Does Python have an equivalent to java.lang.Math.nextUp?

Question

I have a Python float, and I want to have the floats which are 1 ULP greater and lesser.

In Java, I would do this with Math.nextUp(x) and Math.nextAfter(x, Double.NEGATIVE_INFINITY).

Is there a way to do this in Python? I thought about implementing it myself with math.frexp and math.ldexp but as far as I know Python doesn't specify the size of floating point types.

Answer 1

Update: In Python 3.9+ there is math.nextafter():

>>> import math
>>> x = 4
>>> math.nextafter(x, math.inf)
4.000000000000001

---

^{Old answer:}

You could look at how Decimal.next_plus()/Decimal.next_minus() are implemented:

>>> from decimal import Decimal as D
>>> d = D.from_float(123456.78901234567890)
>>> d
Decimal('123456.789012345674564130604267120361328125')
>>> d.next_plus()
Decimal('123456.7890123456745641306043')
>>> d.next_minus()
Decimal('123456.7890123456745641306042')
>>> d.next_toward(D('-inf'))
Decimal('123456.7890123456745641306042')

Make sure that decimal context has values that you need:

>>> from decimal import getcontext
>>> getcontext()
Context(prec=28, rounding=ROUND_HALF_EVEN, Emin=-999999999, Emax=999999999,
capitals=1, flags=[], traps=[InvalidOperation, DivisionByZero, Overflow])

---

Alternatives:

• Call C99 nextafter() using ctypes:

    >>> import ctypes
    >>> nextafter = ctypes.CDLL(None).nextafter
    >>> nextafter.argtypes = ctypes.c_double, ctypes.c_double
    >>> nextafter.restype = ctypes.c_double
    >>> nextafter(4, float('+inf'))
    4.000000000000001
    >>> _.as_integer_ratio()
    (4503599627370497, 1125899906842624)
  

  Using numpy:

    >>> import numpy
    >>> numpy.nextafter(4, float('+inf'))
    4.0000000000000009
    >>> _.as_integer_ratio()
    (4503599627370497, 1125899906842624)
  

  Despite different repr(), the result is the same.

• If we ignore edge cases then a simple frexp/ldexp solution from @S.Lott answer works:

    >>> import math, sys
    >>> m, e = math.frexp(4.0)
    >>> math.ldexp(2 * m + sys.float_info.epsilon, e - 1)
    4.000000000000001
    >>> _.as_integer_ratio()
    (4503599627370497, 1125899906842624)
  

• pure Python next_after(x, y) implementation by @Mark Dickinson that takes into account edge cases. The result is the same in this case.

Answer 2

I am not sure if this is what you want, but sys.float_info.epsilon is the "difference between 1 and the least value greater than 1 that is representable as a float", and you could do x * (1 + sys.float_info.epsilon).

http://docs.python.org/library/sys.html#sys.float_info