Apparatus for performing floating point arithmetic operation and rounding the result thereof

An apparatus comprising:

• a function calculating device for deriving an approximate solution Ya of a function F with respect to a given value X by referring to a relation Y=F(X) at an accuracy at which an error between the approximate solution Ya and an infinitely precise solution Y is smaller than a weight of a digit in a place lower by two places than a lowest place of significant digits for a final solution,
• said function calculating device further operating for deriving a value Xr from an interim solution Yr and from an inverse function F.sup.-1 by referring to a relation Xr=F.sup.-1 (Yr);
• a rounding circuit including an adder and a subtractor,
• said rounding circuit operating for rounding the approximate solution Ya to provide as said interim solution Yr a solution equal to a selected one of a plurality of possible interim solutions which is closest to the approximate solution Ya, the possible interim solutions being represented by digits in predetermined digit places, a lowest of which is arbitrarily selected from a place range starting from a place lower by at least one place than the lowest place of the significant digits for the final solution and ending at a place higher by at least one place than a place of a minimal weight, wherein a weight of a digit in the minimal-weight place is greater than a maximum of an error of the approximate solution Ya;
• a sticky digit generator for deciding which of the infinitely precise solution Y and the interim solution Yr is greater by referring to a relation between the values X and Xr, and for generating a sticky digit S, said sticky digit generator setting the sticky digit to a value 0 when the values Y and Yr are equal, to a value -1 when the infinitely precise solution Y is decided to be smaller than the interim solution Yr, and to a value 1 when the infinitely precise solution Y is decided to be greater than the interim solution Yr,
• wherein said adder of said rounding circuit adds the sticky digit S to a place immediately lower than a lowest place of the interim solution Yr and said rounding circuit rounds a result of the addition performed by the adder in a designated rounding mode,
• said rounding circuit generating a digital signal representing the final solution and outputting said digital signal to an external utilization circuit.