Accuracy of Free42 and DM42
12-20-2017, 08:24 PM
Post: #2
 Massimo Gnerucci Senior Member Posts: 2,448 Joined: Dec 2013
RE: Accuracy of Free42 and DM42
(12-20-2017 08:16 PM)Dieter Wrote:  Swiss Micros' DM42 now is available, and its firmware is based on Free42 Decimal. This reminds me of a remark (was it by Thomas Okken himself?), saying that Free42 works with 34 BCD arithmetics, but the implemented algorithms may not always be good for 34 digit accuracy.

So I started my good old 2014 version of Free42 Decimal, and indeed I got some results that were surprisignly inaccurate. For instance sin(45°) and cos(45°). These should equal √½.

Direct evaluation of the latter yields the correct value: 0,7071067811865475244008443621048490
This agrees with Wolfram Alpha and the WP34s.

But sin(45°) and cos(45°) both return 0,7071067811865475727373109293694142
This means only 16 correct digits and 18 digits of "numeric noise". In my Free42 version, that is.

So let me ask two questions:

- Does the above result only say that I'm using an outdated version of Free42 and current versions are more accurate, possibly with true 34-digit accuracy?

- How does the new DM42 behave in this regard?

Dieter

my DM42 returns: 0,707106781186547524400844362104849

Greetings,
Massimo

-+×÷ ↔ left is right and right is wrong
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 Messages In This Thread Accuracy of Free42 and DM42 - Dieter - 12-20-2017, 08:16 PM RE: Accuracy of Free42 and DM42 - Massimo Gnerucci - 12-20-2017 08:24 PM RE: Accuracy of Free42 and DM42 - Thomas Okken - 12-20-2017, 08:26 PM RE: Accuracy of Free42 and DM42 - Dieter - 12-20-2017, 08:36 PM RE: Accuracy of Free42 and DM42 - Thomas Okken - 12-20-2017, 08:44 PM RE: Accuracy of Free42 and DM42 - grsbanks - 12-20-2017, 08:27 PM RE: Accuracy of Free42 and DM42 - Thomas_Sch - 12-21-2017, 05:54 PM RE: Accuracy of Free42 and DM42 - Thomas Okken - 12-21-2017, 05:58 PM RE: Accuracy of Free42 and DM42 - Thomas_Sch - 12-21-2017, 06:39 PM RE: Accuracy of Free42 and DM42 - salvomic - 12-21-2017, 07:19 PM RE: Accuracy of Free42 and DM42 - Thomas Okken - 12-21-2017, 07:53 PM RE: Accuracy of Free42 and DM42 - salvomic - 12-21-2017, 09:01 PM RE: Accuracy of Free42 and DM42 - Thomas Okken - 12-21-2017, 03:17 AM RE: Accuracy of Free42 and DM42 - Dieter - 12-21-2017, 07:56 AM RE: Accuracy of Free42 and DM42 - J-F Garnier - 12-21-2017, 07:52 AM RE: Accuracy of Free42 and DM42 - Thomas Okken - 12-21-2017, 08:30 AM RE: Accuracy of Free42 and DM42 - toml_12953 - 12-21-2017, 08:45 AM RE: Accuracy of Free42 and DM42 - Thomas Okken - 12-21-2017, 08:57 AM RE: Accuracy of Free42 and DM42 - Dieter - 12-22-2017, 07:17 PM RE: Accuracy of Free42 and DM42 - grsbanks - 12-21-2017, 08:53 AM RE: Accuracy of Free42 and DM42 - Thomas Okken - 12-21-2017, 05:52 PM RE: Accuracy of Free42 and DM42 - Thomas Okken - 12-22-2017, 08:43 PM RE: Accuracy of Free42 and DM42 - Werner - 12-22-2017, 09:11 PM

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