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6546 Views 20 Replies Latest reply: Oct 29, 2010 8:41 AM by lvl107 RSS
lvl107 Gold 334 posts since
Jan 22, 2007
Currently Being Moderated

Aug 29, 2010 9:49 AM

TRUE OR FALSE with this calculation ?

Hello all,

I really don't know that TRUE OR FALSE with this calculation ? Attach File below.

Regard,

Loi.

Attachments:
  • ViktorKorobov Silver 230 posts since
    Jun 3, 2007
    Currently Being Moderated
    Aug 29, 2010 10:00 AM (in response to lvl107)
    Re: TRUE OR FALSE with this calculation ?

    Mathcad says it's true.

    trueorfalse.GIF

  • MikeArmstrong Diamond 4,207 posts since
    Dec 3, 2008
    Currently Being Moderated
    Aug 29, 2010 10:14 AM (in response to lvl107)
    Re: TRUE OR FALSE with this calculation ?

    Excel also says it's true.

     

    151.00000

     

    Mike

  • Platinum 622 posts since
    Jun 22, 2010
    Currently Being Moderated
    Aug 29, 2010 12:41 PM (in response to lvl107)
    Re: TRUE OR FALSE with this calculation ?

    .......................

    MCADkakul.gif

    .......................

  • Platinum 622 posts since
    Jun 22, 2010
    Currently Being Moderated
    Aug 30, 2010 5:45 AM (in response to lvl107)
    Re: TRUE OR FALSE with this calculation ?
    The FPU (Floating Point Unit) is a separate part of your processor chip, dedicated to floating point (i.e., real number) arithmetics. It has been discovered that some parts of Windows 95/98 (or some drivers used by Windows) may affect the functioning of the FPU, reducing the accuracy of computations from about 19 to about 16 decimal digits.
    Most applications will never notice this, as they are usually limited to the 16-digit precision of the C/C++ double type. Kalkulator, however, takes the full advantage of the built-in FPU accuracy, and this advantage is cancelled when your system's FPU performance is degraded.
    Problems with the "old" Windows 95 System Agent
    Microsoft admitted (in a quite understated way) that the System Agent, included with the Win95 Plus, was affecting the FPU performance. The problem has been fixed in one of the Windows 95 Service Packs, and it should not be present at all in Windows 98. The culprit was identified as one of the Windows' components, sage.dll (version 4.40.310), and the fixed version number is 4.40.311. Turning the System Agent off is also a good workaround.
    Problems with other programs
    This is not the end of it. Exactly the same problem may sometimes arise without the System Agent (or sage.dll) running. I have so far identified two programs interfering with the FPU and causing exactly the same symptoms:
    ·     xwheel.exe by LCS/Telegraphics. This driver is included by many vendors with their pointing devices, touchpads in particular; probably more commonly seen on notebook computers. Removing xwheel.exe from the startup sequence fixes the FPU problem right away (in my Windows 98 tests I haven't lost any mouse functionality in the process).
    ·     vshield.exe, a memory-resident part of the McAfee antivirus utilities. Again programs of this kind are known to cause problems often. Disabling the Virus Shield fixes the problem.
    It is possible that these programs are not the real culprits here, but rather one of the Windows libraries they use; the bottom line remains the same.
    Kalkulator work-around
    Kalkulator runs a test for the FPU accuracy loss upon startup. If the problem is detected, the display precision setting will be limited to 16 (instead of 18) digits, and so will be the accuracy of some calculations. You will receive an appropriate warning when the FPU problem is detected the first time. If you change your system configuration (for example, by removing the offending program) and the problem goes away, the next time you run Kalkulator, it will detect this fact and give you a notice to this effect.
    More on the FPU problem
    You can find more details and updates on a Web page I have dedicated to it:
    where you will also find a small diagnostics program checking for this condition, together with the (very brief) source code.
    ____________________________
    Well explained by Richard & Eden
    The "Machine precision" as explained in Mathematica, is 16 for Pentium IV XP , and there is a test for it  it says my box is 16. There was another program causing failure of the floating point [Forge ?]. Ralston [if my recollection is correct] explained that the binary subtraction may eventually fail completely. That particular occurrence of numbers and operators will probably never happen in real engineering work, but nice to know it may cause some headache.
    MCADkakul_1.gif
    jmG 
      • Platinum 622 posts since
        Jun 22, 2010
        Currently Being Moderated
        Aug 31, 2010 5:39 PM (in response to lvl107)
        Re: TRUE OR FALSE with this calculation ?

        Your question has been answered by Eden, Richard, more extensively by jmG

        On my side: no need for more gyzma work sheet.

        • A.Non Diamond 10,237 posts since
          May 11, 2010
          Currently Being Moderated
          Sep 1, 2010 4:54 AM (in response to jeanGiraud)
          Re: TRUE OR FALSE with this calculation ?

          jean Giraud wrote:

           

          Your question has been answered by Eden, Richard, more extensively by jmG

          More wrongly, you mean. It has nothing to do with other programs interfering with the FPU. It's just a property of numeric math.

           

          On my side: no need for more gyzma work sheet.

          No need for rudeness either.

      • superres Silver 7,759 posts since
        Jun 1, 2007
        Currently Being Moderated
        Aug 31, 2010 10:34 PM (in response to lvl107)
        Re: TRUE OR FALSE with this calculation ?

        Your file contains only one of several possible ways that Mathcad can solve and display your particular examples.  The particular method you've used is called "dead" symbolics, since any changes to the input equation will not be reflected in the answer.

         

        The attached shows some of the other ways of seeing the answer, all using "live" symbolics.

      • Platinum 622 posts since
        Jun 22, 2010
        Currently Being Moderated
        Sep 1, 2010 6:23 AM (in response to lvl107)
        Re: TRUE OR FALSE with this calculation ?

        >On my side: no need for more gyzma work sheet.<

        ___________________________________________

         

        You specified "Evaluation in Mathcad 12", thus gyzma version for lower than 12. In fact my Mathcad 11 did open. You can read more in the version 11 attached. Several points of interest [educative]: the fractional representation, PRN, some equivalent forms tough this last point does not apply directly in your examples

        Attachments:
          • Platinum 622 posts since
            Jun 22, 2010
            Currently Being Moderated
            Sep 1, 2010 5:41 PM (in response to lvl107)
            Re: TRUE OR FALSE with this calculation ?

            Read more Pell, attached.

            "151, outside Pell range"

            __________________________________

             

            Often I pass Mathemica as a referee.  Your Mathcad "machine precision" is 16 Pentium IV Win XP. For other Win OS: don't know. I agree that Mathcad is missing the error message or warning message "result outside of machine precision". From the Mathcad help, it is however hinted that gross mistake(s) need more attention. Between you and me, calculate the error in microns or diameter of an atom an error of 10e-16 represents at the top of a tower 1 km height !

             

            jmG

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