How do you implement storing monetary equivalents…

Storing a monetary equivalent in an integer data type using mathematical approaches is usually implemented by storing the value in the smallest possible currency unit (e.g., cents, kopecks) and scaling as needed.

Main approaches:

Storing in minimal units:
- Multiply the monetary value by a factor equal to 10 raised to the number of decimal places in the fractional part.
- For example, ₽123.45 is stored as 12345 (kopecks).
```
int price_in_kopecks = static_cast<int>(123.45 * 100); // 12345
```

Scaling during operations:

All operations (addition, subtraction) are performed directly on integer values.
When displaying or converting back to fractional representation, divide by the same factor.

int cost1 = 500; // 5 rubles
int cost2 = 750; // 7.50 rubles
int total_cost = cost1 + cost2; // 1250 (12.50 rubles)

// Convert back for display
double total_in_rubles = static_cast<double>(total_cost) / 100.0; // 12.50

Handling multiplication and division:

Multiplication: the result is multiplied by the factor, then divided by the factor. Rounding may be necessary.
Division: can be performed as integer division (with loss of precision) or floating-point division with subsequent scaling.

int units = 3;
int price_per_unit = 150; // 1.50 rubles
int total_item_cost = units * price_per_unit; // 450 (4.50 rubles)

int initial_amount = 1000; // 10.00 rubles
int num_items = 2;
// Division: split between 2 items
// Result in int, divide by the factor, then by the number of items, then multiply by the factor
int cost_per_item = static_cast<int>((static_cast<double>(initial_amount) / 100.0 / num_items) * 100.0); // 500 (5.00 rubles)

Using fixed-point:

You can use a custom type or library for fixed-point numbers, where the integer value contains both the integer and fractional parts with an implicit decimal point. This is a more complex but precise approach, which can be implemented manually.

// Conceptual example, without full implementation
struct FixedPoint {
    long long value; // Stores value * scale
    static const int scale = 100; // Multiplier
};
// Addition/subtraction operations are performed directly on value
// Multiplication/division require special logic considering scale

Advantages of this approach:

No issues with the precision inherent in floating-point numbers for financial calculations.
Predictable rounding behavior.
Efficiency in performing basic arithmetic operations (addition, subtraction).

Disadvantages:

Constant scaling needed during input/output and multiplication/division operations.
May require custom functions for complex operations.
Risk of integer overflow when working with very large sums if the multiplier is large or the data type is insufficient.

How do you implement storing monetary equivalents using the integer data type with mathematical approaches?