Floating point arithmetic unit using modified Newton-Raphson technique for division and square root
AssigneeHewlett-Packard Company
InventorsAlan H. Karp, Peter Markstein, Dennis Brzezinski
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Abstract
A floating point processing system which uses a multiplier unit and an adder unit to perform floating point division and square root operations using both a conventional and a modified form of the Newton-Raphson method. The modified form of the Newton-Raphson method is used in place of the final iteration of the conventional Newton-Raphson so as to compute high precision approximated results with a substantial improvement in speed. The invention computes approximated results faster and simplifies hardware requirements because no multiplications of numbers of the precision of the result are required.
Claims9
A floating point arithmetic unit for performing at least one of a division operation to divide a dividend by a divisor to produce an estimated quotient and a square root operation of a value to produce an estimated square root, said arithmetic processing unit comprising:
- a multi-ported storage device for storing data;
- arithmetic means for multiplying two numbers to produce a product and for adding two numbers to produce a sum;
- divide and square root microcode containing iterative procedures for performing at least one of the divide and square root operations;
- reciprocal approximation means for supplying an initial approximation for at least one of a reciprocal value of the divisor and a reciprocal value of the square root of the value;
- and
- a control unit for controlling said floating point arithmetic unit;
- wherein said divide and square microcode carries out at least one of the divide and square root operations to produce at least one of the estimated quotient and square root with a precision of 2N-bits without requiting any 2N-by-2N multiplications;
- where N is a positive integer.
In a floating point arithmetic circuit having an addition unit, a multiplication unit and a control unit, a Newton-Raphson iterative routine is used to respectively produce an estimated reciprocal value using said addition unit and said multiplication unit when said control unit detects a divide or square root instruction for execution, the improvement comprising modifying the last iteration of the Newton-Raphson iterative routine to produce one of a final approximate quotient and a final approximate square root and to have the final approximate quotient or square root produced by the last iteration by estimating the quotient or square root and then improving the precision of the estimated quotient or square root in accordance with a residual error generated based on the estimated quotient or square root, thereby producing the final approximate quotient or square root.
Dependencies are inferred from the claim text.