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Processing-using-DRAM has been proposed for a limited set of basic operations (i.e., logic operations, addition). However, in order to enable the full adoption of processing-using-DRAM, it is necessary to provide support for more complex operations. In this paper, we propose SIMDRAM, a flexible general-purpose processing-using-DRAM framework that enables massively-parallel computation of a wide range of operations by using each DRAM column as an independent SIMD lane to perform bit-serial operations. SIMDRAM consists of three key steps to enable a desired operation in DRAM: (1) building an efficient majority-based representation of the desired operation, (2) mapping the operation input and output operands to DRAM rows and to the required DRAM commands that produce the desired operation, and (3) executing the operation. These three steps ensure efficient computation of any arbitrary and complex operation in DRAM. The first two steps give users the flexibility to efficiently implement and compute any desired operation in DRAM. The third step controls the execution flow of the in-DRAM computation, transparently from the user. We comprehensively evaluate SIMDRAM's reliability, area overhead, operation throughput, and energy efficiency using a wide range of operations and seven diverse real-world kernels to demonstrate its generality. Our results show that SIMDRAM provides up to 5.1x higher operation throughput and 2.5x higher energy efficiency than a state-of-the-art in-DRAM computing mechanism, and up to 2.5x speedup for real-world kernels while incurring less than 1% DRAM chip area overhead. Compared to a CPU and a high-end GPU, SIMDRAM is 257x and 31x more energy-efficient, while providing 93x and 6x higher operation throughput, respectively.