A method includes receiving, by an x-bit adder, first and second addends. The x bits comprise a first portion and a second portion, the first portion is a power of two number of bits, and x is not a power of two. The method also includes computing a first sum of the first and second addends corresponding to the first portion. Computing the first sum provides a carry out bit. The method includes computing a non-incremented sum of the first and second addends corresponding to the second portion; computing an incremented sum of the first and second addends corresponding to the second portion; selecting one of the non-incremented sum and the incremented sum, responsive to the carry out bit, as a second sum; and providing a final sum by concatenating the second sum and the first sum.

The present disclosure relates to a carry chain logic system that leverages carry in and carry out signals from logic blocks to implement logic functions on programmable hardware (e.g., FPGA hardware). In particular, implementations of the carry chain logic system facilitate implementation of logic gates (e.g., AND/OR gates) having high number of input signals without incurring routing delays caused by routing output signals between logic components implemented across different logic stages. For example, implementations described herein involve feeding carry out signals between adders of a logic chain across multiple logic components on a common logic stage, thus reducing routing penalties caused by routing signals via a routing fabric of the programmable hardware.

An apparatus to facilitate large integer multiplication enhancements in a graphics environment is disclosed. The apparatus includes a processor comprising processing resources, the processing resources comprising multiplier circuitry to: receive operands for a multiplication operation, wherein the multiplication operation is part of a chain of multiplication operations for a large integer multiplication; and issue a multiply and add (MAD) instruction for the multiplication operation utilizing at least one of a double precision multiplier or a 48 bit output, wherein the MAD instruction to generate an output in a single clock cycle of the processor.

An apparatus to facilitate large integer multiplication enhancements in a graphics environment is disclosed. The apparatus includes a processor comprising processing resources, the processing resources comprising multiplier circuitry to: receive operands for a multiplication operation, wherein the multiplication operation is part of a chain of multiplication operations for a large integer multiplication; and issue a multiply and add (MAD) instruction for the multiplication operation utilizing at least one of a double precision multiplier or a 48 bit output, wherein the MAD instruction to generate an output in a single clock cycle of the processor.

A non-destructive memory array implements a full adder. The array includes a column connected by a bit line and a full adder unit. The column stores a first bit in a first row of the bit line, a second bit in a second row of the bit line, and an inverse of a carry-in bit in a third row of the bit line. The full adder unit stores, in the second and third rows of the bit line, a sum bit and a carry out bit output, respectively, of adding the first bit, the second bit and the carry-in bit. The full adder unit does not overwrite any of the bits when a full adder table indicates that the sum bit and the carry out bit are equivalent to the second bit and the carry-in bit.

A non-destructive memory array implements a full adder. The array includes a column connected by a bit line and a full adder unit. The column stores a first bit in a first row of the bit line, a second bit in a second row of the bit line, and an inverse of a carry-in bit in a third row of the bit line. The full adder unit stores, in the second and third rows of the bit line, a sum bit and a carry out bit output, respectively, of adding the first bit, the second bit and the carry-in bit. The full adder unit does not overwrite any of the bits when a full adder table indicates that the sum bit and the carry out bit are equivalent to the second bit and the carry-in bit.

The present invention discloses a computing array based on 1T1R device, operation circuits and operating methods thereof. The computing array has 1T1R arrays and a peripheral circuit; the 1T1R array is configured to achieve operation and storage of an operation result, and the peripheral circuit is configured to transmit data and control signals to control operation and storage processes of the 1T1R arrays; the operation circuits are respectively configured to implement a 1-bit full adder, a multi-bit step-by-step carry adder and optimization design thereof, a 2-bit data selector, a multi-bit carry select adder and a multi-bit pre-calculation adder; and in the operating method corresponding to the operation circuit, initialized resistance states of the 1T1R devices, word line input signals, bit line input signals and source line input signals are controlled to complete corresponding operation and storage processes.

An integrated circuit that includes very large adder circuitry is provided. The very large adder circuitry receives more than two inputs each of which has hundreds or thousands of bits. The very large adder circuitry includes multiple adder nodes arranged in a tree-like network. The adder nodes divide the input operands into segments, computes the sum for each segment, and computes the carry for each segment independently from the segment sums. The carries at each level in the tree are accumulated using population counters. After the last node in the tree, the segment sums can then be combined with the carries to determine the final sum output. An adder tree network implemented in this way asymptotically approaches the area and performance latency as an adder network that uses infinite speed ripple carry adders.

An integrated circuit that includes very large adder circuitry is provided. The very large adder circuitry receives more than two inputs each of which has hundreds or thousands of bits. The very large adder circuitry includes multiple adder nodes arranged in a tree-like network. The adder nodes divide the input operands into segments, computes the sum for each segment, and computes the carry for each segment independently from the segment sums. The carries at each level in the tree are accumulated using population counters. After the last node in the tree, the segment sums can then be combined with the carries to determine the final sum output. An adder tree network implemented in this way asymptotically approaches the area and performance latency as an adder network that uses infinite speed ripple carry adders.

A method comprises receiving a first N-bit unsigned number and a second N-bit unsigned number, receiving a control signal indicating a m-bit shifting operation and processing the first N-bit unsigned number, the second N-bit unsigned number and the control signal in an add-and-shift apparatus, wherein an addition/subtraction operation and the m-bit shifting operation are performed in parallel in the add-and-shift apparatus.