The Parallel Evaluation of General Arithmetic Expressions

It is shown that arithmetic expressions with n ≥ 1 variables and constants; operations of addition, multiplication, and division; and any depth of parenthesis nesting can be evaluated in time 4 log 2 n + 10( n - 1)/ p using p ≥ 1 processors which can independently perform arithmetic operations in unit time. This bound is within a constant factor of the best possible. A sharper result is given for expressions without the division operation, and the question of numerical stability is discussed.