std::nextafter, std::nexttoward

 

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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( IntegralType 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).

Parameters

from, to

-

floating point 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.

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

See also

C documentation for nextafter