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

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< cpp‎ | numeric‎ | math

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)
4-6) If from equals to, to is returned, converted from long double to the return type of the function without loss of range or precision.

The library provides overloads of `std::nexttoward` for all cv-unqualified floating-point types as the type of the parameter from. However, an invocation of `std::nexttoward` is ill-formed if the argument corresponding to from has extended floating-point type, because the next representable value (or to) is not guaranteed to be representable as long double. | (since C++23)

A) Additional `std::nextafter` overloads are provided for all other combinations of arithmetic types.
B) Additional `std::nexttoward` overloads are provided for all integer types, which are treated as 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

Run this code

    #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:

    The next representable float after 0 is 1.4012984643248170709e-45 (0x1p-149)
    The next representable float after 1 is 1.0000001192092895508 (0x1.000002p+0)
    The number 0.1 lies between two valid doubles:
        0.09999999999999999167332731531132594682276248931884765625 (0x1.9999999999999p-4)
    and 0.1000000000000000055511151231257827021181583404541015625  (0x1.999999999999ap-4)

    Difference between nextafter and nexttoward:
    With nextafter, next float after 0 is 0
    With nexttoward, next float after 0 is 1.4012984643248170709e-45

    Special values:
    The next representable double after 1.79769e+308 (0x1.fffffffffffffp+1023) is inf (inf)
       raised FE_OVERFLOW
       raised FE_INEXACT
    std::nextafter(+0.0, -0.0) gives -0.000000

    Precision loss demo for float:
    nextafter(1e+01, INF) gives 10.000001; Δ = 0.000001
    nextafter(1e+02, INF) gives 100.000008; Δ = 0.000008
    nextafter(1e+03, INF) gives 1000.000061; Δ = 0.000061
    nextafter(1e+04, INF) gives 10000.000977; Δ = 0.000977
    nextafter(1e+05, INF) gives 100000.007812; Δ = 0.007812
    nextafter(1e+06, INF) gives 1000000.062500; Δ = 0.062500
    nextafter(1e+07, INF) gives 10000001.000000; Δ = 1.000000
    nextafter(1e+08, INF) gives 100000008.000000; Δ = 8.000000

    Precision loss demo for double:
    nextafter(1e+10, INF) gives 10000000000.000002; Δ = 0.000002
    nextafter(1e+11, INF) gives 100000000000.000015; Δ = 0.000015
    nextafter(1e+12, INF) gives 1000000000000.000122; Δ = 0.000122
    nextafter(1e+13, INF) gives 10000000000000.001953; Δ = 0.001953
    nextafter(1e+14, INF) gives 100000000000000.015625; Δ = 0.015625
    nextafter(1e+15, INF) gives 1000000000000000.125000; Δ = 0.125000
    nextafter(1e+16, INF) gives 10000000000000002.000000; Δ = 2.000000

    Precision loss demo for long double:
    nextafter(1e+18, INF) gives 1000000000000000000.062500; Δ = 0.062500
    nextafter(1e+19, INF) gives 10000000000000000001.000000; Δ = 1.000000
    nextafter(1e+20, INF) gives 100000000000000000008.000000; Δ = 8.000000

### See also

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