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Fault-Tolerant Newton-Raphson and Goldschmidt Dividers Using Time Shared TMR

Iterative division algorithms based on multiplication are popular because they are fast and may utilize an already existing hardware multiplier. Two popular methods based on multiplication are Newton-Raphson and Goldschmidt's algorithm. To achieve concurrent error correction, Time Shared Triple Modular Redundancy (TSTMR) may be applied to both kinds of dividers. The hardware multiplier is divided into thirds, and the rest of the divider logic replicated around each part, to provide three independent dividers. While this reduces the size of the fault-tolerant dividers over that of traditional TMR, latency may be increased. However, both division algorithms can be modified to use lower precision multiplications during the early iterations. This saves multiply cycles and, hence, produces a faster divider.