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Recently, learned image compression methods have developed rapidly and exhibited excellent rate-distortion performance when compared to traditional standards, such as JPEG, JPEG2000 and BPG. However, the learning-based methods suffer from high computational costs, which is not beneficial for deployment on devices with limited resources. To this end, we propose shift-addition parallel modules (SAPMs), including SAPM-E for the encoder and SAPM-D for the decoder, to largely reduce the energy consumption. To be specific, they can be taken as plug-and-play components to upgrade existing CNN-based architectures, where the shift branch is used to extract large-grained features as compared to small-grained features learned by the addition branch. Furthermore, we thoroughly analyze the probability distribution of latent representations and propose to use Laplace Mixture Likelihoods for more accurate entropy estimation. Experimental results demonstrate that the proposed methods can achieve comparable or even better performance on both PSNR and MS-SSIM metrics to that of the convolutional counterpart with an about 2x energy reduction.