Abstract: An integrated circuit comprises divider circuitry configured to perform a division operation. The divider circuitry may be part of an arithmetic logic unit or other computational unit of a microprocessor, digital signal processor, or other type of processor. The divider circuitry iteratively determines bits of a quotient over multiple stages of computation. In determining the quotient in one embodiment, the divider circuitry is configured to estimate a partial remainder for a given one of the stages and to predict one or more of the quotient bits for one or more subsequent stages based on the estimated partial remainder so as to allow one or more computations to be skipped for said one or more subsequent stages, thereby reducing power consumption. The integrated circuit may be incorporated in a computer, a mobile telephone, a storage device or other type of processing device.

Abstract: A system and method are provided for synthesizing signal frequencies using rational division. The method accepts a reference frequency value and a synthesized frequency value. In response to dividing the synthesized frequency value by the reference frequency value, an integer value numerator (dp) and an integer value denominator (dq) are determined. The method reduces the ratio of dp/dq to an integer N and a ratio of p/q (dp/dq=N(p/q)), where p/q<1 (decimal). The numerator (p) and the denominator (q) are supplied to a flexible accumulator module, and a divisor is generated as a result. N is summed with a k-bit quotient to create the divisor. In a phase-locked loop (PLL), the divisor and the reference signal are used to generate a synthesized signal having a frequency equal to the synthesized frequency value.

Abstract: A method and apparatus are provided for manufacturing integrated circuits performing invariant integer division x/d. A desired rounding mode is provided and an integer triple (a,b,k) for this rounding mode is derived. Furthermore, a set of conditions for the rounding mode is derived. An RTL representation is then derived using the integer triple. From this a hardware layout can be derived and an integrated circuit manufactured with the derived hardware layout. When the integer triple is derived a minimum value of k for the desired rounding mode and set of conditions is also derived.

Abstract: A method, computer program product and a system for controlling a fixed point division operation are provided. The method includes: receiving an instruction to perform a division operation for a dividend and a divisor, the operation comprising a maximum number of iterations to produce a quotient having a maximum precision; calculating a magnitude of at least one of the dividend and the divisor; determining a quotient precision based on the magnitude; and computing a required number of iterations needed to produce the quotient precision and performing the number of iterations.

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: A system and method are provided for rational division. The method accepts accepting a binary numerator and a binary denominator. A binary first sum is created of the numerator and a binary first count from a previous cycle. A binary first difference is created between the first sum and the denominator. In response to comparing the first sum with the denominator, and first carry bit is generated and added to a first binary sequence. The first binary sequence is used to generate a k-bit quotient. Typically, the denominator value is larger than the numerator value. In one aspect, the numerator and denominator form a rational number. Alternately, the numerator may be an n-bit bit value formed as either a repeating or non-repeating sequence, and the denominator is an (n+1)-bit number with a decimal value of 2(n+1).

Abstract: A pipelined circuit for performing a divide operation on small operand sizes. The circuit includes a plurality of stages connected together in a series to perform a subtractive divide algorithm based on iterative subtractions and shifts. Each stage computes two quotient bits and outputs a partial remainder value to the next stage in the series. The first and last stages utilize a radix-4 serial architecture with edge modifications to increase efficiency. The intermediate stages utilize a radix-4 parallel architecture. The divide architecture is pipelined such that input operands can be applied to the divider on each clock cycle.

Abstract: A complex divider utilized for dividing a first complex number by a second complex number to generate a computing result includes a computing unit and a dividing unit. The computing unit is utilized for receiving the first complex value and the second complex value, generating a third complex value according to the first complex value and the second complex value, and generating a real number according to the second complex value. The dividing unit is coupled to the computing unit, and is utilized for receiving the third complex value and the real number and dividing the third complex value by the real number to obtain the computing result.

Abstract: Systems and methods to perform polynomial division are disclosed. In a particular embodiment, the method includes receiving a codeword and storing a portion of the received codeword at a register. The portion of the received codeword has a first number of terms. A divisor having a second number of terms is also received. During at least one stage of a multi-stage polynomial division operation using the portion of the codeword and the divisor, the portion of the received codeword to be divided by the divisor is adjusted based on a result of a comparison of the first number to the second number.

Abstract: The present invention provides an eigenvalue decomposition apparatus that can perform processing in parallel at high speed and high accuracy.

Abstract: The invention relates to a cryptographic method involving an integer division of type q=a div b and r=a mod b, wherein a is a number of m bits, b is a number of n bits, with n being less than or equal to m, and bn?1 being non-null and the most significant bit of b. In addition, each iteration of a loop subscripted by i, which varies between 1 and m?n+1, involves a partial division of a word A of n bits of number a by number b in order to obtain one bit of quotient q. According to the invention, the same operations are performed with each iteration, regardless of the value of the quotient bit obtained. In different embodiments of the invention, one of the following is also performed with each iteration: the addition and subtraction of number b to/from word A; the addition of number b or a complementary number /b of b to word A; or a complement operation at 2n of an updated datum (b or /b) or a dummy datum (c or /c) followed by the addition of the datum updated with word A.

Abstract: Techniques are described to determine N mod M, where N is a number having a width of n-bits, and M is a number having a width of m-bits. The techniques, generally, involve determining N?=Nrt2f mod M+NL and, subsequently, determining N? mod M.

Abstract: Techniques for efficiently performing division and modulo operations in a programmable logic device. In one set of embodiments, the division and modulo operations are synthesized as one or more alternative arithmetic operations, such as multiplication and/or subtraction operations. The alternative arithmetic operations are then implemented using dedicated digital signal processing (DSP) resources, rather than non-dedicated logic resources, resident on a programmable logic device. In one embodiment, the programmable logic device is a field-programmable gate array (FPGA), and the dedicated DSP resources are pre-fabricated on the FPGA. Embodiments of the present invention may be used in Ethernet-based network devices to support the high-speed packet processing necessary for 100G Ethernet, 32-port (or greater) trunking, 32-port/path (or greater) load balancing (such as 32-path ECMP), and the like.

Abstract: Methods, computer systems, and computer program products for calculating a remainder by division of a sequence of bytes interpreted as a first number by a second number is provided. A pseudo-remainder by division associated with a first subsequence of the sequence of bytes is calculated. A property of this pseudo-remainder is that the first subsequence of the sequence of bytes, interpreted as a third number, and the pseudo-remainder by division have the same remainder by division when divided by the second number. A second subsequence of the sequence of bytes interpreted as the first number is appended to the pseudo-remainder, interpreted as a sequence of bytes, so as to create a sequence of bytes interpreted as a fourth number. The first number and the fourth number have the same remainder by division when divided by the second number.

Abstract: Methods and a system are disclosed for one or more appliances including a controller for managing power consumption within a household. The controller is configured to receive and process a signal indicative of one or more energy parameters of an associated energy utility, including at least a peak demand period or an off-peak demand period. A generated serial number is obtained from an original serial number of the appliance or controller, which is configured for a signal to communicate to the appliance within a population and command the appliance to operate in an energy savings mode and a normal mode at various time periods. The generated serial number (GSN) is used to segregate a total population into segments to provide granularity in assigning DR activations and deactivations based upon the GSN.

Abstract: A method is provided of characterising a data stream of binary symbols, the method comprising sampling the stream at a predetermined rate sufficient to capture at least two samples per binary symbol, identifying the shortest continuous run of samples having the same logic level and assigning a symbol rate to the stream on the basis that the identified run is one symbol in length.

Abstract: One embodiment of the present invention sets forth a technique for performing fast integer division using commonly available arithmetic operations. The technique may be implemented in a two-stage process using a single-precision floating point reciprocal in conjunction with integer addition and multiplication. Furthermore, the technique may be fully pipelined on many conventional processors for performance that is comparable to the best available high-performance alternatives.

Abstract: Provided are a divider having a small area and an improved operation speed and a method of operating the same. The divider includes a memory, a controller, and a multiplier. The memory is configured to store table values included in a predetermined range. The controller is configured to receive a divisor, generate an address expressed in a plurality of bits according to the bits except the most significant bit of the divisor, and receive the table value corresponding to the address from the memory. The multiplier is configured to receive a dividend and calculate an initial value by multiplying the dividend and the table value corresponding to the address. Herein, the controller determines an exponent of the divisor and right-shifts the initial value by the exponent of the divisor.

Abstract: Methods and a system are disclosed for one or more appliances including a controller for managing power consumption within a household. The controller is configured to receive and process a signal indicative of one or more energy parameters of an associated energy utility, including at least a peak demand period or an off-peak demand period. A generated serial number is obtained from an original serial number of the appliance or controller, which is configured for a signal to communicate to the appliance within a population and command the appliance to operate in an energy savings mode and a normal mode at various time periods. The generated serial number (GSN) is used to segregate a total population into segments to provide granularity in assigning DR activations and deactivations based upon the GSN.

Abstract: A hybrid greatest common divisor (GCD) calculator analyzes characteristics of polynomials and selects a particular GCD algorithm from multiple available GCD algorithms based on a combination of characteristics of the polynomials. The selected GCD algorithm is then applied to calculate the GCD of the polynomials.

Abstract: A method, computer program product, and information handling system for generating loop code to execute on Single-Instruction Multiple-Datapath (SIMD) architectures, where the loop contains multiple non-stride-one memory accesses that operate over a contiguous stream of memory is disclosed. A preferred embodiment identifies groups of isomorphic statements within a loop body where the isomorphic statements operate over a contiguous stream of memory over the iteration of the loop. Those identified statements are then converted into virtual-length vector operations. Next, the hardware's available vector length is used to determine a number of virtual-length vectors to aggregate into a single vector operation for each iteration of the loop. Finally, the aggregated, vectorized loop code is converted into SIMD operations.

Abstract: A division unit, an image analysis unit and a display apparatus using the same capable of simplifying the computation of overall average gray scale are provided. The division unit includes an adder for receiving a first to an Nth bus signals to produce an addition result, wherein the first to the Nth bus signals shift the input signal by a different number of bits and adding logic zeros to the shifted bits as compensation, where N is a positive whole number, and a multiplexer for receiving a most significant bit (MSB) of the addition result, wherein, when the MSB has a first value, the multiplexer treats P bits of the addition result as a division result, and when the MSB has a second value, the multiplexer outputs P logic 1 to serve as the division result, where P is a positive whole number.

Abstract: A method, system and computer program product that involves receiving and initializing a digital image. Quantization is preformed on the digital image using at least two multiplication operations. Finally, a compressed version of the digital image is presented for viewing and/or storage or transport.

Abstract: A division and square root arithmetic unit carries out a division operation of a higher radix and a square root extraction operation of a lower radix. A certain bit number (determined on the basis of a radix of an operation) of data selected from upper bits of the output of a carry save adder and the output of the adder are input to convert the data into twos complement representation data, and the twos complement representation data is shifted a certain bit number (determined on the basis of the radix of the operation) to use the shifted data for a partial remainder of the next digit. Hence, a large number of parts such as registers of a divisor and a partially extracted square root can be commonly used in a divider and a square root extractor to realize an effective and high performance arithmetic unit.

Abstract: A device for calculating the quotient q and remainder r of the division (y·k1+x)/k2, wherein k1 and k2 are integers and constant, and wherein x and y are integers. The device comprises a first digital circuit for receiving as input values of y and identifying corresponding values of the quotient qy and the remainder ry of the function y·k1/k2, a second digital circuit for calculating the remainder r of the division, by a) calculating a combined value (x+ry) of the remainder ry and the value of x, b) verifying if the combined value (x+ry) is less than k2, c) correcting the combined value (x+ry) if the verification indicates that the combined value (x+ry) is not less than k2, and d) assigning the corrected combined value (x+ry) to the remainder r, a third digital circuit for calculating the quotient q of the division, by a) correcting the quotient qy if the verification (2206) indicates that the combined value (x+ry) is not less than k2, and b) assigning the corrected quotient qy to the quotient q.

Abstract: A multiplication or division operation X·K or X·1/K is performed in an electronic circuit. A software circuit area of the circuit calculates a digit shift sv such that psv is an approximate value for K. In a hardware circuit area, the value X is shifted sv digits to the left in the case of multiplication or sv digits to the right in the case of division. The software circuit area calculates a suitable correction factor Kf. The value X is multiplied by the correction factor Kf.

Abstract: The disclosure describes a method for performing a fixed point calculation of a floating point operation (A // B) in a coding device, wherein A // B represents integer division of A divided by B rounded to a nearest integer. The method may comprise selecting an entry from a lookup table (LUT) having entries generated as an inverse function of an index B, wherein B defines a range of values that includes every DC scalar value and every quantization parameter associated with a coding standard, and calculating A // B for coding according to the coding standard based on values A, B1 and B2, wherein B1 and B2 comprise high and low portions of the selected entry of the LUT. The techniques may simplify digital signal processor (DSP) implementations of video coders, and are specifically useful for MPEG-4 coders and possibly others.

Abstract: A technique that can contribute to improvement of processing efficiency in performing image processing employing an SIMD command is provided.

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: The present invention provides an eigenvalue decomposition apparatus that can perform processing in parallel at high speed and high accuracy.

Abstract: Methods and apparatus to provide rounding of a binary integer are described. In one embodiment, a value that indicates whether a divisor divides a binary integer is extracted from a product of the binary integer and a scaled approximate reciprocal of the divisor.

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: The present disclosure provides a system and method for performing multi-precision division. A method according to one embodiment may include generating a first product by multiplying a modulus having a most significant bit and/or a least significant bit equal to one and a quotient approximation of the modulus. The method may also include generating the 1's complement of the first product, generating a second product by multiplying the 1's complement and the quotient approximation, normalizing and truncating the second product to obtain a quotient, and storing the quotient in memory. Of course, many alternatives, variations and modifications are possible without departing from this embodiment.

Abstract: A variable radix divider uses dividend, divisor and quotient as division operators and includes an adder/subtractor having inputs of the dividend and the divisor. The divider further includes a first and second quotient/radix generator having inputs of the dividend and the divisor, a first multiplexer having input of the output from the first quotient/radix generator, and a second multiplexer having input of the output from the second quotient/radix generator. The first and second generators each includes a prediction adder/subtractor having inputs of bits in prediction range of the dividend and bits in prediction range of the divisor, a radix generator, and a quotient generator. The radix generator and the quotient generator have input of the output of the prediction adder/subtractor. The divider iterates a recursive cycle operation until the division operation through a feedback path to the dividend is completed.

Abstract: An apparatus and method for allowing a digital signal processor (DSP) in a data processing system to perform high speed division operations. In one embodiment of the invention a division operation is performed in no more than two cycles. In another embodiment of the invention, the division operations are in fractional format. The data processing apparatus comprises a random access memory, a processor (12, 168), and an interface (102) coupling said random access memory (104) to said processor, said interface enables high speed division operations associated with said processor. The interface of the present invention can also be combined with a dual or co-processor system to increase the data processing efficiency.

Abstract: One embodiment of the present invention provides a system that efficiently performs an accuracy-check computation for Newton-Raphson divide and square-root operations. During operation, the system performs Newton-Raphson iterations followed by a multiply for the divide or square-root operation. This result is then rounded to produce a proposed result. Next, the system performs an accuracy-check computation to determine whether rounding the result to a desired precision produces the correct result. This accuracy-check computation involves performing a single pass through a multiply-add pipeline to perform a multiply-add operation. During this single pass, a Booth encoding of an operand in a multiply portion of the multiply-add pipeline is modified, if necessary, to cause an additional term for the accuracy-check computation to be added to the result of the multiply-add operation.

Abstract: One embodiment of the present invention provides a system that performs a carry-save division operation that divides a numerator, N, by a denominator, D, to produce an approximation of the quotient, Q=N/D. The system approximates Q by iteratively selecting an operation to perform based on higher order bits of a remainder, r, and then performing the operation, wherein the operation can include, subtracting D from r and adding a coefficient c to a quotient calculated thus far q, or adding D to r and subtracting c from q. These subtraction and addition operations maintain r and q in carry-save form, which eliminates the need for carry propagation and thereby speeds up the division operation. Furthermore, the selection logic is simpler than previous SRT division implementations, which provides another important speed up.

Abstract: A system of equations with a Toeplitz coefficient matrix [T] can be efficiently solved by approximating the coefficient matrix [T] with an approximately Toeplitz coefficient matrix [Tapp] that can be efficiently transformed to a banded form. The system of equations with the banded coefficient matrix is then efficiently solved and this solution is used to obtain the solution to the original system of equations with the Toeplitz coefficient matrix [T].

Abstract: Methods and apparatus which reduce or completely eliminate non-shift based divisions as part of estimating transmitted symbols and/or generating slicing parameters corresponding to two symbol transmission streams in a wireless communication system are described. A linear least squares error estimation filtering module performs symbol estimations and/or slicing parameter generation while avoiding non-shift based division operations. The linear least squares estimation module generates intermediate parameters, and implements equations which facilitate symbol estimation utilizing shift based divisions while avoiding non-shift based divisions.

Abstract: A data processing system 2 includes an instruction decoder 22 responsive to polynomial divide instructions DIVL.PN to generate control signals that control processing circuitry 26 to perform a polynomial division operation. The denominator polynomial is represented by a denominator value stored within a register with an assumption that the highest degree term of the polynomial always has a coefficient of “1” such that this coefficient need not be stored within the register storing the denominator value and accordingly the denominator polynomial may have a degree one higher than would be possible with the bit space within the register storing the denominator value alone. The polynomial divide instruction returns a quotient value and a remainder value respectively representing the quotient polynomial and the remainder polynomial.

Abstract: Methods are provided for the classification of search engine queries and associated documents based on search engine query click logs. One or more seed documents or queries are provided that contain content that is representative of a category. A query click log containing information regarding queries entered by at least one user into the search engine and documents subsequently clicked in search engine results corresponding with the queries is analyzed to determine which one or more queries resulted in clicks on the seed documents. Information is stored associating the one or more queries with the category if they resulted in clicks on the seed documents.

Abstract: A method and mechanism for performing division. A processor includes a divider configured to perform arithmetic division operations. Prior to dividing a dividend by a divisor, the divider manipulates the dividend and divisor to reduce the number of bits considered and the computations required to perform the division. The divisor is normalized by eliminating sign bits. The dividend is prescaled to eliminate one or more sign bits. Prescaling of the dividend may not be precise as sign bits of the dividend may be shifted out as groups of bits, rather than individual bits. Prescaling of the dividend may be adjusted to account for the fact that the divider considers multiple bits of the dividend at a time. Subsequent to prescaling and adjustment, the dividend may be adjusted in dependence upon the normalization of the divisor. Further adjustment may be utilized to maintain a significance relationship between the divisor and dividend. Subsequent to further adjustment, the division operation may be completed.

Abstract: A method, computer program product and a system for detecting errors in a result of a fixed-point division operation are provided. The method includes: receiving a result of a fixed-point division operation for a dividend and a divisor; performing a first comparison of the divisor and a remainder of the result; performing a second comparison of a sign of the dividend and a sign of the remainder; and determining whether the result is correct based on the first comparison and the second comparison.

Abstract: A dividing unit sets an actual packet length transferred from a packet receiving section to a variable U, and then sets 2? to a variable V. If a positive number determining section determines that a subtraction result of subtracting a remainder N0 from a quotient M0, both found by dividing U by V, is a positive number, the dividing unit overwrites the subtraction result to U. The dividing unit repeats such operations of dividing the subtraction result by V, until the positive number determining section determines that the subtraction result of subtracting the remainder from the quotient, both found by dividing U by V, is a non-positive number. When the subtraction result becomes a non-positive number and the quotient and the remainder match, a packet length determining section determines that received data has a normal size, and notifies it to a discard determining section.

Abstract: A device for calculating a result or an integer multiple of the result of a division of a numerator by a denominator includes a unit for providing a factor which is selected such that a product of the factor and the denominator is greater than the result. The device further includes a unit for modularly reducing a first product of the numerator and the factor using a modulus equaling a sum of a second product of the denominator and the factor and of an integer to obtain an auxiliary quantity having the result. A unit is used to extract the result or the integer multiple of the result from the auxiliary quantity. A division is thus reduced to a modular reduction and an extraction which is uncomplicated as far as calculation is concerned so that, in particular in long-number division tasks, the speed on the one hand and the safety on the other hand are increased.

Abstract: A method and device divides a dividend by a divisor, the dividend and the divisor both being integers. The method and device determine a maximum possible number of quotient digits (NDQ) based on a number of significant digits of the divisor and the dividend, normalizes the dividend and divisor, and calculates NDQ number of quotient digits from the normalized divisor and dividend.

Abstract: A method for an extended precision integer divide algorithm includes separating an L-bit integer dividend into two equal width integer format portions, a first portion including lower M bits of the integer dividend and a second portion including upper M bits of the integer dividend, where M is equal to ½ L. An N-bit wide integer divisor is converted from an integer format into a floating point format divisor. The first integer portion is converted into a floating point format and divided by the floating point format divisor to obtain a first floating point quotient, which is converted into a first integer format quotient. The second integer portion is converted into a floating point format and divided by the floating point format divisor to obtain a second floating point quotient which is also converted to a second integer format quotient. Then first and second integer format quotients are summed together to generate a third integer format quotient.

Abstract: A fast division method which uses a smaller quotient digit set of {?1, 1} than {?1, 0, 1} that is used by known algorithms, therefore accelerates the speed of calculation. Partial remainders can be computed with the signals of remainders decided independently and in parallel. By taking the absolute values of the remainders, we can successively subtract the remainders without the need of knowing the signs of remainders, while signs of the remainders can be decided in parallel and independently at the same time. The algorithm adopts non-restoring division operation and CSA type of operation for fast subtraction. The algorithm is also an on-line algorithm that facilitates highly pipelined operation while it is much simpler than the existing on-line algorithms.

Abstract: A method for performing a division operation in a system includes a) determining an approximate quotient of a numerator value and a denominator value; b) determining an initial error of the approximate quotient; c) determining a quotient adjustment value based on the initial error; d) determining whether to apply the quotient adjustment value to the approximate quotient; e) if the determination at d) is YES, then applying the quotient adjustment value to the approximate quotient; f) determining an iterative error of the approximate quotient; g) updating the quotient adjustment value based on the iterative error; h) repeating acts d) through g) until the determination at d) is NO, thereby determining a final value for the approximate quotient; i) generating an integer quotient based on the final value of the approximate quotient; and j) using the integer quotient with regard to at least one aspect of the system.

Abstract: In scalar multiplication method using a Montgomery-type elliptic curve, a high-speed elliptic curve calculation device effectively uses a table that stores coordinates of certain scalar multiple points like points multiplied by exponentiation of two to a certain point G and so forth. The elliptic curve calculation device receives an arbitrary integer k of n bits and outputs scalar-multiplied points against a point G on a Montgomery-type elliptic curve E on a finite field F that is given in advance. The elliptic curve calculation device includes a calculation procedure generation unit that generates a calculation procedure that addition on the elliptic curve E with either of G, 2 *G, 22*G., . . .