# Rez-9 ALU

The Rez-9 ALU is the world’s first general purpose residue processor! Never before has the true power of residue arithmetic been unleashed until now!

What’s so unique about residue number processing? Everything! Imagine performing calculations on very accurate, very wide numbers without any slowing due to carry. Imagine performing calculations which retain their full precision and run even faster. Imagine new fractional data representations, which inherently represent significantly more unique ratios, like the value 1/3! Now, imagine that all of it results from a brand new form of arithmetic! An exciting new world of machine computation has indeed arrived!

The Rez-9 ALU is a unique co-processor which off-loads arithmetic calculations from a binary host CPU and performs them using the residue number system, thereby accelerating overall arithmetic performance. Since residue numbers do not require carry from digit to digit, many arithmetic operations execute much faster, despite the resolution or range of the values under calculation. This allows the residue processor to operate on very wide data, or to represent very accurate fractional values. Of special merit of the Rez-9 ALU is its ability to operate on fractional data formats, derived directly from fixed and floating point binary formats. This makes the Rez-9 a breakthrough versus traditional known methods of residue number arithmetic.

Not evident by casual observation is the fact that many more discoveries stem from the new developments at DSR. For example, algorithm design itself changes since the residue number system has different characteristics than the binary number system. Furthermore, DSR has discovered that the residue number system is oddly symmetrical to the binary number system, exhibiting nearly opposing advantages and disadvantages. When both binary and residue systems are combined, a hybrid processing paradigm is formed, and the advantages of both number systems is brought forth together.

However, the Rez-9 ALU does not cheat! The Rez-9 ALU is capable of performing highly repetitive, fractional arithmetic calculations entirely in residue number format. Data is input to the Rez-9 through high speed conversion apparatus, or initial data may be derived via calculation within the Rez-9 itself. All calculations within the Rez-9 are performed entirely using residue numbers. When the calculations are complete, the Rez-9 processor converts the residue number results to binary using high speed, fully extensible converters. Once converted to binary, the results of the residue calculations can be used to affect the real world via the binary host CPU.

The Rez-9 ALU has been developed as an IP core suitable for connection to the Altera NIOS-II CPU using Altera’s QSYS SOC builder tool. The Rez-9 targets the -IV series of Altera FPGA devices, and may be scaled to perform calculations in a broad range of applications and industries.

*Rez-9 and its associated components are patent pending in the US and abroad.

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