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Old 04-28-2006, 05:22 PM
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Default 50-th Anniversary of the CORDIC Algorithm

50-th Anniversary of the CORDIC Algorithm

Exactly 50 years ago - in the 1956 - the first Jack Volder's
publication, describing
CORDIC algorithm:

"Binary computation algorithm for coordinate rotation and function
generation ",
Report IAR-I 14S , Aeroelectronic group, June, 1956 Convair
was published.

Until now CORDIC technique is one of the most effective method of
many computational problems.

Since 1956, when this method was firstly suggested, about 1500
publications were issued
in more than 30 countries: Australia, Canada, China, France, Germany,
Great Britain,
Greece, Hong- Kong, India, Israel, Italy, Japan, The Netherlands,
Romania, Spain,
Switzerland, Taiwan, United Kingdom, USA, the former USSR (mainly
Russia, Ukraine, and Belorussia) and many others. Only in the USA
similar researches
have been made in about 25 universities.

VLSI, based on CORDIC or its modifications, have been made in
commercial production since from the beginning of 70-th.
They were used for trigonometric and logarithmic functions
evaluation in Hewlett-Packard's calculators: HP-35, 45, 65.
Many other companies in different countries use this method
in calculators for the same purpose.

Still further field of application of CORDIC method are
coprocessors INTEL: 8087, 80287, 80387 etc. included in
the personal computers IBM PC.

Firm TRW manufactures in commercial scale microcircuit
TRW 2330 designed for plane rotations of coordinates,
based on CORDIC technique, for digital signal processing.
NEC corporation produces coprocessor VLSI PD 72691, dedi-
cated for elementary functions evaluation and coordinate
transformation with floating point based on Volder's

Currently the major part of publications is related to using
of CORDIC algorithm for digital signal processing,
many-dimensional coordinate transforms.
The other part concerns with generalization of the CORDIC
algorithm for solving linear systems equations, eigenvalue
problems, statistical characteristics estimation.

Many publications are related to application of the CORDIC
and CORDIC-like algorithms and structures to robotics control,
display processors, numerical control systems.

So I suggest firstly to create the list of the bibliography in the
CORDIC field, like it was done in 1995:


One of the purpose of this coordination is not to duplicate the
research, that were made by the other authors many years ago, as say
in Russia
" not to invent the bicycle again". Now due to the Internet it is very
easy to do.

The short lists of some publications in the CORDIC field are in:

All the investigations related to CORDIC method could be divided into
the following

- theory of properly CORDIC (convergence:conditions and domain, error
fixed and floating point representation,
using of
nonbinary number representation,
unification of the
algorithms, methods of
acceleration,comparing with the
other methodes)
- expandings of CORDIC possibilities ( new kinds of functions of one
and two va-
riables, functions of functions, three and
mension coordinate transforms, solving
linear and
nonlinear systems equations, eigenvalue
and singular
value problems)
- implementation and application of CORDIC (standard and nonstandard
chitectures: on-line, pipeline, matrix,
VLSI and ULSI, based on CORDIC,
coprocessors, cal-
culators, DSP processors, display
robotic processors).


Vladimir Baykov
PhD, DrSci, Professor

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