std::round,...td::lroundl,(3)

💅 <cmath> round girlies — bestie edition 🎀

okay so this is the <cmath> rounding page from the C++ Standard Libary manual, aka std::round,...td::lroundl,(3). we’re talking about the whole squad: std::round, std::roundf, std::roundl, std::lround, std::lroundf, std::lroundl — and their llround cousins too. they all snap numbers to the nearest integer, but the return types and edge cases are where the plot twists live. no cap. 🫶

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🌸 NAME 🌸

std::round, std::roundf, std::roundl, std::lround, std::lroundf, std::lroundl — and yep, the NAME line repeats the whole set exactly like this: std::round,std::roundf,std::roundl,std::lround,std::lroundf,std::lroundl, 💖

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✨ Synopsis ✨

Defined in header <cmath>
Rounding to floating-point types

float       round ( float num );         (1)
double      round ( double num );        (since C++11) (until C++23)
long double round ( long double num );
constexpr /* floating-point-type */ round ( /* floating-point-type */ num );  (since C++23)

float       roundf( float num );         (since C++11) (2) (constexpr since C++23)
long double roundl( long double num );   (since C++11) (3) (constexpr since C++23)

Rounding to long

long lround ( float num );               (4)
long lround ( double num );              (since C++11) (until C++23)
long lround ( long double num );
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

long long llround ( float num );         (7)
long long llround ( double num );        (since C++11) (until C++23)
long long llround ( long double num );
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)

Additional overloads
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)

okay so what do the labels mean? (1)–(3) are the floating-point-returning squad: round, roundf, roundl. (4)–(9) are the integer-returning squad: lround, lroundf, lroundl, llround, llroundf, llroundl. and (A)–(C) are the extra integer overloads. slay. 💅

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.

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🔍 Parameters 🔍

• num — floating-point or integer value 🍓

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🎁 Return value 🎁

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

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🎁 Return value (the sequel, because the manpage said so) 🎁

the original drops a lil diagram reference here: math-round away zero.svg over num. 🦋

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

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🚨 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), then listen up bestie:

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.

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📝 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)).

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💻 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";
}

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🌈 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

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👀 See also 👀

• floor — nearest integer not greater than the given value (function)
• floorf — (function) (C++11)
• floorl — (function) (C++11)
• ceil — nearest integer not less than the given value (function)
• ceilf — (function) (C++11)
• ceill — (function) (C++11)
• trunc — nearest integer not greater in magnitude than the given value (C++11) (function)
• truncf — (C++11) (function)
• truncl — (C++11) (function)
• C documentation for round

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and that’s the whole page, bestie 🫶 source: http://cppreference.com · version/date: 2024.06.10 · manual page: std::round,...td::lroundl,(3). now go round some numbers, but keep an eye on your ranges 💅✨