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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
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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RE: HP41: accuracy of 13-digit routines - Dieter - 09-04-2015 10:24 PM



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