Accurate Bernoulli numbers on the 41C, or "how close can you get"?
03-21-2014, 05:54 AM (This post was last modified: 03-21-2014 10:48 AM by Ángel Martin.)
Post: #25
 Ángel Martin Senior Member Posts: 1,305 Joined: Dec 2013
RE: Accurate Bernoulli numbers on the 41C, or "how close can you get"?
(03-20-2014 09:07 PM)Dieter Wrote:  Polynomials are very nice in compiled computer languages where it does not matter whether a constant has 2 or 15 digits, but on a calculator every single digit requires at least one byte of memory.

Using MCODE the advantage is obvious, as the coefficients are sort of pre-compiled. Rational approximations allow simpler operations (basically sum and multiplication), which avoids slower routines even in MCODE. It's also nice to have the same execution time for all arguments.

How does your method hold up in the vicinity of one? That's where the CUDA approach really surpasses any other approximation I tried in the past. Unfortunately I only used 10 digits to implement the double-precision expression (ran out of ROM space), but even then it returns decent results.

For instance,

ICPF(0.9999) = 3,719016392
ICPF(0.99999) = 4,264890427

accurate to the 8th. and 7th decimal digits respectively, according to the results in Wolfram Alpha:
https://www.wolframalpha.com/input/?i=sq...9999+-1%29

BTW, V41 is not good for benchmarking execution speed - even using default settings it's still a function of the PC's CPU. I'm using an old-reliable XP machine, 9-years old so likely slower than yours ;-)

Cheers,
'AM
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 Messages In This Thread Accurate Bernoulli numbers on the 41C, or "how close can you get"? - Dieter - 03-09-2014, 07:12 PM RE: Accurate Bernoulli numbers on the 41C, or "how close can you get"? - Thomas Klemm - 03-10-2014, 12:20 AM RE: Accurate Bernoulli numbers on the 41C, or "how close can you get"? - Dieter - 03-10-2014, 08:23 PM RE: Accurate Bernoulli numbers on the 41C, or "how close can you get"? - Thomas Klemm - 03-12-2014, 04:34 PM RE: Accurate Bernoulli numbers on the 41C, or "how close can you get"? - Ángel Martin - 03-14-2014, 10:05 AM RE: Accurate Bernoulli numbers on the 41C, or "how close can you get"? - Dieter - 03-14-2014, 09:37 PM RE: Accurate Bernoulli numbers on the 41C, or "how close can you get"? - Thomas Klemm - 03-14-2014, 10:00 PM RE: Accurate Bernoulli numbers on the 41C, or "how close can you get"? - Thomas Klemm - 03-14-2014, 10:21 PM RE: Accurate Bernoulli numbers on the 41C, or "how close can you get"? - Thomas Klemm - 03-14-2014, 10:04 PM RE: Accurate Bernoulli numbers on the 41C, or "how close can you get"? - Ángel Martin - 03-15-2014, 09:32 AM RE: Accurate Bernoulli numbers on the 41C, or "how close can you get"? - Thomas Klemm - 03-15-2014, 12:26 PM RE: Accurate Bernoulli numbers on the 41C, or "how close can you get"? - Dieter - 03-15-2014, 06:12 PM RE: Accurate Bernoulli numbers on the 41C, or "how close can you get"? - Thomas Klemm - 03-15-2014, 07:17 PM RE: Accurate Bernoulli numbers on the 41C, or "how close can you get"? - Ángel Martin - 03-15-2014, 12:56 PM RE: Accurate Bernoulli numbers on the 41C, or "how close can you get"? - Ángel Martin - 03-15-2014, 08:47 PM RE: Accurate Bernoulli numbers on the 41C, or "how close can you get"? - Dieter - 03-18-2014, 09:24 PM RE: Accurate Bernoulli numbers on the 41C, or "how close can you get"? - Ángel Martin - 03-19-2014, 06:47 AM RE: Accurate Bernoulli numbers on the 41C, or "how close can you get"? - Dieter - 03-19-2014, 01:37 PM RE: Accurate Bernoulli numbers on the 41C, or "how close can you get"? - Ángel Martin - 03-19-2014, 07:32 PM RE: Accurate Bernoulli numbers on the 41C, or "how close can you get"? - Dieter - 03-19-2014, 08:31 PM RE: Accurate Bernoulli numbers on the 41C, or "how close can you get"? - Ángel Martin - 03-20-2014, 06:46 AM RE: Accurate Bernoulli numbers on the 41C, or "how close can you get"? - Dieter - 03-20-2014, 12:44 PM RE: Accurate Bernoulli numbers on the 41C, or "how close can you get"? - Ángel Martin - 03-20-2014, 02:21 PM RE: Accurate Bernoulli numbers on the 41C, or "how close can you get"? - Dieter - 03-20-2014, 09:07 PM RE: Accurate Bernoulli numbers on the 41C, or "how close can you get"? - Ángel Martin - 03-21-2014 05:54 AM RE: Accurate Bernoulli numbers on the 41C, or "how close can you get"? - Dieter - 03-21-2014, 01:37 PM RE: Accurate Bernoulli numbers on the 41C, or "how close can you get"? - Dieter - 03-28-2014, 07:56 PM

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