Hi Leonard,
it seems, that I have not been clear enough. sin() is a function in the
math library of C and C++ compilers and is nowadays accurate in double
precision up to x<2^64. To prevent larger arguments the special
implementation ::rtl::math::sin() is used in OOo. But inside the
implementation of IMSIN() in the module scaddins a constraint
"x<134217728" is used. I only want to know, why this has been
introduced. I doubt, that this restriction is still necessary.
I know, that a lot of binary values give different results for sin(),
although they are shown with the same decimal values in 15 digit
precision (the highest precision Calc UI has). But that is not central
point of my question.
kind regards
Regina
Leonard Mada schrieb:
Dear Regina,
I believe that sin() should have as constraint the largest float
(or integer) that fulfills the following condition:
sin(max) = correct result + epsilon
sin(max + lambda) = correct result + epsilon ,
where lambda is a float in the interval (0, pi/2).
Let me explain this a little bit.
sin: [any float] -> [-1, 1]
sin(pi/2) = 1
sin(pi/2 + pi/2) = 0
So basically, if we want to compute sin() at some precision,
we have to guarantee that the number we compute the sinus of,
can be accurately represented. Else, we risk a total fiasco, because
sin(a_very_big_number) may correspond to any value in [-1, +1],
as the last digits in a_very_big_number are not accurate.
So, big_number +/- pi/2 may be represented as big_number,
although the sinus would have different signs for those
"theoretically" different numbers.
Therefore, the number which still makes sense to compute the sinus off,
should fulfill the requirements set above.
We still need to determine what values lambda and epsilon take,
but I hope that the general idea is clear.
Basically, this also depends on the implementation of general numbers
in the particular software (Calc in this example).
Some may store 16 decimal digits, so 1.xxx * 10^16 is still ok
to compute the sin() (or marginally so), some may store 32 digits,
so 1.xxx * 10^32 would be fine in that case.
I believe that lambda should be not bigger than pi/4,
while epsilon is flexible in this case (e.g. 10^-6 is probably
sufficient).
Sincerely,
Leonard Mada
-------- Original-Nachricht --------
Datum: Sat, 08 May 2010 21:02:45 +0200
Von: Regina Henschel<[email protected]>
An: Calc dev<[email protected]>
Betreff: [sc-dev] constraint of x in sin(x) in scaddins
Hi all,
I have notice a constraint "SinOverflow" (which is x>=134217728) in
analysishelper.cxx in scaddins. What is the special reason for it?
In other places with sin() the version ::rt::math::sin() is used to get
a guard for overflow. That would result in constraint
x<=9,22337203685478E+018, which is much larger.
If there is no special reason, should I replace it, while I work on the
missing complex trigonometric functions?
kind regards
Regina
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