Float precision and float equality

[Mark Dickinson]

On Dec 7, 12:16 am, David Cournapeau <courn... at gmail.com> wrote:
> If you can depend on IEEE 754 semantics, one relatively robust method
> is to use the number of representable floats between two numbers. The
> main advantage compared to the proposed methods is that it somewhat
> automatically takes into account the amplitude of input numbers:

FWIW, there's a function that can be used for this in Lib/test/
test_math.py in Python svn;  it's used to check that math.gamma isn't
out by more than 20 ulps (for a selection of test values).

def to_ulps(x):
    """Convert a non-NaN float x to an integer, in such a way that
    adjacent floats are converted to adjacent integers.  Then
    abs(ulps(x) - ulps(y)) gives the difference in ulps between two
    floats.

    The results from this function will only make sense on platforms
    where C doubles are represented in IEEE 754 binary64 format.

    """
    n = struct.unpack('<q', struct.pack('<d', x))[0]
    if n < 0:
        n = ~(n+2**63)
    return n

--
Mark