Arithmetic operators
Returns the result of specific arithmetic operation.
Operator name  Syntax  Overloadable  Prototype examples (for class T)  

Inside class definition  Outside class definition  
unary plus  +a

Yes  T T::operator+() const;  T operator+(const T &a); 
unary minus  a

Yes  T T::operator() const;  T operator(const T &a); 
addition  a + b

Yes  T T::operator+(const T2 &b) const;  T operator+(const T &a, const T2 &b); 
subtraction  a  b

Yes  T T::operator(const T2 &b) const;  T operator(const T &a, const T2 &b); 
multiplication  a * b

Yes  T T::operator*(const T2 &b) const;  T operator*(const T &a, const T2 &b); 
division  a / b

Yes  T T::operator/(const T2 &b) const;  T operator/(const T &a, const T2 &b); 
modulo  a % b

Yes  T T::operator%(const T2 &b) const;  T operator%(const T &a, const T2 &b); 
bitwise NOT  ~a

Yes  T T::operator~() const;  T operator~(const T &a); 
bitwise AND  a & b

Yes  T T::operator&(const T2 &b) const;  T operator&(const T &a, const T2 &b); 
bitwise OR  a  b

Yes  T T::operator(const T2 &b) const;  T operator(const T &a, const T2 &b); 
bitwise XOR  a ^ b

Yes  T T::operator^(const T2 &b) const;  T operator^(const T &a, const T2 &b); 
bitwise left shift  a << b

Yes  T T::operator<<(const T2 &b) const;  T operator<<(const T &a, const T2 &b); 
bitwise right shift  a >> b

Yes  T T::operator>>(const T2 &b) const;  T operator>>(const T &a, const T2 &b); 

Contents 
[edit] Explanation
All arithmetic operators compute the result of specific arithmetic operation and returns its result. The arguments are not modified.
[edit] Conversions
If the operand passed to an arithmetic operator is integral or unscoped enumeration type, then before any other action (but after lvaluetorvalue conversion, if applicable), the operand undergoes integral promotion. If an operand has array or function type, arraytopointer and functiontopointer conversions are applied.
For the binary operators (except shifts), if the promoted operands have different types, additional set of implicit conversions is applied, known as usual arithmetic conversions with the goal to produce the common type (also accessible via the std::common_type type trait)
 If either operand has scoped enumeration type, no conversion is performed: the other operand and the return type must have the same type
 Otherwise, if either operand is long double, the other operand is converted to long double
 Otherwise, if either operand is double, the other operand is converted to double
 Otherwise, if either operand is float, the other operand is converted to float
 Otherwise, the operand has integer type (because bool, char, char16_t, char32_t, wchar_t, and unscoped enumeration were promoted at this point) and integral conversions are applied to produce the common type, as follows:
 If both operands are signed or both are unsigned, the operand with lesser conversion rank is converted to the operand with the greater integer conversion rank
 Otherwise, if the unsigned operand's conversion rank is greater or equal to the conversion rank of the signed operand, the signed operand is converted to the unsigned operand's type.
 Otherwise, if the signed operand's type can represent all values of the unsigned operand, the unsigned operand is converted to the signed operand's type
 Otherwise, both operands are converted to the unsigned counterpart of the signed operand's type.
The conversion rank above increases in order bool, signed char, short, int, long, long long. The rank of any unsigned type is equal to the rank of the corresponding signed type. The rank of char is equal to the rank of signed char and unsigned char. The ranks of char16_t, char32_t, and wchar_t are equal to the ranks of their underlying types.
[edit] Overflows
Unsigned integer arithmetic is always performed modulo 2n
where n is the number of bits in that particular integer. E.g. for unsigned int, adding one to UINT_MAX gives 0, and subtracting one from 0 gives UINT_MAX.
When signed integer arithmetic operation overflows (the result does not fit in the result type), the behavior is undefined: it may wrap around according to the rules of the representation (typically 2's complement), it may trap on some platforms or due to compiler options (e.g. ftrapv
in GCC and Clang), or may be completely optimized out by the compiler.
[edit] Floatingpoint environment
If
#pragma STDC FENV_ACCESS is supported and set to ON
, all floatingpoint arithmetic operators obey the current floatingpoint rounding direction and report floatingpoint arithmetic errors as specified in math_errhandling unless part of a static initializer (in which case floatingpoint exceptions are not raised and the rounding mode is to nearest)
[edit] Floatingpoint contraction
Unless
#pragma STDC FP_CONTRACT is supported and set to OFF
, all floatingpoint arithmetic may be performed as if the intermediate results have infinite range and precision, that is, optimizations that omit rounding errors and floatingpoint exceptions are allowed. For example, C++ allows the implementation of (x*y) + z with a single fused multiplyadd CPU instruction or optimization of a = x*x*x*x; as tmp = x *x; a = tmp*tmp.
Unrelated to contracting, intermediate results of floatingpoint arithmetic may have range and precision that is different from the one indicated by its type, see FLT_EVAL_METHOD
Formally, the C++ standard makes no guarantee on the accuracy of floatingpoint operations.
[edit] Unary arithmetic operators
The unary arithmetic operator expressions have the form
+ expression

(1)  
 expression

(2)  
The builtin unary plus operator returns the value of its operand. The only situation where it is not a noop is when the operand has integral type or unscoped enumeration type, which is changed by integral promotion, e.g, it converts char to int or if the operand is subject to lvaluetorvalue, arraytopointer, or functiontopointer conversion.
The builtin unary minus operator calculates the negative of its promoted operand. For unsigned a
, the value of a
is 2b
a, where b
is the number of bits after promotion.
In overload resolution against userdefined operators, for every promoted arithmetic type A
and for every type T
, the following function signatures participate in overload resolution:
A operator+(A) 

T* operator+(T*) 

A operator(A) 

#include <iostream> int main() { char c = 0x6a; int n1 = 1; unsigned char n2 = 1; unsigned int n3 = 1; std::cout << "char: " << c << " int: " << +c << '\n' << "1, where 1 is signed: " << n1 << '\n' << "1, where 1 is unsigned char: " << n2 << '\n' << "1, where 1 is unsigned int: " << n3 << '\n'; char a[3]; std::cout << "size of array: " << sizeof a << '\n' << "size of pointer: " << sizeof +a << '\n'; }
Output:
char: j int: 106 1, where 1 is signed: 1 1, where 1 is unsigned char: 1 1, where 1 is unsigned int: 4294967295 size of array: 3 size of pointer: 8
[edit] Additive operators
The binary additive arithmetic operator expressions have the form
lhs + rhs

(1)  
lhs  rhs

(2)  
 both have arithmetic or unscoped enumeration type. In this case, the usual arithmetic conversions are performed on both operands and determine the type of the result..
 one is a pointer to complete object type, the other has integral or unscoped enumeration type. In this case, the result type has the type of the pointer.
 both have arithmetic or unscoped enumeration type. In this case, the usual arithmetic conversions are performed on both operands and determine the type of the result..
 lhs is a pointer to complete object type, rhs has integral or unscoped enumeration type. In this case, the result type has the type of the pointer.
 both are pointers to the same complete object types, ignoring cvqualifiers. In this case, the result type is std::ptrdiff_t.
With operands of arithmetic or enumeration type, the result of binary plus is the sum of the operands (after usual arithmetic conversions), and the result of the binary minus operator is the result of subtracting the second operand from the first (after usual arithmetic conversions), except that, if the type supports IEEE floatingpoint arithmetic (see std::numeric_limits::is_iec559),
 if one operand is NaN, the result is NaN
 infinity minus infinity is NaN and FE_INVALID is raised
 infinity plus the negative infinity is NaN and FE_INVALID is raised
If any of the operands is a pointer, the following rules apply:
 A pointer to nonarray object is treated as a pointer to the first element of an array with size 1.
 If the pointer
P
points to thei
th element of an array, then the expressionsP+n
,n+P
, andPn
are pointers of the same type that point to thei+n
th,i+n
th, andin
th element of the same array, respectively. The result of pointer addition may also be a onepasttheend pointer (that is, pointerP
such that the expressionP1
points to the last element of the array). Any other situations (that is, attempts to generate a pointer that isn't pointing at an element of the same array or one past the end) invoke undefined behavior.  If the pointer
P
points to thei
th element of an array, and the pointerQ
points at thej
th element of the same array, the expressionPQ
has the value ij, if the value fits in std::ptrdiff_t. Both operands must point to the elements of the same array (or one past the end), otherwise the behavior is undefined. If the result does not fit in std::ptrdiff_t, the behavior is undefined.  In any case, if the pointedto type is different from the array element type, disregarding cv qualifications, at every level if the elements are themselves pointers, the behavior of pointer arithmetic is undefined. In particular, pointer arithmetic with pointer to base, which is pointing at an element of an array of derived objects is undefined.
 If the value 0 is added or subtracted from a pointer, the result is the pointer, unchanged. If two pointers point at the same object or are both one past the end of the same array, or both are null pointers, then the result of subtraction is equal to (std::ptrdiff_t)0.
These pointer arithmetic operators allow pointers to satisfy the RandomAccessIterator
concept.
In overload resolution against userdefined operators, for every pair of promoted arithmetic types L
and R
and for every object type T
, the following function signatures participate in overload resolution:
LR operator+(L, R) 

LR operator(L, R) 

T* operator+(T*, std::ptrdiff_t) 

T* operator+(std::ptrdiff_t, T*) 

T* operator(T*, std::ptrdiff_t) 

std::ptrdiff_t operator(T*, T*) 

where LR
is the result of usual arithmetic conversions on L
and R
#include <iostream> int main() { char c = 2; unsigned int un = 2; int n = 10; std::cout << " 2 + (10), where 2 is a char = " << c + n << '\n' << " 2 + (10), where 2 is unsigned = " << un + n << '\n' << " 10  2.12 = " << n  2.12 << '\n'; char a[4] = {'a', 'b', 'c', 'd'}; char* p = &a[1]; std::cout << "Pointer addition examples: " << *p << *(p + 2) << *(2 + p) << *(p  1) << '\n'; char* p2 = &a[4]; std::cout << "Pointer difference: " << p2  p << '\n'; }
Output:
2 + (10), where 2 is a char = 8 2 + (10), where 2 is unsigned = 4294967288 10  2.12 = 12.12 Pointer addition examples: bdda Pointer difference: 3
[edit] Multiplicative operators
The binary multiplicative arithmetic operator expressions have the form
lhs * rhs

(1)  
lhs / rhs

(2)  
lhs % rhs

(3)  
For all three operators, the usual arithmetic conversions are performed on both operands and determine the type of the result.
The binary operator * performs multiplication of its operands (after usual arithmetic conversions), except that, for floatingpoint multiplication,
 multiplication of a NaN by any number gives NaN
 multiplication if infinity by zero gives NaN and FE_INVALID is raised
The binary operator / divides the first operand by the second (after usual arithmetic conversions).
For integral operands, it yields the algebraic quotient.
The quotient is rounded in implementationdefined direction.  (until C++11) 
The quotient is truncated towards zero (fractional part is discarded).  (since C++11) 
If the second operand is zero, the behavior is undefined, except that if floatingpoint division is taking place and the type supports IEEE floatingpoint arithmetic (see std::numeric_limits::is_iec559), then:
 if one operand is NaN, the result is NaN
 dividing a nonzero number by ±0.0 gives the correctlysigned infinity and FE_DIVBYZERO is raised
 dividing 0.0 by 0.0 gives NaN and FE_INVALID is raised
The binary operator % yields the remainder of the integer division of the first operand by the second (after usual arithmetic conversions; note that the operand types must be integral types). If the quotient a/b
is representable in the result type, (a/b)*b + a%b == a. If the second operand is zero, the behavior is undefined. If the quotient a/b
is not representable in the result type, the behavior of both a/b
and a%b
is undefined (that means INT_MIN%1 is undefined on 2's complement systems)
Note: Until C++11, if one or both operands to binary operator % were negative, the sign of the remainder was implementationdefined, as it depends on the rounding direction of integer division. The function std::div provided welldefined behavior in that case.
Note: for floatingpoint remainder, see std::remainder and std::fmod.
In overload resolution against userdefined operators, for every pair of promoted arithmetic types LA
and RA
and for every pair of promoted integral types LI
and RI
the following function signatures participate in overload resolution:
LRA operator*(LA, RA) 

LRA operator/(LA, RA) 

LRI operator%(LI, RI) 

where LRx
is the result of usual arithmetic conversions on Lx
and Rx
#include <iostream> int main() { char c = 2; unsigned int un = 2; int n = 10; std::cout << "2 * (10), where 2 is a char = " << c * n << '\n' << "2 * (10), where 2 is unsigned = " << un * n << '\n' << "10 / 2.12 = " << n / 2.12 << '\n' << "10 / 21 = " << n / 21 << '\n' << "10 % 21 = " << n % 21 << '\n'; }
Output:
2 * (10), where 2 is a char = 20 2 * (10), where 2 is unsigned = 4294967276 10 / 2.12 = 4.71698 10 / 21 = 0 10 % 21 = 10
[edit] Bitwise logic operators
The bitwise arithmetic operator expressions have the form
~ rhs

(1)  
lhs & rhs

(2)  
lhs  rhs

(3)  
lhs ^ rhs

(4)  
The result of operator~ is the bitwise NOT (one's complement) value of the argument (after promotion). The result of operator& is the bitwise AND value of the operands (after usual arithmetic conversions). The result of operator is the bitwise OR value of the operands (after usual arithmetic conversions). The result of operator^ is the bitwise XOR value of the operands (after usual arithmetic conversions)
In overload resolution against userdefined operators, for every pair of promoted integral types L
and R
the following function signatures participate in overload resolution:
R operator~(R) 

LR operator&(L, R) 

LR operator^(L, R) 

LR operator(L, R) 

where LR
is the result of usual arithmetic conversions on L
and R
#include <iostream> int main() { std::cout << std::hex << std::showbase; uint16_t mask = 0x00f0; uint32_t a = 0x12345678; std::cout << "Value: " << a << " mask: " << mask << '\n' << "Setting bits: " << (a  mask) << '\n' << "Clearing bits: " << (a & ~mask) << '\n' << "Selecting bits: " << (a & mask) << '\n'; }
Output:
Value: 0x12345678 mask: 0xf0 Setting bits: 0x123456f8 Clearing bits: 0x12345608 Selecting bits: 0x70
[edit] Bitwise shift operators
The bitwise shift operator expressions have the form
lhs << rhs

(1)  
lhs >> rhs

(2)  
The return type is the type of the left operand after integral promotions.
For unsigned and positive a
, the value of a << b
is the value of a * 2b
, reduced modulo maximum value of the return type plus 1 (that is, bitwise left shift is performed and the bits that get shifted out of the destination type are discarded).
For signed and positive a
,
the value of a << b is a * 2bif it is representable the return type, otherwise the behavior is undefined. 
(until C++14) 
the value of a << b is a * 2bif it is representable in the unsigned version of the return type (which is then converted to signed: this makes it legal to create INT_MIN as 1<<31), otherwise the behavior is undefined. 
(since C++14) 
For negative a
, the behavior of a << b
is undefined.
For unsigned a
and for signed a
with nonnegative values, the value of a >> b
is the integer part of a/2b
. For negative a
, the value of a >> b
is implementationdefined (in most implementations, this performs arithmetic right shift, so that the result remains negative).
In any case, if the value of the right operand is negative or is greater or equal to the number of bits in the promoted left operand, the behavior is undefined.
In overload resolution against userdefined operators, for every pair of promoted integral types L
and R
, the following function signatures participate in overload resolution:
L operator<<(L, R) 

L operator>>(L, R) 

#include <iostream> enum {ONE=1, TWO=2}; int main() { std::cout << std::hex << std::showbase; char c = 0x10; unsigned long long ull = 0x123; std::cout << "0x123 << 1 = " << (ull << 1) << '\n' << "0x123 << 63 = " << (ull << 63) << '\n' // overflow in unsigned << "0x10 << 10 = " << (c << 10) << '\n'; // char is promoted to int long long ll = 1000; std::cout << std::dec << "1000 >> 1 = " << (ll >> ONE) << '\n'; }
Output:
0x123 << 1 = 0x246 0x123 << 63 = 0x8000000000000000 0x10 << 10 = 0x4000 1000 >> 1 = 500
[edit] Standard library
Arithmetic operators are overloaded for many standard library types.
[edit] Unary arithmetic operators
implements unary + and unary  (public member function of std::chrono::duration )
 
applies unary operators to complex numbers (function template)  
applies a unary arithmetic operator to each element of the valarray (public member function of std::valarray )

[edit] Additive operators
performs add and subtract operations involving a time point (function template)  
concatenates two strings or a string and a char (function template)  
advances or decrements the iterator (public member function of std::reverse_iterator )
 
advances or decrements the iterator (public member function of std::move_iterator )
 
performs complex number arithmetics on two complex values or a complex and a scalar (function template)  
applies binary operators to each element of two valarrays, or a valarray and a value (function template) 
[edit] Multiplicative operators
implements arithmetic operations with durations as arguments (function template)  
performs complex number arithmetics on two complex values or a complex and a scalar (function template)  
applies binary operators to each element of two valarrays, or a valarray and a value (function template) 
[edit] Bitwise logic operators
performs binary AND, OR, XOR and NOT (public member function of std::bitset )
 
performs binary logic operations on bitsets (function template)  
applies a unary arithmetic operator to each element of the valarray (public member function of std::valarray )
 
applies binary operators to each element of two valarrays, or a valarray and a value (function template) 
[edit] Bitwise shift operators
applies binary operators to each element of two valarrays, or a valarray and a value (function template)  
performs binary shift left and shift right (public member function of std::bitset )

[edit] Stream insertion/extraction operators
Throughout the standard library, bitwise shift operators are commonly overloaded with I/O stream (std::ios_base& or one of the classes derived from it) as both the left operand and return type. Such operators are known as stream insertion and stream extraction operators:
extracts formatted data (public member function of std::basic_istream )
 
extracts characters and character arrays (function template)  
inserts formatted data (public member function of std::basic_ostream )
 
inserts character data (function template)  
serializes and deserializes a complex number (function template)  
performs stream input and output of bitsets (function template)  
performs stream input and output on strings (function template)  
performs stream input and output on pseudorandom number engine (function template)  
performs stream input and output on pseudorandom number distribution (function template) 
[edit] See also
Common operators  

assignment  increment decrement 
arithmetic  logical  comparison  member access 
other 
a = b 
++a 
+a 
!a 
a == b 
a[b] 
a(...) 
Special operators  
static_cast converts one type to another related type 