Apart from determining the value of G or the fine constant, or a few other
esoteric determination of funadamental constants, what practical issues require
more than 7-8 significant figures of precision?
Yes, some interplanetary differentials might at times. (Our moon recedes from
us as fast as your fingernails grow, and GPS internals can need sub-nanosecond
differential time intervals) but what ones we might encounter in the XML world.
The ‘fetish’ of chasing decimal places in most, but not all, cases shows a
lack of understanding of the essence of the problem.
The (artificial) epitome of this is the well-trodden problem of a railway
around the world that must be lifted up 1 cm, but stays circular... how much
more rail is needed?
‘Where angels fear to tread’ rush in with finding the difference by
2*pi*6,357,000.01 - 2*pi*6,357,000
which requires 9-10 places of numerical precision (i.e. approaching 30 bits of
mantissa) neglecting the deeper structure of the mathematics..
John Lumley
john(_at_)johnlumley(_dot_)net
On 2 May 2020, at 19:09, Michael Kay mike(_at_)saxonica(_dot_)com
<xsl-list-service(_at_)lists(_dot_)mulberrytech(_dot_)com> wrote:
On 2 May 2020, at 18:55, Costello, Roger L. costello(_at_)mitre(_dot_)org
<xsl-list-service(_at_)lists(_dot_)mulberrytech(_dot_)com> wrote:
I want to compute the result of evaluating this sigmoid function:
1
----------------
(1 + e**-x)
That is, compute 1 divided by (1 + e raised to the -x power)
In recent versions of XPath, you can simply do
(1 div (1 + math:exp(-$x)))
(However, it already appears to be mighty accurate -- look at all those
digits to the right of the decimal point)
I hope you don't seriously believe that precision implies accuracy - that
someone who claims the population of the world is 7,345,651,523 is more
likely to be right than someone who says it is 7 billion.
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?
For calculations like this it's best to use xs:double. You don't need any
more precision than this, and exponential/trigonometric functions are likely
to be implemented as double-precision floating point by whatever underlying
library is used.
Michael Kay
Saxonica
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