Abstract: A method and apparatus for accumulating arbitrary length strings of input values, such as floating point values, in a layered tree structure such that the order of adds at each layer is maintained. The accumulating utilizes a shared adder, and includes means for directing initial inputs and intermediate result values.

Abstract: A Xiu-accumulator circuit including N cascaded adders is provided. Each adder includes two registers, wherein one register stores an addition result information and the other register stores a carry-in information. Respective addition result information from respective adder is further fed back to itself for accumulation. The carry-in information outputted from a previous stage adder is fed to a next stage adder at a next clock cycle. After N clock cycles, the carry-in information outputted from the first stage adder is fed to the last stage adder.

Abstract: Embodiments of a near optimal configurable adder tree for arbitrary shaped 2D block sum of absolute differences (SAD) calculation engine are generally described herein. Other embodiments may be described and claimed. In some embodiments, a configurable two-dimensional adder tree architecture for computing a sum of absolute differences (SAD) for various block sizes up to 16 by 16 comprises a first stage of one-dimensional adder trees and a second stage of one-dimensional adder trees, wherein each one-dimensional adder tree comprises an input routing network, a plurality of adder units, and an output routing network.

Abstract: A fast, flexible carry scheme for use in clustered field programmable gate array architectures is described. Each cluster has a cluster carry input node, a cluster carry output node, a cluster carry output circuit having an output coupled to the cluster carry output node, a first input coupled to the cluster carry input node, and a second input and a plurality of logic modules each comprising a logic function generator circuit coupled to a carry circuit. The logic modules are coupled in a series carry arrangement between the cluster carry input node and the second input of the cluster carry output circuit such that the least significant bit of an arithmetic logic circuit can be programmably placed in any of the logic modules.

Abstract: A system for evaluating the convergence to a solution for a matrix equation comprises at least one reconfigurable computing device such as a field programmable gate array (FPGA), an update storage element, a conversion element, a summation unit, and a comparator. The FPGA includes a plurality of configurable logic elements and a plurality of configurable storage elements, which are utilized to form the update storage element, the conversion element, the summation unit, and the comparator. The update storage element is configured to store a plurality of updates. The conversion element determines the absolute value of the updates. The summation unit accumulates the absolute values of the updates to produce a total sum, which is compared to a convergence factor by the comparator. Convergence is signaled when the total sum is less than the convergence factor.

Abstract: A Chinese abacus adder is disclosed. The Chinese abacus adder includes a B/A (binary to abacus) circuit, a P/A (parallel addition) circuit and a T/B (thermometric to binary) circuit. The Chinese abacus adder has a multiple radix calculating structure, which could reduce power consumption of the system and lower the calculation delay time.

Abstract: A time-invariant method and apparatus for performing modular reduction that is protected against cache-based and branch-based attacks is provided. The modular reduction technique adds no performance penalty and is side-channel resistant. The side-channel resistance is provided through the use of lazy evaluation of carry bits, elimination of data-dependent branches and use of even cache accesses for all memory references.

Abstract: Aggressive pipelining allows Field Programmable Gate Arrays (FPGAs) to achieve high throughput on many Digital Signal Processing applications. However, cyclic data dependencies in the computation can limit pipelining and reduce the efficiency and speed of an FPGA implementation. Saturated accumulation is an important example where such a cycle limits the throughput of signal processing applications. A reformulation of saturated addition as an associative operation permits a parallel-prefix calculation to be used to perform saturated accumulation at any data rate supported by the device. The method may be extended to other operations containing loops with one or more loop-carried dependencies.

Abstract: A system is used to determine if a sum of a first operand and a second operand is the same as a third operand wherein a comparison to the third operand is of variable length. This is particularly useful in a content addressable memory (CAM) where the likelihood of hit is commonly improved over a set associative cache and allows for the CAM to identify different things. For example, an entry can be one length to identify a page of a memory and another entry be a different length to identify a page of memory. This is better understood by reference to the following description and the drawings.

Abstract: An arithmetic unit of arbitrary-precision, including: a main processing unit, which splits up the first and the second arbitrary-precision values into N-bit (where N is a natural number) operands respectively in the-least-significant-bit-first order for computing with the arbitrary-precision data and consecutively outputting a series of pairs of the first and second N-bit operands; and an N-bit arithmetic unit, which performs computing with the N-bit operands, while requesting the main processing unit to feed the next N-bit operands each time the computation completes. The carry bit generated by the operation is fed to the next N-bit operation.

Abstract: A computing device includes: a deciding unit which, in computation of values of nodes on a lattice in a direction where a value of m representing a horizontal axis coordinate of the lattice increases, decides dummy nodes to be added to m=n?1, so as to enable values of nodes on m=n to be calculated by adding the dummy nodes to m=n?1 and executing a vector operation through the use of the SIMD function by using values of nodes on m=n?1 and values of the added dummy nodes; an adding unit adding the dummy nodes decided by the deciding unit to m=n?1; and a calculating unit calculating the values of the nodes present on m=n by executing the vector operation through the use of the SIND function by using the values of the nodes on m=n?1 and the values of the dummy nodes added by the adding unit.

Abstract: According to embodiments of the subject matter disclosed in this application, decimal floating-point additions and/or decimal fixed-point additions may be implemented using existing hardware for binary number operations. The implementation can be carried out in software, in hardware, or in a combination of software and hardware. Pre-calculated constants that are approximations to negative powers of 10 and stored in binary format may be used for rounding addition results to a designated precision by multiplying the results with a pre-calculated constant. Additionally, several parts of a decimal multiplication may be carried out in parallel. Furthermore, a simple comparison with a constant instead of an expensive remainder calculation may be used for midpoint detection and exactness determination.

Abstract: An information processing apparatus includes: a register holding a value input thereto; a first communication path through which an addition command is input; a second communication path through which a subtraction command is input; addition means adding a predetermined value to a register value held in the register according to the addition command input through the first communication path and causing the register to hold a value resulting from the addition; and subtraction means subtracting a predetermined value from a register value held in the register according to the subtraction command input through the second communication path and causing the register to hold a value resulting from the subtraction, wherein the addition means and the subtraction means operate exclusively of each other.

Abstract: An information processing device includes: plural input registers including a first input register and a second input register; an added value register; a first adding unit that performs addition processing for stored data of the first input register and stored data of the second input register; a second adding unit that performs addition processing for connected data, which is obtained by connecting the stored data of the first input register and the stored data of the second input register, and stored data of the added value register; and plural output registers in which a processing result of the first adding unit or the second adding unit is stored, wherein in each of given execution cycles, the first adding unit stores a processing result of the first adding unit in any one of the plural output registers and the second adding unit stores a processing result of the second adding unit in any one of the plural output registers.

Abstract: A signal conversion system includes a compensation module and a conversion module coupled to the compensation module. The compensation module is operable for adjusting a first compensation signal according to a dynamic signal and adding the first compensation signal to a first input signal. The compensation module is also operable for subtracting a second compensation signal, indicative of an accumulation of the dynamic signal, from the output signal. The conversion module is operable for receiving a second input signal that is the sum of the first input signal and the first compensation signal, and converting the second input signal to the output signal.

Abstract: Embodiments of the invention disclose a virtual manipulative to facilitate math learning. The virtual manipulative comprises a user interface to progressively form one on more columns to hold partial sums or number decompositions to assist a learner in computing a sum.

Abstract: A method of simplifying a combinational circuit establishes an initial combinational circuit operable to calculate a set of target signals. A quantity of multiplication operations performed in a first portion of the initial combinational circuit is reduced to create a first, simplified combinational circuit. The first portion includes only multiplication operations and addition operations. A quantity of addition operations performed in a second portion of the first, simplified combinational circuit is reduced to create a second, simplified combinational circuit. The second portion includes only addition operations. Also, the second, simplified combinational circuit is operable to calculate the target signals using fewer operations than the initial combinational circuit.

Abstract: Configurable adder circuitry is provided on an integrated circuit that includes redundant circuitry. The integrated circuit may contain nonvolatile memory and logic circuitry that produces a redundancy control signal. During manufacturing, the integrated circuitry may be tested. If a defect is identified on the integrated circuit, the redundancy control signal may be used in switching redundant circuitry into place bypassing the defect. The integrated circuit may contain an array of logic regions. Each logic region may contain adders and multiplexer circuitry for selectively combining the multiplexers to form larger adders. The multiplexer circuitry in each logic region may be controlled by propagate signals from the adders and by static redundancy control signals.

Abstract: A system for determining the median of a plurality of data values comprises a plurality of field programmable gate arrays (FPGA), a plurality of inter FPGA links, an input router, a plurality of median modules, and a plurality of output transfer modules. Each FPGA includes a plurality of configurable logic elements and configurable storage elements from which the other components are formed. The inter FPGA link allows communication from one FPGA to another. The input router receives the plurality of data values and creates a plurality of data streams. The median module receives at least one data stream, increments a plurality of counters corresponding to a single data value within the range of data values, and determines the median by accumulating the contents of each counter. The output transfer module transfers the median to an external destination along with performance statistics of the determination of the median.

Abstract: A multi-operand decimal adder is described that performs addition on multiple binary coded decimal (BCD) operands. The multi-operand decimal adder uses binary carry-save adders to produce intermediate sums and carries, and outputs a decimal result based on the intermediate sums and carries. In various configurations, the multi-operand decimal adder may perform speculative or non-speculative binary carry-save addition. The multioperand decimal adders achieve a reasonable critical path. As a result, the decimal adders and the techniques described herein may be especially suited for numerically intensive commercial applications, such as spreadsheet or financial applications where large amounts of decimal data typically need to be processed quickly.

Abstract: A method and system for performing a binary mode and hexadecimal mode Multiply-Add floating point operation in a floating point arithmetic unit according to a formula A*C+B, wherein A, B and C operands each have a fraction and an exponent part expA, expB and expC and the exponent of the product A*C is calculated and compared to the exponent of the addend under inclusion of an exponent bias value dedicated to use unsigned biased exponents, wherein the comparison yields a shift amount used for aligning the addend with the product operand, wherein a shift amount calculation provides a common value CV for both binary and hexadecimal according to the formula (expA+expC?expB+CV).

Abstract: A logic module (400) that is capable of implementing data-path and random logic (command Z in block 42) uses control logic for selectively coupling one or more of the input terminals (10, 12, 14, 16, 18, 40) to the at least one output terminal (20). The control logic comprises a plurality of logic elements (26, 28, 30, 32) arranged to generate a first set of two-input logic functions (f, (a, b)) and a programmable inverter (36) arranged to generate a second set of two-input logic functions, the second set of two-input logic functions being the complement functions of the first set of two-input logic functions. SRAM memory cells (4 bit memory batch (38)) may be used for configuration purposes, realizing a compact logic module or block that is also re-programmable.

Abstract: Various embodiments of the present invention provide systems and methods for estimating signal and noise powers in a received signal set. For example, one embodiment of the present invention provides a method for determining signal power and noise power. The method uses a storage medium that includes a Na×Nw data pattern. The Na×Nw data pattern includes Na bits repeated Nw times. Both Na and Nw are each greater than one. The methods further include performing an initial read of the Na×Nw data pattern, which is stored to a first register.

Abstract: In one embodiment of the invention, programmable circuits, such as FPGAs, may be used to implement different types of functions, such as a multi-bit adder, using look-up table (LUT) circuits as their building blocks. Efficient generation of carry-out signals and fast-carry generation signals using available SRAM cells in the various embodiments of the LUT circuit can reduce and/or eliminate area-inefficient look-ahead carry logic without a significant delay in signal generation.

Abstract: In a computing device that calculates a square of an element in a finite field, a vector representation of the element in the finite field is accepted. The vector representation includes a plurality of elements. The computing device performs a multiplication operation on a base field using the accepted elements, and obtains a multiplication value. The multiplication operation is determined by a condition under which the element in the finite field is placed in an algebraic torus. The computing device performs an addition and subtraction operation using the obtained multiplication value and the accepted elements, and obtains a calculation result of the square of the element. The addition and subtraction operation is determined by the condition. The computing device then outputs the calculation result.

Abstract: A method in an integrated circuit for generating an address value having a contiguous address range from a first selection result and a second selection result each being an one-of-k selection result includes selecting multiple multiplication factors being power-of-two multiplication factors and the sum of the multiplication factors being equal to k; shifting the first selection result towards the most significant bit by each of the multiplication factors to generate multiple shifted input values where each shifted input value is shifted towards the most significant bit by one of the multiplication factors; adding the shifted input values and the second selection result; and generating the address value having a contiguous address range. The method can be extended to combine more than two selection results by applying the shifting and addition steps in a hierarchical manner.

Abstract: A shared parallel adder tree for executing multiple different population count operations on a single datum includes a number of carry-save adders (CSAs) and/or half adders (HAs), arranged in rows, where certain CSAs and HAs are dedicated to a single population count operation, while other CSAs and HAs are shared among two or more population count operations. The datum is applied to the first row in the tree. Partial sums of the number of ones at various locations within the tree are routed to certain CSAs and/or HAs “down” the tree to propagate the particular population count operations. Carry-propagate adders generate at least a portion of the final sum of the number of ones in certain population count operations. An “AND” operation on a particular number of the bits in the datum provides the high order bit of the resulting sum of the particular population count operation.

Abstract: In one embodiment, a reconfigurable adder has first and second five-bit non-reconfigurable adders and is selectively configurable to operate in a five-bit mode or a ten-bit mode. In five-bit mode, the first non-reconfigurable adder adds first and second messages to generate a first sum, and the second non-reconfigurable adder adds third and fourth messages to generate a second sum. In ten-bit mode, the first non-reconfigurable adder adds a first half of a first ten-bit message and a first half of a second ten-bit message to generate a first partial sum and a carry-over bit. The second non-reconfigurable adder adds a second half of the first ten-bit message, a second half of the second ten-bit message, and the carry-over bit to generate a second partial sum. A ten-bit sum is then generated by combining the first and second partial sums.

Abstract: A fast, flexible carry scheme for use in clustered field programmable gate array architectures is described. Each cluster has a cluster carry input node, a cluster carry output node, a cluster carry output circuit having an output coupled to the cluster carry output node, a first input coupled to the cluster carry input node, and a second input and a plurality of logic modules each comprising a logic function generator circuit coupled to a carry circuit. The logic modules are coupled in a series carry arrangement between the cluster carry input node and the second input of the cluster carry output circuit such that the least significant bit of an arithmetic logic circuit can be programmably placed in any of the logic modules.

Abstract: A conventional multi-input adder has a problem that only either the number of stages of operation blocks or the number of half adders and full adders can be reduced. In order to solve the problem of the prior art, half adders (HA201, HA203, HA204, HA202, HA205) are used only in a position at a lower digit having two inputs in an operation block (2a), a position having five inputs and two carries from the lower digit in a stage three stages prior to a final-stage operation block (2d), and a position one stage prior to the final-stage operation block (2d).

Abstract: A method of modifying a group of full adder circuits to compute a Boolean function of a set number of input bits, each full adder circuit having first and second data inputs, a data output, a carry input and a carry output, the full adder circuits being interconnected so as to form a carry chain. The method comprises the steps of setting the first input of each full adder circuit to a same fixed value, connecting each respective input bit of the set number of input bits to the second input of a respective one of the full adder circuits and using the output of the carry chain of the array of full adder circuits as the result of the Boolean function.

Abstract: A system, method, and apparatus for performing hardware-based cryptographic operations are disclosed. The apparatus can include an encryption device with a hardware accelerator having an accumulator, a multiplier circuit, an adder circuit, and a state machine. The state machine can control successive operation of the hardware accelerator to carry out a rapid, multiplier-based reduction of a large integer by a prime modulus value. Optionally, the hardware accelerator can include a programmable logic device such as a field-programmable gate array with one or more dedicated multiple-accumulate blocks.

Abstract: Hybrid adder circuitry is provided for integrated circuits such as programmable integrated circuits. The hybrid adder may combine the capabilities of multiple adder architectures. Hybrid adders may include carry select and carry ripple adder circuits. The adder circuits may be combined using a carry look-ahead architecture. Adder functionality may be implemented using the resources of logic regions on the programmable integrated circuits. Each logic region may include combinatorial logic such as look-up table logic and register circuitry. The hybrid adder circuitry may receive input words to be added from the combinatorial circuitry and may produce corresponding arithmetic sum output signals to the register circuitry.

Abstract: Disclosed are an adder for obtaining a maximum accumulated value of correlation for mode detection in a communication system, and an adding method using the adder. According to the present disclosure, an adder for obtaining a maximum accumulated value of correlation values used to detect a mode in an orthogonal frequency division multiplexing (OFDM) system, includes one or more adding logic circuits for adding input values constituting the correlation values to stored values and outputting accumulated values, by using one or more memories; and one or more controllers for, if one of the accumulated values stored in the memories is greater than a predetermined value, shifting all of the accumulated values and the input values of the memories in a direction for decreasing the accumulated values and transmitting the shifted accumulated values and the input values to the adding logic circuits.

Abstract: A packed half-word addition and subtraction operation is performed by a microprocessor in parallel upon half-word operands obtained from designated top or bottom half-word locations of designated source registers of a register file and the sum and difference results of such operation are packed into respective top and bottom half-word locations of a designated destination register. The microprocessor includes an arithmetic-logic unit (ALU) with adder circuitry that can be selectively split into separate half-word adders that are independently selectable to perform either an addition operation or subtraction operation upon the selected half-word operands. The half-word adders of the ALU access the operands from source registers via a set of multiplexers that select among the top and bottom half-word locations. Operations with halving and saturation modifications to the sum and difference results may also be provided.

Abstract: The field of the invention is that of the reception of a radionavigation signal originating from a satellite positioning system such as the GPS system. The present invention concerns a method for calculating correlations between a first sequence and a second sequence, said first sequence and said second sequence having a duration DCode, the first sequence being extracted from a digital signal comprising a code, said code comprising elementary time divisions, called chips, of mean duration Dchip, said chips being synchronized with pulses delivered by an NCO oscillator at the mean frequency 2/Dchip, the second sequence resulting from a sampling at a frequency Fe of an analog signal, the frequency Fe being greater than 2/Dchip. According to the invention, the method comprises a step of aggregating samples of the second sequence, over consecutive integration intervals of duration equal on average to Dchip/2, starting at each pulse of the NCO oscillator, so as to determine results of elementary aggregates.

Abstract: A co-processor system is provided that includes an array of configurable logic blocks (CLBs). Each CLB including a plurality of look-up tables and a plurality of adders. Each CLB may be dynamically reconfigurable to perform a plurality of logical functions.

Abstract: A Generalized Programmable Counter Array (GPCA) is a reconfigurable multi-operand adder, which can be reprogrammed to sum a plurality of operands of arbitrary size. The GPCA is configured to compress the input words down to two operands using parallel counters. Resulting operands are then summed using a standard Ripple Carry Adder to produce the final result. The GPCA consists of a linear arrangement of identical compressor slices (CSlice).

Abstract: A packed half-word addition and subtraction operation is performed by a microprocessor in parallel upon half-word operands obtained from designated top or bottom half-word locations of designated source registers of a register file and the sum and difference results of such operation are packed into respective top and bottom half-word locations of a designated destination register. The microprocessor includes an arithmetic-logic unit (ALU) with adder circuitry that can be selectively split into separate half-word adders that are independently selectable to perform either an addition operation or subtraction operation upon the selected half-word operands. The half-word adders of the ALU access the operands from source registers via a set of multiplexers that select among the top and bottom half-word locations. Operations with halving and saturation modifications to the sum and difference results may also be provided.

Abstract: A configurable logic device configured to add or subtract inputs using a carry signal with a fixed value of 0 is described. In embodiment(s), inputs are received by a device. The device is configured to add or subtract the inputs using a carry signal that has a fixed value of logic 0. The device is further configured to provide an output that has a value of the sum or the difference of the received inputs.

Abstract: A pattern detection circuit detects a pattern in a received bit stream, for example a repetitive 8-bit silence pattern in a stream of digital audio data. Summing circuitry forms during first alternate time periods a sum of a first sequence comprising a predetermined number of alternate bits in the bit stream; and forms during second alternate time periods an inverse of a sum of a second sequence comprising the predetermined number of alternate bits in the bit stream. It is then determined whether successive sums formed by the summing circuitry are equal.

Abstract: An arithmetic unit for performing an arithmetic operation on at least first and second input operands, each of the input operands being separable into a first portion and a second portion, such as respective less significant and more significant portions. The arithmetic unit comprises first arithmetic circuitry, second arithmetic circuitry, selection circuitry and saturation circuitry. The first arithmetic circuitry, which may comprise a carry-propagate adder, processes the first portions of the input operands to generate at least a temporary sum and a carry output. The second arithmetic circuitry, which may comprise a dual adder and a preliminary saturation detector, processes the second portions of the input operands to generate one or more temporary sums and a number of saturation flags. The selection circuitry is configured to select one or more of the outputs of the second arithmetic circuitry based on the carry output of the first arithmetic circuitry.

Abstract: A zero crossing detector employs carry save adders combined with fully pipelined logic to provide two-bit, three-bit or four-bit zero crossing detection. The detector offers the advantages of very high operating speed, very low power dissipation, low adder cell count and reduced chip area.

Abstract: A logic circuit has a decoder converting first input data into a plurality of first bit data having a constant Hamming weight regardless of the Hamming weight of the first input data, a wiring network, and an encoder converting a plurality of second bit data generated by the wiring network into at least one or at least two binary output data. The wiring network is connected to the decoder to receive the plurality of first bit data into which the first input data has been converted by the decoder and to change bit positions of the plurality of received first bit data in accordance with a control input and second input data specifying which of a first logical calculation and a second logical calculation to be executed, to change a bit pattern of the plurality of first bit data to generate a plurality of second bit data.

Abstract: A system and method for connecting service providers with service requesters within a social network. The system and method may operate even if the service requestor does not provide any compensation and is not subject to any obligation in return for the service provided by the at least one service provider. The system and method may be based on user feedback and/or a point system. The system and method may be applied to a social network for connecting pet owners with pet sitters for provision of pet-sitting services.

Abstract: A method and apparatus for including in a processor instructions for performing horizontal intra-add operations on packed data. One embodiment of the processor is coupled to a memory. The memory has stored therein at least a first packed data. The processor performs operations on data elements in the first packed data to generate a plurality of data elements in a second packed data in response to receiving an instruction. At least two of the plurality of data elements in the second packed data store the results of an intra-add operation, at least one of these results coming from the operation on data elements of the first packed data. One embodiment of a software method utilizes horizontal intra-add instructions for performing butterfly computations as may be employed, for example, in Walsh-Hadamard transforms or in Fast-Fourier Transforms.

Abstract: A method for converting a first time and a first date in a first format to a second time in a second format includes determining a number of seconds that have elapsed between a predetermined date and a beginning of a current year of the first date. The method further includes adding to the determined number of seconds, a calculated number of seconds calculated from the beginning of the current year to a current month and a current day of the first date to obtain a first sum. The first sum varies based on whether the current month is within a leap year and is subsequent to a leap day of the leap year. A number of seconds that have elapsed between a beginning of the current day of the first date and the first time is added to the first sum. Lastly, a predetermined number of seconds is added to the first sum when Daylight Savings Time is in effect to obtain the second time in the second format.

Abstract: The present invention discloses an ALU (Arithmetic Logic Unit) that can be operated as an OR gate, an AND gate, an adder gate and an exclusive OR gate using a half adder that uses a superconductor rapid single flux quantum logic device. The ALU using a half adder includes a half adder using a superconductor rapid single flux quantum logic device as a logic circuit, and a switching unit that has input ports respectively connected to a sum output port and a carry output port of the half adder and is operated as an OR gate, an AND gate, an adder gate and an exclusive OR gate using output signals of the half adder. The switching unit includes a first switch having an input port connected to the sum output port of the half adder, a second switch having an input port connected to the carry output port of the half adder and an output port connected to an output port of the first switch, and a third switch having an input port connected to the carry output port of the half adder.

Abstract: A method and system for performing floating point additive arithmetic operations of long operands in a narrow dataflow. The operands include first and second floating point numbers having first and second mantissas, respectively, the second operand greater than the first operand. The mantissas are both separated into a low portion and a high portion, the high portions are loaded into N-bit operand registers. The high portion of the first mantissa is aligned with respect to the high portion of the second mantissa, the high portions are then moved into 2N-bit registers. The low portion of the first mantissa is aligned in accordance with the alignment of the first mantissa high portion. The low portions of both mantissas are then concatenated into the registers, the first mantissa concatenated using a hold-function circuit. A 2N-bit-wide adder performs the additive arithmetic operation on the concatenated mantissas.

Abstract: A circuit (26) performs a discrete Walsh transform using a reduced set of arithmetic operators. The circuit (26) comprises a first memory component (32), an adder (36), a subtractor (38), a second memory component (40), and a controller (52). In each of a plurality of stages, the controller (52) enables the first memory component (32) to communicate each of a plurality of pairs of values stored therein to the adder (36) and to the subtractor (38). The controller (52) enables the second memory component (40) to store each of a plurality of results from the adder (36) and the subtractor (38) and to communicate the stored results to the first memory component (32) for use in a subsequent stage.