Commercial FPGAs, such as AMD Versal devices, increasingly incorporate AI engines that exploit low-precision packed-SIMD fused multiply-accumulate (FMA) to achieve proportional throughput gains. However, trans-precision FMA (e.g., multiplying two FP16 numbers and adding their result to an FP32 accumulator), which preserves numerical stability by accumulating in higher precision, remains bottlenecked by the highest-precision, lowest-throughput operation. Dot-product accumulation (DPA) (e.g., performing a dot-product on two 4-element FP8 vectors and adding its result to an FP32 accumulator) can fully utilize the input/output bandwidth and computational resources. Existing flexible open-source FPUs, such as FPnew, do not support DPA and implement SIMD FMA on low-precision formats by replicating independent FMA lanes, which increases area, underutilizes shared arithmetic resources, and complicates the integration of DPA operations. This paper presents TransDot, a reconfigurable FPU that unifies multi-precision SIMD FMA and trans-precision DPA within a shared, reconfigurable datapath. TransDot extends the baseline design with 2-term FP16, 4-term FP8, and 8-term FP4 dot-product accumulation into FP32 using reconfigurable subcomponents. Evaluation shows that TransDot delivers 2$\times$ FP16, 4$\times$ FP8, and 8$\times$ FP4 throughput via DPA with FP32 accumulation, and 1.46$\times$ area efficiency in FP16 DPA and 2.92$\times$ area efficiency in FP8 DPA, at the cost of 37.3% larger area on average and an additional pipeline stage in dot-product mode compared to the FPnew baseline. These results demonstrate that TransDot's area-efficient design enables scalable deployment in next-generation AMD Versal AI engines.

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