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SAM-CORDIC: A Scaling Free Accurate Memoryless CORDIC for Logarithm Computation
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DOI：10.1109/tcsi.2026.3699980.png)
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Abstract
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Traditional Coordinate Rotation Digital Computer (CORDIC) relies on Look-up Tables (LUTs) for scaling and rotation, which introduce memory limitations, especially in resource-limited applications. This work proposes a Scaling-free, Accurate, Memory-less CORDIC (SAM-CORDIC) algorithm, a novel, ultra-lightweight architecture that eliminates the need for ROM. By replacing mutually exclusive micro-rotations in CORDIC with dynamically derived single-constant decay, SAM-CORDIC provides a continuous datapath without the need to store threshold values. An extensive analysis of different radices and expansion orders found that Radix-8 order-2 provides an optimal balance between mathematical convergence and hardware complexity. The proposed system, during architectural simulation, provides an error reduction of up to 87% during multiplication application. The ASIC synthesis using the Cadence Genus tool using 90nm technology validated the proposed system’s efficiency. The implementation achieves a strictly 0-byte memory footprint. It requires only 359 standard cells, representing a 50% reduction in area and a 41% reduction in total power compared to state-of-the-art scale-free variants, while maintaining a robust absolute error floor of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$1.43 \times 10^{-4}$ </tex-math></inline-formula>.
Keywords:
CORDIC
memoryless CORDIC
scaling free CORDIC
logarithmic arithmetic
low-complexity computation
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