Difference between revisions of "cpp/numeric/math/round"

Revision as of 13:55, 19 May 2021

Parameters

Return value

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

Return value

Argument

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 arg is ±∞, it is returned, unmodified
• If arg is ±0, it is returned, unmodified
• If arg 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 arg 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 arg is NaN, FE_INVALID is raised and an implementation-defined value is returned.

Notes

FE_INEXACT may be (but isn't 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 <cmath>
#include <cfenv>
#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;
}

Example

#include <iostream>
#include <cmath>
#include <cfenv>
#include <climits>
 
#pragma STDC FENV_ACCESS ON
 
int main()
{
    // 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";
}

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

See also