The Solution
bounded floating point
True North bounded floating point is a method of performing operations on floating point numbers that calculates and saves the error information with the floating point values.
This is accomplished by adding an error field to the floating point representation of real numbers.
The error information is saved with the floating point value. Implemented in hardware, this circuit provides real-time, fail safe representation of real numbers.
Features of True North Bounded Floating Point
ACCURACY
Guarantees the display of every floating point value to be accurate to plus or minus one in the last fractional digit.
CONTROL
Detects and records how many significant bits have been lost. Allows you to designate how many significant digits you require.
IMPLEMENTATION
Can be implemented in hardware or software.
INTEROPERABLE
Conversion between the bounded floating point format and the current standard floating point format can be accomplished when needed. Therefore, existing software that is dependent upon the current floating point standard need not be discarded.
ASSURANCE
Standard floating point values are converted to external representation without indication of loss of significant digits - even when no significant digits exist. True North bounded floating point records all loss of significant digits and signals if the result of a computation no longer provides a sufficient number of significant digits.
NO PERFORMANCE IMPACT
Stores and provides error information with little impact on space or performance.
ALL-IN-ONE
Addresses both types of floating point error, rounding error and truncation error.
REAL-TIME
Operates in mission-critical real time.
Recent Publications
Bounded Floating Point: Identifying and Revealing Floating-Point Error | ASTES Journal, Vol. 6, Issue 1, pp. 519-531 | Published Online: 28 January 2021 | https://astesj.com/v06/i01/p57/
Exact Floating Point | July 27-30, 2020 | Luxor Hotel, 3900 Las Vegas Blvd. South, Las Vegas, 89109, USA | American Council on Science & Education | The 2020 World Congress in Computer Science, Computer Engineering, and Applied Computing | CSCE 2020 | ISBN # 1-60132-512-6
Testing Floating-Point Applications | PNSQC 2020 Conference | https://www.pnsqc.org/testing-floating-point-applications/
Assurance of Accuracy in Floating-Point Calculations - A Software Model Study | CSCI 2019 Conference | https://ieeexplore.ieee.org/document/9070998
Dangerously Invisible Failures: Floating Point | PNSQC 2018 Conference | https://www.pnsqc.org/dangerously-invisible-failures-floating-point/
The Man Behind the Solution
Dr. Alan A. Jorgensen
Educational foundation
A long-time computer systems engineer with degrees in electrical engineering and computer science.
Leader in technology
Designed a high performance four-channel microprogrammed synchronous communications controller that was still operational 15 years after its introduction.
He owned and operated a computer system consulting business that offered system troubleshooting services to operators of real-time process control systems, particularly main plant computers in nuclear power stations.
As adjunct faculty he has taught university courses in microprogrammed design, programming, system design, and other computer science related courses.
He has been an international keynote speaker on software testing and quality.
Why floating point
His interest in floating point dates back to logic and compatibility testing of early floating-point units. The discovery of system failures that were traced back to floating point error has led him to design and patent a circuit for calculating and retaining the error of a floating point representation of an exact value.
More about the man
He has performed professionally as a musician and loves to read and paint and solve puzzles when he has time.
