Techniques related to triple and quad coloring of shape layouts are provided. A computer-implemented method comprises coloring, by a system operatively coupled to a processor, a shape layout with a plurality of colors in accordance with a defined design rule based on a determination that a first defined shape within the shape layout satisfies a layout specification and a second defined shape within the shape layout satisfies a defined rule.

According to an embodiment, a waveform generator includes a phase accumulator configured to generate a digital phase signal representing a phase angle, and a phase-to-amplitude converter configured to receive the digital phase signal as a phase input, and generate sine and cosine waveform values as digital amplitude signals, wherein the phase-to-amplitude converter does not include a look-up table.

According to an embodiment, a waveform generator includes a phase accumulator configured to generate a digital phase signal representing a phase angle, and a phase-to-amplitude converter configured to receive the digital phase signal as a phase input, and generate sine and cosine waveform values as digital amplitude signals, wherein the phase-to-amplitude converter does not include a look-up table.

A numerical control device wherein a sinusoidal signal generated by a sine wave generation part is input by a control loop excitation part to a control loop of the control object, the input signal input to the control loop and the output signal from the control object are sampled by the data acquisition part periodically, and the sampling data is used by the frequency characteristic calculation part to calculate the frequency characteristic of the control loop to control the control object, wherein the frequency characteristic calculation part uses data obtained by inputting a sinusoidal signal obtained by shifting an initial phase of the sinusoidal signal by a phase shift part provided at a sine wave generation part by exactly a certain amount to the control loop a plurality of times to calculate the frequency characteristic of the control loop to thereby improve the measurement precision regardless of the sampling frequency.

Examples described herein relate to instructions to request performance of tanh and sigmoid instructions. For example, a compiler can generate native tanh instructions to perform tanh. In some examples, a tanh function can be compiled into instructions that include an instruction to perform either tanh(input) or tanh(input)/input depending on a value of the input to generate an intermediate output; an instruction to cause a performance of generation of scale factor based on the input; and an instruction to cause performance of a multiplication operation on the intermediate result with the scale factor. For example, a sigmoid function can be compiled to cause a math pipeline to perform a range check and performs operations based on a range.

Implementations of the present specification provide methods and apparatuses for training a behavior prediction model. In the implementations of the present specification, a sequence (a behavior sequence of a user) that includes multiple behavior types is split according to behavior types to obtain multiple single-behavior sequences. Time coding is performed on all time points of each of the multiple single-behavior sequences, to obtain multiple single-behavior time sequences corresponding to the multiple single-behavior sequences. Each single-behavior time sequence in the multiple single-behavior time sequences is modeled by using a behavior prediction model, and attention is paid to all time points of each single-behavior time sequence in the multiple single-behavior time sequences, so as to obtain a distribution situation of behaviors corresponding to the multiple single-behavior time sequences in terms of time as predicted by the behavior prediction model. The behavior prediction model is trained based on a loss value between the distribution situation of the behaviors corresponding to the multiple single-behavior time sequences in terms of time and the multiple single-behavior time sequences.

Apparatuses, systems, and methods for sine wave generation based on a flexible pulse width modulation (PWM) technique. An exemplary apparatus may comprise a sine wave generator circuitry and a pulse width modulation timer circuitry coupled to the sine wave generator circuitry. The sine wave generator circuitry may comprise a phase accumulator circuitry and a phase to amplitude conversion circuitry coupled to the phase accumulator circuitry. The phase accumulator circuitry may be configured to receive a digital input value and output phase values. The phase to amplitude conversion circuitry may be configured to receive the phase values and output digital sine values. The pulse width modulation timer circuitry may be configured to receive the digital sine values and output at least one pulse width modulation signal for generation of an analog carrier wave signal. A frequency of the analog carrier wave signal may be based on the digital input value.