680 results about "Matrix multiplication" patented technology

To perform multiplication of matrices in a vector processing system, partial products are obtained by dot multiplication of vector registers containing multiple copies of elements of a first matrix and vector registers containing values from rows of a second matrix. The dot products obtained from this dot multiplication are subsequently added to vector registers which form a product matrix. Each matrix can be divided into submatrices to facilitate the rapid and efficient multiplication of large matrices, which is done in parts by computing partial products of each submatrix. The matrix multiplication avoids rounding errors as it is bit-by-bit compatible with conventional matrix multiplication methods.

The present invention enables efficient matrix multiplication operations on parallel processing devices. One embodiment is a method for mapping CTAs to result matrix tiles for matrix multiplication operations. Another embodiment is a second method for mapping CTAs to result tiles. Yet other embodiments are methods for mapping the individual threads of a CTA to the elements of a tile for result tile computations, source tile copy operations, and source tile copy and transpose operations. The present invention advantageously enables result matrix elements to be computed on a tile-by-tile basis using multiple CTAs executing concurrently on different streaming multiprocessors, enables source tiles to be copied to local memory to reduce the number accesses from the global memory when computing a result tile, and enables coalesced read operations from the global memory as well as write operations to the local memory without bank conflicts.

Modular multiplication of two elements X(t) and Y(t), over GF(2), where m is a field degree, may utilize field degree to determine, at least in part, the number of iterations. An extra shift operation may be employed when the number of iterations is reduced. Modular multiplication of two elements X(t) and Y(t), over GF(2), may include a shared reduction circuit utilized during multiplication and reduction. In addition, a modular multiplication of binary polynomials X(t) and Y(t), over GF(2), may utilize the Karatsuba algorithm, e.g., by recursively splitting up a multiplication into smaller operands determined according to the Karatsuba algorithm.

A matrix multiplication module and matrix multiplication method are provided that use a variable number of multiplier-accumulator units based on the amount of data elements of the matrices are available or needed for processing at a particular point or stage in the computation process. As more data elements become available or are needed, more multiplier-accumulator units are used to perform the necessary multiplication and addition operations. To multiply an N×M matrix by an M×N matrix, the total (maximum) number of used MAC units is “2*N−1”. The number of MAC units used starts with one (1) and increases by two at each computation stage, that is, at the beginning of reading of data elements for each new row of the first matrix. The sequence of the number of MAC units is {1, 3, 5, . . . , 2*N−1} for computation stages each of which corresponds to reading of data elements for each new row of the left hand matrix, also called the first matrix. For the multiplication of two 8×8 matrices, the performance is 16 floating point operations per clock cycle. For an FPGA running at 100 MHz, the performance is 1.6 Giga floating point operations per second. The performance increases with the increase of the clock frequency and the use of larger matrices when FPGA resources permit. Very large matrices are partitioned into smaller blocks to fit in the FPGA resources. Results from the multiplication of sub-matrices are combined to form the final result of the large matrices.