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+--- Thread: Free42: Modulo Powering Programme (/thread-4018.html)
Free42: Modulo Powering Programme - Gerald H - 05-29-2015 03:48 PM
Free42 can reliably deal with exact calculations on integer arguments with 11 digits (possibly higher, but I'm not sure).
The programme MOD↑ calculates the Yth power of Z modulo base X.
eg For input
7777777
7777777
10^21
the programme returns
951673149961995347697.
Remember: modulo powering provides a quick pseudo-prime test, namely if
a ^ (b - 1) mod b = 1
it's a fairly safe bet b is prime.
Code:
0. { 60-Byte Prgm }
1. LBL “MOD↑”
2. STO 01
3. +/-
4. STO 00
5. R↓
6. LBL “M↑”
7. STO 02
8. R↓
9. STO 03
10. SIGN
11. GTO 00
12. LBL 01
13. 2
14. MOD
15. X≠0?
16. GTO 02
17. LASTX
18. STO/ 02
19. RCL 03
20. XEQ “SQM”
21. STO 03
22. RCL 02
23. GTO 01
24. LBL 02
25. STO- 02
26. RCL 04
27. RCL 03
28. XEQ “M*”
29. LBL 00
30. STO 04
31. RCL 02
32. X≠0?
33. GTO 01
34. R↓
35. END
0. { 45-Byte Prgm }
1. LBL “SQM”
2. STO ST Y
3. 1E11
4. MOD
5. STO ST Z
6. –
7. ENTER
8. X^2
9. RCL 00
10. MOD
11. X<>Y
12. R↑
13. STO* ST T
14. *
15. RCL 01
16. MOD
17. RCL- ST L
18. RCL+ ST L
19. RCL 01
20. MOD
21. +
22. RCL 00
23. MOD
24. +
25. RCL 01
26. MOD
27. END
0. { 60-Byte Prgm }
1. LBL “M*”
2. RCL ST X
3. 1E11
4. MOD
5. X<>Y
6. RCL- ST Y
7. COMPLEX
8. X<>Y
9. 1E11
10. MOD
11. RCL ST Z
12. RCL- ST Y
13. RCL* ST Z
14. X<>Y
15. RCL* ST Z
16. COMPLEX
17. RCL 00
18. MOD
19. +
20. RCL 01
21. MOD
22. X<>Y
23. COMPLEX
24. RCL 00
25. MOD
26. X<>Y
27. RCL 01
28. MOD
29. +
30. RCL 00
31. MOD
32. +
33. RCL 01
34. MOD
35. END