Big Integer Arithmetics

#1 Опубликовано: 10.01.2021 14:48:15

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Extension can be install via Plugin Manager in SMath.

At first I had coded my own calculation algorithms which were slow, obviously.
Then I had implemented GNU Multiple Precision Library, which require a lot of work and extra download.
At last I have noticed there is a numerics library within visual studio if I use Net Framework 4.

So here is compiled DLL, which should be extracted to "%AppData%\SMath\extensions\plugins\".
Compiled dll should work out of box if there is Net Framework > 4 is installed on your system.
Source code to check and recompile, system.numerics file if you have not installed .Net4 framework.
If there is no Net4, just copy "system.numerics.dll" file under the folder of "BigIntegerArtihmetics.dll".

It also works under Linux with Mono if you copy files to "/home//.config/SMath".
If you use linux you would know where to copy extension.

Regards

~~biginteger_compiled.7z (4 КиБ) скачан 60 раз(а).~~
~~source_code.7z (6 КиБ) скачан 52 раз(а).~~
~~System.Numerics.7z (43 КиБ) скачан 61 раз(а).~~

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Alvaro Diaz Falconi 10.01.2021 16:15:00

#2 Опубликовано: 04.10.2021 17:07:08

overlord

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Thanks to Andrey, I have uploaded plugin in to repository.
Now you don't have to manually install it.
Plugin can be added into SMath via plugins download page.
If you have this added into your SMath, please remove this plugin directory.
After removal, plugin can be available to download in SMath.

Regards

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Davide Carpi 04.10.2021 18:09:00, Alvaro Diaz Falconi 04.10.2021 19:58:00, NDTM Amarasekera 05.10.2021 00:15:00

#3 Опубликовано: 11.11.2021 02:24:38

Alvaro Diaz Falconi

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Hi. Arbitrary precission algebra, but with rationals, extending the big integers operations and introducing continued fractions expansions.

bigRationals.sm (212 КиБ) скачан 33 раз(а).
bigRationals.pdf (378 КиБ) скачан 39 раз(а).

Best regards.
Alvaro.

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sergio 11.11.2021 05:55:00, overlord 11.11.2021 02:29:00

#4 Опубликовано: 11.11.2021 04:01:29

overlord

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Wrote
Hi. Arbitrary precission algebra, but with rationals, extending the big integers operations and introducing continued fractions expansions.

bigRationals.sm (212 КиБ) скачан 33 раз(а).
bigRationals.pdf (378 КиБ) скачан 39 раз(а).

Best regards.
Alvaro.

This is very nice. Good job Alvaro.
Very beautiful, elegant and elaborated document.

I was writing some functions for this purpose too.
I think I will complete what I have started.
I am going to write a Big Number Plugin for SMath.
With mixed functions/ideas of yours and mine, it can be done.

Regards

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Alvaro Diaz Falconi 11.11.2021 05:05:00

#5 Опубликовано: 11.11.2021 05:14:14

Alvaro Diaz Falconi

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Hi overlord. A plugin is definitely needed. This version also generates the rational approximation of any real with arbitrary precision without any plugin, but its efficiency is minimal.

ContFrac_Figures.sm (54 КиБ) скачан 32 раз(а).
ContFrac_Figures.pdf (139 КиБ) скачан 30 раз(а).

Best regards.
Alvaro.

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sergio 11.11.2021 05:57:00

#6 Опубликовано: 11.11.2021 14:02:53

overlord

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Wrote
...but its efficiency is minimal.

When (If) I complete the Big Number plugin, it will be much faster.
I know this because I witnessed first hand while programming Big Integer plugin.
Same algorithms shall execute faster on C# than internal SMath programming.

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Alvaro Diaz Falconi 11.11.2021 17:24:00

#7 Опубликовано: 11.11.2021 22:58:40

Alvaro Diaz Falconi

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Hi. Improved version. Newton-raphson method and row reduced echelon form were also added, both with arbitrary arithmetic precision.

bigRationals.sm (276 КиБ) скачан 43 раз(а).
bigRationals.pdf (458 КиБ) скачан 45 раз(а).

Best regards.
Alvaro.

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Davide Carpi 19.01.2022 18:44:00

#8 Опубликовано: 12.11.2021 18:09:40

Jean Giraud

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Hola Alvaro,
Great piece of work.
For pi, you may want to check Simon Plouffe
to avoid continued fraction ... timing ?
Take care ... Jean.

Pi for Alvaro BigNumber.sm (4 КиБ) скачан 30 раз(а).

#9 Опубликовано: 12.11.2021 18:12:05

overlord

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Wrote
you may want to check Simon Plouffe

▲▲▲▲▲
Don't bother Alvaro, just a regular pi series calculation.
Not related with arbitrary precision results.

#10 Опубликовано: 19.01.2022 14:59:10

overlord

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Well, promise is a promise.
I shall release the Big Rational Library when finished very soon.
Just a couple of essential functions remained.
Then I will try to add complex ones.

Big rationals has a niche and limited usage.
Though sometimes it is necessary for floating point precision.
Near none CAS including SMath is not capable such calculations.
It is due to electronic hardware and IEEE74 design.

Regards

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Davide Carpi 19.01.2022 18:43:00

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Big Integer Arithmetics - Functions for big integer calculations - Сообщения