Hudson/Yang-Lee

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Hudson/Yang-Lee

This website contains an archive of files for the Acorn Electron, BBC Micro, Acorn Archimedes, Commodore 16 and Commodore 64 computers, which Dominic Ford has rescued from his private collection of floppy disks and cassettes.

Some of these files were originally commercial releases in the 1980s and 1990s, but they are now widely available online. I assume that copyright over them is no longer being asserted. If you own the copyright and would like files to be removed, please contact me.

Tape/disk:	Home » Archimedes archive » Acorn User » AU 1994-01.adf » !StarInfo_StarInfo
Filename:	Hudson/Yang-Lee
Read OK:	✔
File size:	0741 bytes
Load address:	0000
Exec address:	0000

File contents

    1REM    >Yang-Lee
    2REM By  Philip Hudson
    3REM For 32-bit machinesw
    4REM (c) BAU January 1994
    5:
    6ON ERROR PROCerror
    7PROCsetup
    8PROCwhich
    9PROCscan
   10PROCplot
   11REPEATt=TIME:REPEATUNTILTIME>t+100:VDU7:UNTIL0
   12END
   13:
   14DEFPROCsetup
   15MODE 13
   16OFF
   17ORIGIN 640,512
   18Z%=16
   19acc=1E-5
   20ENDPROC
   21:
   22DEFPROCwhich
   23INPUT "Model (1 or 2) :"M%'
   24M%=(M%=1)
   25INPUT "Q-plane or X-plane :"Q$'
   26Q%=(Q$="Q" OR Q$="q")
   27IF Q% THEN
   28INPUT "Real Q ="Q
   29INPUT "Imag Q ="R
   30ENDIF
   31CLS
   32CASE Q% OF
   33WHEN TRUE:size=100/(M%+2)
   34OTHERWISE:size=100*(M%+3)
   35ENDCASE
   36ENDPROC
   37:
   38DEFPROCscan
   39FOR E%=-512 TO 511 STEP Z%
   40FOR F%=-512 TO 511 STEP Z%
   41GCOL FNiterate(E%,F%)
   42RECTANGLE FILL E%,F%,Z%-1,Z%-1
   43NEXT
   44NEXT
   45ENDPROC
   46:
   47DEFPROCplot
   48LOCAL C1%,C2%,C3%,C4%,C%
   49FOR E%=-512 TO 511 STEP Z%
   50FOR F%=-512 TO 511 STEP Z%
   51C1%=POINT(E%,F%)
   52C2%=POINT(E%+Z%,F%)
   53C3%=POINT(E%,F%+Z%)
   54C4%=POINT(E%+Z%,F%+Z%)
   55C%=C1%=C2%ANDC1%=C3%ANDC1%=C4%
   56IF NOT C% THEN PROCrig
   57NEXT
   58NEXT
   59ENDPROC
   60:
   61DEFFNiterate(E%,F%)
   62LOCAL T1%,T2%,T3%
   63IF Q% THEN
   64U=E%/size:V=F%/size
   65ELSE
   66Q=E%/size+1.5:R=F%/size:U=0:V=0
   67ENDIF
   68N%=0
   69REPEAT
   70IF M% PROCmodelI ELSE PROCmodelII
   71N%+=1
   72T1%=(ABS(U-1)<acc AND ABS(V)<acc)
   73T2%=(ABS(U)<acc AND ABS(V)<acc)
   74T3%=(U*U+V*V)>1E6
   75UNTIL T1% OR T2% OR T3% OR N%>63
   76N%=N%MOD16
   77IF T2% N%+=16 ELSE IF T3% N%+=48
   78=N%
   79:
   80DEFPROCrig
   81LOCAL X%,Y%,GX%,GY%
   82FOR X%=0 TO Z%-1 STEP 4
   83FOR Y%=0 TO Z%-1 STEP 4
   84GX%=X%+E%:GY%=Y%+F%
   85GCOL FNiterate(GX%,GY%)
   86POINT GX%,GY%
   87NEXT
   88NEXT
   89ENDPROC
   90:
   91DEFPROCmodelI
   92LOCAL X,Y,E,F,A
   93X=2*U+Q-2:Y=2*V+R
   94E=U*U-V*V+Q-1
   95F=2*U*V+R
   96A=X*X+Y*Y
   97IF A=0 A=1E-32
   98U=(X*E+Y*F)/A
   99V=(F*X-E*Y)/A
  100X=U*U-V*V
  101V=2*U*V
  102U=X
  103ENDPROC
  104:
  105DEFPROCmodelII
  106LOCAL X,Y,E,F,M,N,A
  107X=U*(U*U-3*V*V+3*Q-3)-R*(3*V+R)+(Q-1)*(Q-2)
  108Y=3*U*(U*V+R)+V*(3*Q-V*V-3)+R*(2*Q-3)
  109M=3*U*(U+Q-2)+Q*(Q-3)-3*V*(V+R)-R*R+3
  110N=3*V*(2*U+Q-2)+R*(3*U+2*Q-3)
  111A=M*M+N*N
  112IF A=0 THEN A=1E-20
  113U=(X*M+Y*N)/A
  114V=(M*Y-X*N)/A
  115X=U*U-V*V
  116V=2*U*V
  117U=X
  118ENDPROC
  119:
  120DEF PROCerror
  121ON ERROR OFF
  122IF ERR=17 THEN PRINT:END
  123PRINT REPORT$;" at line ";ERL
  124END

�    >Yang-Lee
� By  Philip Hudson
� For 32-bit machinesw
� (c) BAU January 1994
:
� � �error

�setup

�which
		�scan

	�plot
�t=�:���>t+100:�7:�0
�

:
��setup
� 13
�
ȑ 640,512
	Z%=16
acc=1E-5
�
:
��which
� "Model (1 or 2) :"M%'

M%=(M%=1)
� "Q-plane or X-plane :"Q$'
Q%=(Q$="Q" � Q$="q")

� Q% �
� "Real Q ="Q
� "Imag Q ="R
�
�
 Ȏ Q% �
!� �:size=100/(M%+2)
":size=100*(M%+3)
#�
$�
%:
&
��scan
'� E%=-512 � 511 � Z%
(� F%=-512 � 511 � Z%
)� �iterate(E%,F%)
*ȓ Ȑ E%,F%,Z%-1,Z%-1
+�
,�
-�
.:
/
��plot
0� C1%,C2%,C3%,C4%,C%
1� E%=-512 � 511 � Z%
2� F%=-512 � 511 � Z%
3C1%=�E%,F%)
4C2%=�E%+Z%,F%)
5C3%=�E%,F%+Z%)
6C4%=�E%+Z%,F%+Z%)
7C%=C1%=C2%�C1%=C3%�C1%=C4%
8� � C% � �rig
9�
:�
;�
<:
=ݤiterate(E%,F%)
>� T1%,T2%,T3%
?
� Q% �
@U=E%/size:V=F%/size
A�
B#Q=E%/size+1.5:R=F%/size:U=0:V=0
C�
DN%=0
E�
F� M% �modelI � �modelII
G	N%+=1
HT1%=(�(U-1)<acc � �(V)<acc)
IT2%=(�(U)<acc � �(V)<acc)
JT3%=(U*U+V*V)>1E6
K� T1% � T2% � T3% � N%>63
LN%=N%�16
M� T2% N%+=16 � � T3% N%+=48
N=N%
O:
P	��rig
Q� X%,Y%,GX%,GY%
R� X%=0 � Z%-1 � 4
S� Y%=0 � Z%-1 � 4
TGX%=X%+E%:GY%=Y%+F%
U� �iterate(GX%,GY%)
VȒ GX%,GY%
W�
X�
Y�
Z:
[��modelI
\� X,Y,E,F,A
]X=2*U+Q-2:Y=2*V+R
^E=U*U-V*V+Q-1
_
F=2*U*V+R
`
A=X*X+Y*Y
a� A=0 A=1E-32
bU=(X*E+Y*F)/A
cV=(F*X-E*Y)/A
d
X=U*U-V*V
eV=2*U*V
fU=X
g�
h:
i
��modelII
j� X,Y,E,F,M,N,A
k/X=U*(U*U-3*V*V+3*Q-3)-R*(3*V+R)+(Q-1)*(Q-2)
l)Y=3*U*(U*V+R)+V*(3*Q-V*V-3)+R*(2*Q-3)
m)M=3*U*(U+Q-2)+Q*(Q-3)-3*V*(V+R)-R*R+3
n!N=3*V*(2*U+Q-2)+R*(3*U+2*Q-3)
o
A=M*M+N*N
p� A=0 � A=1E-20
qU=(X*M+Y*N)/A
rV=(M*Y-X*N)/A
s
X=U*U-V*V
tV=2*U*V
uU=X
v�
w:
x� �error
y	� � �
z� �=17 � �:�
{� �$;" at line ";�
|�
�

00000000  0d 00 01 12 f4 20 20 20  20 3e 59 61 6e 67 2d 4c  |.....    >Yang-L|
00000010  65 65 0d 00 02 17 f4 20  42 79 20 20 50 68 69 6c  |ee..... By  Phil|
00000020  69 70 20 48 75 64 73 6f  6e 0d 00 03 1a f4 20 46  |ip Hudson..... F|
00000030  6f 72 20 33 32 2d 62 69  74 20 6d 61 63 68 69 6e  |or 32-bit machin|
00000040  65 73 77 0d 00 04 1a f4  20 28 63 29 20 42 41 55  |esw..... (c) BAU|
00000050  20 4a 61 6e 75 61 72 79  20 31 39 39 34 0d 00 05  | January 1994...|
00000060  05 3a 0d 00 06 0e ee 20  85 20 f2 65 72 72 6f 72  |.:..... . .error|
00000070  0d 00 07 0a f2 73 65 74  75 70 0d 00 08 0a f2 77  |.....setup.....w|
00000080  68 69 63 68 0d 00 09 09  f2 73 63 61 6e 0d 00 0a  |hich.....scan...|
00000090  09 f2 70 6c 6f 74 0d 00  0b 18 f5 74 3d 91 3a f5  |..plot.....t=.:.|
000000a0  fd 91 3e 74 2b 31 30 30  3a ef 37 3a fd 30 0d 00  |..>t+100:.7:.0..|
000000b0  0c 05 e0 0d 00 0d 05 3a  0d 00 0e 0b dd f2 73 65  |.......:......se|
000000c0  74 75 70 0d 00 0f 08 eb  20 31 33 0d 00 10 05 87  |tup..... 13.....|
000000d0  0d 00 11 0e c8 91 20 36  34 30 2c 35 31 32 0d 00  |...... 640,512..|
000000e0  12 09 5a 25 3d 31 36 0d  00 13 0c 61 63 63 3d 31  |..Z%=16....acc=1|
000000f0  45 2d 35 0d 00 14 05 e1  0d 00 15 05 3a 0d 00 16  |E-5.........:...|
00000100  0b dd f2 77 68 69 63 68  0d 00 17 1b e8 20 22 4d  |...which..... "M|
00000110  6f 64 65 6c 20 28 31 20  6f 72 20 32 29 20 3a 22  |odel (1 or 2) :"|
00000120  4d 25 27 0d 00 18 0d 4d  25 3d 28 4d 25 3d 31 29  |M%'....M%=(M%=1)|
00000130  0d 00 19 1f e8 20 22 51  2d 70 6c 61 6e 65 20 6f  |..... "Q-plane o|
00000140  72 20 58 2d 70 6c 61 6e  65 20 3a 22 51 24 27 0d  |r X-plane :"Q$'.|
00000150  00 1a 18 51 25 3d 28 51  24 3d 22 51 22 20 84 20  |...Q%=(Q$="Q" . |
00000160  51 24 3d 22 71 22 29 0d  00 1b 0a e7 20 51 25 20  |Q$="q")..... Q% |
00000170  8c 0d 00 1c 11 e8 20 22  52 65 61 6c 20 51 20 3d  |...... "Real Q =|
00000180  22 51 0d 00 1d 11 e8 20  22 49 6d 61 67 20 51 20  |"Q..... "Imag Q |
00000190  3d 22 52 0d 00 1e 05 cd  0d 00 1f 05 db 0d 00 20  |="R............ |
000001a0  0b c8 8e 20 51 25 20 ca  0d 00 21 17 c9 20 b9 3a  |... Q% ...!.. .:|
000001b0  73 69 7a 65 3d 31 30 30  2f 28 4d 25 2b 32 29 0d  |size=100/(M%+2).|
000001c0  00 22 15 7f 3a 73 69 7a  65 3d 31 30 30 2a 28 4d  |."..:size=100*(M|
000001d0  25 2b 33 29 0d 00 23 05  cb 0d 00 24 05 e1 0d 00  |%+3)..#....$....|
000001e0  25 05 3a 0d 00 26 0a dd  f2 73 63 61 6e 0d 00 27  |%.:..&...scan..'|
000001f0  18 e3 20 45 25 3d 2d 35  31 32 20 b8 20 35 31 31  |.. E%=-512 . 511|
00000200  20 88 20 5a 25 0d 00 28  18 e3 20 46 25 3d 2d 35  | . Z%..(.. F%=-5|
00000210  31 32 20 b8 20 35 31 31  20 88 20 5a 25 0d 00 29  |12 . 511 . Z%..)|
00000220  15 e6 20 a4 69 74 65 72  61 74 65 28 45 25 2c 46  |.. .iterate(E%,F|
00000230  25 29 0d 00 2a 19 c8 93  20 c8 90 20 45 25 2c 46  |%)..*... .. E%,F|
00000240  25 2c 5a 25 2d 31 2c 5a  25 2d 31 0d 00 2b 05 ed  |%,Z%-1,Z%-1..+..|
00000250  0d 00 2c 05 ed 0d 00 2d  05 e1 0d 00 2e 05 3a 0d  |..,....-......:.|
00000260  00 2f 0a dd f2 70 6c 6f  74 0d 00 30 18 ea 20 43  |./...plot..0.. C|
00000270  31 25 2c 43 32 25 2c 43  33 25 2c 43 34 25 2c 43  |1%,C2%,C3%,C4%,C|
00000280  25 0d 00 31 18 e3 20 45  25 3d 2d 35 31 32 20 b8  |%..1.. E%=-512 .|
00000290  20 35 31 31 20 88 20 5a  25 0d 00 32 18 e3 20 46  | 511 . Z%..2.. F|
000002a0  25 3d 2d 35 31 32 20 b8  20 35 31 31 20 88 20 5a  |%=-512 . 511 . Z|
000002b0  25 0d 00 33 0f 43 31 25  3d b0 45 25 2c 46 25 29  |%..3.C1%=.E%,F%)|
000002c0  0d 00 34 12 43 32 25 3d  b0 45 25 2b 5a 25 2c 46  |..4.C2%=.E%+Z%,F|
000002d0  25 29 0d 00 35 12 43 33  25 3d b0 45 25 2c 46 25  |%)..5.C3%=.E%,F%|
000002e0  2b 5a 25 29 0d 00 36 15  43 34 25 3d b0 45 25 2b  |+Z%)..6.C4%=.E%+|
000002f0  5a 25 2c 46 25 2b 5a 25  29 0d 00 37 1e 43 25 3d  |Z%,F%+Z%)..7.C%=|
00000300  43 31 25 3d 43 32 25 80  43 31 25 3d 43 33 25 80  |C1%=C2%.C1%=C3%.|
00000310  43 31 25 3d 43 34 25 0d  00 38 11 e7 20 ac 20 43  |C1%=C4%..8.. . C|
00000320  25 20 8c 20 f2 72 69 67  0d 00 39 05 ed 0d 00 3a  |% . .rig..9....:|
00000330  05 ed 0d 00 3b 05 e1 0d  00 3c 05 3a 0d 00 3d 14  |....;....<.:..=.|
00000340  dd a4 69 74 65 72 61 74  65 28 45 25 2c 46 25 29  |..iterate(E%,F%)|
00000350  0d 00 3e 11 ea 20 54 31  25 2c 54 32 25 2c 54 33  |..>.. T1%,T2%,T3|
00000360  25 0d 00 3f 0a e7 20 51  25 20 8c 0d 00 40 17 55  |%..?.. Q% ...@.U|
00000370  3d 45 25 2f 73 69 7a 65  3a 56 3d 46 25 2f 73 69  |=E%/size:V=F%/si|
00000380  7a 65 0d 00 41 05 cc 0d  00 42 23 51 3d 45 25 2f  |ze..A....B#Q=E%/|
00000390  73 69 7a 65 2b 31 2e 35  3a 52 3d 46 25 2f 73 69  |size+1.5:R=F%/si|
000003a0  7a 65 3a 55 3d 30 3a 56  3d 30 0d 00 43 05 cd 0d  |ze:U=0:V=0..C...|
000003b0  00 44 08 4e 25 3d 30 0d  00 45 05 f5 0d 00 46 1b  |.D.N%=0..E....F.|
000003c0  e7 20 4d 25 20 f2 6d 6f  64 65 6c 49 20 8b 20 f2  |. M% .modelI . .|
000003d0  6d 6f 64 65 6c 49 49 0d  00 47 09 4e 25 2b 3d 31  |modelII..G.N%+=1|
000003e0  0d 00 48 1f 54 31 25 3d  28 94 28 55 2d 31 29 3c  |..H.T1%=(.(U-1)<|
000003f0  61 63 63 20 80 20 94 28  56 29 3c 61 63 63 29 0d  |acc . .(V)<acc).|
00000400  00 49 1d 54 32 25 3d 28  94 28 55 29 3c 61 63 63  |.I.T2%=(.(U)<acc|
00000410  20 80 20 94 28 56 29 3c  61 63 63 29 0d 00 4a 15  | . .(V)<acc)..J.|
00000420  54 33 25 3d 28 55 2a 55  2b 56 2a 56 29 3e 31 45  |T3%=(U*U+V*V)>1E|
00000430  36 0d 00 4b 1d fd 20 54  31 25 20 84 20 54 32 25  |6..K.. T1% . T2%|
00000440  20 84 20 54 33 25 20 84  20 4e 25 3e 36 33 0d 00  | . T3% . N%>63..|
00000450  4c 0c 4e 25 3d 4e 25 83  31 36 0d 00 4d 1f e7 20  |L.N%=N%.16..M.. |
00000460  54 32 25 20 4e 25 2b 3d  31 36 20 8b 20 e7 20 54  |T2% N%+=16 . . T|
00000470  33 25 20 4e 25 2b 3d 34  38 0d 00 4e 07 3d 4e 25  |3% N%+=48..N.=N%|
00000480  0d 00 4f 05 3a 0d 00 50  09 dd f2 72 69 67 0d 00  |..O.:..P...rig..|
00000490  51 13 ea 20 58 25 2c 59  25 2c 47 58 25 2c 47 59  |Q.. X%,Y%,GX%,GY|
000004a0  25 0d 00 52 15 e3 20 58  25 3d 30 20 b8 20 5a 25  |%..R.. X%=0 . Z%|
000004b0  2d 31 20 88 20 34 0d 00  53 15 e3 20 59 25 3d 30  |-1 . 4..S.. Y%=0|
000004c0  20 b8 20 5a 25 2d 31 20  88 20 34 0d 00 54 17 47  | . Z%-1 . 4..T.G|
000004d0  58 25 3d 58 25 2b 45 25  3a 47 59 25 3d 59 25 2b  |X%=X%+E%:GY%=Y%+|
000004e0  46 25 0d 00 55 17 e6 20  a4 69 74 65 72 61 74 65  |F%..U.. .iterate|
000004f0  28 47 58 25 2c 47 59 25  29 0d 00 56 0e c8 92 20  |(GX%,GY%)..V... |
00000500  47 58 25 2c 47 59 25 0d  00 57 05 ed 0d 00 58 05  |GX%,GY%..W....X.|
00000510  ed 0d 00 59 05 e1 0d 00  5a 05 3a 0d 00 5b 0c dd  |...Y....Z.:..[..|
00000520  f2 6d 6f 64 65 6c 49 0d  00 5c 0f ea 20 58 2c 59  |.modelI..\.. X,Y|
00000530  2c 45 2c 46 2c 41 0d 00  5d 15 58 3d 32 2a 55 2b  |,E,F,A..].X=2*U+|
00000540  51 2d 32 3a 59 3d 32 2a  56 2b 52 0d 00 5e 11 45  |Q-2:Y=2*V+R..^.E|
00000550  3d 55 2a 55 2d 56 2a 56  2b 51 2d 31 0d 00 5f 0d  |=U*U-V*V+Q-1.._.|
00000560  46 3d 32 2a 55 2a 56 2b  52 0d 00 60 0d 41 3d 58  |F=2*U*V+R..`.A=X|
00000570  2a 58 2b 59 2a 59 0d 00  61 11 e7 20 41 3d 30 20  |*X+Y*Y..a.. A=0 |
00000580  41 3d 31 45 2d 33 32 0d  00 62 11 55 3d 28 58 2a  |A=1E-32..b.U=(X*|
00000590  45 2b 59 2a 46 29 2f 41  0d 00 63 11 56 3d 28 46  |E+Y*F)/A..c.V=(F|
000005a0  2a 58 2d 45 2a 59 29 2f  41 0d 00 64 0d 58 3d 55  |*X-E*Y)/A..d.X=U|
000005b0  2a 55 2d 56 2a 56 0d 00  65 0b 56 3d 32 2a 55 2a  |*U-V*V..e.V=2*U*|
000005c0  56 0d 00 66 07 55 3d 58  0d 00 67 05 e1 0d 00 68  |V..f.U=X..g....h|
000005d0  05 3a 0d 00 69 0d dd f2  6d 6f 64 65 6c 49 49 0d  |.:..i...modelII.|
000005e0  00 6a 13 ea 20 58 2c 59  2c 45 2c 46 2c 4d 2c 4e  |.j.. X,Y,E,F,M,N|
000005f0  2c 41 0d 00 6b 2f 58 3d  55 2a 28 55 2a 55 2d 33  |,A..k/X=U*(U*U-3|
00000600  2a 56 2a 56 2b 33 2a 51  2d 33 29 2d 52 2a 28 33  |*V*V+3*Q-3)-R*(3|
00000610  2a 56 2b 52 29 2b 28 51  2d 31 29 2a 28 51 2d 32  |*V+R)+(Q-1)*(Q-2|
00000620  29 0d 00 6c 29 59 3d 33  2a 55 2a 28 55 2a 56 2b  |)..l)Y=3*U*(U*V+|
00000630  52 29 2b 56 2a 28 33 2a  51 2d 56 2a 56 2d 33 29  |R)+V*(3*Q-V*V-3)|
00000640  2b 52 2a 28 32 2a 51 2d  33 29 0d 00 6d 29 4d 3d  |+R*(2*Q-3)..m)M=|
00000650  33 2a 55 2a 28 55 2b 51  2d 32 29 2b 51 2a 28 51  |3*U*(U+Q-2)+Q*(Q|
00000660  2d 33 29 2d 33 2a 56 2a  28 56 2b 52 29 2d 52 2a  |-3)-3*V*(V+R)-R*|
00000670  52 2b 33 0d 00 6e 21 4e  3d 33 2a 56 2a 28 32 2a  |R+3..n!N=3*V*(2*|
00000680  55 2b 51 2d 32 29 2b 52  2a 28 33 2a 55 2b 32 2a  |U+Q-2)+R*(3*U+2*|
00000690  51 2d 33 29 0d 00 6f 0d  41 3d 4d 2a 4d 2b 4e 2a  |Q-3)..o.A=M*M+N*|
000006a0  4e 0d 00 70 13 e7 20 41  3d 30 20 8c 20 41 3d 31  |N..p.. A=0 . A=1|
000006b0  45 2d 32 30 0d 00 71 11  55 3d 28 58 2a 4d 2b 59  |E-20..q.U=(X*M+Y|
000006c0  2a 4e 29 2f 41 0d 00 72  11 56 3d 28 4d 2a 59 2d  |*N)/A..r.V=(M*Y-|
000006d0  58 2a 4e 29 2f 41 0d 00  73 0d 58 3d 55 2a 55 2d  |X*N)/A..s.X=U*U-|
000006e0  56 2a 56 0d 00 74 0b 56  3d 32 2a 55 2a 56 0d 00  |V*V..t.V=2*U*V..|
000006f0  75 07 55 3d 58 0d 00 76  05 e1 0d 00 77 05 3a 0d  |u.U=X..v....w.:.|
00000700  00 78 0c dd 20 f2 65 72  72 6f 72 0d 00 79 09 ee  |.x.. .error..y..|
00000710  20 85 20 87 0d 00 7a 10  e7 20 9f 3d 31 37 20 8c  | . ...z.. .=17 .|
00000720  20 f1 3a e0 0d 00 7b 16  f1 20 f6 24 3b 22 20 61  | .:...{.. .$;" a|
00000730  74 20 6c 69 6e 65 20 22  3b 9e 0d 00 7c 05 e0 0d  |t line ";...|...|
00000740  ff                                                |.|
00000741

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