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The posit number system is arguably the most promising and discussed topic inArithmetic nowadays. The recent breakthroughs claimed by the format proposed byJohn L. Gustafson have put posits in the spotlight. In this work, we firstdescribe an algorithm for multiplying two posit numbers, even when the numberof exponent bits is zero. This configuration, scarcely tackled in literature,is particularly interesting because it allows the deployment of a fast sigmoidfunction. The proposed multiplication algorithm is then integrated as atemplate into the well-known FloPoCo framework. Synthesis results are shown tocompare with the floating point multiplication offered by FloPoCo as well.Second, the performance of posits is studied in the scenario of Neural Networksin both training and inference stages. To the best of our knowledge, this isthe first time that training is done with posit format, achieving promisingresults for a binary classification problem even with reduced positconfigurations. In the inference stage, 8-bit posits are as good as floatingpoint when dealing with the MNIST dataset, but lose some accuracy withCIFAR-10.

Template-Based Posit Multiplication for Training and Inferring in Neural Networks