The present invention discloses an apparatus and a method for performing a variety of transcendental function operations. The apparatus comprises a pre-processing unit group, a core unit and a post-processing unit group, wherein the pre-processing unit group is configured to transform an externally input independent variable a into x, y coordinates, an angle z, and other information k, and determine an operation mode to be used by the core unit; the core unit is configured to perform trigonometric or hyperbolic transformation on the x, y coordinates and the angle z, obtain transformed x, y coordinates and angle z, and output them to the post-processing unit group; and the post-processing unit group is configured to transform the x, y coordinates and the angle z input by the core unit according to the other information k and a function f input by the pre-processing unit group to obtain an output result c. The present invention solves the problems of excessive overheads in the general-purpose processor manner and poor precision in the pure linear approximation manner, and efficiently strengthens the support for various transcendental function operations.

A system and an accelerator circuit including a register file comprising instruction registers to store a trigonometric calculation instruction for evaluating a trigonometric function, and data registers comprising a first data register to store a floating-point input value associated with the trigonometric calculation instruction. The accelerator circuit further includes a determination circuit to identify the trigonometric calculation function and the floating-point input value associated with the trigonometric calculation instruction and determine whether the floating-point input value is in a small value range, and an approximation circuit to responsive to determining that the floating-point input value is in the small value, receive the floating-point input value and calculate an approximation of the trigonometric function with respect to the input value.

Aspects for generating a dot product for two vectors in neural network are described herein. The aspects may include a controller unit configured to receive a transcendental function instruction that includes an address of a vector and an operation code that identifies a transcendental function. The aspects may further include a CORDIC processor configured to receive the vector that includes one or more elements based on the address of the vector in response to the transcendental function instruction. The CORDIC processor may be further configured to apply the transcendental function to each element of the vector to generate an output vector.

Processor architectures and associated methods provide interruptible, instruction-based trigonometric function computation based on CORDIC iterations, receiving and outputting floating-point values (e.g., 64-bit). The architectures and methods can provide multiple CORDIC-like iterations in as little as a single CPU processing cycle to provide an overall faster execution of trigonometric operations while having zero additional overhead for service of time-critical interrupts. Post interrupt service, a CORDIC operation can be resumed from where it was interrupted.

A reduced COordinate Rotation DIgital Computer (CORDIC) cell in a parallel CORDIC has an xy-path from x and y inputs to x and y outputs, and a z-path from a z-input to a z-output. Bit-shifts in the xy-path are hardwired. The z-path has a shortened adder/subtractor with a built-in or hardwired fixed parameter. Input bits from the z-input are split into most significant and least significant bits. The number of most significant bits equals the shortened adder/subtractor width. The most significant bits are input to the non-inverting inputs of the adder/subtractor for calculating the most significant z-output bits. The least significant bits are connected directly (or via buffers) from the z-input to the z-output.

A method may generate a demodulated sine component for a sequence of samples of a servo burst window of a position error signal using a sine weight look up table and generate a demodulated cosine component for the sequence of samples of the servo burst window of the position error signal using a cosine weight look up table. The sine weight and the cosine weight look up tables may have indexes representing a phase range. The method may generate a demodulated phase component signal and a demodulated amplitude component signal for the sequence of samples of the servo burst window of the position error signal based on the demodulated sine component and the demodulated cosine component using a Coordinate Rotation Digital Computer at least in part by iteratively rotating a vector based on the demodulated sine component and the demodulated cosine component and summing angular changes in the vector.

A phase shifter controller arranged to generate phase shift control signals for at least one phase shifter. The phase shifter controller is arranged to receive a first phase value .sub.1, receive a second phase value .sub.2, and output phase shift control signals. The phase shifter controller comprises a digital synthesizer arranged to compute a first digital phase shift control value based on the received first phase value .sub.1, and compute a second digital phase shift control value based on the received second phase value .sub.2. The phase shifter controller further comprises digital to analogue converters arranged to generate the phase shift control signals based on the derived first and second digital phase shift control values.

Coordinate descent is applied to recover a signal-of-interest from only magnitude information. In doing so, a single unknown value is solved at each iteration, while all other variables are held constant. As a result, only minimization of a univariate quartic polynomial is required, which is efficiently achieved by finding the closed-form roots of a cubic polynomial. Cyclic, randomized, and/or a greedy coordinate descent technique can be used. Each coordinate descent technique globally converges to a stationary point of the nonconvex problem, and specifically, the randomized coordinate descent technique locally converges to the global minimum and attains exact recovery of the signal-of-interest at a geometric rate with high probability when the sample size is sufficiently large. The cyclic and randomized coordinate descent techniques can also be modified via minimization of the l.sub.1-regularized quartic polynomial for phase retrieval of sparse signals-of-interest, i.e., those signals with only a few nonzero elements.

An arithmetic apparatus comprises a plurality of cascade-connected arithmetic units. Each of the plurality of arithmetic units comprises: a calculator configured to operate in one of a rotation mode of performing a rotation calculation, and a vectoring mode of calculating a rotation angle; and a holding unit configured to hold rotational direction information output from the calculator in the vectoring mode. In addition, when operating in the rotation mode, the calculator performs the rotation calculation on data input from an arithmetic unit in a preceding stage, based on the rotational direction information held in the holding unit.

A method and system for computing the phase shift or the amplitude of an electromagnetic three-phase system. The method comprises the following steps of: detecting vector values corresponding to an electromagnetic quantity by three sensors, the three sensors delivering signals that are offset from each other substantially by 0, 120 and 240; computing changed vector values by logically adjusting one of the detected vector values to a phase of 0; and iteratively computing the phase shift of the three-phase system using the changed vector values.