Home - News ( United States | United Kingdom | Italy | Germany ) - Football scores

Showing content from https://en.cppreference.com/w/cpp/language/../keywords/../language/operator_arithmetic.html below:

Arithmetic operators - cppreference.com

Returns the result of specific arithmetic operation.

Notes

• All operators in this table are overloadable.
• All built-in operators return values, and most user-defined overloads also return values so that the user-defined operators can be used in the same manner as the built-ins. However, in a user-defined operator overload, any type can be used as return type (including void). In particular, stream insertion and stream extraction overloads of operator<< and operator>> return T&.
• T2 can be any type including T.

All built-in arithmetic operators compute the result of specific arithmetic operation and returns its result. The arguments are not modified.

If the operand passed to a built-in 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, usual arithmetic conversions are applied.

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, — the possible manifestations of such an operation include:

• it wraps around according to the rules of the representation (typically two's complement),
• it traps — on some platforms or due to compiler options (e.g. -ftrapv in GCC and Clang),
• it saturates to minimal or maximal value (on many DSPs),
• it is completely optimized out by the compiler.

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).

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.

The unary arithmetic operator expressions have the form

1) Unary plus (promotion).

2) Unary minus (negation).

Unary + and - operators have higher precedence than all binary arithmetic operators, so expression cannot contain top-level binary arithmetic operators. These operators associate from right to left:

+a - b; // equivalent to (+a) - b, NOT +(a - b)
-c + d; // equivalent to (-c) + d, NOT -(c + d)
 
+-e; // equivalent to +(-e), the unary + is a no-op if “e” is a built-in type
     // because any possible promotion is performed during negation already

1) For the built-in unary plus operator, expression must be a prvalue of arithmetic, unscoped enumeration, or pointer type. Integral promotion is performed on expression if it has integral or unscoped enumeration type. The type of the result is the (possibly promoted) type of expression.

The result of the built-in promotion is the value of

. The built-in unary operation is no-op if the operand is a prvalue of a promoted integral type or a pointer type. Otherwise, the type or value category of the operand is changed by integral promotion or lvalue-to-rvalue, array-to-pointer, function-to-pointer, or user-defined conversion. For example,

is converted to

in unary plus expressions.

2) For the built-in unary minus operator, expression must be a prvalue of arithmetic or unscoped enumeration type. Integral promotion is performed on expression. The type of the result is the type of the promoted type of expression.

The result of the built-in negation is the negative of the promoted

. For unsigned

, the value of

is

, where

is the number of bits after promotion.

• In other words, the result is the two’s complement of the operand (where operand and result are considered as unsigned).

In overload resolution against user-defined operators, for every cv-unqualified 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';
}

Possible 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

The additive operator expressions have the form

1) Binary plus (addition).

2) Binary minus (subtraction).

Binary + and - operators have higher precedence than all other binary arithmetic operators except *, / and %. These operators associate from left to right:

a + b * c;  // equivalent to a + (b * c),  NOT (a + b) * c
d / e - f;  // equivalent to (d / e) - f,  NOT d / (e - f)
g + h >> i; // equivalent to (g + h) >> i, NOT g + (h >> i)
 
j - k + l - m; // equivalent to ((j - k) + l) - m

For built-in binary plus and binary minus operators, both of lhs and rhs must be prvalues, and one of the following conditions must be satisfied:

• Both operands have arithmetic or unscoped enumeration type. In this case, usual arithmetic conversions are performed on both operands.
• Exactly one operand has integral or unscoped enumeration type. In this case, integral promotion is applied to that operand.

In the remaining description in this section, "operand(s)", lhs and rhs refer to the converted or promoted operand(s).

For built-in addition, one of the following conditions must be satisfied:

• Both operands have arithmetic type. In this case, the result is the sum of the operands.
• One operand is a pointer to a completely-defined object type, and the other operand has integral type. In this case, the integral value is added to the pointer (see pointer arithmetic).

For built-in subtraction, one of the following conditions must be satisfied:

• Both operands have arithmetic type. In this case, the result is the difference resulting from the subtraction of rhs from lhs.
• lhs is a pointer to a completely-defined object type, and rhs has integral type. In this case, the integral value is subtracted from the pointer (see pointer arithmetic).
• Both operands are pointers to cv-qualified or cv-unqualified versions of the same completely-defined object type. In this case rhs is subtracted from lhs (see pointer arithmetic).

If both operands have a floating-point type, and 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.

When an expression J that has integral type is added to or subtracted from an expression P of pointer type, the result has the type of P.

• If P evaluates to a null pointer value and J evaluates to ​0​, the result is a null pointer value.
• Otherwise, if P points to the ith element of an array object x with n elements, given the value of J as j, P is added or subtracted as follows:

• The expressions P + J and J + P

• point to the i+jth element of x if i + j is in [​0​, n), and
• are pointers past the end of the last element of x if i + j is n.

• The expression P - J

• points to the i-jth element of x if i - j is in [​0​, n), and
• is a pointer past the end of the last element of x if i - j is n.

• Other j values result in undefined behavior.

• Otherwise, if P points to a complete object, a base class subobject or a member subobject y, given the value of J as j, P is added or subtracted as follows:

• The expressions P + J and J + P

• point to y if j is ​0​, and
• are pointers past the end of y if j is 1.

• The expression P - J

• points to y if j is ​0​, and
• is a pointer past the end of y if j is -1.

• Other j values result in undefined behavior.

• Otherwise, if P is a pointer past the end of an object z, given the value of J as j:

• If z is an array object with n elements, P is added or subtracted as follows:

• The expressions P + J and J + P

• point to the n+jth element of z if n + j is in [​0​, n), and
• are pointers past the end of the last element of z if j is ​0​.

• The expression P - J

• points to the n-jth element of z if n - j is in [​0​, n), and
• is a pointer past the end of the last element of z if j is ​0​.

• Other j values result in undefined behavior.

• Otherwise, P is added or subtracted as follows:

• The expressions P + J and J + P

• point to z if j is -1, and
• are pointers past the end of z if j is ​0​.

• The expression P - J

• points to z if j is 1, and
• is a pointer past the end of z if j is ​0​.

• Other j values result in undefined behavior.

• Otherwise, the behavior is undefined.

When two pointer expressions P and Q are subtracted, the type of the result is std::ptrdiff_t.

• If P and Q both evaluate to null pointer values, the result is ​0​.
• Otherwise, if P and Q point to, respectively, the ith and jth array elements of the same array object x, the expression P - Q has the value i − j.

• If i − j is not representable by std::ptrdiff_t, the behavior is undefined.

• Otherwise, if P and Q point to the same complete object, base class subobject or member subobject, the result is ​0​.
• Otherwise, the behavior is undefined.

These pointer arithmetic operators allow pointers to satisfy the LegacyRandomAccessIterator requirements.

For addition and subtraction, if P or Q have type “pointer to (possibly cv-qualified) T”, where T and the array element type are not similar, the behavior is undefined:

int arr[5] = {1, 2, 3, 4, 5};
unsigned int *p = reinterpret_cast<unsigned int*>(arr + 1);
unsigned int k = *p; // OK, the value of “k” is 2
unsigned int *q = p + 1; // undefined behavior: “p” points to int, not unsigned int

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:

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

The multiplicative operator expressions have the form

1) Multiplication.

2) Division.

3) Remainder.

Multiplicative operators have higher precedence than all other binary arithmetic operators. These operators associate from left to right:

a + b * c;  // equivalent to a + (b * c),  NOT (a + b) * c
d / e - f;  // equivalent to (d / e) - f,  NOT d / (e - f)
g % h >> i; // equivalent to (g % h) >> i, NOT g % (h >> i)
 
j * k / l % m; // equivalent to ((j * k) / l) % m

For built-in multiplication and division operators, both operands must have arithmetic or unscoped enumeration type. For the built-in remainder operator, both operands must have integral or unscoped enumeration type. Usual arithmetic conversions are performed on both operands.

In the remaining description in this section, "operand(s)", lhs and rhs refer to the converted operand(s).

1) The result of built-in multiplication is the product of the operands.

If both operands have a floating-point type, and the type supports IEEE floating-point arithmetic (see

):

• Multiplication of a NaN by any number gives NaN.
• Multiplication of infinity by zero gives NaN and FE_INVALID is raised.

2) The result of built-in division is lhs divided by rhs. If rhs is zero, the behavior is undefined.

If both operands have an integral type, the result is the algebraic quotient (performs integer division): the quotient is truncated towards zero (fractional part is discarded).

If both operands have a floating-point type, and the type supports IEEE floating-point arithmetic (see

):

• 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.

3) The result of built-in remainder is the remainder of the integer division of lhs by rhs. If rhs is zero, the behavior is undefined.

If a / b is representable in the result type, (a / b) * b + a % b == a.

If

is not representable in the result type, the behavior of both

and

is undefined (that means

is undefined on two's complement systems).

Note: Until CWG issue 614 was resolved (N2757), 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';
}

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

The bitwise logic operator expressions have the form

1) Bitwise NOT.

2) Bitwise AND.

3) Bitwise OR.

4) Bitwise XOR.

The bitwise NOT operator has higher precedence than all binary arithmetic operators. It associates from right to left:

~a - b; // equivalent to (~a) - b, NOT ~(a - b)
~c * d; // equivalent to (~c) * d, NOT ~(c * d)
 
~-e; // equivalent to ~(-e)

There is an ambiguity in the grammar when ~ is followed by a type name or decltype specifier(since C++11): it can either be operator~ or start a destructor identifier). The ambiguity is resolved by treating ~ as operator~. ~ can start a destructor identifier only in places where forming an operator~ is syntactically invalid.

All other bitwise logic operators have lower precedence than all other binary arithmetic operators. Bitwise AND has higher precedence than bitwise XOR, which has higher precedence than bitwise OR. They associate from left to right:

a & b * c;  // equivalent to a & (b * c),  NOT (a & b) * c
d / e ^ f;  // equivalent to (d / e) ^ f,  NOT d / (e ^ f)
g << h | i; // equivalent to (g << h) | i, NOT g << (h | i)
 
j & k & l; // equivalent to (j & k) & l
m | n ^ o  // equivalent to m | (n ^ o)

For the built-in bitwise NOT operator, rhs must be a prvalue of integral or unscoped enumeration type, and integral promotion is performed on rhs. For other built-in bitwise logic operators, both operands must have integral or unscoped enumeration type, and usual arithmetic conversions are performed on both operands.

In the remaining description in this section, "operand(s)", lhs and rhs refer to the converted or promoted operand(s).

Given the operand as

and the result of the built-in bitwise NOT operation as

. For each coefficient

of the base-2 representation of

, the corresponding coefficient

of the base-2 representation of

is

if

is

, and

otherwise.

• In other words, the result is the one’s complement of the operand (where operand and result are considered as unsigned).

The type of the result r is the type of the operand x.

2-4) Given the operands as x and y respectively and the result of the built-in binary bitwise logic operations as r. For each pair of coefficients x_i and y_i of the base-2 representations of x and y respectively, the corresponding coefficient r_i of the base-2 representation of r is

2) 1 if both x_i and y_i are 1, and ​0​ otherwise.

3) 1 if at least one of x_i and y_i is 1, and ​0​ otherwise.

4) 1 if either (but not both) of x_i and y_i is 1, and ​0​ otherwise.

The type of the result r is the type of the operands x and y.

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.

Output:

Mask: 0xf0                                 0000000011110000
Value: 0x12345678          00010010001101000101011001111000
Setting bits: 0x123456f8   00010010001101000101011011111000
Clearing bits: 0x12345608  00010010001101000101011000001000
Selecting bits: 0x70       00000000000000000000000001110000
XOR-ing bits: 0x12345688   00010010001101000101011010001000
Inverting bits: 0xedcba987 11101101110010111010100110000111

The bitwise shift operator expressions have the form

1) Bitwise left-shift.

2) Bitwise right-shift.

Bitwise shift operators have higher precedence than bitwise logic operators, but have lower precedence than additive and multiplicative operators. These operators associate from left to right:

a >> b * c;  // equivalent to a >> (b * c),  NOT (a >> b) * c
d << e & f;  // equivalent to (d << e) & f,  NOT d << (e & f)
 
g << h >> i; // equivalent to (g << h) >> i, NOT g << (h >> i)

For the built-in bitwise shift operators, both operands must be prvalues of integral or unscoped enumeration type. Integral promotions are performed on both operands.

In the remaining description in this section, "operand(s)", a, b, lhs and rhs refer to the converted or promoted operand(s).

If the value of rhs is negative or is not less than the number of bits in lhs, the behavior is undefined.

For unsigned a, the value of a << b is the value of a * 2b
, reduced modulo 2N
where N is the number of bits in the return type (that is, bitwise left shift is performed and the bits that get shifted out of the destination type are discarded).

For signed and non-negative a, if a * 2b
is representable in the unsigned version of the return type, then that value, converted to signed, is the value of a << b (this makes it legal to create INT_MIN as 1 << 31); otherwise the behavior is undefined.

For negative a, the behavior of a << b is undefined.

For unsigned a and for signed and non-negative a, 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).

The value of a << b is the unique value congruent to a * 2b
modulo 2N
where N is the number of bits in the return type (that is, bitwise left shift is performed and the bits that get shifted out of the destination type are discarded).

The value of a >> b is a/2b
, rounded towards negative infinity (in other words, right shift on signed a is arithmetic right shift).

The type of the result is that of lhs.

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';
}

Output:

0x123 << 1 = 0x246
0x123 << 63 = 0x8000000000000000
0x10 << 10 = 0x4000
-1000 >> 1 = -500

Arithmetic operators are overloaded for many standard library types.

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:

The following behavior-changing defect reports were applied retroactively to previously published C++ standards.

Operator precedence

Operator overloading

a = b
a += b
a -= b
a *= b
a /= b
a %= b
a &= b
a |= b
a ^= b
a <<= b
a >>= b

++a
--a
a++
a--

+a
-a
a + b
a - b
a * b
a / b
a % b
~a
a & b
a | b
a ^ b
a << b
a >> b

!a
a && b
a || b

a == b
a != b
a < b
a > b
a <= b
a >= b
a <=> b

a[...]
*a
&a
a->b
a.b
a->*b
a.*b

a(...)

a, b

a ? b : c

static_cast converts one type to another related type
dynamic_cast converts within inheritance hierarchies
const_cast adds or removes cv-qualifiers
reinterpret_cast converts type to unrelated type
C-style cast converts one type to another by a mix of static_cast, const_cast, and reinterpret_cast
new creates objects with dynamic storage duration
delete destructs objects previously created by the new expression and releases obtained memory area
sizeof queries the size of a type
sizeof... queries the size of a pack (since C++11)
typeid queries the type information of a type
noexcept checks if an expression can throw an exception (since C++11)
alignof queries alignment requirements of a type (since C++11)

RetroSearch is an open source project built by @garambo | Open a GitHub Issue

Search and Browse the WWW like it's 1997 | Search results from DuckDuckGo

HTML: 3.2 | Encoding: UTF-8 | Version: 0.7.4