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Another Big Numbers Library

WARNING: This library has been created for educational and research purposes. It is not recommended for use in production environments.

Another Big Numbers Library is developed to explore low-level features of the language and operator overloading, providing high performance objects with an easy to use interface, which each class have the same behavior of the built-in data types, or at least the most of its features are simulated.

In theory, the precision limit is defined by the size of the system memory. Despite all this, not enough tests have been performed, so it may contain several unknown critic errors. If important calculations need to be performed with arbitrary precision, the use of revised and stable libraries such as GMP is recommended.

See main.cpp for example of use.

Features

  • Written in C++98. See the other branches for C++11 (recommended) and MSVC versions
  • Dependencies free
  • All the classes and functions are defined inside the bnl namespace
  • Arbitrary precision integer class with all operators overloaded
  • Licensed under the MIT license

The bnl::integer class

The bnl::integer class provides an arbitrary precision integer implementation. The numerical data is stored in raw binary format by a self-managed dynamic array of unsigned long int assuming the data type is 8 bytes wide, ordered from the least significant to the most significant data block. Each block of data can store values in the interval [0, 232) simulating a base 232 - 1 representation.

The numeric data is converting from raw binary to std::string and from std::string to raw binary with the Double-Dabble and Reverse Double-Dabble algorithm respectively.

All methods are own implementations and optimal performance is not guaranteed.

Helpful checker functions

Function Description
bnl::iseven Returns whether the value is even
bnl::isneg Returns whether the value is negative
bnl::isodd Returns whether the value is odd
bnl::isone Returns whether the value equals to one, positive or negative
bnl::ispos Returns whether the value is positive
bnl::iszero Returns whether the value equals to zero

Helpful arithmetic functions

Function Description
bnl::abs Returns the absolute value of a number
bnl::max Returns largest number between two numbers
bnl::min Returns smaller number between two numbers
bnl::pow Returns the given number raised to the given exponent
bnl::integer::div Returns the quotient and remainder of integer division*

*See bnl::div_t for more details.

Miscelaneous functions

Function Description
bnl::integer::checkstr Check if a string has a valid decimal representation and process it
bnl::integer::precision Returns the number presicion

Constructors

Constructor Description
Default Creates a new instance initialized to zero
Copy Creates a new instance from already existing bnl::integer
From std::string Creates a new instance from std::string
From const char * Creates a new instance from const char *
From long double Creates a new instance from long double

Operators

The operator are listing by descending precedence order.

Type conversion operators

Operator Description
std::string Conversion to std::string

Increment and decrement operators

Operator Description
++ Prefix and postfix increment
-- Prefix and postfix decrement

Unary operators

Operator Description
+ Integer promotion
- Additive inverse
! Logical NOT
~ Bitwise NOT (one's complement)

Arithmetic operators

Operator Description
* Multiplication
/ Division
% Modulo
+ Addition
- Subtraction
<< Left shift, also used for I/O
>> Right shift, also used for I/O

Comparison and relational operators

Operator Description
> Greater than
< Less than
>= Greater than or equal to
<= Less than or equal to
== Equal to
!= Not equal to

Bitwise operators

Operator Description
& Bitwise AND
| Bitwise OR (inclusive or)
^ Bitwise XOR (exclusive or)

Logic operators

Operator Description
&& Logical AND
|| Logical OR

Assignment operators

Operator Description
= Direct assignation
+= Assignation by addition
-= Assignation by subtraction
*= Assignation by multiplication
/= Assignation by division
%= Assignation by modulo
<<= Assignation by left shift
>>= Assignation by right shift
&= Assignation by bitwise AND
|= Assignation by bitwise OR
^= Assignation by bitwise XOR

The bnl::div_t struct

Similar to std::div_t defined in cmath, represents the result value of an integral division performed by function bnl::integer::div.

It has two int members: quot and rem.

Member Description
quot Represents the quotient of the integral division
rem Represents the remainder of the integral division

Requirements and considerations

Since the code is written in C++98 standard and is dependencies free, can be compiled by most compilers, but some data sizes have been assumed, so not defined errors may occurs if the target system have different data types sizes to the next table.

Data type Size in bytes
unsigned char 1
unsigned int 4
unsigned long int 8
long double 16

However, the C++11 version is recommended to avoid portability issues. A version for MSVC is also available.