PC-1211, PC-1250, etc. TVM

[robve]

(06-06-2024 12:27 AM)Albert Chan Wrote:  If you have good EXP, LN, you can build accurate EXPM1 LNP1

(02-04-2019 07:28 PM)Dieters formula Wrote:  expm1(x) = (u-1) - (ln(u) - x) * u, where u = exp(x), rounded

log1p( x ) = ln(u) - ((u-1) - x) / u, where u = 1+x, rounded

Like this cryptic line to compute L=LN(1+J) and S=(1+J)^-N and R=S-1:

Code:

40 J=.01*I,K=1+J*B,C=0,L=1+J,L=LN L-(L-1-J)/L,S=-N*L,R=EXP S,R=R-1-(LN R-S)*R,S=R+1 : RETURN

Replace line 40 to 43 with the above line. With Dieters formulas there are a few minor changes for the more extreme examples, while the other examples and the 27 TVM problems I tested remain unaffected:

2)
comp FV => -900 (which is closer to -1000 and the same result as TI BA, but is a tricky one)

4)
comp FV=5527.782902 (tiny bit better in the very last digit +/- 3)
comp I%=1.902587522E-05 (slightly better in the last 2 digits)

5)
comp FV=5260.382453 (slightly better in the last 2 digits)
comp I%=3.170988253E-07 (somewhat worse, but in both cases only first 5 digits are precise and this result just differs by more)

6)
comp I%=3.1248997E-06 (somewhat worse, but in both cases only the first 3 digits are precise and this result just differs by more)

It is a bit mixed pro/cons perhaps, but I do like the improved FV accuracy.

EDIT: I should mention that SHARP PC round to 10 digits when storing values in variables. But internally 12 digits are used. This matters when calculating EXPM1 and LNP1.

EDIT 2: do not use this method to compute EXPM1 and LNP1, because for larger negative S we get R=0 and LN(R) stops with an error.

- Rob