Natural logarithm of 2 [HP-15C/HP-42S/Free42 & others]

[C.Ret]

(06-19-2022 02:10 PM)Thomas Klemm Wrote:  This program for the HP-42S uses formula (19):

\(
\begin{align}
\ln 2= \sum_{k=1}^{\infty} \frac{1}{k \cdot 2^k}
\end{align}
\)

Code:

.. HP42S code ...

I have no idea how long it takes on a real HP-42S.

I like the way Thomas get rid of the \( 2^k \) factor by using a factorized division by 2 in his code. This spare several program steps and globally speed up all the process.

So, I immediately convert his program for my HP-15C:

Code:

001 - {    44,25 }    STO I
002 - {        0 }     0
003 - { 42,21, 0 }  f LBL 0
002 - {    45 25 }    RCL I
005 - {       33 }    1/x
006 - {       40 }     +
007 - {        2 }     2
008 - {       10 }     ÷
009 - { 42, 5,25 }  f DSE I
010 - {     22 0 }    GTO 0

The fastest and accurate result obtained with 27 as argument :
f FIX 9 f PRGM 27 R/S display 0.693147181 in least than 23"97.
The f PREFIX reveals digits 6931471805