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Re: A Problem To Solve :-)

Cross-posted to 2 groups.

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On 2/6/2024 3:43 PM, Physfitfreak wrote:
> On 2/6/2024 3:00 PM, Farley Flud wrote:
>> On Mon, 5 Feb 2024 19:39:57 -0600, Physfitfreak wrote:
>>
>>>
> 
> Put yourself in the shoes of a computer (inside the drones and missiles) 
> that rounds every number off (not just the result! But every number it 
> comes upon in computing the results) to keep only three significant 
> digits. Follow what happens from begin to end of the computation for 
> each expression. Then argue why one computed result is better than the 
> other computed result. Lot's of math lines to write, but all are needed 
> to see for sure why one result is better than the other.
> 
> I may have accidentally chosen the coordinate numbers that don't quite 
> show the difference, I don't know. I haven't solved this yet (just 
> concocted it last night). If that's the case, then I'll find coordinate 
> numbers that will show the difference.
> 
> But so far, I'm assuming just about any coordinates measured might work 
> to show the difference in the results of computations. So I'm asking 
> that you do that and show it here.
> 
> 
> 

I shouldn't have said, "three significant digits". Significant digit 
concept is somewhat different.

Ok, let's talk more accurately.

Machine numbers are in binary form. But these machine numbers can be 
expressed in decimal machine numbers like:

0.d_1d_2 ... d_k x 10^n

, where d_1 digit is _not_ zero, and d_2, d_3 ... d_k digits can each be 
an integer from zero to 9.

Since this example has k digits after the decimal point, it is called 
k-digit decimal machine number.

The decimal machine number form is not exactly equal to the binary form 
that machine handles, and the difference has to do with the machine 
epsilon. But nevertheless, the two form are very closely the same number.

In this problem, I'm assuming the computers on missiles work on such 
binary numbers that have 3-digit decimal machine numbers. And forget the 
binary form of them, cause this problem is not about the machine 
epsilon. Just assume that the computers deal with decimal machine 
numbers and k=3. So for example the number

0.0033169 x 10^4

is rounded off to

0.332 x 10^2

So depending on how your code computes the two given expressons, any 
time the computer handles a number, if it is not already in 3-digit 
decimal machine number form, it converts it to 3-digit machine number 
before using it for computations.

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Re: A Problem To Solve :-) Physfitfreak <Physfitfreak@gmail.com> - 2024-01-27 17:22 -0600
  Re: A Problem To Solve :-) Farley Flud <ff@linux.rocks> - 2024-01-28 12:31 +0000
    Re: A Problem To Solve :-) Physfitfreak <Physfitfreak@gmail.com> - 2024-01-28 16:44 -0600
      Re: A Problem To Solve :-) Farley Flud <ff@linux.rocks> - 2024-01-29 08:28 +0000
        Re: A Problem To Solve :-) Athel Cornish-Bowden <me@yahoo.com> - 2024-01-29 11:53 +0100
          Re: A Problem To Solve :-) Physfitfreak <Physfitfreak@gmail.com> - 2024-02-02 23:56 -0600
        Re: A Problem To Solve :-) Physfitfreak <Physfitfreak@gmail.com> - 2024-01-30 01:25 -0600
        Re: A Problem To Solve :-) Physfitfreak <Physfitfreak@gmail.com> - 2024-01-31 18:18 -0600
      Re: A Problem To Solve :-) Stéphane CARPENTIER <sc@fiat-linux.fr> - 2024-02-02 21:49 +0000
  Re: A Problem To Solve :-) Physfitfreak <Physfitfreak@gmail.com> - 2024-02-03 04:00 -0600
    Re: A Problem To Solve :-) Farley Flud <ff@linux.rocks> - 2024-02-03 16:19 +0000
      Re: A Problem To Solve :-) Physfitfreak <Physfitfreak@gmail.com> - 2024-02-03 16:17 -0600
      Re: A Problem To Solve :-) Stéphane CARPENTIER <sc@fiat-linux.fr> - 2024-02-04 14:24 +0000
    Re: A Problem To Solve :-) Physfitfreak <Physfitfreak@gmail.com> - 2024-02-04 19:53 -0600
    Re: A Problem To Solve :-) Physfitfreak <Physfitfreak@gmail.com> - 2024-02-05 01:51 -0600
      Re: A Problem To Solve :-) Physfitfreak <Physfitfreak@gmail.com> - 2024-02-05 19:39 -0600
        Re: A Problem To Solve :-) Farley Flud <ff@linux.rocks> - 2024-02-06 21:00 +0000
          Re: A Problem To Solve :-) Physfitfreak <Physfitfreak@gmail.com> - 2024-02-06 15:43 -0600
            Re: A Problem To Solve :-) Physfitfreak <Physfitfreak@gmail.com> - 2024-02-06 18:19 -0600
              Re: A Problem To Solve :-) Physfitfreak <Physfitfreak@gmail.com> - 2024-02-09 10:58 -0600
          Re: A Problem To Solve :-) Physfitfreak <Physfitfreak@gmail.com> - 2024-02-06 21:55 -0600
            Re: A Problem To Solve :-) Physfitfreak <Physfitfreak@gmail.com> - 2024-02-06 22:06 -0600
        Re: A Problem To Solve :-) Physfitfreak <Physfitfreak@gmail.com> - 2024-02-12 01:39 -0600
          Re: A Problem To Solve :-) Physfitfreak <Physfitfreak@gmail.com> - 2024-02-14 12:50 -0600
            Re: A Problem To Solve :-) Lester Thorpe <lt@gnu.rocks> - 2024-02-14 20:33 +0000
              Re: A Problem To Solve :-) Athel Cornish-Bowden <me@yahoo.com> - 2024-02-15 11:11 +0100
              Re: A Problem To Solve :-) Physfitfreak <Physfitfreak@gmail.com> - 2024-02-15 13:22 -0600
            Re: A Problem To Solve :-) Physfitfreak <Physfitfreak@gmail.com> - 2024-02-18 01:51 -0600
              Re: A Problem To Solve :-) Physfitfreak <Physfitfreak@gmail.com> - 2024-02-21 00:38 -0600
                Re: A Problem To Solve :-) Physfitfreak <Physfitfreak@gmail.com> - 2024-02-27 16:13 -0600
                Re: A Problem To Solve :-) Kuang Tze Kui <ugdiun@kgknudu.cn> - 2024-02-27 22:46 +0000
                Re: A Problem To Solve :-) Physfitfreak <Physfitfreak@gmail.com> - 2024-03-01 20:50 -0600
                Re: A Problem To Solve :-) Farley Flud <ff@linux.rocks> - 2024-03-02 12:10 +0000
                Re: A Problem To Solve :-) Physfitfreak <Physfitfreak@gmail.com> - 2024-03-02 12:06 -0600
                Re: A Problem To Solve :-) Farley Flud <ff@linux.rocks> - 2024-03-02 19:44 +0000
                Re: A Problem To Solve :-) Farley Flud <ff@linux.rocks> - 2024-03-02 14:09 +0000
                Re: A Problem To Solve :-) Farley Flud <fflud@gnu.rocks> - 2024-03-02 19:18 +0000
  Re: A Problem To Solve :-) Arindam Banerjee <banerjeeadda1234@gmail.com> - 2024-02-09 09:47 -0800
    Re: A Problem To Solve :-) Arindam Banerjee <banerjeeadda1234@gmail.com> - 2024-02-12 04:41 -0800

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