Spiking Neural Networks (SNNs) are considered to have enormous potential in the future development of Artificial Intelligence (AI) due to their brain-inspired and energy-efficient properties. In the current supervised learning domain of SNNs, compared to vanilla Spatial-Temporal Back-propagation (STBP) training, online training can effectively overcome the risk of GPU memory explosion and has received widespread academic attention. However, the current proposed online training methods cannot tackle the inseparability problem of temporal dependent gradients and merely aim to optimize the training memory, resulting in no performance advantages compared to the STBP training models in the inference phase. To address the aforementioned challenges, we propose Efficient Multi-Precision Firing (EM-PF) model, which is a family of advanced spiking models based on floating-point spikes and binary synaptic weights. We point out that EM-PF model can effectively separate temporal gradients and achieve full-stage optimization towards computation speed and memory footprint. Experimental results have demonstrated that EM-PF model can be flexibly combined with various techniques including random back-propagation, parallel computation and channel attention mechanism, to achieve state-of-the-art performance with extremely low computational overhead in the field of online learning.