AI 中文总结
针对计算中对大动态范围低误差数字表示的需求，提出WINT格式，开发计算MRE的框架，引入近似方法，实验表明不同指数位分配能在降低MRE的同时扩大范围。
AI 中文摘要
在计算中，需要能提供大动态范围且低误差的数字表示方案。许多应用（如嵌入式系统和边缘机器学习）内存受限但需大动态范围来表示数据。我们提出加权整数（WINT），一种简单且可配置的尾数指数数字格式，用户可选择尾数（m）和指数（e）位分配。我们开发了计算平均相对误差（MRE）的完整分析框架。因精确计算MRE随尾数大小指数增长，我们引入谐波和泰勒级数近似方法，时间复杂度为O(1)。实验表明，对于12位及以上配置，分配2个指数位可使MRE降低12 - 33%，范围比整数基线大2倍；对于16位及以上配置，分配3个指数位可使范围扩大16倍，MRE降低15 - 50%。
英文摘要
In computing, there is a need for number representation schemes that provide large dynamic range with low error. Many applications, including embedded systems and edge machine learning, have stringent memory constraints yet require large dynamic range for data representation. We present Weighted Integer (WINT), a simple and configurable mantissa exponent number format with user-selectable mantissa (m) and exponent (e) bit allocations (also referred to as configurations) that enables application-specific precision versus range tradeoffs at design time. We develop a complete analytical framework for computing Mean Relative Error (MRE), the primary metric for characterizing WINT's error. Since exact MRE calculations grow exponentially with mantissa size, we introduce harmonic and Taylor series approximation methods that achieve O(1) time complexity regardless of configuration. The Taylor series and harmonic approximations demonstrate significant speedups over the exact method while maintaining accuracy within 0.2% for the configurations presented. Our experiments across 8 to 32-bit configurations show that allocating 2 exponent bits consistently yields both lower MRE by 12-33% and 2X greater range than the integer baseline for bit widths of 12 and above. Allocating 3 exponent bits extends range by 16X while reducing MRE by 15-50% for bit widths of 16 and above
