0.0 / 0.0 = -NAN ?...

[Ricky]

On Monday, May 2, 2022 at 1:04:34 PM UTC-4, John Larkin wrote:

On Mon, 02 May 2022 11:54:32 -0400, Joe Gwinn <joeg...@comcast.net
wrote:
On Mon, 2 May 2022 15:28:46 +0100, Martin Brown
\'\'\'newspam\'\'\'@nonad.co.uk> wrote:

On 02/05/2022 15:10, jla...@highlandsniptechnology.com wrote:
On Sun, 1 May 2022 20:27:33 -0700 (PDT), whit3rd <whi...@gmail.com
wrote:

On Saturday, April 30, 2022 at 1:23:21 PM UTC-7, legg wrote:
On Sat, 30 Apr 2022 10:47:30 -0700 (PDT), Ricky
gnuarm.del...@gmail.com> wrote:

On Saturday, April 30, 2022 at 12:11:41 PM UTC-4, jla...@highlandsniptechnology.com wrote:

I wrote an s32.32 saturating math package for the 68K that always did
what was most reasonable.

0/0 = 0

I\'m sure no one can explain why 0/0 = 0 makes sense. Zero does not represent just exactly zero. Just as 1 is the range from 1/2 to 1-1/2, zero is the range from -1/2 to +1/2.

If the denominator is not zero, as the numerator approaches zero, yes, in the limit, the result approaches zero. But if the numerator is not zero, as the denominator approaches zero, in the limit, the result approaches infinity. So why would 0/0=0 make sense?

I would have expected 0/0=1 ie no rational difference.

That\'s the case if you consider lim x/x as x approaches zero. But,
what of the limit of 2x/x, or -x/x, as x approaches zero? NAN is the
best way to get a thinking human to understanding what the computer
is trying to express.

What does a control system do when the heater voltage is computed to
be NAN?

Shut down. The situation should never arise if you have scaled the
problem correctly and you should never be dividing by zero anyway.

If the denominator of a division is zero then you haven\'t thought out
the representation of your problem correctly. Testing for zero is
usually quick (and often implicitly available in integer arithmetic).

Umm. Testing for zero doesn\'t necessarily change anything.

I have a war story here. Many decades ago, I was the software
architect for the mission software of a ship self defense system that
shoots incoming cruise missiles down, if it can. From detection at
the horizon to impact on ownship is maybe twenty seconds.

One fine day, a mob of software engineers turned up, locked in
argument about what to do if the engageability calculation suffered a
divide-by-zero exception.

This is not a coding error per se, it\'s a mathematical singularity in
the equations - some engagement geometries will hit the singularity,
and the embedded realtime computers of that day could not handle the
more complicated math needed to avoid such things fast enough to
matter.

There were two schools: Just provide a very large number and proceed,
praying. Stop and print out a bunch of diagnostic information.

Hmm. So the user, an ordinary sailor operating the self-defense
system is in the middle of an engagement with an incoming cruise
missile, and is suddenly handed a bunch or error messages, with less
than twenty seconds to live ... Really??? No! Just silently return
the best answer possible given the situation and press on, praying.

Joe Gwinn
Yes. A best guess is better than an exception trap. Or a crash.

Or, you can code to handle such cases in a way that is logical, such as not dividing by zero in the first place. A \"trap\" is just the detection of the condition and implies nothing about how it is handled. So it is not inherently bad.

The crash is the sort of behavior that happens when the situation is ignored or handled poorly. Yeah, it\'s always better to not crash. That\'s a bit of a \"Duh!\"

--

Rick C.

-- Get 1,000 miles of free Supercharging
-- Tesla referral code - https://ts.la/richard11209

 

[Phil Hobbs]

jlarkin@highlandsniptechnology.com wrote:

On Sun, 1 May 2022 20:27:33 -0700 (PDT), whit3rd <whit3rd@gmail.com
wrote:

On Saturday, April 30, 2022 at 1:23:21 PM UTC-7, legg wrote:
On Sat, 30 Apr 2022 10:47:30 -0700 (PDT), Ricky
gnuarm.del...@gmail.com> wrote:

On Saturday, April 30, 2022 at 12:11:41 PM UTC-4, jla...@highlandsniptechnology.com wrote:

I wrote an s32.32 saturating math package for the 68K that always did
what was most reasonable.

0/0 = 0

I\'m sure no one can explain why 0/0 = 0 makes sense. Zero does not represent just exactly zero. Just as 1 is the range from 1/2 to 1-1/2, zero is the range from -1/2 to +1/2.

If the denominator is not zero, as the numerator approaches zero, yes, in the limit, the result approaches zero. But if the numerator is not zero, as the denominator approaches zero, in the limit, the result approaches infinity. So why would 0/0=0 make sense?

I would have expected 0/0=1 ie no rational difference.

That\'s the case if you consider lim x/x as x approaches zero. But,
what of the limit of 2x/x, or -x/x, as x approaches zero? NAN is the
best way to get a thinking human to understanding what the computer
is trying to express.

What does a control system do when the heater voltage is computed to
be NAN?

Log it, skip the update, and press on to the next measurement.

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs
Principal Consultant
ElectroOptical Innovations LLC / Hobbs ElectroOptics
Optics, Electro-optics, Photonics, Analog Electronics
Briarcliff Manor NY 10510

http://electrooptical.net
http://hobbs-eo.com

 

[Lasse Langwadt Christensen]

mandag den 2. maj 2022 kl. 22.52.48 UTC+2 skrev Phil Hobbs:

jla...@highlandsniptechnology.com wrote:
On Sun, 1 May 2022 20:27:33 -0700 (PDT), whit3rd <whi...@gmail.com
wrote:

On Saturday, April 30, 2022 at 1:23:21 PM UTC-7, legg wrote:
On Sat, 30 Apr 2022 10:47:30 -0700 (PDT), Ricky
gnuarm.del...@gmail.com> wrote:

On Saturday, April 30, 2022 at 12:11:41 PM UTC-4, jla...@highlandsniptechnology.com wrote:

I wrote an s32.32 saturating math package for the 68K that always did
what was most reasonable.

0/0 = 0

I\'m sure no one can explain why 0/0 = 0 makes sense. Zero does not represent just exactly zero. Just as 1 is the range from 1/2 to 1-1/2, zero is the range from -1/2 to +1/2.

If the denominator is not zero, as the numerator approaches zero, yes, in the limit, the result approaches zero. But if the numerator is not zero, as the denominator approaches zero, in the limit, the result approaches infinity. So why would 0/0=0 make sense?

I would have expected 0/0=1 ie no rational difference.

That\'s the case if you consider lim x/x as x approaches zero. But,
what of the limit of 2x/x, or -x/x, as x approaches zero? NAN is the
best way to get a thinking human to understanding what the computer
is trying to express.

What does a control system do when the heater voltage is computed to
be NAN?
Log it, skip the update, and press on to the next measurement.

hoping that that doesn\'t slow the system down to much

 

[Ricky]

On Monday, May 2, 2022 at 5:02:22 PM UTC-4, lang...@fonz.dk wrote:

mandag den 2. maj 2022 kl. 22.52.48 UTC+2 skrev Phil Hobbs:
jla...@highlandsniptechnology.com wrote:
On Sun, 1 May 2022 20:27:33 -0700 (PDT), whit3rd <whi...@gmail.com
wrote:

On Saturday, April 30, 2022 at 1:23:21 PM UTC-7, legg wrote:
On Sat, 30 Apr 2022 10:47:30 -0700 (PDT), Ricky
gnuarm.del...@gmail.com> wrote:

On Saturday, April 30, 2022 at 12:11:41 PM UTC-4, jla...@highlandsniptechnology.com wrote:

I wrote an s32.32 saturating math package for the 68K that always did
what was most reasonable.

0/0 = 0

I\'m sure no one can explain why 0/0 = 0 makes sense. Zero does not represent just exactly zero. Just as 1 is the range from 1/2 to 1-1/2, zero is the range from -1/2 to +1/2.

If the denominator is not zero, as the numerator approaches zero, yes, in the limit, the result approaches zero. But if the numerator is not zero, as the denominator approaches zero, in the limit, the result approaches infinity. So why would 0/0=0 make sense?

I would have expected 0/0=1 ie no rational difference.

That\'s the case if you consider lim x/x as x approaches zero. But,
what of the limit of 2x/x, or -x/x, as x approaches zero? NAN is the
best way to get a thinking human to understanding what the computer
is trying to express.

What does a control system do when the heater voltage is computed to
be NAN?
Log it, skip the update, and press on to the next measurement.
hoping that that doesn\'t slow the system down to much

If it does, it is a crappy system. That\'s what almost killed the first moon landing. You can test until you are blue in the face and you have not proven anything. You have to deal with these sorts of issues up front in the design requirements stage. Screw that up and you will have a system that does what you asked for, but not what you want.

Thinking 0/0 is an ok thing to approximate is not a way to design critical systems.

--

Rick C.

-+ Get 1,000 miles of free Supercharging
-+ Tesla referral code - https://ts.la/richard11209

 

[Lasse Langwadt Christensen]

mandag den 2. maj 2022 kl. 23.26.42 UTC+2 skrev Ricky:

On Monday, May 2, 2022 at 5:02:22 PM UTC-4, lang...@fonz.dk wrote:
mandag den 2. maj 2022 kl. 22.52.48 UTC+2 skrev Phil Hobbs:
jla...@highlandsniptechnology.com wrote:
On Sun, 1 May 2022 20:27:33 -0700 (PDT), whit3rd <whi...@gmail.com
wrote:

On Saturday, April 30, 2022 at 1:23:21 PM UTC-7, legg wrote:
On Sat, 30 Apr 2022 10:47:30 -0700 (PDT), Ricky
gnuarm.del...@gmail.com> wrote:

On Saturday, April 30, 2022 at 12:11:41 PM UTC-4, jla...@highlandsniptechnology.com wrote:

I wrote an s32.32 saturating math package for the 68K that always did
what was most reasonable.

0/0 = 0

I\'m sure no one can explain why 0/0 = 0 makes sense. Zero does not represent just exactly zero. Just as 1 is the range from 1/2 to 1-1/2, zero is the range from -1/2 to +1/2.

If the denominator is not zero, as the numerator approaches zero, yes, in the limit, the result approaches zero. But if the numerator is not zero, as the denominator approaches zero, in the limit, the result approaches infinity. So why would 0/0=0 make sense?

I would have expected 0/0=1 ie no rational difference.

That\'s the case if you consider lim x/x as x approaches zero. But,
what of the limit of 2x/x, or -x/x, as x approaches zero? NAN is the
best way to get a thinking human to understanding what the computer
is trying to express.

What does a control system do when the heater voltage is computed to
be NAN?
Log it, skip the update, and press on to the next measurement.
hoping that that doesn\'t slow the system down to much
If it does, it is a crappy system. That\'s what almost killed the first moon landing. You can test until you are blue in the face and you have not proven anything. You have to deal with these sorts of issues up front in the design requirements stage. Screw that up and you will have a system that does what you asked for, but not what you want.

Thinking 0/0 is an ok thing to approximate is not a way to design critical systems.

if it is the safe choice that keeps the system running with no ill effects why not?

 

[legg]

On Sun, 01 May 2022 07:29:30 -0700, jlarkin@highlandsniptechnology.com
wrote:

On Sat, 30 Apr 2022 16:24:03 -0400, legg <legg@nospam.magma.ca> wrote:

On Sat, 30 Apr 2022 10:47:30 -0700 (PDT), Ricky
gnuarm.deletethisbit@gmail.com> wrote:

On Saturday, April 30, 2022 at 12:11:41 PM UTC-4, jla...@highlandsniptechnology.com wrote:
On Sat, 30 Apr 2022 08:31:47 -0700 (PDT), Skybuck Flying
skybuc...@gmail.com> wrote:

When exception masks are all enabled to stop the processor from throwing floating point exceptions the following calculation produces a somewhat strange result:

0.0 / 0.0 = -nan

(At least in Delphi).

For now I will assume this is the case in C/C++ as well and with that I mean on x86/x64 which should and seems to be following IEEE 754 floating-point format.

I am a little bit surprised by this and I want/need to know more. Where is this defined that 0.0 / 0.0 should be -NAN ?!?

Problem is with the code, example:

T := 0;
D := 0.0 / 0.0;
P := T * D;

This screws up P. instead of P being zero, P is now also -NAN ?!?

I find this very strange but ok.

I guess a simple solution could be to set D to 0 explicitly for this case, is there perhaps another solution ? Maybe some kind of mask or rounding mode so that additional branch is not necessary ???

Bye for now,
Skybuck.
I wrote an s32.32 saturating math package for the 68K that always did
what was most reasonable.

0/0 = 0

I\'m sure no one can explain why 0/0 = 0 makes sense. Zero does not represent just exactly zero. Just as 1 is the range from 1/2 to 1-1/2, zero is the range from -1/2 to +1/2.

If the denominator is not zero, as the numerator approaches zero, yes, in the limit, the result approaches zero. But if the numerator is not zero, as the denominator approaches zero, in the limit, the result approaches infinity. So why would 0/0=0 make sense?

That is exactly why anything divided by zero is NAN in a good math package. If you want to produce a result for 0/0, then that should be hard coded with clear documentation of what is being done and why it is acceptable.

The rationale that, \"it works\" means it works for the cases tested. Very sloppy indeed.

I would have expected 0/0=1 ie no rational difference.

RL

0 is the safest heater power.

Is that possible, if it\'s ON ?

If it\'s OFF and cooling, values should still look positive, as
it\'s not the power application that is immediately responsible
for heat transfer.

RL

 

[Joe Gwinn]

On Mon, 2 May 2022 13:41:52 -0700 (PDT), Ricky
<gnuarm.deletethisbit@gmail.com> wrote:

On Monday, May 2, 2022 at 11:54:53 AM UTC-4, Joe Gwinn wrote:
On Mon, 2 May 2022 15:28:46 +0100, Martin Brown
\'\'\'newspam\'\'\'@nonad.co.uk> wrote:
On 02/05/2022 15:10, jla...@highlandsniptechnology.com wrote:
On Sun, 1 May 2022 20:27:33 -0700 (PDT), whit3rd <whi...@gmail.com
wrote:

On Saturday, April 30, 2022 at 1:23:21 PM UTC-7, legg wrote:
On Sat, 30 Apr 2022 10:47:30 -0700 (PDT), Ricky
gnuarm.del...@gmail.com> wrote:

On Saturday, April 30, 2022 at 12:11:41 PM UTC-4, jla...@highlandsniptechnology.com wrote:

I wrote an s32.32 saturating math package for the 68K that always did
what was most reasonable.

0/0 = 0

I\'m sure no one can explain why 0/0 = 0 makes sense. Zero does not represent just exactly zero. Just as 1 is the range from 1/2 to 1-1/2, zero is the range from -1/2 to +1/2.

If the denominator is not zero, as the numerator approaches zero, yes, in the limit, the result approaches zero. But if the numerator is not zero, as the denominator approaches zero, in the limit, the result approaches infinity. So why would 0/0=0 make sense?

I would have expected 0/0=1 ie no rational difference.

That\'s the case if you consider lim x/x as x approaches zero. But,
what of the limit of 2x/x, or -x/x, as x approaches zero? NAN is the
best way to get a thinking human to understanding what the computer
is trying to express.

What does a control system do when the heater voltage is computed to
be NAN?

Shut down. The situation should never arise if you have scaled the
problem correctly and you should never be dividing by zero anyway.

If the denominator of a division is zero then you haven\'t thought out
the representation of your problem correctly. Testing for zero is
usually quick (and often implicitly available in integer arithmetic).
Umm. Testing for zero doesn\'t necessarily change anything.

I have a war story here. Many decades ago, I was the software
architect for the mission software of a ship self defense system that
shoots incoming cruise missiles down, if it can. From detection at
the horizon to impact on ownship is maybe twenty seconds.

One fine day, a mob of software engineers turned up, locked in
argument about what to do if the engageability calculation suffered a
divide-by-zero exception.

This is not a coding error per se, it\'s a mathematical singularity in
the equations - some engagement geometries will hit the singularity,
and the embedded realtime computers of that day could not handle the
more complicated math needed to avoid such things fast enough to
matter.

There were two schools: Just provide a very large number and proceed,
praying. Stop and print out a bunch of diagnostic information.

Hmm. So the user, an ordinary sailor operating the self-defense
system is in the middle of an engagement with an incoming cruise
missile, and is suddenly handed a bunch or error messages, with less
than twenty seconds to live ... Really??? No! Just silently return
the best answer possible given the situation and press on, praying.

Was this because they could not use quaternions? I\'ve heard of 3D calculations that are problematic because of issues in the math. They solve that in 3 dimensional control by adding a forth coordinate, quaternions, but obviously more calculations.

The problem was the extremely limited computer power available then.
Later missiles do use quaternions in their autopilots for just that
reason. Quaternions have their own oddities to be managed.

Nor is it clear that quaternions would have solved a singularity in
engagement math, which is not a form of gimbal lock. I don\'t know
what is done these days, but I have run into essential singularities
in modern stuff.

Joe Gwinn

 

[John Larkin]

On Mon, 2 May 2022 16:52:35 -0400, Phil Hobbs
<pcdhSpamMeSenseless@electrooptical.net> wrote:

jlarkin@highlandsniptechnology.com wrote:
On Sun, 1 May 2022 20:27:33 -0700 (PDT), whit3rd <whit3rd@gmail.com
wrote:

On Saturday, April 30, 2022 at 1:23:21 PM UTC-7, legg wrote:
On Sat, 30 Apr 2022 10:47:30 -0700 (PDT), Ricky
gnuarm.del...@gmail.com> wrote:

On Saturday, April 30, 2022 at 12:11:41 PM UTC-4, jla...@highlandsniptechnology.com wrote:

I wrote an s32.32 saturating math package for the 68K that always did
what was most reasonable.

0/0 = 0

I\'m sure no one can explain why 0/0 = 0 makes sense. Zero does not represent just exactly zero. Just as 1 is the range from 1/2 to 1-1/2, zero is the range from -1/2 to +1/2.

If the denominator is not zero, as the numerator approaches zero, yes, in the limit, the result approaches zero. But if the numerator is not zero, as the denominator approaches zero, in the limit, the result approaches infinity. So why would 0/0=0 make sense?

I would have expected 0/0=1 ie no rational difference.

That\'s the case if you consider lim x/x as x approaches zero. But,
what of the limit of 2x/x, or -x/x, as x approaches zero? NAN is the
best way to get a thinking human to understanding what the computer
is trying to express.

What does a control system do when the heater voltage is computed to
be NAN?

Log it, skip the update, and press on to the next measurement.

Cheers

Phil Hobbs

Fine as long as I don\'t fry a few hundred kilobucks of gear.

These systems didn\'t have anywhere to log errors. If things got scary,
I\'d shut down and light a red LED.

NAN wouldn\'t be useful. A saturating math package let me make range
checks when prudent, but not every step of every expression. No traps
to handle.

The s32.32 saturating math package was fun to write, in 68332
assembly. It was fast because it didn\'t need any normalizing. Well,
divide was a nuisance.

Integer in/out conversions were fast. As in zero.

--

If a man will begin with certainties, he shall end with doubts,
but if he will be content to begin with doubts he shall end in certainties.
Francis Bacon

 

[John Larkin]

On Mon, 02 May 2022 18:23:38 -0400, legg <legg@nospam.magma.ca> wrote:

On Sun, 01 May 2022 07:29:30 -0700, jlarkin@highlandsniptechnology.com
wrote:

On Sat, 30 Apr 2022 16:24:03 -0400, legg <legg@nospam.magma.ca> wrote:

On Sat, 30 Apr 2022 10:47:30 -0700 (PDT), Ricky
gnuarm.deletethisbit@gmail.com> wrote:

On Saturday, April 30, 2022 at 12:11:41 PM UTC-4, jla...@highlandsniptechnology.com wrote:
On Sat, 30 Apr 2022 08:31:47 -0700 (PDT), Skybuck Flying
skybuc...@gmail.com> wrote:

When exception masks are all enabled to stop the processor from throwing floating point exceptions the following calculation produces a somewhat strange result:

0.0 / 0.0 = -nan

(At least in Delphi).

For now I will assume this is the case in C/C++ as well and with that I mean on x86/x64 which should and seems to be following IEEE 754 floating-point format.

I am a little bit surprised by this and I want/need to know more. Where is this defined that 0.0 / 0.0 should be -NAN ?!?

Problem is with the code, example:

T := 0;
D := 0.0 / 0.0;
P := T * D;

This screws up P. instead of P being zero, P is now also -NAN ?!?

I find this very strange but ok.

I guess a simple solution could be to set D to 0 explicitly for this case, is there perhaps another solution ? Maybe some kind of mask or rounding mode so that additional branch is not necessary ???

Bye for now,
Skybuck.
I wrote an s32.32 saturating math package for the 68K that always did
what was most reasonable.

0/0 = 0

I\'m sure no one can explain why 0/0 = 0 makes sense. Zero does not represent just exactly zero. Just as 1 is the range from 1/2 to 1-1/2, zero is the range from -1/2 to +1/2.

If the denominator is not zero, as the numerator approaches zero, yes, in the limit, the result approaches zero. But if the numerator is not zero, as the denominator approaches zero, in the limit, the result approaches infinity. So why would 0/0=0 make sense?

That is exactly why anything divided by zero is NAN in a good math package. If you want to produce a result for 0/0, then that should be hard coded with clear documentation of what is being done and why it is acceptable.

The rationale that, \"it works\" means it works for the cases tested. Very sloppy indeed.

I would have expected 0/0=1 ie no rational difference.

RL

0 is the safest heater power.

Is that possible, if it\'s ON ?

If we have a broken thermocouple, or some cable disconnected, or a
shorted mosfet, we want to kill heater power.

In same cases, hundreds of rabbits died to make enough of some enzyme
to analyze. We didn\'t want to poach the samples. Or toast an NMR
probe.

If it\'s OFF and cooling, values should still look positive, as
it\'s not the power application that is immediately responsible
for heat transfer.

RL
--

If a man will begin with certainties, he shall end with doubts,
but if he will be content to begin with doubts he shall end in certainties.
Francis Bacon

 

[whit3rd]

On Monday, May 2, 2022 at 5:01:46 PM UTC-7, John Larkin wrote:

On Mon, 02 May 2022 18:23:38 -0400, legg <le...@nospam.magma.ca> wrote:

On Sun, 01 May 2022 07:29:30 -0700, jla...@highlandsniptechnology.com
wrote:

On Sat, 30 Apr 2022 16:24:03 -0400, legg <le...@nospam.magma.ca> wrote:

I would have expected 0/0=1 ie no rational difference.

0 is the safest heater power.

Is that possible, if it\'s ON ?

If we have a broken thermocouple, or some cable disconnected, or a
shorted mosfet, we want to kill heater power.

That comment belongs embedded in the code that handles NAN
for the particular case where it indicates a broken thermocouple.
Otherwise it\'s a write-only bit of a program, and hazard in future.

 

[Ricky]

On Monday, May 2, 2022 at 9:48:42 PM UTC-4, whit3rd wrote:

On Monday, May 2, 2022 at 5:01:46 PM UTC-7, John Larkin wrote:
On Mon, 02 May 2022 18:23:38 -0400, legg <le...@nospam.magma.ca> wrote:

On Sun, 01 May 2022 07:29:30 -0700, jla...@highlandsniptechnology.com
wrote:

On Sat, 30 Apr 2022 16:24:03 -0400, legg <le...@nospam.magma.ca> wrote:

I would have expected 0/0=1 ie no rational difference.
0 is the safest heater power.

Is that possible, if it\'s ON ?

If we have a broken thermocouple, or some cable disconnected, or a
shorted mosfet, we want to kill heater power.
That comment belongs embedded in the code that handles NAN
for the particular case where it indicates a broken thermocouple.
Otherwise it\'s a write-only bit of a program, and hazard in future.

1+

It\'s no different from a trap, really, except there is no opportunity to do anything unique given the code that is doing the calculation. It works the same in all uses, which, obviously may or may not be appropriate. In other words, very sloppy and hard to maintain.

--

Rick C.

+- Get 1,000 miles of free Supercharging
+- Tesla referral code - https://ts.la/richard11209

 

[Phil Hobbs]

Lasse Langwadt Christensen wrote:

mandag den 2. maj 2022 kl. 22.52.48 UTC+2 skrev Phil Hobbs:
jla...@highlandsniptechnology.com wrote:
On Sun, 1 May 2022 20:27:33 -0700 (PDT), whit3rd <whi...@gmail.com
wrote:

On Saturday, April 30, 2022 at 1:23:21 PM UTC-7, legg wrote:
On Sat, 30 Apr 2022 10:47:30 -0700 (PDT), Ricky
gnuarm.del...@gmail.com> wrote:

On Saturday, April 30, 2022 at 12:11:41 PM UTC-4, jla...@highlandsniptechnology.com wrote:

I wrote an s32.32 saturating math package for the 68K that always did
what was most reasonable.

0/0 = 0

I\'m sure no one can explain why 0/0 = 0 makes sense. Zero does not represent just exactly zero. Just as 1 is the range from 1/2 to 1-1/2, zero is the range from -1/2 to +1/2.

If the denominator is not zero, as the numerator approaches zero, yes, in the limit, the result approaches zero. But if the numerator is not zero, as the denominator approaches zero, in the limit, the result approaches infinity. So why would 0/0=0 make sense?

I would have expected 0/0=1 ie no rational difference.

That\'s the case if you consider lim x/x as x approaches zero. But,
what of the limit of 2x/x, or -x/x, as x approaches zero? NAN is the
best way to get a thinking human to understanding what the computer
is trying to express.

What does a control system do when the heater voltage is computed to
be NAN?
Log it, skip the update, and press on to the next measurement.

hoping that that doesn\'t slow the system down to much

Well, if the error and the slope are both zero, it doesn\'t matter if the
update occurs or not.

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs
Principal Consultant
ElectroOptical Innovations LLC / Hobbs ElectroOptics
Optics, Electro-optics, Photonics, Analog Electronics
Briarcliff Manor NY 10510

http://electrooptical.net
http://hobbs-eo.com

 

[Phil Hobbs]

John Larkin wrote:

On Mon, 2 May 2022 16:52:35 -0400, Phil Hobbs
pcdhSpamMeSenseless@electrooptical.net> wrote:

jlarkin@highlandsniptechnology.com wrote:
On Sun, 1 May 2022 20:27:33 -0700 (PDT), whit3rd <whit3rd@gmail.com
wrote:

On Saturday, April 30, 2022 at 1:23:21 PM UTC-7, legg wrote:
On Sat, 30 Apr 2022 10:47:30 -0700 (PDT), Ricky
gnuarm.del...@gmail.com> wrote:

On Saturday, April 30, 2022 at 12:11:41 PM UTC-4, jla...@highlandsniptechnology.com wrote:

I wrote an s32.32 saturating math package for the 68K that always did
what was most reasonable.

0/0 = 0

I\'m sure no one can explain why 0/0 = 0 makes sense. Zero does not represent just exactly zero. Just as 1 is the range from 1/2 to 1-1/2, zero is the range from -1/2 to +1/2.

If the denominator is not zero, as the numerator approaches zero, yes, in the limit, the result approaches zero. But if the numerator is not zero, as the denominator approaches zero, in the limit, the result approaches infinity. So why would 0/0=0 make sense?

I would have expected 0/0=1 ie no rational difference.

That\'s the case if you consider lim x/x as x approaches zero. But,
what of the limit of 2x/x, or -x/x, as x approaches zero? NAN is the
best way to get a thinking human to understanding what the computer
is trying to express.

What does a control system do when the heater voltage is computed to
be NAN?

Log it, skip the update, and press on to the next measurement.


Fine as long as I don\'t fry a few hundred kilobucks of gear.

These systems didn\'t have anywhere to log errors. If things got scary,
I\'d shut down and light a red LED.

Well, horses for courses. If the temperature controller is trying to
hold something just above 0 C in a subzero environment, shutting down
might be exactly the wrong answer.

And a system that can produce NaNs in the normal operation of a control
system is just plain broken--it\'s got serious algorithmic problems, not
so much numerical ones.

NAN wouldn\'t be useful. A saturating math package let me make range
checks when prudent, but not every step of every expression. No traps
to handle.

The s32.32 saturating math package was fun to write, in 68332
assembly. It was fast because it didn\'t need any normalizing. Well,
divide was a nuisance.

Integer in/out conversions were fast. As in zero.

Sure thing, but correctness is more important than efficiency.

Cheers

Phil Hobbs


--
Dr Philip C D Hobbs
Principal Consultant
ElectroOptical Innovations LLC / Hobbs ElectroOptics
Optics, Electro-optics, Photonics, Analog Electronics
Briarcliff Manor NY 10510

http://electrooptical.net
http://hobbs-eo.com

 

[server]

On Tue, 3 May 2022 10:05:26 -0400, Phil Hobbs
<pcdhSpamMeSenseless@electrooptical.net> wrote:

John Larkin wrote:
On Mon, 2 May 2022 16:52:35 -0400, Phil Hobbs
pcdhSpamMeSenseless@electrooptical.net> wrote:

jlarkin@highlandsniptechnology.com wrote:
On Sun, 1 May 2022 20:27:33 -0700 (PDT), whit3rd <whit3rd@gmail.com
wrote:

On Saturday, April 30, 2022 at 1:23:21 PM UTC-7, legg wrote:
On Sat, 30 Apr 2022 10:47:30 -0700 (PDT), Ricky
gnuarm.del...@gmail.com> wrote:

On Saturday, April 30, 2022 at 12:11:41 PM UTC-4, jla...@highlandsniptechnology.com wrote:

I wrote an s32.32 saturating math package for the 68K that always did
what was most reasonable.

0/0 = 0

I\'m sure no one can explain why 0/0 = 0 makes sense. Zero does not represent just exactly zero. Just as 1 is the range from 1/2 to 1-1/2, zero is the range from -1/2 to +1/2.

If the denominator is not zero, as the numerator approaches zero, yes, in the limit, the result approaches zero. But if the numerator is not zero, as the denominator approaches zero, in the limit, the result approaches infinity. So why would 0/0=0 make sense?

I would have expected 0/0=1 ie no rational difference.

That\'s the case if you consider lim x/x as x approaches zero. But,
what of the limit of 2x/x, or -x/x, as x approaches zero? NAN is the
best way to get a thinking human to understanding what the computer
is trying to express.

What does a control system do when the heater voltage is computed to
be NAN?

Log it, skip the update, and press on to the next measurement.


Fine as long as I don\'t fry a few hundred kilobucks of gear.

These systems didn\'t have anywhere to log errors. If things got scary,
I\'d shut down and light a red LED.

Well, horses for courses. If the temperature controller is trying to
hold something just above 0 C in a subzero environment, shutting down
might be exactly the wrong answer.

And a system that can produce NaNs in the normal operation of a control
system is just plain broken--it\'s got serious algorithmic problems, not
so much numerical ones.

Ergo, a math package that doesn\'t make NANs, doesn\'t trap, doesn\'t
crash.

NAN wouldn\'t be useful. A saturating math package let me make range
checks when prudent, but not every step of every expression. No traps
to handle.

The s32.32 saturating math package was fun to write, in 68332
assembly. It was fast because it didn\'t need any normalizing. Well,
divide was a nuisance.

Integer in/out conversions were fast. As in zero.

Sure thing, but correctness is more important than efficiency.

My control code checked the things that really matter.

After the PWM mosfet, to the heater, there was a relay driven by a
one-shot.

The O***** I********** controller would fry NMR probes. Ours never
did.



--

Anybody can count to one.

- Robert Widlar

 

[Phil Hobbs]

Joe Gwinn wrote:

On Mon, 2 May 2022 09:05:37 -0700 (PDT), Lasse Langwadt Christensen
langwadt@fonz.dk> wrote:

mandag den 2. maj 2022 kl. 17.54.53 UTC+2 skrev Joe Gwinn:
On Mon, 2 May 2022 15:28:46 +0100, Martin Brown
\'\'\'newspam\'\'\'@nonad.co.uk> wrote:
On 02/05/2022 15:10, jla...@highlandsniptechnology.com wrote:
On Sun, 1 May 2022 20:27:33 -0700 (PDT), whit3rd <whi...@gmail.com
wrote:

On Saturday, April 30, 2022 at 1:23:21 PM UTC-7, legg wrote:
On Sat, 30 Apr 2022 10:47:30 -0700 (PDT), Ricky
gnuarm.del...@gmail.com> wrote:

On Saturday, April 30, 2022 at 12:11:41 PM UTC-4, jla...@highlandsniptechnology.com wrote:

I wrote an s32.32 saturating math package for the 68K that always did
what was most reasonable.

0/0 = 0

I\'m sure no one can explain why 0/0 = 0 makes sense. Zero does not represent just exactly zero. Just as 1 is the range from 1/2 to 1-1/2, zero is the range from -1/2 to +1/2.

If the denominator is not zero, as the numerator approaches zero, yes, in the limit, the result approaches zero. But if the numerator is not zero, as the denominator approaches zero, in the limit, the result approaches infinity. So why would 0/0=0 make sense?

I would have expected 0/0=1 ie no rational difference.

That\'s the case if you consider lim x/x as x approaches zero. But,
what of the limit of 2x/x, or -x/x, as x approaches zero? NAN is the
best way to get a thinking human to understanding what the computer
is trying to express.

What does a control system do when the heater voltage is computed to
be NAN?

Shut down. The situation should never arise if you have scaled the
problem correctly and you should never be dividing by zero anyway.

If the denominator of a division is zero then you haven\'t thought out
the representation of your problem correctly. Testing for zero is
usually quick (and often implicitly available in integer arithmetic).
Umm. Testing for zero doesn\'t necessarily change anything.

I have a war story here. Many decades ago, I was the software
architect for the mission software of a ship self defense system that
shoots incoming cruise missiles down, if it can. From detection at
the horizon to impact on ownship is maybe twenty seconds.

One fine day, a mob of software engineers turned up, locked in
argument about what to do if the engageability calculation suffered a
divide-by-zero exception.

This is not a coding error per se, it\'s a mathematical singularity in
the equations - some engagement geometries will hit the singularity,
and the embedded realtime computers of that day could not handle the
more complicated math needed to avoid such things fast enough to
matter.

There were two schools: Just provide a very large number and proceed,
praying. Stop and print out a bunch of diagnostic information.

Hmm. So the user, an ordinary sailor operating the self-defense
system is in the middle of an engagement with an incoming cruise
missile, and is suddenly handed a bunch or error messages, with less
than twenty seconds to live ... Really??? No! Just silently return
the best answer possible given the situation and press on, praying.

sorta like: <https://en.wikipedia.org/wiki/Battleshort

Yes, same kind of thinking.

With software taking the world over battleshort is often an operating
mode, not necessarily a bit of hardware.

So that\'s where Douglas Adams got the idea!

https://hitchhikers.fandom.com/wiki/Vl\'Hurgs

Cheers

Phil Hobbs

 

[Phil Hobbs]

jlarkin@highlandsniptechnology.com wrote:

On Tue, 3 May 2022 10:05:26 -0400, Phil Hobbs
pcdhSpamMeSenseless@electrooptical.net> wrote:

John Larkin wrote:
On Mon, 2 May 2022 16:52:35 -0400, Phil Hobbs
pcdhSpamMeSenseless@electrooptical.net> wrote:

jlarkin@highlandsniptechnology.com wrote:
On Sun, 1 May 2022 20:27:33 -0700 (PDT), whit3rd <whit3rd@gmail.com
wrote:

On Saturday, April 30, 2022 at 1:23:21 PM UTC-7, legg wrote:
On Sat, 30 Apr 2022 10:47:30 -0700 (PDT), Ricky
gnuarm.del...@gmail.com> wrote:

On Saturday, April 30, 2022 at 12:11:41 PM UTC-4, jla...@highlandsniptechnology.com wrote:

I wrote an s32.32 saturating math package for the 68K that always did
what was most reasonable.

0/0 = 0

I\'m sure no one can explain why 0/0 = 0 makes sense. Zero does not represent just exactly zero. Just as 1 is the range from 1/2 to 1-1/2, zero is the range from -1/2 to +1/2.

If the denominator is not zero, as the numerator approaches zero, yes, in the limit, the result approaches zero. But if the numerator is not zero, as the denominator approaches zero, in the limit, the result approaches infinity. So why would 0/0=0 make sense?

I would have expected 0/0=1 ie no rational difference.

That\'s the case if you consider lim x/x as x approaches zero. But,
what of the limit of 2x/x, or -x/x, as x approaches zero? NAN is the
best way to get a thinking human to understanding what the computer
is trying to express.

What does a control system do when the heater voltage is computed to
be NAN?

Log it, skip the update, and press on to the next measurement.


Fine as long as I don\'t fry a few hundred kilobucks of gear.

These systems didn\'t have anywhere to log errors. If things got scary,
I\'d shut down and light a red LED.

Well, horses for courses. If the temperature controller is trying to
hold something just above 0 C in a subzero environment, shutting down
might be exactly the wrong answer.

And a system that can produce NaNs in the normal operation of a control
system is just plain broken--it\'s got serious algorithmic problems, not
so much numerical ones.

Ergo, a math package that doesn\'t make NANs, doesn\'t trap, doesn\'t
crash.

No, a temperature control algorithm that can be proved not to lead to
singularities. In some cases it can be as simple as

(small difference)
update = ------------------------------------
sgn(denom) * (epsilon + fabs(denom))

NAN wouldn\'t be useful. A saturating math package let me make range
checks when prudent, but not every step of every expression. No traps
to handle.

The s32.32 saturating math package was fun to write, in 68332
assembly. It was fast because it didn\'t need any normalizing. Well,
divide was a nuisance.

Integer in/out conversions were fast. As in zero.

Sure thing, but correctness is more important than efficiency.

My control code checked the things that really matter.

Sure, I\'m not looking at your control system design.

After the PWM mosfet, to the heater, there was a relay driven by a
one-shot.

The O***** I********** controller would fry NMR probes. Ours never
did.

I believe that, but it wasn\'t on account of the NaN-handling strategy.

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs
Principal Consultant
ElectroOptical Innovations LLC / Hobbs ElectroOptics
Optics, Electro-optics, Photonics, Analog Electronics
Briarcliff Manor NY 10510

http://electrooptical.net
http://hobbs-eo.com

 

[server]

On Tue, 3 May 2022 10:37:49 -0400, Phil Hobbs
<pcdhSpamMeSenseless@electrooptical.net> wrote:

jlarkin@highlandsniptechnology.com wrote:
On Tue, 3 May 2022 10:05:26 -0400, Phil Hobbs
pcdhSpamMeSenseless@electrooptical.net> wrote:

John Larkin wrote:
On Mon, 2 May 2022 16:52:35 -0400, Phil Hobbs
pcdhSpamMeSenseless@electrooptical.net> wrote:

jlarkin@highlandsniptechnology.com wrote:
On Sun, 1 May 2022 20:27:33 -0700 (PDT), whit3rd <whit3rd@gmail.com
wrote:

On Saturday, April 30, 2022 at 1:23:21 PM UTC-7, legg wrote:
On Sat, 30 Apr 2022 10:47:30 -0700 (PDT), Ricky
gnuarm.del...@gmail.com> wrote:

On Saturday, April 30, 2022 at 12:11:41 PM UTC-4, jla...@highlandsniptechnology.com wrote:

I wrote an s32.32 saturating math package for the 68K that always did
what was most reasonable.

0/0 = 0

I\'m sure no one can explain why 0/0 = 0 makes sense. Zero does not represent just exactly zero. Just as 1 is the range from 1/2 to 1-1/2, zero is the range from -1/2 to +1/2.

If the denominator is not zero, as the numerator approaches zero, yes, in the limit, the result approaches zero. But if the numerator is not zero, as the denominator approaches zero, in the limit, the result approaches infinity. So why would 0/0=0 make sense?

I would have expected 0/0=1 ie no rational difference.

That\'s the case if you consider lim x/x as x approaches zero. But,
what of the limit of 2x/x, or -x/x, as x approaches zero? NAN is the
best way to get a thinking human to understanding what the computer
is trying to express.

What does a control system do when the heater voltage is computed to
be NAN?

Log it, skip the update, and press on to the next measurement.


Fine as long as I don\'t fry a few hundred kilobucks of gear.

These systems didn\'t have anywhere to log errors. If things got scary,
I\'d shut down and light a red LED.

Well, horses for courses. If the temperature controller is trying to
hold something just above 0 C in a subzero environment, shutting down
might be exactly the wrong answer.

And a system that can produce NaNs in the normal operation of a control
system is just plain broken--it\'s got serious algorithmic problems, not
so much numerical ones.

Ergo, a math package that doesn\'t make NANs, doesn\'t trap, doesn\'t
crash.

No, a temperature control algorithm that can be proved not to lead to
singularities. In some cases it can be as simple as

(small difference)
update = ------------------------------------
sgn(denom) * (epsilon + fabs(denom))





NAN wouldn\'t be useful. A saturating math package let me make range
checks when prudent, but not every step of every expression. No traps
to handle.

The s32.32 saturating math package was fun to write, in 68332
assembly. It was fast because it didn\'t need any normalizing. Well,
divide was a nuisance.

Integer in/out conversions were fast. As in zero.

Sure thing, but correctness is more important than efficiency.

My control code checked the things that really matter.

Sure, I\'m not looking at your control system design.

Well, my concern was physical reality, not mathematical elegance.
Checking for NAN after every math operation would be a nuisance. As
would writing a trap handler.

After the PWM mosfet, to the heater, there was a relay driven by a
one-shot.

The O***** I********** controller would fry NMR probes. Ours never
did.

I believe that, but it wasn\'t on account of the NaN-handling strategy.

Part of the problem was absurd EMI sensitivity... in an NMR system! I
could shut one down from across the room with an old GR RF sig gen.
The controller had some very sharp, very sensitive resonances around
the thermocouple input.

But software bugs too.

We did things like this:

https://www.dropbox.com/s/noapeoyk10iayoz/Chimera_Ref_Junction.JPG?raw=1

Cheers

Phil Hobbs

--

Anybody can count to one.

- Robert Widlar

 

[Ricky]

On Tuesday, May 3, 2022 at 10:27:03 AM UTC-4, jla...@highlandsniptechnology..com wrote:

On Tue, 3 May 2022 10:05:26 -0400, Phil Hobbs
pcdhSpamM...@electrooptical.net> wrote:

John Larkin wrote:
On Mon, 2 May 2022 16:52:35 -0400, Phil Hobbs
pcdhSpamM...@electrooptical.net> wrote:

jla...@highlandsniptechnology.com wrote:
On Sun, 1 May 2022 20:27:33 -0700 (PDT), whit3rd <whi...@gmail.com
wrote:

On Saturday, April 30, 2022 at 1:23:21 PM UTC-7, legg wrote:
On Sat, 30 Apr 2022 10:47:30 -0700 (PDT), Ricky
gnuarm.del...@gmail.com> wrote:

On Saturday, April 30, 2022 at 12:11:41 PM UTC-4, jla...@highlandsniptechnology.com wrote:

I wrote an s32.32 saturating math package for the 68K that always did
what was most reasonable.

0/0 = 0

I\'m sure no one can explain why 0/0 = 0 makes sense. Zero does not represent just exactly zero. Just as 1 is the range from 1/2 to 1-1/2, zero is the range from -1/2 to +1/2.

If the denominator is not zero, as the numerator approaches zero, yes, in the limit, the result approaches zero. But if the numerator is not zero, as the denominator approaches zero, in the limit, the result approaches infinity. So why would 0/0=0 make sense?

I would have expected 0/0=1 ie no rational difference.

That\'s the case if you consider lim x/x as x approaches zero. But,
what of the limit of 2x/x, or -x/x, as x approaches zero? NAN is the
best way to get a thinking human to understanding what the computer
is trying to express.

What does a control system do when the heater voltage is computed to
be NAN?

Log it, skip the update, and press on to the next measurement.


Fine as long as I don\'t fry a few hundred kilobucks of gear.

These systems didn\'t have anywhere to log errors. If things got scary,
I\'d shut down and light a red LED.

Well, horses for courses. If the temperature controller is trying to
hold something just above 0 C in a subzero environment, shutting down
might be exactly the wrong answer.

And a system that can produce NaNs in the normal operation of a control
system is just plain broken--it\'s got serious algorithmic problems, not
so much numerical ones.
Ergo, a math package that doesn\'t make NANs, doesn\'t trap, doesn\'t
crash.

How is reporting an invalid answer not a \"crash\"? Oh, it\'s just an error.... that can lead to a crash depending on the skill level of the pilots to recognize and override the system.

Yeah, maybe an inconsequential heater would do fine. This is not a general solution to the math issues in a system.

What Hobbs is talking about if designing the algorithm so the NAN never happens in the first place. That also works and works for every type of system.

--

Rick C.

++ Get 1,000 miles of free Supercharging
++ Tesla referral code - https://ts.la/richard11209

 

[John Larkin]

On Mon, 2 May 2022 18:48:38 -0700 (PDT), whit3rd <whit3rd@gmail.com>
wrote:

On Monday, May 2, 2022 at 5:01:46 PM UTC-7, John Larkin wrote:
On Mon, 02 May 2022 18:23:38 -0400, legg <le...@nospam.magma.ca> wrote:

On Sun, 01 May 2022 07:29:30 -0700, jla...@highlandsniptechnology.com
wrote:

On Sat, 30 Apr 2022 16:24:03 -0400, legg <le...@nospam.magma.ca> wrote:

I would have expected 0/0=1 ie no rational difference.

0 is the safest heater power.

Is that possible, if it\'s ON ?

If we have a broken thermocouple, or some cable disconnected, or a
shorted mosfet, we want to kill heater power.

That comment belongs embedded in the code that handles NAN
for the particular case where it indicates a broken thermocouple.
Otherwise it\'s a write-only bit of a program, and hazard in future.

My code is well commented. The saturating math package doesn\'t have
NAN.

We sold thousands of controllers and never fried a probe. Other
peoples\' controllers did.



--

If a man will begin with certainties, he shall end with doubts,
but if he will be content to begin with doubts he shall end in certainties.
Francis Bacon

 

[Carlos E.R.]

On 2022-04-30 17:31, Skybuck Flying wrote:

When exception masks are all enabled to stop the processor from throwing floating point exceptions the following calculation produces a somewhat strange result:

0.0 / 0.0 = -nan

(At least in Delphi).

For now I will assume this is the case in C/C++ as well and with that I mean on x86/x64 which should and seems to be following IEEE 754 floating-point format.

I am a little bit surprised by this and I want/need to know more. Where is this defined that 0.0 / 0.0 should be -NAN ?!?

Problem is with the code, example:

T := 0;
D := 0.0 / 0.0;
P := T * D;

This screws up P. instead of P being zero, P is now also -NAN ?!?

I have not read the entire thread, so maybe someone has already said it;
but yes, NAN is correct in math, because 0/0 is \"undefined\" (think
limits). It can be zero, one, any number, even infinite. So multiplying
T·D can actually be 0·∞, which is again \"undefined\", so NAN.

I find this very strange but ok.

I guess a simple solution could be to set D to 0 explicitly for this case, is there perhaps another solution ? Maybe some kind of mask or rounding mode so that additional branch is not necessary ???

Bye for now,
Skybuck.

--
Cheers, Carlos.