A communication system includes: a transmitter including: an arithmetic decoder configured to generate an output symbol based on input bits and a symbol frequency table that sets frequencies of excluded symbols to 0 and frequencies of allowed symbols to non-zero values, the transmitter being configured to iteratively generate a sequence of restricted packets and an ending state, the sequence of restricted packets excluding instances of the one or more excluded symbols and to transmit the sequence of restricted packets and the ending state on a channel; and a receiver including: an arithmetic encoder configured to compute an output state based on an input state, an input symbol, and the symbol frequency table, the receiver being configured to: supply an ending state received from the channel and the restricted packets to the arithmetic encoder to iteratively generate a final state, and recover a bit sequence from the final state.

Certain aspects provide methods and apparatus for multiplication of digital signals. In accordance with certain aspects, a multiplication circuit may be used to multiply a portion of a first digital input signal with a portion of a second digital input signal via a first multiplier circuit to generate a first multiplication signal, and multiply another portion of the first digital input signal with another portion of the second digital input signal via a second multiplier circuit to generate a second multiplication signal. A third multiplier circuit and multiple adder circuits may be used to generate an output of the multiplication circuit based on the first and second multiplication signals.

Approaches for logic compaction include inputting an optimization directive that specifies one of area optimization or speed optimization to a synthesis tool executing on a computer processor. The synthesis tool identifies a multiplier and/or an adder specified in a circuit design and synthesizing the multiplier into logic having LUT-to-LUT connections between LUTs on separate slices of a programmable integrated circuit (IC) in response to the optimization directive specifying speed optimization. The synthesis tool synthesizes the multiplier and/or adder into logic having LUT-carry connections between LUTs and carry logic within a single slice of the programmable IC in response to the optimization directive specifying area optimization. The method includes implementing a circuit on the programmable IC from the logic having LUT-carry connections in response to the optimization directive specifying area optimization.

A multiplier is configured to implement multiplication of a first value of M bits and a second value of N bits, and includes P groups of encoders and W layers of inversion compressors. Each group include N encoders and are configured to encode a part of bits in the second value, and a group selection signal and a symbol control input signal corresponding to the each group. The group selection signal and the symbol control input signal are generated based on a part of bits in the first value, and the P groups of encoders perform encoding to obtain P partial products. The W layers of inversion compressors are configured to compress the P partial products.

Certain aspects provide methods and apparatus for multiplication of digital signals. In accordance with certain aspects, a multiplication circuit may be used to multiply a portion of a first digital input signal with a portion of a second digital input signal via a first multiplier circuit to generate a first multiplication signal, and multiply another portion of the first digital input signal with another portion of the second digital input signal via a second multiplier circuit to generate a second multiplication signal. A third multiplier circuit and multiple adder circuits may be used to generate an output of the multiplication circuit based on the first and second multiplication signals.

According to the embodiments, a semiconductor device includes: an adder configured to generate positive multiple data of the multiplicand which is used for a plurality of the multiplication in plurality and does not include a value of 2.sup.n (n is a positive integer) of the multiplicand; a Wallace tree circuit provided in each of the multiplier circuits and configured to operate a sum of a plurality of partial products by using a plurality of adders; and a selection circuit provided in each of the multiplier circuits and configured to select, according to a plurality of bits selected from the multiplier, data falling in a multiple of one of the multiplicand, data of 2.sup.n of the multiplicand, and the positive multiple data from the adder in order to output as one partial product of the plurality of partial products to the Wallace tree circuit.

Disclosed herein includes a system, a method, and a device including shift circuitry and add circuitry for performing multiplication of a first value and a second value for a neural network. The first value has a predetermined format including a first bit, and two or more second bits to represent a value of zero or 2.sup.n where n is an integer greater than or equal to 0. The device shifts, when the two or more second bits represent the value of 2.sup.n, the second value by (n+1) bits via the shift circuitry to provide a first result, selectively outputs zero or the second value, based on a value of the first bit of the first value, to provide a second result, and adds the first result and the second results via the add circuitry to provide a result of the multiplication of the first and second values.

According to the embodiments, a semiconductor device includes: an adder configured to generate positive multiple data of the multiplicand which is used for a plurality of the multiplication in plurality and does not include a value of 2.sup.n (n is a positive integer) of the multiplicand; a Wallace tree circuit provided in each of the multiplier circuits and configured to operate a sum of a plurality of partial products by using a plurality of adders; and a selection circuit provided in each of the multiplier circuits and configured to select, according to a plurality of bits selected from the multiplier, data falling in a multiple of one of the multiplicand, data of 2.sup.n of the multiplicand, and the positive multiple data from the adder in order to output as one partial product of the plurality of partial products to the Wallace tree circuit.

An example multiply accumulate (MACC) circuit includes a multiply-accumulator having an accumulator output register, a scaler, coupled to the multiply accumulator, and a control circuit coupled to the multiply-accumulator and the scaler. The control circuit is configured to provide control data to the scaler, the control data indicative of: a most-significant bit (MSB) to least significant bit (LSB) range for selecting bit indices from the accumulator output register for implementing a first right shift; a multiplier; and a second right shift.

In a novel computation device, a plurality of partial product generators is communicatively coupled to a binary number multiplier. The binary number is partitioned in the computation device into non-overlapping subsets of binary bits and each subset is coupled to one of the plurality of partial product generators. Each partial product generator, upon receiving a subset of binary bits representing a number, generates a multiplication product of the number and a predetermined constant. The multiplication products from all partial product generators are summed to generate the final product between the predetermined constant and the binary number. The partial product generators are constructed by logic gates and wires connected the logic gates including a AND gate. The partial product generators are free of memory elements.