При старте работы над проектом просим тебя постараться хронометрировать время работы над проектом. По завершении работы над проектом, пожалуйста, ответь на два вопроса в этом опросе.

Implementation of your own s21_decimal.h library.

The russian version of the task can be found in the repository.

1. Chapter I
   1.1. Introduction
2. Chapter II
   2.1. Information
3. Chapter III
   3.1. Part 1

Planet Earth, 1990s.

The world economy is growing exponentially, the stock market is increasing year on year, more and more companies are going public and their shares are being quoted. The number of users, the number of transactions, the price, the commission, the interest, the calculation of technical financial indicators... It's hard to overestimate the accuracy of all this data, and there are serious problems with the current outdated data types used in the financial sector.

Millions of dollars are lost every year due to a miscalculation in the standard IEEE 754 (float), which simply disappears from the system.

Along with the FIX (Financial Information eXchange) protocol, which is being developed to process data between the broker and the exchange, another tool is needed to transfer and store data.
At the follow-up meeting:

-- So, gentlemen, please note that our group of specialists, who have already proven themselves in many successful projects, have been commissioned by the government to develop a completely new type of data, code-named Decimal. Its purpose is to make it possible to significantly reduce, and in some cases eliminate, errors in the world's financial transactions for several decades. It is required to describe all the necessary logical and arithmetic operations that would allow the necessary calculations to be performed quickly and conveniently.

- Wow, that's quite an order we got, and from such a customer! We have to keep this client - it promises us big contracts in the future if we do well!

-- Yes, you're right, that's why we need to think about what features to implement... Any suggestions?

-- Sum and difference....

-- Multiplication and division...

-- Agreed, but we need more!

- Take the remainder, comparison and conversion operations!

-- Mathematical rounding in all directions!

-- Yes, I think that's enough, let's get to work! We only have a few days left, don't let us down!

In this project you will implement the s21_decimal.h library in the C programming language. This library should add the ability to work with the "decimal" type, which is not in the language standard. Nevertheless, this type is critically important. For financial calculations, for example, where errors of calculations characteristic of types with floating point are unacceptable. As part of the project you will work with the tasks of processing financial information, dive into the issues of internal representation of different types of data, and solidify knowledge of structured programming.

The Decimal value type represents decimal numbers ranging from positive 79,228,162,514,264,337,593,543,950,335 to negative 79,228,162,514,264,337,593,543,950,335. The default value of a Decimal is 0. The Decimal value type is suitable for financial calculations that require a large number of significant integral and fractional digits and no rounding errors. The Decimal type does not eliminate the need for rounding. Rather, it minimises rounding errors.

When the result of the division and multiplication is passed to the Round method, the result suffers no loss of precision.

A decimal number is a floating point value that consists of a sign, a numerical value where each digit in the value ranges from 0 to 9, and a scaling factor that indicates the position of a floating decimal point that separates the integral and fractional parts of the numerical value.

The binary representation of a Decimal value consists of a 1-bit sign, a 96-bit integer number, and a scaling factor used to divide the 96-bit integer and specify what portion of it is a decimal fraction. The scaling factor is implicitly the number 10, raised to an exponent ranging from 0 to 28. Therefore, the binary representation of a Decimal value the form, ((-2^96 to 2^96) / 10^(0 to 28)), where -(2^96-1) is equal to MinValue, and 2^96-1 is equal to MaxValue.

The scaling factor also can preserve any trailing zeros in a Decimal number. Trailing zeros do not affect the value of a Decimal number in arithmetic or comparison operations.

The binary representation of a Decimal number consists of a 1-bit sign, a 96-bit integer number, and a scaling factor used to divide the integer number and specify what portion of it is a decimal fraction. The scaling factor is implicitly the number 10, raised to an exponent ranging from 0 to 28.

Decimal number can be implemented as a four-element array of 32-bit signed integers (int bits[4];).

bits[0], bits[1], and bits[2] contain the low, middle, and high 32 bits of the 96-bit integer number accordingly.

bits[3] contains the scale factor and sign, and consists of following parts:

• Bits 0 to 15, the lower word, are unused and must be zero.
• Bits 16 to 23 must contain an exponent between 0 and 28, which indicates the power of 10 to divide the integer number.
• Bits 24 to 30 are unused and must be zero.
• Bit 31 contains the sign; 0 meaning positive, and 1 meaning negative.

Note that the bit representation differentiates between negative and positive zero. These values can be treated as being equal in all operations.

typedef struct 
{
    int bits[4];
} s21_decimal;

The functions return the error code:

• 0 - OK
• 1 - the number is too large or equal to infinity
• 2 - the number is too small or equal to negative infinity
• 3 - division by 0

Note on the numbers that do not fit into the mantissa:

• When getting numbers that do not fit into the mantissa during arithmetic operations, use bank rounding (for example, 79,228,162,514,264,337,593,543,950,335 - 0.6 = 79,228,162,514,264,337,593,543,950,334)

Return value:

• 0 - FALSE
• 1 - TRUE

Return value - code error:

• 0 - OK
• 1 - convertation error

Note on the conversion of a float type number:

• If the numbers are too small (0 < |x| < 1e-28), return an error and value equal to 0
• If the numbers are too large (|x| > 79,228,162,514,264,337,593,543,950,335) or are equal to infinity, return an error
• When processing a number with the float type, convert all the significant decimal digits contained in it. If there are more than 7 such digits, the number is rounded to the closest one that does not have more than 7 significant decimal digits.

Note on the conversion from decimal type to int:

• If there is a fractional part in a decimal number, it should be discarded (for example, 0.9 is converted to 0)

Return value - code error:

• 0 - OK
• 1 - calculation error

The functions of the decimal.h library described above must be implemented:

• The library must be developed in C language of C11 standard using gcc compiler;
• The library code must be located in the src folder on the develop branch;
• Do not use outdated and legacy language constructions and library functions. Pay attention to the legacy and obsolete marks in the official documentation on the language and the libraries used. Use the POSIX.1-2017 standard;
• When writing code it is necessary to follow the Google style;
• Make it as a static library named s21_decimal (with the s21_decimal.h header file);
• The library must be developed according to the principles of structured programming;
• Use prefix s21_ before each function;
• Prepare full coverage of library functions code with unit-tests using the Check library;
• Unit tests must cover at least 80% of each function (checked using gcov);
• Provide a Makefile for building the library and tests (with targets all, clean, test, s21_decimal.a, gcov_report);
• The gcov_report target should generate a gcov report in the form of an html page. Unit tests must be run with gcov flags to do this;
• When implementing decimal, stick to the binary representation with the integer bits array as specified in the example above. Observe the position of the digits of a number in the bits array;
• It is forbidden to use the __int128 type;
• Trailing zeros can be as preserved as deleted (except for the s21_truncate function);
• The defined type must support numbers from -79,228,162,514,264,337,593,543,950,335 to +79,228,162,514,264,337,593,543,950,335.

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