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How to do very long division and mod operations

Posted on 2000-03-31
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Last Modified: 2010-05-18
Does anyone have any ideas on how to implement in C, (or any other modern language) algorithms that will do long division and compute modulo values for very long numbers, on the order of 512 bits?  Most integers are 16, 32, or at most 64 bits.  Any known URLs about this subject would be helpful.  I would also be interested in any books that address the subject with good examples.
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Question by:mzehner
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stochastic earned 100 total points
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a. http://www.bearcave.com/software/divide.htm

b. http://barnyard.syr.edu/longdiv.html

Strangely, I am not finding many good URLs with ready downloadable code. Am tempted to write it myself :-)

- stochastic
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by:cookre
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Donald E. Knuth
The Art of Computer Programming
Vol. 2
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by:ntdragon
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i got idea for you
use strings instead of int or anyother

write your numbers in string's and make
the operations on it
like

operation +
first num 894
second num 327

 894
+
 327
-----
1221
the same with the other operations
what i mean is that you will have to do the operation by yourself for each place in the string

first the last place 4+7=11 so in the answer string you put 1 and move 1 forward
then 9+2+1<this 1 moved from the last>
=12 then you put 2 and move 1 to the next level
then 8+3+1<the 1 from the last level>=12
you put 2 in the answer string and
you put 1 in the next level of the answer string
 
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by:ntdragon
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i made it with operation +
you can do that with all the other operations like /,%,*,-
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by:rbr
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I can send you a code which will do all basic operations /, *, +, -, %, for integers any length and base. The functions are not very fast but well tested and gives you a first impress who to do so. Writen an email to

rbr@tip-informatik.at because the code is to long to be pasted here.
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by:mzehner
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Thanks for taking the time to answer.  Although this code should work, it performs division on long ASCII strings and I do not believe it will be fast enough for my application.
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by:mzehner
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The "barnyard" web site was not helpful since it did long division over the web and the code seemed to be on the server side.  However the "bearcave" web site was helpful since it had several references to other documents which described long division algorithms.  The comment by cookre was also very good and I would have split the points between the two of you if I could.  I accepted this answer since some of the documents brought the theoretical algorithms closer to the practical.  It also referenced Knuth.  Thanks for posting your comments.
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