More robust tests in algorithm-based fault-tolerant matrix multiplication

The authors propose a novel algorithm-based testing scheme for matrix multiplication that supplements the standard sum test. An integer-based equality test is presented for matrix multiplication that is able to detect up to three errors in the scalar floating-point multiplication component of the computation. They present schemes that augment this integer-based test by a floating-point equality test so that errors in the floating-point addition component of matrix multiplication are also covered. As shown by simulation results, the hybrid testing method is much more accurate in detecting errors than previous floating-point equality tests with thresholding. A small architectural change is suggested in the floating-point multiplication unit that restricts the time overhead of the scheme to only 18% over that of the simple floating-point equality test.<>