Hewlett-packard Development Company, L.p.

Digital Equipment Corporation

Compaq Information Technologies Group, L.p.

Compaq Computer Corporation, Inc.

Sridhar Samudrala

Mark D Matson

Robert J Dupcak

Jonathan D Krause

William R Grundmann

Nachum M Gavrielov

Andrew J Beaumont-Smith

William C Madden

Victor Peng

Sharon Marie Britton

John D Clouser

Roy Badeau

Vidya Rajagopalan

Randy Allmon

Vijay Maheshwari

The specification discloses a structure of and a method of operating a subtractive division (SD) cell where a portion of the partial remainder or estimated partial remainder directly indicates the next quotient digit. More particularly, by sufficiently constraining the prescaled range for each possible divisor, only a few bits of the partial remainder (the exact number dependent upon the radix), along with their related carries (if any), directly indicate the value of the next quotient digit. Because fewer bits of the partial remainder are needed to make this determination than needed in related art devices, and further because no look-up table or hard-coded decision tree is required, calculation time within each SD cell is shorter than related art devices. Having a shorter calculation time within each SD cell allows for either completion of a greater number of SD cells within each clock cycle, or completion of the calculation to full precision in less time.

Method and system of a microprocessor subtraction-division floating point divider

Computer method and apparatus for performing a square root or division operation generating a root or quotient. A partial remainder is stored in radix-2 or radix-4 signed digit format. A decoder is provided for computing a root or quotient digit, and a correction term dependent on a number of the most significant digits of the partial remainder. An adder is provided for computing the sum of the signed digit partial remainder and the correction term in binary format, and providing the result in signed digit format. The adder computes a carry out independent of a carry in bit and a sum dependent on a Carry_in bit providing a fast adder independent of carry propagate delays. The scaler performs a multiplication by two of the result output from the adder in signed digit format to provide a signed digit next partial remainder.

Computer method and apparatus for division and square root operations using signed digit

In a digital processor performing division, quotient accumulation apparatus is formed of a set of muxes and a single carry save adder. Partial quotients are accumulated in carry-save form with proper sign extension. Delay of partial quotient bit fragments from one iteration to a following iteration enables the apparatus to limit use to one carry save adder. By enlarging minimal logic, the quotient accumulation apparatus operates at a rate fast enough to support the rate of fast dividers.

Method and apparatus for accumulating partial quotients in a digital processor

Computer method and apparatus for performing a square root or division operation generating a root or quotient is presented. A partial remainder is stored in radix- or radix- signed digit format. A decoder is provided for computing a root or quotient digit, and a correction term dependent on a number of the most significant digits of the partial remainder. An adder is provided for computing the sum of the signed digit partial remainder and the correction term in binary format, and providing the result in signed digit format. The adder computes a carry out independent of a carry in bit and a sum dependent on a Carry_in bit providing a fast adder independent of carry propagate delays. The scaler performs a multiplication by two of the result output from the adder in signed digit format to provide a signed digit next partial remainder.

A method and apparatus for operating on floating point numbers is provided that accepts two floating point numbers as operands in order to perform addition, a rounding adder circuit is provided which can accept the operands and a rounding increment bit at various bit positions. The circuit uses full adders at required bit positions to accommodate a bit from each operand and the rounding bit. Since the proper position in which the rounding bit should be injected into the addition may be unknown at the start, respective low and high increment bit addition circuits are provided to compute a result for both a low and a high increment rounding bit condition. The final result is selected based upon the most significant bit of the low rounding bit increment result. In this manner, the present rounding adder circuit eliminates the need to perform a no increment calculation used to select a result, as in the prior art. Through the use of full adders, the circuit not only accounts for the round increment bit, but can accept increment bits at any bit position to perform operations such as two's complement, thus further reducing the operations required to perform a desired floating point mathematical operation.

Method and apparatus for rounding floating point results in a digital processing system

The invention provides computer apparatus for performing a square root or division operation generating a root or quotient. A partial remainder is stored in radix-2 or radix-4 signed digit format. A decoder is provided for computing a root or quotient digit, and a correction term dependent on a number of the most significant digits of the partial remainder. An adder is provided for computing the sum of the signed digit partial remainder and the correction term in binary format, and providing the result in signed digit format. The adder computes a carry out independent of a carry in bit and a sum dependent on a Carry_in bit providing a fast adder independent of carry propagate delays. The scaler performs a multiplication by two of the result output from the adder in signed digit format to provide a signed digit next partial remainder.

A method and apparatus are presented for efficient implementation of logic and arithmetic functions that generate sets of mutually exclusive output signals. Such a logic family includes a network of NMOS transistors that implements a desired logic function. Coupled to that network is a minimal number of PMOS devices for providing logic level restoration and for compensating for any voltage drops due to the NMOS transistors. With such a structure, the speed, area and power consumption characteristics of logic functions are improved.

Generalized push-pull cascode logic technique

A floating point multiply of two n-bit operands creams a 2n-bit result, but ordinarily only n-bit precision is needed, so rounding is performed. Some rounding algorithms require the knowledge of the presence of any '1' in the n-2 low-order bits of the 2n-bit result. The presence of such a '1', indicates the so-called 'sticky bit' is set. The sticky bit is calculated in a path separate from the multiply operation, so the n-2 least significant sums need not be calculated. This saves time and circuitry in an array multiplier, for example. In an example method, the difference between n and the number of trailing zeros, 'x', in one of the n-bit operands is detected, by transposing the operand and detecting the leading one. The other operand is right-shifted by a number of bit positions equal to this difference. A sticky bit is generated if any logic '1's' are in the low-order n-x-2 bits fight shifted out of the second operand.

Method and apparatus for controlling a rounding operation in a floating

A circuit is provided for using the input operands of a floating point addition or subtraction operation to detect the leading one or zero bit position in parallel with the arithmetic operation. This allows the alignment to be performed on the available result in the next cycle of the floating point operation and results in a significant performance advantage. The leading I/O detection is decoupled from the adder that is computing the result in parallel, eliminating the need for special circuitry to compute a carry-dependent adjustment signal. The single-bit fraction overflow that can result from leading I/O misprediction is corrected with existing circuitry during a later stage of computation.

Leading one/zero bit detector for floating point operation

The arithmetic operations performed for floating point format numbers involve procedures having a multiplicity of major steps. The effective subtraction operation can be accelerated by using two methods of execution depending on whether the absolute value of the difference between the arguments of the exponents, ABS{DELTA(E)} is .ltoreq.1 or &gt;1. The procedure for ABS{DELTA(E)}.ltoreq.1 requires more major process steps than the situation where ABS{DELTA(E)}.ltoreq.1. To accelerate only the procedure having more major process steps, the two least significant bits of both exponent arguments are examined and based on the examination, the lengthier procedure can be initiated in parallel with the process step determining the value of ABS{DELTA(E)}. When the lengthier procedure is determined to be inappropriate based on the determined value, the results of the lengthier process can be discarded. Otherwise, the lengthier process, already in progress, is continued.

Apparatus and method for accelerating floating point addition and

In a floating point arithmetic execution unit, an additional adder unit and a selection network are added to the apparatus typically performing the arithmetic floating point function. The additional apparatus permits certain processes forming part of arithmetic operations to be executed in parallel. For selected arithmetic operations, the final result can be one of two values typically related by an intermediate shifting operation. By performing the processes in parallel and selecting the appropriate result, the execution time can be reduced when compared to the execution of the process in a serial implementation. The fundamental arithmetic operations of addition, subtraction, multiplication and division can each have the execution time decreased using the disclosed additional apparatus.

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Westboro, MA, United States of America

Sridhar Samudrala