Multiprecision floating point addition
George Ernest Collins, Werner Krandick · 2000
An efficient algorithm is presented that returns the exactly rounded sum of two multiprecision floating point numbers. Depending on the input signs and exponents the algorithm distinguishes five cases. In each case, the method minimizes the number of computer words that are subject to de-normalization, addition or subtraction, and normalization. The method achieves further efficiency by trying to combine these three steps into one single pass over the mantissas. To do this, the method guesses the shift amount of the normalizing shift before the sum is known.