Category : BASIC Source Code
Archive   : UBAS830.ZIP
Filename : PRTEST1.UB


˜prtest1 version 2.5
P˜ ADLEMAN-POMERANCE-RUMELY's primality test
x˜ improved by H.W. Lenstra Jr.
 (˜ programmed by Yuji KIDA 1988
©2˜
´<ŸÞñx
çF™" ADLEMAN-POMERANCE-RUMELY's primality test"

P™" Lenstra's version"À™

Z§"Integer ="ÁƒN
L
d³õAdleman(ƒN)Ž™ƒNÁ"is a prime."
m
nÀ™ƒNÁ"is a composite."
t
x¿
}
‚˜
•
Œ³õADLEMAN(ƒN)
ë
–ºEETGHIJMWNPNQOKPQSWWWKX
2 ºƒEƒINƒM1ƒP1ƒSƒTƒUƒU1ƒVƒV1ƒW…U…W
_ª¤‚IndexñB$)À˜index mod Q with base G
y´¤‚PhiñB$)‚PsiñB$)
Ò¾¤„Tauñ)„Tau1ñ)„Tau2ñ)„Tau_eñ)„Sumñ)„Tau_pñ)À˜16=max of P-1
Ȥ‚Pñ)‚Qñ)‚Gñ)À˜6=no of P -1,27=no of Q -1
2Ò¤‚WKñÂñ)‚EtañÂñ)
;ܘ
Pæõ
PrimeData1
nð‰IÑðŠñÀ›‚PI)ÀŒ
ƒúõ
PrimeData2
«
‰IÑðŠñÀ›‚QI)‚GI)ÀŒ
´
˜
È
õ
PrimeData1
ê"
œñÂñÂñÂñÂñÂñ
Âñ
ó,
˜
6
õ
PrimeData2
-@
œñÂñÂñÂñÂñÂñÂñÂñ
KJ
œñ+ÂñÂñGÂñÂñÓÂñ
yT
œñÂñÂñCÂñÂñK
ÂñÂñÏ
ÂñÂñ Âñ
¿^
œñOÂñÂñƒÂñÂñ#ÂñÂñ[ÂñÂñÂñÂñÓÂñÂñ«
ÂñÂñwÂñ
h
œñgÂñÂñïÂñÂñ»
ÂñÂñcÂñÂñ/ÂñÂñOÂñÂñó
ÂñÂñC$Âñ
r
˜
%|
ƒNÑðŽ•(ƒN)
.†
˜
<
ƒSÑñ

Mš
‰NQÑðŠñ
~¤
ƒSуSå‚QNQ)ÀƒSïñ҃NŽ”‰À¶
…®
Œ
œ¸
™À™"Too big."À–À¿
£Â
·
ÝÌ
NPÑñÝ(NQÒñ)Ý(NQÒñ)Ý(NQÒñ)Ý(NQÒñ)
æÖ
˜
øà
ƒWруN)
ê
ƒW‡õDIVISOR?
ô
˜
3þ
˜** TEST FOR P=2
<˜
\™À™"main test for P="ÁñÁ
nˆõTest4_2
 &HÑñ
ŽSWÑñ
ˆõTest3_2SWсOK
®0MWÑñ

À:‰JÑðŠNQ
ãDQтQJ)ÀGтGJ)
õN™" Q="ÁQÁ
XˆõTest2_2
$bµOKŽ”‰À‡õFAILED
;lSWŽWKсH
QvÀˆõTest5_2
p€ÀµOKŽ”‰À‡õDIVISOR
¯Š‚WKðJ)сWKÀ‚EtaðJ)сETÀWKҁMWŽMWсWK
¶”Œ
Ýž˜* decide max of W and eta(chi)
嗀MWÖñ
Ž
²À‰JÑðŠNQ
,¼ÀMW҂WKðJ)Ž‚EtaðJ)Ñð—
4ÆÀŒ
LЙÀ™" passed!"
UÚ˜
mä˜** TEST for P>2
vî˜
Šø‰IÑñ
ŠNP
žPтPI)
¿ ™À™"main test for P="ÁPÁ
шõTest4_P
 HÑñ
ŽSWÑñ
ˆõTest3_PSWсOK
*˜
 4MWÑñ

, >‰JÑðŠNQ
O HQтQJ)ÀGтGJ)
w R(QÞñ
)çPŽ¨WKÀ¨ETÀ¶
‰ \™" Q="ÁQÁ
› fˆõTest2_P
º pµOKŽ”‰Â‰À‡õFAILED
ñ zSWŽWKсHÀETтIndexƒNçQ)çPÀ¶

„ˆõTest5_P
"
ŽµOKŽ”‰Â‰À‡õFAILED
)
˜·
W
¢‚WKIJ)сWKÀ‚EtaIJ)сET
s
¬WKҁMWŽMWсWK
~
¶ŒJ
¥
À˜* decide max of W and eta(chi)
·
ʍMWÖñ
Ž
Ê
ÔÀ‰JÑðŠNQ
ä
Þ ÀWKтWKIJ)
è ÀWKŽMWҁWKŽ‚EtaIJ)Ñð——
òÀŒJ
7ü™À™" passed!"
BŒI
K˜
a˜** final test
j$˜
z.ˆõGET_V
š8™À™"final test using"ÁƒV
¨BƒWÑñ

ÙLƒTÑñ
À‰IÑðŠNPÀƒTуTå‚PI)ÀŒ
æVƒT
 `ƒWуWåƒVçƒSÀƒWÑñ
‡õALLOK
8 jƒNçƒWÑð‡õ
GETDIVISOR
C t¡ƒT
L ~‘
U ˆ˜
d ’õALLOK
p œ•(ñ
)
y ¦˜
‰ °õFAILED
“ º•(ð)
œ Ę
® ÎõDIVISOR?
Ê ØƒWуN‡õALLOK
Þ âõ
GETDIVISOR
è ì•(ð)
ñ ö˜

˜** Subroutines for P=2

˜
=
˜* Check condition 3 for P=2
F
˜
W
(õTest3_2
b
2ºJ
t
<‰JÑðŠNQ
ˆ
FQтQJ)
±
P€ÈƒNQ)Öñ
Ž”‰ÀOKÑñ
˦
¿
ZŒÀOKÑð
Æ
d·
Í
n•
Ö
x˜
ú
‚˜* Check condition 4 for P=2
Œ˜
–õTest4_2
1 …WуNÞñ
ÀHÑÞñ

[ª’…UхWÀ…WхWèñÀ H“£
b´•
k¾˜
È˜* Check condition 2 for P=2
˜Ò˜
©ÜõTest2_2
ÙæƒWсQÀ(QÞñ
)çñŽƒWуNރW
ÿðƒUрڃWÂ(ƒNÞñ
)èñƒN)
4ú€ÈƒNQ)ÔðŽETÑñ
ÀOKÑ(ƒUуNÞñ
)
TÀETÑðÀOKÑ(ƒUÑñ
)
[•
d˜
ˆ"˜* Check condition 5 for P=2
‘,˜
¢6õTest5_2
Æ@ƒTрÈÞñ
Q)åQÀ˜ƒÑ^2
ûJƒTрڃT…UƒN)ÀWKÑñ
ÀOKÑñ
ÀETÑð
TƒTÑñ
Ž¶
3^ƒTуNÞñ
ŽETÑñ
˦
<h’
dr WKÀƒWуTÀƒTуTïñçƒN
‡|ƒTуNÞñ
ŽETÑñ
˦
˜†“ƒTÑñ

¿ƒWрăWƒN)ÀOKÑ(ƒWÑñ
)
Æš·
ͤ•
Ö®˜
õ¸˜** Subroutines for P>2
þ˜
"̘* Check condition 3 for P>2
+Ö˜
<àõTest3_P
G꺁J
Yô‰JÑðŠNQ
‚þQтQJ)ÀEÑ(QÞñ
)èP
Žµ£Ž
½
À€ÚƒNEQ)Öñ
Ž”‰ÀOKÑñ
˦
ËŒÀOKÑð
Ò&·
Ù0•
â:˜
D˜* Check condition 4 for P>2
0N˜ decompose N^(P%-1)-1 to P%^H%*U
9X˜
JbõTest4_P
rl…WуNï(PÞñ
)Þñ
ÀHÑÞñ

v’…UхWÀ…WхWèPÀ H“£
¤€•
­Š˜
Ñ”˜* Check condition 2 for P>2
Úž˜
¨˜ Calculation of tau(chi)^n/tau(chi^n)
²õTest2_P
$¼ºI
€ÆWÑñ
À‰IÑñ
ŠQÞñ
ÀWсWåGçQÀ‚IndexW)сIçPÀŒÀ˜calc index
ÐˆõTAU_P
ÄڍµSWŽ¢„Tau_pðÁPÞñ)Ñ¢„TauðÁPÞñ)
Íä˜
êîƒEуNèPÀˆõT_E
ø¢„Tau_eðÁPÞñ)Ñ¢„TauðÁPÞñ)
5EуNçPÀˆõJACOBI
D ˆõT_TM
Z˜MAIN OF TEST2
ƒ EтIndexƒNçQ)å(ރN)çP
µ*EсPÞñ
ŽƒWÑÞ(ƒNÞñ
)å(PÞñ
)
Û4À„TauE)Öñ
Ž¨OKÀ¶—
ó>À¡„TauE)À¨ƒW
H‰IÑðŠPÞñÀƒWуW݄TauI)ÀŒ
3ROKÑ(ƒWÑð)
:\·
Af•
Jp˜
nz˜* Check condition 5 for P>2
w„˜
œŽ˜ calculation of tan(chi)^p^u
­˜õTest5_P
½¢ºIJ
鬢„Tau1ðÁPÞñ)Ñ¢„Tau_pðÁPÞñ)
¶„Tauð)Ññ
À¢„Tauñ
ÁPÞñ)Ñð
)À‰IÑðŠ€Â…U)Þñ
Gʍ€ÃI…U)ˆõT_T1
WÔˆõT1_T1
^ތ
mèˆõT_T1
Ÿò˜ check condition 5 by making tau(chi)^p^u
ÃüWKÑñ
ÀˆõW_chiOKŽ¶
Ì ’
ö ¢„Tau1ðÁPÞñ)Ñ¢„TauðÁPÞñ)
! ¢„Tau_eðÁPÞñ)Ñ¢„TauðÁPÞñ)
<$ ‰IÑñ
Š€ÂP)Þñ
L.
ˆõT1_T1
j8
€ÃIP)ˆõT_T1
qB Œ
L ˆõT1_T1
V ˆõT_T1
¦`  WKÀˆõW_chi
³j “OK
Ït ETÒðŽOKÑñ
˦
ç~ ˜ MAIN OF TEST 5
óˆ IÑð
ü’ ¸
œ ƒTфTau_eI)
0¦ €ÄƒTƒN)Ññ
‡ñØ
Y° ƒTŽƒWрăTƒN)À¨OKÀ¶
dº  I
mÄ ¹
vÎ ˜
ˆØ ƒTÖñ
Ž
«â À€ÄƒTÞñ
ƒN)Ññ
‡ñ<
—
Ñì ÀƒWрăTÞñ
ƒN)À¨OKÀ¶
èö ÀJсIÝñ

ò
À¸
#

ÀƒTфTau_eJ)À€ÄƒTƒN)Ññ
‡ñ<
—
N
ÀƒTŽƒWрăTƒN)À¨OKÀ¶—
Z
À J
d(
À¹
m2
˜
y<
IÑð
‚F
¸
™P
ƒTфTau_eI)
ÃZ
€ÄƒTÝñ
ƒN)Ññ
ŽOKÑñ
˦
ùd
ƒTԃNÞñ
ŽƒWрăTÝñ
ƒN)À¨OKÀ¶
n
 I

x
¹
‚
·
Œ
•
$–
˜
< 
˜* decide w(chi)
Eª
˜
T´
õW_chi
_¾
ºI
qÈ
ƒTфTauð)
ƒÒ
ƒTÕñ
Ž
™Ü
ÀƒWуTÀ¨ET
²æ
À‰IÑñ
ŠPÞñ
êð
ÀƒTфTauI)ÀƒTŽƒWуW݃TÀETсI—
òú
ÀŒ
ÀOKÑ(ƒWÑñ
)
(ÀƒTԃNÞñ
Ž¨OK
DÀ‰IÑñ
ŠPÞñ
k"
À„TauI)ԃTŽ”‰À¨OKÀ¶—
Š, ÀŒÀOKÑñ
ÀETсPÞñ

‘6—
˜@·
ŸJ•
¨T˜
Ì^˜* calculation of tau(chi)^p
Õh˜
ärõTAU_P
ô|ºIJ
#†¢‚Psiñ
ÁQÞñ
)Ñ¢‚Indexñ
ÁQÞñ
)
R¢‚Phiñ
ÁQÞñ
)Ñ¢‚Indexñ
ÁQÞñ
)
‚š„Tauð)Ññ
À¢„Tauñ
ÁPÞñ)ÑðÀ˜SET 1
´¤„Tau1ð)Ññ
À¢„Tau1ñ
ÁPÞñ)ÑðÀ˜SET 1
Ï®‰IÑñ
Š€ÂP)Þñ
ḈõPSI_PSI
€ÃIP)ˆõPHY_PSI
̌
ÖˆõPSI_PSI
*àˆõT_T1
TꢄTau1ðÁPÞñ)Ñ¢„TauðÁPÞñ)
jô¨„Tau1PÞñ
)
ƒþJтPhiQÞñ
)
È ‰IÑðŠPÞñ
ÀWÑ(I݁J)çPÀ„TauW)фTau1I)ÀŒ
á ƒWфTauPÞñ
)
 ‰IÑðŠPÞñÀ„TauI)Ñ(„TauI)ރW)åQçƒNÀŒ
'& •
00 ˜
N: ˜* calculation of T^E
WD ˜
dN õT_E
tX ºIJ
žb ¢„Tau1ðÁPÞñ)Ñ¢„TauðÁPÞñ)
ªl JÑð
»v €æƒE)Ž
ç€ À€ÃJƒE)ÑðÀˆõT1_T1 JÀ‘
Š À¢„TauðÁPÞñ)Ñ¢„Tau1ðÁPÞñ)
2” ‰IсJÝñ
Š€ÂƒE)Þñ

Bž ˆõT1_T1
`¨ €ÃIƒE)ˆõT_T1
g² Œ
n¼ •
wÆ ˜
¦Ð ˜* calculation of tau(chi)^e/tau(chi^e)
¯Ú ˜
¿ä õJACOBI
Ïî ºIJ
úø ¢‚PsiðÁQÞñ
)Ñ¢‚IndexðÁQÞñ
)
# 
„Tau1ð)Ññ
À¢„Tau1ñ
ÁPÞñ)Ñð
W
JÑðÀ€ÃJE)ÑðÀˆõPSI_PSI JÀ‘
 
¢„TauðÁPÞñ)Ñ¢„Tau1ðÁPÞñ)
ª
¢‚PhiðÁQÞñ
)Ñ¢‚PsiðÁQÞñ
)
Ê *
‰IсJÝñ
Š€ÂE)Þñ

Ü 4
ˆõPSI_PSI
ý >
€ÃIE)ˆõPHY_PSI
!H
Œ
!R
•
!\
˜
5!f
˜* calculation of T=T*TM
>!p
˜
L!z
õT_TM
\!„
ºIJ
«!Ž
‰JÑðŠPÞñÀ„Tau2J)фTauð)å„Tau_eJ)çƒNÀŒÀ¨„Tau2PÞñ
)
Ã!˜
‰IÑñ
ŠPÞñ
Ù!¢
‰JÑðŠPÞñ
)"¬
WÑ(I݁J)çPÀ„Tau2W)фTau2W)݄TauI)å„Tau_eJ)çƒN
0"¶
Œ
7"À
Œ
Q"Ê
ƒWфTau2PÞñ
)
Œ"Ô
‰IÑðŠPÞñÀ„TauI)Ñ(„Tau2I)ރW)çƒNÀŒ
¶"Þ
¢„Tau2ðÁPÞñ)Ñ¢„TauðÁPÞñ)
½"è
•
Æ"ò
˜
û"ü
˜* calculation of the sum of PSI(A)*PSI(1-A)
#˜
#õPSI_PSI
%#ºIJ
>#$¢„SumðÁPÞñ
)Ñð
…#.‰IÑñŠQÞñ
À „Sum(‚PsiI)݂PsiQÝñ
ށI))çP)ÀŒ
©#8˜ calculation of T1=T1*T1*U
ì#B‰IÑðŠ(PÞñ
)èñÀ„Tau2ñåI)фTau1I)ïñçƒNÀŒ
L$L‰IÑ(PÝñ
)èñŠPÞñÀ„Tau2ñåIށP)фTau1I)ïñçƒNÀŒÀ¨„Tau2PÞñ)
b$V‰IÑðŠPÞñ
$`‰JсIÝñ
ŠPÞñ
Ó$j
WÑ(I݁J)çPÀ„Tau2W)фTau2W)Ýñå„Tau1I)å„Tau1J)çƒN
Ú$tŒ
á$~Œ
%ˆ‰JÑðŠPÞñ
À„Tau1J)фTau2ð)å„SumJ)çƒNÀŒ
6%’‰IÑñ
ŠPÞñ

L%œ‰JÑðŠPÞñ

›%¦
WÑ(I݁J)çPÀ„Tau1W)фTau1W)݄Tau2I)å„SumJ)çƒN
¢%°Œ
©%ºŒ
Ã%ăWфTau1PÞñ
)
ÿ%ΉIÑðŠPÞñÀ„Tau1I)Ñ(„Tau1I)ރW)çƒNÀŒ
&ؘ calculation of PSI^2
U&≁IÑðŠQÞñ
À‚PsiI)Ññå‚PsiI)çPÀŒ
\&ì•
e&ö˜
š&˜* calculation of the sum of PHY(A)*PSI(1-A)
£&
˜
´&õPHY_PSI
Ä&ºIJ
Ý&(¢„SumðÁPÞñ
)Ñð
$'2‰IÑñŠQÞñ
À „Sum(‚PhiI)݂PsiQÝñ
ށI))çP)ÀŒ
G'<˜ calculation of T=T*T1*SU
•'F‰JÑðŠPÞñÀ„Tau2J)фTauð)å„Tau1J)çƒNÀŒÀ¨„Tau2PÞñ
)
­'P‰IÑñ
ŠPÞñ
Ã'Z‰JÑðŠPÞñ
(d
WÑ(I݁J)çPÀ„Tau2W)фTau2W)݄TauI)å„Tau1J)çƒN
(nŒ
(xŒ
\(‚‰JÑðŠPÞñ
À„TauJ)фTau2ð)å„SumJ)çƒNÀŒ
t(Œ‰IÑñ
ŠPÞñ

Š(–‰JÑðŠPÞñ

×( 
WÑ(I݁J)çPÀ„TauW)фTauW)݄Tau2I)å„SumJ)çƒN
Þ(ªŒ
å(´Œ
þ(¾ƒWфTauPÞñ
)
8)ȉIÑðŠPÞñÀ„TauI)Ñ(„TauI)ރW)çƒNÀŒ
])Ò˜ calculation of PHY=PHY*PSY
)܉IÑðŠQÞñ
À‚PhiI)Ñ(‚PhiI)݂PsiI))çPÀŒ
¤)æ•
­)ð˜
Î)ú˜* calculation of T=T*T1
×)˜
å)õT_T1
õ)ºIJ
C*"‰JÑðŠPÞñÀ„Tau2J)фTauð)å„Tau1J)çƒNÀŒÀ¨„Tau2PÞñ
)
[*,‰IÑñ
ŠPÞñ
q*6‰JÑðŠPÞñ
À*@
WÑ(I݁J)çPÀ„Tau2W)фTau2W)݄TauI)å„Tau1J)çƒN
Ç*JŒ
Î*TŒ
è*^ƒWфTau2PÞñ
)
#+h‰IÑðŠPÞñÀ„TauI)Ñ(„Tau2I)ރW)çƒNÀŒ
*+r•
3+|˜
V+†˜* calculation of T1=T1*T1
_+˜
n+šõT1_T1
~+¤ºIJ
Á+®‰IÑðŠ(PÞñ
)èñÀ„Tau2ñåI)фTau1I)ïñçƒNÀŒ
!,¸‰IÑ(PÝñ
)èñŠPÞñÀ„Tau2ñåIށP)фTau1I)ïñçƒNÀŒÀ¨„Tau2PÞñ)
7,‰IÑðŠPÞñ
T,̉JсIÝñ
ŠPÞñ
¨,Ö
WÑ(I݁J)çPÀ„Tau2W)фTau2W)Ýñå„Tau1I)å„Tau1J)çƒN
¯,àŒ
¶,êŒ
Ð,ôƒWфTau2PÞñ
)
-þ‰IÑðŠPÞñÀ„Tau1I)Ñ(„Tau2I)ރW)çƒNÀŒ
-•
-˜
E-˜** subroutine for the final test
N-&˜
q-0˜ * calculation of V mod S
z-:˜
‰-DõGET_V
™-NºIJ
«-X‰JÑðŠNQ
Ë-bƒINтEtaðJ)ÀƒP1Ññ
ß-l‰IÑñ
ŠNP
÷-v
‚WKIJ)Ž
1.€
ÀPтPI)ÀƒU1уP1å€ÛƒP1P)ÀƒV1Ññ
ރU1
q.Š
ÀƒP1уP1åPÀƒINÑ(ƒINåƒV1݂EtaIJ)åƒU1)çƒP1
x.”Œ
¨.žQтQJ)ÀXрڂGJ)ƒINQ)
¶.¨JŽ
á.²
ÀƒU1уM1å€ÛƒM1Q)ÀƒV1Ññ
ރU1
/¼
ÀƒM1уM1åQÀƒVÑ(ƒVåƒV1݁XåƒU1)çƒM1
3/ÆÀƒM1сQÀƒVсX
:/Ќ
A/Ú•