Category : BASIC Source Code
Archive   : UBAS830.ZIP
Filename : RHO.UB


˜RHO version 2.3
!˜
I˜ Factorization with rho method
R(˜
c2ŸÞñxÀ©Þñ
“<™"Pseudo prime decomposition (RHO method)"
œF˜
¶P˜ for each number
¿Z˜
ád™À§"Input an integer ="ÁƒN
ònƒNÑðŽ¿

xˆõ
Factoring_RHo(ƒN)

‚‡ñd
#
Œ˜
:
–˜ main routine
C
 ˜
`
ªõ
Factoring_Rho(ƒN)
§
´¤„SSñ)„PDñ)À˜for intermediate divisors and prime factors
Í
¾ƒNNуNÀS1Ññ
ÀSPÑðÀDPÑð
Ö
Ș
÷
Ò˜ divide by small primes
ܘ
æƒDруN)ÀƒDÑð‡ñ@

6ðƒNуD‡ñ

\ú™ƒDÁ"*"ÁÀƒNуNèƒDÀS1Ñð
f
‡ñæ
‹
S1Ž™ƒNÁ"is a prime"À‡ñä
›
™ƒNÀ‡ñä
¤"
˜
Ä,
˜ if N has a big factor
Í6
˜
Ô@
™
ÝJ
˜
þT
˜ pseudo primality check
^
˜
.h
³õPrpChk(ƒN)ÑðŽ¨S1À‡ñÖ

7r
˜
]|
˜ store in PD if pseudo prime
f†
˜
€
„PDDP)уNÀ DP
§š
SPŽ¡SPÀƒNфSSSP)À‡ñh

±¤
‡ñ
º®
˜
ä¸
˜ if composite then find a factor
þÂ
˜ with rho method
Ì
˜
/Ö
ƒN1ѳõRHO(ƒN)ÀƒN2уNèƒN1
Là
ƒN1҃N2Ž¥ƒN1ƒN2
uê
„SSSP)уN2À SPÀƒNуN1À‡ñh

~ô
˜
˜þ
˜ display results
¡˜
͍S1Ž™ƒNÁ"is a pseudo prime"À‡ñä
Ö˜
ö&˜ display small factors
ÿ0˜
:ƒNуNNÀ™À™ƒNÁ"="
:DƒDруN)ÀƒDÑð‡ñb
YN™ƒDÁ"*"ÁÀƒNуNèƒD
cX‡ñD
bDPÑñ
Ž™„PDð)À‡ñä
Šl˜
ºv˜ display big factors after re_ordering
À˜
Ί¨SW
䔉ƒIÑðŠDPÞñ
&ž„PDƒI)҄PDƒIÝñ
)Ž¥„PDƒI)„PDƒIÝñ
)ÀSWÑñ

-¨Œ
>²SW‡ñŠ
T¼‰ƒIÑðŠDPÞñ
iÆ™„PDƒI)Á"*"Á
pЌ
„Ú™„PDDPÞñ
)
‹ä•
”î˜
Âø˜ pseudo primality test w.r.t. 2,3,5,7
˘
â ³õPrpChk(ƒN)
íºOK
( €è(€ÚñÂ(ƒNÞñ
)èñƒN)ހÈñƒN))çƒNÂ
]* À(€ÚñÂ(ƒNÞñ
)èñƒN)ހÈñƒN))çƒNÂ
’4 À(€ÚñÂ(ƒNÞñ
)èñƒN)ހÈñƒN))çƒNÂ
Ç> À(€ÚñÂ(ƒNÞñ
)èñƒN)ހÈñƒN))çƒN}
ÕHÀŽOKÑð
çRÀOKÑñ

ô\•(OK)
ýf˜
+p˜RHO METHOD ver 1.2 (function version)
Oz˜ originally by J.M.Pollard
n„˜ inplemented by Y.KIDA
wŽ˜
‹˜³õRho(ƒN)
¯¢ºƒAƒX1ƒX2IƒGDƒCt
¸¬’
ö ƒA
ëÀƒX1ÑñÀƒX2Ñ(ƒX1ïñ݃A)çƒN
ôÊ’

Ô
 ƒCtÀ™€Óñ
)ÁƒCtÁ
 Þ
ƒGDÑñ

. è
‰IÑñ
Šñd
’ ò
ƒGDуGDå(ƒX2ރX1)çƒNÀƒX1Ñ(ƒX1ïñ݃A)çƒNÀƒX2Ñ((ƒX2ïñçƒN݃A)ïñ݃A)çƒN
™ ü
Œ
° 
ƒGDрăGDƒN)
Á “ƒGDÒñ

Ó “ƒGDԃN
à $•(ƒGD)