.if SYSPAGE = ODD .pn pref D- .pn 1

Appendix D: A few programs for the TI-57

This appendix gives a short description of a few extended precision programs for the TI-57 [The old LED-display version!]

The programs included in this appendix are: :dl tsize=9 :dt.EPF57-I :dd.Extended Precision Factorials I
This program can calculate factorials up to 34! :dt.EPF57-II :dd.Extended Precision Factorials II
This program can calculate factorials up to 52! :dt.EPe57-I :dd.Extended Precision e I
This program calculates e to 32 places. :dt.EPe57-II :dd.Extended Precision e II
This program calculates e to 48 places. :edl .sk

Extended Precision Factorials I

About the program

This program can calculate factorials up to 34!, using more or less the same method as in the TI-58/59/66 versions. The main difference is the fact that this program cannot avoid multiplications with zero!

The execution time of the program for 34! is about 2'45".

User Instructions

The instructions for this program are:

  1. Enter the program.
  2. Initialise the program by pressing RST\INV\CT.
  3. Enter the number you want to "factorialize".
  4. Start the program by pressing R/S.
  5. When the program has finished, you can find the result in R5\[MSD] through R1\[LSD].

Listing of EPF57-I

00  66    X=T            17 -49   IINT            34  25    1/X
01  01     1             18  38 2  EXC 2          35  86 1  LBL 1
02  32 0  STO 0          19  61 2  SBR 2          36  39 1  PRD 1
03  08     8             20  34 3  SUM 3          37  39 2  PRD 2
04  84    +/-            21  33 3  RCL 3          38  39 3  PRD 3
05 -18   ILOG            22 -49   IINT            39  39 4  PRD 4
06  32 1  STO 1          23  38 3  EXC 3          40  39 5  PRD 5
07  32 6  STO 6          24  61 2  SBR 2          41  00     0
08  86 0  LBL 0          25  34 4  SUM 4          42 -61   ISBR
09  33 0  RCL 0          26  33 4  RCL 4          43  86 2  LBL 2
10  61 1  SBR 1          27 -49   IINT            44  49    INT
11  33 1  RCL 1          28  38 4  EXC 4          45  42    EE
12 -49   IINT            29  61 2  SBR 2          46  08     8
13  38 1  EXC 1          30  34 5  SUM 5          47  84    +/-
14  61 2  SBR 2          31  56    DSZ            48 -42   IEE
15  34 2  SUM 2          32  51 0  GTO 0          49 -61   ISBR
16  33 2  RCL 2          33  33 6  RCL 6

It should be noted that all arithmetic in this program is done by means of the registers!!

Extended Precision Factorials II

About the program

This program can calculate factorials up to 52!, using more or less the same method as in the TI-58/59/66 versions. Just as EPF57-I, this program cannot avoid multiplications with zero!

The extended range, compared to EPF57-I, is obtained by using a rotating stack with wrap-around. A disadvantage of this method is a severe increase in execution time!

The execution time of the program for 52! is about 8'20".

User Instructions

The instructions for this program are:

  1. Enter the program.
  2. Initialise the program by pressing RST\INV\CT.
  3. Enter the number you want to "factorialize".
  4. Start the program by pressing R/S.
  5. When the program has finished, you can find the result in all 7 registers, but the format may need some clarification:

Some examples, leading zeroes are indicated by a .: .sk

       48!          50!          52!
R7: 15592536     .1713378     43878571
R6: .7267086     .4361260     66063685
R5: 22890473     81660647     64037669
R4: 73375083     68844377     75289505
R3: 52148635     64156896     44088327
R2: 46777600     .5120003     78248065
R1:   124139     .4140932     81751709

The above indicates that the actual values of 48!, 50! and 52! are:

Listing of EPF57-II

00  66    X=T            17  49    INT            34  32 0  STO 0
01  01     1             18  42    EE             35  56    DSZ
02  32 0  STO 0          19  08     8             36  51 0  GTO 0
03  08     8             20  84    +/-            37  08     8
04  84    +/-            21 -42   IEE             38 -18   ILOG
05 -18   ILOG            22  38 1  EXC 1          39  86 2  LBL 2
06  32 1  STO 1          23  38 7  EXC 7          40  39 1  PRD 1
07  86 0  LBL 0          24  38 6  EXC 6          41  39 2  PRD 2
08  43     (             25  38 5  EXC 5          42  39 3  PRD 3
09  07     7             26  38 4  EXC 4          43  39 4  PRD 4
10  38 0  EXC 0          27  38 3  EXC 3          44  39 5  PRD 5
11  75     +             28  38 2  EXC 2          45  39 6  PRD 6
12  61 2  SBR 2          29  34 1  SUM 1          46  39 7  PRD 7
13  86 1  LBL 1          30  56    DSZ            47  00     0
14  33 1  RCL 1          31  51 1  GTO 1          48 -61   ISBR
15 -49   IINT            32  00     0
16  38 1  EXC 1          33  44     )

Extended Precision e I

About the program

This program calculates "e" to 32 places, using the same method as used in the TI-58/59/66 versions.

The execution time of the program is about 3"20', which translates to about 6" per digit.

User Instructions

The instructions for this program are:

  1. Enter the program.
  2. Start the program by pressing SBR\0.
  3. When the program has finished, you can find the result in R2\[MSD] through R5\[LSD].

Listing of EPe57-I

00  43     (             17  32 5  STO 5          34  86 2  LBL 2
01  00     0             18  44     )             35  55     x
02  61 2  SBR 2          19  86 1  LBL 1          36  33 0  RCL 0
03  33 2  RCL 2          20  07     7             37  44     )
04  61 3  SBR 3          21 -18   ILOG            38  43     (
05  32 2  STO 2          22  34 2  SUM 2          39 -42   IEE
06  61 2  SBR 2          23  56    DSZ            40  42    EE
07  33 3  RCL 3          24  71    RST            41  08     8
08  61 3  SBR 3          25 -39 2 IPRD 2          42  75     +
09  32 3  STO 3          26  15    CLR            43 -61   ISBR
10  61 2  SBR 2          27 -61   ISBR            44  86 3  LBL 3
11  33 4  RCL 4          28  86 0  LBL 0          45  65     -
12  61 3  SBR 3          29 -19   ICT             46  32 1  STO 1
13  32 4  STO 4          30  03     3             47  89    |x
14  61 2  SBR 2          31  00     0             48  49    INT
15  33 5  RCL 5          32  32 0  STO 0          49 -61   ISBR
16  61 3  SBR 3          33  51 1  GTO 1

Extended Precision e II

About the program

This program calculates "e" to 48 places, using the same method as used in the TI-58/59/66 versions. The extended capability, compared to the program on the previous page, is obtained by using a rotating stack, which allows repeated calculations to be performed on one single register. The disadvantage is once again a much longer execution time! [7'40", or almost 10" per digit]

User Instructions

The instructions for this program are:

  1. Enter the program.
  2. Start the program by pressing SBR\0.
  3. When the program has finished, you can find the result in R1\[MSD] through R6\[LSD].

Listing of EPe57-II

00  06     6             17  65     -             34  86 2  LBL 2
01  38 0  EXC 0          18  89    |x             35  32 0  STO 0
02  22    X:T            19  49    INT            36  07     7
03  43     (             20  55     x             37 -18   ILOG
04  00     0             21  38 6  EXC 6          38  34 1  SUM 1
05  55     x             22  38 5  EXC 5          39  56    DSZ
06  86 1  LBL 1          23  38 4  EXC 4          40  71    RST
07  33 0  RCL 0          24  38 3  EXC 3          41 -39 1 IPRD 1
08  22    X:T            25  38 2  EXC 2          42  15    CLR
09  32 0  STO 0          26  38 1  EXC 1          43 -61   ISBR
10  44     )             27  33 0  RCL 0          44  86 0  LBL 0
11 -42   IEE             28  22    X:T            45 -19   ICT
12  42    EE             29  32 0  STO 0          46  04     4
13  08     8             30  56    DSZ            47  00     0
14  34 1  SUM 1          31  51 1  GTO 1          48  51 2  GTO 2
15  43     (             32  44     )
16  33 1  RCL 1          33  22    X:T