Java equivalent to Matlab's `eps` or Numpy/Python's `spacing` function (floating-point relative accuracy)

Question

Background

Matlab's built-in eps function [1] can take a numeric value X and return "the positive distance from abs(X) to the next larger in magnitude floating point number of the same precision".

>> eps(1)
ans =
   2.2204e-16
>> eps(single(1))
ans =
   1.1921e-07
>> eps(1e6)
ans =
   1.1642e-10
>> eps(single(1e6))
ans =
       0.0625

Equivalently, Numpy provides the spacing function [2]:

In [18]: import numpy as np

In [19]: np.spacing(1)
Out[19]: 2.2204460492503131e-16

In [20]: np.spacing(np.single(1))
Out[20]: 1.1920929e-07

In [21]: np.spacing(1e6)
Out[21]: 1.1641532182693481e-10

In [22]: np.spacing(np.single(1e6))
Out[22]: 0.0625

Question

Is there an equivalent function in Java (and therefore JVM languages like Clojure)?

References

• [1] http://www.mathworks.com/help/matlab/ref/eps.html
• [2] Documentation at https://github.com/numpy/numpy/blob/master/numpy/core/code_generators/ufunc_docstrings.py#L2905.
  • The actual function implementation in C seems to be at https://github.com/numpy/numpy/blob/master/numpy/core/src/npymath/ieee754.c.src#L323 (the license banner before npy_nextafter gives my question some irony).

Answer 1

You want java.lang.math.ulp:

Returns the size of an ulp of the argument. An ulp of a double value is the positive distance between this floating-point value and the double value next larger in magnitude. Note that for non-NaN x, ulp(-x) == ulp(x)

Also, available for floats. Some background on ULPs.