# Wanted: A calculator that can handle really big integers and fractions

• Svein
In summary, there are several online calculators and libraries available for performing calculations with very large numbers and fractions, such as Wolfram Alpha and Python's Fractions module. Additionally, programs like Sieclator and Revelator can be downloaded for occasional use. These tools utilize algorithms and data structures such as GMP and __mpz_struct to handle arbitrary precision rational arithmetic.
Svein
TL;DR Summary
I need a calculator that can handle fractions with really large denominators
I am trying to get one step further with my search for $\sum_{n=1}^{\infty}\frac{1}{n^{2s+1}}$. Part of the way is to calculate some algebraic expressions containing fractions with really huge numbers (as in $(\frac{1}{5^{9}}+\frac{1}{7^{9}}-\frac{1}{17^{9}}-\frac{1}{19^{9}})\div (\frac{2}{6^{9}}-\frac{2}{18^{9}})$). Does anybody know of such a calculator or do I have to write it myself?

Yes, I know about mpir.org, but they are based on 64-bit numbers which is too small for me (since 5, 7, 17 and 19 are all prime numbers, adding the fractions will end up in a really huge denominator).

Computer science news on Phys.org
Perhaps one of the arbitrary precision online calculators will do?

Example from my first search hit (notice result is a fraction):
https://apfloat.appspot.com/:
(1/(5^9)+1/(7^9)-1/(17^9)-1/(19^9))/(2/(6^9)-2/(18^9))
80281486442205051414723549292278888963072/29680713166750710362839900905033947265625

davenn
Why not use python? Big integers are baked in.

As an example:

Python:
\$ python

>>> 2**500
3273390607896141870013189696827599152216642046043064789483291368096133796404674554883270092325904157150886684127560071009217256545885393053328527589376L

>>> 2**5000
141246703213942603683520966701614733366889617518454111681368808585711816984270751255808912631671152637335603208431366082764203838069979338335971185726639923431051777851865399011877999645131707069373498212631323752553111215372844035950900535954860733418453405575566736801565587405464699640499050849699472357900905617571376618228216434213181520991556677126498651782204174061830939239176861341383294018240225838692725596147005144243281075275629495339093813198966735633606329691023842454125835888656873133981287240980008838073668221804264432910894030789020219440578198488267339768238872279902157420307247570510423845868872596735891805818727796435753018518086641356012851302546726823009250218328018251907340245449863183265637987862198511046362985461949587281119139907228004385942880953958816554567625296086916885774828934449941362416588675326940332561103664556982622206834474219811081872404929503481991376740379825998791411879802717583885498575115299471743469241117070230398103378615232793710290992656444842895511830355733152020804157920090041811951880456705515468349446182731742327685989277607620709525878318766488368348965015474997864119765441433356928012344111765735336393557879214937004347568208665958717764059293592887514292843557047089164876483116615691886203812997555690171892169733755224469032475078797830901321579940127337210694377283439922280274060798234786740434893458120198341101033812506720046609891160700284002100980452964039788704335302619337597862052192280371481132164147186514169090917191909376L

>>> 2**50000  // is left to the OP to try out.
...

jim mcnamara and FactChecker
Svein said:
Yes, I know about mpir.org, but they are based on 64-bit numbers.
Is that true? mpir is based on GMP and that caters for arbitrary size integer (numerator, denominator) pairs.

If you just want an online calculator then Wolfram Alpha is the obvious first stop - the answer is apparently $$\frac{80,281,486,442,205,051,414,723,549,292,278,888,963,072}{29,680,713,166,750,710,362,839,900,905,033,947,265,625}$$
if I copied it correctly.

For many other online calculators and libraries in your favourite language (most of which link in GMP), search for "arbitrary precision rational arithmetic" (or just e.g. "rational arithmetic python").

jedishrfu said:
Why not use python? Big integers are baked in.
Well Big Integers are not very helpful here, but fortunately Python also has Fractions baked in

pbuk said:
Is that true? mpir is based on GMP and that caters for arbitrary size integer (numerator, denominator) pairs.
You may well be right, I just scanned through a couple of the header files and only found paragraphs dealing with long and long long.

Svein said:
You may well be right, I just scanned through a couple of the header files and only found paragraphs dealing with long and long long.
You didn't see this?
C:
typedef struct
{
int _mp_alloc;        /* Number of *limbs* allocated and pointed
to by the _mp_d field.  */
int _mp_size;            /* abs(_mp_size) is the number of limbs the
last field points to.  If _mp_size is
negative this is a negative number.  */
mp_limb_t *_mp_d;        /* Pointer to the limbs.  */
} __mpz_struct;
The data will be in dynamically allocated memory pointed to by mp_d

## 1. How big of integers and fractions can this calculator handle?

This calculator is designed to handle integers and fractions of any size, including numbers with millions or even billions of digits.

## 2. Can this calculator perform all basic operations with these large numbers?

Yes, this calculator is capable of performing addition, subtraction, multiplication, and division with these big integers and fractions.

## 3. Is there a limit to the number of digits that can be entered into the calculator?

No, there is no limit to the number of digits that can be entered. The calculator will display as many digits as necessary to accurately represent the number.

## 4. How accurate are the calculations with such large numbers?

The accuracy of the calculations is not affected by the size of the numbers. The calculator uses precise algorithms to ensure accurate results.

## 5. Can this calculator handle both positive and negative numbers?

Yes, this calculator can handle both positive and negative numbers, including combinations of both in the same operation.

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