Precedence and associativity

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 calledoperator precedence. Using normal mathematical precedence rules (which states that multiplication is resolved before addition), we know that the above expression should evaluate as 4 + (2 * 3) = 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.

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.

Prec/Ass	Operator	Description	Example
1 None	:: ::	Global scope (unary) Class scope (binary)	::g_nGlobalVar = 5; Class::m_nMemberVar = 5;
2 L->R	() () () [] . -> ++ –– typeid const_cast dynamic_cast reinterpret_cast static_cast	Parenthesis Function call Implicit assignment 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	(x + y) * 2; Add(x, y); int nValue(5); aValue[3] = 2; cObject.m_nValue = 4; pObject->m_nValue = 4; nValue++; nValue––; typeid(cClass).name(); const_cast<int*>(pnConstValue); dynamic_cast<Shape*>(pShape); reinterpret_cast<Class2>(cClass1); fValue = static_cast<float>(nValue);
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	nValue = +5;M nValue = -1; ++nValue; ––nValue; if (!bValue) nFlags = ~nFlags; float fValue = (float)nValue; sizeof(int); address = &nValue; nValue = *pnValue; int *pnValue = new int; int *panValue = new int[5]; delete pnValue; delete[] panValue;
4 L->R	->* .*	Member pointer selector Member object selector	pObject->*pnValue = 24; cObject->.*pnValue = 24;
5 L->R	* / %	Multiplication Division Modulus	int nValue = 2 * 3; float fValue = 5.0 / 2.0; int nRemainder = 10 % 3;
6 L->R	+ -	Addition Subtraction	int nValue = 2 + 3; int nValue = 2 – 3;
7 L->R	<< >>	Bitwise shift left Bitwise shift right	int nFlags = 17 << 2; int nFlags = 17 >> 2;
8 L->R	< <= > >=	Comparison less than Comparison less than or equals Comparison greater than Comparison greater than or equals	if (x < y) if (x <= y) if (x > y) if (x >= y)
9 L->R	== !=	Equality Inequality	if (x == y) if (x != y)
10 L->R	&	Bitwise AND	nFlags = nFlags & 17;
11 L->R	^	Bitwise XOR	nFlags = nFlags ^ 17;
12 L->R	|	Bitwise OR	nFlags = nFlags | 17;
13 L->R	&&	Logical AND	if (bValue1 && bValue2)
14 L->R	||	Logical OR	if (bValue1 || bValue2)
15 L->R	?:	Arithmetic if	return (x < y) ? true : false;
16 R->L	= *= /= %= += -= <<= >>= &= |= ^=	Assignment Multiplication assignment Division assignment Modulus assignment Addition assignment Subtraction assignment Bitwise shift left assignment Bitwise shift right assignment Logical AND assingment Logical OR assignment Logical XOR assignment	nValue = 5; nValue *= 5; fValue /= 5.0; nValue %= 5; nValue += 5; nValue -= 5; nFlags <<= 2; nFlags >>= 2; nFlags &= 17; nFlags |= 17; nFlags ^= 17;
17 L->R	,	Comma operator	iii++, jjj++, kkk++;

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 at this point in time. 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.