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+--- Thread: (33S) Pollard's Rho Factorisation (/thread-3764.html)
(33S) Pollard's Rho Factorisation - Gerald H - 05-02-2015 10:40 AM
The main programme is SPLIT: given a positive composite integer input N, SPLIT returns a factor < N , possibly neither the smallest nor prime. Maximum value of N is 10^12-1.
LN= gives the size of the programme, CK= is the check sum - these two measures are depressingly meaningful in this calculator, if length or check sum is different on your machine, this has no transcendent meaning, you have simply mis-typed the programme.
The sub programme F takes input integer & calculates the square modulo A, -A must be in B.
F1 LBL F SQUARE MODULO
F2 ENTER
F3 ENTER
F4 1000000
F5 RMDR
F6 STO Z
F7 -
F8 ENTER
F9 x2
F10 RCL B
F11 RMDR
F12 x<>y
F13 RCL* Z
F14 RCL A
F15 RMDR
F16 ENTER
F17 RCL- A
F18 +
F19 RCL A
F20 RMDR
F21 +
F22 RCL B
F23 RMDR
F24 RCL Z
F25 x2
F26 +
F27 RCL A
LN=99
F28 RMDR
CK=9D84
F29 RTN
Given integers in stack levels X & Y programme X returns the greatest common divisor of the two integers.
X1 LBL X GREATEST COMMON FACTOR
X2 RMDR
X3 LASTx
X4 x<>y
X5 x≠0?
X6 GTO X
X7 R↓
LN=27
X8 ABS
CK=848A
X9 RTN
Programme L finds small factors of input N, the number to be factored. Line 21 suggests alternative upper limits for the search.
L1 LBL L SMALL FACTORS
L2 +/-
L3 STO B
L4 +/-
L5 STO A
L6 4
L7 x>y?
L8 RTN
L9 CLx
L10 2
L11 RMDR
L12 x=0?
L13 RTN
L14 RCL A
L15 √x
L16 FP
L17 x=0?
L18 RTN
L19 LASTx
L20 IP
L21 113 Or 199 Or 283
L22 x>y?
L23 x<>y
L24 1000
L25 ÷
L26 300.002
LN=144
L27 +
CK=BFDC
L28 STO I
A1 LBL A
A2 RCL A
A3 RCL I
A4 IP
A5 RMDR
A6 x=0?
A7 RTN
A8 ISG I
A9 GTO A
A10 1
LN=48
A11 STO C
CK=1B8C
A12 RTN
N1 LBL N
N2 CLx
N3 RCL A
N4 x<>y
N5 x≠y?
LN=21
N6 RTN
CK=33B3
N7 ISG C
D1 LBL D POLLARD’S RHO
D2 1
D3 STO V
D4 STO U
D5 RANDOM
D6 RCL* A
LN=36
D7 IP
CK=9C81
D8 STO X
J1 LBL J
J2 XEQ F
J3 RCL+ C
J4 ENTER
J5 RCL- X
J6 RCL A
J7 XEQ X
J8 1
J9 x≠y?
J10 GTO N
J11 R↓
J12 R↓
J13 DSE U
J14 GTO J
J15 RCL V
J16 RCL+ V
J17 STO V
LN=69
J18 STO U
CK=3D16
J19 R↓
V1 LBL V
V2 XEQ F
V3 RCL+ C
V4 DSE U
V5 GTO V
V6 STO X
V7 RCL V
LN=30
V8 STO U
V9 R↓
CK=098A
V10 GTO J
S1 LBL S SPLIT
S2 XEQ L
S3 x≠0?
S4 GTO D
S5 RCL A
LN=21
S6 LASTx
CK=90F8
S7 RTN