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From: friend on 27 Aug 2006 18:16 On Sun, 27 Aug 2006 17:43:17 GMT, pausch (a)saaf.se (Paul Schlyter)wrote: >In article <08j3f2t3dm6nnm9lhmvp9dp8sjru6de145 (a)4ax.com>,>friend <digital (a)forever.com> wrote:>>On 27 Aug 2006 09:00:29 -0700, "JB" <wjbudd (a)yahoo.com> wrote:>> >>> >>>Zeno wrote: >>>> In article <1156641823.419972.220970 (a)b28g2000cwb.googlegroups.com>, JB>>>> <wjbudd (a)yahoo.com> wrote:>>>> >>>> > I have a TI voyage 200 that I well satidfied with but I am curious >>>> > about the HP50g. If I get an HP 50g, after using the TI v200 >>>> > extensively, will I likely be disappointed in the quality of the HP >>>> > item or it's performance? Will the HP be similiar to use compared to >>>> > the TI or will it be an all new learning curve. I find the >>>> > construction quality and performance of the TI to both be flawless. >>>> > Will the HP be the same? How about the infamous keyboard problems? Or >>>> > major OS bugs? I have never used RPN, so is it necessary? What would >>>> > be a simple RPN example? Do you think there is an advantage to having >>>> > both calculators? >>>> > >>>> The HP cals are much more accurate when compuitng Trig functions. >>>> >>>> An example, is to computer the SIN of exactly 3.141592654 (NOT Pi, but >>>> the just given rounding of it) radians....the HPs get the correct >>>> answer to 12 significant digits, while all other brand do not even come >>>> close in accuracy. >>>> >>>> The correct answer is >>>> -4.10206761537 E-10 >>>> which only HPs give. >>> >>>What sort of application would require such accuracy ? >> >>Amateur radio: Tracking satellites. > >Do you really have to compute sines accurate to 1E-21 in amateur radio? Depends on things like how long you wish to track the sat. and various orbital mechanics you might wish to include. Now if the Patriot anti missile system could be just a little more versatile ...
From: GWB on 27 Aug 2006 19:07 Zeno wrote: > The HP cals are much more accurate when compuitng Trig functions. > > An example, is to computer the SIN of exactly 3.141592654 (NOT Pi, but > the just given rounding of it) radians....the HPs get the correct > answer to 12 significant digits, while all other brand do not even come > close in accuracy. > > The correct answer is > -4.10206761537 E-10 > which only HPs give. Surely they are, but I fear the correct answer is -4,10206857034707E-10 (according to my own RPN calc written in Delphi) or -4,10206857035E-10 to 12 significant places Anyway, the HP-48/49/50 is not bad. It appears TI gives -4.102E-10 Regards, Gerson.
From: Jean-Yves Avenard on 27 Aug 2006 20:27 Chuck Rushton wrote: > Without the 15-digit capability of the 49g+/50g, these conversions are > unable to avoid the round-off error inherent even at 12 digits. All TI calculators have a 14 digits accuracy... So I don't think the sin(pi rounded to 12 digits) will be a problem as earlier mentioned... JY
From: GWB on 27 Aug 2006 21:46 GWB wrote: > Zeno wrote: > > The HP cals are much more accurate when compuitng Trig functions. > > > > An example, is to computer the SIN of exactly 3.141592654 (NOT Pi, but > > the just given rounding of it) radians....the HPs get the correct > > answer to 12 significant digits, while all other brand do not even come > > close in accuracy. > > > > The correct answer is > > -4.10206761537 E-10 > > which only HPs give. > > Surely they are, but I fear the correct answer is > > -4,10206857034707E-10 (according to my own RPN calc written in Delphi) > > or > > -4,10206857035E-10 to 12 significant places > > Anyway, the HP-48/49/50 is not bad. It appears TI gives -4.102E-10 > Oops, I was wrong! Even Delphi extended type slips on this. Recalculating sin(3.141592654) as 3 sin(3.141592654/3) - 4(sin(3.141592654/3))^3 I obtained -4.10206535406132E-10 (in Delphi). This should be a more accurate result since the sine function would have no problem in the pi/3 boundary. But I am not sure about this result either because of rounding errors and other issues I am not aware of. Could someone compute both sin(3.141592654) and the trigonometric identity above in Maple to 30 places so we can see how many digits match? Thanks, Gerson.
From: Zeno on 27 Aug 2006 23:01
In article <1156729581.785305.19530 (a)b28g2000cwb.googlegroups.com>, GWB<gerson.w.barbosa (a)gmail.com> wrote:> GWB wrote: > > Zeno wrote: > > > The HP cals are much more accurate when compuitng Trig functions. > > > > > > An example, is to computer the SIN of exactly 3.141592654 (NOT Pi, but > > > the just given rounding of it) radians....the HPs get the correct > > > answer to 12 significant digits, while all other brand do not even come > > > close in accuracy. > > > > > > The correct answer is > > > -4.10206761537 E-10 > > > which only HPs give. > > > > Surely they are, but I fear the correct answer is > > > > -4,10206857034707E-10 (according to my own RPN calc written in Delphi) > > > > or > > > > -4,10206857035E-10 to 12 significant places > > > > Anyway, the HP-48/49/50 is not bad. It appears TI gives -4.102E-10 > > > > Oops, I was wrong! Even Delphi extended type slips on this. > > Recalculating sin(3.141592654) as 3 sin(3.141592654/3) - > 4(sin(3.141592654/3))^3 I obtained -4.10206535406132E-10 (in Delphi). > This should be a more accurate result since the sine function would > have no problem in the pi/3 boundary. But I am not sure about this > result either because of rounding errors and other issues I am not > aware of. Could someone compute both sin(3.141592654) and the > trigonometric identity above in Maple to 30 places so we can see how > many digits match? > > Thanks, > > Gerson. > Sorry, but both your Delphi answer are wrong What i stated before is correct |