Calculating With Very Big Numbers

Question

I'm -kind of- a beginner to C.

I made several searches but I haven't seen this question asked. When I try to calculate very big numbers (let's say... Adding 45235432412321312 to 5495034095872309238) my calculator gives answers which are not true. (The answer of my calculator was -2 for the numbers I've given in the previous sentence).

But both Linux's and Windows's own calculators calculate these numbers precisely.

What causes my calculator written in C/C++ to give these wrong answers with big numbers? What can I do to calculate these?

Every data type has a specific range of values which is limited. — Khalil Khalaf, Apr 27 '16 at 19:41
_"What causes my calculator written in C/C++ to give these wrong answers with big numbers?"_ - The problem is caused by a bug in your code. Although I'm a bit skeptical there's any code since there is no language called _C/C++_ — Captain Obvlious, Apr 27 '16 at 19:42
There are no built-in data types for arbitrary-precision calculations, but you can certainly roll your own. Look at Java's `java.math.BigDecimal`, for instance. — Dolda2000, Apr 27 '16 at 19:43
Possible duplicate of [How to work with BIG numbers?](http://stackoverflow.com/questions/3290173/how-to-work-with-big-numbers) — Steve Summit, Apr 27 '16 at 20:01
May I suggest your program also prints the supposed value of the two operands? Errors can happen on the first step. — Weather Vane, Apr 27 '16 at 20:01

score 3 · Answer 1 · answered Apr 27 '16 at 19:50

Digital data is represented as binary information. So, for an 8-bit integer you would have: 0=00000000, 1=00000001, 2=00000010, 3=00000011, etc. As you can imagine, the larger the numbers grow, the more storage is required to represent this information in binary form. What happens with your calculator is called overflow, where the resulting number is simply too large to represent in binary form (there are not enough bits to hold the information).

Now as to why you get accurate results in your computer, it depends on how their software is implemented. Possible explanations are that they either use higher precision arithmetic (they dedicate more bits) the use multiple precision arithmetic, or perform floating point calculations internally. My money would be on multiple precision arithmetic though.

iksemyonov · Answer 2 · 2016-04-27T19:55:26.423

Simply put, the built-in numeric data types that you're using within C and C++, such as float, int, etc., are limited due to them being represented with a finite and fixed amount of bits, such as 32, 64, etc. bits. You can't "stuff" more information into 32 bits than you can, that's the theory of information (read up). Now, when you add two "very big" numbers, due to the machine representation, a so-called "overflow" occurs (read up), which means that a bit sequence is being created as a result of the operation that represents a "meaningless" number; and if the data type is signed, a negative number is likely to appear (again, due to the internal representation).

Now your calculators use so-called "big numbers arithmetic", or "long numbers arithmetic", implemented in the corresponding libraries. With this approach, the number is represented as an array of numbers, and is thus virtually unlimited (of course, there are limits to the length of an array too, but the range that you can represent this way is a lot wider than that of the built-in types.)

To sum up, read on:

theory of information
binary number system and conversions decimal <-> binary
binary arithmetics with signed numbers
big number arithmetics

score 1 · Answer 3 · answered Apr 27 '16 at 19:58

1

Short answer (and I'm not sure why you didn't find it, because it's been asked many, many times): you want a multiple-precision arithmetic library, such as GMP.

answered Apr 27 '16 at 19:58

Steve Summit

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7
70
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Also try the synonym "c++ Big Number library". :-) – Thomas Matthews Apr 27 '16 at 20:55

Calculating With Very Big Numbers

3 Answers3