Free42 possible accuracy flaw
03-22-2022, 07:11 PM
Post: #5
 Albert Chan Senior Member Posts: 2,711 Joined: Jul 2018
RE: Free42 possible accuracy flaw
(03-22-2022 05:18 PM)Thomas Okken Wrote:  The repeated squaring is not the issue by itself, you're not losing 7 digits of precision from calculatiāng 39 multiplications unless something else is wrong. Note that if you calculate this using LN instead of LN1+X, you end up way off as well.

When we keep squaring, the errors also blows up exponentially.

x = 1e8 = 0b101 111 101 011 110 000 100 000 000
b = 1+1/x

Free42 (internally only do squarings)
b^(2^08) = 1.000002560003264002763521747927282
b^(2^13) = 1.000081923355125194292436470243333
...
b^(2^26) = 1.956365933428064586618947538663749

All terms to multiply has errors on the *same* side; losing 7 digits precision is normal.

Note that b^(2^8) only lost 1 ULP here.
If the base is worse, it might even lose log10(x) = 8 digits precision.

Quote:That logic is there for a reason, bid128_pow() is not very good when raising integers to integer powers, and the 2.0u2 revision of the library even includes a patch that does the same thing as the work-around I'm applying to 2.0u1.

Just because the new revision has the patch does not make it right.
Unless bid128_pow() loses *millions* of ULP's, we should limit exponent range.

Patch should only help, stop if it pass the break-even point.
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 Messages In This Thread Free42 possible accuracy flaw - J-F Garnier - 03-22-2022, 12:33 PM RE: Free42 possible accuracy flaw - Albert Chan - 03-22-2022, 04:31 PM RE: Free42 possible accuracy flaw - Thomas Okken - 03-22-2022, 05:18 PM RE: Free42 possible accuracy flaw - Albert Chan - 03-22-2022 07:11 PM RE: Free42 possible accuracy flaw - J-F Garnier - 03-24-2022, 10:20 AM RE: Free42 possible accuracy flaw - J-F Garnier - 03-24-2022, 07:18 PM RE: Free42 possible accuracy flaw - Thomas Okken - 03-22-2022, 05:39 PM RE: Free42 possible accuracy flaw - Thomas Okken - 03-22-2022, 07:38 PM RE: Free42 possible accuracy flaw - Werner - 03-23-2022, 07:30 AM RE: Free42 possible accuracy flaw - Thomas Okken - 03-22-2022, 10:08 PM RE: Free42 possible accuracy flaw - J-F Garnier - 03-23-2022, 07:57 AM RE: Free42 possible accuracy flaw - Albert Chan - 03-25-2022, 02:58 PM RE: Free42 possible accuracy flaw - Thomas Okken - 03-23-2022, 08:05 AM RE: Free42 possible accuracy flaw - Werner - 03-23-2022, 08:49 AM RE: Free42 possible accuracy flaw - Thomas Okken - 03-23-2022, 12:07 PM RE: Free42 possible accuracy flaw - Albert Chan - 03-24-2022, 04:53 PM RE: Free42 possible accuracy flaw - Thomas Okken - 03-23-2022, 06:02 PM RE: Free42 possible accuracy flaw - Thomas Okken - 03-23-2022, 07:43 PM RE: Free42 possible accuracy flaw - Albert Chan - 03-23-2022, 07:50 PM RE: Free42 possible accuracy flaw - Albert Chan - 03-23-2022, 09:11 PM RE: Free42 possible accuracy flaw - Thomas Okken - 03-24-2022, 11:02 AM RE: Free42 possible accuracy flaw - J-F Garnier - 03-24-2022, 01:02 PM RE: Free42 possible accuracy flaw - Thomas Okken - 03-24-2022, 05:01 PM RE: Free42 possible accuracy flaw - Thomas Okken - 03-24-2022, 07:45 PM RE: Free42 possible accuracy flaw - Werner - 03-25-2022, 07:03 AM RE: Free42 possible accuracy flaw - J-F Garnier - 03-25-2022, 08:03 AM RE: Free42 possible accuracy flaw - Werner - 03-30-2022, 08:04 AM RE: Free42 possible accuracy flaw - Albert Chan - 03-30-2022, 11:51 PM RE: Free42 possible accuracy flaw - Thomas Okken - 03-25-2022, 08:35 AM RE: Free42 possible accuracy flaw - Albert Chan - 03-27-2022, 10:58 PM RE: Free42 possible accuracy flaw - Werner - 03-25-2022, 08:53 AM RE: Free42 possible accuracy flaw - J-F Garnier - 03-25-2022, 11:12 AM RE: Free42 possible accuracy flaw - Thomas Okken - 03-25-2022, 09:06 AM RE: Free42 possible accuracy flaw - Thomas Okken - 03-25-2022, 09:18 AM

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