Markov chain Monte Carlo (MCMC) is a widely used sampling method in modern artificial intelligence and probabilistic computing systems. It involves repetitive random number generations and thus often dominates the latency of probabilistic model computing. Hence, we propose a compute-in-memory (CIM) based MCMC design as a hardware acceleration solution. This work investigates SRAM bitcell stochasticity and proposes a novel ``pseudo-read'' operation, based on which we offer a block-wise random number generation circuit scheme for fast random number generation. Moreover, this work proposes a novel multi-stage exclusive-OR gate (MSXOR) design method to generate strictly uniformly distributed random numbers. The probability error deviating from a uniform distribution is suppressed under $10^{-5}$. Also, this work presents a novel in-memory copy circuit scheme to realize data copy inside a CIM sub-array, significantly reducing the use of R/W circuits for power saving. Evaluated in a commercial 28-nm process development kit, this CIM-based MCMC design generates 4-bit$\sim$32-bit samples with an energy efficiency of $0.53$~pJ/sample and high throughput of up to $166.7$M~samples/s. Compared to conventional processors, the overall energy efficiency improves $5.41\times10^{11}$ to $2.33\times10^{12}$ times.

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