On-line multiplication in real and complex base
Christiane Frougny
LIAFA, CNRS UMR 7089
2 place Jussieu, 75251 Paris Cedex 05, France
and Universit´e Paris 8
Christiane.
Frougny@liafa.
jussieu.
fr
Athasit Surarerks
Computer Engineering Department
Faculty of...
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On-line multiplication in real and complex base
Christiane Frougny
LIAFA, CNRS UMR 7089
2 place Jussieu, 75251 Paris Cedex 05, France
and Universit´e Paris 8
Christiane.
Frougny@liafa.
jussieu.
fr
Athasit Surarerks
Computer Engineering Department
Faculty of Engineering
Chulalongkorn University
Phayathai road, Bangkok 10330, Thailand
athasit@cp.
eng.
chula.
ac.
th
Abstract
Multiplication of two numbers represented in base
is
shown to be computable by an on-line algorithm when
is a negative integer, a positive non-integer real number, or
a complex number of the form ¡£¢ ¤ , where ¤ is a positive
integer.
1 Introduction
On-line arithmetic, introduced in [24], is a mode of computation where operands and results flow through arithmetic
units in a digit serial manner, starting with the most significant digit.
To generate the first digit of the result, the ¥
first digits of the operands are required.
The integer ¥ is
called the delay of the algorithm.
This technique allows the
pipelin
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