Approximate pi to 24 digits via keyboard

[PANAMATIK]

(02-05-2015 02:32 PM)Dieter Wrote:  Then let's start a 41C bug list, a 67/97 bug list, any many others. Loss of accuracy in the sine function (and probably others) for arguments close to pi is a common problem. Let's look at our good old trusted and beloved 41C:

Code:

 x             41C sin(x)       comment
---------------------------------------------------
3,1           4,158066243 E-2   exact
3,14          1,592652917 E-3   almost exact
3,141         5,926533553 E-4   1 digit off
3,1415        9,265358987 E-5   2 digits off
3,14159       2,65359 E-6       3(4) digits lost *)
3,141592      6,5359 E-7        4(5) digits lost *)
3,1415926     5,359 E-8         5(6) digits lost *)
3,14159265    3,59 E-9          6(7) digits lost *)
3,141592653   5,9 E-10          7(8) digits lost *)
---------------------------------------------------
                                *) last digit is 0

I assume the 67/97, the 34C, 25/29 and other well-reputed HPs will behave in a similar way.

Dieter

I verified HP-67/97 HP34C HP29C, they compute the same values as above. But HP-21 HP-25/HP-25C both produce the same even less accurate values, interestingly with more decimals. Obviously they use a different algorithm.

Code:


3,141592653  1.160469873 E-9

Bernhard