A note on multiple precision arithmetic

Abstract

Since computers have means to detect overflow on addition or subtraction, this can be used in a multiple precision addition-subtraction subroutine to obviate a sign analysis. Consider all integers in the computer to be expressed “radix t ”, that is, in the form a = a ₀ + a ₁ t + ··· + a _n t ⁿ where a _i are of like sign and have magnitudes less than t . t is a positive integer determined by the word length of the computer. Consider the expression c = a ± b = ( a ₀ ± b ₀ ) + ( a ₁ ± b ₁ ) t + ··· + ( a _n ± b _n ) t ⁿ . Here a _i ± b _i may exceed the storage capacity of one word or may have a sign different from c .