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Gerson W. Barbosa · 02-02-2015, 02:43 AM

(02-01-2015 10:25 PM)Dieter Wrote:
(02-01-2015 09:17 PM)Rick314 Wrote: (I checked with extended-precision software and Dieter's 3 answers are indeed the best 12-digit answers possible. They are also what my HP-35S returns, so kudos to the HP-35S same as for its sin(x) algorithm.) I don't think there is any "relative error" on the 3 different inputs, and the 3 different answers are the correct 12-digit answers.

Yes, the 35s does return these three results – actually that's the calculator I used for the calculation. But you should not be too generous with your kudos: take a look at these results by the 35s and probably also other HPs:

Code:

3,1 [SIN] 4,15806624333 E-2 exact 3,14 [SIN] 1,59265291648 E-3 last digit off (-1 ULP) 3,141 [SIN] 5,92653555096 E-4 last digit off (-3 ULP) 3,1415 [SIN] 9,26535896582 E-5 last 2 digits off (-25 ULP) 3,14159 [SIN] 2,65358979 E-6 last 3 digits lost 3,141592 [SIN] 6,5358979 E-7 last 4 digits lost 3,1415926 [SIN] 5,358979 E-8 last 5 digits lost 3,14159265 [SIN] 3,58979 E-9 last 6 digits lost 3,141592653 [SIN] 5,89793238463 E-10 exact 3,1415926535 [SIN] 8,97932384626 E-11 exact 3,14159265358 [SIN] 9,79323846264 E-12 exact

;-)

Dieter

Not all other 12-digit HP calculators, only the HP-33s from which the HP-35s inherited this and many other bugs.

These are the HP-42S results:

Code:

3,1           [SIN]  4,15806624333 E-2    exact

3,14          [SIN]  1,59265291649 E-3    exact

3,141         [SIN]  5,92653555099 E-4    exact

3,1415        [SIN]  9,26535896607 E-5    exact

3,14159       [SIN]  2,65358979324 E-6    exact

3,141592      [SIN]  6,53589793238 E-7    exact

3,1415926     [SIN]  5,35897932385 E-8    exact

3,14159265    [SIN]  3,58979323846 E-9    exact

3,141592653   [SIN]  5,89793238463 E-10   exact

3,1415926535  [SIN]  8,97932384626 E-11   exact

3,14159265358 [SIN]  9,79323846264 E-12   exact

Gerson.