Abstract: An execution unit for a processor, the execution unit comprising: a look up table having a plurality of entries, each of the plurality of entries comprising an initial estimate for a result of an operation; a preparatory circuit configured to search the look up table using an index value dependent upon the operand to locate an entry comprising a first initial estimate for a result of the operation; a plurality of processing circuits comprising at least one multiplier circuit; and control circuitry configured to provide the first initial estimate to the at least one multiplier circuit of the plurality of processing circuits so as perform processing, by the plurality of processing units, of the first initial estimate to generate the function result, said processing comprising applying one or more Newton Raphson iterations to the first initial estimate.

Abstract: Methods and apparatus for approximation using polynomial functions are disclosed. In one embodiment, a processor comprises decoding and execution circuitry. The decoding circuitry is to decode an instruction, where the instruction comprises a first operand specifying an output location and a second operand specifying a plurality of data element values to be computed. The execution circuitry is to execute the decoded instruction. The execution includes to compute a result for each of the plurality of data element values using a polynomial function to approximate a complex function, where the computation uses coefficients stored in a lookup location for the complex function, and where data element values within different data element value ranges use different sets of coefficients. The execution further includes to store results of the computation in the output location.

Abstract: Methods and systems for determining whether an infinitely precise result of a reciprocal square root operation performed on an input floating point number is greater than a particular number in a first floating point precision. The method includes calculating the square of the particular number in a second lower floating point precision; calculating an error in the calculated square due to the second floating point precision; calculating a first delta value in the first floating point precision by calculating the square multiplied by the input floating point number less one; calculating a second delta value by calculating the error multiplied by the input floating point number plus the first delta value; and outputting an indication of whether the infinitely precise result of the reciprocal square root operation is greater than the particular number based on the second delta term.

Abstract: In one embodiment, a graphics processor includes a register file having a plurality of storage segments to store information and output a plurality of segment outputs via a plurality of segmented bitlines to a static logic circuit to receive the plurality of segment outputs from the plurality of storage segments and to output read data based on the plurality of segment outputs. The register file may output the read data with a same amount of power without regard to a logic state of the read data. Other embodiments are described and claimed.

Abstract: A method is provided. The method is executable by a processor. The method includes receiving, by an instruction issue unit of the processor as an input, a preferred instruction variant from an instruction variant selection logic. The method includes executing, by an execution unit of the processor, the preferred instruction variant. The method includes providing, by the execution unit of the processor, quality feedback to the instruction variant selection logic and evaluating, by the instruction variant selection logic of the processor, the preferred instruction variant based on the quality feedback.

Abstract: A data processing apparatus is provided to convert a plurality of signed digits to an output value. Receiver circuitry receives, at each of a plurality of iterations, one of the plurality of signed digits, each of the signed digits comprising a number of bits dependent on a radix. The signed digits being used to form an unrounded output value followed by zero or more extra bits. Adjustment circuitry adjusts a least-significant digit of the unrounded output value to produce an incremented unrounded output value after the plurality of iterations. Rounding circuitry selects from among the unrounded output value and the incremented unrounded output value to produce the output value. The adjustment circuitry is adapted, when a value of a position of a least-significant bit of the unrounded output value is greater than or equal to the radix divided by two, to adjust a subset of the digits of the unrounded output value.

Abstract: An apparatus and method for performing an operation which are secure against side-channel attack are provided. According to one embodiment of the present disclosure, the apparatus includes a first outputter configured to output a first output value corresponding to a seed value using a first parameter candidate value set, a second outputter configured to output a second output value using a second parameter candidate value set wherein the second output value corresponds to the seed value and is capable of being generated using the first output value, a third outputter configured to output a third output value using the seed value and the first output value, and a fourth outputter configured to output a fourth output value using the second output value and the third output value, wherein the fourth output value is capable of being generated using the seed value.

Abstract: In an example, an apparatus comprises a plurality of execution units comprising at least a first type of execution unit and a second type of execution unit and logic, at least partially including hardware logic, to expose embedded cast operations in at least one of a load instruction or a store instruction; determine a target precision level for the cast operations; and load the cast operations at the target precision level. Other embodiments are also disclosed and claimed.

Abstract: Technologies for provisioning cryptographic keys include hardcoding identical cryptographic key components of a Rivest-Shamir-Adleman (RSA) public-private key pair to each compute device of a plurality of compute devices. A unique cryptographic exponent that forms a valid RSA public-private key pair with cryptographic key components hardcoded into each compute device is provided to each compute device so that each compute device has a unique public key. The public key of each compute device may be used to provision unique secrets to the corresponding compute device.

Abstract: A data processing apparatus is provided, for performing a digit-recurrence square root operation on an input value. Receiver circuitry receives a remainder value of a previous iteration of the digit-recurrence square root operation. Comparison circuitry compares most significant bits of the remainder value of the previous iteration with a number of selection constants, in order to output a next digit of a result of the digit-recurrence square root operation. The comparison circuitry compares at most 3 fractional bits of the remainder value of the previous iteration with the plurality of selection constants.

Abstract: Aspects of the technology provide solutions for determining a time period (“epoch”) required to monitor or analyze a tenant network. Some implementations of the technology include a process for making automatic epoch determinations, which includes steps for identifying one or more network parameters for a tenant network, analyzing the tenant network using the network parameters to discover one or more configuration settings of the tenant network, and determining a first epoch for the tenant network, the first epoch corresponding with a period of time to complete analysis of the tenant network using the network parameters. In some aspects, the process can further include steps for generating a tenant profile for the tenant network, the tenant profile based on the network parameters, the first epoch, and the one or more configuration settings of the tenant network. Systems and machine-readable media are also provided.

Abstract: Embodiments relate to lightweight interrupts for condition checking. An aspect includes determining, by a condition checker in a computer system, that a condition occurs for an application executing on the computer system. Another aspect includes, based on determining that the condition occurs for the application, determining whether lightweight interrupts are enabled. Yet another aspect includes based on determining that lightweight interrupts are enabled, issuing a lightweight interrupt to the application and handling the instruction by the application.

Abstract: A data processing apparatus is provided, to calculate an at least partial square root of a floating point number having an exponent and significand. Recurrence circuitry performs one or more iterations of an iterative square root operation, each of the one or more iterations receiving an input at least partial square root and an input remainder to produce the at least partial square root and a remainder of performing the iterative square root operation. The recurrence circuitry provides the at least partial square root and the remainder as the input at least partial square root and the input remainder for a subsequent iteration of the iterative square root operation. The recurrence circuitry includes initialization circuitry to provide the at least partial square root and the remainder after at least an initial iteration of the one or more iterations.

Abstract: A data processing system 2 supports conversion of fixed point numbers to floating point numbers. The result floating point numbers may be subnormal. A first shifter 28 shifts input signals representing the fixed point number by a first shift amount depending upon a leading zero count within an integer portion followed by a fractional portion of the fixed point number. A second shifter 30 shifts the input signals by a second shift amount depending upon the variable point position within the fixed point number. A subnormal result detector 34 generates a selection signal in dependence upon detection of a combination of a variable point position and the count of leading zeros which corresponds to the floating point number having a subnormal value. Selection circuitry 32 selects one of the outputs from the first shifter or the second shifter to form the significand in dependence upon the selection signal generated by the subnormal result detector.

Abstract: A floating-point arithmetic block for performing arithmetic operations on floating-point numbers on an integrated circuit includes a unit to handle exceptions, a unit to handle the exponent, a unit for normalization and rounding, and a core having a multiplier, a subtractor, storage circuitry to store multiple initial mantissa values, and configurable interconnect circuitry. The configurable interconnect circuitry may be configured to route signals throughout the floating-point arithmetic block. The configuration may be performed by a finite state machine that controls the configurable interconnect depending on the selected floating-point arithmetic operation. The floating-point arithmetic block may be configured to implement a variety of floating-point arithmetic operations including the inverse square root operation, the square root operation, the inverse operation, the division, the multiplication, the addition, and the subtraction.

Abstract: Systems and methods for level-shifting multiplexing are described herein. In one embodiment, a method for level-shifting multiplexing comprises selecting one of a plurality of inputs based on one or more select signals, and pulling down one of first and second nodes based on a logic state of the selected one of the plurality of inputs. The method also comprises pulling up the first node if the second node is pulled down, and pulling up the second node if the first node is pulled down.

Abstract: A processing apparatus has combined divide-square root circuitry for performing a radix-N SRT divide algorithm and a radix-N SRT square root algorithm, where N is an integer power-of-2. The combined circuitry has shared remainder updating circuitry which performs remainder updates for a greater number of iterations per cycle for the SRT divide algorithm than for the SRT square root algorithm. This allows reduced circuit area while avoiding the SRT square root algorithm compromising the performance of the SRT divide algorithm.

Abstract: A processor includes a decoder that decodes an instruction that instructs the processor to perform subsequent computations in an approximate manner and a functional unit that performs the subsequent computations in the approximate manner in response to the instruction. An instruction instructs the processor to clear an error amount associated with a value stored in a general purpose register of the processor. The error amount indicates an amount of error associated with a result of a computation performed by the processor in an approximate manner. The processor also clears the error amount in response to the instruction. Another instruction specifies a computation to be performed and includes a prefix that indicates the processor is to perform the computation in an approximate manner. The functional unit performs the computation specified by the instruction in the approximate manner specified by the prefix.

Abstract: Methods and circuitry for evaluating reciprocal, square root, inverse square root, logarithm, and exponential functions of an input value, Y. In one embodiment, an approximate value, RA, of the reciprocal of Y is generated. One Newton-Raphson iteration is performed as a function of RA and Y, resulting in a truncated approximate value, R. R is multiplied by Y and 1 is subtracted, resulting in a reduced argument, A. A Taylor series evaluation of A is performed, resulting in an evaluated argument, B. B is multiplied by a post-processing factor for the final result.

Abstract: A data processing apparatus and method are provided for performing a reciprocal operation on an input value d to produce a result value X. The reciprocal operation involves iterative execution of a refinement step to converge on the result value, the refinement step performing the computation: Xi=Xi-1*M, where Xi is an estimate of the result value for the i-th iteration of the refinement step, and M is a value determined by a portion of the refinement step. The data processing apparatus comprises a register data store having a plurality of registers operable to store data, and processing logic operable to execute instructions to perform data processing operations on data held in the register data store.

Abstract: A system and method for accelerating evaluation of functions. In one embodiment, a method includes receiving, by a processor, a value to be processed, and notification of a function to be applied to the value. The value is represented in a floating point format. The value is converted, by the processor, to a fixed point format. Which of Newton-Raphson and polynomial approximation is to be used to apply the function to the value in the fixed point format is determined by the processor. The function is applied to the value in the fixed point format to generate a result in the fixed point format. The result is converted to the floating point format by the processor.

Abstract: A system including: an input processing unit configured to: extract a significant and a bias exponent from the decimal floating-point radicand; and calculate a normalized significand; a square root unit configured to: calculate, using a FMA unit, a refined reciprocal square-root of the normalized significand; calculate an unrounded square-root of the normalized significand by multiplying the refined reciprocal square-root by the normalized significand; and generate a rounded square-root based on a first difference between the normalized significand and a square of the unrounded square-root; a master control unit operatively connected to the input processing hardware unit and the square-root hardware unit and configured to calculate an exponent for the unrounded square-root based on the number of leading zeros and a precision of the decimal floating-point radicand; and an output formulation unit configured to output a decimal floating-point square-root of the radicand based on the rounded square-root and the e

Abstract: A method, system and computer program product for verifying a result of a floating point square root operation is provided. The method includes: receiving a result of a floating point square root operation for an operand; performing a comparison of a magnitude of a least significant bit (LSB) of the operand and a magnitude of a most significant bit (MSB) of a remainder; and determining whether the result is correct based on the comparison.

Abstract: Methods and apparatuses for constructing a multi-level solver, comprising decomposing a graph into a plurality of pieces, wherein each of the pieces has a plurality of edges and a plurality of interface nodes, and wherein the interface nodes in the graph are fewer in number than the edges in the graph; producing a local preconditioner for each of the pieces; and aggregating the local preconditioners to form a global preconditioner.

Abstract: Precision of arithmetic operations on floating-point numbers is improved while also preventing an increase in the amount of processing. A second converter converts an exponent included in an exponent field according to an exponent conversion rule defined in accordance with a function. A storage stores in a table a value obtained by converting a mantissa field according to a mantissa conversion rule defined in accordance with the function. A retrieving unit derives an index of the table, by extracting the most significant 8 bits from the 23 bits constituting the mantissa field. The retrieving unit adds 1 to the mantissa field approximated by the most significant 8 bits so as to derive a second index. A deriving unit derives a tentative return value A and a tentative return value B. Further, the deriving unit interpolates between the tentative return value A and the tentative return value B so as to derive a return value of the function.

Abstract: An apparatus for general powering computation is disclosed. The apparatus is capable of computing a powering function of a floating-point number with an unrestricted exponent. The unrestricted exponent can be a fixed-point or a floating-point exponent. Additionally, the unrestricted exponent can be an inverse of a number in order to enable for q-th root computation using the same hardware processor and architecture.

Abstract: Approximations of reciprocal square roots are provided in IEEE floating point binary format by obtaining an index from an input value, accessing a pair of table values and performing a limited number of simple and rapidly performed manipulations. The maximum relative error in the approximation thus provided is less than 0.75/2(2k+1) as compared with a maximum relative error of 1/2k+2 of known methods, where 2k is the number of table entries.

Abstract: A system and methods for reducing memory traffic and power consumption when solving systems of linear equations. Certain embodiments provide several aspects for improved performance in solving a consistent system of linear equations and in computing a generalized inverse. One aspect involves performing row transformations on AX=B, so that the transformed A contains row vectors that are either zero or are part of an orthonormal set. Another aspect involves performing column transformations on A, so that A contains column vectors that are either zero or are part of an orthonormal set. Another aspect involves performing row eliminations differently so that a variation of an LU factorization is obtained that is in a more directly useful form.

Abstract: An amplitude calculation apparatus or an amplitude calculation program of an output signal of an encoder dividing a resurge waveform into a predetermined number of angle areas, presetting and storing coefficient ? of the A-phase and the coefficient ? of the B-phase corresponding to the divided angle areas, the coefficients being set so that ?A+?B approximates the radius of the theoretical resurge waveform, calculating the radius of the resurge waveform as ?A+?B, and making the calculated radius the amplitude of the output signal of the encoder or converting a phase angle ? of a quadrant n to a phase angle ?? of the quadrant 1, and calculating the radius of the resurge waveform as ?|A|+?|B|, whereby the circuit size of the apparatus for calculating the resurge radius from the output of the encoder is reduced and the processing time by software for calculating the resurge radius is shortened.

Abstract: There is provided a semiconductor integrated circuit including: a plurality of first logic blocks which are reconfigurable, the plurality of first logic blocks inputting data of a first bit width and performing computation; a first network connecting the plurality of first logic blocks in a dynamically reconfigurable manner; a plurality of second logic blocks inputting data of a second bit width different from the first bit width and performing computation; a second network connected to outputs of the plurality of second logic blocks; and a third network connecting a carry bit output of a computing unit included in the first logic block to an input of a computing unit included in the second logic block in a dynamically reconfigurable manner.

Abstract: A computer-implemented method for executing a floating-point calculation where an exact value of an associated result cannot be expressed as a floating-point value is disclosed. The method involves: generating an estimate of the associated result and storing the estimate in memory; calculating an amount of error for the estimate; determining whether the amount of error is less than or equal to a threshold of error for the associated result; and if the amount of error is less than or equal to the threshold of error, then concluding that the estimate of the associated result is a correctly rounded result of the floating-point calculation; or if the amount of error is greater than the threshold of error, then testing whether the floating-point calculation constitutes an exception case.

Abstract: Multipurpose arithmetic functional units can perform planar attribute interpolation and unary function approximation operations. In one embodiment, planar interpolation operations for coordinates (x, y) are executed by computing A*x+B*y+C, and unary function approximation operations for operand x are executed by computing F2(xb)*xh2+F1(xb)*xh+F0(xb), where xh=x?xb. Shared multiplier and adder circuits are advantageously used to implement the product and sum operations for both classes of operations.

Abstract: When division X/Y of floating point numbers is performed, bit string data of a mantissa x including a fraction xf of X or a mantissa y including a fraction yf of Y is shifted in accordance with magnitude relation between them to perform a fraction computation. Thereby, a fraction division result in which the position of the most significant bit is fixed at a prescribed digit is generated. When a square root operation ?Y is performed, a fraction square root operation result in which the position of the most significant bit is fixed at a prescribed digit is generated by an exception handling if all of the three conditions that all the bits in the fraction of Y are one, a difference between the exponent ye of Y and a bias value b is an odd number, and a rounding mode is a positive infinity direction are satisfied.

Abstract: A method and arrangements for increased precision in the computation of a reciprocal square root is disclosed. In accordance with the present invention, it is possible to achieve fifty three (53) bits of precision in less processing time than previously possible.

Abstract: In one aspect, there is provided a digital logic circuit that comprises circuitry for generating a new iteration xn+1 of the reciprocal square root of A from the previous iteration xn by (i) multiplying the previous iteration xn by the number A; (ii) multiplying the result of (i) by the previous iteration xn; (iii) subtracting the result of (ii) from 3; and (iv) multiplying the result of (iii) by half of the previous iteration xn. According to another aspect there is provided a calculator unit for determining an initial value for use in a iterative process for calculating an estimate of the reciprocal square root of a number A, the calculator unit comprising circuitry for (a) rounding the number A to the nearest number of the form 2J, where J is an integer; (b) if J is odd, rounding J up to the nearest even number to give J?; (c) if J is even, setting J to J?; and (d) calculating 2?(J?/2) to determine the initial value for the reciprocal square root of A.

Abstract: A data processing apparatus and method are provided for performing a reciprocal operation on an input value d to produce a result value X. The reciprocal operation involves iterative execution of a refinement step to converge on the result value, the refinement step performing the computation: Xi=Xi?1*M, where Xi is an estimate of the result value for the i-th iteration of the refinement step, and M is a value determined by a portion of the refinement step. The data processing apparatus comprises a register data store having a plurality of registers operable to store data, and processing logic operable to execute instructions to perform data processing operations on data held in the register data store.

Abstract: A device for executing a cryptoalgorithm including a central processing unit for a first sub-group of operations and for a flow control of the cryptoalgorithm as well as a hardware circuit for a second sub-group of operations, wherein the first sub-group preferably includes arithmetic and/or logic operations, while the second sub-group includes rotation operations, permutation operations, substitution operations or selection operations.

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: Systems, methods and computer program products for hardware assists for microcoded floating point divide and square root operations. Exemplary embodiments include a method including receiving a first microcoded instruction in the pipeline, decoding the first microcoded instruction in a decode stage of the pipeline, initiating a microcode engine coupled to the processor, with the microcode engine configured to process the streamlined microcode routine.

Abstract: A method, system and computer program product for verifying a result of a floating point square root operation is provided. The method includes: receiving a result of a floating point square root operation for an operand; performing a comparison of a magnitude of a least significant bit (LSB) of the operand and a magnitude of a most significant bit (MSB) of a remainder; and determining whether the result is correct based on the comparison.

Abstract: When division X/Y of floating point numbers is performed, bit string data of a mantissa x including a fraction xf of X or a mantissa y including a fraction yf of Y is shifted in accordance with magnitude relation between them to perform a fraction computation. Thereby, a fraction division result in which the position of the most significant bit is fixed at a prescribed digit is generated. When a square root operation ?Y is performed, a fraction square root operation result in which the position of the most significant bit is fixed at a prescribed digit is generated by an exception handling if all of the three conditions that all the bits in the fraction of Y are one, a difference between the exponent ye of Y and a bias value b is an odd number, and a rounding mode is a positive infinity direction are satisfied.

Abstract: Systems, methods and computer program products for hardware assists for microcoded floating point divide and square root operations. Exemplary embodiments include a method including receiving a first microcoded instruction in the pipeline, decoding the first microcoded instruction in a decode stage of the pipeline, initiating a microcode engine coupled to the processor, with the microcode engine configured to process the streamlined microcode routine.

Abstract: A system for providing a floating point square root comprises an analyzer circuit configured to determine a first status of a first floating point operand based upon data within the first floating point operand. In addition, the system comprises a results circuit coupled to the analyzer circuit. The results circuit is configured to assert a resulting floating point operand containing the square root of the first floating point operand and a resulting status embedded within the resulting floating point operand.

Abstract: High-precision floating-point function estimates are split in two instructions each: a low precision table lookup instruction and a linear interpolation instruction. Estimates of different functions can be implemented using this scheme: A separate table-lookup instruction is provided for each different function, while only a single interpolation instruction is needed, since the single interpolation instruction can perform the interpolation step for any of the functions to be estimated. Thus, significantly less overhead is incurred than would be incurred with specialized hardware, while still maintaining a uniform FPU latency, which allows for much simpler control logic.

Abstract: Methods for determining the square root, reciprocal square root, or reciprocal of a number performed by a processor of a computer system. The methods produce high precision estimates without using iterative steps. In addition, the methods taught herein utilize compressed tables for the coefficient terms A, B, and C from the quadratic expression Ax2+Bx+C, thus minimizing hardware requirements.

Abstract: The invention provides circuitry for carrying out a square root operation and a division operation. The circuitry utilizes common iteration circuitry for carrying out a plurality of iterations and means for identifying if an square root operation or a division operation is to be performed. The iteration circuitry is controlled in accordance with whether a square root or division operation is to be performed.

Abstract: One embodiment of the present invention provides a system that performs a carry-save square root operation that calculates an approximation of a square root, Q, of a radicand, R. The system calculates Q by iteratively selecting an operation to perform based on higher-order bits of a remainder, r, and then performs the operation. This operation can include subtracting two times a square root calculated thus far, q, and a coefficient, c, from r, and adding c to q. During this operation, the system maintains r in carry-save form, which eliminates the need for carry propagation while updating r, thereby speeding up the square root operation. Furthermore, the selection logic, which decides what operation to perform next, is simpler than previous square-root implementations, thereby providing a further speedup.

Abstract: The invention provides circuitry for carrying out at least one of a square root operation and a division operation. The circuitry utilizes a carry slave adder and a carry propagate adder part. The carry save adder and the carry propagate adder part are arranged in parallel.

Abstract: The accuracy of approximating the reciprocal and the reciprocal square root of a number (N) is improved. Approximating the reciprocal of N includes: (a) estimating the reciprocal of N to produce an estimate (Xi); (b) determining a first intermediate result (IR1) according to the equation: IR1=1?N*Xi; (c) multiplying IR1 by Xi to produce a second intermediate result (IR2); and (d) adding Xi to IR2 to produce an approximation of the reciprocal of N. Approximating the reciprocal square root includes: (a) estimating the reciprocal square root of N to produce Xi; (b) multiplying Xi by N to produce IR1; (c) determining IR2 according to the equation: IR2=(1?Xi*IR1)/2; (d) multiplying IR2 by Xi to produce a third intermediate result (IR3); and (e) adding IR3 to Xi to produce an approximation of the reciprocal square root of the number.

Abstract: An iterative mantissa calculator calculates a quotient mantissa for a divide mode or a result mantissa for a square-root mode. The calculator includes at least first and second summing devices. In the divide mode, each summing device calculates a respective estimated partial remainder W[j+1] for the next iteration, j+1, as 2*W[j]?Sj+1*D, where W[j] is the estimated partial remainder for the current iteration calculated during the prior iteration, Sj+1 is the quotient bit estimated for the next iteration, and D is the respective divisor bit. The estimated quotient bit for the next iteration is selected based on the calculated partial remainder. In the square-root mode, the first summing device calculates 2W[j]?2S[j]Sj+1, where W[j] is the estimated partial remainder and Sj+1 is the estimated result generated during the current iteration, j.