[xsl] Is this the best way to compute a sigmoid function?

Subject: [xsl] Is this the best way to compute a sigmoid function?
From: "Costello, Roger L. costello@xxxxxxxxx" <xsl-list-service@xxxxxxxxxxxxxxxxxxxxxx>
Date: Sat, 2 May 2020 17:55:28 -0000
Hi Folks,

I have a variable $x that has a value such as 0.6

I want to compute the result of evaluating this sigmoid function:

(1 + e**-x)

That is, compute 1 divided by (1 + e raised to the -x power)

I am using the exp template in Dimitre's FXSL library.

[Dimitre, incredible library]

I created a wrapper function that simply calls Dimitre's exp template:

<xsl:function name="f:e" as="xs:decimal">
    <xsl:param name="x" as="xs:decimal" />

    <xsl:call-template name="exp">
        <xsl:with-param name="pX" select="$x" />

Then I computed the sigmoid function this way:

<xsl:variable name="e-to-the-minus-x-power" select="f:e(-$x)" as="xs:decimal"
<xsl:value-of select="1 div (1 + $e-to-the-minus-x-power)"/>

When $x has the value 0.6 I get this result: 0.645656306189717285

Do you see any errors in how I am computing the sigmoid function?

Is there a better way to do it? That is, one that returns more accurate
results? (However, it already appears to be mighty accurate -- look at all
those digits to the right of the decimal point) Notice that for the variable
$e-to-the-minus-x-power I specified it this way: as="xs:decimal". Should I
have specified it this way: as="xs:float" instead? Would that yield
better/more-accurate/more-reliable/more-whatever results?

Any suggestions you might have would be greatly appreciated.


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