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Topic: Operation with very big integer numbers

Now there are the whole positive numbers, which size of the order 1,0E+50 and more.
It is possible to shatter and present such numbers in the form of an array.
Somebody dealt with such arrays at carrying out of calculations in between? Or it somewhere is already considered?
Or to leave only digits of the high order and to work with one cell?

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Re: Operation with very big integer numbers

GMP

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Re: Operation with very big integer numbers

STFW "long arithmetics".

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Re: Operation with very big integer numbers

Thanks!

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Re: Operation with very big integer numbers

Gennadiy Usov;
double

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Re: Operation with very big integer numbers

Gennadiy Usov wrote:

Now appears the whole positive numbers, which size of the order 1,0E+50 and more.
It is possible to shatter and present such numbers in the form of an array.
Somebody dealt with such arrays at carrying out of calculations in between? Or it somewhere is already considered?
Or to leave only digits of the high order and to work with one cell?

It - in a section of chess tasks?

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Re: Operation with very big integer numbers

mayton wrote:

It - in a section of chess tasks?

Certainly.
And here is how to add following numbers:
2,23487E+41
496
121790
6,69449E+17
5,37882E+78.
And thus not to lose any digit.

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Re: Operation with very big integer numbers

Gennadiy Usov wrote:

And here is how to add following numbers:
2,23487E+41
496
121790
6,69449E+17
5,37882E+78.
And thus not to lose any digit.

And why you are assured, what in the initial data of record in the scientific notation are exact?
You generally read though something about approximate calculations, the relative and absolute exactitudes?

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Re: Operation with very big integer numbers

mayton wrote:

It - in a section of chess tasks?

And still: there are task directions where it is calculated 2 in a level 40, 125, 250 and other levels.
And it
1,09951E+12
4,25353E+37
1,80925E+75
And how many thus digits will be cut off"?

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Re: Operation with very big integer numbers

Basil A. Sidorov wrote:

And why you are assured, what in the initial data of record in the scientific notation are exact?
You generally read though something about approximate calculations, the relative and absolute exactitudes?

Such data turns out owing to calculations on algorithms.
Once on  listened to lectures about about (small).
Therefore in the first message also it is told about, whether that it is necessary to chase for about (small).

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Re: Operation with very big integer numbers

Gennadiy Usov wrote:

Or it somewhere is already considered?

Take the Python and not : there support of long arithmetics "from a box".

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Re: Operation with very big integer numbers

Gennadiy Usov wrote:

Such data turns out owing to calculations on algorithms.

Here directly with  in significant decimal digits, but, thus it is required to add the values different on tens of orders???

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Re: Operation with very big integer numbers

Basil A. Sidorov wrote:

it is passed...
Here directly with  in significant decimal digits, but, thus it is required to add the values different on tens of orders???

The mathematics demands accuracy in calculations. Time such different items.

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Re: Operation with very big integer numbers

Gennadiy Usov wrote:

it is passed...
The mathematics demands accuracy in calculations. Time such different items.

The mathematics operates not with numbers and characters. In your case.
Over accuracy can  for example for that proof that
A numerical row converges.
Question. That at you for comparing to which did not suffice double.?

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Re: Operation with very big integer numbers

mayton wrote:

Question. That at you for comparing to which did not suffice double.?

In EXCEL accuracy of representation of number - 15 digits. And what accuracy of representation of number at double?
2 in a level 200 - 60 digits.

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Re: Operation with very big integer numbers

Gennadiy Usov wrote:

In EXCEL accuracy of representation of number - 15 digits. And what accuracy of representation of number at double?

Same.

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Re: Operation with very big integer numbers

Gennadiy Usov wrote:

it is passed...
In EXCEL accuracy of representation of number - 15 digits. And what accuracy of representation of number at double?
2 in a level 200 - 60 digits.

It is a fake. Demands specification more truly.
At double there is no decimal representation. And the point floats.  on very great numbers
At double - rough accuracy (it is possible to compare distances between ) and on very
Small (distances between atoms of substance) accuracy raises.
Ghost effect - it is impossible to add very big and very small values.
The big value does not receive any gain. But it for double also is not required.
It is value for scientific computations where mantissa high orders since they are important
Are important for estimations and comparing.
And that you compare that is an accounts department. For it there are other formats of numbers which
On a subject quite right named.
Look here at online at the calculator
http://www.binaryconvert.com/convert_double.html
It most precisely shows internal representation.

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Re: Operation with very big integer numbers

If was impatient to add very different numbers - sort by increase and add them in this order - you will lose a minimum

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Re: Operation with very big integer numbers

mayton wrote:

At double there is no decimal representation. And the point floats.  on very great numbers
At double - rough accuracy (it is possible to compare distances between ) and on very
Small (distances between atoms of substance) accuracy raises.

In cases when with double it is necessary to work as with whole - the size of a mantissa is important, and it of 52 bits, i.e. lost-free it is possible to present number to 2^52 or 4.5*1015, here whence those 15 decimal signs.

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Re: Operation with very big integer numbers

Gennadiy Usov wrote:

the Mathematics demands accuracy in calculations. Time such different items.

Silly to speak about accuracy at record from 15-18 significant figures and a difference in 60 decimal orders.
I transport: you already lost accuracy and can add nothing - the result from it does not change.

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Re: Operation with very big integer numbers

Gennadiy Usov;
 

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Re: Operation with very big integer numbers

Gennadiy Usov wrote:

Or to leave only digits of the high order and to work with one cell?

looking that for the task.

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Re: Operation with very big integer numbers

Saw recently on page the message on operation with an array where all information on number when it is considered is stored!, also I can not find.
From its part I will try to make simple algorithm by the same principle.
The task: to find numbers for 2 in level N for any N.
There is number Q which defines a level of sharing of number on groups, for example Q=10000000000. (10 in 10th level)
There is array  (), 1 <=j <=K. P (1 =1. We admit To = 10. Any more did not meet.
1 <=i <=N,
1 <=j <=K.
If P (j)> 0 that P (j) = P (j) x 2
If P (j)> =Q that (P (j) =P (j)-Q, P (j+1) =P (j+1) +1)
Then the number will look as total P (j)  (Q in a level (j-1))
There can be a case, when after addition 1 all P (j)> = Q.
Then a cycle
If P (j+1)> =Q that (P (j+1) =P (j+1)-Q, P (j+2) =P (j+2) +1) etc. with loop termination if <Q.

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Re: Operation with very big integer numbers

On the base above the specified algorithm value 2 in a level 100 has been defined:
1267650600228229401496703205376
If to do calculations with usage of one variable it turns out:
1267650600228230000000000000000

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Re: Operation with very big integer numbers

Gennadiy Usov wrote:

Saw recently on page the message on operation with an array where all information on number when it is considered is stored!, also I can not find.
From its part I will try to make simple algorithm by the same principle.

It is clear nothing, if it is fair. Set easier an example, number 100500 as should look on yours?