Accuracy of Free42 and DM42

[Thomas Okken]

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- Does the above result only say that I'm using an outdated version of Free42 and current versions are more accurate, possibly with true 34-digit accuracy?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

It sounds like you're using an old version, from before I added Werner Huysegoms' angle reduction logic for DEG- and GRAD-mode trigs.