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Title: Verifying the error bound of numerical computation implemented in computer systems

Abstract

A verification tool receives a finite precision definition for an approximation of an infinite precision numerical function implemented in a processor in the form of a polynomial of bounded functions. The verification tool receives a domain for verifying outputs of segments associated with the infinite precision numerical function. The verification tool splits the domain into at least two segments, wherein each segment is non-overlapping with any other segment and converts, for each segment, a polynomial of bounded functions for the segment to a simplified formula comprising a polynomial, an inequality, and a constant for a selected segment. The verification tool calculates upper bounds of the polynomial for the at least two segments, beginning with the selected segment and reports the segments that violate a bounding condition.

Inventors:
Issue Date:
Research Org.:
International Business Machines Corp., Armonk, NY (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1083046
Patent Number(s):
8397187
Application Number:
12/766,163
Assignee:
International Business Machines Corporation (Armonk, NY)
Patent Classifications (CPCs):
G - PHYSICS G06 - COMPUTING G06F - ELECTRIC DIGITAL DATA PROCESSING
DOE Contract Number:  
B554331
Resource Type:
Patent
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING

Citation Formats

Sawada, Jun. Verifying the error bound of numerical computation implemented in computer systems. United States: N. p., 2013. Web.
Sawada, Jun. Verifying the error bound of numerical computation implemented in computer systems. United States.
Sawada, Jun. Tue . "Verifying the error bound of numerical computation implemented in computer systems". United States. https://www.osti.gov/servlets/purl/1083046.
@article{osti_1083046,
title = {Verifying the error bound of numerical computation implemented in computer systems},
author = {Sawada, Jun},
abstractNote = {A verification tool receives a finite precision definition for an approximation of an infinite precision numerical function implemented in a processor in the form of a polynomial of bounded functions. The verification tool receives a domain for verifying outputs of segments associated with the infinite precision numerical function. The verification tool splits the domain into at least two segments, wherein each segment is non-overlapping with any other segment and converts, for each segment, a polynomial of bounded functions for the segment to a simplified formula comprising a polynomial, an inequality, and a constant for a selected segment. The verification tool calculates upper bounds of the polynomial for the at least two segments, beginning with the selected segment and reports the segments that violate a bounding condition.},
doi = {},
journal = {},
number = ,
volume = ,
place = {United States},
year = {2013},
month = {3}
}

Works referenced in this record:

Oblivious Polynomial Evaluation
journal, January 2006


Fast Probabilistic Algorithms for Verification of Polynomial Identities
journal, October 1980