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by testaccount282 days ago |
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upvoteby NooneAtAll32 days ago|
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yeah, it's annoying that author talks about RPN notation, but only gives found formulas in form of images

looks like it computes ln(1)=0, then computes e-ln(0)=+inf, then computes e-ln(+inf)=-inf

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upvoteby testaccount282 days ago|
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ah, the paper acknowledges this. my bad for jumping to the diagrams!
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upvoteby Rubicund2 days ago|
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On page 11, the paper explicitly states:

> EML-compiled formulas work flawlessly in symbolic Mathematica and IEEE754 floating-point… This is because some formulas internally might rely on the following properties of extended reals: ln 0 = −∞, e^(−∞) = 0.

And then follows with:

> But EML expressions in general do not work ‘out of the box’ in pure Python/Julia or numerical Mathematica.

Thus, the paper’s completeness claim depends on a non-standard arithmetic convention (ln(0) = -∞), not just complex numbers as it primarily advertises. While the paper is transparent about this, it is however, buried on page 11 rather than foregrounded as a core caveat. Your comment deserves credit for flagging it.

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upvoteby adrian_b2 days ago|
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I would not call a "non-standard arithmetic convention" that ln(0) = -∞.

This is the standard convention when doing operations in the extended real number line, i.e. in the set of the real numbers completed with positive and negative infinities.

When the overflow exception is disabled, any modern CPU implements the operations with floating-point numbers as operations in the extended real number line.

So in computing this convention has been standard for more than 40 years, while in mathematics it has been standard for a couple of centuries or so.

As always in mathematics, when computing expressions, i.e. when computing any kind of function, you must be aware very well which are the sets within which you operate.

If you work with real numbers (i.e. in a computer you enable the FP overflow exception), then ln(0) is undefined. However, if you work with the extended real number line, which is actually the default setting in most current programming languages, then ln(0) is well defined and it is -∞.

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upvoteby zarzavat2 days ago|
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Apparently Python throws an exception. This surprised me, I expected it to only throw for integers. Throwing for floats is weird and unsafe.

    >>> import math
    >>> math.log(0.0)
    Traceback (most recent call last):
      File "<python-input-2>", line 1, in <module>
        math.log(0.0)
        ~~~~~~~~^^^^^
    ValueError: expected a positive input, got 0.0
though if you use numpy floats you only get a warning:

    >>> import numpy as np
    >>> np.log(np.float64(0))
    <python-input-1>:1: RuntimeWarning: divide by zero encountered in log
    np.float64(-inf)
JavaScript works as expected:

    > Math.log(0.0)
    -Infinity
    > Math.log(-0.0)
    -Infinity
    > Math.log(-0.1)
    NaN
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upvoteby Rubicund2 days ago|
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The author does address this further on page 14 of SI and provides an alternative of:

−z = 1 − (e − ((e − 1) − z))

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