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Hi Ken, among others, you wrote this:
"Some software packages will use double precision floating point numbers
to
help improve the accuracy of floating point representation. As I said,
this
comes at the cost of double the memory requirements."
What one should think is it is completely unnecessary to store the
OHLC data in doubles. The opposite often is true, for example for
the S&P cash where one number after the comma would be MORE
than what is really useful.
Instead, it would be required to do the calculations using doubles!
Even to the final result could be applied the same, so, that is NOT
the problem. Instead, lots of algorithms use transforms that require
as much precision as possible *during the calculations*. This very
commonly known topic relates to the numeric stability of algorithms,
so, while very interesting and easy algorithms in terms of pure math
are very well known it is impossible to actually USE them because they
are unstable in *numeric* terms. That is also true if the input of the
time series would be e.g. "4,5,6,7,5,7,9,7,4,5,7...", i.e. the input
is represented in something "like no precision" at all (-:).
Conclusion is, your statement is false since it is *not* the precision
of the representation of the input does count in and thus enhance the
storage requirements BUT the precision of the representation of
the math that is done *internally*.
I hope I don't fail here, if so, please let me know
Thanks and Regards - jr
----- Original Message -----
From: "PD Manager" <pdmanager@xxxxxxxxxxxxxxxxx>
To: <metastock@xxxxxxxxxxxxx>
Sent: Dienstag, 5. September 2000 17:52
Subject: RE: First calculation problem
> As an additional piece of information, please reference the following
> document:
>
> http://www.cpearson.com/excel/rounding.htm
>
> Ken Hunt
> Programming Manager
> Equis International
>
>
> -----Original Message-----
> From: PD Manager [mailto:pdmanager@xxxxxxxxxxxxxxxxx]
> Sent: Tuesday, September 05, 2000 8:41 AM
> To: 'metastock@xxxxxxxxxxxxx'
> Subject: RE: First calculation problem
>
>
> Guy:
>
> Regardless of where the numbers come from (download, keyboard or wherever)
> the error occurs when the numbers are translated from the ASCII
> representation and stored in the machine. The other software packages
> suffer from the same problem. What they have chosen to do is to
> automatically mask the problem by truncating the OUTPUT before display. I
> assure you that INTERNALLY, the numbers are the same. MetaStock does not
> modify the output numbers. Regardless of the software package, the
internal
> storage is a HARDWARE approximation of a floating point number. Some
> software packages simply truncate and round the output BEFORE DISPLAY to
> mask the problem away from the user. The approximation and the associated
> accuracy problems are still there.
>
> Some software packages will use double precision floating point numbers to
> help improve the accuracy of floating point representation. As I said,
this
> comes at the cost of double the memory requirements.
>
> Ken Hunt
> Programming Manager
> Equis International
>
>
> -----Original Message-----
> From: Guy Tann [mailto:grt@xxxxxxxxxxxx]
> Sent: Monday, September 04, 2000 6:28 PM
> To: metastock@xxxxxxxxxxxxx
> Subject: RE: First calculation problem
>
>
> Ken,
>
> Sorry for the delay, but my DSL modem crapped out and then I was visiting
> Murder City until today.
>
> I wasn't typing anything into the computer. I used Equis' Downloader and
> Reuter's data service to download my data. I then use MS to massage it.
> Interestingly, TAS uses the Downloader data as well without any of these
> problems. Using OLE to access the data in Excel works properly as well.
It
> appears that these other software packages manage to keep track of the
> correct number of decimal places, whereas MS just sort of goes with the
flow
> and takes whatever it might find stored. I really don't care as long as I
> know that accuracy isn't one of MS' strong suits. I can understand your
> points, but in working with many programming languages, they all manage to
> do something to keep track of significant digits without barfing. Again,
if
> I was doing anything complex, I could understand your point completely,
but
> the inability to subtract two numbers and consistently come up with the
> correct answer is still hard for me to fathom.
>
> Anyway, here is a sample of some of the code I've had to use to get around
> this in one instance. By the way, none of my other programming languages
or
> Excel require these mechanizations. It appears that MS was designed as a
> charting or graphics program with computational capabilities added as an
> afterthought. What we need to remember is that if we want to use it as
> such, we'll need to work around its deficiencies ourselves.
>
> COMN0:= C - COMMODLOW; {simple subtraction of C - L}
> COMN:= PREC( If( COMN0 > 0 , (COMN0+.005), If( COMN0 < 0 , (COMN0 - .005 )
,
> COMN0 )) , 2 ); {needed to fix MS inability to maintain significant
digits}
> COMN1:= COMN / COMAR; {simple divide}
> COMN2:= COMN1 - .5; {Simple subtraction}
> COMN3:= COMN2 * 2; {simple multiplication}
> COMN3R:= If( COMN3 > 0 , (COMN3 + .00005 ) ,
> If( COMN3 < 0 , (COMN3 - .00005 ) ,
> 0 ) ); {rounding to 4 decimal places performed manually}
> COMN4:= ( PREC( COMN3R, 4 ) * 10); {take answer to 4 decimals and
multiply
> by 10}
> COMN5:= If( COMN4 > 0 , ( COMN4 ) + .5 , If( COMN4 < 0 , ( COMN4 ) - .5 ,
> ( COMN4 ) )); {round to nearest whole number}
> COMY:= Int( COMN5 ); {store integer}
>
> This does work, albeit in a slightly confused manner and requires 8 more
> variables than it should. Using this fixed the one erroneous calculation
I
> had and let me move on for further testing.
>
> OTOH, I am now working on trying to get the Ref() function to work per the
> manual and will try to get some time to spend on it tonight if I can stay
> awake. I was up at 4AM Detroit time (1AM local time) and have over 400
> e-mails to wade through since 8/29 (most of which I deleted).
>
> Guy
>
> " When I die, I want to go peacefully like my grandfather did, in his
sleep.
> Not yelling and screaming like the passengers in his car."
>
> -----Original Message-----
> From: owner-metastock@xxxxxxxxxxxxx
[mailto:owner-metastock@xxxxxxxxxxxxx]On
> Behalf Of PD Manager
> Sent: Tuesday, August 29, 2000 10:05 AM
> To: 'metastock@xxxxxxxxxxxxx'
> Subject: RE: First calculation problem
>
> Guy:
>
> The precision error occurs as soon as the number is stored in your
computer.
> If you are typing a number into a computer (such as 12.1), as soon as that
> number is stored in a single precision floating point number in your
> computer, the precision error is there. The number is already stored as
an
> approximation. This is a CPU / hardware issue and is not related to the
> software itself.
>
> Most software will mask this error by doing rounding of a floating point
> number before it is displayed. In the case of the 1469.3999999, if you
ask
> a computer to display that number with two digits to the right of the
> decimal point, rounding occurs and you will see 1469.40, but the number is
> actually stored in the computer as 1469.3999999. This is true even if you
> entered a number at the keyboard (or downloaded the number or read it from
> some other source) that was 1469.40.
>
> The difference between MetaStock and your other packages is that the other
> software is performing the rounding before the results are displayed on
the
> screen. MetaStock is not doing this and is displaying the numbers out to
> the maximum possible length. I assure you that if other software packages
> are displaying 1469.40, the internal representation is actually
> 1469.3999999. The approximation and actual storage of the numbers is a
> function of the CPU hardware and not the software package itself.
>
> Ken Hunt
> Programming Manager
> Equis International
>
>
> -----Original Message-----
> From: Guy Tann [mailto:grt@xxxxxxxxxxxx]
> Sent: Monday, August 28, 2000 12:34 PM
> To: metastock@xxxxxxxxxxxxx
> Subject: RE: First calculation problem
>
>
> Ken,
>
> I guess I still don't understand what's happening here.
>
> These numbers were downloaded from Reuters and were stored in the O, H, L,
C
> data arrays, all handled internally by Equis. My assumption is that these
> numbers were downloaded properly and that they contain only the two
decimal
> places shown in the data and in the data window. Going out and looking at
> the numbers in Downloader and in the related Chart supports that
assumption.
> Is that an invalid assumption? These numbers only have two decimal places
> to begin with. Did MS somehow managed to "modify" the original input and
> store them as something like 1469.3999999?
>
> If that's the case, then using Precision in order to insure that simple
> arithmetic calculations to maintain the two decimals places appears to be
a
> requirement.
>
> Generally, there are very few problems occurring, but they are sufficient
to
> throw off some of our results.
>
> We have these calculations running in Clipper, Excel, COBOL, and TAS
without
> problems.
>
> We only have three different levels of precision in our system and they
are
> 0, 2, and 4. We either use the Rnd() function or in cases like the one
I'm
> working on right now, manually code our own rounding.
>
> Guy
>
> " When I die, I want to go peacefully like my grandfather did, in his
sleep.
> Not yelling and screaming like the passengers in his car."
>
> -----Original Message-----
> From: owner-metastock@xxxxxxxxxxxxx
[mailto:owner-metastock@xxxxxxxxxxxxx]On
> Behalf Of PD Manager
> Sent: Monday, August 28, 2000 8:15 AM
> To: 'metastock@xxxxxxxxxxxxx'
> Subject: RE: First calculation problem
>
> Isn't programming with floating point numbers fun? <g>
>
> Floating point errors tend to compound as more calculations are performed.
> I could write an entire book on the subject (I'm sure there are books
> written on just this subject). Typically, floating point numbers are
> guaranteed to have 6-7 digits of precision. When you start doing
> mathematical operations on these numbers, there are times when some of
these
> strange issues will creep in.
>
> What I have found is that you should use the precision function only if
you
> are trying to compare floating point numbers. Otherwise just stick with
the
> standard calculations.
>
> What is amazing is that although your numbers look good to start with
> (1486.20 and 1469.40) the error is probably already there. The actual
> numbers stored in the computer may already be something like
(1486.20000001
> or 1469.3999999). Usually when these numbers are prepared for output
> (display or printed) the software will perform rounding to get them to
look
> like the numbers you entered. When you perform a mathematical operation
on
> these numbers, the error becomes more apparent so that the rounding before
> output didn't make your result look correct.
>
> Virtually any computer that stored floating point numbers has this
problem.
> I worked on flight simulations for several years and the only way we could
> get around the problem was to do EVERYTHING in integer math and keep track
> of assumed decimal points.
>
> Ken Hunt
> Programming Manager
> Equis International
>
>
> -----Original Message-----
> From: Guy Tann [mailto:grt@xxxxxxxxxxxx]
> Sent: Sunday, August 27, 2000 1:50 AM
> To: metastock@xxxxxxxxxxxxx
> Subject: RE: First calculation problem
>
>
> Ken,
>
> Are you saying that I need to add the prec() function to each one of my
> variable calculations? Does this problem compound when building systems
> using calculations upon calculations or will the prec() function used at
> each level take care of the problem?
>
> Guy
>
> Never be afraid to try something new. Remember, amateurs built the ark,
> professionals built the Titanic.
>
> -----Original Message-----
> From: owner-metastock@xxxxxxxxxxxxx
[mailto:owner-metastock@xxxxxxxxxxxxx]On
> Behalf Of PD Manager
> Sent: Friday, August 25, 2000 7:35 AM
> To: 'metastock@xxxxxxxxxxxxx'
> Subject: RE: First calculation problem
>
> MetaStock does indeed use single precision floating point numbers. As you
> mentioned, going to double precision would literally double the memory
> requirements for data storage for charts and would also slow down
> calculations. When you get into mathematical calculations, however, going
> to double precision doesn't necessarily make the problem better. PC
> computer hardware still cannot accurately store a number as simple as 0.1
> whether you are using single or double precision. It is stored as an
> approximation. When it comes to floating point numbers, the hardware can
> really only accurately store fractional numbers that are powers of two
(1/2,
> 1/4, 1/8, 1/16 etc).
>
> Other software packages suffer from the same problem (including VB and
> Excel) although some manage to mask it better than others. If you don't
> believe this, I can submit a set of "simple" calculations that will cause
> Excel to show precision errors also.
>
> Some software packages will use other methods to store and/or calculate
> floating point numbers. This usually involves something like BCD encoding
> or some type of integer encoded fixed point real numbers. While this
> ultimately solves the precision problem, it has other problems with speed
of
> calculations as well as a reduced ability to store large or very small
> numbers.
>
> We have always been aware of this issue and that is why we added the
> precision function to the formula language. It was put there in an
attempt
> to help those writing formulas to work with the precision they needed.
>
> Ken Hunt
> Programming Manager
> Equis International
>
>
> -----Original Message-----
> From: Kent Rollins [mailto:kentr@xxxxxxxxxxxxxx]
> Sent: Friday, August 25, 2000 12:40 AM
> To: metastock@xxxxxxxxxxxxx
> Subject: Re: First calculation problem
>
>
> Looks like you may have hit the old single-precision problem. PCs
basically
> have 3 native ways of storing floating point numbers: single-precision (4
> bytes), double-precision (8 bytes), and long double (10 bytes). The
problem
> is that each one of these representations has a limited number of
"numbers"
> that it can represent and from time to time you will hit a calculation
that
> reveals this limitation in all it's splendor. Single-precision floats can
> represent approximately 4 billion different numbers. That's a lot until
you
> consider that between 0 and 1 there are an infinite number of floating
point
> numbers. Double-precision has many, many more number that it can
represent
> (4 billion times 4 billion) and you RARELY see the kind of error you have
> hit when you are dealing with numbers on the scale of 1486 with only 2
> places of precision. That leads me to suspect that Equis is using
> single-precision numbers for these calculations (Omega does the same
thing).
> Saves memory, SLIGHTLY faster in computation, loses precision. There is
> really no good reason for using singles in an app like this and there is a
> (now obvious) good reason not to. I would scream and yell at Equis. Tell
> Little Guy that if he convinces Equis to use doubles you'll buy him a pony
> and then drop him off in the programmer's offices.
>
> Ken Hunt, does MetaStock use single precision for these calculations?
>
> Kent
>
>
> -----Original Message-----
> From: Guy Tann <grt@xxxxxxxxxxxx>
> To: Metastock User Group <metastock-list@xxxxxxxxxxxxx>
> Date: Friday, August 25, 2000 1:29 AM
> Subject: First calculation problem
>
>
> List,
>
> Well, I decided to do a little more work and discovered my first problem.
>
> Somehow, MS came up with the following:
>
> 1486.20
> - 1469.40
> 16.7999 instead of the more commonly expected 16.80
>
> Now the first number is the Close and the second number is the day's low,
so
> we can't blame this on any previous calculation or anything left over from
> something else. Well, that's not quite true. The Low used in the
> calculation was the result of an IF() statement that made sure that the
Low
> was really the Low by our definition (by checking it against the previous
> day's Close).
>
> What internal methodology might cause this excellent bit of subtraction?
>
> Granted, in checking out the 170-member dataset, I didn't check them all.
I
> checked the first 20 and the last 20. Now I'll probably have to go back
and
> sample some in the middle.
>
> I used my trusty, solar powered calculator to double-check my Clipper
output
> and they both agree that MS is wrong. Any suggestions?
>
> This is making me very nervous and might force me back to Excel and/or VB.
> So far I've spent over two week on this relatively simple program and I
have
> to admit that I never thought it would be necessary to go back and
> double-check such basic arithmetic.
>
>
> Guy
>
> Never be afraid to try something new. Remember, amateurs built the ark,
> professionals built the Titanic.
>
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