Calculation

Stack's expression is Reverse Polish Notation (RPN). That's result of stack oriented approach.

RPN is a mathematical notation wherein every operator follows all of its operands. It is also known as postfix notation. In contrast to the more common infix notation, where operators are placed between operands (e.g., 3 + 4), RPN eliminates the need for parentheses to define operation order.

Advantages of RPN

• No Need for Parentheses: RPN eliminates the need for parentheses that are required in Usual notation to dictate the order of operations.
• Efficient for Computers: RPN is easier to implement on computers as it suits stack-based calculations.
• Reduces Errors: Human errors related to misplacing parentheses are reduced.

Addition

In Stack, to add two numbers, you would write the operands first, followed by the operator.

the "Usual" is based on Python's syntax

Example:
Usual: 3 + 4
Stack: 3 4 add

Result:

Stack〔  〕 ←  3
Stack〔 3 〕 ←  4
Stack〔 3 | 4 〕 ←  add
Stack〔 7 〕

Subtraction

For subtraction, the Stack format follows the same pattern: operands first, then the operator.

Example:
Usual: 7 - 2
Stack: 7 2 sub

Result:

Stack〔  〕 ←  7
Stack〔 7 〕 ←  2
Stack〔 7 | 2 〕 ←  sub
Stack〔 5 〕

Multiplication

Multiplication in Stack is handled similarly.

Example:
Usual: 5 * 6
Stack: 5 6 mul

Result:

Stack〔  〕 ←  5
Stack〔 5 〕 ←  6
Stack〔 5 | 6 〕 ←  mul
Stack〔 30 〕

Division

Division follows the same postfix notation rules.

Example:
Usual: 8 / 4
Stack: 8 4 div

Result:

Stack〔  〕 ←  8
Stack〔 8 〕 ←  4
Stack〔 8 | 4 〕 ←  div
Stack〔 2 〕

Modulo

If we want modulo of division, we can use mod command. Example:
Usual: 90 % 7
Stack: 90 7 mod

Result:

Stack〔  〕 ←  90
Stack〔 90 〕 ←  7
Stack〔 90 | 7 〕 ←  mod
Stack〔 6 〕

Power

Sometimes, we have to powering number. If so case, we can use pow command.

Example:
Usual: 2 ** 10
Stack: 2 10 pow

Result:

Stack〔  〕 ←  2
Stack〔 2 〕 ←  10
Stack〔 2 | 10 〕 ←  pow
Stack〔 1024 〕

Rounding off

Disision isn't always divisible, It need rounding off. Example:
Usual: round(22 / 7)
Stack: 22 7 div round

Result:

Stack〔  〕 ←  22
Stack〔 22 〕 ←  7
Stack〔 22 | 7 〕 ←  div
Stack〔 3.142857142857143 〕 ←  round
Stack〔 3 〕

Combining Operations

Stack can also handle more complex expressions by maintaining the order of operations through its postfix structure.

Example 1:
Usual: (3 + 4) * 2
Stack: 3 4 add 2 mul

Result 1:

Stack〔  〕 ←  3
Stack〔 3 〕 ←  4
Stack〔 3 | 4 〕 ←  add
Stack〔 7 〕 ←  2
Stack〔 7 | 2 〕 ←  mul
Stack〔 14 〕

Example 2:
Usual: 5 + ((1 + 2) * 4) - 3
Stack: 5 1 2 add 4 mul add 3 sub

Result 2:

Stack〔  〕 ←  5
Stack〔 5 〕 ←  1
Stack〔 5 | 1 〕 ←  2
Stack〔 5 | 1 | 2 〕 ←  add
Stack〔 5 | 3 〕 ←  4
Stack〔 5 | 3 | 4 〕 ←  mul
Stack〔 5 | 12 〕 ←  add
Stack〔 17 〕 ←  3
Stack〔 17 | 3 〕 ←  sub
Stack〔 14 〕