ACURACY

06222016, 05:33 PM
(This post was last modified: 06222016 06:15 PM by RPL Calcs.)
Post: #1




ACURACY
The result from the evaluation of this equation
ARCSIN(ARCCOS(ARCTAN(TAN(COS(SIN(9)))))) is 8.99999864267 in the Saturn models: HP19BII HP20S HP22S HP27S HP28C/S HP32S/SII HP38G HP39G HP42S HP48SX/S/G/GX/G+/GII HP49G/G+ HP50G HP71B Look other results: http://www.rskey.org/~mwsebastian/miscprj/models.htm Best regards, 

06222016, 05:51 PM
Post: #2




RE: ACURACY
HP35S 8.99999986001
HPPrime 8.99999864267 In rpn mode HPPrime 9 in CAS mode Did we actually find a case where the 35s is actually more accurate at a trig function? 

06222016, 06:18 PM
(This post was last modified: 06222016 06:24 PM by RPL Calcs.)
Post: #3




RE: ACURACY
:0 My HP 15C LE, in DEG mode, evaluates to
9.000417403 the same value of the table. The HP 42S emulator evaluates to 9. Quote:HPPrime 8.99999864267 In rpn modeQuestion: HP Prime also emulates Saturn? :) 

06222016, 07:08 PM
Post: #4




RE: ACURACY
(06222016 06:18 PM)RPL Calcs Wrote: :0 My HP 15C LE, in DEG mode, evaluates to FWIW, in doubleprecision mode, on the WP34S I get: 8.999 999 999 999 999 999 999 999 999 937 535 Jake 

06222016, 10:35 PM
(This post was last modified: 06222016 10:37 PM by Dieter.)
Post: #5




RE: ACURACY
(06222016 06:18 PM)RPL Calcs Wrote: My HP 15C LE, in DEG mode, evaluates to That's the perfect result for a 10digit calculator. If it would return anything closer to 9 or even a plain 9 it would run faulty software. BTW the other mentioned value 8,99999864267 is the perfect result for a correctly operating 12digit calculator. (06222016 06:18 PM)RPL Calcs Wrote: The HP 42S emulator evaluates to 9. I don't think that e.g. Free42 returns 9. Maybe that's what you see, but this is not the calculated result. Subtract 9 from this and see what you get. ;) Dieter 

06222016, 11:18 PM
Post: #6




RE: ACURACY
(06222016 10:35 PM)Dieter Wrote:(06222016 06:18 PM)RPL Calcs Wrote: My HP 15C LE, in DEG mode, evaluates to That's exactly what I get on my HP12C Prestige running this 399step program :) Gerson. 

06222016, 11:44 PM
Post: #7




RE: ACURACY
Quote:I don't think that e.g. Free42 returns 9. Maybe that's what you see, but this is not the calculated result. Subtract 9 from this and see what you get. ;) The emulator is Free42. You´re RIGHT. 9 9  returns 6.2466E29 

06232016, 07:49 AM
(This post was last modified: 06232016 07:53 AM by Dieter.)
Post: #8




RE: ACURACY
(06222016 11:44 PM)RPL Calcs Wrote: The emulator is Free42. You´re RIGHT. 9 9  returns 6.2466E29 Sure. A little bit of calculus shows that about six digits are lost. So this is the expected result. BTW the WP34s returns virtually the same result, here the difference is 6,2465 E–29. You obviously use Free42 Decimal which AFAIK is based on the same 34digit floating point library. Dieter 

06232016, 08:05 AM
Post: #9




RE: ACURACY
(06222016 05:51 PM)dalupus Wrote: HP35S 8.99999986001 No, we didn't. The correct result for a 12digit calculator is 8,99999864267. The 35s rounds down the arctan although it should round up: the exact value is 0,999996272743 534... which is rounded to ...43 on the 35s and to ...44 on other calculators. Once this is adjusted the 35s yields the same correct result as the Saturn calculators. On the other hand this is a close case, and the trig functions may have an error of 0,6 ULP, so this still is within the allowed tolerance. Dieter 

06252016, 06:44 PM
Post: #10




RE: ACURACY  
06252016, 11:09 PM
Post: #11




RE: ACURACY
(06232016 07:49 AM)Dieter Wrote: BTW the WP34s returns virtually the same result, here the difference is 6,2465 E–29. You obviously use Free42 Decimal which AFAIK is based on the same 34digit floating point library. The floating point library only provides basic arithmetic, square root and natural logarithm and exponential. The trigonometric functions are implemented differently on each. I believe that Free42 Decimal has moved to the Intel decimal library which is different again. It is much faster than the 34S's code but it is also much larger  there are quite a few large lookup tables and it uses binary arithmetic and transcendental functions to get initial approximations for decimal results. In effect, you end up with two mathematics libraries. Pauli 

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