Efficient Implementations of Reduced Precision Redundancy (RPR) Multiply and Accumulate (MAC) Articles uri icon


  • CHEN, KE

publication date

  • May 2019

start page

  • 784

end page

  • 790


  • 5


  • 68

International Standard Serial Number (ISSN)

  • 0018-9340

Electronic International Standard Serial Number (EISSN)

  • 1557-9956


  • Multiply and Accumulate (MAC) is one of the most common operations in modern computing systems. It is for example used in matrix multiplication and in new computational environments such as those executed on neural networks for deep machine learning. MAC is also used in critical systems that must operate reliably such as object recognition for vehicles. Therefore, MAC implementations must be able to cope with errors that may be caused for example by radiation. A common scheme to deal with soft errors in arithmetic circuits is the use of Reduced Precision Redundancy (RPR). RPR instead of replicating the entire circuit, uses reduced precision copies which significantly reduce the overhead while still being able to correct the largest errors. This paper considers the implementation of RPR Multiply and Accumulate circuits. First, it is shown that the properties of signed integer multiplication (two's complement format) can be used to make RPR more efficient. Then its principles are extended to the MAC operation by proposing RPR implementations that improve the error correction capabilities with a limited impact on circuit overhead. The proposed schemes have been implemented and tested. The results show that they can significantly reduce the Mean Square Error (MSE) at the output when the circuit is affected by a soft error and the implementation overhead of the proposed schemes is extremely low.


  • soft errors; multiply and accumulate; reduced precision redundancy; integer