Trig algorithms on HP RPN?

[Gerson W. Barbosa]

(12-01-2024 07:30 PM)Albert Chan Wrote:  

(12-01-2024 05:17 PM)Gerson W. Barbosa Wrote:  For example, arctan(0.00001) ~ ln (1.00001). That’s the fifth element in the arctangent table starting at register 1, generated by the HP-15C program B below, when in RAD mode. Program A computes tan(x) using the CORDIC algorithm.

Can you explain in words (better, example) how tan and log1p is used to get atan?

Actually, atan and log1p lookup tables are used to get tan and log (and exp) functions (please see https://archived.hpcalc.org/laporte/TheS...rithms.htm). Sorry if my text was not clear enough.

.x arctan(1/10^x) ln(1+1/10^x)
00 0.785398163397 0.693147180560
01 0.099668652491 0.095310179804
02 0.009999666687 0.009950330853
03 0.000999999667 0.000999500333
04 0.000100000000 0.000099995000
05 0.000010000000 0.000009999950
06 0.000001000000 0.000000999999
07 0.000000100000 0.000000100000
08 0.000000010000 0.000000010000
09 0.000000001000 0.000000001000
10 0.000000000100 0.000000000100
11 0.000000000010 0.000000000010
12 0.000000000001 0.000000000001

As Thomas Klemm has correctly pointed out, tan(x) would accept arguments in degrees if the atan table elements were in degrees rather than radians. It appears they chose radians in order do save memory, as thus the second half of the elements would be common to both tables.