Accurate Bernoulli numbers on the 41C, or "how close can you get"?

03212014, 05:54 AM
(This post was last modified: 03212014 10:48 AM by Ángel Martin.)
Post: #25




RE: Accurate Bernoulli numbers on the 41C, or "how close can you get"?
(03202014 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 precompiled. 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 doubleprecision 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 oldreliable XP machine, 9years old so likely slower than yours ;) Cheers, 'AM 

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