(41) Integer Decomposing (fibonacci number system)

[SlideRule]

from Number Theory in Science and Communication, M.R. Schroeder, second enlarged edition, Springer-Verlag {pgs. 346-348}

PHP Code:

C. A Calculator Program for Decomposing an Integer According to the
Fibonacci Number System
To call the program, press
     GTO "FNS"
and enter the integer to be decomposed, for example,
     1000 .
Then press
     R/S
to start the calculation. The display will show in rapid succession the
Fibonacci decomposition of 1000 and the least significant term once more
with two zeroes after the decimal point (because this is important in a
winning strategy for nim-like games; see Chap. 5):
     987.     13.     13.00
More specifically, in such a parlor game, when confronted with a pile of 1000
chips, take 13 away to start your winning strategy. (Rules of the game: No
player can take more than twice the number of chips his predecessor just
took, but each player must take at least one chip, and the first player may not
take all the chips. He who takes the last chip(s) wins.)
                            Listing for "FNS"
_________________________________________________________
Comment                                  Step  Code
_________________________________________________________
                                         01     LBL "FNS"
initialize by calculating                02     5
two constants                            03     SQRT
√5                                       04     STO 01
                                         05     1
                                         06     +
                                         07     0.5
                                         08     •
Golden ratio                             09     STO 02
                                         10     LN
                                         11     STO 03
                                         12     RDN
subroutine for                           13     LBL 14
storing new integer
subroutine for                           14     STO 04
Fibonacci decomposition
                                         15     LBL 15
                                         16     0
                                         17     RCL 04
decomposition completed?                 18     x ≤ y?
                                         19     GTO 13
                                         20     RCL 01
                                         21     •
                                         22     LN
hyperbolic cosine                        23     COSH
from MATH 1                              24     2
                                         25     •
                                         26     LN
                                         27     RCL 03
                                         28     /
                                         29     INT
                                         30     RCL 02
                                         31     x < > y
                                         32     y^x
                                         33     RCL 01
                                         34     /
                                         35     0.5
                                         36     +
                                         37     INT
                                         38     FIX 0
display Fibonacci decomposition          39     PSE
                                         40     ST- 04
                                         41     STO 05
                                         42     GTO 12
subroutine for recalling and             43     LBL 13
displaying least significant term        44     RCL05
                                         45     FIX 2
display least significant term           46     STOP
ready to start over                      47     GTO 14
                                         48     END 


real gems are yet to be revealed from 'obscure' sources.

BEST!
SlideRule

ps: follow-on to this thread, HP-41 Modulo function, in the General Forum HP Calculators (and very old HP Computers)