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nextafter, nextafterf, nextafterl, nexttoward, nexttowardf, nexttowardl

Defined in header `<math.h>`
float nextafterf( float from, float to );	(1)	(since C99)
double nextafter( double from, double to );	(2)	(since C99)
long double nextafterl( long double from, long double to );	(3)	(since C99)
float nexttowardf( float from, long double to );	(4)	(since C99)
double nexttoward( double from, long double to );	(5)	(since C99)
long double nexttowardl( long double from, long double to );	(6)	(since C99)
Defined in header `<tgmath.h>`
#define nextafter(from, to)	(7)	(since C99)
#define nexttoward(from, to)	(8)	(since C99)

1-3) First, converts both arguments to the type of the function, then returns the next representable value of from in the direction of to. If from equals to to, to is returned.

4-6) First, converts the first argument to the type of the function, then returns the next representable value of from in the direction of to. 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.

7) Type-generic macro: If any argument has type long double, nextafterl is called. Otherwise, if any argument has integer type or has type double, nextafter is called. Otherwise, nextafterf is called.

8) Type-generic macro: If the argument from has type long double, nexttowardl is called. Otherwise, if from has integer type or the type double, nexttoward is called. Otherwise, nexttowardf is called.

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, 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 <math.h>
#include <stdio.h>
#include <float.h>
#include <fenv.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);
}

Output:

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

C17 standard (ISO/IEC 9899:2018):

7.12.11.3 The nextafter functions (p: 187)
7.12.11.4 The nexttoward functions (p: 187)
7.25 Type-generic math <tgmath.h> (p: 272-273)
F.10.8.3 The nextafter functions (p: 386)
F.10.8.4 The nexttoward functions (p: 386)

C11 standard (ISO/IEC 9899:2011):

7.12.11.3 The nextafter functions (p: 256)
7.12.11.4 The nexttoward functions (p: 257)
7.25 Type-generic math <tgmath.h> (p: 373-375)
F.10.8.3 The nextafter functions (p: 529)
F.10.8.4 The nexttoward functions (p: 529)

C99 standard (ISO/IEC 9899:1999):

7.12.11.3 The nextafter functions (p: 237)
7.12.11.4 The nexttoward functions (p: 238)
7.22 Type-generic math <tgmath.h> (p: 335-337)
F.9.8.3 The nextafter functions (p: 466)
F.9.8.4 The nexttoward functions (p: 466)