Arithmetic operators

Returns the result of specific arithmetic operation.

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 lvalue-to-rvalue conversion, if applicable), the operand undergoes integral promotion. If an operand has array or function type, array-to-pointer and function-to-pointer 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, prior to any integral promotion, one operand is of enumeration type and the other operand is of a floating-point type or a different enumeration type, this behavior is deprecated. (since C++20).

• 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.

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.

Floating-point environment

If #pragma STDC FENV_ACCESS is supported and set to ON, all floating-point arithmetic operators obey the current floating-point rounding direction and report floating-point arithmetic errors as specified in math_errhandling unless part of a static initializer (in which case floating-point exceptions are not raised and the rounding mode is to nearest).

Floating-point contraction

Unless #pragma STDC FP_CONTRACT is supported and set to OFF, all floating-point arithmetic may be performed as if the intermediate results have infinite range and precision, that is, optimizations that omit rounding errors and floating-point exceptions are allowed. For example, C++ allows the implementation of (x*y) + z with a single fused multiply-add CPU instruction or optimization of a = x*x*x*x; as tmp = x *x; a = tmp*tmp.

Unrelated to contracting, intermediate results of floating-point 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 floating-point operations.

Unary arithmetic operators

The unary arithmetic operator expressions have the form.

The built-in unary plus operator returns the value of its operand. The only situation where it is not a no-op 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 lvalue-to-rvalue, array-to-pointer, or function-to-pointer 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 user-defined 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';
}

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

The binary additive arithmetic operator expressions have the form.

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 floating-point 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 non-array object is treated as a pointer to the first element of an array with size 1.
• If the pointer P points to the ith element of an array, then the expressions P+n, n+P, and P-n are pointers of the same type that point to the i+nth, i+nth, and i-nth element of the same array, respectively. The result of pointer addition may also be a one-past-the-end pointer (that is, pointer P such that the expression P-1 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 the ith element of an array, and the pointer Q points at the jth element of the same array, the expression P-Q has the value i-j, 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 pointed-to 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 requirements.

In overload resolution against user-defined 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';
}

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

The binary multiplicative arithmetic operator expressions have the form.

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 floating-point multiplication,

• multiplication of a NaN by any number gives NaN
• multiplication of 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.

If the second operand is zero, the behavior is undefined, except that if floating-point division is taking place and the type supports IEEE floating-point arithmetic (see std::numeric_limits::is_iec559), then:

• if one operand is NaN, the result is NaN
• dividing a non-zero number by ±0.0 gives the correctly-signed 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 implementation-defined, as it depends on the rounding direction of integer division. The function std::div provided well-defined behavior in that case.

Note: for floating-point remainder, see std::remainder and std::fmod.

In overload resolution against user-defined 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';
}

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

The bitwise arithmetic operator expressions have the form.

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 user-defined 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';
}

Value: 0x12345678 mask: 0xf0
Setting bits: 0x123456f8
Clearing bits: 0x12345608
Selecting bits: 0x70

Bitwise shift operators

The bitwise shift operator expressions have the form.

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,

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 implementation-defined (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 user-defined 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';
}

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

Additive operators

Multiplicative operators

Bitwise logic operators

Bitwise shift operators

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:

See also

Operator precedence.

Operator overloading.