Abstract: Processing for generating a plurality of pieces of distributed data from original data or processing for restoring original data from a plurality of pieces of distributed data is performed safely and quickly. A distribution and restoration apparatus 200 generates a plurality of pieces of distributed data SD1 to SD3 by dividing original data OD into a plurality of divided blocks DB1 to DB16 and performing an operation of exclusive OR using divided blocks of different combinations. A combination including divided blocks used in common in a plurality of pieces of distributed data and a combination including divided blocks used only in specific distributed data are present in combinations of divided blocks in each piece of distributed data. Therefore, the distribution and restoration apparatus 200 can generate a plurality of pieces of safe distributed data having high information entropy at high speed.

Abstract: Systems and methods are provided for efficiently counting detected events via a multiplicative group counter. An equivalent class polynomial congruent with a first of a plurality of elements comprising a multiplicative group is represented as a series of binary values. The represented polynomial is subjected to a state transition function as each event is detected, such that the series of binary values is altered to represent a new equivalent class polynomial congruent with a second of the plurality of elements of a multiplicative group. The series of binary values is decoded to determine a number of detected events recorded by the counter.

Abstract: Digital signal processing (“DSP”) circuit blocks are provided that can more easily work together to perform larger (e.g., more complex and/or more arithmetically precise) DSP operations if desired. These DSP blocks may also include redundancy circuitry that facilitates stitching together multiple such blocks despite an inability to use some block (e.g., because of a circuit defect). Systolic registers may be included at various points in the DSP blocks to facilitate use of the blocks to implement systolic form, finite-impulse-response (“FIR”), digital filters.

Abstract: A calculation method executed by a computer, the calculation method includes calculating, using a processor, a length of one side of a second module based on an area of the second module that is included in a first module in a circuit and includes devices; and calculating, using the processor, a length of a wiring of the first module based on the calculated length and the number of fan-outs of the first module.

Abstract: To perform a binary-coded decimal (BCD) calculation, a processor receives values on which the BCD calculation is to be performed. A carry resulting from the BCD calculation is stored in a flag register of the processor, and the carry stored in the flag register is used to compute a result of the BCD calculation.

Abstract: In one exemplary embodiment of the invention, a method for computing a resultant and a free term of a scaled inverse of a first polynomial v(x) modulo a second polynomial fn(x), including: receiving the first polynomial v(x) modulo the second polynomial fn(x), where the second polynomial is of a form fn(x)=xn±1, where n=2k and k is an integer greater than 0; computing lowest two coefficients of a third polynomial g(z) that is a function of the first polynomial and the second polynomial, where g ? ( z ) ? = def ? ? i = 0 n - 1 ? ? ( v ? ( ? i ) - z ) , where ?0, ?1, . . . , ?n?1 are roots of the second polynomial fn(x) over a field; outputting the lowest coefficient of g(z) as the resultant; and outputting the second lowest coefficient of g(z) divided by n as the free term of the scaled inverse of the first polynomial v(x) modulo the second polynomial fn(x).

Abstract: Techniques for implementing multipliers using memory blocks in an integrated circuit (IC) are provided. The disclosed techniques may reduce the number of memory blocks required to implement various multiplication operations. A plurality of generated products is normalized. The normalized products are scaled to generate a plurality of scaled products. Scaled products with the least root mean square (RMS) error are identified. The scaled products with the least RMS error are then stored in a plurality of memory blocks in an IC. The scaled products may have a reduced number of bits compared to the plurality of generated products that have not been normalized and scaled.

Abstract: Circuits for a multiplier with a built-in accumulator and a method of performing multiplication with accumulation are disclosed. An embodiment of the disclosed circuits includes a logic circuit coupled to receive two inputs. The logic circuit is capable of generating a plurality of value bits from the inputs received. In one embodiment, the logic circuit includes a Booth recoder circuit that generates a plurality of partial products. A block of adders is coupled to logic circuit to receive and sum up the value bits. An adder adds the summation result from the block of adders to a previous accumulated value to generate intermediate sum and carry values. An accumulator, coupled to the adder, receives and stores the intermediate values.

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: Method, apparatus, and program means for nonlinear filtering and deblocking applications utilizing SIMD sign and absolute value operations. The method of one embodiment comprises receiving first data for a first block and second data for a second block. The first data and said second data are comprised of a plurality of rows and columns of pixel data. A block boundary between the first block and the second block is characterized. A correction factor for a deblocking algorithm is calculated with a first instruction for a sign operation that multiplies and with a second instruction for an absolute value operation. Data for pixels located along said block boundary between the first and second block are corrected.

Abstract: A system and method for parallelization of saturated accumulation is provided. In the method, an input sequence is divided into a plurality of subsequences. For each subsequence, three parallel saturating additions are performed. The local saturation minimum is the saturating addition of the global saturation minimum and the values of the subsequence. The local midpoint is the saturating addition of the values of the subsequence and the local saturation maximum is the saturating addition of the global saturation maximum and the values of the subsequence. In embodiments, the accumulation total for a subsequence is calculated as the saturating addition of the accumulation total for prior subsequences and the local midpoint of the current subsequence, wherein the accumulation total of the last subsequence is the result of the saturated accumulation for the sequence. In another embodiment, the saturated addition of subsequence results are further parallelized before the final result is reached.

Abstract: Minimizing memory access by converting a given matrix computation into a set of low-order polynomials. The low-order polynomials can be used by dividing the domain of the polynomials into smaller subregions. If the domain is divided into equal intervals, the low-order polynomial can be used to approximate results from the matrix computation. The set of polynomials is processed using parallel computational hardware such as graphical processing units.

Abstract: Embodiments of the present invention include an apparatus, method, and system for acoustic modeling. In an embodiment, an arithmetic logic unit for computing a one-dimensional score between a feature vector and a Gaussian probability distribution vector is provided. The arithmetic logic unit includes a computational logic unit configured to compute a first value based on a mean value and a variance value associated with a dimension of the Gaussian probability distribution vector and a dimension of a feature vector, a look up table module configured to output a second value based on the variance value, and a combination module configured to combine the first value and the second value to generate the one-dimensional score.

Abstract: Various implementations of a digital signal processing (DSP) block architecture of a programmable logic device (PLD) and related methods are provided. In one example, a PLD includes a dedicated DSP block. The DSP block includes a first multiplier adapted to multiply a first plurality of input signals to provide a first plurality of product signals. The DSP block also includes a second multiplier adapted to multiply a second plurality of input signals to provide a second plurality of product signals. The DSP block further includes an arithmetic logic unit (ALU) adapted to operate on the first product signals and the second product signals received at first and second operand inputs, respectively, of the ALU to provide a plurality of output signals.

Abstract: A method and apparatus for distributing objects. In one embodiment, the method comprises computing a modulus operand based on a number of objects to be distributed and a number of objects pertaining to a first category; computing a modulus operation based on a number of distributed objects and the modulus operand; and distributing a first object or a second object based on a result of computing the modulus operation.

Abstract: Digital signal processing (“DSP”) block circuitry on an integrated circuit (“IC”) is adapted for use (e.g., in multiple instances of the DSP block circuitry on the IC) for implementing finite-impulse-response (“FIR”) digital filters in systolic form. Each DSP block may include (1) first and second multiplier circuitry and (2) adder circuitry for adding (a) outputs of the multipliers and (b) signals chained in from a first other instance of the DSP block circuitry. Systolic delay circuitry is provided for either the outputs of the first multiplier (upstream from the adder) or at least one of the sets of inputs to the first multiplier. Additional systolic delay circuitry is provided for outputs of the adder, which are chained out to a second other instance of the DSP block circuitry.

Abstract: A CORDIC processor has a plurality of stages, each of the stages having a X input, Y input, a sign input, a sign output, an X output, a Y output, a mode control input having a ROTATE or VECTOR value, and a stage number k input, each CORDIC stage having a first shift generating an output by shifting the Y input k times, a second shift generating an output by shifting X input k times, a multiplexer having an output coupled to the sign input when the mode control input is ROTATE and to the sign of the Y input when the mode input is VECTOR, a first multiplier forming the product of the first shift output and the multiplexer output, a second multiplier forming the product of the second shift output and an inverted the multiplexer output, a first adder forming the X output from the sum of the first multiplier output and the X input, and a second adder forming the Y output from the sum of the second multiplier output and the Y input.

Abstract: The present invention relates to a method and device for detecting a transmission signal on the basis of a received signal by applying a division and detection algorithm. An embodiment of the invention provides a method of detecting a transmission signal including: obtaining a unitary matrix and an upper triangular matrix by performing a sorted QR-decomposition algorithm with respect to a matrix indicating a channel state; calculating a vector y by multiplying a transpose matrix of the unitary matrix by the received signal Y; dividing the upper triangular matrix R into a plurality of sub-upper triangular matrices and dividing the calculated vector y into a plurality of sub-vectors so as to correspond to the divided plurality of sub-upper triangular matrices; and detecting a lattice point corresponding to each of the divided sub-vectors using the divided plurality of sub-upper triangular matrices.

Abstract: Coding within noisy communications channels is essential but a theoretical maximum rate defines the rate at which information can be reliably transmitted on this noisy channel. Capacity-achieving codes with an explicit construction eluded researchers until polar codes were proposed. However, whilst asymptotically reaching channel capacity these require increasing code lengths, and hence increasingly complex hardware implementations. It would be beneficial to address architectures and decoding processes to reduce polar code decoder complexity both in terms of the number of processing elements required, but also the number of memory elements and the number of steps required to decode a codeword. Beneficially architectures and design methodologies established by the inventors address such issues whilst reducing overall complexity as well as providing methodologies for adjusting decoder design based upon requirements including, but not limited to, cost (e.g. through die area) and speed (e.g.

Abstract: A processor including instruction support for implementing large-operand multiplication may issue, for execution, programmer-selectable instructions from a defined instruction set architecture (ISA). The processor may include an instruction execution unit comprising a hardware multiplier datapath circuit, where the hardware multiplier datapath circuit is configured to multiply operands having a maximum number of bits M.

Abstract: An analog optical adder system that achieves high precision results. The system uses an analog optical carry function to provide a result having a precision higher than the precision of the individual elements of the system. The optical carry function is created by optical carry determinators that are configured to add an optical carry, if any, to an optical signal associated with a next adjacent byte of the digital signals being added. The use of optical carry enables greater overall addition precision.

Abstract: Methods and apparatus is provided for computing mathematical functions comprising a single pipeline for performing a polynomial approximation (e.g. a quadratic polynomial approximation, or the like); and one or more data tables corresponding to at least one of the RCP, SQRT, EXP or LOG functions operable to be coupled to the single pipeline according to one or more opcodes; wherein the single pipeline is operable for computing at least one of RCP, SQRT, EXP or LOG functions according to the one or more opcodes.

Abstract: For calculating a result of a modular multiplication with long operands, at least the multiplicand is divided into at least three shorter portions. Using the three shorter portions of the multiplicand, the multiplier and the modulus, a modular multiplication is performed within a cryptographic calculation, wherein the portions of the multiplicand, the multiplier and the modulus are parameters of the cryptographic calculation. The calculation is performed sequentially using the portions of the multiplicand and using an intermediate result obtained in a previous calculation, until all portions of the multiplicand are processed, to obtain the final result of the modular multiplication. The calculation of an intermediate result is performed using a multiplication addition operation, in which MMD operations and updating operations are performed sequentially, and short auxiliary registers and short result registers are used.

Abstract: A processor or other device, such as a programmable and/or massively parallel processor or other device, includes processing elements designed to perform arithmetic operations (possibly but not necessarily including, for example, one or more of addition, multiplication, subtraction, and division) on numerical values of low precision but high dynamic range (“LPHDR arithmetic”). Such a processor or other device may, for example, be implemented on a single chip. Whether or not implemented on a single chip, the number of LPHDR arithmetic elements in the processor or other device in certain embodiments of the present invention significantly exceeds (e.g., by at least 20 more than three times) the number of arithmetic elements, if any, in the processor or other device which are designed to perform high dynamic range arithmetic of traditional precision (such as 32 bit or 64 bit floating point arithmetic).

Abstract: Provided is a method of calculating a negative inverse of a modulus, wherein the negative inverse, which is an essential element in Montgomery multiplication, is quickly obtained. The method includes setting a modulus, defining P obtained by converting the modulus to a negative number, and defining S obtained by subtracting 1 from P, and calculating a negative inverse of the modulus by using P and S.

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 floating point unit includes a floating point adder to perform a floating point addition operation between first and second floating point numbers each having an exponent and a mantissa. The floating point unit also includes an alignment shifter that may calculate a shift value corresponding to a number of bit positions to shift the second mantissa such that the second exponent value is the same as the first exponent value. The alignment shifter may detect an overshift condition, in which the shift value is greater than or equal to a selected overshift threshold value. The selected overshift threshold value comprises a base 2 number in a range of overshift values including a minimum overshift threshold value and a maximum overshift threshold value, and which has a largest number of a consecutive of bits that are zero beginning at a least significant bit.

Abstract: A technique for reducing memory usage during signal processing includes storing least significant portions of a plurality of intermediate results in a first memory. Most significant portions of a subset the plurality of intermediate results are stored in a second memory having a smaller length than the first memory. A data linkage is maintained between the most significant portions and corresponding least significant portions.

Abstract: The invention relates to a secure data processing method comprising the steps of generating (E204; E304) a first random value (A1); executing (E206; E306) a first cryptographic algorithm (FK) using the first random value (A1); generating (E208; E308) a second random value (A2); executing (E210; E310) a second cryptographic algorithm (FK; GK) using the second random value (A2); and generating a result (V) to verify that the first algorithm (FK) was properly executed.

Abstract: A filter operation unit that performs a multiply-accumulate operation on input data and a filter coefficient group including a plurality of coefficients using Booth's algorithm. The filter operation unit includes: at least two filter multiplier units that multiply the input data and a difference between adjacent filter coefficients in a filter coefficient group to obtain multiplication results; and an adder that adds the multiplication results of the multiplier units adjacent to each other. The filter multiplier units each include: a partial product generation unit that repeatedly generates a partial product according to Booth's algorithm; and an adder that cumulatively adds the partial products generated by the partial product generation unit.

Abstract: A method and apparatus for including in a processor instructions for performing logical-comparison and branch support operations on packed or unpacked data. In one embodiment, a processor is coupled to a memory. The memory has stored therein a first data and a second data. The processor performs logical comparisons on the first and second data. The logical comparisons may be performed on each bit of the first and second data, or may be performed only on certain bits. For at least one embodiment, at least the first data includes packed data elements, and the logical comparisons are performed on the most significant bits of the packed data elements. The logical comparisons may include comparison of the same respective bits of the first and second data, and also includes logical comparisons of bits of the first data with the complement of the corresponding bits of the second data. Based on these comparisons, branch support actions are taken.

Abstract: The overall material constant of a composite material is computed where the composite material includes multiple kinds of material components in a matrix phase, each of the material constants of the material components and the matrix phase being known. First, for the composite material, an equation, having the material constant of a virtual composite material as an unknown, is prepared by defining the virtual composite material in which each of the material components is dispersed in a form of spherical particles in the matrix phase at a known volume fractions. Next, the overall material constant of the virtual composite material is found as the overall material constant of the composite material by solving the equation. In this case, the equation is a recursive equation which is obtained using the self-consistent method. The volume fraction of a material component in the composite material is computed using the equation.

Abstract: Provided are an arithmetic circuit and an arithmetic apparatus capable of performing comparison involving conditional branch of three or more values at high speed. The arithmetic circuit includes a plurality of computing units, a plurality of selection circuits and a decision unit. The plurality of computing units perform arithmetic computations on input data and output flag information generated based on a result of the computations. The plurality of selection circuits select any one of the data input to the plurality of computing units. The decision unit receives the flag information from the plurality of computing units and controls select operation of each of the plurality of selection circuits.

Abstract: For calculating the result of a sum of a first operand and a second operand, a modified second operand is calculated, which is negative and less than the modulus. Based on this modified second operand, a sum is calculated which is less than a maximally processable number of a calculating unit executing the calculation. Finally, the sum calculated using the modified second operand is reduced, namely with respect to the modulus, to obtain the result of the sum of the first and second operands.

Abstract: The present invention relates to a efficient implementation of integer and fractional 8-length or 4-length, or 8×8 or 4×4 DCT in a SIMD processor as part of MPEG and other video compression standards.

Abstract: Configuration information is used to make a determination to bypass fragment shading by a shader unit of a graphics processing unit, the shader unit capable of performing both vertex shading and fragment shader. Based on the determination, the shader unit performs vertex shading and bypasses fragment shading. A processing element other than the shader unit, such as a pixel blender, can be used to perform some fragment shading. Power is managed to “turn off” power to unused components in a case that fragment shading is bypassed. For example, power can be turned off to a number of arithmetic logic units, the shader unit using the reduced number of arithmetic logic unit to perform vertex shading. At least one register bank of the shader unit can be used as a FIFO buffer storing pixel attribute data for use, with texture data, to fragment shading operations by another processing element.

Abstract: Sum and carry signals are formed representing a product of a first and a second operand. A bias signal is formed having a value determined by a sign of a product of the first and the second operand. An output signal is provided based on an addition of the sum signal, the carry signal, a sign-extended addend, and the bias signal. A portion of the output signal, a saturated minimum value, or a saturated maximum value, is selected as a final result based on the sign of the product and a sign of the output signal.

Abstract: Disclosed is directed to a speed-level calculator and calculating method for dynamic voltage scaling. The speed-level calculator comprises a deadline counter, a shifter, and a fixed-point multiplier. The deadline counter calculates the residual time D from current time to each task deadline for completing an episode. The shifter generates a D? value by shifting the D value to the right for e-m bits, and takes the decimal fraction part of the D? value for m bits. The speed-level calculator further comprises a saturation control circuit to detect if an overflow occurs on the D? value. According to a pre-calculated parameter ?i corresponding to each task Ti, the fixed-point multiplier performs the multiplication of D? and ?i. After completing saturation and rounding on the multiplication result, a corresponding clock period is generated by taking the integer part. This clock period is used as speed-level to switch the processor voltage and frequency.

Abstract: Efficiency of computation of logarithmic and exponential functions may be improved using multiplication by pre-computed coefficients to obtain intermediate products.

Abstract: A device for determining an inverse of an initial value related to a modulus, comprising a unit configured to process an iterative algorithm in a plurality of iterations, wherein an iteration includes two modular reductions and has, as an iteration loop result, values obtained by an iteration loop of an extended Euclidean algorithm.

Abstract: A computer executable method of performing a modal interval operation, and system for performing same is provided. The method includes providing representations of first and second modal interval operands. Each modal interval operand of the operands is delimited by first and second marks of a digital scale, each mark of the marks comprises a bit-pattern. Each bit-pattern of the bit-patterns of the marks of each of the modal interval operands are examined, and conditions of a set of status flags corresponding to each bit-pattern of the bit-patterns of the marks are set. A bit-mask is computed wherein the mask is based upon the set condition of the status flag sets and a presence/absence of an exceptional arithmetic condition, and a presence/absence of an indefinite operand are each represented by a bit of said bits of said bit mask.

Abstract: Methods, and corresponding codec-containing devices are provided that have source coding schemes for encoding a component of an excitation. In some cases, the source coding scheme is an enumerative source coding scheme, while in other cases the source coding scheme is an arithmetic source coding scheme. In some cases, the source coding schemes are applied to encode a fixed codebook component of the excitation for a codec employing codebook excited linear prediction, for example an AMR-WB (Adaptive Multi-Rate-Wideband) speech codec.

Abstract: A device for determining an inverse of an initial value related to a modulus, comprising a unit configured to process an iterative algorithm in a plurality of iterations, wherein an iteration includes two modular reductions and has, as an iteration loop result, values obtained by an iteration loop of an extended Euclidean algorithm.

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

Abstract: An apparatus and method are provided for performing rearrangement operations and arithmetic operations on data. The data processing apparatus has processing circuitry for performing Single Instruction Multiple Data (SIMD) processing operations and scalar processing operations, a register bank for storing data and control circuitry responsive to program instructions to control the processing circuitry to perform data processing operations. The control circuitry is arranged to responsive to a combined rearrangement arithmetic instruction to control the processing circuitry to perform a rearrangement operation and at least one SIMD arithmetic operation on a plurality of data elements stored in the register bank. The rearrangement operation is configurable by a size parameter derived at least in part from the register bank. The size parameter provides an indication of a number of data elements forming a rearrangement element for the purposes of the rearrangement operation.

Abstract: A method for converting a sampling frequency of a digital signal sampled at a first sampling frequency includes receiving digital signal input samples, and forming output samples corresponding to a second sampling frequency based on the digital signal input samples and an interpolation filter. The first sampling frequency may be larger than the second sampling frequency. The method may further include delivering the output samples. Forming output samples includes, for each of the digital signal input samples, updating current values of N successive output samples with N contributions. The N contributions may be respectively calculated based on a value of a current input sample of the digital input samples weighted by values of N filter coefficients associated with the current input sample, N being fixed and identical for all the digital signal input samples regardless of a value of the conversion ratio between the first and second sampling frequencies.

Abstract: A semiconductor integrated circuit device, having a plurality of processing elements accommodated on a single semiconductor chip, has a latch circuit and a selecting circuit. The latch circuit is provided at an output of each of the processing elements. The selecting circuit selects an input source from a group consisting of upper, lower, left, and right processing elements and a zero signal.

Abstract: Embodiments of the invention provide methods and apparatus for executing a multiple operand instruction. Executing the multiple operand instruction comprises transferring more than two operands to a vector unit, each operand being transferred to a respective one of a plurality of processing lanes of the vector unit. The operands may be transferred from the vector unit to a dot product unit wherein an arithmetic operation using the more than two operands may be performed.

Abstract: Embodiments of the invention provide methods and apparatus for executing a multiple operand instruction. Executing the multiple operand instruction comprises computing an arithmetic result of a pair of operands in each processing lane of a vector unit. The arithmetic results generated in each processing lane of the vector unit may be transferred to a dot product unit. The dot product unit may compute an arithmetic result using the arithmetic result computed by each processing lane of the vector unit to generate an arithmetic result of more than two operands.

Abstract: A Montgomery inverse calculation device includes a plurality of registers each storing a value of a variable, a modulus register storing a modulus, a multiplier performing multiplication on the modulus. A comparator compares the value of the variable stored in each of the registers with an output value of the multiplier and generates a plurality of control signals. A plurality of shifters shifts bits of a value of a variable stored in a corresponding register among the registers in response to at least one first control signal, and a quotient generation block calculates a quotient of mod 2m with respect to values output from some of the shifters in response to a second control signal. A calculation block calculates an updated value of an output value of each of the shifters using the quotient in response to at least one third control signal.