Re: WMS FORTRAN: what are SIND, COSD, etc?

James Giles wrote: 
Rich Townsend wrote:
...

I disagree; I would be very happy if SIN(ACOS(-1.)) returns zero. Why
would that be an error?



I wouldn't be very happy with that at all.  Suppose I explicitly
input a representable number that's very close to the transcendental
number pi. That number isn't pi, but it's close.  The sine of that
number is not zero.  In fact, it's further from zero than the smallest
representable floating-point value (by a very large margin).  When
I apply SIN to that number I expect an accurate calculation of
the sine of the input value - I do *NOT* want the implementation
to guess that I must really have meant pi!  It's perfectly plausible
that I didn't mean pi at all, but some value that was, in a way that's
important to my problem, explicitly different from pi.


Some might want a value that is near 3.14 and has a sin() of zero.
Especially those multiplying a value by pi/180 before sending it to sin().

Now, since the SIN function have no way of detecting where its
argument came from, any result of a claculation that generates that
same "nearly pi" value must return the same value for SIN as rthe
explicitly input argument did.  To do otherwise complicates
numneric stability calculations intolerably.  Do you really want
to have to guess about what guesses the implementation made
about your computation?  Or would you rather have all operations
be well-defined and operate consistently?


On the other hand, I would expect a proper implementation of
SIND(ACOSD(-1.0)) to compare exactly equal to zero.


That would be nice.

-- glen

.

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