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Showing content from https://en.cppreference.com/w/cpp/language/../numeric/math/round.html below:

std::round, std::roundf, std::roundl, std::lround, std::lroundf, std::lroundl, std::llround, std::llroundf

Rounding to floating-point types

(1) float       round ( float num );

double      round ( double num );

long double round ( long double num ); (since C++11)
(until C++23)

constexpr /* floating-point-type */
            round ( /* floating-point-type */ num );

(since C++23)

float       roundf( float num );

(2) (since C++11)
(constexpr since C++23)

long double roundl( long double num );

(3) (since C++11)
(constexpr since C++23)

Rounding to long

(4) long lround ( float num );

long lround ( double num );

long lround ( long double num ); (since C++11)
(until C++23)

constexpr long lround( /* floating-point-type */ num );

(since C++23)

long lroundf( float num );

(5) (since C++11)
(constexpr since C++23)

long lroundl( long double num );

(6) (since C++11)
(constexpr since C++23)

Rounding to long long

(7) long long llround ( float num );

long long llround ( double num );

long long llround ( long double num ); (since C++11)
(until C++23)

constexpr long long llround( /* floating-point-type */ num );

(since C++23)

long long llroundf( float num );

(8) (since C++11)
(constexpr since C++23)

long long llroundl( long double num );

(9) (since C++11)
(constexpr since C++23)

template< class Integer >
double round( Integer num );

(A) (since C++11)
(constexpr since C++23)

template< class Integer >
long lround( Integer num );

(B) (since C++11)
(constexpr since C++23)

template< class Integer >
long long llround( Integer num );

(C) (since C++11)
(constexpr since C++23)

1-3) 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.(since C++23)

4-9) 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.(since C++23)

A-C) Additional overloads are provided for all integer types, which are treated as double.

[edit] Parameters num - floating-point or integer value [edit] Return value

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

Return value

num

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

[edit] 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:
For std::lround and std::llround functions:
[edit] 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:

The additional overloads are not required to be provided exactly as (A-C). They only need to be sufficient to ensure that for their argument num of integer type:

[edit] Example 
#include <cassert>
#include <cfenv>
#include <cfloat>
#include <climits>
#include <cmath>
#include <iostream>
 
// #pragma STDC FENV_ACCESS ON
 
double custom_round(double x)
{
    const int save_round = std::fegetround();
    std::fesetround(FE_TOWARDZERO);
    const double result = std::rint(std::copysign(0.5 + std::fabs(x), x));
    std::fesetround(save_round);
    return result;
}
 
void test_custom_round()
{
    for (const double x :
        {
            0.0, 0.3,
            0.5 - DBL_EPSILON / 2,
            0.5,
            0.5 + DBL_EPSILON / 2,
            0.7, 1.0, 2.3, 2.5, 2.7, 3.0,
            static_cast<double>(INFINITY)
        })
        assert(round(+x) == custom_round(+x) && round(-x) == custom_round(-x));
}
 
int main()
{
    test_custom_round();
 
    std::cout << std::showpos;
 
    // round
    std::cout << "round(+2.3) = " << std::round(2.3)
              << "  round(+2.5) = " << std::round(2.5)
              << "  round(+2.7) = " << std::round(2.7) << '\n'
              << "round(-2.3) = " << std::round(-2.3)
              << "  round(-2.5) = " << std::round(-2.5)
              << "  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)
              << "  lround(+2.5) = " << std::lround(2.5)
              << "  lround(+2.7) = " << std::lround(2.7) << '\n'
              << "lround(-2.3) = " << std::lround(-2.3)
              << "  lround(-2.5) = " << std::lround(-2.5)
              << "  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 output:

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
[edit] See also

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