Functionally-Complete Boolean Logic in Real DRAM Chips: Experimental Characterization and Analysis

Processing-using-DRAM (PuD) is an emerging paradigm that leverages the analog operational properties of DRAM circuitry to enable massively parallel in-DRAM computation. PuD has the potential to significantly reduce or eliminate costly data movement between processing elements and main memory. A common approach for PuD architectures is to make use of bulk bitwise computation (e.g., AND, OR, NOT). Prior works experimentally demonstrate three-input MAJ (i.e., MAJ3) and two-input AND and OR operations in commercial off-the-shelf (COTS) DRAM chips. Yet, demonstrations on COTS DRAM chips do not provide a functionally complete set of operations (e.g., NAND or AND and NOT). We experimentally df performing 1) functionally-complete Boolean operations: NOT, NAND, and NOR and 2) many-input (i.e., more than two-input) AND and OR operations. We present an extensive characterization of new bulk bitwise operations in 256 off-theshelf modern DDR4 DRAM chips. We evaluate the reliability of these operations using a metric called success rate: the fraction of correctly performed bitwise operations. Among our 19 new observations, we highlight four major results. First, we can perform the NOT operation on COTS DRAM chips with a 98.37% success rate on average. Second, we can perform up to 16-input NAND, NOR, AND, and OR operations on COTS DRAM chips with high reliability (e.g., 16-input NAND, NOR, AND, and OR with an average success rate of 94.94%, 95.87%, 94.94%, and 95.85%, respectively). Third, data pattern only slightly affects NAND, NOR, AND, and OR operations. Our results show that executing NAND, NOR, AND, and OR operations with random data patterns decreases the success rate compared to all logic-1/logic-0 patterns by 1.39%, 1.97%, 1.43%, and 1.98%, respectively. Fourth, NOT, NAND, NOR, AND, and OR operations are highly resilient to temperature changes, with small success rate fluctuations of at most 1.66% among all the tested operations when the temperature is increased from 50°C to 95°C. We believe these empirical results demonstrate the promising potential of using DRAM as a computation substrate.