[VA] SRC #010 - Pi Day 2022 Special

[J-F Garnier]

(03-22-2022 12:14 AM)Valentin Albillo Wrote:  

Quote:PI * PI + → 3.141608361513791562872866895754895      // true PN

VA (products for PN) errors = 15,684,238,090 ULP             // O(n^2) error ?
JFG (log sum for PN) errors = 106 ULP

Regrettably, presently I have no software available to compute the product for n = 2 to n = 100,000 with high accuracy (say, to 100 digits) so I can't check for sure, but I find it somewhat hard to believe that my computation using the 34 digits afforded by Free42 Decimal would lose 11 digits in the process, I'd rather expect 6-7 digits lost at most.

Likewise, Jean-François Garnier computation of said product using logarithms performs about 100,000 multiplications, divisions (1/x) and logarithms (LN1+X) but only loses 3 digits ? Really ?

Honestly, I'm surprised by this result too, confirmed then by Albert.
I looked further and it may be an accuracy flaw in Free42. I will open an other thread to discuss it.

J-F