nextafter, nextafterf, nextafterl, nexttoward, nexttowardf, nexttowardl

Parameters

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, converted to the type of the function.

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: nextafter(-0.0, +0.0) returns + 0.0 and nextafter(+0.0, -0.0) returns - 0.0 .

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

Example

#include <fenv.h>
#include <float.h>
#include <math.h>
#include <stdio.h>
 
int main(void)
{
    float from1 = 0, to1 = nextafterf(from1, 1);
    printf("The next representable float after %.2f is %.20g (%a)\n", from1, to1, to1);
 
    float from2 = 1, to2 = nextafterf(from2, 2);
    printf("The next representable float after %.2f is %.20f (%a)\n", from2, to2, to2);
 
    double from3 = nextafter(0.1, 0), to3 = 0.1;
    printf("The number 0.1 lies between two valid doubles:\n"
           "    %.56f (%a)\nand %.55f  (%a)\n", from3, from3, to3, to3);
 
    // difference between nextafter and nexttoward:
    long double dir = nextafterl(from1, 1); // first subnormal long double
    float x = nextafterf(from1, dir); // first converts dir to float, giving 0
    printf("Using nextafter, next float after %.2f (%a) is %.20g (%a)\n",
           from1, from1, x, x);
    x = nexttowardf(from1, dir);
    printf("Using nexttoward, next float after %.2f (%a) is %.20g (%a)\n",
           from1, from1, x, x);
 
    // special values
    {
        #pragma STDC FENV_ACCESS ON
        feclearexcept(FE_ALL_EXCEPT);
        double from4 = DBL_MAX, to4 = nextafter(from4, INFINITY);
        printf("The next representable double after %.2g (%a) is %.23f (%a)\n",
               from4, from4, to4, to4);
        if(fetestexcept(FE_OVERFLOW)) puts("   raised FE_OVERFLOW");
        if(fetestexcept(FE_INEXACT)) puts("   raised FE_INEXACT");
    } // end FENV_ACCESS block
 
    float from5 = 0.0, to5 = nextafter(from5, -0.0);
    printf("nextafter(+0.0, -0.0) gives %.2g (%a)\n", to5, to5);
}

The next representable float after 0.00 is 1.4012984643248170709e-45 (0x1p-149)
The next representable float after 1.00 is 1.00000011920928955078 (0x1.000002p+0)
The number 0.1 lies between two valid doubles:
    0.09999999999999999167332731531132594682276248931884765625 (0x1.9999999999999p-4)
and 0.1000000000000000055511151231257827021181583404541015625  (0x1.999999999999ap-4)
Using nextafter, next float after 0.00 (0x0p+0) is 0 (0x0p+0)
Using nexttoward, next float after 0.00 (0x0p+0) is 1.4012984643248170709e-45 (0x1p-149)
The next representable double after 1.8e+308 (0x1.fffffffffffffp+1023) is inf (inf)
   raised FE_OVERFLOW
   raised FE_INEXACT
nextafter(+0.0, -0.0) gives -0 (-0x0p+0)

References

See also