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Eliminating redundancies in sum-of-product array computations

2001
*
Proceedings of the 15th international conference on Supercomputing - ICS '01
*

) S
Number

doi:10.1145/377792.377807
dblp:conf/ics/DeitzCS01
fatcat:hphzyfjawnhjlmejhrrcug2yii
*of*Processors 16 1 1 1 1 1 1 1 1 1 1 1 1 S V 1 + 1 1 ...+ 1 1 + 1 1 S V 2 Sweep 1 Sweep 2 1 1 ... ... 3.1 Normalized*array*statement sequences c ¥ 0 3 ) 1 U T @ ¦ 5 % ) U % ) g i ' % d @ ¤ ! T Q X 6 ¡ ¤ £ ( ¤ ª R 6 ¤ ¦ £ p £ e g ¡ g £ ¤ c i ¢ ¦ 0 t @ ! ...##
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Using of Redundant Signed-Digit Numeral System for Accelerating and Improving the Accuracy of Computer Floating-Point Calculations

2020
*
International Journal of Advanced Computer Science and Applications
*

The effect

doi:10.14569/ijacsa.2020.0110942
fatcat:45qklytg6bbzbhizkrabykwbwy
*of*accelerating*computations*is obtained for the problems*of*calculating the*sum**of*an*array**of*numbers and determining the dot*product**of*vectors. ... The article proposes a method for software implementation*of*floating-point*computations*on a graphics processing unit (GPU) with an increased accuracy, which*eliminates*sharp increase*in*rounding errors ... If the*array*contains k numbers, then this summation method requires k-1 synchronizations*in*the process*of**summing*this*array*. ...##
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Subregion Analysis and Bounds Check Elimination for High Level Arrays
[chapter]

2011
*
Lecture Notes in Computer Science
*

For example, high-level

doi:10.1007/978-3-642-19861-8_14
fatcat:vvondsmiknes3a6ha2opwe27vu
*arrays**in*the X10 language support rank-independent specification*of*multidimensional loop and*array**computations*using regions and points. ... | R ::= restriction*of**array*onto region R A.sum(), A.max() ::=*sum*/max*of*elements*in**array*A1 A2 ::= result*of*applying point-wise op on A1 and A2, when A1.region = A2. region ( can include +, -, * ... For simplicity, an additional loop is introduced to*compute*the weighted*sum*using the elements*in*the stencil, but this loop could be replaced by a high level*array**sum*() operation as well. ...##
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Fast multiplication without carry-propagate addition

1990
*
IEEE transactions on computers
*

4] [5] [6] [7] Abstract-Conventional schemes for fast multiplication accumulate the partial

doi:10.1109/12.61047
fatcat:njn6aqomh5cvldx7qnnhn4xvtm
*products**in**redundant*form (carry-save or signed-digit) and convert the result to conventional representation ...*in*the last step. ... Since a*product**of*n bits is to be*computed*, those digits*of*the*array*that do not influence the result can be*eliminated*. ...##
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GLORE: generalized loop redundancy elimination upon LER-notation

2017
*
Proceedings of the ACM on Programming Languages
*

This paper presents GLORE, a novel approach to enabling the detection and removal

doi:10.1145/3133898
dblp:journals/pacmpl/DingS17
fatcat:jeam5uobn5cincs2lbqcp2jfby
*of*large-scope*redundant**computations**in*nested loops. ... GLORE works on LER-notation, a new representation*of**computations**in*both regular and irregular loops. ... Any opinions, findings, and conclusions or recommendations expressed*in*this material are those*of*the authors and do not necessarily reflect the views*of*DOE or NSF. ...##
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Algorithm-Based Fault Tolerance for Matrix Operations

1984
*
IEEE transactions on computers
*

The rapid progress

doi:10.1109/tc.1984.1676475
fatcat:esqcnwz4nff7xbbxbaisezj2jm
*in*VLSI technology has reduced the cost*of*hardware, allowing multiple copies*of*low-cost processors to provide a large amount*of**computational*capability for a small cost. ...*In*addition to achieving high performance, high reliability is also important to ensure that the results*of*long*computations*are valid. ...*of*the*computed**sum**of*the row or column data elements and the checksum to the erroneous element*in*the information part, (ii) or by replacing the checksum by the*computed**sum**of*the information elements ...##
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Compiling stencils in high performance Fortran

1997
*
Proceedings of the 1997 ACM/IEEE conference on Supercomputing (CDROM) - Supercomputing '97
*

from the translation

doi:10.1145/509593.509605
dblp:conf/sc/RothMKB97
fatcat:f5vd27hdvvhu7cdbvay6y57tym
*of*Fortran90*array*constructs. ... For many F ortran90 and HPF programs performing dense matrix*computations*, the main*computational*portion*of*the program belongs to a class*of*k ernels kno wn as stencils. ... Acknowledgments This work has been supported*in*part by the IBM Corporation, the Center for Research on Parallel*Computation*(an NSF Science and Technology Center), and DARPA Contract DABT63-92-C-0038. ...##
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Fast Multiplication Based on Different Compressors

IJIREEICE - Electrical, Electronics, Instrumentation and Control

2015
*
IJIREEICE
*

IJIREEICE - Electrical, Electronics, Instrumentation and Control

*In*many

*of*digital systems like graphic processors, digital signal processors fast parallel multiplication using adder trees are present. To speed up the

*computation*like addition is very important. ... This approach is defined

*in*parameterizable HDL code, which makes it compatible with any FPGA family. ... Figure 2 show the CSA

*compute*flow and Table 1 will show the CSA working. The

*computation*can be

*in*two steps, first we

*compute*S and C using a CSA, and then we use CPA to

*compute*the total

*sum*. ...

##
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FPGA-Based Data Storage System on NAND Flash Memory in RAID 6 Architecture for In-Line Pipeline Inspection Gauges

2018
*
IEEE transactions on computers
*

At the hardware level, we interleaved 8 NAND flash chips

doi:10.1109/tc.2018.2794986
fatcat:p5uqu2wpifeizgefxzqrhey2qi
*in*a*Redundant**Array**of*Independent Disks (RAID) type-6 architecture. ... Our controller*computes*the ECC and*redundancy*bytes while it transfers the information to the cache register*of*the selected die*in*the memory chips. ... All authors would like to thank Joseph Moeller for his help*in*improving the English manuscript. ...##
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Nanofabric PLA Architecture with Double Variable Redundancy

2007
*
2007 IEEE Region 5 Technical Conference
*

It has been shown that fundamental electronic crosspoint can be programmed ON or OFF by applying a structures such as Diodes, and FET's can be constructed using voltage Differential

doi:10.1109/tpsd.2007.4380347
fatcat:sn2f5lhzhrbzzdngtmeaub4cvq
*of*3.6V. ... OUR APPROACH: DOUBLE VARIABLE*REDUNDANCY*determines the working*of*the*array*as AND*array*or OR*array*, as seen*in*We have successfully simulated the configuration*of*this DVR*in*MATLAB to verify the ... We*product*-*sum*terms using DVR-based PLA. allocate two vertical Nanowires per*Product*(or*Sum*) term*in*i=l Pcp= 0.05 to 0.2 (Probability that a single crosspoint is non programmable) Expression (3) gives ...##
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Space-time trade-off optimization for a class of electronic structure calculations

2002
*
Proceedings of the ACM SIGPLAN 2002 Conference on Programming language design and implementation - PLDI '02
*

Its utility is demonstrated by applying it to a

doi:10.1145/512529.512551
dblp:conf/pldi/CociorvaBLSRNBH02
fatcat:hdy6zbuuhrggjf7kwlalazbcmi
*computation*representative*of*a component*in*the CCSD(T) formulation*in*the NWChem quantum chemistry suite from Pacific Northwest National Laboratory. ...*In*this paper, we present an algorithm that starts with an operationminimal form*of*the*computation*and systematically explores the possible space-time trade-offs to identify the form with lowest cost ...*of*the*product**of*several input*arrays*. ...##
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Space-time trade-off optimization for a class of electronic structure calculations

2002
*
SIGPLAN notices
*

Its utility is demonstrated by applying it to a

doi:10.1145/543552.512551
fatcat:dotf2cim75e3vftocdzhc3hvki
*computation*representative*of*a component*in*the CCSD(T) formulation*in*the NWChem quantum chemistry suite from Pacific Northwest National Laboratory. ...*In*this paper, we present an algorithm that starts with an operationminimal form*of*the*computation*and systematically explores the possible space-time trade-offs to identify the form with lowest cost ...*of*the*product**of*several input*arrays*. ...##
###
Space-time trade-off optimization for a class of electronic structure calculations

2002
*
Proceedings of the ACM SIGPLAN 2002 Conference on Programming language design and implementation - PLDI '02
*

Its utility is demonstrated by applying it to a

doi:10.1145/512549.512551
fatcat:y3zuziytzjallmtgysjt2472dq
*computation*representative*of*a component*in*the CCSD(T) formulation*in*the NWChem quantum chemistry suite from Pacific Northwest National Laboratory. ...*In*this paper, we present an algorithm that starts with an operationminimal form*of*the*computation*and systematically explores the possible space-time trade-offs to identify the form with lowest cost ...*of*the*product**of*several input*arrays*. ...##
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Arithmetic operators based on the binary stored-carry-or-borrow representation

2010
*
2010 Conference Record of the Forty Fourth Asilomar Conference on Signals, Systems and Computers
*

*In*the latter design, the conventional initial AND matrix is transformed and expressed with a

*redundant*radix-2 representation. ... Several BSCB arithmetic elements, including full-adder, ripple-carry adder, and carry-lookahead adder are presented, followed by detailed design

*of*an

*array*multiplier. ... Introduction

*Redundant*number representations allow fast addition by

*eliminating*the carry propagation chains [Aviz61] . ...

##
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Optimizing array bound checks using flow analysis

1993
*
ACM Letters on Programming Languages and Systems
*

The optimizations reduce the program execution time through

doi:10.1145/176454.176507
fatcat:r4wbngdpfvhb5jzq5u4rjwzsm4
*elimination**of*checks and propagation*of*checks out*of*loops. ... Bound checks are introduced*in*programs for the run-time detection*of**array*bound violations. Compile-time optimizations are employed to reduce the execution-time overhead due to bound checks. ... The range information is used to*eliminate**redundant*bound checks on*array*subscripts. ...
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