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Mixing precision SpMV optimization system and method applied to computing equipment

A computing equipment and precision technology, applied in the field of mixed-precision SpMV optimization systems, can solve problems affecting memory-intensive applications, mixed-precision algorithm concerns, etc., achieve high theoretical significance and practical application value, and reduce memory access overhead.

Active Publication Date: 2022-05-13
BEIJING INSTITUTE OF TECHNOLOGYGY
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  • Summary
  • Abstract
  • Description
  • Claims
  • Application Information

AI Technical Summary

Problems solved by technology

However, the data movement aspect primarily affects memory-intensive, bandwidth-constrained applications, and has historically not attracted much attention to mixed-precision algorithms

Method used

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  • Mixing precision SpMV optimization system and method applied to computing equipment
  • Mixing precision SpMV optimization system and method applied to computing equipment
  • Mixing precision SpMV optimization system and method applied to computing equipment

Examples

Experimental program
Comparison scheme
Effect test

Embodiment 1

[0041] Such as figure 1 As shown, the mixed-precision SpMV optimization system applied to computing equipment includes:

[0042] An acquisition module, a first processing module, and a second processing module.

[0043] The obtaining module is used to obtain the input data of the computing device;

[0044] The first processing module is used to divide the sparse matrix into sub-matrices of different precisions based on the precision of floating-point numbers of non-zero elements in the sparse matrix;

[0045] The second processing module is used to calculate the multiplication of the sub-matrix and the vector with different precisions to obtain a mixed-precision SpMV calculation result;

[0046] Specifically, the division of the sparse matrix by the first processing module is performed only once before the mixed-precision SpMV calculation.

[0047] Specifically, the floating point number includes: a sign, an exponent and a mantissa.

[0048] Specifically, the sub-matrices ...

Embodiment 2

[0055] Such as figure 2 As shown, the mixed-precision SpMV optimization method applied to computing equipment includes the following steps:

[0056] Obtain a computing device input sparse matrix;

[0057] Divide the sparse matrix into sub-matrices of different precision based on the precision of the floating-point numbers of the non-zero elements in the sparse matrix;

[0058] The multiplication of the sub-matrix and the vector with different precisions is calculated to obtain a mixed-precision SpMV calculation result.

Embodiment 3

[0060] (1) Matrix lossless division

[0061] The key of the present invention is to represent the sparse matrix with mixed precision based on the precision of non-zero elements, so as to reduce its memory access overhead and calculation intensity in SpMV calculation. Mixed-precision representation divides a sparse matrix into up to 3 matrices (half-precision, single-precision, and double-precision submatrices) according to the actual floating-point precision of the nonzero elements. Storing more non-zero elements with low precision means less memory usage and data transfer between CPU memory and GPU global memory, as well as memory access transactions on the GPU side. In addition, low-precision calculations are expected to achieve higher performance than high-precision calculations. Therefore, different storage and computation precision may help to improve the performance of SpMV computation.

[0062] The representation of floating-point numbers in memory is divided into thr...

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Abstract

The invention discloses a mixed precision SpMV optimization system and method applied to computing equipment. The system comprises an acquisition module, a first processing module and a second processing module, the acquisition module is used for reading a sparse matrix into computing equipment; the first processing module divides a sparse matrix into sub-matrixes with different precisions based on floating-point number precisions of non-zero elements in the sparse matrix; and the second processing module is used for calculating multiplication of the sub-matrixes with different precisions and the vectors to obtain a mixed precision SpMV calculation result. According to the method, the calculation overhead of the SpMV is reduced by utilizing the mixing precision, the memory access efficiency is improved, and the method has relatively high theoretical significance and practical application value.

Description

technical field [0001] The invention belongs to the field of sparse linear algebra solution optimization, in particular to a mixed precision SpMV optimization system and method applied to computing equipment. Background technique [0002] The solution of large-scale sparse linear equations has very important applications in many fields such as computational electromagnetics, computational fluid dynamics, and aerodynamics, and the time spent on solving large-scale sparse linear systems occupies a very large part of the time required to solve the entire problem. Therefore, how to quickly and efficiently solve large sparse linear systems has always been one of the current research hotspots. The direct method provides a numerically stable method for solving linear systems with a predictable number of floating-point operations. However, for large-scale linear systems, the storage and computation costs of direct factorization may be impractical. In contrast, iterative solvers su...

Claims

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Application Information

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IPC IPC(8): G06F17/16
CPCG06F17/16
Inventor 计卫星刘洁高建花王一拙石峰
Owner BEIJING INSTITUTE OF TECHNOLOGYGY