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\( \newcommand{\R}{\mathbb R} \newcommand{\Rm}{\mathbb R^m} \newcommand{\Rn}{\mathbb R^n} \newcommand{\Rnxn}{\mathbb R^{n \times n}} \newcommand{\Rmxn}{\mathbb R^{m \times n}} \newcommand{\C}{\mathbb C} \newcommand{\Cm}{\mathbb C^m} \newcommand{\Cmxm}{\mathbb C^{m \times m}} \newcommand{\Cnxn}{\mathbb C^{n \times n}} \newcommand{\Cmxn}{\mathbb C^{m \times n}} \newcommand{\Cn}{\mathbb C^n} \newcommand{\Null}{{\cal N}} \newcommand{\Col}{{\cal C}} \newcommand{\Rowspace}{{\cal R}} \newcommand{\Span}{{\cal Span}} \newcommand{\rank}{{\rm rank}} \newcommand{\FlaTwoByTwo}[4]{ \left( \begin{array}{c | c} #1 \amp #2 \\ \hline #3 \amp #4 \end{array} \right) } \newcommand{\FlaTwoByTwoSingleLine}[4]{ \left( \begin{array}{c c} #1 \amp #2 \\ #3 \amp #4 \end{array} \right) } \newcommand{\FlaTwoByTwoSingleLineNoPar}[4]{ \begin{array}{c c} #1 \amp #2 \\ #3 \amp #4 \end{array} } \newcommand{\FlaOneByTwo}[2]{ \left( \begin{array}{c | c} #1 \amp #2 \end{array} \right) } \newcommand{\FlaOneByTwoSingleLine}[2]{ \left( \begin{array}{c c} #1 \amp #2 \end{array} \right) } \newcommand{\FlaTwoByOne}[2]{ \left( \begin{array}{c} #1 \\ \hline #2 \end{array} \right) } \newcommand{\FlaTwoByOneSingleLine}[2]{ \left( \begin{array}{c} #1 \\ #2 \end{array} \right) } \newcommand{\FlaThreeByOneB}[3]{ \left( \begin{array}{c} #1 \\ \hline #2 \\ #3 \end{array} \right) } \newcommand{\FlaThreeByOneT}[3]{ \left( \begin{array}{c} #1 \\ #2 \\ \hline #3 \end{array} \right) } \newcommand{\FlaOneByThreeR}[3]{ \left( \begin{array}{c | c c} #1 \amp #2 \amp #3 \end{array} \right) } \newcommand{\FlaOneByThreeL}[3]{ \left( \begin{array}{c c | c} #1 \amp #2 \amp #3 \end{array} \right) } \newcommand{\FlaThreeByThreeBR}[9]{ \left( \begin{array}{c | c c} #1 \amp #2 \amp #3 \\ \hline #4 \amp #5 \amp #6 \\ #7 \amp #8 \amp #9 \end{array} \right) } \newcommand{\FlaThreeByThreeTL}[9]{ \left( \begin{array}{c c | c} #1 \amp #2 \amp #3 \\ #4 \amp #5 \amp #6 \\ \hline #7 \amp #8 \amp #9 \end{array} \right) } \newcommand{\diag}[1]{{\rm diag}( #1 )} \newcommand{\URt}{{\sc HQR}} \newcommand{\FlaAlgorithm}{ \begin{array}{|l|} \hline \routinename \\ \hline \partitionings \\ ~~~ \begin{array}{l} \partitionsizes \end{array} \\ {\bf \color{blue} {while}~} \guard \\ ~~~ \begin{array}{l} \repartitionings \end{array} \\ ~~~ \color{red} { \begin{array}{l} \hline \color{black} {\update} \\ \hline \end{array}} \\ ~~~ \begin{array}{l} \moveboundaries \end{array} \\ {\bf \color{blue} {endwhile}} \\ \hline \end{array} } \newcommand{\FlaAlgorithmWithInit}{ \begin{array}{|l|} \hline \routinename \\ \hline \initialize \\ \partitionings \\ ~~~ \begin{array}{l} \partitionsizes \end{array} \\ {\bf \color{blue} {while}~} \guard \\ ~~~ \begin{array}{l} \repartitionings \end{array} \\ ~~~ \color{red} { \begin{array}{l} \hline \color{black} {\update} \\ \hline \end{array}} \\ ~~~ \begin{array}{l} \moveboundaries \end{array} \\ {\bf \color{blue} {endwhile}} \\ \hline \end{array} } \newcommand{\FlaBlkAlgorithm}{ \begin{array}{|l|} \hline \routinename \\ \hline \partitionings \\ ~~~ \begin{array}{l} \partitionsizes \end{array} \\ {\bf \color{blue} {while}~} \guard \\ ~~~ {\bf choose~block~size~} \blocksize \\ ~~~ \begin{array}{l} \repartitionings \end{array} \\ ~~~ ~~~ \repartitionsizes \\ ~~~ \color{red} { \begin{array}{l} \hline \color{black} {\update} \\ \hline \end{array}} \\ ~~~ \begin{array}{l} \moveboundaries \end{array} \\ {\bf \color{blue} {endwhile}} \\ \hline \end{array} } \newcommand{\complexone}{ \begin{array}{|c|}\hline \!\pm\! \\ \hline \end{array}~ } \newcommand{\HQR}{{\rm HQR}} \newcommand{\QR}{{\rm QR}} \newcommand{\st}{{\rm \ s.t. }} \newcommand{\QRQ}{{\rm {\normalsize \bf Q}{\rm \tiny R}}} \newcommand{\QRR}{{\rm {\rm \tiny Q}{\bf \normalsize R}}} \newcommand{\deltaalpha}{\delta\!\alpha} \newcommand{\deltax}{\delta\!x} \newcommand{\deltay}{\delta\!y} \newcommand{\deltaz}{\delta\!z} \newcommand{\deltaw}{\delta\!w} \newcommand{\DeltaA}{\delta\!\!A} \newcommand{\meps}{\epsilon_{\rm mach}} \newcommand{\fl}[1]{{\rm fl( #1 )}} \newcommand{\becomes}{:=} \newcommand{\defrowvector}[2]{ \left(#1_0, #1_1, \ldots, #1_{#2-1}\right) } \newcommand{\tr}[1]{{#1}^T} \newcommand{\LUpiv}[1]{{\rm LU}(#1)} \newcommand{\maxi}{{\rm maxi}} \newcommand{\Chol}[1]{{\rm Chol}( #1 )} \newcommand{\lt}{<} \newcommand{\gt}{>} \newcommand{\amp}{&} \)

Index Index

\(k_C \), Item

\(m_C \), Item

\(m_R \), Item

\(n_R \), Item

autotuning, Paragraph

AVX2 vector instructions, Paragraph

Basic Linear Algebra Subprograms, Remark Unit

BLAS, Remark Unit

BLAS-like Library Instantiation Software, Unit

BLIS, Unit

BLIS Object-Based API, Item

BLIS Typed API, Item

blocked algorithm, Paragraph

cache memory, Paragraph

cache replacement policy, Remark

conformal partitioning, Remark

floating point unit, Paragraph

fused multiply add, Paragraph

Gemm, Paragraph

Goto's algorithm, Paragraph

GotoBLAS algorithm, Paragraph

hardware prefetching, Paragraph

immintrin.h, Paragraph

instruction-level parallelism, Paragraph

Kazushige Goto, Paragraph

kernel, Paragraph

memops, Item

micro-kernel, Paragraph

micro-panel, Item Item

micro-tile, Item Item

omp.h, Item

OpenMP, Paragraph

replacement policy, Remark

SIMD, Paragraph Remark

Single Instruction, Multiple Data, Remark

Single-Instruction, Multiple Data, Paragraph

vector instrinsic functions, Paragraph