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Added tile
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src/qmckl_tile.org
Normal file
496
src/qmckl_tile.org
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@ -0,0 +1,496 @@
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#+TITLE: Tiled arrays
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#+SETUPFILE: ../docs/theme.setup
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To increase performance, matrices may be stored as tiled
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arrays. Instead of storing a matrix in a two-dimensional array, it may
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be stored as a two dimensional array of small matrices (a rank 4
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tensor). This improves the locality of the data in matrix
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multiplications, and also enables the possibility to use BLAS3
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while also exploiting part of the sparse structure of the matrices.
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Tile
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│ ┌──────┬──────┬──────┐
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│ │1 4 7 │ │ │
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└───────►│2 5 8 │ T_12 │ T_13 │
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│3 6 9 │ │ │
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├──────┼──────┼──────┤
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│ │ │ │
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│ T_21 │ T_22 │ T_23 │
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│ │ │ │
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├──────┼──────┼──────┤
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│ │ │ │
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│ T_31 │ T_32 │ T_33 │
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│ │ │ │
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└──────┴──────┴──────┘
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In this file, tiled matrice will be produced for the following
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types:
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#+NAME: types
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| float |
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| double |
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* Headers :noexport:
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#+NAME: filename
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#+begin_src elisp :tangle no
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(file-name-nondirectory (substring buffer-file-name 0 -4))
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#+end_src
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#+begin_src c :tangle (eval h_private_type)
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#ifndef QMCKL_TILE_HPT
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#define QMCKL_TILE_HPT
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#+end_src
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#+begin_src c :tangle (eval c_test) :noweb yes
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#include "qmckl.h"
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#include "munit.h"
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MunitResult test_<<filename()>>() {
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qmckl_context context;
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context = qmckl_context_create();
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#+end_src
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#+begin_src c :tangle (eval c)
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#include <stdint.h>
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#include <stdlib.h>
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#include <string.h>
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#include <assert.h>
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#include <limits.h>
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#include "qmckl_context_type.h"
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#include "qmckl_error_type.h"
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#include "qmckl_memory_private_type.h"
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#include "qmckl_tile_private_type.h"
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#include "qmckl_context_func.h"
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#include "qmckl_error_func.h"
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#include "qmckl_memory_private_func.h"
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#include "qmckl_tile_private_func.h"
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#+end_src
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* Data structures
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** Tile
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A tile is a small matrix of fixed size. The dimensions of the
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tiles is fixed at compile-time to increase performance. It is
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defined as $2^s$:
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| s | tile size |
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|----+-----------|
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| 2 | 4 |
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| 3 | 8 |
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| 4 | 16 |
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| 55 | 32 |
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| 6 | 64 |
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| 7 | 128 |
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#+begin_src c :tangle (eval h_private_type)
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#define TILE_SIZE_SHIFT 3
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#define TILE_SIZE 8
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#+end_src
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#+NAME: tile_hpt
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#+begin_src c
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typedef struct $T$_tile_struct {
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$T$ element[TILE_SIZE][TILE_SIZE];
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int32_t is_null;
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int32_t padding;
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} $T$_tile_struct;
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#+end_src
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** Tiled matrix
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A tiled matrix is a two-dimensional array of tiles.
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#+NAME: matrix_hpt
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#+begin_src c
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typedef struct $T$_tiled_matrix {
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$T$_tile_struct** tile;
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size_t rows;
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size_t cols;
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} $T$_tiled_matrix;
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#+end_src
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When a tiled matrix is initialized, it is set to zero.
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#+NAME: init_hpf
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#+begin_src c
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qmckl_exit_code $T$_tiled_matrix_init (qmckl_context context,
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$T$_tiled_matrix* m,
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size_t rows,
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size_t cols);
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#+end_src
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#+NAME: init_c
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#+begin_src c
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qmckl_exit_code $T$_tiled_matrix_init (qmckl_context context,
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$T$_tiled_matrix* m,
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size_t rows,
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size_t cols) {
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if (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
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return QMCKL_INVALID_CONTEXT;
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}
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if (m == NULL) {
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return qmckl_failwith(context,
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QMCKL_INVALID_ARG_2,
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"$T$_tiled_matrix_init",
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NULL);
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}
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if (rows == (size_t) 0) {
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return qmckl_failwith(context,
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QMCKL_INVALID_ARG_3,
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"$T$_tiled_matrix_init",
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NULL);
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}
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if (cols == (size_t) 0) {
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return qmckl_failwith(context,
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QMCKL_INVALID_ARG_4,
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"$T$_tiled_matrix_init",
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NULL);
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}
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qmckl_memory_info_struct info = qmckl_memory_info_struct_zero;
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size_t n = rows * cols;
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/* Check overflow */
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if (n/cols != rows
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|| n > SIZE_MAX / sizeof($T$_tile_struct) ) {
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return qmckl_failwith(context,
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QMCKL_ALLOCATION_FAILED,
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"$T$_tiled_matrix_init",
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"rows * cols overflows" );
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}
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/* Allocate array of column pointers */
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info.size = cols * sizeof($T$_tile_struct*) ;
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m->tile = ($T$_tile_struct**) qmckl_malloc(context, info);
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if (m->tile == NULL) {
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return qmckl_failwith(context,
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QMCKL_ALLOCATION_FAILED,
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"$T$_tiled_matrix_init",
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NULL);
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}
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/* Allocate array of tiles */
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info.size = n * sizeof($T$_tile_struct) ;
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m->tile[0] = ($T$_tile_struct*) qmckl_malloc(context, info);
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if (m->tile[0] == NULL) {
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return qmckl_failwith(context,
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QMCKL_ALLOCATION_FAILED,
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"$T$_tiled_matrix_init",
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NULL);
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}
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/* Compute array of pointers to the 1st element of columns */
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for (size_t i=1 ; i<cols ; ++i) {
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m->tile[i] = m->tile[i-1] + rows;
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}
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m->rows = rows;
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m->cols = cols;
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return QMCKL_SUCCESS;
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}
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#+end_src
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* Write templates
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#+begin_src python :noweb yes :results drawer :var types=types :exports results
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def generate(f, text):
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result = [ f"#+begin_src c :tangle (eval {f})" ]
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for t in types:
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t=t[0]
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result += [ text.replace("$T$",t), "" ]
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result += [ "#+end_src" ]
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return '\n'.join(result)
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return '\n'.join( [ ""
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, generate("h_private_type", """
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<<tile_hpt>>
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<<matrix_hpt>>
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""")
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, ""
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, generate("h_private_func", """
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<<init_hpf>>
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""")
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, ""
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, generate("c", """
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<<init_c>>
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""")
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] )
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#+end_src
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#+RESULTS:
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:results:
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#+begin_src c :tangle (eval h_private_type)
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typedef struct float_tile_struct {
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float element[TILE_SIZE][TILE_SIZE];
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int32_t is_null;
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int32_t padding;
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} float_tile_struct;
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typedef struct float_tiled_matrix {
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float_tile_struct** tile;
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size_t rows;
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size_t cols;
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} float_tiled_matrix;
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typedef struct double_tile_struct {
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double element[TILE_SIZE][TILE_SIZE];
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int32_t is_null;
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int32_t padding;
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} double_tile_struct;
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typedef struct double_tiled_matrix {
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double_tile_struct** tile;
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size_t rows;
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size_t cols;
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} double_tiled_matrix;
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#+end_src
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#+begin_src c :tangle (eval h_private_func)
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qmckl_exit_code float_tiled_matrix_init (qmckl_context context,
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float_tiled_matrix* m,
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size_t rows,
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size_t cols);
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qmckl_exit_code double_tiled_matrix_init (qmckl_context context,
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double_tiled_matrix* m,
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size_t rows,
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size_t cols);
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#+end_src
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#+begin_src c :tangle (eval c)
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qmckl_exit_code float_tiled_matrix_init (qmckl_context context,
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float_tiled_matrix* m,
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size_t rows,
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size_t cols) {
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if (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
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return QMCKL_INVALID_CONTEXT;
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}
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if (m == NULL) {
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return qmckl_failwith(context,
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QMCKL_INVALID_ARG_2,
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"float_tiled_matrix_init",
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NULL);
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}
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if (rows == (size_t) 0) {
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return qmckl_failwith(context,
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QMCKL_INVALID_ARG_3,
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"float_tiled_matrix_init",
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NULL);
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}
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if (cols == (size_t) 0) {
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return qmckl_failwith(context,
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QMCKL_INVALID_ARG_4,
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"float_tiled_matrix_init",
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NULL);
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}
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qmckl_memory_info_struct info = qmckl_memory_info_struct_zero;
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size_t n = rows * cols;
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/* Check overflow */
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if (n/cols != rows
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|| n > SIZE_MAX / sizeof(float_tile_struct) ) {
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return qmckl_failwith(context,
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QMCKL_ALLOCATION_FAILED,
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"float_tiled_matrix_init",
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"rows * cols overflows" );
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}
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/* Allocate array of column pointers */
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info.size = cols * sizeof(float_tile_struct*) ;
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m->tile = (float_tile_struct**) qmckl_malloc(context, info);
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if (m->tile == NULL) {
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return qmckl_failwith(context,
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QMCKL_ALLOCATION_FAILED,
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"float_tiled_matrix_init",
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NULL);
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}
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/* Allocate array of tiles */
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info.size = n * sizeof(float_tile_struct) ;
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m->tile[0] = (float_tile_struct*) qmckl_malloc(context, info);
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if (m->tile[0] == NULL) {
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return qmckl_failwith(context,
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QMCKL_ALLOCATION_FAILED,
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"float_tiled_matrix_init",
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NULL);
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}
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/* Compute array of pointers to the 1st element of columns */
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for (size_t i=1 ; i<cols ; ++i) {
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m->tile[i] = m->tile[i-1] + rows;
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}
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m->rows = rows;
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m->cols = cols;
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return QMCKL_SUCCESS;
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}
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qmckl_exit_code double_tiled_matrix_init (qmckl_context context,
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double_tiled_matrix* m,
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size_t rows,
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size_t cols) {
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if (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
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return QMCKL_INVALID_CONTEXT;
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}
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if (m == NULL) {
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return qmckl_failwith(context,
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QMCKL_INVALID_ARG_2,
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"double_tiled_matrix_init",
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NULL);
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}
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if (rows == (size_t) 0) {
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return qmckl_failwith(context,
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QMCKL_INVALID_ARG_3,
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"double_tiled_matrix_init",
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NULL);
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}
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if (cols == (size_t) 0) {
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return qmckl_failwith(context,
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QMCKL_INVALID_ARG_4,
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"double_tiled_matrix_init",
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NULL);
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}
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qmckl_memory_info_struct info = qmckl_memory_info_struct_zero;
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size_t n = rows * cols;
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/* Check overflow */
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if (n/cols != rows
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|| n > SIZE_MAX / sizeof(double_tile_struct) ) {
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return qmckl_failwith(context,
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QMCKL_ALLOCATION_FAILED,
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"double_tiled_matrix_init",
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"rows * cols overflows" );
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}
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/* Allocate array of column pointers */
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info.size = cols * sizeof(double_tile_struct*) ;
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m->tile = (double_tile_struct**) qmckl_malloc(context, info);
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if (m->tile == NULL) {
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return qmckl_failwith(context,
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QMCKL_ALLOCATION_FAILED,
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"double_tiled_matrix_init",
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NULL);
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}
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/* Allocate array of tiles */
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info.size = n * sizeof(double_tile_struct) ;
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m->tile[0] = (double_tile_struct*) qmckl_malloc(context, info);
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if (m->tile[0] == NULL) {
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return qmckl_failwith(context,
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QMCKL_ALLOCATION_FAILED,
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"double_tiled_matrix_init",
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NULL);
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}
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/* Compute array of pointers to the 1st element of columns */
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for (size_t i=1 ; i<cols ; ++i) {
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m->tile[i] = m->tile[i-1] + rows;
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}
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m->rows = rows;
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m->cols = cols;
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return QMCKL_SUCCESS;
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}
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#+end_src
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:end:
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* End of files :noexport:
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#+begin_src c :tangle (eval h_private_type)
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#endif
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#+end_src
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*** Test
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#+begin_src c :tangle (eval c_test)
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if (qmckl_context_destroy(context) != QMCKL_SUCCESS)
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return QMCKL_FAILURE;
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return MUNIT_OK;
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}
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#+end_src
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**✸ Compute file names
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#+begin_src emacs-lisp
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; The following is required to compute the file names
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(setq pwd (file-name-directory buffer-file-name))
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(setq name (file-name-nondirectory (substring buffer-file-name 0 -4)))
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(setq f (concat pwd name "_f.f90"))
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(setq fh (concat pwd name "_fh.f90"))
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(setq c (concat pwd name ".c"))
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(setq h (concat name ".h"))
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(setq h_private (concat name "_private.h"))
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(setq c_test (concat pwd "test_" name ".c"))
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(setq f_test (concat pwd "test_" name "_f.f90"))
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; Minted
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(require 'ox-latex)
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(setq org-latex-listings 'minted)
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(add-to-list 'org-latex-packages-alist '("" "listings"))
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(add-to-list 'org-latex-packages-alist '("" "color"))
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#+end_src
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#+RESULTS:
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| | color |
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| | listings |
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# -*- mode: org -*-
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# vim: syntax=c
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