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std::nextafter, std::nextafterf, std::nextafterl, std::nexttoward, std::nexttowardf, std::nexttowardl

Defined in header `<cmath>`
	(1)
float nextafter ( float from, float to ); double nextafter ( double from, double to ); long double nextafter ( long double from, long double to );		(since C++11) (until C++23)
constexpr /* floating-point-type / nextafter ( / floating-point-type / from, / floating-point-type */ to );		(since C++23)
float nextafterf( float from, float to );	(2)	(since C++11) (constexpr since C++23)
long double nextafterl( long double from, long double to );	(3)	(since C++11) (constexpr since C++23)
	(4)
float nexttoward ( float from, long double to ); double nexttoward ( double from, long double to ); long double nexttoward ( long double from, long double to );		(since C++11) (until C++23)
constexpr /* floating-point-type / nexttoward ( / floating-point-type */ from, long double to );		(since C++23)
float nexttowardf( float from, long double to );	(5)	(since C++11) (constexpr since C++23)
long double nexttowardl( long double from, long double to );	(6)	(since C++11) (constexpr since C++23)
Additional overloads
Defined in header `<cmath>`
template< class Arithmetic1, class Arithmetic2 > /* common-floating-point-type */ nextafter( Arithmetic1 from, Arithmetic2 to );	(A)	(since C++11) (constexpr since C++23)
template< class Integer > double nexttoward( Integer from, long double to );	(B)	(since C++11) (constexpr since C++23)

Returns the next representable value of from in the direction of to.

1-3) If from equals to, to is returned. The library provides overloads of std::nextafter for all cv-unqualified floating-point types as the type of the parameters from and to. (since C++23)

long double

A) Additional std::nextafter overloads are provided for all other combinations of arithmetic types.

double

Parameters

from, to

floating-point or integer values

Return value

If no errors occur, the next representable value of from in the direction of to. is returned. If from equals to, then to is returned.

If a range error due to overflow occurs, ±HUGE_VAL, ±HUGE_VALF, or ±HUGE_VALL is returned (with the same sign as from).

If a range error occurs due to underflow, the correct result is returned.

Error handling

Errors are reported as specified in math_errhandling.

If the implementation supports IEEE floating-point arithmetic (IEC 60559),

if from is finite, but the expected result is an infinity, raises FE_INEXACT and FE_OVERFLOW
if from does not equal to and the result is subnormal or zero, raises FE_INEXACT and FE_UNDERFLOW
in any case, the returned value is independent of the current rounding mode
if either from or to is NaN, NaN is returned

Notes

POSIX specifies that the overflow and the underflow conditions are range errors (errno may be set).

IEC 60559 recommends that from is returned whenever from == to. These functions return to instead, which makes the behavior around zero consistent: std::nextafter(-0.0, +0.0) returns +0.0 and std::nextafter(+0.0, -0.0) returns -0.0.

std::nextafter is typically implemented by manipulation of IEEE representation (glibc, musl).

The additional std::nextafter overloads are not required to be provided exactly as (A). They only need to be sufficient to ensure that for their first argument num1 and second argument num2:

If num1 or num2 has type long double, then std::nextafter(num1, num2) has the same effect as std::nextafter(static_cast<long double>(num1), static_cast<long double>(num2)).
Otherwise, if num1 and/or num2 has type double or an integer type, then std::nextafter(num1, num2) has the same effect as std::nextafter(static_cast<double>(num1), static_cast<double>(num2)).
Otherwise, if num1 or num2 has type float, then std::nextafter(num1, num2) has the same effect as std::nextafter(static_cast<float>(num1), static_cast<float>(num2)).

(until C++23)

If num1 and num2 have arithmetic types, then std::nextafter(num1, num2) has the same effect as std::nextafter(static_cast</* common-floating-point-type */>(num1), static_cast</* common-floating-point-type */>(num2)), where /* common-floating-point-type */ is the floating-point type with the greatest floating-point conversion rank and greatest floating-point conversion subrank between the types of num1 and num2, arguments of integer type are considered to have the same floating-point conversion rank as double.

If no such floating-point type with the greatest rank and subrank exists, then overload resolution does not result in a usable candidate from the overloads provided.

(since C++23)

The additional std::nexttoward overloads are not required to be provided exactly as (B). They only need to be sufficient to ensure that for their argument num of integer type, std::nexttoward(num) has the same effect as std::nexttoward(static_cast<double>(num)).

Example

#include <cfenv>
#include <cfloat>
#include <cmath>
#include <concepts>
#include <iomanip>
#include <iostream>
 
int main()
{
    float from1 = 0, to1 = std::nextafter(from1, 1.f);
    std::cout << "The next representable float after " << std::setprecision(20) << from1
              << " is " << to1
              << std::hexfloat << " (" << to1 << ")\n" << std::defaultfloat;
 
    float from2 = 1, to2 = std::nextafter(from2, 2.f);
    std::cout << "The next representable float after " << from2 << " is " << to2
              << std::hexfloat << " (" << to2 << ")\n" << std::defaultfloat;
 
    double from3 = std::nextafter(0.1, 0), to3 = 0.1;
    std::cout << "The number 0.1 lies between two valid doubles:\n"
              << std::setprecision(56) << "    " << from3
              << std::hexfloat << " (" << from3 << ')' << std::defaultfloat
              << "\nand " << to3 << std::hexfloat << "  (" << to3 << ")\n"
              << std::defaultfloat << std::setprecision(20);
 
    std::cout << "\nDifference between nextafter and nexttoward:\n";
    long double dir = std::nextafter(from1, 1.0L); // first subnormal long double
    float x = std::nextafter(from1, dir); // first converts dir to float, giving 0
    std::cout << "With nextafter, next float after " << from1 << " is " << x << '\n';
    x = std::nexttoward(from1, dir);
    std::cout << "With nexttoward, next float after " << from1 << " is " << x << '\n';
 
    std::cout << "\nSpecial values:\n";
    {
        // #pragma STDC FENV_ACCESS ON
        std::feclearexcept(FE_ALL_EXCEPT);
        double from4 = DBL_MAX, to4 = std::nextafter(from4, INFINITY);
        std::cout << "The next representable double after " << std::setprecision(6)
                  << from4 << std::hexfloat << " (" << from4 << ')'
                  << std::defaultfloat << " is " << to4
                  << std::hexfloat << " (" << to4 << ")\n" << std::defaultfloat;
 
        if (std::fetestexcept(FE_OVERFLOW))
            std::cout << "   raised FE_OVERFLOW\n";
        if (std::fetestexcept(FE_INEXACT))
            std::cout << "   raised FE_INEXACT\n";
    } // end FENV_ACCESS block
 
    float from5 = 0.0, to5 = std::nextafter(from5, -0.0);
    std::cout << "std::nextafter(+0.0, -0.0) gives " << std::fixed << to5 << '\n';
 
    auto precision_loss_demo = []<std::floating_point Fp>(const auto rem, const Fp start)
    {
        std::cout << rem;
        for (Fp from = start, to, Δ;
            (Δ = (to = std::nextafter(from, +INFINITY)) - from) < Fp(10.0);
            from *= Fp(10.0))
            std::cout << "nextafter(" << std::scientific << std::setprecision(0) << from 
                      << ", INF) gives " << std::fixed << std::setprecision(6) << to
                      << "; Δ = " << Δ << '\n';
    };
 
    precision_loss_demo("\nPrecision loss demo for float:\n", 10.0f);
    precision_loss_demo("\nPrecision loss demo for double:\n", 10.0e9);
    precision_loss_demo("\nPrecision loss demo for long double:\n", 10.0e17L);
}

Output: