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A simple scheme is presented for computing the exponential of a floating point number using only shift, add, and multiply instructions. The algorithm involves no range reduction and handles overflow and underflow conditions automatically. It can be used to provide a result of any desired accuracy, provided only that sufficient precision is used during the calculation. The basic algorithm and three improvements are described. Both computational complexity and numerical precision are discussed. For the sake of symmetry, a method for computing the logarithm along similar lines is given.