# Arithmetical operation

## Subclass of:

## 708 - Electrical computers: arithmetic processing and calculating

## 708100000 - ELECTRICAL DIGITAL CALCULATING COMPUTER

## 708200000 - Particular function performed

### Patent class list (only not empty are listed)

#### Deeper subclasses:

Class / Patent application number | Description | Number of patent applications / Date published |
---|---|---|

708495000 | Floating point | 153 |

708670000 | Addition/subtraction | 58 |

708620000 | Multiplication | 45 |

708491000 | Residue number | 44 |

708523000 | Multiplication followed by addition (i.e., x*y+z) | 35 |

708520000 | Matrix array | 35 |

708650000 | Division | 31 |

708607000 | Multiplication of matrices | 29 |

708492000 | Galois field | 20 |

708550000 | Compensation for finite word length | 12 |

708517000 | Logarithmic format | 10 |

708530000 | Error detection or correction | 10 |

708524000 | Multiple parallel operations | 9 |

708606000 | Evaluation of powers | 9 |

708521000 | Pipeline | 5 |

20100121899 | Methods and apparatus for efficient complex long multiplication and covariance matrix implementation - Efficient computation of complex long multiplication results and an efficient calculation of a covariance matrix are described. A parallel array VLIW digital signal processor is employed along with specialized complex long multiplication instructions and communication operations between the processing elements which are overlapped with computation to provide very high performance operation. Successive iterations of a loop of tightly packed VLIWs may be used allowing the complex multiplication pipeline hardware to be efficiently used. | 05-13-2010 |

20140317164 | ARITHMETIC PROCESSING DEVICE - An arithmetic processing device includes: an arithmetic unit configured to execute an arithmetic operation; and a stream engine configured to execute stream processing, wherein a data bus of the arithmetic unit and a data bus of the stream engine are tightly coupled with each other. | 10-23-2014 |

20120233234 | SYSTEM AND METHOD OF BYPASSING UNROUNDED RESULTS IN A MULTIPLY-ADD PIPELINE UNIT - A processing unit, system, and method for performing a multiply operation in a multiply-add pipeline. To reduce the pipeline latency, the unrounded result of a multiply-add operation is bypassed to the inputs of the multiply-add pipeline for use in a subsequent operation. If it is determined that rounding is required for the prior operation, then the rounding will occur during the subsequent operation. During the subsequent operation, a Booth encoder not utilized by the multiply operation will output a rounding correction factor as a selection input to a Booth multiplexer not utilized by the multiply operation. When the Booth multiplexer receives the rounding correction factor, the Booth multiplexer will output a rounding correction value to a carry save adder (CSA) tree, and the CSA tree will generate the correct sum from the rounding correction value and the other partial products. | 09-13-2012 |

20090132628 | Method for Performing Decimal Division - A method for performing decimal division including receiving a scaled divisor and a scaled dividend into input registers. A subset of multiples of the scaled divisor is stored in a plurality of multiples registers. Quotient digits are calculated in response to the scaled divisor and the scaled dividend. Each quotient digit is calculated in three clock cycles by a pipeline mechanism. The calculating includes selecting a new quotient digit, and calculating a new remainder. Input to the calculating a new remainder includes data from one or more of the multiples registers. | 05-21-2009 |

20090037508 | METHOD FOR IMPLEMENTING MONTGOMERY MODULAR MULTIPLICATION AND DEVICE THEREFORE - Device for implementing modular multiplication, characterized in that it comprises at least one computation cell comprising a multiplier-adder comprising p pipelined logic-register pairs, receiving several digits to be added together and multiplied, at least two outputs corresponding to the low order and to the high order, an adder receiving the two outputs of the multiplier-adder, the number p being chosen in such a way that the maximum frequency of the multiplier-adder is greater than or equal to the maximum frequency of the adder. | 02-05-2009 |

708605000 | Evaluation of root | 5 |

20120066282 | Whole 1 number method of integer factorization - Disclosed is a method for factoring integers by squaring computation time. The present invention uses binary numbers to process invert function of multiplication as factorization. Inverse method of integer factorization uses a diamond expansion form to arrange the digit positions of 1-numbers and 0-numbers subtracted from the product number P and its complement number No. The complement number N | 03-15-2012 |

20160041947 | IMPLEMENTING A SQUARE ROOT OPERATION IN A COMPUTER SYSTEM - A method and computer system are provided for implementing a square root operation using an iterative converging approximation technique. The method includes fewer computations than conventional methods, and only includes computations which are simple to implement in hardware on a computer system, such as multiplication, addition, subtraction and shifting. Therefore, the methods described herein are adapted specifically for being performed on a computer system, e.g. in hardware, and allow the computer system to perform a square root operation with low latency and with low power consumption. | 02-11-2016 |

20100198902 | COMPUTING MINIMAL POLYNOMIALS OF RADICAL EXPRESSIONS - Described is a technology, such as implemented in a computational software program, by which a minimal polynomial is efficiently determined for a radical expression based upon its structure of the radical expression. An annihilation polynomial is found based upon levels of the radical to obtain roots of the radical. A numerical method performs a zero test or multiple zero tests to find the minimal polynomial. In one implementation, the set of roots corresponding to a radical expression is found. The annihilation polynomial is computed by grouping roots of the set according to their conjugation relationship and multiplying factor polynomials level by level. A selection mechanism selects the minimal polynomial based upon the annihilation polynomial's factors. | 08-05-2010 |

20150081754 | NUMERICAL ALGORITHM FOR NTH ROOT - Presently a direct analytical method, vide the Babylonian method developed in 1800 B.C., is available for the digit-by-digit extraction of the square root of a given positive real number. To calculate the n | 03-19-2015 |

20090083359 | APPARATUS FOR CALCULATING SQUARE ROOT - Provided is a square root calculation apparatus. The apparatus includes a section judgment unit, a coefficient storing unit, and an adder. The section judgment unit stores information regarding a plurality of sections obtained by dividing an entire range of an input value into predetermined intervals, and judges one of the sections to which the input value belongs when the input value is input. The coefficient storing unit stores, in advance, first-order term coefficients and constant terms of first-order approximate equations obtained by approximating square root curves for respective sections, multiplies a first-order term coefficient of the first-order approximate equation in the section to which the input value belongs, by the input value to output a first-order term, and outputs a constant term in the section to which the input value belongs. The adder adds the first-order term and the constant term output from the coefficient storing unit to calculate an approximated square root value. | 03-26-2009 |

708603000 | Sum of products generation | 4 |

20110106871 | Apparatus and method for performing multiply-accumulate operations - A data processing apparatus and method for performing multiply-accumulate operations is provided. The data processing apparatus includes data processing circuitry responsive to control signals to perform data processing operations on at least one input data element. Instruction decoder circuitry is responsive to a predicated multiply-accumulate instruction specifying as input operands a first input data element, a second input data element, and a predicate value, to generate control signals to control the data processing circuitry to perform a multiply-accumulate operation by: multiplying said first input data element and said second input data element to produce a multiplication data element; if the predicate value has a first value, producing a result accumulate data element by adding the multiplication data element to an initial accumulate data element; and if the predicate value has a second value, producing the result accumulate data element by subtracting the multiplication data element from the initial accumulate data element. Such an approach provides a particularly efficient mechanism for performing complex sequences of multiply-add and multiply-subtract operations, facilitating improvements in performance, energy consumption and code density when compared with known prior art techniques. | 05-05-2011 |

20130054666 | METHOD FOR PREDICTING THE DURATION OF A FUTURE TIME INTERVAL - A method for predicting a value for a length of a future time interval in which a physical variable changes is described, in which at least one measured value for the length of a past time interval and an instantaneously measured value for a length of an instantaneous time interval are taken into account, m values for lengths of past time intervals being added. A first value precedes the instantaneously measured value by k−1, and an mth value precedes the instantaneously measured value by k−m. The m added values are divided by a value for a length of a past time interval which precedes the instantaneously measured value by k. A ratio of the mentioned values is formed. For determining the value to be predicted, an average error is initially added to the instantaneously measured value, forming a sum. The formed ratio is subsequently applied to this sum. | 02-28-2013 |

20120278375 | Exponentiation System - A method for computation, including defining a sequence of n bits that encodes an exponent d, such that no more than a specified number of successive bits in the sequence are the same, initializing first and second registers using a value of a base x that is to be exponentiated, whereby the first and second registers hold respective first and second values, which are successively updated during the computation, successively, for each bit in the sequence computing a product of the first and second values, depending on whether the bit is one or zero, selecting one of the first and second registers, and storing the product in the selected one of the registers, whereby the first and second registers hold respective first and second final values upon completion of the sequence, and returning x | 11-01-2012 |

20080307031 | Fast Modular Zero Sum and Ones Sum Determination - In one embodiment, a state determiner comprises a plurality of logic circuits and a second logic circuit. Each logic circuit corresponds to a respective bit position of a result of an adder. A first logic circuit corresponds to a least significant bit of the result and is coupled to receive a least significant bit of each operand of the adder and a carry-in input to the adder. Each remaining logic circuit is coupled to receive a respective bit from the respective bit position of each operand and a less significant bit adjacent to the respective bit of each operand. Each logic circuit is configured to generate an output signal indicative of whether or not a specific result occurs in the respective bit position of the result responsive only to inputs that the logic circuit is coupled to receive as stated previously. Coupled to receive the output signals from the logic circuits, the second logic circuit is configured to generate a sum signal indicative, when asserted, that the specific result occurs in each bit position of the result of the adder. | 12-11-2008 |

708604000 | All four basic functions | 3 |

20140207839 | Spatial Arithmetic Method of Integer Factorization - A computer system represents numbers as three-dimensional relations, which may be represented as collections of points in three-dimensional space. The three-dimensional representations may use values of +1 and −1 as complements of each other to overcome limitations of binary representations which use values of 1 and 0 to represent numbers. The computer system may use such three-dimensional relations to perform arithmetic and to factorize numbers. | 07-24-2014 |

20130218939 | EXPONENTIATION CALCULATION APPARATUS AND METHOD FOR CALCULATING SQUARE ROOT IN FINITE EXTENSION FIELD - 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. | 08-22-2013 |

20110153708 | COMMUNICATION DEVICE, RECEPTION DATA LENGTH DETERMINATION METHOD, MULTIPLE DETERMINATION CIRCUIT, AND RECORDING MEDIUM - A communication device includes a storage unit to store quotients and remainders associated with multiplication values obtained by multiplying a specified integer number, which is expressed in a form of (2 | 06-23-2011 |

708522000 | Systolic | 2 |

20100250640 | SYSTOLIC ARRAY AND CALCULATION METHOD - A linear systolic array is added to the lower side of a trapezoid systolic array created by combining a triangular systolic array and a square systolic array. In order to make the connection among the cells fixed, the intermediate result output from each row of the trapezoid systolic array to a lower row is shifted in phase with respect to the intermediate result of the complex MFA algorithm, the phase shift is absorbed by the next row, and the phase shift in the intermediate result output from the last row of the trapezoid systolic array is corrected by the linear systolic array. Each cell is implemented by a CORDIC circuit that processes vector angle computation, vector rotation, division, and multiply-and-accumulate with a constant delay. | 09-30-2010 |

20090204658 | DECIMAL COMPUTING APPARATUS, ELECTRONIC DEVICE CONNECTABLE DECIMAL COMPUTING APPARATUS, ARITHMETIC OPERATION APPARATUS, ARITHMETIC OPERATION CONTROL APPARATUS, AND PROGRAM-RECORDED RECORDING MEDIUM - A decimal calculation apparatus, which performs multidigit decimal calculation with the number of calculation digits set in a calculation instruction, includes a multidigit memory section which stores values with greater numbers of digits than the number of digits of a predetermined digit unit in a plurality of memory areas, a calculation-instruction memory section which stores the calculation instruction having the number of calculation digits and a type of calculation set therein, and a decimal calculation section which performs decimal calculation of sequentially calculating numerical values of corresponding digit units respectively stored in the plurality of memory areas of the multidigit memory section, digit unit by digit unit in the number of calculation digits set in the calculation instruction stored in calculation-instruction memory section, in decimal calculation according to type of calculation set in the calculation instruction stored in calculation-instruction memory section, and sequentially writing calculation results in the plurality of memory areas of the multidigit memory section digit unit by digit unit. | 08-13-2009 |

708525000 | Status condition/flag generation or use | 1 |

20100030834 | Performing A Binary Coded Decimal (BCD) Calculation - 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. | 02-04-2010 |

708494000 | Incremental mode | 1 |

20140108480 | APPARATUS AND METHOD FOR VECTOR COMPUTE AND ACCUMULATE - An apparatus and method are described for comparing elements between two immediate values. For example, a method according to one embodiment includes the following operations: reading values of a first set of elements stored in a first immediate value, each element having a defined element position in the first immediate value; comparing each element from the first set of elements with each of a second set of elements stored in a second immediate value; counting the number of times the value of each element of the first set of elements is found in the second set of elements to arrive at a final count for each element of the first set of elements; and transferring the final count for each element to a third immediate value, wherein the final count is stored in an element position in the third immediate value corresponding to the defined element position in the first immediate value. | 04-17-2014 |

708493000 | Multi-valued | 1 |

20090030962 | QUANTUM COMPUTING METHOD AND QUANTUM COMPUTER - An (N+1) number of physical systems each having five energy levels |0>, |1>, |2>, |3>, and |4>, a qubit being expressed by |0> and |1>, are provided in an optical cavity having a cavity mode resonant with |2>-|3>, such that an N number of control systems and a target system are prepared. The target system is irradiated with light pulses resonant with |0>-|4>, |1>-|4>, and |2>-|4> to change a superposed state |c> to |2>. All of the physical systems are irradiated with light pulses resonant with |0>-|3> and |1>-|3>, and a phase of the light pulse resonant with the target system is shifted by a specific value dependent on a unitary transformation U. The target system is irradiated with light pulses resonant with |0>-|4>, |1>-|4>, and |2>-|4>, with a phase difference between them being set to a specific value dependent on the unitary transformation U, to return |2> to |c>. | 01-29-2009 |

Entries | ||

Document | Title | Date |
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20130159371 | Arithmetic Logic Unit Architecture - 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. | 06-20-2013 |

20130290392 | INSTRUCTION AND LOGIC FOR PERFORMING A DOT-PRODUCT OPERATION - Method, apparatus, and program means for performing a dot-product operation. In one embodiment, an apparatus includes execution resources to execute a first instruction. In response to the first instruction, said execution resources store to a storage location a result value equal to a dot-product of at least two operands. | 10-31-2013 |

20100281092 | STANDARD CELL FOR ARITHMETIC LOGIC UNIT AND CHIP CARD CONTROLLER - A masked ALU cell for a certain bit position p is provided. The cell comprises a base unit operable to generate a masked inverted carry out bit co*_n and an inverted masked sum bit s*_n based on a first masked output a*, a second masked output b*, and a re-masked carry bit input ci*; a transformation unit coupled to the base unit, the transformation unit having a first masked input bit a | 11-04-2010 |

20100191793 | Symbolic Computation Using Tree-Structured Mathematical Expressions - A method for performing symbolic computations on a mathematical expression. The mathematical expression may be converted to a tree structure having one or more parent nodes and one or more child nodes. Each parent node may be a mathematical operation. Each child node may be a mathematical expression on which the mathematical operation is performed in a specified order. Each child node may be in a hierarchical relationship to one of the parent nodes. The parent nodes, the child nodes or both may be manipulated to perform a first symbolic computation on the mathematical expression. | 07-29-2010 |

20130246494 | CALCULATION METHOD AND COMPUTER-READABLE RECORDING MEDIUM - 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. | 09-19-2013 |

20140244703 | SYSTEM, METHOD, AND COMPUTER PROGRAM PRODUCT FOR IMPLEMENTING LARGE INTEGER OPERATIONS ON A GRAPHICS PROCESSING UNIT - A system, method, and computer program product for generating executable code for performing large integer operations on a parallel processing unit is disclosed. The method includes the steps of compiling a source code linked to a large integer library to generate an executable file and executing the executable file to perform a large integer operation using a parallel processing unit. The large integer library includes functions for processing large integers that are optimized for the parallel processing unit. | 08-28-2014 |

20150347350 | METHOD AND APPARATUS FOR PERFORMING CALCULATIONS IN CHARACTER INPUT MODE OF ELECTRONIC DEVICE - A method and apparatus for performing calculations in a character input mode of an electronic device. Character input is received in the character input mode, and input characters are displayed in a character input window. If determined that an arithmetic expression is present in the displayed input characters, the arithmetic expression is evaluated, and an evaluation result is displayed. A calculation enabling condition may be satisfied prior to, or after, the arithmetic expression identification. The method may be applied to character input modes of a text messaging or email application, or of a word processing application. | 12-03-2015 |

20140214912 | PERFORMING BATCHES OF SELECTIVE ASSIGNMENTS IN A VECTOR FRIENDLY MANNER - Embodiments of the invention relate to processing queries. A query operation to be performed on a table of data is translated into a series of bit level logical operations using expansion and/or saturation operations. A mask is created from the series of bit level logical operations. This mask is then simultaneously applied to multiple rows from the table of data. | 07-31-2014 |

20130117344 | Methods and Systems for Decoding Polar Codes - 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. through latency, number of cycles, number of elements etc). | 05-09-2013 |

20130091189 | Single datapath floating point implementation of RCP, SQRT, EXP and LOG functions and a low latency RCP based on the same techniques - 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. | 04-11-2013 |

20130144924 | METHOD AND APPARATUS FOR DISTRIBUTING OBJECTS - 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. | 06-06-2013 |

20150095392 | ARITHMETIC CIRCUIT AND ARITHMETIC APPARATUS - 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. | 04-02-2015 |

20150088952 | ARITHMETIC PROCESSING DEVICE - An arithmetic processing device includes: a reception unit for receiving information including a numerical value and an operator; a generation unit generating arithmetic information regarding an arithmetic operation and having a plurality of codes including the numerical value and the operator that are received; and an information transmission unit transmitting the generated arithmetic information to an external device. The generation unit generates the arithmetic information in which the codes are arranged so that, when a plurality of rows including numerical values and operators are displayed on a display unit of the external device in accordance with the arithmetic information, an arrangement of a numerical value and an operator in each displayed row and an arrangement of a numerical value and an operator in another displayed row are matched to each other. | 03-26-2015 |

20150363358 | METHOD AND SYSTEM FOR CONTINUOUS OPTIMIZATION USING A BINARY SAMPLING DEVICE - A method and system are disclosed for continuous optimization. The method comprises obtaining an optimization problem involving continuous or semi-continuous variables in a digital computer; initiating a stochastic search process in the digital computer in order to solve the optimization problem; until a stopping criterion is met constructing in the digital computer at least one stochastically generated polynomial in binary variables representative of choices of candidate future state of the stochastic search process, providing the at least one polynomial in binary variables to a binary sampling device, sampling from domains of the at least one polynomial in binary variables using the binary sampling device to generate binary sample points, receiving the generated binary sample points in the digital computer and transiting to next state of the stochastic search process and providing a best known solution found as a solution of the optimization problem using the digital computer. | 12-17-2015 |

20130311531 | MODULAR ARITHMATIC UNIT AND SECURE SYSTEM INCLUDING THE SAME - A modular arithmetic unit includes a first input generator receiving first data to generate a first operand; a second input generator receiving second data to generate a second operand; an accumulator performing an accumulate/shift operation to add the first and second operands and outputting the carry and sum; a carry propagation adder adding the carry and the sum to output a result; and a data handler receiving either external data or the result and outputting the first data and the second data. | 11-21-2013 |

20140067893 | Squaring Circuit - Methods, apparatuses, and computer program products for squaring an operand include identifying a fixed-point value with a fixed word size and a substring size for substrings of the fixed-point value, wherein the fixed-point value comprises a binary bit string. A square of the fixed-point value can be determined using the fixed point value, the substring size, and least significant bits of the fix-point value equal to the substring size. | 03-06-2014 |

20120254275 | RELIABLE AND EFFICIENT COMPUTATION OF MODAL INTERVAL ARITHMETIC OPERATIONS - 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. | 10-04-2012 |

20080281896 | INDUSTRIAL CONTROLLER - A first arithmetic operator ( | 11-13-2008 |