Seed ROM for reciprocal computation

An apparatus for computing the reciprocal of a binary input operand, comprising:

• a normalizing component for normalizing the input operand to a normalized operand;
• a first look-up table storing a plurality of estimated reciprocal values indexed by a corresponding first plurality of associated index values;
• a second look-up table storing a plurality of reciprocal error values indexed by a corresponding second plurality of associated index values;
• a summing component coupled to the normalizing component, and the first and second look-up tables, the summing component summing the estimated reciprocal value associated with the index value corresponding to a first portion of the normalized operand and the reciprocal error value associated with the index value matching a second portion of the normalized operand;
• and
• a denormalizing component coupled to the summing component for denormalizing the sum or the summing component to provide the reciprocal value of the binary input operand.

An apparatus for calculating a quotient from a dividend value and a divisor value, comprising:

• a first table tabulating a plurality of estimated reciprocal values, each estimated reciprocal value associated with a reciprocal index value, in response to receipt of a portion of the divisor value matching one of the reciprocal index values, the first table providing the estimated reciprocal value associated thereto;
• a second table tabulating a plurality of reciprocal error values, each reciprocal error value associated with an error index value, in response to receipt of a portion of the divisor value matching one of the error index values, the second table providing the reciprocal error value associated thereto;
• a combining component coupled to the first and second tables to receive the estimated reciprocal values and the reciprocal error values, the combining component further calculating a reciprocal value for the divisor value therefrom;
• and
• a multiplying component for calculating the product of a first and second value, the multiplying component receiving as the first value the dividend value and coupled to the output of the combining component to receive the reciprocal value of the divisor value as the second value, the multiplying component calculating the quotient by multiplying the dividend value and reciprocal value of the divisor value.

A method for calculating a reciprocal for an input value, comprising:

• selecting from a table of estimated reciprocal values an estimated reciprocal value based on a first portion of the input value;
• selecting from a table of reciprocal error values a reciprocal error value based on a second portion of the input value;
• and
• summing the estimated reciprocal value and the reciprocal error value together to calculate the reciprocal for the input value.

A method of computing the reciprocal of a binary input operand, comprising:

• normalizing the input operand to a normalized operand;
• selecting from a first look-up table storing a plurality of estimated reciprocal values indexed by a corresponding first plurality of a associated index values an estimated reciprocal value based on a first portion of the normalized operand;
• selecting from a second look-up table storing a plurality of reciprocal error values indexed by a corresponding second plurality of associated index values a reciprocal error value based on a second portion of the normalized operand;
• summing the selected estimated reciprocal value and the reciprocal error value;
• and
• denormalizing the sum or the summing component to provide the reciprocal value of the binary input operand.