The takum machine number format has been recently proposed as an enhancement over the posit number format, which is considered a promising alternative to the IEEE 754 floating-point standard. Takums retain the useful posit properties, but feature a novel exponent coding scheme that yields more precision for small and large magnitude numbers. Takum's dynamic range is larger and bounded, as reflected in its name, derived from the Icelandic 'takmarka{\dh} umfang', meaning 'limited range'. Consequently, the selection of bit string lengths becomes determined solely by precision requirements and independent of dynamic range considerations. Takum is defined in both a logarithmic number system (LNS) format and a traditional floating-point format. This paper presents the design and implementation of a hardware codec for both the logarithmic and floating-point takum formats. The design primarily focuses on the codec, as both formats share a common internal arithmetic representation. Non-essential aspects of current posit designs, such as fused or pipelined architectures and the choice of floating-point IP cores, are thus omitted. The proposed takum codec, implemented in VHDL, demonstrates near-optimal scalability and performance on an FPGA, matching or exceeding state-of-the-art posit codecs in terms of both latency and LUT utilisation.

翻译：Takum机器数格式是最近提出的一种对posit数格式的增强方案，而posit数格式被认为是IEEE 754浮点标准的一种有前景的替代方案。Takum保留了posit的有用特性，但采用了一种新颖的指数编码方案，为小量级和大量级数值提供了更高的精度。Takum的动态范围更大且有限，如其名称所示（源自冰岛语'takmarkað umfang'，意为“有限范围”）。因此，位串长度的选择完全由精度要求决定，而与动态范围考量无关。Takum既以对数数字系统（LNS）格式定义，也以传统浮点格式定义。本文介绍了针对对数格式和浮点格式takum的硬件编解码器的设计与实现。该设计主要聚焦于编解码器，因为两种格式共享一个共同的内部算术表示。当前posit设计中非核心的方面，例如融合或流水线架构以及浮点IP核的选择，因此被省略。所提出的takum编解码器采用VHDL实现，在FPGA上展示了近乎最优的可扩展性和性能，在延迟和LUT利用率方面均达到或超越了最先进的posit编解码器。