A system and method which allows the basic checkpoint-reverse-mode AD strategy (of recursively decomposing the computation to reduce storage requirements of reverse-mode AD) to be applied to arbitrary programs: not just programs consisting of loops, but programs with arbitrarily complex control flow. The method comprises (a) transforming the program into a formalism that allows convenient manipulation by formal tools, and (b) introducing a set of operators to allow computations to be decomposed by running them for a given period of time then pausing them, while treating the paused program as a value subject to manipulation.

A system and method which allows the basic checkpoint-reverse-mode AD strategy (of recursively decomposing the computation to reduce storage requirements of reverse-mode AD) to be applied to arbitrary programs: not just programs consisting of loops, but programs with arbitrarily complex control flow. The method comprises (a) transforming the program into a formalism that allows convenient manipulation by formal tools, and (b) introducing a set of operators to allow computations to be decomposed by running them for a given period of time then pausing them, while treating the paused program as a value subject to manipulation.

An audio amplifier system includes a delta-sigma modulator configured to receive an m-bit digital audio input signal and to generate a pulse density modulated signal based on the m-bit digital audio input signal. An analog power stage is coupled to the delta-sigma modulator to receive the pulse density modulated signal and amplify the pulse density modulated signal to generate an amplified pulse density modulated signal. A feedback circuit is coupled to the delta-sigma modulator and the analog power stage. The feedback circuit is configured to receive the amplified pulse density modulated signal and the pulse density modulated signal and to determine a digital error signal representative of a difference between the amplified pulse density modulated signal and the pulse density modulated signal. The feedback circuit is further configured to provide the digital error signal to the delta-sigma modulator for applying the digital error signal to a representation of the m-bit digital audio input signal.

An integrated circuit including a data architecture including N adders and N multipliers configured to receive operands. The data architecture receives instructions for selecting a data flow between the N multipliers and the N adders of the data architecture. The selected data flow includes the options: (1) a first data flow using the N multipliers and the N adders to provide a multiply-accumulate mode and (2) a second data flow to provide a multiply-reduce mode.

Systems, apparatuses, and methods related to bit string conversion are described. A memory resource and/or logic circuitry may be used in performance of bit string conversion operations. The logic circuitry can perform operations on bit strings, such as universal number and/or posit bit strings, to alter a level of precision (e.g., a dynamic range, resolution, etc.) of the bit strings. For instance, the memory resource can receive data comprising a bit string having a first quantity of bits that correspond to a first level of precision. The logic circuitry can alter the first quantity of bits to a second quantity of bits that correspond to a second level of precision.

Systems, apparatuses, and methods related to bit string conversion are described. A memory resource and/or logic circuitry may be used in performance of bit string conversion operations. The logic circuitry can perform operations on bit strings, such as universal number and/or posit bit strings, to alter a level of precision (e.g., a dynamic range, resolution, etc.) of the bit strings. For instance, the memory resource can receive data comprising a bit string having a first quantity of bits that correspond to a first level of precision. The logic circuitry can alter the first quantity of bits to a second quantity of bits that correspond to a second level of precision.

An exemplary method includes solving on a computing system an optimal power flow formulation for a plurality of generators in a power system. The solving includes computing using multi-threaded parallelism a plurality of constraints for the formulation, computing using multi-threaded parallelism a plurality of Jacobian functions of the constraints, and computing using multi-threaded parallelism a Hessian of Lagrangian functions. The method further includes outputting results of the solving, wherein the results comprise values of generation levels for the plurality of generators. Apparatus and program products are also disclosed.

An exemplary method includes solving on a computing system an optimal power flow formulation for a plurality of generators in a power system. The solving includes computing using multi-threaded parallelism a plurality of constraints for the formulation, computing using multi-threaded parallelism a plurality of Jacobian functions of the constraints, and computing using multi-threaded parallelism a Hessian of Lagrangian functions. The method further includes outputting results of the solving, wherein the results comprise values of generation levels for the plurality of generators. Apparatus and program products are also disclosed.

Performing processing using hardware counters in a computer system includes storing, in association with greatest common divisor (GCD) processing of the system, a first variable in a first redundant binary representation and a second variable in a second redundant binary representation. Each such redundant binary representation includes a respective sum term and a respective carry term, and a numerical value being represented by a redundant binary representation is equal to a sum of the sum and carry terms of the redundant binary representation. The process performs redundant arithmetic operations of the GCD processing on the first variable and second variables using hardware counter(s), of the computer system, that take input values in redundant binary representation form and provide output values in redundant binary representation form. The process uses output of the redundant arithmetic operations of the GCD processing to obtain an output GCD of integer inputs to the GCD processing.

A computer-implemented method, computer program product, and system is provided for creating calculated metrics. In an implementation, a method may include providing a user interface including a calculator with a plurality of buttons. The method may also include receiving, via the user interface, a selection of at least one stored metric and a selection of at least one operation, resulting in a new metric. The method may further include storing the new metric with a new metric name.