“The era of unreliable, inaccurate, and sequential computing is over.”
What does building a skyscraper, sending a spaceship to Mars, computer animation, and artificial intelligence all have in common? They all use optimization to solve an engineering problem. Optimization is a mathematical model that defines the best solution for a given set of constraints like time, cost, materials, and sources.
High Performance Computing (HPC) is the practice of using massive amounts of computing resources to automatically calculate the solutions. Floating point arithmetic is the current technology which the HPC industry relies on to solve these engineering problems. The limitations of floating point arithmetic has led to a popular belief that optimization problems cannot always be solved accurately, efficiently, or reliably.
Modal Technology Corporation (MTC)offers new and proven solutions for superior High Performance Computing. The company has managed to address the disadvantages of floating point arithmetic and solve some of the biggest challenges faced by the computing industry with a new math called Modal Interval Arithmetic (MIA).
A pioneer in MIA
MIA is new and relatively unknown. Unlike floating point arithmetic, which uses finite approximations of real numbers to calculate results containing rounding errors, MIA calculates on sets of numbers, each set represented by a lower and upper bound (an interval), in order to guarantee that a correct answer is never lost due to rounding errors. MIA computing methods are highly parallel, making it easy to keep hundreds or thousands of processing cores running at maximum efficiency.
MTC owns key patents in hardware design and software method for MIA.Unlike floating point arithmetic, MIA can solve important classes of scientific problems such as global optimization, solutions of nonlinear equations, and constraint satisfaction. MIA has been recognized by the Institute of Electrical and Electronics Engineers (IEEE) as part of the recent IEEE 1788 Standard for Interval Arithmetic (2015), and MTC has a vision of introducing the benefits of MIA to many vertical industries including artificial intelligence, finance, aerospace, defense, chemistry, and computer animation to name a few.
Addressing daunting tasks of the semiconductor industry
Moore’s Law is the observation that the number of transistors in a dense integrated circuit doubles approximately every two years. This miniaturization process allows multiple processing cores to be added to computer chips, where each “core” is a separate central processing unit, the part of a chip that performs calculations.
The Department of Energy (DOE), charged with the task of building exascale supercomputers by 2023, has concluded that “making the transition to exascale poses numerous unavoidable scientific and technological challenges.” At the hardware level, feature size in silicon will almost certainly continue to decrease at Moore’s Law pace at least over the next decade, meaning that computer chips in high-end computing systems and consumer electronics will contain 100 times more cores than they do today. Even by 2020, the clock frequency (speed) of computer chips is unlikely to change but supercomputing systems will have more than one billion processing cores.
Exploiting massive parallelism is therefore critical, since typical applications only achieve about 5% parallel efficiency. According to the DOE, new mathematical models, numerical methods, and software implementations are needed to enable effective use of parallelism on unprecedented levels, and rewriting computer applications will become a necessity. The DOE also stresses that “an important problem formulation that represents many real-world problems yet tends to be avoided because of its known intractability is constrained nonlinear optimization.”
MIA addresses these challenges. MIA can be inserted into current chips and reside next to floating point, allowing end users to take full advantage of the new hardware without disturbing legacy software implementations. For a proficient semiconductor company, manufacturing MIA-enable chips is therefore a simple and cost effective solution to their market pain.
Surpassing profound archaic methods
Floating point arithmetic is inaccurate, unreliable, and in general cannot solve complex mathematical problems such as nonlinear optimization. However, floating point also prevents parallel computing.
Each time a parallel calculation is performed, the order of operations change, so rounding errors accumulate differently to produce varying results. By comparison, sequential floating point calculation produces consistent results because the order of operations never change, which is why people often rely on sequential calculation.
However, repeatability does not assure accuracy and conflating the two may lead to a false sense of security.
MIA by definition can guarantee to compute an accurate and precise answer in a highly efficient, reliable, and parallel manner. With MIA, the era of unreliable, inaccurate, and sequential computing is over.
Meet the Master
Nathan Hayes is the Founder, President, and CTO of Modal Technology Corporation, recently rebranded from Sunfish Studio, LLC. Nathan was a member of the IEEE 1788 committee, which set the industry standard for interval arithmetic in 2015. His company has experience in computer arithmetic and high-performance computing and is seeking business partnerships and licensing opportunities with others in the semiconductor industry.
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