  This paper lays out insights and opportunities for implementing
higher-precision matrix-matrix multiplication (GEMM) from (in terms of)
lower-precision high-performance GEMM. The driving case study approximates
double-double precision (FP64x2) GEMM in terms of double precision (FP64) GEMM,
leveraging how the BLAS-like Library Instantiation Software (BLIS) framework
refactors the Goto Algorithm. With this, it is shown how approximate FP64x2
GEMM accuracy can be cast in terms of ten ``cascading'' FP64 GEMMs. Promising
results from preliminary performance and accuracy experiments are reported. The
demonstrated techniques open up new research directions for more general
cascading of higher-precision computation in terms of lower-precision
computation for GEMM-like functionality.
