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 = {Tue Mar 12 00:00:00 EDT 2013},
month = {Tue Mar 12 00:00:00 EDT 2013}
}
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