Abstract: Computationally efficient mixed precision floating point waveform generation takes advantage of the high-speed generation of waveforms with single-precision floating point numbers while reducing the generally unacceptable loss of precision of pure single-precision floating point to generate any waveform that repeats in 2?. This approaches computes a reference phase in double precision as the modulus of the phase with 2? and then computes offsets to that value in single precision. The double precision reference phase is recomputed as needed depending on how quickly the phase grows and how large a machine epsilon is desired.

Abstract: A multiply-accumulate calculation device, a multiply-accumulate calculation method, and a system for efficiently performing a multiply-accumulate calculation are provided. The multiply-accumulate operation device includes a plurality of memory blocks that store a plurality of multiplied elements and performs a multiply-accumulate operation on input data. Each of memory blocks includes stores one bit value of the same bit digit of a plurality of multiplied elements. An input data generation unit generates input data by extracting data of a same bit digit from the plurality of multiplication elements. A control unit that accumulates and adds value of the multiply-accumulate operation result, and a data memory that stores the accumulated addition value as a multiplication element of the next multiply-accumulate operation.

Abstract: Examples of techniques for hexadecimal exponent alignment for a binary floating point unit (BFU) of a computer processor are described herein. An aspect includes receiving, by the BFU, a first operand comprising a first fraction and a first exponent, and a second operand comprising a second fraction and a second exponent. Another aspect includes, based on the first operand and the second operand being in a first floating point format, multiplying each of the first exponent and the second exponent by a factor corresponding to a number of bits in a digit in the first floating point format.

Abstract: Disclosed embodiments relate to performing floating-point addition with selected rounding. In one example, a processor includes circuitry to decode and execute an instruction specifying locations of first and second floating-point (FP) sources, and an opcode indicating the processor is to: bring the FP sources into alignment by shifting a mantissa of the smaller source FP operand to the right by a difference between their exponents, generating rounding controls based on any bits that escape; simultaneously generate a sum of the FP sources and of the FP sources plus one, the sums having a fuzzy-Jbit format having an additional Jbit into which a carry-out, if any, select one of the sums based on the rounding controls, and generate a result comprising a mantissa-wide number of most-significant bits of the selected sum, starting with the most significant non-zero Jbit.

Abstract: A hardware module comprising at least one of: one or more field programmable gate arrays and one or more application specific integrated circuits configured to: receive a number in floating-point representation at a first precision level, the number comprising an exponent and a first mantissa; apply a first random number to the first mantissa to generate a first carry; truncate the first mantissa to a level specified by a second precision level; add the first carry to the least significant bit of the mantissa truncated to the level specified by the second precision level to form a mantissa for the number in floating-point representation at the second precision level.

Abstract: Low precision computers can be efficient at finding possible answers to search problems. However, sometimes the task demands finding better answers than a single low precision search. A computer system augments low precision computing with a small amount of high precision computing, to improve search quality with little additional computing.

Abstract: A method and apparatus for handling overflow conditions resulting from arithmetic operations involving floating point numbers. An indication is stored as part of a thread's context indicating one of two possible modes for handling overflow conditions. In a first mode, a result of an arithmetic operation is set to the limit representable in the floating point format. In a second mode, a result of an arithmetic operation is set to a NaN.

Abstract: Apparatus for evaluating a mathematical function for a received input value includes a polynomial block configured to identify a domain interval containing the received input value over which the mathematical function can be evaluated, the mathematical function over the identified interval being approximated by a polynomial function; and evaluate the polynomial function for the received input value using a set of one or more stored values representing the polynomial function over the identified interval to calculate a first evaluation of the mathematical function for the received input value; and a CORDIC block for performing a CORDIC algorithm, configured to initialise the CORDIC algorithm using the first evaluation of the mathematical function for the received input value calculated by the polynomial block; and implement the CORDIC algorithm to calculate a refined evaluation of the mathematical function for the received input value.

Abstract: Some embodiments provide a neural network inference circuit (NNIC) for executing a neural network that includes multiple computation nodes, that include dot products, at multiple layers. The NNIC includes multiple dot product core circuits and a bus, including one or more aggregation circuits, that connects the core circuits. Each core circuit includes (i) a set of memories for storing multiple input values and multiple weight values and (ii) a set of adder tree circuits for computing dot products of sets of input values and sets of weight values stored in the set of memories. For a particular computation node, at least two of the core circuits compute partial dot products using input values and weight values stored in the memories of the respective core circuits and at least one of the aggregation circuits of the bus combines the partial dot products to compute the dot product for the computation node.

Abstract: A computer processing system for reducing a processing footprint in cryptosystems utilizing quadratic extension field arithmetic such as pairing-based cryptography, elliptic curve cryptography, code-based cryptography and post-quantum elliptic curve cryptography that includes at least one computer processor having a register file with three processor registers operably configured to implement quadratic extension field arithmetic equations in a finite field of Fp2 and a multiplexer operably configured to selectively shift from each of the three processor registers in sequential order to generate modular additional results and modular multiplication results from the three processor registers.

Abstract: In some examples, memristive dot product circuit based floating point computations may include ascertaining a matrix and a vector including floating point values, and partitioning the matrix into a plurality of sub-matrices according to a size of a plurality of memristive dot product circuits. For each sub-matrix of the plurality of sub-matrices, the floating point values may be converted to fixed point values. Based on the conversion and selected ones of the plurality of memristive dot product circuits, a dot product operation may be performed with respect to a sub-matrix and the vector. Each ones of the plurality of memristive dot product circuits may include rows including word line voltages corresponding to the floating point values of the vector, conductances corresponding to the floating point values of an associated sub-matrix, and columns that include bitline currents corresponding to dot products of the voltages and conductances.

Abstract: According to one embodiment, a processing device includes: a first circuit configured to execute first processing using a first matrix to first data of a size of 5×5 within input data to generate second data; a second circuit configured to execute second processing using a second matrix to third data of a size of 3×3 to generate fourth data; a third circuit configured to execute a product-sum operation on the second data and the fourth data; and a fourth circuit configured to execute third processing using a third matrix on a result of the product-sum operation on the second data and the fourth data to obtain a first value corresponding to a result of a product-sum operation on the first data and the third data.

Abstract: According to an aspect of an embodiment, operations may include displaying a electronic user interface that includes a plurality of user-selectable options corresponding to taxonomy information for a plurality of optimization problems. The operations may further include receiving a first user input selecting a first template for a specific optimization problem of the plurality of optimization problems. The first user input may include a selection of at least one user-selectable option of the plurality of user-selectable options. The operations may further include receiving a second user input via the selected first template for the specific optimization problem and providing a call to the optimization solver machine to generate a solution for the specific optimization problem based on the received second user input. The second user input may include input data for a plurality of parameters of the specific optimization problem, specified in the selected first template.

Abstract: Provided herein resistive random access memory matrix multiplication structures and methods. A non-volatile memory logic system can comprise a bit line and at a set of wordlines. Also included can be a set of resistive switching memory cells at respective intersections between the bit line and the set of wordlines. The set of resistive switching memory cells are programmed with a value of an input data bit of a first data matrix and receive respective currents on the set of wordlines. The respective currents comprise respective values of an activation data bit of a second data matrix. A resulting value based on a matrix multiplication corresponds to an output value of the bit line.

Abstract: This disclosure relates matrix operation acceleration for different matrix sparsity patterns. A matrix operation accelerator may be designed to perform matrix operations more efficiently for a first matrix sparsity pattern rather than for a second matrix sparsity pattern. A matrix with the second sparsity pattern may be converted to a matrix with the first sparsity pattern and provided to the matrix operation accelerator. By rearranging the rows and/or columns of the matrix, the sparsity pattern of the matrix may be converted to a sparsity pattern that is suitable for computation with the matrix operation accelerator.

Abstract: The present invention extends to methods, systems, and computing system program products for elimination of rounding error accumulation in iterative calculations for Big Data or streamed data. Embodiments of the invention include iteratively calculating a function for a primary computation window of a pre-defined size while incrementally calculating the function for one or more backup computation windows started at different time points and whenever one of the backup computation windows reaches a size of the pre-define size, swapping the primary computation window and the backup computation window. The result(s) of the function is/are always generated by the iterative calculation performed for the primary computation window. Elimination of rounding error accumulation enables a computing system to steadily and smoothly run iterative calculations for unlimited number of iterations without rounding error accumulation.

Abstract: A floating-point adding circuitry is provided to add first and second floating-point operands each comprising a significand and an exponent. Alignment shift circuitry shifts a smaller-operand significand to align with a larger-operand significand, based on an exponent difference. Incrementing circuitry generates alternative versions of the larger-operand significand, each version based on a different rounding increment applied to the larger-operand significand. A number of candidate sum values are generated by adding circuits, each candidate sum value representing a sum of the shifted smaller-operand significand and a respective one of the alternative versions of the larger-operand significand. One of the candidate sum values is selected as a rounded result of adding the first and second floating-point operands. This allows floating-point addition to be performed faster as the latency of the rounding increment can be hidden in the shadow of the latency of the alignment shift.

Abstract: A system and method predict whether or not a plant is abnormal and perform an accurate prediction even if a modeling is executed in a state where the understanding for a target to abnormality determination is low, or when a person unfamiliar with system designs a prediction model. The system includes a correlation coefficient calculation unit for calculating a correlation coefficient for each of two tags among a plurality of tags; a relevant tag determination unit for determining a relevant tag for each tag of the plurality of tags by comparing the correlation coefficient with a reference value; and an independent tag determination unit for determining one or more among the plurality of tags as an independent tag based on the relevant tag. The relevant tag determination unit includes primary and second tag extraction sections for extracting primary and second tags for each tag of the plurality of tags.

Abstract: A circuit and method for calculating a non-linear function of floating-point numbers using hierarchical look-up tables are provided. The look-up tables are programmable to hold non-linear ranges of values for any of a variety of non-linear functions. The circuit includes computation modules in respective stages of a high-throughput computation pipeline. A first computation module in a first stage receives one or more floating-point numbers and, for each floating-point number, selects a first entry from a first look-up table based on the floating-point number. The first computation module then calculates and outputs a table index and a variable based on the first floating-point number and the first entry. The second compute module in a second stage, selects a second entry from a second look-up table based on the table index, and calculates and outputs an approximate value for the non-linear function using the variable and the second entry.

Abstract: A processor sequences the application of submatrices at a matrix multiplier to reduce the number of input changes at an input register of the matrix multiplier. The matrix multiplier is configured to perform a matrix multiplication for a relatively small matrix. To multiply two larger matrices the GPU decomposes the larger matrices into smaller submatrices and stores the submatrices at input registers of the matrix multiplier in a sequence, thereby calculating each column of a result matrix. The GPU sequences the storage of the submatrices at the input registers to maintain input data at one of the input registers over multiple calculation cycles of the matrix multiplier thereby reducing power consumption at the GPU.