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 
Explanation
All arithmetic operators compute the result of specific arithmetic operation and returns its result. The arguments are not modified.
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 signer 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.
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.
Unary arithmetic operators
For every promoted arithmetic type A
and for every type T
, the following function signatures participate in overload resolution:
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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 operand. For unsigned a
, the value of a
is 2b
a, where b
is the number of bits after promotion.
#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
Additive 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:
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where LR
is the result of usual arithmetic conversions on L
and R
With operands of arithmetic or enumeration type, the result of binary plus is the sum of the operands (after usual arithmetic converesions), and the result of the binary minus operator is the result of subtracting the second operand from the first (after usual arithmetic conversions).
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.  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.
#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
Multiplicative 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:
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where LRx
is the result of usual arithmetic conversions on Lx
and Rx
The binary operator * performs multiplication of its operands (after usual arithmetic conversions).
The binary operator / divides the first operand by the second (after usual arithmetic conversions).If the second operand is zero, the behavior is undefined. For integral operands, it yields the algebraic quotient. Template:rev list begin Template:rev list item Template:rev list item Template:rev list end
The binary operator % yields the remainder of the division of the first operand by the second (after usual arithmetic conversions). If the quotient a/b
is representible in the result type, (a/b)*b + a%b == a. If the second operand is zero, the behavior is undefined.
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.
#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
Bitwise logic operators
For every pair of promoted integral types L
and R
the following function signatures participate in overload resolution:
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where LR
is the result of usual arithmetic conversions on L
and R
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)
#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
Bitwise shift operators
For every pair of promoted integral types L
and R
, the following function signatures participate in overload resolution:
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<td class="tdclnopad"><td class="tdclnopad"> </td> <td class="tdclnopad"> </td> </tr> Template:ddcl list end The operands of the builtin bitwise shift operators have either integral types or unscoped enumeration type. Integral promotions are performed on both operands before evaluation. The return type is the type of the left operand after integal promotions.
For unsigned 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 a
, the value of a << b
is a * 2b
if it is representable by the return type, otherwise the behavior 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.
#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
Standard library
Arithmetic operators are overloaded for many standard library types.
Unary arithmetic operators
Template:cpp/chrono/duration/dcl list operator arithTemplate:cpp/numeric/complex/dcl list operator arith2Template:cpp/numeric/valarray/dcl list operator arithAdditive operators
Template:cpp/chrono/time point/dcl list operator arith2Template:cpp/string/basic string/dcl list operator+Template:cpp/numeric/complex/dcl list operator arith3Template:cpp/numeric/valarray/dcl list operator arith3 advances the iterator (public member function of std::reverse_iterator )
 
decrements the iterator (public member function of std::reverse_iterator )
 
advances the iterator (public member function of std::move_iterator )
 
decrements the iterator (public member function of std::move_iterator )

Multiplicative operators
Template:cpp/chrono/duration/dcl list operator arith4Template:cpp/numeric/complex/dcl list operator arith3Template:cpp/numeric/valarray/dcl list operator arith3Bitwise 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) 
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 )

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:
Template:cpp/io/basic istream/dcl list operator gtgtTemplate:cpp/io/basic istream/dcl list operator gtgt2Template:cpp/io/basic ostream/dcl list operator ltltTemplate:cpp/io/basic ostream/dcl list operator ltlt2Template:cpp/numeric/complex/dcl list operator ltltgtgtTemplate:cpp/string/basic string/dcl list operator ltltgtgtTemplate:cpp/numeric/random/engine/dcl list operator ltltgtgtTemplate:cpp/numeric/random/distribution/dcl list operator ltltgtgt performs stream input and output of bitsets (function template) 
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 compatible type 