The subject matter described herein provides systems and techniques for the design and use of multiply-and-accumulate (MAC) units to perform matrix multiplication by systolic arrays, such as those used in accelerators for deep neural networks (DNNs). These MAC units may take advantage of the particular way in which matrix multiplication is performed within a systolic array. For example, when a matrix A is multiplied with a matrix B, the scalar value, a, of the matrix A is reused many times, the scalar value, b, of the matrix B may be streamed into the systolic array and forwarded to a series of MAC units in the systolic array, and only the final values and not the intermediate values of the dot products, computed for the matrix multiplication, may be correct. MAC unit hardware that is particularized to take advantage of these observations is described herein.

An embodiment of an apparatus comprises one or more fractional width fused multiply-accumulate (FMA) circuits configured as a shared Wallace tree, and circuitry coupled to the one or more fractional width FMA circuits to provide one or more fractional width FMA operations through the one or more fractional width FMA circuits. Other embodiments are disclosed and claimed.

A multiplier circuit is provided to multiply a first operand and a second operand. The multiplier circuit includes a carry-save adder network comprising a plurality of carry-save adders to perform partial product additions to reduce a plurality of partial products to a redundant result value that represents a product of the first operand and the second operand. A number of the carry-save adders that is used to generate the redundant result value is controllable and is dependent on a width of at least one of the first operand and the second operand.

Various embodiments described herein provide for a digital In-Memory Computing (IMC) macro circuit that utilizes approximate arithmetic hardware to reduce the number of transistors and devices in the circuit relative to a convention digital IMC, thereby improving the area-efficiency of the digital IMC, but while retaining the benefits of reduced variability relative to an analog-mixed-signal (AMS) circuit. The proposed digital IMC macro circuit also includes custom full adder (FA) circuits with pass gate logic in a ripple carry adder (RCA) tree. The disclosed digital IMC macro circuit can also perform a vector-matrix dot product in one cycle while achieving high energy and area efficiency.

A method for designing a system on a target device includes identifying a length for a carry chain that is supported by predefined quanta of a resource on the target device. A plurality of logical adders is mapped onto a single logical adder implemented on the carry chain subject to the identified length to increase logic utilization in a design for the system.

A multiplier circuit is provided to multiply a first operand and a second operand. The multiplier circuit includes a carry-save adder network comprising a plurality of carry-save adders to perform partial product additions to reduce a plurality of partial products to a redundant result value that represents a product of the first operand and the second operand. A number of the carry-save adders that is used to generate the redundant result value is controllable and is dependent on a width of at least one of the first operand and the second operand.

Multiplier circuitry includes first combinatorial circuitry configured to perform a combinatorial function, based at least in part on redundant form arithmetic, to generate a first subset of two or more partial products. The two or more partial products are based at least in part on a first input to the multiplier circuitry and a second input to the multiplier circuitry. The multiplier circuitry also includes a carry chain that includes a second combinatorial circuitry configured to generate a second subset of the two or more partial products based at least in part on the first input and the second input. Furthermore, the carry chain includes one or more binary ripple-carry adders configured to generate a product of the multiplier circuitry based at least in part on a sum of the two or more partial products.

A method for designing and configuring a system on a field programmable gate array (FPGA) is disclosed. A portion of the system that is implemented greater than a predetermined number of times is identified. A structural netlist that describes how to implement the portion of the system a plurality of times on the FPGA and that leverages a repetitive nature of implementing the portion is generated. The identifying and generating is performed prior to synthesizing and placing other portions of the system that are not implemented greater than the predetermined number of time. Synthesizing, placing, and routing the other portions of the system on the FPGA is performed in accordance with the structural netlist. The FPGA is configured with a configuration file that includes a design for the system that reflects the synthesizing, placing, and routing, wherein the configuring physically transforms resources on the FPGA to implement the system.

A multiplier circuit is described in which sub-products calculated in a first stage of a carry-save adder (CSA) network are output early, processed by applying a processing function, and re-injected into a subsequent stage of the CSA network to add the processed sub-products. This allows a CSA network provided for multiplication operations to be reused for operations which require sub-products to be processed and added, such as floating-point dot product operations performed on floating-point values represented in bfloatl6 format.

A computing device to implement fast floating-point adder tree for the neural network applications is disclosed. The fast float-point adder tree comprises a data preparation module, a fast fixed-point Carry-Save Adder (CSA) tree, and a normalization module. The floating-point input data comprises a sign bit, exponent part and fraction part. The data preparation module aligns the fraction part of the input data and prepares the input data for subsequent processing. The fast adder uses a signed fixed-point CSA tree to quickly add a large number of fixed-point data into 2 output values and then uses a normal adder to add the 2 output values into one output value. The fast adder uses for a large number of operands is based on multiple levels of fast adders for a small number of operands. The output from the signed fixed-point Carry-Save Adder tree is converted to a selected floating-point format.