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std::numeric_limits<T>::round_style - cppreference.com

From cppreference.com

static const std::float_round_style round_style;
(until C++11) 
static constexpr std::float_round_style round_style;
(since C++11)

The value of std::numeric_limits<T>::round_style identifies the rounding style used by the floating-point type T whenever a value that is not one of the exactly repesentable values of T is stored in an object of that type.

Standard specializations

T value of std::numeric_limits<T>::round_style
/* non-specialized */ std::round_toward_zero
bool std::round_toward_zero
char std::round_toward_zero
signed char std::round_toward_zero
unsigned char std::round_toward_zero
wchar_t std::round_toward_zero
char8_t (since C++20) std::round_toward_zero
char16_t (since C++11) std::round_toward_zero
char32_t (since C++11) std::round_toward_zero
short std::round_toward_zero
unsigned short std::round_toward_zero
int std::round_toward_zero
unsigned int std::round_toward_zero
long std::round_toward_zero
unsigned long std::round_toward_zero
long long (since C++11) std::round_toward_zero
unsigned long long (since C++11) std::round_toward_zero
float usually std::round_to_nearest
double usually std::round_to_nearest
long double usually std::round_to_nearest

Notes

These values are constants, and do not reflect the changes to the rounding made by std::fesetround. The changed values may be obtained from FLT_ROUNDS or std::fegetround.

Example

The decimal value 0.1 cannot be represented by a binary floating-point type. When stored in an IEEE-754 double, it falls between 0x1.9999999999999*2-4
 and 0x1.999999999999a*2-4
. Rounding to nearest representable value results in 0x1.999999999999a*2-4
.

Similarly, the decimal value 0.3, which is between 0x1.3333333333333*2-2
 and 0x1.3333333333334*2-2
 is rounded to nearest and is stored as 0x1.3333333333333*2-2
. 

#include <iostream>
#include <limits>

auto print(std::float_round_style frs)
{
    switch (frs)
    {
        case std::round_indeterminate:
            return "Rounding style cannot be determined";
        case std::round_toward_zero:
            return "Rounding toward zero";
        case std::round_to_nearest:
            return "Rounding toward nearest representable value";
        case std::round_toward_infinity:
            return "Rounding toward positive infinity";
        case std::round_toward_neg_infinity:
            return "Rounding toward negative infinity";
    }
    return "unknown round style";
}

int main()
{
    std::cout << std::hexfloat
              << "The decimal 0.1 is stored in a double as "
              << 0.1 << '\n'
              << "The decimal 0.3 is stored in a double as "
              << 0.3 << '\n'
              << print(std::numeric_limits<double>::round_style) << '\n';
}

Output: 

The decimal 0.1 is stored in a double as 0x1.999999999999ap-4
The decimal 0.3 is stored in a double as 0x1.3333333333333p-2
Rounding toward nearest representable value

See also