DSP Builder for Intel® FPGAs (Advanced Blockset): Handbook

ID 683337
Date 6/26/2023

A newer version of this document is available. Customers should click here to go to the newest version.

Document Table of Contents
Give Feedback

7.14.20. QRD Solver

The QRD Solver reference design is a complete linear equations system solution using QR decomposition. The input of the design is a system matrix A [n x m] and input vector [b].
Figure 83. QRD SolverThe design decomposes the system matrix A to Q and R matrices using the Gram-Schmidt method. The design calculates the solution of the system by completing backward substitution.

The reference design is fully parameterizable over system dimensions n and m and the processing vector size, which defines the parallelization ratio of the dot product engine. This design implements parallel dot product engine using single-precision Multiply and Add blocks that perform most of the floating-point calculations. The design routes different phases of the calculation through these blocks with a controlling processor that executes a fixed set of microinstructions and generates operation indexes. The design implements the controlling processor using for-loop macro blocks, which allow very efficient, flexible, and high-level implementation of iterative operations.

This design uses the Run All Testbenches block to access enhanced features of the automatically generated testbench. An application-specific m-function verifies the simulation output, to correctly handle the complex results and the numerical approximation because of the floating-point format. Intel optimized the design for Intel® Stratix® 10 FPGAs. The design implements hardened floating-point operators in the FPGA DSP blocks.

Table 24.  Performance

Intel tested the design with Intel® Quartus® Prime v18.1.1 build 259, targeting a 1SG280LN3F43E2VG device

Matrix Size Parallel Processing Vector Size fMAX (MHz) Resources Throughput Latency
ALM DSPs M20K Cycles Matrices/s Cycles ms
512x256 512 320 461K (49%) 4,370 (76%) 1,313 (11%) 71,232 4,492 137,545 0.43
64x64 64 418 60.5 (6%) 562 (10%) 160 (1%) 7,920 52,777 12,392 0.03

The model file is demo_qrd_s10.mdl.