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Yngvi:
I couldn't have said it better.
You are correct that the power users are the ones that understand the
program and how it could be made better.
Lionel Issen
lissen@xxxxxxxxx
----- Original Message -----
From: Yngvi Hardarson <hardy@xxxxxxxxxxxxx>
To: <metastock@xxxxxxxxxxxxx>
Sent: Thursday, September 07, 2000 2:29 PM
Subject: RE: First calculation problem
> Ken!
>
> (1) Wouldn't it be possible to leave it to the user to decide whether he
> wants
> to use single or double precision floating point calculations, e.g. via a
> setting in the Tools/Options menu?
>
> This would enable those with the hardware resources and accuracy
> requirements
> to use double precisions and others to stick with single precision. I
recall
> from
> my days using statistical and econometric software on mainframes that some
> of those
> applications actually gave you the choice of precision. Then my computing
> bill would
> depend on my choice as well as the time it took to complete the
> calculations.
>
> (2) You have stated that some requests for features brought up by members
of
> the list
> are not commonly requested by the mass of users. In my opinion the mass
> opinion doesn't
> matter as much as input from "power users" of this list. The mass doesn't
> realize what
> a tremendous value there would be in implementing some of the suggestions
> put forth on
> this front. The mass might realize the value once you implement the
features
> and the
> mass might become even bigger.
>
> Best regards,
> Yngvi Hardarson
> hardy@xxxxxxxxxxxxx
>
> P.s. Many thanks to you for sticking to the list Ken. I believe you may
have
> greater
> influence on the application features than you say yourself, directly or
> indirectly.
>
> -----Original Message-----
> From: owner-metastock@xxxxxxxxxxxxx
> [mailto:owner-metastock@xxxxxxxxxxxxx]On Behalf Of PD Manager
> Sent: Thursday, September 07, 2000 15:18
> To: 'metastock@xxxxxxxxxxxxx'
> Subject: RE: First calculation problem
>
>
> Guy:
>
> Through all the arguing both directions and all of the shots from people
on
> the sidelines it all boils down to the fact that we are using single
> precision floating point numbers and your other software is using double
> precision. Both methods have errors (as evidenced by your example and
> mine), but double precision does manage to provide more precision and
> therefore manages to hide the problem a little better.
>
> The differences you are seeing are based on the differences between single
> and double precision. As I have stated, we have considered going to
double
> precision but it comes at a cost in computer resources and therefore we do
> not take the decision lightly. Also, double precision does not guarantee
> absolute accuracy. If we went to double precision, we would only be
> duplicating the errors that appear in other double precision based
> applications. I would agree that the precision of MetaStock would indeed
> improve but if you are interested in ABSOLUTE accuracy of your
computations,
> you are going to have to avoid floating point calculations altogether,
> regardless of which software package you use. Unfortunately, to do that
you
> are going to have to use more traditional programming languages and write
> your own math routines that use scaled integers or BCD or something along
> those lines. You could do this with our MSX capability, but again, you
> would have to program at a lower level. Based on your credentials, I
don't
> think it would be a problem but only you could decide if it would be worth
> the effort.
>
> We all have to remember that engineers designed the floating point format
> (IEEE standard) and they can usually get away with "close enough". That
is
> unacceptable to the mathematicians however. The 8.999999999999999999
value
> is "close enough" to 9 for an engineer, but to a mathematician, it just
> doesn't work.
>
> I sympathize with your dilemma and I apologize if I have seemed too
> defensive about the issue. Believe me, I fight with the issue of
precision
> every day and I have thrown a few heated comments myself.
>
> We may indeed go to double precision numbers in the future but only if we
> can minimize the impact on the large percentage of our users who are
already
> "running on the edge" of their computer resource capacity. In the
meantime,
> I am finished with the jousting. If I can help you find the accuracy you
> want in MetaStock, I am more than willing to help. Feel free to email me
> privately and I will do all I can.
>
> Ken Hunt
> Programming Manager
> Equis International
>
>
> -----Original Message-----
> From: Guy Tann [mailto:grt@xxxxxxxxxxxx]
> Sent: Wednesday, September 06, 2000 5:38 PM
> To: metastock@xxxxxxxxxxxxx
> Subject: RE: First calculation problem
>
>
> Ken,
>
> Fine. I'll grant you your example. Now if you take the results of that
> cell and multiple it by some other cell, does Excel multiply by .9 or
> .899999999999? I'm interested in how Excel handles subsequent
calculations.
>
> In my tests, they appear to use the .9 as opposed to.8999999999 like MS,
> otherwise I wouldn't be able to create output that matches exactly the
> output from Clipper code and from TAS. All I know is that somewhere in
all
> three of these other languages, they have somehow managed to be able to
> "handle" any problems of this type. Right now I'm comparing my MS output
to
> output from Clipper (Spring97 version, I believe) running under DOS. I
had
> hoped that in working with a more "modern" language I could eventually
drop
> all of our DOS stuff.
>
> Ken, I guess what I'm saying is provide us with the same Floating Point
> Error Masking in Excel so that we can eliminate these problems. Let those
> who don't want it turn it off the same way Excel does.
>
> 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: Wednesday, September 06, 2000 8:02 AM
> To: 'metastock@xxxxxxxxxxxxx'
> Subject: RE: First calculation problem
>
> Guy:
>
> What I have been saying all along is that numerically, in your computer
> (regardless of which software you are using) there are floating point
> rounding errors. Here is an example for Excel 2000:
>
> 1. Enter the following in a cell: =(43.1-43.2)+1
> 2. Using the Format Cells command TO TURN OFF THE FLOATING POINT ERROR
> MASKING THAT EXCEL DOES BY DEFAULT, change the format of the cell to show
> Scientific 15-digits precision. This accurately displays the format that
> the number is stored in in your computer. There is no masking of the
output
> (to hide the floating point error inherent in all floating point
> calculations) before display.
> 3. Look at the result. To you and I it is supposed to be 0.9. Excel,
> however, shows that the internal floating point representation is
> 0.899999999999999.
>
> The errors that you worry about are always there. Excel, by default, sets
a
> cell format that hides these errors from you. In MetaStock, we chose not
to
> try and determine the absolute precision that anyone wanted to see. We
> provided the Round() and Prec() functions to let the formula writer
> determine that for themselves.
>
> Ken Hunt
> Programming Manager
> Equis International
>
>
> -----Original Message-----
> From: Guy Tann [mailto:grt@xxxxxxxxxxxx]
> Sent: Tuesday, September 05, 2000 6:53 PM
> To: metastock@xxxxxxxxxxxxx
> Subject: RE: First calculation problem
>
>
> Ken,
>
> All I'm saying is my point has absolutely nothing to do with rounding.
This
> calculation works, without fail, in Excel. To make sure, I went back and
> did a couple of thousand of them and Excel never made an error. Now, I
> don't know how they were handling it internally, I only know how they
> presented and used the results correctly and that's all I care about.
> Regardless of all of the documentation you have presented, only MS has the
> particular problem I have presented.
>
> The other software never once failed to subtract properly. They never
once
> failed to provide me with a two decimal result even if I specified a 4
> decimal precision result field. And finally, they never once failed to
use
> the correct result with future calculations (which I think is the most
> important point and what you are missing).
>
> Again, I think you are confusing effort with results. Regardless of how
you
> represent the number internally, you are displaying it wrong and you are
> using the wrong value in further calculations. If any of these other
> languages or packages performed such simple arithmetic functions like
> subtraction similarly to MS, they have smarter internal algorithms to
insure
> that the results as presented are correct and are used correctly
internally.
> Something that MS is missing.
>
> The Microsoft article you referred me referenced rounding. My situation
has
> nothing to do with rounding, other than with what you refer to as the
> implied internal processing. There is no rounding necessary when
> subtracting a 2 decimal number from another 2 decimal number. Now you can
> cop out saying that internally, single precision may or may not represent
> the values correctly. That's irrelevant. If I bought a $2.99 calculator
> and ran this calculation, the entire batch of calculators would be
scrapped
> as defective. I consider MS to be defective, just like those calculators,
> until this problem is fixed!
>
> Now, if I was doing more sophisticated calculations I have no problem
> handling my own rounding and controlling my own precision. I do this all
> the time in other languages. My Clipper code, for example, has all of
that
> coded and it works without a problem. I've been doing this on
> microcomputers for over 25 years. In Clipper, for example, I haven't had
to
> add tons of code to insure that their basic functions (+ and -) calculate
> correctly. My complaint with MS is that I shouldn't have to build in all
> sorts of controls to compensate for MS' inability to perform basic
> arithmetic. Once I get past simple arithmetic, I have no problem handling
> rounding and precision. What I can't tolerate are errors in basic
> representation of my beginning calculations. If you'll notice, I
> specifically used the same input in testing Clipper, MS and Excel. I also
> used the same computer, CPU, memory and disk drive in order to eliminate
any
> external influencing factors. By carefully controlling my environment,
I'm
> able to drill down to the exact point where MS failed. And surprise, it
was
> a simple subtraction. No ifs ands or buts, the answer is wrong. Again,
you
> can try to hide behind single precision, or whatever representation you'd
> like, but a wrong answer is a wrong answer. If all of these other
languages
> have this same problem, why does it only appear in MS? It seems to me
that
> they are doing something right and that you guys are missing something.
> Continuing this discussion is a moot point. We should be looking at what
we
> (either us users or you at Equis) need to do in order to put the code into
> the system to fix this problem, and believe me it is a problem, especially
> if you are trading over 6 figures.
>
> Maybe it's me, but does anybody here not think this is a problem? If I'm
> the only one who thinks that MS should be able to subtract two numbers and
> come up with a correct answer is important, then I apologize and will pack
> up my stuff and leave. If the people developing systems think that 4 - 2
=
> 1.9999999 is OK and that they're able to use that number in further
> calculations without a problem, then either they aren't working with the
> precision required by our system, or they have somehow been able to
develop
> a methodology to filter these errors out as noise. Regardless, we require
> slightly more accuracy.
>
> If your answer is, we get as close as we can and are limited by the
> limitations of single precision and don't really care that everyone else
> does it correctly, we're happy being close, then just say that and I won't
> waste any more time. If on the other hand, you understand that your
> response is not sufficient and you are going to take some action to fix
> this, say that. I think we have beaten this into the ground enough and
> unless you agree that there is a problem, I'm going to move on. No sense
> beating my head against a wall, especially if Equis' Programming Manager
> doesn't think there is a problem. I'll know that MS is strictly a
charting
> program and that it can't be used for developing serious trading systems,
> since it can randomly impact your testing by generating noise.
>
> No problem, I'll just write off all of the time I've spent trying to get
our
> stuff running in MS and move on to one of the other languages I own.
>
> 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, September 05, 2000 3:36 PM
> To: 'metastock@xxxxxxxxxxxxx'
> Subject: RE: First calculation problem
>
> Guy:
>
> This is a direct cut and paste from a Microsoft Product Support Services
web
> site. All I am saying is that I understand your frustration from
precision
> errors. I am also saying that virtually all software suffers from the
same
> problem. I provide this in hopes that everyone will realize that floating
> point errors are not unique to MetaStock.
>
> http://support.microsoft.com/support/kb/articles/Q196/6/52.asp
>
> ----------------------------------------------------------------------
>
> Floating Point Limitations
> All of the rounding implementations presented here use the double data
type,
> which can represent approximately 15 decimal digits.
>
> Since not all fractional values can be expressed exactly, you might get
> unexpected results because the display value does not match the stored
> value.
>
> For example, the number 2.25 might be stored internally as 2.2499999...,
> which would round down with arithmetic rounding, instead of up as you
might
> expect. Also, the more calculations a number is put through, the greater
> possibility that the stored binary value will deviate from the ideal
decimal
> value.
>
> -----------------------------------------------------------------------
>
> Also below is another cut and paste from Microsoft
> http://support.microsoft.com/support/kb/articles/Q125/0/56.ASP
>
> There are many situations in which precision, rounding, and accuracy in
> floating-point calculations can work to generate results that are
surprising
> to the programmer. There are four general rules that should be followed:
>
> In a calculation involving both single and double precision, the result
will
> not usually be any more accurate than single precision. If double
precision
> is required, be certain all terms in the calculation, including constants,
> are specified in double precision.
>
>
> Never assume that a simple numeric value is accurately represented in the
> computer. Most floating-point values can't be precisely represented as a
> finite binary value. For example .1 is .0001100110011... in binary (it
> repeats forever), so it can't be represented with complete accuracy on a
> computer using binary arithmetic, which includes all PCs.
>
>
> Never assume that the result is accurate to the last decimal place. There
> are always small differences between the "true" answer and what can be
> calculated with the finite precision of any floating point processing
unit.
>
>
> Never compare two floating-point values to see if they are equal or not-
> equal. This is a corollary to rule 3. There are almost always going to be
> small differences between numbers that "should" be equal. Instead, always
> check to see if the numbers are nearly equal. In other words, check to see
> if the difference between them is very small or insignificant.
>
> ------------------------------------------------------------------------
>
> What I have said all along is that we chose not to mask the errors (by
> assuming how much precision our customers want) because our users have
such
> a wide range of precision that they require. We provided the tools for
our
> users to determine their own precision in calculations. You can get
> COMPLETELY accurate results from MetaStock but you have to do some extra
> programming in the formula language to get it. We chose simply to make no
> assumptions about how much precision our formula writing users would
> require. We gave them the tools to apply precision for themselves.
>
> Ken Hunt
> Programming Manager
> Equis International
>
>
> -----Original Message-----
> From: Guy Tann [mailto:grt@xxxxxxxxxxxx]
> Sent: Tuesday, September 05, 2000 12:22 PM
> To: metastock@xxxxxxxxxxxxx
> Subject: RE: First calculation problem
>
>
> Ken,
>
> I understand what you're saying completely. You have missing my point
> entirely.
>
> As a user, I really don't care how the numbers are represented internally.
> I just care that the answers are CORRECT. Again, in order to reemphasize,
> you have missed my point entirely. The other software I have, including
> several different programming languages, all manage to provide the correct
> results, regardless of how they're represented internally. If, as you
say,
> the other software only modified the results before displaying them or
> played some other internal game and still maintained the single precision
> result internally, then all of their subsequent calculations would be off
by
> the same amount as MS (0.2) for each calculation, since they would be
using
> this internal, erroneous result. My point that you're missing, is that
> these other languages, regardless of precision, are able to not only
display
> the correct result (and I really don't care how they do it), they are also
> able to use that correct result internally in subsequent calculations,
which
> MS DOESN'T!
>
> So, I guess I still don't understand your point. Having majors in
> Mathematics, Statistics, and Economics, and having almost 40 years
> experience programming (my first job was as a Systems Engineer at IBM),
this
> is very frustrating. While I admit to getting older, I still haven't
> reached my dad's 91 years yet. My 10 year old, my brother and I, and my
> "old man" (who refuses to use MS because of this) still can't understand
how
> every other package or language we have is able to subtract two numbers
and
> use the results in further calculations without a problem regardless of
what
> is taking place internally. Notice I'm not referring to just what is
> displayed.
>
> If we were talking theory or some esoteric mathematical methodology, I
> understand that 2.379999999 can accurately approximate 2.38, a real world
> number. In calculus and statistics, I'm used to getting close but not
exact
> results as n goes from 1 and approaches infinity. We're talking
subtraction
> and 2.379999999 is NOT the correct result of the calculation 14.89 - 12.51
=
> 2.38, regardless of whatever planet you're on. More importantly, any
> further calculations that use the result of that first subtraction should
> use 2.38 and not 2.379999999! Again, all of my other software has managed
> to figure out that they not only need to display the correct answer but
that
> they also have to use that correct answer in further calculations.
>
> What about this is so hard to understand?
>
> Regardless of precision, any language that purports to provide basic
> arithmetic capabilities should be required to provide correct results.
> Again, this internal representation of numbers is not the issue here; it's
> what you display and what you use internally in subsequent calculations.
>
> The bottom line is, MS contains a major flaw insofar as it is unable to
> perform simple arithmetic and use the results in subsequent calculations.
> You should put a warning on MS stating this, much like the warning on
> cigarettes. Something like, even though MS uses single precision
arithmetic
> like Excel and others, it is unable to duplicate their results, which may
> affect your financial health. Seriously, can you see what I'm saying?
What
> you display and how you display it is symptomatic of a more invasive
> problem. What you display is also what you use in your further
> calculations, and since you have calculated an incorrect result, all of
your
> subsequent calculations will be wrong. This is the problem, and in my
mind,
> a very significant one.
>
> 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, September 05, 2000 7:41 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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