In order to properly evaluate an expression such as `4 + 2 * 3`

, we must understand both what the operators do, and the correct order to apply them. The order in which operators are evaluated in a compound expression is called **operator precedence**. Using normal mathematical precedence rules (which state that multiplication is resolved before addition), we know that the above expression should evaluate as `4 + (2 * 3)`

to produce the value 10.

In C++, all operators are assigned a level of precedence. Those with the highest precedence are evaluated first. You can see in the table below that multiplication and division (precedence level 5) have a higher precedence than addition and subtraction (precedence level 6). The compiler uses these levels to determine how to evaluate expressions it encounters.

Thus, 4 + 2 * 3 evaluates as 4 + (2 * 3) because multiplication has a higher level of precedence than addition.

If two operators with the same precedence level are adjacent to each other in an expression, the **associativity rules** tell the compiler whether to evaluate the operators from left to right or from right to left. For example, in the expression `3 * 4 / 2`

, the multiplication and division operators are both precedence level 5. Level 5 has an associativity of left to right, so the expression is resolved from left to right: `(3 * 4) / 2 = 6`

.

**Table of operators**

Notes:

- Precedence level 1 is the highest precedence level, and level 18 is the lowest. Operators with a higher precedence level get evaluated first.
- L->R means left to right associativity.
- R->L means right to left associativity.

Prec/Ass | Operator | Description | Pattern |
---|---|---|---|

1 None |
:: :: |
Global scope (unary) Class scope (binary) |
::name class_name::member_name |

2 L->R |
() () () type() [] . -> ++ –– typeid const_cast dynamic_cast reinterpret_cast static_cast |
Parenthesis Function call Initialization Value construction Array subscript Member access from object Member access from object ptr Post-increment Post-decrement Run-time type information Cast away const Run-time type-checked cast Cast one type to another Compile-time type-checked cast |
(expression) function_name(parameters) type name(expression) type(expression) pointer[expression] object.member_name object_pointer->member_name lvalue++ lvalue–– typeid(type) or typeid(expression) const_cast<type>(expression) dynamic_cast<type>(expression) reinterpret_cast<type>(expression) static_cast<type>(expression) |

3 R->L |
+ - ++ –– ! ~ (type) sizeof & * new new[] delete delete[] |
Unary plus Unary minus Pre-increment Pre-decrement Logical NOT Bitwise NOT C-style cast Size in bytes Address of Dereference Dynamic memory allocation Dynamic array allocation Dynamic memory deletion Dynamic array deletion |
+expression -expression ++lvalue ––lvalue !expression ~expression (type)expression sizeof(type) or sizeof(expression) &lvalue *expression new type new type[expression] delete pointer delete[] pointer |

4 L->R |
->* .* |
Member pointer selector Member object selector |
object_pointer->*pointer_to_member object.*pointer_to_member |

5 L->R |
* / % |
Multiplication Division Modulus |
expression * expression expression / expression expression % expression |

6 L->R |
+ - |
Addition Subtraction |
expression + expression expression - expression |

7 L->R |
<< >> |
Bitwise shift left Bitwise shift right |
expression << expression expression >> expression |

8 L->R |
< <= > >= |
Comparison less than Comparison less than or equals Comparison greater than Comparison greater than or equals |
expression < expression expression <= expression expression > expression expression >= expression |

9 L->R |
== != |
Equality Inequality |
expression == expression expression != expression |

10 L->R | & | Bitwise AND | expression & expression |

11 L->R | ^ | Bitwise XOR | expression ^ expression |

12 L->R | | | Bitwise OR | expression | expression |

13 L->R | && | Logical AND | expression && expression |

14 L->R | || | Logical OR | expression || expression |

15 R->L | ?: | Conditional | expression ? expression : expression |

16 R->L |
= *= /= %= += -= <<= >>= &= |= ^= |
Assignment Multiplication assignment Division assignment Modulus assignment Addition assignment Subtraction assignment Bitwise shift left assignment Bitwise shift right assignment Bitwise AND assignment Bitwise OR assignment Bitwise XOR assignment |
lvalue = expression lvalue *= expression lvalue /= expression lvalue %= expression lvalue += expression lvalue -= expression lvalue <<= expression lvalue >>= expression lvalue &= expression lvalue |= expression lvalue ^= expression |

17 R->L | throw | Throw expression | throw expression |

18 L->R | , | Comma operator | expression, expression |

A few operators you should already recognize: +, -, *, /, (), =, <, >, <=, and >=. These arithmetic and relational operators have the same meaning in C++ as they do in every-day usage.

However, unless you have experience with another programming language, it’s likely the majority of the operators in this table will be incomprehensible to you right now. That’s expected at this point. We’ll cover many of them in this chapter, and the rest will be introduced as there is a need for them.

The above table is primarily meant to be a reference chart that you can refer back to in the future to resolve any precedence or associativity questions you have.

**How do I do exponents?**

You’ll note that the ^ operator (commonly used to denote exponentiation in standard mathematical nomenclature) is a Bitwise XOR operation in C++. C++ does not include an exponent operator. To do exponents in C++, #include the <cmath> header, and use the pow() function:

1 2 3 |
#include <cmath> double x = pow(3.0, 4.0); // 3 to the 4th power |

Note that the parameters and return value of pow are of type double. If you try to assign the return value of pow() to an integer variable, you’ll likely get a compiler warning about a possible loss of data. The compiler is warning you that assigning a double value to an int will drop any fractional results.

If you’re okay with this (and in the case of taking 3 to the 4th power, you know the result will be an integer), you can use a static_cast

1 2 3 |
#include <cmath> int x = static_cast<int>(pow(3.0, 4.0)); |

This tells the compiler you’re intentionally doing the conversion from double to int, and to stop making noise about it.

**Quiz**

1) You know from everyday mathematics that expressions inside of parenthesis get evaluated first. For example, in the expression `(2 + 3) * 4`

, the `(2 + 3)`

part is evaluated first.

For this exercise, you are given a set of expressions that have no parenthesis. Using the operator precedence and associativity rules in the table above, add parentheses to each expression to make it clear how the compiler will evaluate the expression.

Hint: Use the pattern column in the table above to determine whether the operator is unary (has one operand) or binary (has two operands). Review section 1.5 -- A first look at operators if you need a refresher on what unary and binary operators are.

Sample problem: x = 2 + 3 % 4
Binary operator % has higher precedence than operator + or operator =, so it gets evaluated first: x = 2 + (3 % 4) Binary operator + has a higher precedence than operator =, so it gets evaluated next: Final answer: x = (2 + (3 % 4)) We now no longer need the table above to understand how this expression will evaluate. |

a) x = 3 + 4 + 5;

b) x = y = z;

c) z *= ++y + 5;

d) a || b && c || d;

**Solutions**

3.2 -- Arithmetic operators |

Index |

2.10 -- Chapter 2 comprehensive quiz |

Just a suggestion towards readability and clarity. The R->L and L->R could maybe be changed into R -> L and R <- L ?

just a suggestion; if you could make the chart in to an image file as well so people could save it and pull it up at any time it might be easier for referencing in the future.

Hey Alex,

I cannot seem to find the exponent operator, ^. Am I missing it, or was it not included.

Thanks

Wintur

Strangely enough, C++ does not include an exponent operator. You have to use the pow() function.

pow(base, exponent) will return the results of base.

^{exponent}. To access the pow() function, you need to #includeSorry to correct you, but you left out what header to include here! If I remember right it is #include <cmath> ,but I could be wrong.

Yes, pow() lives in the <cmath> header.

The quiz is really unclear in this one. I don’t understand even a bit of it.

I’ve updated the quiz question and answer to try and make it more comprehensible. Let me know if it makes more sense now.

Hello Alex,

Thank you for this very well made tutorial.

I’d like to suggest you to put 3.2 (arithmetic operators) before 3.1 (operator precedence and associativity), I think it will be easier to understand the quizz as unary arithmetic operators (+x and -x) has higher precedence than binary operators (x + y and x - y) which make this a bit confusing.

Hi there, Alex!

Am I getting right that "+" operator (#6 Table) would be evaluated before "*" operator (#5 in Table) due to precedence level?

But mathematically "*" should be done first…

No, operator* is evaluated before operator+. I’ll try to make this more clear in the table.

Hey I have a question

What does the % operator do?

Returns the remainder in an integer division. For example: 9 % 4 = 1 (9 / 4 = 2 remainder 1, so 9 % 4 = 1).

This is discussed in section 3.2 -- arithmetic operators.

hi Alex! good job keep it up (y)

i have a question, i’m wondering! is those tutorials are all about console programs?!

Thanks!

Yes.

It’s possible to create other kinds of applications in C++, such as windowed applications or graphical applications, but I don’t cover those here, as doing so requires operating system specific functionality or add-ons.

For someone who wants to learn GUI programming, is it worth it to continue with all those tutorials or should i start over with maybe other tutorials or books …!

Much of the GUI stuff builds on the fundamentals you’ll learn here. If you finish these tutorials, you’ll have a great foundation for anything you want to do later.

hi!Alex.

I wanted to know if it is necessary to learn the entire table for the correct sequence of these operators. Or there are some specific operators needed for daily programming.

Thank you.

It’s not really necessary to memorize all of the precedence levels, as most of them are pretty intuitive, and you can always look them up if something isn’t working like it should. If you have any doubts, you can always disambiguate using parenthesis.

Thanks a ton.

I found the pow() function interesting so incorporated it into the quiz from the previous lesson. You can see where I changed "* seconds * seconds" to the pow() function. My question is, is this considered acceptable and/or recommended use? Thanks v much.

It’s totally acceptable.

My personal rule of thumb is that if the exponent is both an integer and 3 or less, I just do the multiplication by hand (it’s easy enough to understand, and it saves me from having to #include the math header. If the exponent is 4 or more, or a floating point number, then I’ll favor pow().

what is the difference between :

which one is recommended ?

int(myChar) is a C-style cast, and is not recommended in C++.(myChar) is a C++-style static cast, and should be preferred in C++.

static_cast

This is covered in lesson 4.4a -- Explicit type conversion (casting).

Thank Info

Hello,

I encountered a really strange thing with ++ and -- operators!

look at this snipped :

I expected that the result (result of m) of above code should be 10 (even when I compiled it in the php the result was 10) but in C++ the result was 9!

how is that possible!?

-----

an other question >

result(m) of following code in code::blocks : 19

result(m) of following code in borland C++ : 20

How is that possible!?

This kind of inconsistency usually results from compilers evaluating things in a different order. The C++ specification doesn’t specify the order that parameters should be evaluated, for example.

Generally speaking, in C++ you should never use a variable that has a side effect applied to it more than once in a given expression. Doing so is asking for trouble.

Is it considered acceptable to use parenthesis often when in doubt about this issue, or would the purists poo-poo it and say it should be done without parenthesis and according to the rules in the above table? I, for one, doubt i’ll ever memorize all that stuff!

You can never have too many parenthesis in my opinion. Parenthesis make it clear what your intent is, and reduce precedence mistakes. Use them liberally!

Hi, Alex, I can’t understand c) in your quiz. ++/- are both in level 2 and level 3. What is the difference? I assumed that if one in level 2 is called post- and one in level 3 is called pre- it matters on which side of operator they are. But in solution is z *= ((++y) + 5) so it seems ++y is level 2. How is it? Can you explain it little more?

Yes, you are correct on all counts. pre is ++y, and post is y++. So in the quiz, we’re looking at the pre version (++y) which is level 2.

Thanks a lot. Pre- is level 3 btw in table provided, but I got it now. My thinking was if + and ++ are both in level 3 and level 3 is R->L it should be z *= ((++(y + 5))) but lol at me now I see the difference in + in level 3 ( unary ) and + in level 6 ( addition ). All clear now Great tutorial!