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

From cppreference.com
< cpp‎ | numeric‎ | math
(Applied P1467R9.)
m (→‎Possible implementation: fixed: `rint` uses "current rounding mode", e.g. "toward-zero", which issued wrong result in half-way cases by rounding to smaller (by absolute value) integer; e.g., old round(2.5) gave 2.0 instead of 3.0.)
 
(One intermediate revision by one user not shown)
Line 85: Line 85:
 
If the implementation supports IEEE floating-point arithmetic (IEC 60559),
 
If the implementation supports IEEE floating-point arithmetic (IEC 60559),
 
: For the {{tt|std::round}} function:
 
: For the {{tt|std::round}} function:
−
* The current [[cpp/numeric/fenv/FE_round|rounding mode]] has no effect.
+
:* The current [[cpp/numeric/fenv/FE_round|rounding mode]] has no effect.
−
* If {{c|num}} is ±∞, it is returned, unmodified
+
:* If {{c|num}} is ±∞, it is returned, unmodified.
−
* If {{c|num}} is ±0, it is returned, unmodified
+
:* If {{c|num}} is ±0, it is returned, unmodified.
−
* If {{c|num}} is NaN, NaN is returned
+
:* If {{c|num}} is NaN, NaN is returned.
 
: For {{tt|std::lround}} and {{tt|std::llround}} functions:
 
: For {{tt|std::lround}} and {{tt|std::llround}} functions:
−
* {{lc|FE_INEXACT}} is never raised
+
:* {{lc|FE_INEXACT}} is never raised.
−
* The current [[cpp/numeric/fenv/FE_round|rounding mode]] has no effect.
+
:* The current [[cpp/numeric/fenv/FE_round|rounding mode]] has no effect.
−
* If {{c|num}} is ±∞, {{lc|FE_INVALID}} is raised and an implementation-defined value is returned
+
:* If {{c|num}} is ±∞, {{lc|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, {{lc|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, {{lc|FE_INVALID}} is raised and an implementation-defined value is returned.
−
* If {{c|num}} is NaN, {{lc|FE_INVALID}} is raised and an implementation-defined value is returned.
+
:* If {{c|num}} is NaN, {{lc|FE_INVALID}} is raised and an implementation-defined value is returned.
  
 
===Notes===
 
===Notes===
Line 101: Line 101:
 
The largest representable floating-point values are exact integers in all standard floating-point formats, so {{tt|std::round}} never overflows on its own; however the result may overflow any integer type (including {{lc|std::intmax_t}}), when stored in an integer variable.
 
The largest representable floating-point values are exact integers in all standard floating-point formats, so {{tt|std::round}} never overflows on its own; however the result may overflow any integer type (including {{lc|std::intmax_t}}), when stored in an integer variable.
  
−
[http://pubs.opengroup.org/onlinepubs/9699919799/functions/lround.html POSIX specifies] that all cases where {{tt|std::lround}} or {{tt|std::llround}} raise {{lc|FE_INEXACT}} are domain errors.
+
[https://pubs.opengroup.org/onlinepubs/9699919799/functions/lround.html POSIX specifies] that all cases where {{tt|std::lround}} or {{tt|std::llround}} raise {{lc|FE_INEXACT}} are domain errors.
  
 
The {{c/core|double}} version of {{tt|std::round}} behaves as if implemented as follows:
 
The {{c/core|double}} version of {{tt|std::round}} behaves as if implemented as follows:
Line 112: Line 112:
 
double round(double x)
 
double round(double x)
 
{
 
{
−
     std::fenv_t save_env;
+
     const int save_round = std::fegetround();
−
    std::feholdexcept(&save_env);
+
    std::fesetround(FE_TOWARDZERO);
−
    double result = std::rint(x);
+
    const double result = std::rint(std::copysign(0.5 + std::fabs(x), x));
−
    if (std::fetestexcept(FE_INEXACT))
+
    std::fesetround(save_round);
−
    {
+
−
        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;
 
     return result;
 
}
 
}
Line 132: Line 125:
 
{{example
 
{{example
 
|code=
 
|code=
 +
#include <cassert>
 
#include <cfenv>
 
#include <cfenv>
 +
#include <cfloat>
 
#include <climits>
 
#include <climits>
 
#include <cmath>
 
#include <cmath>
Line 138: Line 133:
  
 
// #pragma STDC FENV_ACCESS ON
 
// #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()
 
int main()
 
{
 
{
 +
    test_custom_round();
 +
 +
    std::cout << std::showpos;
 +
 
     // round
 
     // round
 
     std::cout << "round(+2.3) = " << std::round(2.3)
 
     std::cout << "round(+2.3) = " << std::round(2.3)
Line 173: Line 195:
 
|p=true
 
|p=true
 
|output=
 
|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(-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(-0.0) = -0
 
round(-Inf) = -inf
 
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(-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(-0.0) = +0
 
lround(-Inf) = -9223372036854775808
 
lround(-Inf) = -9223372036854775808
 
std::lround(LONG_MAX+1.5) = -9223372036854775808
 
std::lround(LONG_MAX+1.5) = -9223372036854775808

Latest revision as of 13:13, 11 February 2024

 
C++
 
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roundlroundllround
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Defined in header <cmath>
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)
Defined in header <cmath>
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.

Contents

[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
math-round away zero.svg
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:
  • 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.

[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: 

#include <cfenv>
#include <cmath>
 
#pragma STDC FENV_ACCESS ON
 
double 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;
}

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:

  • 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)).

[edit] Example

Run this code
#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

(C++11)(C++11)
 nearest integer not greater than the given value
(function) [edit]
(C++11)(C++11)
 nearest integer not less than the given value
(function) [edit]
(C++11)(C++11)(C++11)
 nearest integer not greater in magnitude than the given value
(function) [edit]
C documentation for round
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