Legacy Document

nextafter

You can use the nextafter functions to find out the next value that can be represented after a given value in a particular floating-point type.

float       nextafterf (float x, float y);
double      nextafterd (double x, double y);

x

Any floating-point number.

y

Any floating-point number.

DESCRIPTION

The nextafter functions (one for each data type) generate the next representable neighbor of x in the direction of y in the proper format.

The floating-point values representable in single and double formats constitute a finite set of real numbers. The nextafter functions illustrate this fact by returning the next representable value.

If $x\; =\; y$ , $nextafter(x,y)$ returns x if x and y are not signed zeros.

EXCEPTIONS

When x and y are finite and nonzero, either the result of $nextafter(x,y)$ is exact or it raises one of the following exceptions:

• inexact (if an overflow or underflow exception occurs)
• overflow (if x is finite and the result is infinite)
• underflow (if the result is inexact, must be represented as a denormalized number
  or 0, and x y)

SPECIAL CASES

Table 10-39 shows the results when one of the arguments to a nextafter function is a zero, a NaN, or an Infinity. In this table, x and y are finite, nonzero floating-point numbers.

Table 10-39 Special cases for the nextafter functions

Operation	Result	Exceptions raised
$nextafter(+0,y)$	Next representable number in direction of y	Underflow
$nextafter(x,+0)$	Next representable number in direction of 0	None
$nextafter(-0,y)$	Next representable number in direction of y	Underflow
$nextafter(-0,+0)$	+0	None
$nextafter(x,-0)$	Next representable number in direction of 0	None
$nextafter(+0,-0)$	$-0$	None
$nextafter(NaN,y)$	NaN[63]	None[64]
$nextafter(x,NaN)$	NaN	None
$nextafter(+$ ,y)	Largest respresentable number	None[64]
$nextafter(x,+$ )	Next representable number greater than x	None
$nextafter(-$ ,y)	Smallest representable number	None
$nextafter(x,-$ )	Next representable number smaller than x	None

EXAMPLES

z = nextafterf(1.0, +  );/* z = 1.000000000000000000000012 
                              1.000000119209289551 */
z = nextafterd(1.0, +  );/* z = 1.00000000...0000000000000000012 
                              1.000000000000000222 */ 

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[63] If both arguments are NaNs, the value of the first NaN is returned.

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[64] If the NaN is a signaling NaN, the invalid exception is raised.