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Blanton et al., 2023 - Google Patents

Secure and accurate summation of many floating-point numbers

Blanton et al., 2023

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Document ID
7128287779825291010
Author
Blanton M
Goodrich M
Yuan C
Publication year
Publication venue
arXiv preprint arXiv:2312.10247

External Links

Snippet

Motivated by the importance of floating-point computations, we study the problem of securely and accurately summing many floating-point numbers. Prior work has focused on security absent accuracy or accuracy absent security, whereas our approach achieves both of them …
Continue reading at arxiv.org (PDF) (other versions)

Classifications

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    • G06F7/38—Methods or arrangements for performing computations using exclusively denominational number representation, e.g. using binary, ternary, decimal representation
    • G06F7/48—Methods or arrangements for performing computations using exclusively denominational number representation, e.g. using binary, ternary, decimal representation using non-contact-making devices, e.g. tube, solid state device; using unspecified devices
    • G06F7/52—Multiplying; Dividing
    • G06F7/523—Multiplying only
    • G06F7/533—Reduction of the number of iteration steps or stages, e.g. using the Booth algorithm, log-sum, odd-even
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING; COUNTING
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    • G06F7/00—Methods or arrangements for processing data by operating upon the order or content of the data handled
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    • G06F7/48—Methods or arrangements for performing computations using exclusively denominational number representation, e.g. using binary, ternary, decimal representation using non-contact-making devices, e.g. tube, solid state device; using unspecified devices
    • G06F7/52—Multiplying; Dividing
    • G06F7/535—Dividing only
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    • G06F7/48—Methods or arrangements for performing computations using exclusively denominational number representation, e.g. using binary, ternary, decimal representation using non-contact-making devices, e.g. tube, solid state device; using unspecified devices
    • G06F7/50—Adding; Subtracting
    • G06F7/505—Adding; Subtracting in bit-parallel fashion, i.e. having a different digit-handling circuit for each denomination
    • G06F7/506—Adding; Subtracting in bit-parallel fashion, i.e. having a different digit-handling circuit for each denomination with simultaneous carry generation for, or propagation over, two or more stages
    • G—PHYSICS
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    • G06F7/48—Methods or arrangements for performing computations using exclusively denominational number representation, e.g. using binary, ternary, decimal representation using non-contact-making devices, e.g. tube, solid state device; using unspecified devices
    • G06F7/499—Denomination or exception handling, e.g. rounding, overflow
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING; COUNTING
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    • G06F7/00—Methods or arrangements for processing data by operating upon the order or content of the data handled
    • G06F7/60—Methods or arrangements for performing computations using a digital non-denominational number representation, i.e. number representation without radix; Computing devices using combinations of denominational and non-denominational quantity representations, e.g. using difunction pulse trains, STEELE computers, phase computers
    • G06F7/72—Methods or arrangements for performing computations using a digital non-denominational number representation, i.e. number representation without radix; Computing devices using combinations of denominational and non-denominational quantity representations, e.g. using difunction pulse trains, STEELE computers, phase computers using residue arithmetic
    • G06F7/724—Finite field arithmetic
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    • G06F7/00—Methods or arrangements for processing data by operating upon the order or content of the data handled
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    • G06F7/48—Methods or arrangements for performing computations using exclusively denominational number representation, e.g. using binary, ternary, decimal representation using non-contact-making devices, e.g. tube, solid state device; using unspecified devices
    • G06F7/544—Methods or arrangements for performing computations using exclusively denominational number representation, e.g. using binary, ternary, decimal representation using non-contact-making devices, e.g. tube, solid state device; using unspecified devices for evaluating functions by calculation
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    • G06F2207/535—Indexing scheme relating to groups G06F7/535 - G06F7/5375
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    • G06F9/00—Arrangements for programme control, e.g. control unit
    • G06F9/06—Arrangements for programme control, e.g. control unit using stored programme, i.e. using internal store of processing equipment to receive and retain programme
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