Fast On-line Integer Multiplication
Name
MIT-LCS-TM-045.pdf
Size
771.35 KB
Format
Adobe PDF
Checksum (MD5)
e75fb5e45a81232fc03b33eb7219cf4b
Author(s)
Fischer, Michael J.
Stockmeyer, Larry J.
Date Issued
May 1974
Series/Report no.
MIT-LCS-TM-045
MAC-TM-045
Abstract
A Turing machine multiplies binary integers on-line if it receives its inputs low-order digits first and produces the jth digit of the product before reading in the (j+l)st digits of the two inputs. We present a general method for converting any off-line multiplication algorithm which forms the product of two n-digit binary numbers in time F(n) into an on-line method which uses time only O(F(n) log n ), assuming that F is monotone and satisfies n F(n) F(2n)/2 ! kF(n) for some constant k.
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