|WP 34S: Double precision registers - What are your feelings?|
Message #1 Posted by Marcus von Cube, Germany on 25 Dec 2011, 5:58 p.m.
I know here are some numerical analysts which may help to decide about a feature in WP 34S which may, or may not, be exposed to the user: double precision registers.
The decimal64 format used for the registers and stack provide 16 decimal digits. The decimal128 variant has room for 34 decimal digits. All internal computations are done to at least 39 digits and then rounded to the register format.
The latest firmware has added commands to switch to decimal128 as the register format, thus exposing much higher precision to the user. The commands in question are DBLON, DBLOFF (in MODE) and DBL? (in TEST). The reason to implement the feature is that we want to implement more algorithms in user code which is hopefully much more compact than the present native implementations are. We do not want to sacrifice accuracy and will therefore use double precision registers internally for this.
The question is: Is it worthwhile - or even dangerous - to expose this to the user. There will certainly be some functions which will not return results accurate to 34 decimal places. On the other hand, there are many that do, most notably the basic arithmetic but also exponentials and logarithms.
As an example, I tried PI LN EXP PI - and got 1e-33 as the result which looks very promising. 10 Phi Phi^-1 returns infinity in normal mode and (10 - 5e-13) in double precision mode as the result. The usable range of the function is obviously considerably expanded.
What are your feelings about the feature? Leave it user accessible or not? Do you have applications for it?