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J. M.'s missing motivation ♦
J. M.'s missing motivation ♦
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added edit explaining subtleties of floating-point representation
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David Zhang
David Zhang
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In C (and many other programming languages), there is a function

double nextafter(double x, double y)

which takes two (IEEE 754) floating-point numbers and returns the next representable floating-point number after x in the direction of y. What is the Mathematica equivalent of this function for MachinePrecision numbers?

EDIT: This issue has been brought up in the comments, but for the benefit of future readers, note that this is a substantially more subtle task than simply adding or subtracting $MachineEpsilon. The problem is that the distance between one floating-point value and the next changes with magnitude. $MachineEpsilon, by definition, is the smallest positive floating-point value such that 1.0 + $MachineEpsilon > 1.0. The distance between 1.0e-300 and the next number up will be much smaller, while the distance between 1.0e+300 and the next number up will be much greater. In addition, there are issues raised by the transitions between one order of magnitude and the next. Observe that 1.0 + $MachineEpsilon/2 == 1.0, while 1.0 - $MachineEpsilon/2 < 1.0.

In C (and many other programming languages), there is a function

double nextafter(double x, double y)

which takes two (IEEE 754) floating-point numbers and returns the next representable floating-point number after x in the direction of y. What is the Mathematica equivalent of this function for MachinePrecision numbers?

In C (and many other programming languages), there is a function

double nextafter(double x, double y)

which takes two (IEEE 754) floating-point numbers and returns the next representable floating-point number after x in the direction of y. What is the Mathematica equivalent of this function for MachinePrecision numbers?

EDIT: This issue has been brought up in the comments, but for the benefit of future readers, note that this is a substantially more subtle task than simply adding or subtracting $MachineEpsilon. The problem is that the distance between one floating-point value and the next changes with magnitude. $MachineEpsilon, by definition, is the smallest positive floating-point value such that 1.0 + $MachineEpsilon > 1.0. The distance between 1.0e-300 and the next number up will be much smaller, while the distance between 1.0e+300 and the next number up will be much greater. In addition, there are issues raised by the transitions between one order of magnitude and the next. Observe that 1.0 + $MachineEpsilon/2 == 1.0, while 1.0 - $MachineEpsilon/2 < 1.0.

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David Zhang
David Zhang
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Does Mathematica have an equivalent of C's nextafter?

In C (and many other programming languages), there is a function

double nextafter(double x, double y)

which takes two (IEEE 754) floating-point numbers and returns the next representable floating-point number after x in the direction of y. What is the Mathematica equivalent of this function for MachinePrecision numbers?