mustafanatur/s21_decimal_lib

s21_decimal

При старте работы над проектом просим вас постараться хронометрировать время работы над проектом. По завершении работы над проектом просим вас ответить 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.

Contents

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

Chapter I

Planet Earth, 1990s.

The world economy is growing exponentially, the stock exchange increases many times year after year, more and more companies go public and their shares start to be quoted. The number of users, the number of transactions, price, commission, interest, calculation of financial technical indicators... It's hard to overestimate the accuracy of all this data, and there are serious problems with the current obsolete data types used in the financial sector.

Due to a calculation error in the usual IEEE 754 (float) millions of dollars are lost every year, which simply absorbed from the system, disappearing forever.

Together with the FIX (Financial Information eXchange) protocol, which is being developed for data processing in the transfer between the broker and the exchange, one more tool is needed for data transfer and storage.
At the follow-up meeting:

-- So, gentlemen, please note that our group of specialists, who have already proven themselves in many successful projects, has been tasked by the government to develop a completely new type of data, code-named Decimal. Its task is to allow significantly minimise error for several decades, and in some cases remove it completely in the world's financial transactions. It is required to describe all the necessary logical and arithmetic operations, which would allow to make the necessary calculations 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 figure out what functions we need to implement... Any suggestions?

-- Sum and difference....

-- Multiplication and division...

-- Agreed, but we need more!

- Taking the remainder, comparison and conversion operations!

-- Mathematical rounding in all directions!

-- Yes, I think that’s enough, let’s get to work! We've got no more than a couple of days, don't let us down!

Introduction

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.

Chapter II

Information

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 appropriate for financial calculations that require large numbers of significant integral and fractional digits and no round-off errors. The Decimal type does not eliminate the need for rounding. Rather, it minimizes errors due to rounding.

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 numeric 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 numeric 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.

Binary representation

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.

Example:

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

Arithmetic Operators

Operator name	Operators	Function
Addition	+	int s21_add(s21_decimal value_1, s21_decimal value_2, s21_decimal *result)
Subtraction	-	int s21_sub(s21_decimal value_1, s21_decimal value_2, s21_decimal *result)
Multiplication	*	int s21_mul(s21_decimal value_1, s21_decimal value_2, s21_decimal *result)
Division	/	int s21_div(s21_decimal value_1, s21_decimal value_2, s21_decimal *result)
Modulo	Mod	int s21_mod(s21_decimal value_1, s21_decimal value_2, s21_decimal *result)

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)

Note on the mod operation:

• If an overflow occurred as a result, discard the fractional part (for example, 70,000,000,000,000,000,000,000,000,000 % 0.001 = 0.000)

Comparison Operators

Operator name	Operators	Function
Less than	<	int s21_is_less(s21_decimal, s21_decimal)
Less than or equal to	<=	int s21_is_less_or_equal(s21_decimal, s21_decimal)
Greater than	>	int s21_is_greater(s21_decimal, s21_decimal)
Greater than or equal to	>=	int s21_is_greater_or_equal(s21_decimal, s21_decimal)
Equal to	==	int s21_is_equal(s21_decimal, s21_decimal)
Not equal to	!=	int s21_is_not_equal(s21_decimal, s21_decimal)

Return value:

• 0 - FALSE
• 1 - TRUE

Convertors and parsers

Convertor/parser	Function
From int	int s21_from_int_to_decimal(int src, s21_decimal *dst)
From float	int s21_from_float_to_decimal(float src, s21_decimal *dst)
To int	int s21_from_decimal_to_int(s21_decimal src, int *dst)
To float	int s21_from_decimal_to_float(s21_decimal src, float *dst)

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)

Another functions

Description	Function
Rounds a specified Decimal number to the closest integer toward negative infinity.	int s21_floor(s21_decimal value, s21_decimal *result)
Rounds a decimal value to the nearest integer.	int s21_round(s21_decimal value, s21_decimal *result)
Returns the integral digits of the specified Decimal; any fractional digits are discarded, including trailing zeroes.	int s21_truncate(s21_decimal value, s21_decimal *result)
Returns the result of multiplying the specified Decimal value by negative one.	int s21_negate(s21_decimal value, s21_decimal *result)

Return value - code error:

• 0 - OK
• 1 - calculation error

Chapter III

Part 1. Implementation of the decimal.h library functions

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 (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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