[Bug 10073] Problems with the definitions of the trigonometric functions (math:)

http://www.w3.org/Bugs/Public/show_bug.cgi?id=10073





--- Comment #11 from dnovatchev@gmail.com  2010-07-05 18:36:41 ---
(In reply to comment #10)
> >returned result must have all of its k decimal digits
> A definition that relies on converting the result to decimal digits seems only
> to add difficulty; it's better to define the double result without reference to
> its decimal equivalent. I don't think there's a real problem with the
> testability of the current definition. For example, consider sin(0.5e0) (for
> which Java gives 0.479425538604203) 
> (a) Wolfram Alpha gives us the exact result
> 0.4794255386042030002732879352155713880818033679406000675...,
> (b)
> xs:string(xs:double(0.4794255386042030002732879352155713880818033679406000675))
> is 0.479425538604203 which is a bit smaller
> (c) the rules therefore also allow the next double greater than this, which we
> can find by translating to the internal form 3fdeaee8744b05f0, adding one to
> give 3fdeaee8744b05f1, and translating back to a double which displays as the
> decimal 0.47942553860420306. The two acceptable answers for sin(0.5) are
> therefore these two xs:double values, so we can write the test as 
> sin(0.5) = (xs:double(0.479425538604203), xs:double(0.47942553860420306))
> We can write the above as the test query and "true" as the expected result.
> Of course the test results can be challenged if anyone believes that either the
> Wolfram Alpha result or any of the subsequent inferences is wrong.

I agree with this example of how testing is to be done correctly. 

Probably the current definition should be ammended to specify at least a hint
of a testing approach, adding that the value of the "mathemathical function" is
well approximated by well-known reliable resources such as Wolfram Alpha and ..
(at least two need to be listed in order to avoid any bias or overreliance).

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Received on Monday, 5 July 2010 18:36:43 UTC