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That was one of the funniest hurmourus positings for a long time. Pierre is
accusing Bob, who is always very helpful and knowledgable, for beeing
unobjective and not listening. :-)
At the same time he is explaining the likelihood that the old sloppy
Tradestation math engine is kept since the new processors that have come
around since the dawn of the TS4 are still as sensitive to the same speed
limitations as they were at that time. Remember the old record lable
"listening to his masters voice...". It is a very old record... :-)
> -----Original Message-----
> From: pierre.orphelin [mailto:pierre.orphelin@xxxxxxxxxxxxxx]
> Sent: den 28 juli 2001 02:08
> To: omega-list@xxxxxxxxxx
> Subject: RE: TradeStation Precision - Summary
>
>
> This is very kind to you, but I suspect that your current
> gripe against TRAD still continue to produce some negative
> side effects, because you do not want to take in account what
> I explained to you. So, here are the fix of the few errors in
> your summary post. Most of you forget what is the precision
> carried by the original data
> price) and what is the precison expected from any
> calculationthat derives from the original prices. It'sad, but
> it's true...
>
> > -----Message d'origine-----
> > De : Bob Fulks [mailto:bfulks@xxxxxxxxxxxx]
> > Envoye : jeudi 26 juillet 2001 21:16
> > A : omega-list@xxxxxxxxxx
> > Objet : TradeStation Precision - Summary
> >
>
> > SUBTRACTING TWO NEAR-EQUAL NUMBERS
> >
> > There are a lot of functions that subtract two prices to
> find a small
> > difference between the two. For example, The Dow Jones Industrial
> > Average (DJIA) is at about 10300 so
> >
> > 10323.45 - 10321.20 = 2.25
> >
> > is accurate to about 3 digits which is probably OK.
>
> ======1========
> IT IS OK, and by far!
> The DJ is known with a (roughly) relative max precision of
> 0.01 /10 000 = 10^-6 . Absolute error carried by DJ is 0.01
>
> When you perform DJ-DJ[1], the absolute error E is the SUM of
> the errors of boths terms. So E(DJ-DJ[1])= E(DJ)+E(DJ[1])= 2.10^-2.
>
> The relative error will be:
> E(DJ-DJ[1])(DJ-DJ[1])= 2.10^-2 /2.5 # roughtly 10^-2
> far above of the 10^-7 TS relative precision!!!!!
>
> ===========2============
> If now you perform the difference of the squared values S,
> the error "E" must be evaluated from: S= X2-Y2
> E(S) = E(X2)+E(Y2)
>
> Where E(X2) must be evaluated by using the relative error:
>
> E(X2)/X2 = E(X)/X +E(X)/X=
> E(X2) = 2*E(X)/X * X2
> E(X2) = 2*X*E(X)
>
> Same brings E(Y2)= 2*Y*E(Y)
>
> E(S) = E(X2)+E(Y2) = 4*X*E(X) roughly because X and Y are
> very close ( they are DJ and DJ[1]).
>
> So, the final precision for a correct calculus of a
> difference of two close squared numbers is, for the DJ:
> E(S) =4* 10^4* 10^-2 = 4* 10 ^2
> (This of course apply to a squared sum too).
>
> Knowing that X and Y are very close, |S|= X2-Y2 = 2*|X-Y|= 5
> ( roughly)
>
> The relative error of the difference is:
>
> E(S)/S= 4*X*E(X)/2*|X-Y|
>
> ______________________
> E(S)/S= 2*X*E(X)/|X-Y| (I)
> ----------------------
> =2*10^4*10^-2/5 = 4*10^1 = 40 (4,000% in this case)
>
> Now the relative error carried by a TS Float being between
> around 10^-7
> 0.00001%), the squared sum or difference is perfectly exact,
> because the relative error E is not destroyed by the relative
> error from the TS Float intrinsic error, far, far below...
>
> ===========3==========
> For a sum S = X2+Y2, the relative error will be :
> E(S)/S= 4*X*E(X)/2*X2 =
>
> _________________
> E(S)/S = 2*E(X)/X (II)
> -----------------
>
> = 2* 10^-2 /10^4 = 2* 10-6 =0.00002%
>
> Compare the results from I and II and you will see that the
> relative error has nothing to do with a sum of squared and a
> difference of sqared values, and that in any case, the TS
> precision do not damage the precision of the calculus.
>
> Your main error is that you do not understand that if a
> price like DJ is 1000.25, it means that you can write it
> 1000.25***** where **** is garbage translate , by unknown,
> impossible to determine..) It's a nonsense to consider that a
> price has more precision than the number of digit used to display it.
>
> The sequel is that any calculation that derives from prices
> must not use the garbage values of the original data, and
> must no use more precision ( 1 digit more is admitted) for
> intermediate calculus, because all of the precision that you
> expect beyond is garbage, and this is a consequence of the
> error evaluation that any physics student should know and not forget.
>
> Asking for doubles to add more garbage precision in the
> garbage part of the calculus is also a bigger nonsense. The
> TS choice was reasonable to use the type of float they use,
> because they know that the precision of the original material
> ( price) is far below their internal precision, period. No
> need to perform tests, this is the theory
>
>
>
>
> > But many
> > functions subtract the square of price or Price1*Price2 and
> these can
> > give very inaccurate results.
>
> They certainly have not the same precision than garbage
> values produced with 10 digits after the expected level of precision.
>
>
>
> > SUMMARY
> >
> > The use single-precision floating point was probably a good design
> > decision when memory was expensive and TradeStation 4.0 was
> limited to
> > the 64K program size. Unfortunately, Omega did not write their
> > function library so that it produced accurate results with the
> > available arithmetic so the users must be alert for and
> "work-around"
> > such errors.
> >
> > Now days, memory is very much less expensive so most modern
> programs
> > use double-precision floating point arithmetic. Unfortunately Omega
> > retained the single-precision arithmetic in TS2000i so we
> still have
> > to worry about these issues.
>
>
> ========4==========
> I do not believe that it is related to 64K program size!
> This deals more probably with speed: Performing calculus with
> doubles ( 64
> bit) is certainly not as fast as with floats (32 bits),
> knowing that the computer does binary operation after all. So
> think twice if the speed to add two doubles is the same than
> to add two floats, and that it is not necessary to use this
> for 4 or 5 digits data prices).
>
>
> =======5=====For non maths oriented readers======
>
> If you do not understand the true meaning of physical
> precision experimental precision) and its consequences,
> please do this small
> experience:
>
> 1- Measure the lenght of your table very carefully with a
> ruler Write down the result in millimeters ( I supose that
> you will not achieve the 1/10 mm precision). For example,
> you have found L = 1531 mmm = 1.531 10^3 m
>
> 2- I have attached to this post a magic tool that you will
> use now: It is a small device that will add a single atom at
> the end of the table length. The size of this atom is ll= 2
> nanometer (2 *10^ -9 m)
>
> Now, do you think that you are authorized to say that the
> length of the modified table is the sum L+ll? Do you really
> think that the length of your table is now really 1.531000002 m ?
>
> If you are still saying "yes", please continue to ask for
> double precision in technical analysis software, because you
> like garbage, and you need more than what you currently have.
>
> Sincerely,
>
> Pierre Orphelin
> www.sirtrade.com
> TradeStation Technologies representative in France
>
>
>
>
>
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