A method for performing arithmetic encoding in an image coding process, comprising: calculating a probability of each symbol in a set of code symbols to be coded, wherein there are only two symbols of 0 and 1 in the set of code symbols; encoding the symbols in the set of code symbols according to calculated probabilities, symbols in the set of code symbols having a higher probability are named as most probable symbols, symbols in the set of code symbols having a lower probability are named as least probable symbols, during the encoding, iterations are performed on an interval according to the probabilities of the symbols, to finally obtain an updated interval representing information of the whole set of code symbols, wherein when encoding a most probable symbol, performing an update on the interval in the logarithm domain and implementing the interval update computation with add/subtract operations; when encoding a least probable symbol, performing data conversion from the logarithm domain to the original domain, and performing the interval update with a subtraction in the original domain; performing data conversions between the original domain and the logarithm domain by approximations; and wherein during data conversions between the logarithm domain and the original domain, for the data conversion from the original domain to the logarithm domain, for a value X in the original domain, its corresponding value Log_X in the logarithm domain is equal to X-1, and, when the Log_X is computed, it is corrected with a second correcting parameter Δ2, where Δ2 is determined by looking up a pre-stored table, during data conversions between the logarithm domain and the original domain, for the data conversion from the logarithm domain to the original domain, a value X in the original domain is derived by shifting a parameter B by A bits to the left or to the right, or by dividing the parameter B by 2 raised to the power of A, and wherein the parameters A and B are computed by decomposing Log_X in the logarithm domain as Log_X = -A + B - 1, where the parameter A is an integer, and the absolute value for the parameter B minus 1 is less than 1. calculating a probability of each symbol in a set of code symbols to be coded, wherein there are only two symbols of 0 and 1 in the set of code symbols; encoding the symbols in the set of code symbols according to calculated probabilities, symbols in the set of code symbols having a higher probability are named as most probable symbols, symbols in the set of code symbols having a lower probability are named as least probable symbols, during the encoding, iterations are performed on an interval according to the probabilities of the symbols, to finally obtain an updated interval representing information of the whole set of code symbols, wherein when encoding a most probable symbol, performing an update on the interval in the logarithm domain and implementing the interval update computation with add/subtract operations; when encoding a least probable symbol, performing data conversion from the logarithm domain to the original domain, and performing the interval update with a subtraction in the original domain; performing data conversions between the original domain and the logarithm domain by approximations; and wherein during data conversions between the logarithm domain and the original domain, for the data conversion from the original domain to the logarithm domain, for a value X in the original domain, its corresponding value Log_X in the logarithm domain is equal to X-1, and, when the Log_X is computed, it is corrected with a second correcting parameter Δ2, where Δ2 is determined by looking up a pre-stored table, during data conversions between the logarithm domain and the original domain, for the data conversion from the logarithm domain to the original domain, a value X in the original domain is derived by shifting a parameter B by A bits to the left or to the right, or by dividing the parameter B by 2 raised to the power of A, and wherein the parameters A and B are computed by decomposing Log_X in the logarithm domain as Log_X = -A + B - 1, where the parameter A is an integer, and the absolute value for the parameter B minus 1 is less than 1.