Machine Arithmetic in Residual Classes

738 Pages·2008·20.34 MB·English

A0-A098 441 FOREIGN TECHNOCLODGIVY WRIE44T-PATTERSAOF4B 0Om FIG 9/2
MACINE ARITHMETICI N RESIDUALC LASSES(U. )
APR S1 I Y AKUSI4SIIY. 0 I YUOITSKIY
UNCLASSIFIED FTD-IDIRS) T-0239-81 N
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MICROCOPY RESOLUTION TEST CHART
FTD-ID(RS)T-0239-8lv
00 FOREIGN TECHNOLOGY DIVISIO
MACHINE ARITHMETIC IN RESIDUAL CLASSES
by
I. Ya. Alrushskiy, D. 1. Yuditskiy
SELECTE
MAYO 4 198i1
4
' 44 Approved for public release;
i distribution unlimited.
81I 5 Ol 046
FTD-
ID(RS)T-0239-81
UNEDITED MACHINE TRANSLATION
ltFTD-ID (RS)T. 2 39-81 3 Apr0098l
.,ICROFICHE NR: FTD-81-C-000293L
I/ACHIE _ARITHMETIC IN RESIDUAL CLASSES4
English pa es: 717
~b~a hinnaya Arifrnetika v Ostatochnykh
Kl as sakh, u~~~~
.z~z.Moscow, 19684W.-1439*
of origin: USSR
4Country
This document is a machine translation
* Requester: FTD/SD
Aproved for public release; distribution
unlimited.
THIS TRANSLATION IS A RENDITION OF THE ORIGI.
NAL FOREIGN TEXT WITHOUT ANY ANALYTICAL OR
EDITORIAL COMMENT. STATEMENTS OR THEORIES PREPARED 8Y:
ADVOCATED OR IMPLIED ARE THOSE OF THE SOURCE
AND DO NOT NECESSARILY REFLECT THE POSITION TRANSLATION DIVISION
OR OPINION OF THE FOREIGN TECHNOLOGY DI- FOREIGN TECHNOLOGY DIVISION
VISION. WP.AF6. OHIO.
FTP- Date . 19
ID(RS)T-o2iq-81 ~.
TABLE OF CONTENTS
U. S. Board on Geographic Names Transliteration System ....... ii
Preface ...................................................... 3
Chapter 1. :ntroduction to Numeration System in the
Residual Classes .............................................. 8
Chacter 2. Theoretical-Numerical Bases of the System of
N
9
Residual Classes ............................................. 67
* Chapter 3. Bases of Machine Arithmetic in a System of
Residual Classes ............................................. 117
Chapter 4. Self-Correcting Codes in the System of
Residual Classes ............................................. 248
:hapter 5. Algorithms of the Execution Nonmodular
Operations ................................................... 357
Chapter 6. Components of Computers in a System of
Residual Classes ............................................. 483
Chapter 7. System of Residual Classes in Complex Domain ..... 635
References ................................................... 714
4 ACCIZ " l or
,I. --- --
ADcn11ibut ionr
'I lnb-lity CodeS-
I Avn tl snd/or
izt ' Spcci'A
' i
U. S. BOARD ON GEOGRAPHIC NAMES TRANSLITERATION SYSTEM
Block Italic Transliteration Block Italic Transliterati
A A A, a P p p p R, r
"6 B, b C c C S, s
B' V, v T T T m T,t
r Y y y Y T
Ed E Ye, ye; E, e* X x X x Kh, kh
W Zh, zh LA aif Ts, ts
33 Z, z L9 q . Ch, ch
:
' Z, WL U z Im Sh, sil
Ai Ra Y, y L4 ~ L q Shch,
R x K, k b "
J7 A L,1h W Y, y
M A M, m b b b
H H H N ,n 33 , E, e
- 0 0, o id 0 10 Yu, yu
17 PP , p R R Ya, ya
• initially, after vowels, and after b, b; e elsewhere.
';hen written as e in Russian, transliterate as ye or e.
RUSSIAN AND ZEGLISH TRIGONOMETRIC FUNCTIONS
Russian English Russian English Russian Engli-:.
sin sin sh sinh arc sh 5
20s cos ch cosh arc ch
th tanh arc th
- .tan
cot cth coth arc cth
sec sec sch sech arc sch sech
-
osCEc csc csch csch arc csch 25Th
Russian English
rot curl
lg log
• ii
DOC 1fl23901 PAG~F 1
=
M1ACHINE ARIThMETIC IN RFSIDIAL CLASSES.
I~~~~~~ .T ,AkI~SK Y ufiir k i
DOC = ,61 23901 PAGE 2
TRANSLATOR'S NOTE: The word Dale should read dividinw.
Paqe 2.
The book is the original mcncgraph, which contains tha results
tf r-siarch cf thS authors cn 4he davolopgnt of arithmtic svs-:s
in the r sidual classs and th-eir raalizations in computer
t-chnclcgv. By the authors are stated tha bases of the new nu._ratcn
syst~m and is constructed machine arithmetic in this systetm. Svstm
in the residual classes ascendirg by its ideological roots tc thi
classical srct2.ons of the thccr c f numbers, ma-es it poss'h!- in .
new way to approach th* ccnstructicr of the ccmputsrs of high
effici.ncy. In the book ar,. stated the bases cf the special
self-correcting nonpositicnal ccde syst.as.
And to the basis of the th-cry ccmple ones by intgqrs in th.
field of whole real numbers without the distrinution into th. r.al
and alleg-d parts.
-4
Thq baok is intended for enginoers, scientific wcrkers and
students of th,. senior ccurses, which specialize in the area f
computational tichnclcgy.
44 Tables, 51 illustration, 79 titles bibliography.
DOC PA GF .3
=1U23901
Page 3.
77r-'Suls 'A~rC. lIt Gurin'g ':h' last f-w yc-rs by z4:~.
ones to t~h: rollos cf th Q resea tche-s of the sqarches for wa.y s
* in~creasing tha jrol1uctiJvi4:y cf el,?ctronic ccaiju-,rs, rn&.hcds cf
orgirizinj the efficient acqu-.siticn system and correction ocrf :rs
and building of hig~ly r~.iabNI, ccmnputpL complexas :idca-.:; e
authors in. the ooinion that ir t~e1'-2its of tha positional
num~raticr syst'.ms it is not pcssIblt to expect anr y sat4isfactory:,,
aivanc? in thesze dizecticts withcut -a consid-irahle inczaase in-h:
operatini freq'iencies of el,:ments/cells and cc-aplicatior. of ---%
squinvm't Dart of 1figital comp~uter.
As jizk/i-mpulsp- to the rescarch in the ""ield
of th
nonpositional nampratior systms werq used thf published in 19-5-1 57
work of Cz~ch s:i.ntists M. Valakh and A. SvotcAdy, edicated~t
reprgs-ntat-4cm of numbers in the fc-.,n of tne set of non-nsqao-4v=
dqducticrs ct± tn. group of mutually simuple bases/basezs, and
detegrmined ir -ornacticn with this reprasintatiol possibfi-JIy )f
exectitin'g the~ rational cperati-crs viTchout, takin; into accolint t:-.:
DOC bi 1023901 PAiGEi4 ~ iiso ubr
ai.scha~gir-. ccrn~cti-cns iwet dgscfanubr
"Ihs car~i=-i out by the: authors this books in vest igat icns in th-4s
new numerato.system, naired thtesystem of resiltial classss, LF& to
*ha criatior. cf vezy p'culiar mclbriq arithnitic.
Thf-'i-iclt cf: x-!cution in trig systam or th~iz. u-
classes of the operatiors, requiring knowledge of entirs- numnar as a
wholz, but its not single stap-by-ste-p digits (iaterminaticr: c-f t.-:
si.gr cf- a numba!:, th c ccmparison of nuuloers in the valut-, ':~
genreral an(' the like),* Frcvc-d tc te not insurffountable. Cam-zo1iE
* ~the possibilities of eliminating these lifficulties by ~~
in their cont.--t and character of r,,alization by mthods.
zPagei. 4
in tha pro:ass of research of specific charactqr and
4
Possibilities oil the system of residual classes it was possib.s to
censtruct the salf-corrsctirg ccde., completely zarithmpt-ic, ~.
suitable for detacticn and ccrricticn of the fr:ors, which n: -
only dur-inq the transmissicn of irtcrinaticn, hut also liilrj s
arithm-?tic prcc-ssing. Fcr thesp code-s it proval to be possAbL-
(which, until row, was cbssrved nct in what krown speacial pcs--i:ra~.
code systems) to construict the systqm of the correction. o: zr::):s