Apparatus for evaluating a mathematical function for a received input value includes a polynomial block configured to identify a domain interval containing the received input value over which the mathematical function can be evaluated, the mathematical function over the identified interval being approximated by a polynomial function; and evaluate the polynomial function for the received input value using a set of one or more stored values representing the polynomial function over the identified interval to calculate a first evaluation of the mathematical function for the received input value; and a CORDIC block for performing a CORDIC algorithm, configured to initialise the CORDIC algorithm using the first evaluation of the mathematical function for the received input value calculated by the polynomial block; and implement the CORDIC algorithm to calculate a refined evaluation of the mathematical function for the received input value.

In described examples, an apparatus is arranged to generate a linear term, a quadratic term, and a constant term of a transcendental function with, respectively, a first circuit, a second circuit, and a third circuit in response to least significant bits of an input operand and in response to, respectively, a first, a second, and a third table value that is retrieved in response to, respectively, a first, a second, and a third index generated in response to most significant bits of the input operand. The third circuit is further arranged to generate a mantissa of an output operand in response to a sum of the linear term, the quadratic term, and the constant term.

In described examples, an apparatus is arranged to generate a linear term, a quadratic term, and a constant term of a transcendental function with, respectively, a first circuit, a second circuit, and a third circuit in response to least significant bits of an input operand and in response to, respectively, a first, a second, and a third table value that is retrieved in response to, respectively, a first, a second, and a third index generated in response to most significant bits of the input operand. The third circuit is further arranged to generate a mantissa of an output operand in response to a sum of the linear term, the quadratic term, and the constant term.

In one example, a method comprises: receiving input codes, wherein the input codes represent a computational dataflow graph; traversing the computational dataflow graph to identify single-entry-single-exit (SESE) subgraphs of the computational dataflow graph, wherein each SESE subgraph has a sequence of nodes comprising a root node and a child node and representing a sequence of element-wise operators, wherein the root node receives a single input tensor, and wherein the child node outputs a single output tensor; determining a merged operator for each SESE subgraph; and generating executable instructions for the computational dataflow graph to be executed by a hardware accelerator having a first execution unit and a second execution unit, wherein the executable instructions comprise first executable instructions for the merged operators targeted at the first execution unit, and second executable instructions for other operators of the computational dataflow graph targeted at the second execution unit.

In one example, a method comprises: receiving input codes, wherein the input codes represent a computational dataflow graph; traversing the computational dataflow graph to identify single-entry-single-exit (SESE) subgraphs of the computational dataflow graph, wherein each SESE subgraph has a sequence of nodes comprising a root node and a child node and representing a sequence of element-wise operators, wherein the root node receives a single input tensor, and wherein the child node outputs a single output tensor; determining a merged operator for each SESE subgraph; and generating executable instructions for the computational dataflow graph to be executed by a hardware accelerator having a first execution unit and a second execution unit, wherein the executable instructions comprise first executable instructions for the merged operators targeted at the first execution unit, and second executable instructions for other operators of the computational dataflow graph targeted at the second execution unit.

A first multiplier multiplies a first input with a first coefficient and a first adder sums an output of the first multiplier and a second input to generate a first output. A second multiplier multiplies a third input with a second coefficient, a third multiplier multiplies a fourth input with a third coefficient, and a second adder sums outputs of the second and third multipliers to generate a second output. The second and third inputs are derived from the first output and the first and fourth inputs are derived from the second output. The first and second outputs generate digital values for first and second digital sinusoids, respectively.

A first multiplier multiplies a first input with a first coefficient and a first adder sums an output of the first multiplier and a second input to generate a first output. A second multiplier multiplies a third input with a second coefficient, a third multiplier multiplies a fourth input with a third coefficient, and a second adder sums outputs of the second and third multipliers to generate a second output. The second and third inputs are derived from the first output and the first and fourth inputs are derived from the second output. The first and second outputs generate digital values for first and second digital sinusoids, respectively.

According to one embodiment, provided is a chip recognition system that recognizes a chip on a gaming table in an amusement place having the gaming table, the chip recognition system including: a game recording apparatus that records, as an image, a state of chips stacked on the gaming table, using a camera; an image analysis apparatus that performs an image analysis on the recorded image of the state of chips; a plurality of chip determination apparatuses including at least a first artificial intelligence apparatus that determines a number of the chips stacked, using an image analysis result obtained by the image analysis apparatus; and a second artificial intelligence apparatus that decides a correct number of the chips stacked, when the plurality of chip determination apparatuses obtain different determination results for the number of the chips stacked.

According to one embodiment, provided is a chip recognition system that recognizes a chip on a gaming table in an amusement place having the gaming table, the chip recognition system including: a game recording apparatus that records, as an image, a state of chips stacked on the gaming table, using a camera; an image analysis apparatus that performs an image analysis on the recorded image of the state of chips; a plurality of chip determination apparatuses including at least a first artificial intelligence apparatus that determines a number of the chips stacked, using an image analysis result obtained by the image analysis apparatus; and a second artificial intelligence apparatus that decides a correct number of the chips stacked, when the plurality of chip determination apparatuses obtain different determination results for the number of the chips stacked.

A finite rate of innovation (FRI) communications system includes a reference signal generator, an FRI modulator configured to apply an FRI kernel and encode information onto the reference signal, and a transmitter configured to transmit the encoded signal. The FRI kernel is one of a sinc function kernel or a Gaussian kernel. A receiver unit is configured to receive an encoded signal, convert the encoded signal into a digital signal, and demodulate and recover information from finite rate of innovation parameters in the digital signal.