Design of High Precision Low Power Approximate Floating-point Multiplier Based on Partial Product Probability Analysis
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摘要: 浮点乘法器是高动态范围(HDR)图像处理、无线通信等系统中的关键运算单元，其相比于定点乘法器动态范围更广，但复杂度更高。近似计算作为一种新兴范式，在受限的精度损失范围内，可大幅降低硬件资源和功耗开销。该文提出一种16 bit半精度近似浮点乘法器(App-Fp-Mul)，针对浮点乘法器中的尾数乘法模块，根据其部分积阵列中出现1的概率，提出一种对输入顺序不敏感的近似4-2压缩器及低位或门压缩方法，在精度损失较小的条件下有效降低了浮点乘法器资源及功耗。相较于精确设计，所提近似浮点乘法器在归一化平均错误距离(NMED)为0.0014时，面积及功耗延时积方面分别降低20%及58%；相较于现有近似设计，在近似位宽相同时具有更高的精度及更小的功耗延时积。最后将该文所提近似浮点乘法器应用于高动态范围图像处理，相比现有主流方案，峰值信噪比和结构相似性分别达到83.16 dB 和 99.9989%，取得了显著的提升。Abstract: Floating-point multipliers are the key operational units in High Dynamic Range(HDR) image processing and wireless communication systems. Compared to the fixed-point multipliers, floating-point multipliers have a higher dynamic range and also higher complexity. As a newly emerging paradigm, the hardware resources and power consumption of the circuits can be greatly reduced by approximate computing within an acceptable accuracy loss. According to the probability of 1 in the partial product array, an Approximate Floating-point Multiplier(App-Fp-Mul) is proposed in this paper. An approximate 4-2 compressor and or-gate based compression method are proposed to reduce the resource and power consumption of the floating-point multiplier with small precision loss. Compared with the accurate design, the proposed approximate floating-point multiplier can reduce the area, and power delay product by 20%, and 58% respectively when the Normalized Mean Error Distance (NMED) is 0.0014. And the proposed floating-point multiplier has higher accuracy and a smaller power delay product than the existing approximate designs with the same approximate bit width. Finally, the proposed approximate floating-point multiplier is verified with high dynamic range image processing application. The result of processing can reach 83.16 dB peak signal to noise ratio and 99.9989% structure similarity, which is obviously better than the existing approximate design.
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表 1 浮点数的尾数中1的概率
权重 A[10] A[9] A[8] A[7] A[6] A[5] A[4] A[3] A[2] A[1] A[0] 高斯分布 0.97 0.42 0.46 0.48 0.49 0.49 0.50 0.50 0.50 0.50 0.50 
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表 3 近似 4-2 压缩器真值表
P1 P2 P3 P4 Sum Carry Error 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 0 1 0 0 0 0 1 1 0 1 0 0 1 0 0 1 0 0 0 1 0 1 0 1 0 0 1 1 0 0 1 0 0 1 1 1 1 1 0 1 0 0 0 1 0 0 1 0 0 1 0 1 0 1 0 1 0 0 1 0 1 0 1 1 1 1 0 1 1 0 0 0 1 0 1 1 0 1 1 1 0 1 1 1 0 1 1 0 1 1 1 1 0 1 –2
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