Abstract: Data employed in computations is processed so that during computations more of the data can be fit into or maintained in a smaller but higher speed memory than an original source of the data. More specifically, a sensitivity value is determined for various items of the data which reflect the number of bits in the data items that are not garbage bits, and only information in the data items that are indicated by the sensitivity value to not be garbage bits are necessarily effectively retained. At least the information that is not garbage bits and the corresponding associated sensitivity are packed together. The results of computations that are performed using the data items as at least one of the operands for the computation are associated with a sensitivity that is derived from the individual sensitivities of the operands used in the computation.

Abstract: Data employed in computations is processed so that during computations more of the data can be fit into or maintained in a smaller but higher speed memory than an original source of the data. More specifically, a sensitivity value is determined for various items of the data which reflect the number of bits in the data items that are not garbage bits, and only information in the data items that are indicated by the sensitivity value to not be garbage bits are necessarily effectively retained. At least the information that is not garbage bits and the corresponding associated sensitivity are packed together. The results of computations that are performed using the data items as at least one of the operands for the computation are associated with a sensitivity that is derived from the individual sensitivities of the operands used in the computation.

Abstract: Systems and methods for reducing data movement in a computer system. The systems and methods use information or knowledge about the structure of an algorithm, operations to be executed at a receiving processing unit, variables or subsets or groups of variables in a distributed algorithm, or other forms of contextual information, for reducing the number of bits transmitted from at least one transmitting processing unit to at least one receiving processing unit or storage device.

Abstract: Systems and methods for reducing data movement in a computer system. The systems and methods use information or knowledge about the structure of an algorithm, operations to be executed at a receiving processing unit, variables or subsets or groups of variables in a distributed algorithm, or other forms of contextual information, for reducing the number of bits transmitted from at least one transmitting processing unit to at least one receiving processing unit or storage device.

Abstract: Data employed in computations is processed so that during computations more of the data can be fit into or maintained in a smaller but higher speed memory than an original source of the data. More specifically, a sensitivity value is determined for various items of the data which reflect the number of bits in the data items that are not garbage bits, and only information in the data items that are indicated by the sensitivity value to not be garbage bits are necessarily effectively retained. At least the information that is not garbage bits and the corresponding associated sensitivity are packed together. The results of computations that are performed using the data items as at least one of the operands for the computation are associated with a sensitivity that is derived from the individual sensitivities of the operands used in the computation.

Abstract: The Present invention provides a system and method for fast computing the Cholesky factorization of a positive definite matrix. In order to reduce the computation time of matrix factorizations, the present invention uses three atomic components, namely MA atoms, M atoms, and an S atom. The three kinds of components are arranged in a configuration that returns the Cholesky factorization of the input matrix.