Office of Technology Transfer – University of Michigan

High Performance Hardware for Reciprocal Computation

Technology #6429

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Zhengya Zhang
Managed By
Joohee Kim
Licensing Specialist, Physical Sciences & Engineering 734-764-8202
Patent Protection
US Patent Pending

A custom hardware solution for calculating reciprocals with high precision and at high speeds, while minimizing hardware overheads and energy usage, has been developed at the University of Michigan. Reciprocal computation is a key aspect of inversion and division operations on computers and other hardware devices. Specifically, many scientific and practical applications require the computation of reciprocals with high precision. As an example, multiple-input multiple-output wireless receivers require reciprocal calculations with more than 12 bits of precision. Existing techniques for high-precision reciprocal calculation entail large hardware units and high power consumption.

Design Details

The reciprocal calculation hardware developed at the University of Michigan overcomes the challenges of high hardware overheads and high power consumption. The design makes use of two small lookup tables (LUTs) of 32x6 bits and 32x12 bits to calculate the reciprocal by the Newton-Raphson method. The hardware unit calculates reciprocals with an average precision of 2-11.14 and an error of less than 2-9.2. Overall, the design shortens the delay path and reduces the memory usage compared to extant designs, thereby offering performance levels that are better by an order of magnitude or more.


  • MIMO Wireless Communication
  • Scientific computing
  • Graphics processing
  • Communication signal processing
  • Matrix inversion


  • High speed, low latency
  • Low area overhead
  • Reduced memory requirement
  • Simple implementation
  • Low power consumption