Author Topic: Predictive division  (Read 364 times)

mikeburr

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Predictive division
« on: October 01, 2019, 09:44:20 PM »
i dare say many many of you will know that when you divide one number by another you get a repeating sequence [* qualified ] 
example 1/7 = .142857 142857 142857 ..
now suppose instead of conventional division we divide in excess of the number each time [overdivide]
so 10/7 = 2  [ie 14]  and the remainder is now 4
40/7 = 6 and the remainder is now 2
20/7 = 3 and the remainder is now 1 so were back where we started but with a shorter sequence .. this being 263 as opposed to 142857
and instead of a sequence which approaches [but never reaches the true value ???] we now have an Oscillating approximation that bounds the value
by this i mean .. you go up 2 then back 6 [ = 14] then up 3 [=143] then back 2 [=1428] then up 6 [=14286] then back 3 [=142857] etc

There are a whole series of rules that can be deduced about the lengths of sequences 
[in the case of 1/prime these sequences have to divide the prime = prime -1 [eg 7 is 6 long ...13 happens also to be 6 long ..(13-1)/2 ... 41 is 5 long and so is 271 ...
239 and 4649 have lengths of 7  etc etc ]
and the results are evident in the following factors of 9 recuring-length-X  [ie X-1 recurring which is what is effectively happening in division length X and which may then be reduced to finding the factors of (3x3x ) ...1 recuring-length-X  .........]

obviously this enables the prediction of division sequences BUT only if you have the prime components of both the 'thing being divided' and the divisor
i havent got access to all my stuff at the moment  but
i hope you find this interesting
regards   mike b

here this is described as recreational mathematics .. the idiot who wrote that didnt understand the process of division as i suspect most dont
https://ipfs.io/ipfs/QmXoypizjW3WknFiJnKLwHCnL72vedxjQkDDP1mXWo6uco/wiki/Repunit.html






daydreamer

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Re: Predictive division
« Reply #1 on: October 03, 2019, 02:45:40 AM »
what happens if it enough with 1/7 calculated with RCPSD reciprocal instruction maybe good enough to produce the sequence .142857

also seem like a extended task for prime number program,extend it to use the prime numbers to test against predictive division after generated lots of primes
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mikeburr

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Re: Predictive division
« Reply #2 on: October 03, 2019, 05:13:59 AM »
@daydreamer
Approximation to the Reciprocal of Scalar Double-Precision Floating-Point Value with Less Than 2^-28 = Tiny .. theres a couple of ways you can do the same within 32/64 bit but its way too small for large scale calculations ... the  stuff ive programmed  on the machine here is 10^4000 and that is  Small in exploratory mathematics
incidentaly
you dont need a 'prime number look up program' to confirm whether a number is prime .. i sort of outlined at least one method in a previous answer to someones post to test primality and a modification of this idea enables you to locate the components which lie in 'Zones'   .. this is not  the same as the current elliptical methods but requires a lot of parallelism in processing which is one reason why i am interested in trying out FPGA  and commiting the process to Pseudo hardware [prob where it belongs ] and asked if anyone else had tried using one of the boards
regards mike b
id be keen to hear your ideas and anyone elses thoughts on this

daydreamer

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Re: Predictive division
« Reply #3 on: October 04, 2019, 04:24:15 AM »
@daydreamer
Approximation to the Reciprocal of Scalar Double-Precision Floating-Point Value with Less Than 2^-28 = Tiny .. theres a couple of ways you can do the same within 32/64 bit but its way too small for large scale calculations ... the  stuff ive programmed  on the machine here is 10^4000 and that is  Small in exploratory mathematics
incidentaly
you dont need a 'prime number look up program' to confirm whether a number is prime .. i sort of outlined at least one method in a previous answer to someones post to test primality and a modification of this idea enables
id be keen to hear your ideas and anyone elses thoughts on this
I havent tried out fpga or any boards,but maybe SIMD or run on gpu with lots of cuda units or pixelshaders would be the approach?
Quote from Flashdance
Nick  :  When you give up your dream, you die
*wears a flameproof asbestos suit*
Gone serverside programming p:  :D

mikeburr

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Re: Predictive division
« Reply #4 on: October 06, 2019, 11:46:48 PM »
gpu .. turns out not really ..FPGA is good because it can be so low level
bit surprised nobody else seems to have tried predictive routines .. maybe its too low level and more in the realm of hardware than software
regards mikeb 

daydreamer

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Re: Predictive division
« Reply #5 on: October 08, 2019, 04:29:00 AM »
gpu .. turns out not really ..FPGA is good because it can be so low level
bit surprised nobody else seems to have tried predictive routines .. maybe its too low level and more in the realm of hardware than software
regards mikeb
well you can build a circuit with boolean operators <->build a lowlevel program that only make use of boolean operators
what about  div output result in string format and make a string PROC that checks for repeated string,trying different lengths,for example try 142847 if its repeated,if not try a smaller length of string ?
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*wears a flameproof asbestos suit*
Gone serverside programming p:  :D

HSE

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Re: Predictive division
« Reply #6 on: October 08, 2019, 11:39:16 PM »
maybe its too low level and more in the realm of hardware than software
Exactly. Is hardware configuration. Very powerfull but very specific.