior high school on a hydrazine rocket.

That's silly. I teleported.


btw, how many wires on a "discrete" transitor used on a CDC machine? careful
how you speak, for my brother worked the technical end of CDC for over 30
years.

I don't remember, it was about 35 years ago, although 3 wires would be a good
guess for a transistor. I dealt with it at the "gate" level, not the individual
transistors. I think it was a CDC 3000. IIRC, the logic was on small boards
that each had 2 flip-flops, which probably had 2 transistors each. The back of
it was a *lot* of wire wrap. I'd guess around 30,000 "gates" in the machine,
but I could be way off. The logic book was several inches thick, with timing
charts and logic diagrams. ("On the leading edge of this signal, the data from
register x would be latched into buffer y ...") So jaxie, send this off to your
brother and ask him if its a fair description, given that I spent a few weeks
with the machine 35 years ago.



[snip the junk wherein jeffies tries to cover that even to this moment he
doesn't know even WHAT it means to calculate *algebraicly* the nth root of a
number, something every last person with degree in physics [which jeffies
claims to have] knew thoroughly before the graduated high school]

jeffies, you are hopeless. Even now you don't have a clew that you were set
up
with bait a high school kid would have seen from a thousand yards.

comments interlaced

Your claim was that all computers had FPUs

nope. not what I said. you said none were available until the 1980's. I said
1950's

btw, large computers didn't -- and don't -- have Floating Point Units (see
jeffies? today you learned what FPU means). Floating point is designed in
from the start. Takes more time to calc than interger, but it is there from
the get go

BTW, CDC was founded late in the 50s; I'm not sure they actually shipped a
machine with floating point until the mid '60s.

you are wrong.

btw, you "home" computer was 11/23 in the early 80's?

Sure, why not? It only cost a few thousand dollars, used.

bull. a PDP-6, maybe, but not even a PDP-11. check your numbers dude. 11/23
was state of the art at that time. I sold interger machines at the time rather
than scientific machines. I DO know that "home computers" (i.e. 8086 based)
would go for upwards of six grand and those things didn't hardly compete with
an 11/23.

try again.

I had the DEC at mine.

no you didn't

These were floppy based
machines

no they weren't. In 1972 Shugart still worked for IBM and the floppy was still
IBM technology and was used to boot a System 32.

our first in '82 from Apple computer,

which was 68000 based, recently updated from a 6800 (btw yo-yo, Motorola called
the microprocessor chip a "68000" because supposedly it had 68,000 transistors,
which it didn't)

Actually, around 1972 I had at home an IBM 2741 Selectric terminal

a 2741 was part of an RJE station (which used punch cards) and was about the
size of two chest-style home freezers.

with a
134.5
baud modem that I could dial into Multics developement system at MIT, but
that's
another story.

another bogus story.

sure, and you traveled to junior high school on a hydrazine rocket.

That's silly. I teleported.

while you read "Amazing Stories"

btw, how many wires on a "discrete" transitor used on a CDC machine?
careful
how you speak, for my brother worked the technical end of CDC for over 30
years.

I don't remember ... would be a good
guess for a transistor. I dealt with it at the "gate" level,

"gate" level, eh?

not the
individual
transistors.

that is what a "gate" is, yo-yo, in this context

IIRC, the logic was on small boards

you are talking about TTL logic, dude. which is a whole different story than
the one you are telling

that each had 2 flip-flops, which probably had 2 transistors each.

no it didn't

The back
of
it was a *lot* of wire wrap.

yo-yo, you were looking at the semi-conductor replacements for core memory of
older, already installed machines. the "lot of wire" was there to slow the
semiconductor memory response speed down to core memory speed so the machine
didn't get ahead of itself. you know, don't you, that electricity travels one
foot per nano-second?

I'd guess around 30,000 "gates" in the machine,
but I could be way off.

not even frickin close.

The logic book was several inches thick, with timing
charts and logic diagrams. ("On the leading edge of this signal, the data
from
register x would be latched into buffer y ...")

dude, you were looking at a repair manual.

So jaxie, send this off to
your
brother and ask him if its a fair description, given that I spent a few weeks
with the machine 35 years ago.

If I sent it too him without telling him the source he would say, "Some
Internet yo-yo, I see"