Accuracy of Free42 and DM42

12202017, 08:16 PM
(This post was last modified: 12202017 08:18 PM by Dieter.)
Post: #1




Accuracy of Free42 and DM42
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 So let me ask two questions:  Does the above result only say that I'm using an outdated version of Free42 and current versions are more accurate, possibly with true 34digit accuracy?  How does the new DM42 behave in this regard? Dieter 

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