A first multiplex circuit generates a first multiplex signal obtained by time-divisionally multiplexing a first real part and a first imaginary part of a first complex number. A second multiplex circuit generates a second multiplex signal obtained by time-divisionally multiplexing a second real part and a second imaginary part of a second complex number. A multiply-subtract operation circuit performs a multiply-subtract operation of the first and second multiplex signals. A third multiplex circuit generates a third multiplex signal obtained by time-divisionally multiplexing the first and second real parts. A fourth multiplex circuit generates a fourth multiplex signal obtained by time-divisionally multiplexing the first and second imaginary parts. A multiply-accumulate operation circuit performs a multiply-accumulate operation of the third and fourth multiplex signals. A fifth multiplex circuit generates a fifth multiplex signal obtained by time-divisionally multiplexing output values of the multiply-subtract operation circuit and the multiply-accumulate operation circuit.

Provided are embodiments for a circuit comprising for performing hardware acceleration for elliptic curve cryptography (ECC). The circuit includes a code array comprising instructions for performing complex modular arithmetic; and a data array storing values corresponding to one or more complex numbers. The modular arithmetic unit includes a first multiplier and a first accumulation unit, a second multiplier and a second accumulation unit, and a third multiplier and a third accumulation unit, wherein the first, second, and third multiplier and accumulation units are cascaded and configured to perform hardware computation of complex modular operations. Also provided are embodiments of a computer program product and a method for performing the hardware acceleration of super-singular isogeny key encryption (SIKE) operations.

A fast Fourier transform (FFT) circuit of an audio processing device configured to perform an N-points FFT and including a memory circuit and a butterfly operation unit circuit is provided. The butterfly operation unit circuit reads two points input data from the memory circuit, performs a butterfly operation for the two points input data according to a twiddle factor to generate two points output data, and writes the two points output data into the memory circuit. The butterfly operation unit circuit includes a multiplier and a plurality of adders/subtractors. The multiplier sequentially multiplies real or imaginary coefficients of one of the two points input data by real or imaginary coefficients of the twiddle factor in multiple clock cycles. The multiplier performs a multiplication once in each clock cycle. The adders/subtractors perform addition/subtraction, such that the butterfly operation unit circuit generates the two points output data.

Provided are embodiments for a circuit comprising for performing hardware acceleration for elliptic curve cryptography (ECC). The circuit includes a code array comprising instructions for performing complex modular arithmetic; and a data array storing values corresponding to one or more complex numbers. The modular arithmetic unit includes a first multiplier and a first accumulation unit, a second multiplier and a second accumulation unit, and a third multiplier and a third accumulation unit, wherein the first, second, and third multiplier and accumulation units are cascaded and configured to perform hardware computation of complex modular operations. Also provided are embodiments of a computer program product and a method for performing the hardware acceleration of super-singular isogeny key encryption (SIKE) operations.

An apparatus and method for multiplying packed real and imaginary components of complex numbers are described. A processor embodiment includes: a decoder to decode a first instruction to generate a decoded instruction; a first source register to store a first plurality of packed real and imaginary data elements; a second source register to store a second plurality of packed real and imaginary data elements; and execution circuitry to execute the decoded instruction. The execution circuitry includes: multiplier circuitry to select real and imaginary data elements in the first source register and second source, multiply each selected imaginary data element in the first source register with a selected real data element in the second source register, and multiply each selected real data element in the first source register with a selected imaginary data element in the second source register to generate a plurality of imaginary products; adder circuitry to add a first subset of the plurality of imaginary products and subtract a second subset of the plurality of imaginary products to generate a first temporary result, and to add a third subset of the plurality of imaginary products and subtract a fourth subset of the plurality of imaginary products to generate a second temporary result; and accumulation circuitry to combine the first temporary result with first data from a destination register to generate a first final result, combine the second temporary result with second data from the destination register to generate a second final result, and store the first final result and second final result back in the destination register.

A system includes an integrated circuit coupled to the memory. The integrated circuit is configured to receive first and second complex numbers at one or more data inputs. A first value is determined using a first set of product arrays of a first real number multiplier. A second value is determined using a second set of product arrays of the first real number multiplier and a third set of product arrays of a second real number multiplier. A third value is determined using a fourth set of product arrays of the second real number multiplier. A real value of a first product of the first complex number times a second complex number is determined using the first value and the second value. An imaginary value of the first product is determined using the second value and the third value.

Apparatus and method to transform complex data including a processor that comprises: multiplier circuitry to multiply packed complex N-bit data elements with packed complex M-bit data elements to generate at least four real products; adder circuitry to subtract a first real product from a second real product to generate a first temporary result, subtract a third real product from a fourth real product to generate a second temporary result, add the first temporary result to a first packed N-bit data element to generate a first pre-scaled result, subtract the first temporary result from the first packed N-bit data element to generate a second pre-scaled result, add the second temporary result to a second packed N-bit data element to generate a third pre-scaled result, and subtract the second temporary result from the second packed N-bit data element to generate a fourth pre-scaled result; and scaling circuitry to scale the pre-scaled results.

An automotive radar using combinations of the techniques of alternating transmit-receive bursts of digitally frequency modulated millimeter wave carriers; sparse MIMO antenna arrays with sidelobe-suppressive coarse and fine beamforming; frequency hopping; range-walking-compensated Doppler analysis and successive, and subtractive target detection in signal strength order.

A multiplication circuit includes an addition subcircuit configured to obtain logarithmic field data a and b that correspond to A and B, and perform an addition operation on a and b to obtain c, where c includes an integral part and a fractional part, an exponentiation operation subcircuit configured to perform an exponentiation operation in which a base is 2 and an exponent is the fractional part of c, to obtain an exponentiation operation result, a shift subcircuit configured to shift the exponentiation operation result based on the integral part of c to obtain a shift result, and an output subcircuit configured to output a product of A and B based on signs of a and b and with reference to the shift result.

An apparatus and method for multiplying packed real and imaginary components of complex numbers are described. A processor embodiment includes: a decoder to decode a first instruction to generate a decoded instruction; a first source register to store a first plurality of packed real and imaginary data elements; a second source register to store a second plurality of packed real and imaginary data elements; and execution circuitry to execute the decoded instruction. The execution circuitry includes: multiplier circuitry to select real and imaginary data elements in the first source register and second source, multiply each selected imaginary data element in the first source register with a selected real data element in the second source register, and multiply each selected real data element in the first source register with a selected imaginary data element in the second source register to generate a plurality of imaginary products; adder circuitry to add a first subset of the plurality of imaginary products and subtract a second subset of the plurality of imaginary products to generate a first temporary result, and to add a third subset of the plurality of imaginary products and subtract a fourth subset of the plurality of imaginary products to generate a second temporary result; and accumulation circuitry to combine the first temporary result with first data from a destination register to generate a first final result, combine the second temporary result with second data from the destination register to generate a second final result, and store the first final result and second final result back in the destination register.