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# std::nextafter, std::nexttoward

From cppreference.com
< cpp‎ | numeric‎ | math

Defined in header `<cmath>` |  |
float nextafter( float from, float to ); | (1) | (since C++11)
double nextafter( double from, double to ); | (2) | (since C++11)
long double nextafter( long double from, long double to ); | (3) | (since C++11)
Promoted nextafter( Arithmetic from, Arithmetic to ); | (4) | (since C++11)
float nexttoward( float from, long double to ); | (5) | (since C++11)
double nexttoward( double from, long double to ); | (6) | (since C++11)
long double nexttoward( long double from, long double to ); | (7) | (since C++11)
double nexttoward( Integral from, long double to ); | (8) | (since C++11)

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

1-3) If `from` equals to `to`, `to` is returned.
5-7) If `from` equals to `to`, `to` is returned, converted from long double to the return type of the function without loss of range or precision.
4) A set of overloads or a function template for all combinations of arguments of arithmetic type not covered by (1-3). If any argument has integral type, it is cast to double. If any argument is long double, then the return type `Promoted` is also long double, otherwise the return type is always double.
8) A set of overloads or a function template accepting the `from` argument of any integral type. Equivalent to (6) (the argument is cast to double).

### [edit] Parameters

from, to | - | floating point values

### [edit] 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.

### [edit] 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

### [edit] 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`.

### [edit] Example

Run this code

    #include <cmath>
    #include <iomanip>
    #include <iostream>
    #include <cfloat>
    #include <cfenv>

    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);

        // difference between nextafter and nexttoward:
        long double dir = std::nextafter(from1, 1.0L); // first subnormal long double
        float x = 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';

        // special values
        {
            #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';
    }

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)
    With nextafter, next float after 0 is 0
    With nexttoward, next float after 0 is 1.4012984643248170709e-45
    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

### [edit] See also

C documentation for nextafter

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