Dear Regina, It is completely irrelevant how accurate the implementation is.
The problem is that: sin(10000000000000000) = a very accurate number sin(10000000000000000 + pi) = (-1) * (the very accurate number from above) The difference between those 2 numbers is only pi! BUT: pi might be too small with those BIG numbers! If Calc aproximates 10000000000000000 + pi as 10000000000000000, because it cannot store (10000000000000000 + pi) to the relevant digit, then you get bullshit and sinus cannot be computed accurately. Lets give another example: sin(10^16 * pi) = 0 sin(10^16 * pi + pi/2) = -1 However, if the accuracy of storing 10^16 * pi + pi/2 is less than pi/2, then the actual computed result will be anything between -1 and +1, without any resemblance to the truth. And it does NOT depend on the accuracy of the math library. It depends on how Calc stores the number: 10^16 * pi + pi/2. How many decimals are sotred? If it is inaccurate even to the first decimal or, even worse, the first digit (pi/2 ~ 1.57), then it does NOT make sense to compute the sinus of it. I hope this explains why there must be an upper limit (unlike monotone functions, where the value is continuously changing in a single direction, sinus is not a monotone function). Sincerely, Leonard Mada -------- Original-Nachricht -------- > Datum: Sun, 09 May 2010 18:07:22 +0200 > Von: Regina Henschel <[email protected]> > An: [email protected] > Betreff: Re: [sc-dev] constraint of x in sin(x) in scaddins > 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 > >> > >> > >> --------------------------------------------------------------------- > >> To unsubscribe, e-mail: [email protected] > >> For additional commands, e-mail: [email protected] > > > > > --------------------------------------------------------------------- > To unsubscribe, e-mail: [email protected] > For additional commands, e-mail: [email protected] -- GRATIS für alle GMX-Mitglieder: Die maxdome Movie-FLAT! 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