newRPL: Now for 39GS and 40GS! [June 29-2017]

[Claudio L.]

Please flash and try the new official ROMs for the 39gs and 40gs family:

Download the 39gs firmware: https://hpgcc3.org/downloads/newrpl39.bin
Download the 40gs firmware: https://hpgcc3.org/downloads/newrpl40.bin

And of course, the "classic" for the 50g: https://hpgcc3.org/downloads/newrplfw.bin
** NOTE **: For users upgrading from previous version: this ROM had major memory reorganization, backup all your data because it will require a memory wipe. Sorry about that, the reason is below.

As far as changes from the last release, there are a couple of bug fixes but nothing visible to the user. The main change is that the transcendental functions in the math library were completely rewritten from scratch, replaced mostly with table-free algorithms, but 2 of them needed a small table to precondition the arguments, needed perform at a decent speed. All in all, the performance at the default 32 digits precision is about 30 to 50% faster, at 12 digits precision it's about the same. At higher precisions, the old routines were faster, new ones are about 3x slower at 2000 digits. New routines use mostly multiplications, which grow in complexity with n^2 (n=digits), while the old routines used CORDIC style methods growing linearly with n.
The new routines also need some expanded precision, to produce accurate results, which means more memory had to be allocated for the real number registers. This unfortunately is a serious change and causes the need for a memory wipe (only affecting users using previous versions of newRPL).
On the positive side, those huge compressed tables were eliminated, now there's only about 80 kbytes in 2 small tables. The total firmware size now is about 720 kbytes, which fits nicely on the HP39GS 1 MB of flash.

I'm interested to get feedback on:
* Screen glitches at 64 pixels screens (39 and 40 series)
* Proposed keyboard mappings for use on the 39gs and 40gs. Right now the roms are probably not even usable due to the lack of one shift key on those calcs.
* Check power consumption on the 39 and 40.

And of course, any bug reports/comments!