Calculations on LARGE numbers

Discussion in 'ASP General' started by Frinton, Mar 13, 2006.

  1. Frinton

    Frinton Guest

    Hi,

    I am trying to do some calculations on large numbers (ie
    7,768,489,957,892,578,474,792,094 / 12,280) and no matter what I do it
    doesn't get it quite right. Its always somewhere between 10 and and 5000 out
    :(

    I have a suspition is could be down to one of the number functions I am
    using along the way but im not sure.

    Any help or guidance would be greatly appriciated.

    Thanks in advance

    Fred
    Frinton, Mar 13, 2006
    #1
    1. Advertising

  2. Fred wrote:

    > I am trying to do some calculations on large numbers (ie
    > 7,768,489,957,892,578,474,792,094 / 12,280) and no matter what I do it
    > doesn't get it quite right. Its always somewhere between 10 and and 5000
    > out :(
    >
    > I have a suspition is could be down to one of the number functions I am
    > using along the way but im not sure.
    >
    > Any help or guidance would be greatly appriciated.


    VB and VBScript integers are Long datatypes (32-bit) and range
    from -2,147,483,648 to 2,147,483,647, which is -2^31 to 2^31-1. Larger
    values are handled as Float datatype which is 64-bit. Your large number is
    stored as an approximation.

    --
    Richard
    Microsoft MVP Scripting and ADSI
    Hilltop Lab - http://www.rlmueller.net
    Richard Mueller, Mar 13, 2006
    #2
    1. Advertising

  3. "Frinton" <> wrote in message
    news:44158bca@212.67.96.135...
    > Hi,
    >
    > I am trying to do some calculations on large numbers (ie
    > 7,768,489,957,892,578,474,792,094 / 12,280) and no matter what I do it
    > doesn't get it quite right. Its always somewhere between 10 and and 5000
    > out :(


    The best is to convert it to currency.
    dim v
    v=CCur(10)
    v=v * ccur(103030303030.1034)

    > I have a suspition is could be down to one of the number functions I am
    > using along the way but im not sure.
    Egbert Nierop \(MVP for IIS\), Mar 13, 2006
    #3
  4. Frinton

    Evertjan. Guest

    Frinton wrote on 13 mrt 2006 in microsoft.public.inetserver.asp.general:

    > I am trying to do some calculations on large numbers (ie
    > 7,768,489,957,892,578,474,792,094 / 12,280) and no matter what I do it
    > doesn't get it quite right. Its always somewhere between 10 and and
    > 5000 out
    > :(
    >
    > I have a suspition is could be down to one of the number functions I
    > am using along the way but im not sure.
    >
    > Any help or guidance would be greatly appriciated.


    <http://en.wikipedia.org/wiki/Long_division>


    --
    Evertjan.
    The Netherlands.
    (Please change the x'es to dots in my emailaddress)
    Evertjan., Mar 13, 2006
    #4
  5. Frinton

    Frinton Guest

    Thanks for the reply

    Is there any work around to this?

    Im storing the values in SQL, is BigInt the largest exact number possible?

    Thanks

    Fred

    "Richard Mueller" <> wrote in message
    news:...
    > Fred wrote:
    >
    >> I am trying to do some calculations on large numbers (ie
    >> 7,768,489,957,892,578,474,792,094 / 12,280) and no matter what I do it
    >> doesn't get it quite right. Its always somewhere between 10 and and 5000
    >> out :(
    >>
    >> I have a suspition is could be down to one of the number functions I am
    >> using along the way but im not sure.
    >>
    >> Any help or guidance would be greatly appriciated.

    >
    > VB and VBScript integers are Long datatypes (32-bit) and range
    > from -2,147,483,648 to 2,147,483,647, which is -2^31 to 2^31-1. Larger
    > values are handled as Float datatype which is 64-bit. Your large number is
    > stored as an approximation.
    >
    > --
    > Richard
    > Microsoft MVP Scripting and ADSI
    > Hilltop Lab - http://www.rlmueller.net
    >
    Frinton, Mar 13, 2006
    #5
  6. Frinton

    Frinton Guest

    Thanks for the reply

    Im getting an overflow when I try this :(

    Fred

    "Egbert Nierop (MVP for IIS)" <> wrote in
    message news:...
    >
    > "Frinton" <> wrote in message
    > news:44158bca@212.67.96.135...
    >> Hi,
    >>
    >> I am trying to do some calculations on large numbers (ie
    >> 7,768,489,957,892,578,474,792,094 / 12,280) and no matter what I do it
    >> doesn't get it quite right. Its always somewhere between 10 and and 5000
    >> out :(

    >
    > The best is to convert it to currency.
    > dim v
    > v=CCur(10)
    > v=v * ccur(103030303030.1034)
    >
    >> I have a suspition is could be down to one of the number functions I am
    >> using along the way but im not sure.

    >
    Frinton, Mar 13, 2006
    #6
  7. Frinton

    Frinton Guest

    Thanks for the reply

    Its not the calculation that is causing me the problem its the storing of
    values

    Fred

    "Evertjan." <> wrote in message
    news:Xns9785B2358D898eejj99@194.109.133.242...
    > Frinton wrote on 13 mrt 2006 in microsoft.public.inetserver.asp.general:
    >
    >> I am trying to do some calculations on large numbers (ie
    >> 7,768,489,957,892,578,474,792,094 / 12,280) and no matter what I do it
    >> doesn't get it quite right. Its always somewhere between 10 and and
    >> 5000 out
    >> :(
    >>
    >> I have a suspition is could be down to one of the number functions I
    >> am using along the way but im not sure.
    >>
    >> Any help or guidance would be greatly appriciated.

    >
    > <http://en.wikipedia.org/wiki/Long_division>
    >
    >
    > --
    > Evertjan.
    > The Netherlands.
    > (Please change the x'es to dots in my emailaddress)
    Frinton, Mar 13, 2006
    #7
  8. Frinton

    Tim Slattery Guest

    "Frinton" <> wrote:

    >Thanks for the reply
    >
    >Its not the calculation that is causing me the problem its the storing of
    >values


    In VB or VBScript there's probably no way out of this. Java (not
    JavaScript) has a BigInteger class, and there are classes available
    for C++ that can handle integers of arbitrary precision.

    Arithmetic operations in these classes would not be fast, but they
    would preserve and use the full precision.

    --
    Tim Slattery
    MS MVP(DTS)
    Tim Slattery, Mar 13, 2006
    #8
  9. On Mon, 13 Mar 2006 15:12:09 -0000, "Frinton" <> wrote:

    >Hi,
    >
    >I am trying to do some calculations on large numbers (ie
    >7,768,489,957,892,578,474,792,094 / 12,280) and no matter what I do it
    >doesn't get it quite right. Its always somewhere between 10 and and 5000 out
    :mad:
    >
    >I have a suspition is could be down to one of the number functions I am
    >using along the way but im not sure.
    >
    >Any help or guidance would be greatly appriciated.
    >
    >Thanks in advance
    >
    >Fred
    >

    See tip 4533 » How do I perform accurate and/or complex math in a batch? 11-Dec-01
    in the 'Tips & Tricks' at http://www.jsifaq.com

    When I type the following at a CMD.EXE prompt:
    for /f %i in ('domath //nologo "Round(7768489957892578474792094/12280)"') do @echo %i

    I get 6.32613188753467E+20




    Jerold Schulman
    Windows Server MVP
    JSI, Inc.
    http://www.jsiinc.com
    http://www.jsifaq.com
    Jerold Schulman, Mar 13, 2006
    #9
  10. Frinton

    Frinton Guest

    "Jerold Schulman" <> wrote in message
    news:...
    > On Mon, 13 Mar 2006 15:12:09 -0000, "Frinton" <>
    > wrote:
    >
    >>Hi,
    >>
    >>I am trying to do some calculations on large numbers (ie
    >>7,768,489,957,892,578,474,792,094 / 12,280) and no matter what I do it
    >>doesn't get it quite right. Its always somewhere between 10 and and 5000
    >>out
    >:mad:
    >>
    >>I have a suspition is could be down to one of the number functions I am
    >>using along the way but im not sure.
    >>
    >>Any help or guidance would be greatly appriciated.
    >>
    >>Thanks in advance
    >>
    >>Fred
    >>

    > See tip 4533 » How do I perform accurate and/or complex math in a batch?
    > 11-Dec-01
    > in the 'Tips & Tricks' at http://www.jsifaq.com
    >
    > When I type the following at a CMD.EXE prompt:
    > for /f %i in ('domath //nologo "Round(7768489957892578474792094/12280)"')
    > do @echo %i
    >
    > I get 6.32613188753467E+20
    >
    >
    >
    >
    > Jerold Schulman
    > Windows Server MVP
    > JSI, Inc.
    > http://www.jsiinc.com
    > http://www.jsifaq.com
    Frinton, Mar 13, 2006
    #10
  11. Frinton

    Frinton Guest

    Thanks for the reply

    The trouble is when I format this result into a "readable" number (using
    vbscripts FormatNumber function) it comes out as 632,613,188,753,467,000,000

    The true answer and the one im looking for is

    632,613,188,753,467,302,507

    Regards

    Fred





    "Jerold Schulman" <> wrote in message
    news:...
    > On Mon, 13 Mar 2006 15:12:09 -0000, "Frinton" <>
    > wrote:
    >
    >>Hi,
    >>
    >>I am trying to do some calculations on large numbers (ie
    >>7,768,489,957,892,578,474,792,094 / 12,280) and no matter what I do it
    >>doesn't get it quite right. Its always somewhere between 10 and and 5000
    >>out
    >:mad:
    >>
    >>I have a suspition is could be down to one of the number functions I am
    >>using along the way but im not sure.
    >>
    >>Any help or guidance would be greatly appriciated.
    >>
    >>Thanks in advance
    >>
    >>Fred
    >>

    > See tip 4533 » How do I perform accurate and/or complex math in a batch?
    > 11-Dec-01
    > in the 'Tips & Tricks' at http://www.jsifaq.com
    >
    > When I type the following at a CMD.EXE prompt:
    > for /f %i in ('domath //nologo "Round(7768489957892578474792094/12280)"')
    > do @echo %i
    >
    > I get 6.32613188753467E+20
    >
    >
    >
    >
    > Jerold Schulman
    > Windows Server MVP
    > JSI, Inc.
    > http://www.jsiinc.com
    > http://www.jsifaq.com
    Frinton, Mar 13, 2006
    #11
  12. Hi,

    As I recall BigInt is 64-bit, but valid values range from -2^63
    (-9,223,372,036,854,775,808) through 2^63-1 (9,223,372,036,854,775,807).
    VB.NET can handle values in this range, but VB6 and VBScript cannot. In VB6
    I've used Currency datatypes to handle large numbers. VB6 Currency values
    are 64-bit scaled integers (4 digits past the decimal, saved internally as
    an integer), so the maximum value is 922,337,203,685,477.5807. I'm not sure
    about VBScript currency values. I've also written my own functions to do
    math by breaking the value up into parts, like two 31-bit values (high and
    low parts). However, my functions multiplied numbers. I remember having to
    code my own CInt Function because the VB function bombs out at 2^15.
    Division seems harder.

    Your value is 7.77 x 10^24, which would require an 84-bit register. You
    could represent it as two 42-bit numbers. However, even the 42-bit values
    are too large for VB6 or VBScript. That leaves you with representing the
    value as 3 30-bit numbers.

    x = a * 2^60 + b * 2^30 + c

    That would be a lot of work.

    --
    Richard
    Microsoft MVP Scripting and ADSI
    Hilltop Lab - http://www.rlmueller.net

    "Frinton" <> wrote in message
    news:4415a442@212.67.96.135...
    > Thanks for the reply
    >
    > Is there any work around to this?
    >
    > Im storing the values in SQL, is BigInt the largest exact number possible?
    >
    > Thanks
    >
    > Fred
    >
    > "Richard Mueller" <> wrote in message
    > news:...
    >> Fred wrote:
    >>
    >>> I am trying to do some calculations on large numbers (ie
    >>> 7,768,489,957,892,578,474,792,094 / 12,280) and no matter what I do it
    >>> doesn't get it quite right. Its always somewhere between 10 and and 5000
    >>> out :(
    >>>
    >>> I have a suspition is could be down to one of the number functions I am
    >>> using along the way but im not sure.
    >>>
    >>> Any help or guidance would be greatly appriciated.

    >>
    >> VB and VBScript integers are Long datatypes (32-bit) and range
    >> from -2,147,483,648 to 2,147,483,647, which is -2^31 to 2^31-1. Larger
    >> values are handled as Float datatype which is 64-bit. Your large number
    >> is stored as an approximation.
    >>
    >> --
    >> Richard
    >> Microsoft MVP Scripting and ADSI
    >> Hilltop Lab - http://www.rlmueller.net
    >>

    >
    >
    Richard Mueller, Mar 13, 2006
    #12
  13. Frinton wrote:
    > I am trying to do some calculations on large numbers (ie
    > 7,768,489,957,892,578,474,792,094 / 12,280) and no matter
    > what I do it doesn't get it quite right. Its always
    > somewhere between 10 and and 5000 out :(


    Check out the multiple-precision libraries here:
    http://www.ohdave.com/rsa/



    --
    Dave Anderson

    Unsolicited commercial email will be read at a cost of $500 per message. Use
    of this email address implies consent to these terms. Please do not contact
    me directly or ask me to contact you directly for assistance. If your
    question is worth asking, it's worth posting.
    Dave Anderson, Mar 13, 2006
    #13
  14. I wonder if that confirms that the value was handled internally as a
    currency, a scaled 64-bit integer. I note that I get the same answer if I
    omit the Round function. I used the following VBScript program:

    x= Eval("(7768489957892578474792094/12280)")

    Wscript.Echo FormatNumber(x, 4)

    --
    Richard
    Microsoft MVP Scripting and ADSI
    Hilltop Lab - http://www.rlmueller.net

    "Frinton" <> wrote in message
    news:4415b30c@212.67.96.135...
    > Thanks for the reply
    >
    > The trouble is when I format this result into a "readable" number (using
    > vbscripts FormatNumber function) it comes out as
    > 632,613,188,753,467,000,000
    >
    > The true answer and the one im looking for is
    >
    > 632,613,188,753,467,302,507
    >
    > Regards
    >
    > Fred
    >
    >
    >
    >
    >
    > "Jerold Schulman" <> wrote in message
    > news:...
    >> On Mon, 13 Mar 2006 15:12:09 -0000, "Frinton" <>
    >> wrote:
    >>
    >>>Hi,
    >>>
    >>>I am trying to do some calculations on large numbers (ie
    >>>7,768,489,957,892,578,474,792,094 / 12,280) and no matter what I do it
    >>>doesn't get it quite right. Its always somewhere between 10 and and 5000
    >>>out
    >>:mad:
    >>>
    >>>I have a suspition is could be down to one of the number functions I am
    >>>using along the way but im not sure.
    >>>
    >>>Any help or guidance would be greatly appriciated.
    >>>
    >>>Thanks in advance
    >>>
    >>>Fred
    >>>

    >> See tip 4533 » How do I perform accurate and/or complex math in a batch?
    >> 11-Dec-01
    >> in the 'Tips & Tricks' at http://www.jsifaq.com
    >>
    >> When I type the following at a CMD.EXE prompt:
    >> for /f %i in ('domath //nologo "Round(7768489957892578474792094/12280)"')
    >> do @echo %i
    >>
    >> I get 6.32613188753467E+20
    >>
    >>
    >>
    >>
    >> Jerold Schulman
    >> Windows Server MVP
    >> JSI, Inc.
    >> http://www.jsiinc.com
    >> http://www.jsifaq.com

    >
    >
    Richard Mueller, Mar 13, 2006
    #14
  15. Frinton

    Evertjan. Guest

    Frinton wrote on 13 mrt 2006 in microsoft.public.inetserver.asp.general:
    > "Evertjan." <> wrote in message
    > news:Xns9785B2358D898eejj99@194.109.133.242...
    >> Frinton wrote on 13 mrt 2006 in
    >> microsoft.public.inetserver.asp.general:
    >>
    >>> I am trying to do some calculations on large numbers (ie
    >>> 7,768,489,957,892,578,474,792,094 / 12,280) and no matter what I do
    >>> it doesn't get it quite right. Its always somewhere between 10 and
    >>> and 5000 out
    >>> :(
    >>>
    >>> I have a suspition is could be down to one of the number functions I
    >>> am using along the way but im not sure.
    >>>
    >>> Any help or guidance would be greatly appriciated.

    >>
    >> <http://en.wikipedia.org/wiki/Long_division>


    [please do not toppost on usenet]


    > Thanks for the reply
    >
    > Its not the calculation that is causing me the problem its the storing
    > of values


    That is no problem, you can store them as a string.

    In fact, you do the long division also with string parts.

    --
    Evertjan.
    The Netherlands.
    (Please change the x'es to dots in my emailaddress)
    Evertjan., Mar 13, 2006
    #15
  16. JRS: In article <44158bca@212.67.96.135>, dated Mon, 13 Mar 2006
    15:12:09 remote, seen in news:microsoft.public.scripting.vbscript,
    Frinton <> posted :

    >I am trying to do some calculations on large numbers (ie
    >7,768,489,957,892,578,474,792,094 / 12,280) and no matter what I do it
    >doesn't get it quite right. Its always somewhere between 10 and and 5000 out
    :mad:
    >
    >I have a suspition is could be down to one of the number functions I am
    >using along the way but im not sure.


    Others have explained size limits and accuracy. But, at a DOS prompt :

    LONGCALC 7,768,489,957,892,578,474,792,094 12,280 div wrt

    LONGCALC: www.merlyn.demon.co.uk >= 2005-07-22
    compiled with Borland Delphi.
    +632,613,188,753,467,302,507

    (remainder was 6,134)

    LONGCALC handles up to 65520 or 99999999 digits, base 2..16, integers,
    programmed in RPN. If you want the answers, you may use it; but it's
    not VBS (and not quick). Via sig line 3. VASTCALC is a GUI version.

    --
    © John Stockton, Surrey, UK. ?@merlyn.demon.co.uk Turnpike v4.00 MIME. ©
    Web <URL:http://www.merlyn.demon.co.uk/> - FAQqish topics, acronyms & links.
    PAS EXE TXT ZIP via <URL:http://www.merlyn.demon.co.uk/programs/00index.htm>.
    Do not Mail News to me. Before a reply, quote with ">" or "> " (SoRFC1036)
    Dr John Stockton, Mar 13, 2006
    #16
  17. I find that VBScript can represent 2^48 and 2^49 exactly, but not 2^50.

    I see no way to even break up your number into high and low parts, much less
    do math with them. For example, if I attempt to represent your large number
    as:

    x = a * (2^42) + b

    I can possibly find a, but not b.

    a = IntegerPart(x/(2^42))

    where IntegerPart must be coded, since CInt has no chance of working. Then

    b = x - a * (2^42)

    but VBScript cannot represent a * (2^42) exactly, so b is wrong. I see no
    chance of doing long division if I cannot even break up the number as above.
    VBScript cannot do any math exactly where any intermediate value is greater
    than about 2^48.

    --
    Richard
    Microsoft MVP Scripting and ADSI
    Hilltop Lab - http://www.rlmueller.net

    "Richard Mueller" <> wrote in message
    news:%...
    > Hi,
    >
    > As I recall BigInt is 64-bit, but valid values range from -2^63
    > (-9,223,372,036,854,775,808) through 2^63-1 (9,223,372,036,854,775,807).
    > VB.NET can handle values in this range, but VB6 and VBScript cannot. In
    > VB6 I've used Currency datatypes to handle large numbers. VB6 Currency
    > values are 64-bit scaled integers (4 digits past the decimal, saved
    > internally as an integer), so the maximum value is
    > 922,337,203,685,477.5807. I'm not sure about VBScript currency values.
    > I've also written my own functions to do math by breaking the value up
    > into parts, like two 31-bit values (high and low parts). However, my
    > functions multiplied numbers. I remember having to code my own CInt
    > Function because the VB function bombs out at 2^15. Division seems harder.
    >
    > Your value is 7.77 x 10^24, which would require an 84-bit register. You
    > could represent it as two 42-bit numbers. However, even the 42-bit values
    > are too large for VB6 or VBScript. That leaves you with representing the
    > value as 3 30-bit numbers.
    >
    > x = a * 2^60 + b * 2^30 + c
    >
    > That would be a lot of work.
    >
    > --
    > Richard
    > Microsoft MVP Scripting and ADSI
    > Hilltop Lab - http://www.rlmueller.net
    >
    > "Frinton" <> wrote in message
    > news:4415a442@212.67.96.135...
    >> Thanks for the reply
    >>
    >> Is there any work around to this?
    >>
    >> Im storing the values in SQL, is BigInt the largest exact number
    >> possible?
    >>
    >> Thanks
    >>
    >> Fred
    >>
    >> "Richard Mueller" <> wrote in
    >> message news:...
    >>> Fred wrote:
    >>>
    >>>> I am trying to do some calculations on large numbers (ie
    >>>> 7,768,489,957,892,578,474,792,094 / 12,280) and no matter what I do it
    >>>> doesn't get it quite right. Its always somewhere between 10 and and
    >>>> 5000 out :(
    >>>>
    >>>> I have a suspition is could be down to one of the number functions I am
    >>>> using along the way but im not sure.
    >>>>
    >>>> Any help or guidance would be greatly appriciated.
    >>>
    >>> VB and VBScript integers are Long datatypes (32-bit) and range
    >>> from -2,147,483,648 to 2,147,483,647, which is -2^31 to 2^31-1. Larger
    >>> values are handled as Float datatype which is 64-bit. Your large number
    >>> is stored as an approximation.
    >>>
    >>> --
    >>> Richard
    >>> Microsoft MVP Scripting and ADSI
    >>> Hilltop Lab - http://www.rlmueller.net
    >>>

    >>
    >>

    >
    >
    Richard Mueller, Mar 13, 2006
    #17
  18. "Frinton" <> wrote in message
    news:4415a490@212.67.96.135...
    > Thanks for the reply
    >
    > Im getting an overflow when I try this :(


    sad.

    More sadness :)

    The OLEautomation runtime Oleaut32.dll supports 8 byte integers (V_I8), they
    should be called 'very long' or so...
    But vbscript has been feature-frozen, so it does not match the current OS
    when we think about calculation.

    You might try vbscript.net that -has- support for 8 byte calculations.

    > Fred
    Egbert Nierop \(MVP for IIS\), Mar 14, 2006
    #18
  19. Re: Re: Calculations on LARGE numbers

    Is there any documentation on LONGCALC?
    What does wrt mean?
    I can figure out how to use add, sub, mul, div/mod/srt, pow.
    How do I do use the result of 1 calculation in another calculation?


    On Mon, 13 Mar 2006 23:33:01 +0000, Dr John Stockton <> wrote:

    >JRS: In article <44158bca@212.67.96.135>, dated Mon, 13 Mar 2006
    >15:12:09 remote, seen in news:microsoft.public.scripting.vbscript,
    >Frinton <> posted :
    >
    >>I am trying to do some calculations on large numbers (ie
    >>7,768,489,957,892,578,474,792,094 / 12,280) and no matter what I do it
    >>doesn't get it quite right. Its always somewhere between 10 and and 5000 out
    >:mad:
    >>
    >>I have a suspition is could be down to one of the number functions I am
    >>using along the way but im not sure.

    >
    >Others have explained size limits and accuracy. But, at a DOS prompt :
    >
    > LONGCALC 7,768,489,957,892,578,474,792,094 12,280 div wrt
    >
    > LONGCALC: www.merlyn.demon.co.uk >= 2005-07-22
    > compiled with Borland Delphi.
    > +632,613,188,753,467,302,507
    >
    > (remainder was 6,134)
    >
    >LONGCALC handles up to 65520 or 99999999 digits, base 2..16, integers,
    >programmed in RPN. If you want the answers, you may use it; but it's
    >not VBS (and not quick). Via sig line 3. VASTCALC is a GUI version.
    >


    Jerold Schulman
    Windows Server MVP
    JSI, Inc.
    http://www.jsiinc.com
    http://www.jsifaq.com
    Jerold Schulman, Mar 14, 2006
    #19
  20. Richard Mueller wrote:
    > I find that VBScript can represent 2^48 and 2^49 exactly,
    > but not 2^50.


    That depends on what you mean by "represent". Consider:

    p = 2^53

    For i=-10 To 10
    Response.Write(Represent(p+i) & "<br>")
    Next

    Function Represent(N)
    M = Int(N/1000)
    R = N - 1000*M
    If (M = 0) Then
    Represent = R
    Else
    Represent = Represent(M) & "," & Right("00" & R,3)
    End If
    End Function

    [Disclaimer: only "works" with positive integers]

    I chose 2^53 for a reason. VBScript can distinguish between individual
    integers up through 2^53. Above 2^53, numbers are spaced by 2. Above 2^54,
    they are spaced by 4. Above 2^55, by 8. I'll let you work out the sequence
    above that.


    --
    Dave Anderson

    Unsolicited commercial email will be read at a cost of $500 per message. Use
    of this email address implies consent to these terms. Please do not contact
    me directly or ask me to contact you directly for assistance. If your
    question is worth asking, it's worth posting.
    Dave Anderson, Mar 14, 2006
    #20
    1. Advertising

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