🤖 AI Summary
This work addresses the challenge of balancing dynamic range and precision in numerical representation for memory-constrained embedded and edge AI systems. The authors propose WINT, a weighted integer format that enables flexible trade-offs between precision and range through configurable allocation of mantissa and exponent bits at design time. They derive an analytical model for average relative error and introduce, for the first time, a floating-point-like representation supporting user-defined bit widths. Efficient error evaluation is achieved via O(1)-complexity approximations based on harmonic series and Taylor expansions. Experiments demonstrate that with word lengths of 12 bits or more, WINT using just 2 exponent bits reduces average relative error by 12–33% compared to integer baselines while doubling the dynamic range; with 3 exponent bits, it further extends the range by up to 16× and lowers error by 15–50%.
📝 Abstract
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