Abstract: Based on a Modified Gram-Schmidt (MGS) algorithm, QR decomposition techniques are optimized for parallel structures that provide arithmetic-logic unit (ALU) to ALU connectivity. The techniques utilize a different loop organization, but the dependent functional sequences of the algorithm are unchanged, thereby reducing likelihood of affecting error analysis and/or numerical stability. Some integrated circuit devices (e.g., FPGA) may implement hard floating-point (HFP) circuitry, such as a digital signal processing (DSP) block, distributed memories, and/or flexible internal connectivity, which can support the discussed high performance matrix arithmetic.

Abstract: Generating trial states for a variational quantum Eigenvalue solver (VQE) using a quantum computer is described. An example method includes selecting a number of samples S to capture from qubits for a particular trial state. The method further includes mapping a Hamiltonian to the qubits according the trial state. The method further includes setting up an entangler in the quantum computer, the entangler defining an entangling interaction between a subset of the qubits of the quantum computer. The method further includes reading out qubit states after post-rotations associated with Pauli terms in the target Hamiltonian, the reading out being performed for S samples. The method further includes computing an energy state using the S qubit states. The method further includes, in response to the estimated energy state not converging with an expected energy state, computing a new trial state for the VQE and iterating to compute the estimated energy using the new trial state.

Abstract: An apparatus performs interpolation/decimation in a digital circuit that receives an input signal and includes upsampling/downsampling and filtering stages. First and second paths include distinct first and second portions of the upsampling/downsampling and filtering stages. The first path consumes less quiescent state power. A selection circuit uses the first or second path and turns off the unused first or second path based on input signal spectral content or level. A mode includes applying a front-end digital/analog gain and a corresponding back-end analog/digital attenuation in conjunction with the first path being used and the second path being turned off. A cross-fader uses the first and second paths in a weighted mix manner while making a transition between using the first and second paths. The second path has higher filtering performance (e.g., superior stopband attenuation, passband ripple, transition band, e.g., via higher order or greater bit-width filtering).

Abstract: The present embodiments relate to circuitry that efficiently performs floating-point arithmetic operations and fixed-point arithmetic operations. Such circuitry may be implemented in specialized processing blocks. If desired, the specialized processing blocks may include configurable interconnect circuitry to support a variety of different use modes. For example, the specialized processing block may efficiently perform a fixed-point or floating-point addition operation or a portion thereof, a fixed-point or floating-point multiplication operation or a portion thereof, a fixed-point or floating-point multiply-add operation or a portion thereof, just to name a few. In some embodiments, two or more specialized processing blocks may be arranged in a cascade chain and perform together more complex operations such as a recursive mode dot product of two vectors of floating-point numbers or a Radix-2 Butterfly circuit, just to name a few.

Abstract: Electric charges depending on values of N+ electric signals and values of corresponding positive loads are held in first capture-and-storage circuitry. Electric charges having a size depending on values of (N?N+) electric signals and corresponding absolute values of negative loads are held in second capture-and-storage circuitry. A sum of N+ multiplied values obtained by multiplying each of the positive loads by each of the values of the N+ electric signals is calculated when a voltage held in the first capture-and-storage circuitry reaches a first threshold. A sum of (N?N+) multiplied values obtained by multiplying each of the absolute values by each of the values of the (N?N+) electric signals is calculated when a voltage held in the second capture-and-storage circuitry reaches a second threshold A sum of N multiplied values is obtained by subtracting the sum of (N?N+) multiplied values from the sum of N+ multiplied values.

Abstract: Methods, systems, and apparatus, including computer programs encoded on a computer storage medium, for a circuit configured to add multiple inputs. The circuit includes a first adder section that receives a first input and a second input and adds the inputs to generate a first sum. The circuit also includes a second adder section that receives the first and second inputs and adds the inputs to generate a second sum. An input processor of the circuit receives the first and second inputs, determines whether a relationship between the first and second inputs satisfies a set of conditions, and selects a high-power mode of the adder circuit or a low-power mode of the adder circuit using the determined relationship between the first and second inputs. The high-power mode is selected and the first and second inputs are routed to the second adder section when the relationship satisfies the set of conditions.

Abstract: A reconfigurable matrix multiplier (RMM) system/method allowing tight or loose coupling to supervisory control processor application control logic (ACL) in a system-on-a-chip (SOC) environment is disclosed. The RMM provides for C=A*B matrix multiplication operations having A-multiplier-matrix (AMM), B-multiplicand-matrix (BMM), and C-product-matrix (CPM), as well as C=A*B+D operations in which D-summation-matrix (DSM) represents the result of a previous multiplication operation or another previously defined matrix. The RMM provides for additional CPM LOAD/STORE paths allowing overlapping of compute/data transfer operations and provides for CPM data feedback to the AMM or BMM operand inputs from a previously calculated CPM result.

Abstract: Systems and methods are provided to skip multiplication operations with zeros in processing elements of the systolic array to reduce dynamic power consumption. A value of zero can be detected on an input data element entering each row of the array and respective zero indicators may be generated. These respective zero indicators may be passed to all the processing elements in the respective rows. The multiplication operation with the zero value can be skipped in each processing element based on the zero indicators, thus reducing dynamic power consumption.

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: The present disclosure is applied to a variable group calculation apparatus for calculating an undetermined variable group that simultaneously minimizes a difference value and a data value. The difference value is a difference between an added composite value, which is obtained by adding and combining the undetermined variable group and a dictionary data group, and an observation data group. The data value includes the difference value and a regularization term of the undetermined variable group. The variable group calculation apparatus of the present disclosure includes a convolution unit configured to convert the regularization term to a convolution value for an L1 norm using the undetermined variable group and a mollifier function, and a calculation unit configured to perform the calculation using the regularization term, which is converted to the convolution value by the convolution unit.

Abstract: A convolutional layer in a convolutional neural network uses a predetermined horizontal input stride and a predetermined vertical input stride that are greater than 1 while the hardware forming the convolutional layer operates using an input stride of 1. Each original weight kernel of a plurality of sets of original weight kernels is subdivided based on the predetermined horizontal and vertical input strides to form a set of a plurality of sub-kernels for each set of original weight kernels. Each of a plurality of IFMs is subdivided based on the predetermined horizontal and vertical input strides to form a plurality of sub-maps. Each sub-map is convolved by the corresponding sub-kernel for a set of original weight kernels using an input stride of 1. A convolved result of each sub-map and the corresponding sub-kernel is summed to form an output feature map.

Abstract: Methods, apparatus, systems and articles of manufacture to perform dot product calculations using sparse vectors are disclosed. An example dot product calculator includes a counter to determine a trailing binary count of a control vector, the control vector corresponding to a first result of a first logic AND operation on a first bitmap of a first sparse vector and a second bitmap of a second sparse vector. The example dot product calculator further includes a mask generator to generate a mask vector based on the trailing binary count. The example dot product calculator further includes an interface to access a first value of the first sparse vector based on a second result of a second logic AND operation on the first bitmap and the mask vector and access a second value of the second sparse vector based on a third result of a third logic AND operation on the second bitmap and the mask vector.

Abstract: An apparatus to facilitate acceleration of machine learning operations is disclosed. The apparatus comprises accelerator circuitry including a first set of processing elements to perform first computations including matrix multiplication operations, a second set of processing elements to perform second computations including sum of elements of weights and offset multiply operations and a third set of processing elements to perform third computations including sum of elements of inputs and offset multiply operations, wherein the second and third computations are performed in parallel with the first computations.

Abstract: The present embodiments relate to performing reduced-precision floating-point arithmetic operations using specialized processing blocks with higher-precision floating-point arithmetic circuitry. A specialized processing block may receive four floating-point numbers that represent two single-precision floating-point numbers, each separated into an LSB portion and an MSB portion, or four half-precision floating-point numbers. A first partial product generator may generate a first partial product of first and second input signals, while a second partial product generator may generate a second partial product of third and fourth input signals.

Abstract: A random number generator includes an entropy source comprising a first digital device arranged to apply to an input signal a first delay value to obtain a first signal and a second digital device arranged to apply to the input signal a second delay value different from the first delay value to obtain a second signal; a sampling unit configured to sample one of the first and second signals using the other signal as reference clock, thereby obtaining a sampled signal; measurement means to perform measurements of the sampled signal's delay difference with respect to the reference clock; a controller circuit arranged to monitor the measured delay difference of the sampled signal and to check the values of the measured delay difference and, once a given condition related to the values is met, to output a configuration signal.

Abstract: Embodiments of the present disclosure pertain to switch matrix circuit including a data permutation circuit. In one embodiment, the switch matrix comprises a plurality of adjacent switching blocks configured along a first axis, wherein the plurality of adjacent switching blocks each receive data and switch control settings along a second axis. The switch matrix includes a permutation circuit comprising, in each switching block, a plurality of switching stages spanning a plurality of adjacent switching blocks and at least one switching stage that does not span to adjacent switching blocks. The permutation circuit receives data in a first pattern and outputs the data in a second pattern. The data permutation performed by the switching stages is based on the particular switch control settings received in the adjacent switching blocks along the second axis.

Abstract: A device for generating a random number is suggested, the device comprising at least two shift registers, a transformation function that generates the random number based on at least one cell of each of the at least two shift registers.

Abstract: A system performs convolution operations based on an analysis of the input size. The input includes data elements and filter weights. The system includes multiple processing elements. Each processing element includes multipliers and adders, with more of the adders than the multipliers. According to at least the analysis result which indicates whether the input size matches a predetermined size, the system is operative to select a first mode or a second mode. In the first mode, a greater number of the adders than the multipliers are enabled for each processing element to multiply transformed input and to perform an inverse transformation. In the second mode, an equal number of the adders and the multipliers are enabled for each processing element to multiply-and-accumulate the input. One or more of the multipliers are shared by the first mode and the second mode.

Abstract: Some embodiments provide a program. The program receives from a client device a request specifying a plurality of variables comprising set of sources and a set of objects. The program further receives a set of values from the set of sources. Each value in the set of values specifies an object in set of objects. The program also receives a selection of a set of defined scenarios for the request and the set of values. The program further generates a set of linear programming models based on the set of defined scenarios, the request, and the set of values.

Abstract: The embodiments herein describe techniques for monitoring guard bits in multi-result vectors generated by a first arithmetic unit in a chain and using side band logic to add or subtract offset values from guard bits in a second, subsequent arithmetic unit in the chain. In this manner, the guard bits can be adjusted on the fly (e.g., without interrupting or terminating the chain) to ensure the guard bits do not overflow. The side band logic can maintain a guard bits overflow value which is then combined with the output vector from the final arithmetic unit in the chain to compensate for adjusting the guard bits at the various arithmetic units in the chain. In this manner, the chain can have any desired length.