Round

Defined in header <cmath>.

Description

Computes the nearest integer value to num (in floating-point format), rounding halfway cases away from zero, regardless of the current rounding mode.
​The library provides overloads of std::round for all cv-unqualified floating-point types as the type of the parameter num  (od C++23).

​Rounding to long and Rounding to long long Computes the nearest integer value to num (in integer format), rounding halfway cases away from zero, regardless of the current rounding mode.
​The library provides overloads of std::lround and std::llround for all cv-unqualified floating-point types as the type of the parameter num  (od C++23).

​Additional Overloads are provided for all integer types, which are treated as double.

Declarations

C++23

// 1)
constexpr /* floating-point-type */
            round ( /* floating-point-type */ num );
// 2)
constexpr float roundf( float num );
// 3)
constexpr long double roundl( long double num );

Rounding to long

// 4)
constexpr long lround( /* floating-point-type */ num );
// 5)
constexpr long lroundf( float num );
// 6)
constexpr long lroundl( long double num );

Rounding to long long

// 7)
constexpr long long llround( /* floating-point-type */ num );
// 8)
constexpr long long llroundf( float num );
// 9)
constexpr long long llroundl( long double num );

Additional Overloads

// 10)
template< class Integer >
constexpr double round( Integer num );
// 11)
template< class Integer >
constexpr long lround( Integer num );
// 12)
template< class Integer >
constexpr long long llround( Integer num );

C++11

// 1)
float round ( float num );
// 2)
double round ( double num );
// 3)
long double round ( long double num );
// 4)
float roundf( float num );
// 5)
long double roundl( long double num );

Rounding to long

// 6)
long lround ( float num );
// 7)
long lround ( double num );
// 8)
long lround ( long double num );
// 9)
long lroundf( float num );
// 10)
long lroundl( long double num );

Rounding to long long

// 11)
long long llround ( float num );
// 12)
long long llround ( double num );
// 13)
long long llround ( long double num );
// 14)
long long llroundf( float num );
// 15)
long long llroundl( long double num );

Additional Overloads

// 16)
template< class Integer >
double round( Integer num );
// 17)
template< class Integer >
long lround( Integer num );
// 18)
template< class Integer >
long long llround( Integer num );

Parameters

​num - floating-point or integer value

Return value

If no errors occur, the nearest integer value to num, rounding halfway cases away from zero, is returned.

If a domain error occurs, an implementation-defined value is returned.

Error handling

Errors are reported as specified in math_errhandling.

If the result of std::lround or std::llround is outside the range representable by the return type, a domain error or a range error may occur.

If the implementation supports IEEE floating-point arithmetic (IEC 60559):

For the std::round function:

The current rounding mode has no effect.
If num is ±∞, it is returned, unmodified
If num is ±0, it is returned, unmodified
If num is NaN, NaN is returned

For std::lround and std::llround functions:

FE_INEXACT is never raised
The current rounding mode has no effect.
If num is ±∞, FE_INVALID is raised and an implementation-defined value is returned
If the result of the rounding is outside the range of the return type, FE_INVALID is raised and an implementation-defined value is returned
If num is NaN, FE_INVALID is raised and an implementation-defined value is returned.

Notes

FE_INEXACT may be (but is not required to be) raised by std::round when rounding a non-integer finite value.

The largest representable floating-point values are exact integers in all standard floating-point formats, so std::round never overflows on its own; however the result may overflow any integer type (including std::intmax_t), when stored in an integer variable.

POSIX specifies that all cases where std::lround or std::llround raise FE_INEXACT are domain errors.

The double version of std::round behaves as if implemented as follows:

#include <cfenv>
#include <cmath>
 
#pragma STDC FENV_ACCESS ON
 
double round(double x)
{
    std::fenv_t save_env;
    std::feholdexcept(&save_env);
    double result = std::rint(x);
    if (std::fetestexcept(FE_INEXACT))
    {
        auto const save_round = std::fegetround();
        std::fesetround(FE_TOWARDZERO);
        result = std::rint(std::copysign(0.5 + std::fabs(x), x));
        std::fesetround(save_round);
    }
    std::feupdateenv(&save_env);
    return result;
}

The additional overloads are not required to be provided exactly as Additional Overloads. They only need to be sufficient to ensure that for their argument num of integer type:

std::round(num) has the same effect as std::round(static_cast<double>(num))
std::lround(num) has the same effect as std::lround(static_cast<double>(num))
std::llround(num) has the same effect as std::llround(static_cast<double>(num))

Examples

#include <cfenv>
#include <climits>
#include <cmath>
#include <iostream>
 
// #pragma STDC FENV_ACCESS ON
 
int main()
{
    // round
    std::cout 
        << "round(+2.3) = "<< std::round(2.3) <<'\n'
        << "round(+2.5) = " << std::round(2.5) <<'\n'
        << "round(+2.7) = "<< std::round(2.7) <<'\n'
        << "round(-2.3) = "<< std::round(-2.3) <<'\n'
        << "round(-2.5) = " << std::round(-2.5) <<'\n'
        << "round(-2.7) = "<< std::round(-2.7) <<'\n';
 
    std::cout 
        << "round(-0.0) = " 
        << std::round(-0.0)  << '\n'
        
        << "round(-Inf) = " 
        << std::round(-INFINITY) << '\n';
 
    // lround
    std::cout 
        << "lround(+2.3) = "<< std::lround(2.3) <<'\n'
        << "lround(+2.5) = "<< std::lround(2.5) <<'\n'
        << "lround(+2.7) = "<< std::lround(2.7) <<'\n'
        << "lround(-2.3) = "<< std::lround(-2.3) <<'\n'
        << "lround(-2.5) = "<< std::lround(-2.5) <<'\n'
        << "lround(-2.7) = "<< std::lround(-2.7) <<'\n';
 
    std::cout 
        << "lround(-0.0) = " 
        << std::lround(-0.0)  << '\n'
        
        << "lround(-Inf) = " 
        << std::lround(-INFINITY) << '\n';
 
    // error handling
    std::feclearexcept(FE_ALL_EXCEPT);
 
    std::cout 
        << "std::lround(LONG_MAX+1.5) = "
        << std::lround(LONG_MAX + 1.5) << '\n';
    if (std::fetestexcept(FE_INVALID))
        std::cout 
            << "FE_INVALID was raised\n";
}

Possible Result

round(+2.3) = 2  
round(+2.5) = 3  
round(+2.7) = 3
round(-2.3) = -2  
round(-2.5) = -3  
round(-2.7) = -3
round(-0.0) = -0
round(-Inf) = -inf
lround(+2.3) = 2  
lround(+2.5) = 3  
lround(+2.7) = 3
lround(-2.3) = -2  
lround(-2.5) = -3  
lround(-2.7) = -3
lround(-0.0) = 0
lround(-Inf) = -9223372036854775808
std::lround(LONG_MAX+1.5) = -9223372036854775808
FE_INVALID was raised