[Numpy-discussion] [RFC] new function for floating point comparison

[Robert Kern]

On Thu, Oct 29, 2009 at 02:17, David Cournapeau
<david at ar.media.kyoto-u.ac.jp> wrote:
> Hi,
>
>    I have added a couple of utilities for floating point comparison, to
> be used in unit tests mostly, and would like some comments, especially
> from people knowledgeable about floating point.
>
> http://github.com/cournape/numpy/tree/new_ulp_comp
>
> The main difference compared to other functions is that they are
> 'amplitude-independent', and use IEEE-754-specific properties. The
> tolerance is based on ULP, and two numbers x, y are closed depending on
> how many numbers are representable between x and y at the given
> precision. The branch contains the following new functions:
>
>    * spacing(x): equivalent to the F90 intrinsic. Returns the smallest
> representable number needed so that spacing(x) + x > x. Spacing(1) is
> EPS by definition.
>    * assert_array_almost_equal_nulp(x, y, nulp=1): assertion is defined
> as abs(x - y) <= nulps * spacing(max(abs(x), abs(y))).
>    * assert_array_max_ulp(a, b, maxulp=1, dtype=None): given two
> numbers a and b, raise an assertion if there are more than maxulp
> representable numbers between a and b.

That sounds good. Another worthwhile addition would be nextafter().

http://www.opengroup.org/onlinepubs/000095399/functions/nextafter.html

With a little bit of care, a nextafter ufunc can be used to generate a
dense grid of floating point values around a given center. This can be
used to explore the error characteristics of a function at a very fine
level of detail that is otherwise unavailable.

-- 
Robert Kern

"I have come to believe that the whole world is an enigma, a harmless
enigma that is made terrible by our own mad attempt to interpret it as
though it had an underlying truth."
  -- Umberto Eco