A processing device is provided which comprises memory configured to store data and a plurality of processor cores in communication with each other via first and second hierarchical communication links. Processor cores of a first hierarchical processor core group are in communication with each other via the first hierarchical communication links and are configured to store, in the memory, a sub-portion of data of a first matrix and a sub-portion of data of a second matrix. The processor cores are also configured to determine a product of the sub-portion of data of the first matrix and the sub-portion of data of the second matrix, receive, from another processor core, another sub-portion of data of the second matrix and determine a product of the sub-portion of data of the first matrix and the other sub-portion of data of the second matrix.

A tile of an FPGA includes a multiple mode arithmetic circuit. The multiple mode arithmetic circuit is configured by control signals to operate in an integer mode, a floating-point mode, or both. In some example embodiments, multiple integer modes (e.g., unsigned, two's complement, and sign-magnitude) are selectable, multiple floating-point modes (e.g., 16-bit mantissa and 8-bit sign, 8-bit mantissa and 6-bit sign, and 6-bit mantissa and 6-bit sign) are supported, or any suitable combination thereof. The tile may also fuse a memory circuit with the arithmetic circuits. Connections directly between multiple instances of the tile are also available, allowing multiple tiles to be treated as larger memories or arithmetic circuits. By using these connections, referred to as cascade inputs and outputs, the input and output bandwidth of the arithmetic circuit is further increased.

A processing device is provided which comprises memory configured to store data and a plurality of processor cores in communication with each other via first and second hierarchical communication links. Processor cores of a first hierarchical processor core group are in communication with each other via the first hierarchical communication links and are configured to store, in the memory, a sub-portion of data of a first matrix and a sub-portion of data of a second matrix. The processor cores are also configured to determine a product of the sub-portion of data of the first matrix and the sub-portion of data of the second matrix, receive, from another processor core, another sub-portion of data of the second matrix and determine a product of the sub-portion of data of the first matrix and the other sub-portion of data of the second matrix.

Systems and methods are disclosed for processing and executing queries against one or more dataset. As part of processing the query, the system determines whether the query is susceptible to a significantly imbalanced partition. In the event, the query is susceptible to an imbalanced partition, the system monitors the query and determines whether to perform a multi-partitioning determination to avoid a significantly imbalanced partition.

A processing device is provided which includes memory and a processor comprising a plurality of processor cores in communication with each other via first and second hierarchical communication links. Each processor core in a group of the processor cores is in communication with each other via the first hierarchical communication links. Each processor core is configured to store, in the memory, one of a plurality of sub-portions of data of a first matrix, store, in the memory, one of a plurality of sub-portions of data of a second matrix, determine an outer product of the sub-portion of data of the first matrix and the sub-portion of data of the second matrix, receive, from another processor core of the group of processor cores, another sub-portion of data of the second matrix and determine another outer product of the sub-portion of data of the first matrix and the other sub-portion of data of the second matrix.

Systems and methods are disclosed for processing and executing queries against one or more dataset. As part of processing the query, the system determines whether the query is susceptible to a significantly imbalanced partition. In the event, the query is susceptible to an imbalanced partition, the system monitors the query and determines whether to perform a multi-partitioning determination to avoid a significantly imbalanced partition.

Provided is an arithmetic operation device including a multiplying section in which multiplying units are divided and assigned to each of one or more groups such that each group includes one or more of the multiplying units according to a calculation precision mode, and each multiplying unit multiplies together an individual multiplier, which is a digit range of at least a portion of a multiplier for the group, and an individual multiplicand, which is a digit range of at least a portion of a multiplicand for the group, and an adding section in which adding units are divided and assigned to each of one or more groups such that each group includes one or more of the adding units according to the calculation precision mode, and the adding units add together each multiplication result obtained by each multiplying unit and output a product of the multiplier and the multiplicand.

Embodiments detailed herein relate to arithmetic operations of float-point values. An exemplary processor includes decoding circuitry to decode an instruction, where the instruction specifies locations of a plurality of operands, values of which being in a floating-point format. The exemplary processor further includes execution circuitry to execute the decoded instruction, where the execution includes to: convert the values for each operand, each value being converted into a plurality of lower precision values, where an exponent is to be stored for each operand; perform arithmetic operations among lower precision values converted from values for the plurality of the operands; and generate a floating-point value by converting a resulting value from the arithmetic operations into the floating-point format and store the floating-point value.

Embodiments detailed herein relate to arithmetic operations of float-point values. An exemplary processor includes decoding circuitry to decode an instruction, where the instruction specifies locations of a plurality of operands, values of which being in a floating-point format. The exemplary processor further includes execution circuitry to execute the decoded instruction, where the execution includes to: convert the values for each operand, each value being converted into a plurality of lower precision values, where an exponent is to be stored for each operand; perform arithmetic operations among lower precision values converted from values for the plurality of the operands; and generate a floating-point value by converting a resulting value from the arithmetic operations into the floating-point format and store the floating-point value.

A computer-implemented method, computer program product, and apparatus are provided. The method includes substituting NN first integer elements, among a plurality of first integer elements obtained by dividing first integer data expressing a first integer in a first digit direction, into a first matrix having N rows and N columns. The method further includes substituting each of one or more second integer elements, among a plurality of second integer elements obtained by dividing second integer data expressing a second integer in a second digit direction, into at least one matrix element of a second matrix having N rows and N columns. The method also includes calculating a third matrix that is a product of the first matrix and the second matrix. The method includes outputting each matrix element of the third matrix as a partial product in a calculation of a product of the first integer and the second integer.