std::round, std::lround, std::llround

C++

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Technical Specifications

Numerics library

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Common mathematical functions

Functions
Basic operations
abs(int)labsllabsimaxabs (C++11) abs(float)fabs divldivlldivimaxdiv (C++11) fmod	remainder (C++11) remquo (C++11) fma (C++11) fmax (C++11) fmin (C++11) fdim (C++11) nannanfnanl (C++11)(C++11)(C++11)
Exponential functions
exp exp2 (C++11) expm1 (C++11)	log log10 log1p (C++11) log2 (C++11)
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sqrt cbrt (C++11)	hypot (C++11) pow
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sin cos tan asin acos atan atan2	sinh cosh tanh asinh (C++11) acosh (C++11) atanh (C++11)

Error and gamma functions
erf (C++11) erfc (C++11)	lgamma (C++11) tgamma (C++11)
Nearest integer floating point operations
ceil floor roundlroundllround (C++11)(C++11)(C++11)	trunc (C++11) nearbyint (C++11) rintlrintllrint (C++11)(C++11)(C++11)
Floating point manipulation functions
ldexp scalbnscalbln (C++11)(C++11) ilogb (C++11) logb (C++11)	frexp modf nextafternexttoward (C++11)(C++11) copysign (C++11)
Classification/Comparison
fpclassify (C++11) isfinite (C++11) isinf (C++11) isnan (C++11) isnormal (C++11) signbit (C++11)	isgreater (C++11) isgreaterequal (C++11) isless (C++11) islessequal (C++11) islessgreater (C++11) isunordered (C++11)
Macro constants
HUGE_VALFHUGE_VALHUGE_VALL (C++11)(C++11) INFINITY (C++11) NAN (C++11) math_errhandlingMATH_ERRNOMATH_ERREXCEPT (C++11)	FP_NORMALFP_SUBNORMALFP_ZEROFP_INFINITEFP_NAN (C++11)(C++11)(C++11)(C++11)(C++11)

Defined in header <cmath>
float round( float arg );	(1)	(since C++11)
double round( double arg );	(2)	(since C++11)
long double round( long double arg );	(3)	(since C++11)
double round( IntegralType arg );	(4)	(since C++11)
long lround( float arg );	(5)	(since C++11)
long lround( double arg );	(6)	(since C++11)
long lround( long double arg );	(7)	(since C++11)
long lround( IntegralType arg );	(8)	(since C++11)
long long llround( float arg );	(9)	(since C++11)
long long llround( double arg );	(10)	(since C++11)
long long llround( long double arg );	(11)	(since C++11)
long long llround( IntegralType arg );	(12)	(since C++11)

1-3) Computes the nearest integer value to arg (in floating-point format), rounding halfway cases away from zero, regardless of the current rounding mode.

5-7, 9-11) Computes the nearest integer value to arg (in integer format), rounding halfway cases away from zero, regardless of the current rounding mode.

4,8,12) A set of overloads or a function template accepting an argument of any integral type. Equivalent to 2), 6), or 10), respectively (the argument is cast to double).

Parameters

arg

-

floating point value

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

Run this code

#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";
}

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

See also

floor	nearest integer not greater than the given value (function)
ceil	nearest integer not less than the given value (function)
trunc (C++11)	nearest integer not greater in magnitude than the given value (function)