A filter device includes: delay units serially connected to delay an input signal and output a delayed signal; multiplication units multiplying the delayed signal by a filter coefficient based on a predetermined value and a multiplying factor adjustment value; a coefficient adjustment unit that, when a multiplication result obtained by multiplying the predetermined value by the multiplying factor adjustment value exceeds a maximum value of a filter-coefficient representation range, divides the multiplication result exceeding the maximum value by the maximum value, and outputs a quotient of division as a coefficient adjustment value; a signal conversion unit outputting a signal obtained by adding after-filter-coefficient-multiplication signals outputted by the multiplication units and an adjusted signal obtained by adjusting a corresponding delayed signal using the coefficient adjustment value; and a division unit generating an output signal by dividing the signal outputted by the signal conversion unit by the multiplying factor adjustment value.

A filter device includes: delay units serially connected to delay an input signal and output a delayed signal; multiplication units multiplying the delayed signal by a filter coefficient based on a predetermined value and a multiplying factor adjustment value; a coefficient adjustment unit that, when a multiplication result obtained by multiplying the predetermined value by the multiplying factor adjustment value exceeds a maximum value of a filter-coefficient representation range, divides the multiplication result exceeding the maximum value by the maximum value, and outputs a quotient of division as a coefficient adjustment value; a signal conversion unit outputting a signal obtained by adding after-filter-coefficient-multiplication signals outputted by the multiplication units and an adjusted signal obtained by adjusting a corresponding delayed signal using the coefficient adjustment value; and a division unit generating an output signal by dividing the signal outputted by the signal conversion unit by the multiplying factor adjustment value.

A computer implemented method for analyzing and verifying software for safety and security. A software program comprising a sequence of program statements to be executed is provided. A compact representation of the program is computed, and the subset of program statements that are relevant to a property of the software to be verified is identified. A homomorphism that maps non-relevant program statements to an identity is computed, and the property is verified using the homomorphism.

A computer implemented method for analyzing and verifying software for safety and security. A software program comprising a sequence of program statements to be executed is provided. A compact representation of the program is computed, and the subset of program statements that are relevant to a property of the software to be verified is identified. A homomorphism that maps non-relevant program statements to an identity is computed, and the property is verified using the homomorphism.

A MAC operating device comprising a plurality of operation circuits respectively including an operation capacitor and a plurality of switches; and a division capacitor, wherein one end of the operation capacitor is respectively connected to a first operation switch connected to an input terminal and a first reset switch connected to a ground terminal, and the other end of the operation capacitor is connected to both a second operation switch connected to a division capacitor and a second reset switch connected to the ground terminal is provided.

Techniques related to a low-power, low-memory multiply and accumulate (MAC) unit are described. In an example, the MAC unit performs a MAC operation that represents a multiplication of numbers. At least the bit representation of one number is compressed based on a quantization and a clustering of quantization values, whereby index bits are used instead of the actual bit representation. The index bits are loaded in an index buffer and a bit representation of another number is loaded in an input buffer. The index bits are used in a lookup to determine whether the corresponding bit representation and shift operations are applied to the input buffer based on this bit representation, followed by accumulation operations.

Systems, apparatuses, and methods related to arithmetic operations in memory are described. The arithmetic operations may be performed using bit strings and within a memory array without transferring the bit strings to circuitry external to the memory array. For instance, sensing circuitry that can include a sense amplifier and a compute component can be coupled to a memory array. A controller can be coupled to the sensing circuitry and can be configured to cause one or more bit strings to be transferred from the memory array to the sensing circuitry. In addition to the arithmetic operations, the sensing circuitry can also perform a logical operation using the one or more bit strings.

Systems, apparatuses, and methods related to arithmetic operations in memory are described. The arithmetic operations may be performed using bit strings and within a memory array without transferring the bit strings to circuitry external to the memory array. For instance, sensing circuitry that can include a sense amplifier and a compute component can be coupled to a memory array. A controller can be coupled to the sensing circuitry and can be configured to cause one or more bit strings to be transferred from the memory array to the sensing circuitry. In addition to the arithmetic operations, the sensing circuitry can also perform a logical operation using the one or more bit strings.

Methods and systems for performing hardware computations of mathematical functions are provided. In one example, a system comprises a mapping table that maps each base value of a plurality of base values to parameters related to a mathematical function; a selection module configured to select, based on an input value, a first base value and first parameters mapped to the first base value in the mapping table; and arithmetic circuits configured to: receive, from the mapping table, the first base value and the first plurality of parameters; and compute, based on a relationship between the input value and the first base value, and based on the first parameters, an estimated output value of the mathematical function for the input value.

Various embodiments of the disclosure relate to an accelerated mathematical engine. In certain embodiments, the accelerated mathematical engine is applied to image processing such that convolution of an image is accelerated by using a two-dimensional matrix processor comprising sub-circuits that include an ALU, output register and shadow register. This architecture supports a clocked, two-dimensional architecture in which image data and weights are multiplied in a synchronized manner to allow a large number of mathematical operations to be performed in parallel.