Home » Archimedes archive » Acorn User » AU 1995-11.adf » !Regulars » Regulars/StarInfo/Markwick/!Numbers/!Help
Regulars/StarInfo/Markwick/!Numbers/!Help
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 1995-11.adf » !Regulars |
| Filename: | Regulars/StarInfo/Markwick/!Numbers/!Help |
| Read OK: | ✔ |
| File size: | 1BC6 bytes |
| Load address: | 0000 |
| Exec address: | 0000 |
File contents
***********************************************
* *
* Program (C) Andrew J Markwick 1994. *
* Musical entertainment by Duran Duran. *
* *
***********************************************
* You'll find this file easier to read *
* if you put your monitor in Mode 16 *
* and make it a full size !Edit window! *
***********************************************
Overview of task '!Numbers'
----------------------------
'Numbers' can calculate factorials and powers which would normally be impossible on a computer or a calculator.
Loading
-------
When you load the program a box will immediately appear asking you for an expected number of digits. Usually just pressing
<RETURN> or clicking 'OK' will do as 1000 digits is all right, but if you suspect that the calculation you want to do is going totake loads of digits then you'll need to type in a bigger number and then click 'OK' or press <RETURN>.
You can't do any calculations until you've set the maximum number of digits.
The Bar Icon
------------
Clicking the left button over the bar icon brings up the factorial engine, and clicking the right button brings up the power
engine. The middle button brings up the Bar Menu from which you can either
i. show info about the program,
ii. save the current calculated number,
iii. display the factorial engine,
iv. display the power engine,
v. display this help file,
vi. open the stored number directory, or
vii. quit the program.
The Factorial Engine
--------------------
Just enter the number you wish to know the factorial of and either press <RETURN> or click on the 'Calculate' icon.
The Power Engine
----------------
Type into the boxes the power and the base to raise to this power, and either press <RETURN> or click the 'Calculate' icon.
Intelligent Save
----------------
If this option is selected then the program will automatically save the calculated number into the 'Numbers' directory inside
the application directory (ie. '!Numbers.Numbers'), giving it a name which is appropriate to the calculation, eg. 2 to the power 100 would get filename '2�100' and 1000 factorial would get '1000fact'. Also, the resulting file is automatically sent to !Edit
for inspection.
If this option is not selected, a standard RISC-OS save box will appear when the calculation is complete.
You can always save the last calculated result from the item 'Save Current' on the menu.
How it works...
---------------
I'll now attempt to explain the algorithm.
When you load the program you specify the number of digits we'll call this x. This is the size of the array which is
DIMensioned at the start of the program for storing the answer in. That's why if x isn't high enough the program complains about the array size. I thought about just DIMensioning an array to about 30000 digits and not telling you about it but I decided in
the end to make it clear that the program has a maximum length for the answer - which you can change.
So the first thing we do is DIMension an array with x elements.
The whole algorithm depends on long multiplication. Consider the multiplication a*b. If you analyse this you'll discover that
you in fact multiply every digit of a by b but with carry, and this is the essence of the algorithm.
A loop is set up and every digit in the answer is multiplied by the base (for powers) or the next number up in sequence (for
factorials). Then for each digit in the (current) answer a check is made to see if the 'digit' is greater than ten, and if it is the tens are subtracted from that 'digit' and added as ones onto the next 'digit'. If this goes above the current number of
digits, the number of digits is changed and so on.
This is easier to see with an example.
Take 6! for example.
The program will set up an array with 1000 elements (by default, although it'll only need 3 of them!)
A 1 is put into X(0). So X(0)=1, X(1)=0, X(2)=0. #digits=0
Now a loop is enter from C=1 TO 6. Each digit is multiplied by C. So X(0)=1, X(1)=0, X(2)=0.
Now each digit is checked to see if it's >= 10. It's not, so we loop.
Obviously nothing interesting is going to happen until X(0)>=10.
C 1 2 3 4
X(0) 1 2 6 24
So when C=4 , X(0)=24, now X(0) is divided by 10 and the integer result taken (=2), which is added to X(1). The 2 is then
multiplied by 10 and subtracted from X(0). So now X(0)=4, X(1)=2, X(2)=0.
Now C=5, so X(0)=20, X(1)=10, X(0)=0, which after carry becomes... X(0)=0, X(1)=2, X(2)=1.
Finally, C=6, so X(0)=0, X(1)=12, X(2)=6, which after carry becomes... X(0)=0, X(1)=2, X(2)=7.
Now the result is read backwards, ie X(2)X(1)X(0), or 720, which is of course 6!.
Hopefully it should be obvious that the only difference for powers is that instead of multiplying every 'digit' of the answer
by the loop number C, we multiply it by the 'base' number 'power' times, ie. the loop is C=1 TO power.
Here's the algorithm.
START
DIM X(#expected digits)
X()=0 ; set all elements to zero
X(0)=1 ; set first element to 1
T=0:B=0 ; #digits in answer (T)=0
FOR C=1 TO A ; loop either factorial or power number of times.
IF factorial THEN
K=C ; multiplying number is loop number
ELSE ; it must be power
K=V ; multiplying number is always base
ENDIF
FOR E=0 TO T ; loop #digits in answer times
X(E)=X(E)*K ; multiply all digits by K
NEXT E
REPEAT
O=T
FOR E=B TO T
IF X(E)>9 PROCx ; check for 'digit'>=10 and carry if so
NEXT E
UNTIL O>=T ; for all 'digits' currently in answer
B=0
NEXT C ; loop
END
:
DEF PROCx ; PROCedure to sort out carry
H=INT(X(E)/10) ; first determine number of tens
IF H>(X(E)/10):H=H-1
X(E+1)=X(E+1)+H ; then add tens to next digit
X(E)=X(E)-(H*10) ; next subtract from current digit
IF (E+1)>T T=E+1:B=T ; now extend the number of digits in answer (T) if necessary.
ENDPROC
:
It's worth mentioning that I made this myself, by the method which seemed most sensible to me. It's entirely possible that
there's a better method for working these things out, but my way works so I'm happy.
*********************************************************************************************************************************
If anyone needs to contact me the safest bet is my home address;
7 Riversdene,
Stokesley,
Cleveland.
TS9 5DD.
Or, if it's during term time, I can be contacted by s(nail)-mail at;
Hulme Hall,
Oxford Place,
Victoria Park,
Manchester.
M14 5RR.
and by e(asy)-mail at;
AJM@fs1.ma.umist.ac.uk
Andrew J Markwick 7/10/94 1:33am.
00000000 0a 2a 2a 2a 2a 2a 2a 2a 2a 2a 2a 2a 2a 2a 2a 2a |.***************| 00000010 2a 2a 2a 2a 2a 2a 2a 2a 2a 2a 2a 2a 2a 2a 2a 2a |****************| * 00000030 0a 2a 20 20 20 20 20 20 20 20 20 20 20 20 20 20 |.* | 00000040 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 | | 00000050 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 2a | *| 00000060 0a 2a 20 20 50 72 6f 67 72 61 6d 20 28 43 29 20 |.* Program (C) | 00000070 41 6e 64 72 65 77 20 4a 20 4d 61 72 6b 77 69 63 |Andrew J Markwic| 00000080 6b 20 31 39 39 34 2e 20 20 20 20 20 20 20 20 2a |k 1994. *| 00000090 0a 2a 20 20 4d 75 73 69 63 61 6c 20 65 6e 74 65 |.* Musical ente| 000000a0 72 74 61 69 6e 6d 65 6e 74 20 62 79 20 44 75 72 |rtainment by Dur| 000000b0 61 6e 20 44 75 72 61 6e 2e 20 20 20 20 20 20 2a |an Duran. *| 000000c0 0a 2a 20 20 20 20 20 20 20 20 20 20 20 20 20 20 |.* | 000000d0 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 | | 000000e0 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 2a | *| 000000f0 0a 2a 2a 2a 2a 2a 2a 2a 2a 2a 2a 2a 2a 2a 2a 2a |.***************| 00000100 2a 2a 2a 2a 2a 2a 2a 2a 2a 2a 2a 2a 2a 2a 2a 2a |****************| * 00000120 0a 2a 20 20 20 20 59 6f 75 27 6c 6c 20 66 69 6e |.* You'll fin| 00000130 64 20 74 68 69 73 20 66 69 6c 65 20 65 61 73 69 |d this file easi| 00000140 65 72 20 74 6f 20 72 65 61 64 20 20 20 20 20 2a |er to read *| 00000150 0a 2a 20 20 20 20 69 66 20 79 6f 75 20 70 75 74 |.* if you put| 00000160 20 79 6f 75 72 20 6d 6f 6e 69 74 6f 72 20 69 6e | your monitor in| 00000170 20 4d 6f 64 65 20 31 36 20 20 20 20 20 20 20 2a | Mode 16 *| 00000180 0a 2a 20 20 20 20 61 6e 64 20 6d 61 6b 65 20 69 |.* and make i| 00000190 74 20 61 20 66 75 6c 6c 20 73 69 7a 65 20 21 45 |t a full size !E| 000001a0 64 69 74 20 77 69 6e 64 6f 77 21 20 20 20 20 2a |dit window! *| 000001b0 0a 2a 2a 2a 2a 2a 2a 2a 2a 2a 2a 2a 2a 2a 2a 2a |.***************| 000001c0 2a 2a 2a 2a 2a 2a 2a 2a 2a 2a 2a 2a 2a 2a 2a 2a |****************| * 000001e0 0a 0a 0a 0a 0a 20 20 4f 76 65 72 76 69 65 77 20 |..... Overview | 000001f0 6f 66 20 74 61 73 6b 20 27 21 4e 75 6d 62 65 72 |of task '!Number| 00000200 73 27 0a 20 20 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d |s'. -----------| 00000210 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d |----------------| 00000220 2d 20 20 20 0a 0a 20 20 27 4e 75 6d 62 65 72 73 |- .. 'Numbers| 00000230 27 20 63 61 6e 20 63 61 6c 63 75 6c 61 74 65 20 |' can calculate | 00000240 66 61 63 74 6f 72 69 61 6c 73 20 61 6e 64 20 70 |factorials and p| 00000250 6f 77 65 72 73 20 77 68 69 63 68 20 77 6f 75 6c |owers which woul| 00000260 64 20 6e 6f 72 6d 61 6c 6c 79 20 62 65 20 69 6d |d normally be im| 00000270 70 6f 73 73 69 62 6c 65 20 6f 6e 20 61 20 63 6f |possible on a co| 00000280 6d 70 75 74 65 72 20 6f 72 20 61 20 63 61 6c 63 |mputer or a calc| 00000290 75 6c 61 74 6f 72 2e 0a 0a 20 20 0a 20 20 4c 6f |ulator... . Lo| 000002a0 61 64 69 6e 67 0a 20 20 2d 2d 2d 2d 2d 2d 2d 0a |ading. -------.| 000002b0 0a 20 20 57 68 65 6e 20 79 6f 75 20 6c 6f 61 64 |. When you load| 000002c0 20 74 68 65 20 70 72 6f 67 72 61 6d 20 61 20 62 | the program a b| 000002d0 6f 78 20 77 69 6c 6c 20 69 6d 6d 65 64 69 61 74 |ox will immediat| 000002e0 65 6c 79 20 61 70 70 65 61 72 20 61 73 6b 69 6e |ely appear askin| 000002f0 67 20 79 6f 75 20 66 6f 72 20 61 6e 20 65 78 70 |g you for an exp| 00000300 65 63 74 65 64 20 6e 75 6d 62 65 72 20 6f 66 20 |ected number of | 00000310 64 69 67 69 74 73 2e 20 55 73 75 61 6c 6c 79 20 |digits. Usually | 00000320 6a 75 73 74 20 70 72 65 73 73 69 6e 67 20 0a 3c |just pressing .<| 00000330 52 45 54 55 52 4e 3e 20 6f 72 20 63 6c 69 63 6b |RETURN> or click| 00000340 69 6e 67 20 27 4f 4b 27 20 77 69 6c 6c 20 64 6f |ing 'OK' will do| 00000350 20 61 73 20 31 30 30 30 20 64 69 67 69 74 73 20 | as 1000 digits | 00000360 69 73 20 61 6c 6c 20 72 69 67 68 74 2c 20 62 75 |is all right, bu| 00000370 74 20 69 66 20 79 6f 75 20 73 75 73 70 65 63 74 |t if you suspect| 00000380 20 74 68 61 74 20 74 68 65 20 63 61 6c 63 75 6c | that the calcul| 00000390 61 74 69 6f 6e 20 79 6f 75 20 77 61 6e 74 20 74 |ation you want t| 000003a0 6f 20 64 6f 20 69 73 20 67 6f 69 6e 67 20 74 6f |o do is going to| 000003b0 74 61 6b 65 20 6c 6f 61 64 73 20 6f 66 20 64 69 |take loads of di| 000003c0 67 69 74 73 20 74 68 65 6e 20 79 6f 75 27 6c 6c |gits then you'll| 000003d0 20 6e 65 65 64 20 74 6f 20 74 79 70 65 20 69 6e | need to type in| 000003e0 20 61 20 62 69 67 67 65 72 20 6e 75 6d 62 65 72 | a bigger number| 000003f0 20 61 6e 64 20 74 68 65 6e 20 63 6c 69 63 6b 20 | and then click | 00000400 27 4f 4b 27 20 6f 72 20 70 72 65 73 73 20 3c 52 |'OK' or press <R| 00000410 45 54 55 52 4e 3e 2e 20 0a 20 20 59 6f 75 20 63 |ETURN>. . You c| 00000420 61 6e 27 74 20 64 6f 20 61 6e 79 20 63 61 6c 63 |an't do any calc| 00000430 75 6c 61 74 69 6f 6e 73 20 75 6e 74 69 6c 20 79 |ulations until y| 00000440 6f 75 27 76 65 20 73 65 74 20 74 68 65 20 6d 61 |ou've set the ma| 00000450 78 69 6d 75 6d 20 6e 75 6d 62 65 72 20 6f 66 20 |ximum number of | 00000460 64 69 67 69 74 73 2e 0a 0a 0a 20 20 54 68 65 20 |digits.... The | 00000470 42 61 72 20 49 63 6f 6e 0a 20 20 2d 2d 2d 2d 2d |Bar Icon. -----| 00000480 2d 2d 2d 2d 2d 2d 2d 0a 0a 20 20 43 6c 69 63 6b |-------.. Click| 00000490 69 6e 67 20 74 68 65 20 6c 65 66 74 20 62 75 74 |ing the left but| 000004a0 74 6f 6e 20 6f 76 65 72 20 74 68 65 20 62 61 72 |ton over the bar| 000004b0 20 69 63 6f 6e 20 62 72 69 6e 67 73 20 75 70 20 | icon brings up | 000004c0 74 68 65 20 66 61 63 74 6f 72 69 61 6c 20 65 6e |the factorial en| 000004d0 67 69 6e 65 2c 20 61 6e 64 20 63 6c 69 63 6b 69 |gine, and clicki| 000004e0 6e 67 20 74 68 65 20 72 69 67 68 74 20 62 75 74 |ng the right but| 000004f0 74 6f 6e 20 62 72 69 6e 67 73 20 75 70 20 74 68 |ton brings up th| 00000500 65 20 70 6f 77 65 72 20 0a 65 6e 67 69 6e 65 2e |e power .engine.| 00000510 20 54 68 65 20 6d 69 64 64 6c 65 20 62 75 74 74 | The middle butt| 00000520 6f 6e 20 62 72 69 6e 67 73 20 75 70 20 74 68 65 |on brings up the| 00000530 20 42 61 72 20 4d 65 6e 75 20 66 72 6f 6d 20 77 | Bar Menu from w| 00000540 68 69 63 68 20 79 6f 75 20 63 61 6e 20 65 69 74 |hich you can eit| 00000550 68 65 72 0a 20 69 2e 20 20 20 73 68 6f 77 20 69 |her. i. show i| 00000560 6e 66 6f 20 61 62 6f 75 74 20 74 68 65 20 70 72 |nfo about the pr| 00000570 6f 67 72 61 6d 2c 20 0a 20 69 69 2e 20 20 73 61 |ogram, . ii. sa| 00000580 76 65 20 74 68 65 20 63 75 72 72 65 6e 74 20 63 |ve the current c| 00000590 61 6c 63 75 6c 61 74 65 64 20 6e 75 6d 62 65 72 |alculated number| 000005a0 2c 0a 20 69 69 69 2e 20 64 69 73 70 6c 61 79 20 |,. iii. display | 000005b0 74 68 65 20 66 61 63 74 6f 72 69 61 6c 20 65 6e |the factorial en| 000005c0 67 69 6e 65 2c 0a 20 69 76 2e 20 20 64 69 73 70 |gine,. iv. disp| 000005d0 6c 61 79 20 74 68 65 20 70 6f 77 65 72 20 65 6e |lay the power en| 000005e0 67 69 6e 65 2c 0a 20 76 2e 20 20 20 64 69 73 70 |gine,. v. disp| 000005f0 6c 61 79 20 74 68 69 73 20 68 65 6c 70 20 66 69 |lay this help fi| 00000600 6c 65 2c 0a 20 76 69 2e 20 20 6f 70 65 6e 20 74 |le,. vi. open t| 00000610 68 65 20 73 74 6f 72 65 64 20 6e 75 6d 62 65 72 |he stored number| 00000620 20 64 69 72 65 63 74 6f 72 79 2c 20 6f 72 0a 20 | directory, or. | 00000630 76 69 69 2e 20 71 75 69 74 20 74 68 65 20 70 72 |vii. quit the pr| 00000640 6f 67 72 61 6d 2e 0a 0a 0a 20 20 54 68 65 20 46 |ogram.... The F| 00000650 61 63 74 6f 72 69 61 6c 20 45 6e 67 69 6e 65 0a |actorial Engine.| 00000660 20 20 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d | --------------| 00000670 2d 2d 2d 2d 2d 2d 0a 0a 20 20 4a 75 73 74 20 65 |------.. Just e| 00000680 6e 74 65 72 20 74 68 65 20 6e 75 6d 62 65 72 20 |nter the number | 00000690 79 6f 75 20 77 69 73 68 20 74 6f 20 6b 6e 6f 77 |you wish to know| 000006a0 20 74 68 65 20 66 61 63 74 6f 72 69 61 6c 20 6f | the factorial o| 000006b0 66 20 61 6e 64 20 65 69 74 68 65 72 20 70 72 65 |f and either pre| 000006c0 73 73 20 3c 52 45 54 55 52 4e 3e 20 6f 72 20 63 |ss <RETURN> or c| 000006d0 6c 69 63 6b 20 6f 6e 20 74 68 65 20 27 43 61 6c |lick on the 'Cal| 000006e0 63 75 6c 61 74 65 27 20 69 63 6f 6e 2e 0a 0a 0a |culate' icon....| 000006f0 20 20 54 68 65 20 50 6f 77 65 72 20 45 6e 67 69 | The Power Engi| 00000700 6e 65 0a 20 20 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d |ne. -----------| 00000710 2d 2d 2d 2d 2d 0a 0a 20 20 54 79 70 65 20 69 6e |-----.. Type in| 00000720 74 6f 20 74 68 65 20 62 6f 78 65 73 20 74 68 65 |to the boxes the| 00000730 20 70 6f 77 65 72 20 61 6e 64 20 74 68 65 20 62 | power and the b| 00000740 61 73 65 20 74 6f 20 72 61 69 73 65 20 74 6f 20 |ase to raise to | 00000750 74 68 69 73 20 70 6f 77 65 72 2c 20 61 6e 64 20 |this power, and | 00000760 65 69 74 68 65 72 20 70 72 65 73 73 20 3c 52 45 |either press <RE| 00000770 54 55 52 4e 3e 20 6f 72 20 63 6c 69 63 6b 20 74 |TURN> or click t| 00000780 68 65 20 27 43 61 6c 63 75 6c 61 74 65 27 20 69 |he 'Calculate' i| 00000790 63 6f 6e 2e 0a 0a 0a 20 20 49 6e 74 65 6c 6c 69 |con.... Intelli| 000007a0 67 65 6e 74 20 53 61 76 65 0a 20 20 2d 2d 2d 2d |gent Save. ----| 000007b0 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a 0a 20 20 |------------.. | 000007c0 49 66 20 74 68 69 73 20 6f 70 74 69 6f 6e 20 69 |If this option i| 000007d0 73 20 73 65 6c 65 63 74 65 64 20 74 68 65 6e 20 |s selected then | 000007e0 74 68 65 20 70 72 6f 67 72 61 6d 20 77 69 6c 6c |the program will| 000007f0 20 61 75 74 6f 6d 61 74 69 63 61 6c 6c 79 20 73 | automatically s| 00000800 61 76 65 20 74 68 65 20 63 61 6c 63 75 6c 61 74 |ave the calculat| 00000810 65 64 20 6e 75 6d 62 65 72 20 69 6e 74 6f 20 74 |ed number into t| 00000820 68 65 20 27 4e 75 6d 62 65 72 73 27 20 64 69 72 |he 'Numbers' dir| 00000830 65 63 74 6f 72 79 20 69 6e 73 69 64 65 20 0a 74 |ectory inside .t| 00000840 68 65 20 61 70 70 6c 69 63 61 74 69 6f 6e 20 64 |he application d| 00000850 69 72 65 63 74 6f 72 79 20 28 69 65 2e 20 27 21 |irectory (ie. '!| 00000860 4e 75 6d 62 65 72 73 2e 4e 75 6d 62 65 72 73 27 |Numbers.Numbers'| 00000870 29 2c 20 67 69 76 69 6e 67 20 69 74 20 61 20 6e |), giving it a n| 00000880 61 6d 65 20 77 68 69 63 68 20 69 73 20 61 70 70 |ame which is app| 00000890 72 6f 70 72 69 61 74 65 20 74 6f 20 74 68 65 20 |ropriate to the | 000008a0 63 61 6c 63 75 6c 61 74 69 6f 6e 2c 20 65 67 2e |calculation, eg.| 000008b0 20 32 20 74 6f 20 74 68 65 20 70 6f 77 65 72 20 | 2 to the power | 000008c0 31 30 30 20 77 6f 75 6c 64 20 67 65 74 20 66 69 |100 would get fi| 000008d0 6c 65 6e 61 6d 65 20 27 32 8b 31 30 30 27 20 61 |lename '2.100' a| 000008e0 6e 64 20 31 30 30 30 20 66 61 63 74 6f 72 69 61 |nd 1000 factoria| 000008f0 6c 20 77 6f 75 6c 64 20 67 65 74 20 27 31 30 30 |l would get '100| 00000900 30 66 61 63 74 27 2e 20 41 6c 73 6f 2c 20 74 68 |0fact'. Also, th| 00000910 65 20 72 65 73 75 6c 74 69 6e 67 20 66 69 6c 65 |e resulting file| 00000920 20 69 73 20 61 75 74 6f 6d 61 74 69 63 61 6c 6c | is automaticall| 00000930 79 20 73 65 6e 74 20 74 6f 20 21 45 64 69 74 20 |y sent to !Edit | 00000940 0a 66 6f 72 20 69 6e 73 70 65 63 74 69 6f 6e 2e |.for inspection.| 00000950 0a 20 20 49 66 20 74 68 69 73 20 6f 70 74 69 6f |. If this optio| 00000960 6e 20 69 73 20 6e 6f 74 20 73 65 6c 65 63 74 65 |n is not selecte| 00000970 64 2c 20 61 20 73 74 61 6e 64 61 72 64 20 52 49 |d, a standard RI| 00000980 53 43 2d 4f 53 20 73 61 76 65 20 62 6f 78 20 77 |SC-OS save box w| 00000990 69 6c 6c 20 61 70 70 65 61 72 20 77 68 65 6e 20 |ill appear when | 000009a0 74 68 65 20 63 61 6c 63 75 6c 61 74 69 6f 6e 20 |the calculation | 000009b0 69 73 20 63 6f 6d 70 6c 65 74 65 2e 0a 20 20 59 |is complete.. Y| 000009c0 6f 75 20 63 61 6e 20 61 6c 77 61 79 73 20 73 61 |ou can always sa| 000009d0 76 65 20 74 68 65 20 6c 61 73 74 20 63 61 6c 63 |ve the last calc| 000009e0 75 6c 61 74 65 64 20 72 65 73 75 6c 74 20 66 72 |ulated result fr| 000009f0 6f 6d 20 74 68 65 20 69 74 65 6d 20 27 53 61 76 |om the item 'Sav| 00000a00 65 20 43 75 72 72 65 6e 74 27 20 6f 6e 20 74 68 |e Current' on th| 00000a10 65 20 6d 65 6e 75 2e 0a 0a 0a 20 20 48 6f 77 20 |e menu.... How | 00000a20 69 74 20 77 6f 72 6b 73 2e 2e 2e 0a 20 20 2d 2d |it works.... --| 00000a30 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a 0a 20 |-------------.. | 00000a40 20 49 27 6c 6c 20 6e 6f 77 20 61 74 74 65 6d 70 | I'll now attemp| 00000a50 74 20 74 6f 20 65 78 70 6c 61 69 6e 20 74 68 65 |t to explain the| 00000a60 20 61 6c 67 6f 72 69 74 68 6d 2e 0a 20 20 57 68 | algorithm.. Wh| 00000a70 65 6e 20 79 6f 75 20 6c 6f 61 64 20 74 68 65 20 |en you load the | 00000a80 70 72 6f 67 72 61 6d 20 79 6f 75 20 73 70 65 63 |program you spec| 00000a90 69 66 79 20 74 68 65 20 6e 75 6d 62 65 72 20 6f |ify the number o| 00000aa0 66 20 64 69 67 69 74 73 20 77 65 27 6c 6c 20 63 |f digits we'll c| 00000ab0 61 6c 6c 20 74 68 69 73 20 78 2e 20 54 68 69 73 |all this x. This| 00000ac0 20 69 73 20 74 68 65 20 73 69 7a 65 20 6f 66 20 | is the size of | 00000ad0 74 68 65 20 61 72 72 61 79 20 77 68 69 63 68 20 |the array which | 00000ae0 69 73 20 0a 44 49 4d 65 6e 73 69 6f 6e 65 64 20 |is .DIMensioned | 00000af0 61 74 20 74 68 65 20 73 74 61 72 74 20 6f 66 20 |at the start of | 00000b00 74 68 65 20 70 72 6f 67 72 61 6d 20 66 6f 72 20 |the program for | 00000b10 73 74 6f 72 69 6e 67 20 74 68 65 20 61 6e 73 77 |storing the answ| 00000b20 65 72 20 69 6e 2e 20 54 68 61 74 27 73 20 77 68 |er in. That's wh| 00000b30 79 20 69 66 20 78 20 69 73 6e 27 74 20 68 69 67 |y if x isn't hig| 00000b40 68 20 65 6e 6f 75 67 68 20 74 68 65 20 70 72 6f |h enough the pro| 00000b50 67 72 61 6d 20 63 6f 6d 70 6c 61 69 6e 73 20 61 |gram complains a| 00000b60 62 6f 75 74 20 74 68 65 20 61 72 72 61 79 20 73 |bout the array s| 00000b70 69 7a 65 2e 20 49 20 74 68 6f 75 67 68 74 20 61 |ize. I thought a| 00000b80 62 6f 75 74 20 6a 75 73 74 20 44 49 4d 65 6e 73 |bout just DIMens| 00000b90 69 6f 6e 69 6e 67 20 61 6e 20 61 72 72 61 79 20 |ioning an array | 00000ba0 74 6f 20 61 62 6f 75 74 20 33 30 30 30 30 20 64 |to about 30000 d| 00000bb0 69 67 69 74 73 20 61 6e 64 20 6e 6f 74 20 74 65 |igits and not te| 00000bc0 6c 6c 69 6e 67 20 79 6f 75 20 61 62 6f 75 74 20 |lling you about | 00000bd0 69 74 20 62 75 74 20 49 20 64 65 63 69 64 65 64 |it but I decided| 00000be0 20 69 6e 20 0a 74 68 65 20 65 6e 64 20 74 6f 20 | in .the end to | 00000bf0 6d 61 6b 65 20 69 74 20 63 6c 65 61 72 20 74 68 |make it clear th| 00000c00 61 74 20 74 68 65 20 70 72 6f 67 72 61 6d 20 68 |at the program h| 00000c10 61 73 20 61 20 6d 61 78 69 6d 75 6d 20 6c 65 6e |as a maximum len| 00000c20 67 74 68 20 66 6f 72 20 74 68 65 20 61 6e 73 77 |gth for the answ| 00000c30 65 72 20 2d 20 77 68 69 63 68 20 79 6f 75 20 63 |er - which you c| 00000c40 61 6e 20 63 68 61 6e 67 65 2e 0a 20 20 53 6f 20 |an change.. So | 00000c50 74 68 65 20 66 69 72 73 74 20 74 68 69 6e 67 20 |the first thing | 00000c60 77 65 20 64 6f 20 69 73 20 44 49 4d 65 6e 73 69 |we do is DIMensi| 00000c70 6f 6e 20 61 6e 20 61 72 72 61 79 20 77 69 74 68 |on an array with| 00000c80 20 78 20 65 6c 65 6d 65 6e 74 73 2e 0a 20 20 54 | x elements.. T| 00000c90 68 65 20 77 68 6f 6c 65 20 61 6c 67 6f 72 69 74 |he whole algorit| 00000ca0 68 6d 20 64 65 70 65 6e 64 73 20 6f 6e 20 6c 6f |hm depends on lo| 00000cb0 6e 67 20 6d 75 6c 74 69 70 6c 69 63 61 74 69 6f |ng multiplicatio| 00000cc0 6e 2e 20 43 6f 6e 73 69 64 65 72 20 74 68 65 20 |n. Consider the | 00000cd0 6d 75 6c 74 69 70 6c 69 63 61 74 69 6f 6e 20 61 |multiplication a| 00000ce0 2a 62 2e 20 49 66 20 79 6f 75 20 61 6e 61 6c 79 |*b. If you analy| 00000cf0 73 65 20 74 68 69 73 20 79 6f 75 27 6c 6c 20 64 |se this you'll d| 00000d00 69 73 63 6f 76 65 72 20 74 68 61 74 20 0a 79 6f |iscover that .yo| 00000d10 75 20 69 6e 20 66 61 63 74 20 6d 75 6c 74 69 70 |u in fact multip| 00000d20 6c 79 20 65 76 65 72 79 20 64 69 67 69 74 20 6f |ly every digit o| 00000d30 66 20 61 20 62 79 20 62 20 62 75 74 20 77 69 74 |f a by b but wit| 00000d40 68 20 63 61 72 72 79 2c 20 61 6e 64 20 74 68 69 |h carry, and thi| 00000d50 73 20 69 73 20 74 68 65 20 65 73 73 65 6e 63 65 |s is the essence| 00000d60 20 6f 66 20 74 68 65 20 61 6c 67 6f 72 69 74 68 | of the algorith| 00000d70 6d 2e 0a 20 20 41 20 6c 6f 6f 70 20 69 73 20 73 |m.. A loop is s| 00000d80 65 74 20 75 70 20 61 6e 64 20 65 76 65 72 79 20 |et up and every | 00000d90 64 69 67 69 74 20 69 6e 20 74 68 65 20 61 6e 73 |digit in the ans| 00000da0 77 65 72 20 69 73 20 6d 75 6c 74 69 70 6c 69 65 |wer is multiplie| 00000db0 64 20 62 79 20 74 68 65 20 62 61 73 65 20 28 66 |d by the base (f| 00000dc0 6f 72 20 70 6f 77 65 72 73 29 20 6f 72 20 74 68 |or powers) or th| 00000dd0 65 20 6e 65 78 74 20 6e 75 6d 62 65 72 20 75 70 |e next number up| 00000de0 20 69 6e 20 73 65 71 75 65 6e 63 65 20 28 66 6f | in sequence (fo| 00000df0 72 20 0a 66 61 63 74 6f 72 69 61 6c 73 29 2e 20 |r .factorials). | 00000e00 54 68 65 6e 20 66 6f 72 20 65 61 63 68 20 64 69 |Then for each di| 00000e10 67 69 74 20 69 6e 20 74 68 65 20 28 63 75 72 72 |git in the (curr| 00000e20 65 6e 74 29 20 61 6e 73 77 65 72 20 61 20 63 68 |ent) answer a ch| 00000e30 65 63 6b 20 69 73 20 6d 61 64 65 20 74 6f 20 73 |eck is made to s| 00000e40 65 65 20 69 66 20 74 68 65 20 27 64 69 67 69 74 |ee if the 'digit| 00000e50 27 20 69 73 20 67 72 65 61 74 65 72 20 74 68 61 |' is greater tha| 00000e60 6e 20 74 65 6e 2c 20 61 6e 64 20 69 66 20 69 74 |n ten, and if it| 00000e70 20 69 73 20 74 68 65 20 74 65 6e 73 20 61 72 65 | is the tens are| 00000e80 20 73 75 62 74 72 61 63 74 65 64 20 66 72 6f 6d | subtracted from| 00000e90 20 74 68 61 74 20 27 64 69 67 69 74 27 20 61 6e | that 'digit' an| 00000ea0 64 20 61 64 64 65 64 20 61 73 20 6f 6e 65 73 20 |d added as ones | 00000eb0 6f 6e 74 6f 20 74 68 65 20 6e 65 78 74 20 27 64 |onto the next 'd| 00000ec0 69 67 69 74 27 2e 20 49 66 20 74 68 69 73 20 67 |igit'. If this g| 00000ed0 6f 65 73 20 61 62 6f 76 65 20 74 68 65 20 63 75 |oes above the cu| 00000ee0 72 72 65 6e 74 20 6e 75 6d 62 65 72 20 6f 66 20 |rrent number of | 00000ef0 0a 64 69 67 69 74 73 2c 20 74 68 65 20 6e 75 6d |.digits, the num| 00000f00 62 65 72 20 6f 66 20 64 69 67 69 74 73 20 69 73 |ber of digits is| 00000f10 20 63 68 61 6e 67 65 64 20 61 6e 64 20 73 6f 20 | changed and so | 00000f20 6f 6e 2e 0a 20 20 54 68 69 73 20 69 73 20 65 61 |on.. This is ea| 00000f30 73 69 65 72 20 74 6f 20 73 65 65 20 77 69 74 68 |sier to see with| 00000f40 20 61 6e 20 65 78 61 6d 70 6c 65 2e 0a 0a 20 20 | an example... | 00000f50 54 61 6b 65 20 36 21 20 66 6f 72 20 65 78 61 6d |Take 6! for exam| 00000f60 70 6c 65 2e 0a 20 20 54 68 65 20 70 72 6f 67 72 |ple.. The progr| 00000f70 61 6d 20 77 69 6c 6c 20 73 65 74 20 75 70 20 61 |am will set up a| 00000f80 6e 20 61 72 72 61 79 20 77 69 74 68 20 31 30 30 |n array with 100| 00000f90 30 20 65 6c 65 6d 65 6e 74 73 20 28 62 79 20 64 |0 elements (by d| 00000fa0 65 66 61 75 6c 74 2c 20 61 6c 74 68 6f 75 67 68 |efault, although| 00000fb0 20 69 74 27 6c 6c 20 6f 6e 6c 79 20 6e 65 65 64 | it'll only need| 00000fc0 20 33 20 6f 66 20 74 68 65 6d 21 29 0a 20 20 41 | 3 of them!). A| 00000fd0 20 31 20 69 73 20 70 75 74 20 69 6e 74 6f 20 58 | 1 is put into X| 00000fe0 28 30 29 2e 20 20 53 6f 20 58 28 30 29 3d 31 2c |(0). So X(0)=1,| 00000ff0 20 58 28 31 29 3d 30 2c 20 58 28 32 29 3d 30 2e | X(1)=0, X(2)=0.| 00001000 20 23 64 69 67 69 74 73 3d 30 0a 20 20 4e 6f 77 | #digits=0. Now| 00001010 20 61 20 6c 6f 6f 70 20 69 73 20 65 6e 74 65 72 | a loop is enter| 00001020 20 66 72 6f 6d 20 43 3d 31 20 54 4f 20 36 2e 20 | from C=1 TO 6. | 00001030 45 61 63 68 20 64 69 67 69 74 20 69 73 20 6d 75 |Each digit is mu| 00001040 6c 74 69 70 6c 69 65 64 20 62 79 20 43 2e 20 53 |ltiplied by C. S| 00001050 6f 20 58 28 30 29 3d 31 2c 20 58 28 31 29 3d 30 |o X(0)=1, X(1)=0| 00001060 2c 20 58 28 32 29 3d 30 2e 0a 20 20 4e 6f 77 20 |, X(2)=0.. Now | 00001070 65 61 63 68 20 64 69 67 69 74 20 69 73 20 63 68 |each digit is ch| 00001080 65 63 6b 65 64 20 74 6f 20 73 65 65 20 69 66 20 |ecked to see if | 00001090 69 74 27 73 20 3e 3d 20 31 30 2e 20 49 74 27 73 |it's >= 10. It's| 000010a0 20 6e 6f 74 2c 20 73 6f 20 77 65 20 6c 6f 6f 70 | not, so we loop| 000010b0 2e 0a 20 20 4f 62 76 69 6f 75 73 6c 79 20 6e 6f |.. Obviously no| 000010c0 74 68 69 6e 67 20 69 6e 74 65 72 65 73 74 69 6e |thing interestin| 000010d0 67 20 69 73 20 67 6f 69 6e 67 20 74 6f 20 68 61 |g is going to ha| 000010e0 70 70 65 6e 20 75 6e 74 69 6c 20 58 28 30 29 3e |ppen until X(0)>| 000010f0 3d 31 30 2e 0a 0a 20 20 20 20 43 20 20 20 20 20 |=10... C | 00001100 20 20 31 20 20 20 20 20 20 20 32 20 20 20 20 20 | 1 2 | 00001110 20 20 33 20 20 20 20 20 20 20 34 0a 20 20 20 20 | 3 4. | 00001120 58 28 30 29 20 20 20 20 31 20 20 20 20 20 20 20 |X(0) 1 | 00001130 32 20 20 20 20 20 20 20 36 20 20 20 20 20 20 20 |2 6 | 00001140 32 34 0a 0a 20 20 53 6f 20 77 68 65 6e 20 43 3d |24.. So when C=| 00001150 34 20 2c 20 58 28 30 29 3d 32 34 2c 20 6e 6f 77 |4 , X(0)=24, now| 00001160 20 58 28 30 29 20 69 73 20 64 69 76 69 64 65 64 | X(0) is divided| 00001170 20 62 79 20 31 30 20 61 6e 64 20 74 68 65 20 69 | by 10 and the i| 00001180 6e 74 65 67 65 72 20 72 65 73 75 6c 74 20 74 61 |nteger result ta| 00001190 6b 65 6e 20 28 3d 32 29 2c 20 77 68 69 63 68 20 |ken (=2), which | 000011a0 69 73 20 61 64 64 65 64 20 74 6f 20 58 28 31 29 |is added to X(1)| 000011b0 2e 20 54 68 65 20 32 20 69 73 20 74 68 65 6e 20 |. The 2 is then | 000011c0 0a 6d 75 6c 74 69 70 6c 69 65 64 20 62 79 20 31 |.multiplied by 1| 000011d0 30 20 61 6e 64 20 73 75 62 74 72 61 63 74 65 64 |0 and subtracted| 000011e0 20 66 72 6f 6d 20 58 28 30 29 2e 20 53 6f 20 6e | from X(0). So n| 000011f0 6f 77 20 58 28 30 29 3d 34 2c 20 58 28 31 29 3d |ow X(0)=4, X(1)=| 00001200 32 2c 20 58 28 32 29 3d 30 2e 0a 20 20 4e 6f 77 |2, X(2)=0.. Now| 00001210 20 43 3d 35 2c 20 73 6f 20 58 28 30 29 3d 32 30 | C=5, so X(0)=20| 00001220 2c 20 58 28 31 29 3d 31 30 2c 20 58 28 30 29 3d |, X(1)=10, X(0)=| 00001230 30 2c 20 77 68 69 63 68 20 61 66 74 65 72 20 63 |0, which after c| 00001240 61 72 72 79 20 62 65 63 6f 6d 65 73 2e 2e 2e 20 |arry becomes... | 00001250 58 28 30 29 3d 30 2c 20 58 28 31 29 3d 32 2c 20 |X(0)=0, X(1)=2, | 00001260 58 28 32 29 3d 31 2e 0a 20 20 46 69 6e 61 6c 6c |X(2)=1.. Finall| 00001270 79 2c 20 43 3d 36 2c 20 73 6f 20 58 28 30 29 3d |y, C=6, so X(0)=| 00001280 30 2c 20 58 28 31 29 3d 31 32 2c 20 58 28 32 29 |0, X(1)=12, X(2)| 00001290 3d 36 2c 20 77 68 69 63 68 20 61 66 74 65 72 20 |=6, which after | 000012a0 63 61 72 72 79 20 62 65 63 6f 6d 65 73 2e 2e 2e |carry becomes...| 000012b0 20 58 28 30 29 3d 30 2c 20 58 28 31 29 3d 32 2c | X(0)=0, X(1)=2,| 000012c0 20 58 28 32 29 3d 37 2e 0a 20 20 4e 6f 77 20 74 | X(2)=7.. Now t| 000012d0 68 65 20 72 65 73 75 6c 74 20 69 73 20 72 65 61 |he result is rea| 000012e0 64 20 62 61 63 6b 77 61 72 64 73 2c 20 69 65 20 |d backwards, ie | 000012f0 58 28 32 29 58 28 31 29 58 28 30 29 2c 20 6f 72 |X(2)X(1)X(0), or| 00001300 20 37 32 30 2c 20 77 68 69 63 68 20 69 73 20 6f | 720, which is o| 00001310 66 20 63 6f 75 72 73 65 20 36 21 2e 0a 0a 20 20 |f course 6!... | 00001320 48 6f 70 65 66 75 6c 6c 79 20 69 74 20 73 68 6f |Hopefully it sho| 00001330 75 6c 64 20 62 65 20 6f 62 76 69 6f 75 73 20 74 |uld be obvious t| 00001340 68 61 74 20 74 68 65 20 6f 6e 6c 79 20 64 69 66 |hat the only dif| 00001350 66 65 72 65 6e 63 65 20 66 6f 72 20 70 6f 77 65 |ference for powe| 00001360 72 73 20 69 73 20 74 68 61 74 20 69 6e 73 74 65 |rs is that inste| 00001370 61 64 20 6f 66 20 6d 75 6c 74 69 70 6c 79 69 6e |ad of multiplyin| 00001380 67 20 65 76 65 72 79 20 27 64 69 67 69 74 27 20 |g every 'digit' | 00001390 6f 66 20 74 68 65 20 61 6e 73 77 65 72 20 0a 62 |of the answer .b| 000013a0 79 20 74 68 65 20 6c 6f 6f 70 20 6e 75 6d 62 65 |y the loop numbe| 000013b0 72 20 43 2c 20 77 65 20 6d 75 6c 74 69 70 6c 79 |r C, we multiply| 000013c0 20 69 74 20 62 79 20 74 68 65 20 27 62 61 73 65 | it by the 'base| 000013d0 27 20 6e 75 6d 62 65 72 20 27 70 6f 77 65 72 27 |' number 'power'| 000013e0 20 74 69 6d 65 73 2c 20 69 65 2e 20 74 68 65 20 | times, ie. the | 000013f0 6c 6f 6f 70 20 69 73 20 43 3d 31 20 54 4f 20 70 |loop is C=1 TO p| 00001400 6f 77 65 72 2e 0a 0a 20 20 48 65 72 65 27 73 20 |ower... Here's | 00001410 74 68 65 20 61 6c 67 6f 72 69 74 68 6d 2e 0a 0a |the algorithm...| 00001420 20 20 20 53 54 41 52 54 0a 20 20 20 20 44 49 4d | START. DIM| 00001430 20 58 28 23 65 78 70 65 63 74 65 64 20 64 69 67 | X(#expected dig| 00001440 69 74 73 29 0a 20 20 20 20 58 28 29 3d 30 20 20 |its). X()=0 | 00001450 20 20 20 20 20 20 20 3b 20 73 65 74 20 61 6c 6c | ; set all| 00001460 20 65 6c 65 6d 65 6e 74 73 20 74 6f 20 7a 65 72 | elements to zer| 00001470 6f 0a 20 20 20 20 58 28 30 29 3d 31 20 20 20 20 |o. X(0)=1 | 00001480 20 20 20 20 3b 20 73 65 74 20 66 69 72 73 74 20 | ; set first | 00001490 65 6c 65 6d 65 6e 74 20 74 6f 20 31 0a 20 20 20 |element to 1. | 000014a0 20 54 3d 30 3a 42 3d 30 20 20 20 20 20 20 20 3b | T=0:B=0 ;| 000014b0 20 23 64 69 67 69 74 73 20 69 6e 20 61 6e 73 77 | #digits in answ| 000014c0 65 72 20 28 54 29 3d 30 0a 20 20 20 20 46 4f 52 |er (T)=0. FOR| 000014d0 20 43 3d 31 20 54 4f 20 41 20 20 3b 20 6c 6f 6f | C=1 TO A ; loo| 000014e0 70 20 65 69 74 68 65 72 20 66 61 63 74 6f 72 69 |p either factori| 000014f0 61 6c 20 6f 72 20 70 6f 77 65 72 20 6e 75 6d 62 |al or power numb| 00001500 65 72 20 6f 66 20 74 69 6d 65 73 2e 0a 20 20 20 |er of times.. | 00001510 20 20 49 46 20 66 61 63 74 6f 72 69 61 6c 20 54 | IF factorial T| 00001520 48 45 4e 0a 20 20 20 20 20 20 4b 3d 43 20 20 20 |HEN. K=C | 00001530 20 20 20 20 20 20 3b 20 6d 75 6c 74 69 70 6c 79 | ; multiply| 00001540 69 6e 67 20 6e 75 6d 62 65 72 20 69 73 20 6c 6f |ing number is lo| 00001550 6f 70 20 6e 75 6d 62 65 72 0a 20 20 20 20 20 45 |op number. E| 00001560 4c 53 45 20 20 20 20 20 20 20 20 20 3b 20 69 74 |LSE ; it| 00001570 20 6d 75 73 74 20 62 65 20 70 6f 77 65 72 0a 20 | must be power. | 00001580 20 20 20 20 20 4b 3d 56 20 20 20 20 20 20 20 20 | K=V | 00001590 20 3b 20 6d 75 6c 74 69 70 6c 79 69 6e 67 20 6e | ; multiplying n| 000015a0 75 6d 62 65 72 20 69 73 20 61 6c 77 61 79 73 20 |umber is always | 000015b0 62 61 73 65 0a 20 20 20 20 20 45 4e 44 49 46 0a |base. ENDIF.| 000015c0 20 20 20 20 20 46 4f 52 20 45 3d 30 20 54 4f 20 | FOR E=0 TO | 000015d0 54 20 20 3b 20 6c 6f 6f 70 20 23 64 69 67 69 74 |T ; loop #digit| 000015e0 73 20 69 6e 20 61 6e 73 77 65 72 20 74 69 6d 65 |s in answer time| 000015f0 73 0a 20 20 20 20 20 20 58 28 45 29 3d 58 28 45 |s. X(E)=X(E| 00001600 29 2a 4b 20 20 3b 20 6d 75 6c 74 69 70 6c 79 20 |)*K ; multiply | 00001610 61 6c 6c 20 64 69 67 69 74 73 20 62 79 20 4b 0a |all digits by K.| 00001620 20 20 20 20 20 4e 45 58 54 20 45 0a 20 20 20 20 | NEXT E. | 00001630 20 52 45 50 45 41 54 0a 20 20 20 20 20 20 4f 3d | REPEAT. O=| 00001640 54 0a 20 20 20 20 20 20 46 4f 52 20 45 3d 42 20 |T. FOR E=B | 00001650 54 4f 20 54 0a 20 20 20 20 20 20 20 49 46 20 58 |TO T. IF X| 00001660 28 45 29 3e 39 20 50 52 4f 43 78 20 20 20 3b 20 |(E)>9 PROCx ; | 00001670 63 68 65 63 6b 20 66 6f 72 20 27 64 69 67 69 74 |check for 'digit| 00001680 27 3e 3d 31 30 20 61 6e 64 20 63 61 72 72 79 20 |'>=10 and carry | 00001690 69 66 20 73 6f 0a 20 20 20 20 20 20 4e 45 58 54 |if so. NEXT| 000016a0 20 45 20 20 20 20 20 20 20 20 20 20 20 20 20 0a | E .| 000016b0 20 20 20 20 20 55 4e 54 49 4c 20 4f 3e 3d 54 20 | UNTIL O>=T | 000016c0 20 20 20 20 20 20 20 20 20 3b 20 66 6f 72 20 61 | ; for a| 000016d0 6c 6c 20 27 64 69 67 69 74 73 27 20 63 75 72 72 |ll 'digits' curr| 000016e0 65 6e 74 6c 79 20 69 6e 20 61 6e 73 77 65 72 0a |ently in answer.| 000016f0 20 20 20 20 20 42 3d 30 0a 20 20 20 20 4e 45 58 | B=0. NEX| 00001700 54 20 43 20 3b 20 6c 6f 6f 70 0a 20 20 20 45 4e |T C ; loop. EN| 00001710 44 0a 20 20 20 20 3a 0a 20 20 20 20 44 45 46 20 |D. :. DEF | 00001720 50 52 4f 43 78 20 20 20 20 20 20 20 20 20 20 20 |PROCx | 00001730 20 20 3b 20 50 52 4f 43 65 64 75 72 65 20 74 6f | ; PROCedure to| 00001740 20 73 6f 72 74 20 6f 75 74 20 63 61 72 72 79 0a | sort out carry.| 00001750 20 20 20 20 20 48 3d 49 4e 54 28 58 28 45 29 2f | H=INT(X(E)/| 00001760 31 30 29 20 20 20 20 20 20 20 3b 20 66 69 72 73 |10) ; firs| 00001770 74 20 64 65 74 65 72 6d 69 6e 65 20 6e 75 6d 62 |t determine numb| 00001780 65 72 20 6f 66 20 74 65 6e 73 0a 20 20 20 20 20 |er of tens. | 00001790 49 46 20 48 3e 28 58 28 45 29 2f 31 30 29 3a 48 |IF H>(X(E)/10):H| 000017a0 3d 48 2d 31 20 0a 20 20 20 20 20 58 28 45 2b 31 |=H-1 . X(E+1| 000017b0 29 3d 58 28 45 2b 31 29 2b 48 20 20 20 20 20 20 |)=X(E+1)+H | 000017c0 3b 20 74 68 65 6e 20 61 64 64 20 74 65 6e 73 20 |; then add tens | 000017d0 74 6f 20 6e 65 78 74 20 64 69 67 69 74 0a 20 20 |to next digit. | 000017e0 20 20 20 58 28 45 29 3d 58 28 45 29 2d 28 48 2a | X(E)=X(E)-(H*| 000017f0 31 30 29 20 20 20 20 20 3b 20 6e 65 78 74 20 73 |10) ; next s| 00001800 75 62 74 72 61 63 74 20 66 72 6f 6d 20 63 75 72 |ubtract from cur| 00001810 72 65 6e 74 20 64 69 67 69 74 0a 20 20 20 20 20 |rent digit. | 00001820 49 46 20 28 45 2b 31 29 3e 54 20 54 3d 45 2b 31 |IF (E+1)>T T=E+1| 00001830 3a 42 3d 54 20 3b 20 6e 6f 77 20 65 78 74 65 6e |:B=T ; now exten| 00001840 64 20 74 68 65 20 6e 75 6d 62 65 72 20 6f 66 20 |d the number of | 00001850 64 69 67 69 74 73 20 69 6e 20 61 6e 73 77 65 72 |digits in answer| 00001860 20 28 54 29 20 69 66 20 6e 65 63 65 73 73 61 72 | (T) if necessar| 00001870 79 2e 0a 20 20 20 20 45 4e 44 50 52 4f 43 0a 20 |y.. ENDPROC. | 00001880 20 20 20 3a 0a 0a 20 20 49 74 27 73 20 77 6f 72 | :.. It's wor| 00001890 74 68 20 6d 65 6e 74 69 6f 6e 69 6e 67 20 74 68 |th mentioning th| 000018a0 61 74 20 49 20 6d 61 64 65 20 74 68 69 73 20 6d |at I made this m| 000018b0 79 73 65 6c 66 2c 20 62 79 20 74 68 65 20 6d 65 |yself, by the me| 000018c0 74 68 6f 64 20 77 68 69 63 68 20 73 65 65 6d 65 |thod which seeme| 000018d0 64 20 6d 6f 73 74 20 73 65 6e 73 69 62 6c 65 20 |d most sensible | 000018e0 74 6f 20 6d 65 2e 20 49 74 27 73 20 65 6e 74 69 |to me. It's enti| 000018f0 72 65 6c 79 20 70 6f 73 73 69 62 6c 65 20 74 68 |rely possible th| 00001900 61 74 20 0a 74 68 65 72 65 27 73 20 61 20 62 65 |at .there's a be| 00001910 74 74 65 72 20 6d 65 74 68 6f 64 20 66 6f 72 20 |tter method for | 00001920 77 6f 72 6b 69 6e 67 20 74 68 65 73 65 20 74 68 |working these th| 00001930 69 6e 67 73 20 6f 75 74 2c 20 62 75 74 20 6d 79 |ings out, but my| 00001940 20 77 61 79 20 77 6f 72 6b 73 20 73 6f 20 49 27 | way works so I'| 00001950 6d 20 68 61 70 70 79 2e 0a 0a 0a 0a 2a 2a 2a 2a |m happy.....****| 00001960 2a 2a 2a 2a 2a 2a 2a 2a 2a 2a 2a 2a 2a 2a 2a 2a |****************| * 000019d0 2a 2a 2a 2a 2a 2a 2a 2a 2a 2a 2a 2a 2a 0a 0a 20 |*************.. | 000019e0 49 66 20 61 6e 79 6f 6e 65 20 6e 65 65 64 73 20 |If anyone needs | 000019f0 74 6f 20 63 6f 6e 74 61 63 74 20 6d 65 20 74 68 |to contact me th| 00001a00 65 20 73 61 66 65 73 74 20 62 65 74 20 69 73 20 |e safest bet is | 00001a10 6d 79 20 68 6f 6d 65 20 61 64 64 72 65 73 73 3b |my home address;| 00001a20 0a 0a 20 20 20 20 20 20 20 37 20 52 69 76 65 72 |.. 7 River| 00001a30 73 64 65 6e 65 2c 0a 20 20 20 20 20 20 20 20 53 |sdene,. S| 00001a40 74 6f 6b 65 73 6c 65 79 2c 0a 20 20 20 20 20 20 |tokesley,. | 00001a50 20 20 43 6c 65 76 65 6c 61 6e 64 2e 0a 20 20 20 | Cleveland.. | 00001a60 20 20 20 20 20 54 53 39 20 35 44 44 2e 0a 0a 20 | TS9 5DD... | 00001a70 4f 72 2c 20 69 66 20 69 74 27 73 20 64 75 72 69 |Or, if it's duri| 00001a80 6e 67 20 74 65 72 6d 20 74 69 6d 65 2c 20 49 20 |ng term time, I | 00001a90 63 61 6e 20 62 65 20 63 6f 6e 74 61 63 74 65 64 |can be contacted| 00001aa0 20 62 79 20 73 28 6e 61 69 6c 29 2d 6d 61 69 6c | by s(nail)-mail| 00001ab0 20 61 74 3b 0a 0a 20 20 20 20 20 20 20 48 75 6c | at;.. Hul| 00001ac0 6d 65 20 48 61 6c 6c 2c 0a 20 20 20 20 20 20 20 |me Hall,. | 00001ad0 20 4f 78 66 6f 72 64 20 50 6c 61 63 65 2c 0a 20 | Oxford Place,. | 00001ae0 20 20 20 20 20 20 20 56 69 63 74 6f 72 69 61 20 | Victoria | 00001af0 50 61 72 6b 2c 0a 20 20 20 20 20 20 20 20 4d 61 |Park,. Ma| 00001b00 6e 63 68 65 73 74 65 72 2e 0a 20 20 20 20 20 20 |nchester.. | 00001b10 20 20 4d 31 34 20 35 52 52 2e 0a 0a 20 20 20 20 | M14 5RR... | 00001b20 20 61 6e 64 20 62 79 20 65 28 61 73 79 29 2d 6d | and by e(asy)-m| 00001b30 61 69 6c 20 61 74 3b 0a 0a 20 20 20 20 20 20 20 |ail at;.. | 00001b40 41 4a 4d 40 66 73 31 2e 6d 61 2e 75 6d 69 73 74 |AJM@fs1.ma.umist| 00001b50 2e 61 63 2e 75 6b 0a 0a 0a 20 20 20 20 20 20 20 |.ac.uk... | 00001b60 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 | | * 00001b90 20 20 20 20 20 20 20 20 20 20 20 20 20 20 41 6e | An| 00001ba0 64 72 65 77 20 4a 20 4d 61 72 6b 77 69 63 6b 20 |drew J Markwick | 00001bb0 20 20 37 2f 31 30 2f 39 34 20 20 31 3a 33 33 61 | 7/10/94 1:33a| 00001bc0 6d 2e 0a 0a 0a 0a |m.....| 00001bc6
.