HP41: accuracy of 13-digit routines
09-04-2015, 10:24 PM (This post was last modified: 09-05-2015 05:51 AM by Dieter.)
Post: #16
 Dieter Senior Member Posts: 2,397 Joined: Dec 2013
RE: HP41: accuracy of 13-digit routines
(09-04-2015 09:53 PM)Ángel Martin Wrote:  Great to hear you're on to an updated coefficient set - I look forward to it and getting the code squeaky clean with the new values

This is not the final result, but for the time being you may try these values:

Code:
 c =  3.838 a0 =  3.2743 15106 67  E-02 a1 =  1.1882 42945 545 a2 = -1.0667 84960 2 a3 =  1.8797 42975 77  E-01 a4 = -2.7122 78856     E-03

Evaluated exactly, the relative error should be less than 3,2 E–11 for x=0,5...71. At x=0.5 the result should even be more or less exact. Without this restriction the error may drop slightly below 3 E–11.

(09-04-2015 09:53 PM)Ángel Martin Wrote:  - those .3 seconds and 44 bytes do make a difference - remember than GAMMA is used as subroutine in several other functions in the module, like Bessel and a few more.

Hmmm... if GAMMA is used by other functions maybe a bit more accuracy would be helpful. Which means one more term and an estimated relative error near 1E–12.

Dieter
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 Messages In This Thread HP41: accuracy of 13-digit routines - Dieter - 09-01-2015, 09:23 PM RE: HP41: accuracy of 13-digit routines - Thomas Klemm - 09-02-2015, 04:45 AM RE: HP41: accuracy of 13-digit routines - Dieter - 09-25-2015, 10:46 PM RE: HP41: accuracy of 13-digit routines - Joe Horn - 09-02-2015, 06:11 AM RE: HP41: accuracy of 13-digit routines - Dieter - 09-02-2015, 10:18 AM RE: HP41: accuracy of 13-digit routines - Ángel Martin - 09-02-2015, 11:05 AM RE: HP41: accuracy of 13-digit routines - Michael Fehlhammer - 09-02-2015, 11:19 AM RE: HP41: accuracy of 13-digit routines - Ángel Martin - 09-02-2015, 12:03 PM RE: HP41: accuracy of 13-digit routines - Dieter - 09-02-2015, 06:07 PM RE: HP41: accuracy of 13-digit routines - Ángel Martin - 09-03-2015, 06:22 AM RE: HP41: accuracy of 13-digit routines - Dieter - 09-03-2015, 12:36 PM RE: HP41: accuracy of 13-digit routines - Ángel Martin - 09-03-2015, 01:33 PM RE: HP41: accuracy of 13-digit routines - Dieter - 09-03-2015, 06:17 PM RE: HP41: accuracy of 13-digit routines - Ángel Martin - 09-04-2015, 12:07 PM RE: HP41: accuracy of 13-digit routines - Dieter - 09-04-2015, 07:36 PM RE: HP41: accuracy of 13-digit routines - Ángel Martin - 09-04-2015, 09:53 PM RE: HP41: accuracy of 13-digit routines - Dieter - 09-04-2015 10:24 PM RE: HP41: accuracy of 13-digit routines - Dieter - 09-25-2015, 01:53 PM RE: HP41: accuracy of 13-digit routines - Thomas Klemm - 09-25-2015, 11:33 PM

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