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sparse.c
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/* sparse.c
A library for large sparse histograms, and compressed sparse matrices,
tailored to support the generation of channel matrices for side-channel
analysis.
This code is experimental, and error-handling is primitive.
*/
/* Copyright 2013, NICTA. See COPYRIGHT for license details. */
#include <assert.h>
#include <limits.h>
#include <malloc.h>
#include <math.h>
#include <pthread.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include "sparse.h"
#undef DEBUG_SPARSE
#ifdef DEBUG_SPARSE
#define D(f,...) printf("%s: " f, __func__, __VA_ARGS__)
#else
#define D(f,...)
#endif
/* Allocate and return an empty histogram. */
bsc_hist_t*
bsc_hist_new(void) {
bsc_hist_t *H;
H= (bsc_hist_t *)calloc(1, sizeof(bsc_hist_t));
if(!H) { perror("malloc"); abort(); }
return H;
}
/* Deallocate a histogram. */
void
bsc_hist_destroy(bsc_hist_t *H) {
int c;
assert(H);
if(H->row_total) free(H->row_total);
if(H->entries) {
for(c= 0; c < H->end_col; c++) {
if(H->entries[c]) free(H->entries[c]);
}
free(H->entries);
}
if(H->start_rows) free(H->start_rows);
if(H->end_rows) free(H->end_rows);
free(H);
}
/* Extend histogram to include (at least) column c. */
void
bsc_extend(bsc_hist_t *H, int c) {
int new_end;
int i;
D("%p, %d\n", H, c);
assert(H);
assert(0 <= c);
assert(c < INT_MAX);
/* Nothing to do */
if(c < H->end_col) return;
/* Round from c up the next block size. */
new_end= c+1;
assert(H->end_col < new_end);
/* Extend arrays. New columns start at INT_MAX... */
H->start_rows= (int *)realloc(H->start_rows, new_end * sizeof(int));
if(!H->start_rows) { perror("realloc"); abort(); }
for(i= H->end_col; i < new_end; i++) H->start_rows[i]= INT_MAX;
/* and end before 0. Sentinels. */
H->end_rows= (int *)realloc(H->end_rows, new_end * sizeof(int));
if(!H->end_rows) { perror("realloc"); abort(); }
memset(H->end_rows + H->end_col, 0, (new_end - H->end_col) * sizeof(int));
H->entries= (int **)realloc(H->entries, new_end * sizeof(int *));
if(!H->entries) { perror("realloc"); abort(); }
memset(H->entries + H->end_col, 0, (new_end - H->end_col) * sizeof(int *));
H->end_col= new_end;
}
/* Extend column c to include all existing rows, plus (at least) row r. */
void
bsc_extend_col(bsc_hist_t *H, int c, int r) {
int new_start, new_end;
int *new_col;
D("%p, %d, %d\n", H, c, r);
assert(H);
assert(0 <= c);
assert(c < H->end_col);
assert(0 <= r);
/* Extend the row total array. */
if(r >= H->end_row) {
H->row_total= (int *)realloc(H->row_total, (r+1) * sizeof(int));
if(!H->row_total) { perror("realloc"); abort(); }
memset(H->row_total + H->end_row, 0,
(r+1 - H->end_row) * sizeof(int));
H->end_row= r + 1;
}
/* Nothing more to do */
if(H->start_rows[c] <= r && r < H->end_rows[c]) return;
new_start= H->start_rows[c];
new_end= H->end_rows[c];
if(r < H->start_rows[c]) {
/* Round r down to block size */
new_start= r - (r % ROW_BLOCK);
}
if(H->end_rows[c] <= r) {
/* Round r up to block size */
new_end= r + ROW_BLOCK;
new_end-= new_end % ROW_BLOCK;
}
assert(new_start <= H->start_rows[c]);
assert(H->end_rows[c] <= new_end);
assert(new_start <= new_end);
/* Reallocate column */
new_col= (int *)calloc(new_end - new_start, sizeof(int));
if(!new_col) { perror("calloc"); abort(); }
/* Copy existing entries */
if(H->start_rows[c] < H->end_rows[c]) { /* Guard against sentinels. */
assert(H->entries[c] != (void *)0);
memcpy(new_col + (H->start_rows[c] - new_start),
H->entries[c],
(H->end_rows[c] - H->start_rows[c]) * sizeof(int));
H->nalloc+= (H->start_rows[c] - new_start) +
(new_end - H->end_rows[c]);
}
else {
H->nalloc+= ROW_BLOCK;
}
/* Free the old column */
free(H->entries[c]);
/* Update bookkeeping */
H->start_rows[c]= new_start;
H->end_rows[c]= new_end;
H->entries[c]= new_col;
}
/* Increment the count at (r,c), extending as required. */
void
bsc_hist_count(bsc_hist_t *H, int c, int r, int n) {
assert(H);
assert(n > 0);
D("%p, %d, %d, %d\n", H, c, r, n);
/* Extend as required */
bsc_extend(H, c);
bsc_extend_col(H, c, r);
assert(c < H->end_col);
assert(H->start_rows[c] <= r);
assert(r < H->end_rows[c]);
/* Increment the appropriate entry */
if(H->entries[c][r - H->start_rows[c]] == 0) H->nnz++;
H->entries[c][r - H->start_rows[c]]+= n;
/* Increment the totals */
H->total+= n;
H->row_total[r]+= n;
}
/* Normalize a histogram, to give a conditional probability matrix. */
csc_mat_t *
bsc_normalise(bsc_hist_t *H) {
int c, r, i;
csc_mat_t *M;
assert(H);
M= (csc_mat_t *)calloc(1, sizeof(csc_mat_t));
if(!M) { perror("calloc"); abort(); }
/* Allocate and initialise */
M->ver= CSC_VERSION;
M->flags= 0; /* No stride. */
M->nrow= H->end_row;
M->ncol= H->end_col;
M->nnz= H->nnz;
M->ci= memalign(64, (M->ncol + 1) * sizeof(int));
if(!M->ci) { perror("malloc"); abort(); }
M->rows= memalign(64, M->nnz * sizeof(int));
if(!M->rows) { perror("malloc"); abort(); }
M->entries= memalign(64, M->nnz * sizeof(float));
if(!M->entries) { perror("malloc"); abort(); }
i= 0;
for(c= 0; c < H->end_col; c++) {
/* Record the start of column. */
M->ci[c]= i;
for(r= H->start_rows[c]; r < H->end_rows[c]; r++) {
int n;
n= H->entries[c][r - H->start_rows[c]];
if(n > 0) { /* Drop zeros */
assert(i < M->nnz);
assert(0 < H->row_total[r]);
/* Record row number. */
M->rows[i]= r;
/* Scale and store count. */
M->entries[i]= (float)n / H->row_total[r];
/* Increment in destination array. */
i++;
}
}
}
M->ci[c]= i;
return M;
}
/* Size (in bytes) of the allocated histogram. */
uint64_t
bsc_size(bsc_hist_t *H) {
int cols= H->end_col;
int rows= H->end_row;
assert(H);
/* The root struct. */
return sizeof(bsc_hist_t) +
/* start_rows and end_rows */
2 * cols * sizeof(int) +
/* row_total */
1 * rows * sizeof(int) +
/* entries */
cols * sizeof(int *) +
/* The entries themselves. */
H->nalloc * sizeof(int);
}
#define FAIL(s,...) { if(verbose) { fprintf(stderr, s, ##__VA_ARGS__); } \
return 0; }
#define SUCCEED() { return 1; }
/* Sanity check the histogram structure. */
int
bsc_check(bsc_hist_t *H, int verbose) {
int r, c;
int64_t nnz;
int total;
int *row_total;
if(!H) FAIL("H is null\n");
if(H->nalloc < 0) FAIL("nalloc (%ld) is negative\n", H->nalloc);
if(H->nnz < 0) FAIL("nnz (%ld) is negative\n", H->nnz);
if(H->nnz > H->nalloc) FAIL("nnz (%ld) > nalloc (%ld)\n",
H->nnz, H->nalloc);
if(H->end_col < 0) FAIL("end_col (%d) is negative\n", H->end_col);
if(H->end_row < 0) FAIL("end_row (%d) is negative\n", H->end_row);
if(!H->start_rows) FAIL("start_rows is NULL\n");
for(c= 0; c < H->end_col; c++) {
if(H->start_rows[c] < 0)
FAIL("start_rows[%d] (%d) is negative\n", c, H->start_rows[c]);
}
row_total= calloc(H->end_row, sizeof(int));
if(!row_total) {
perror("calloc");
abort();
}
nnz= 0; total= 0;
for(c= 0; c < H->end_col; c++) {
for(r= H->start_rows[c]; r < H->end_rows[c]; r++) {
int e= H->entries[c][r - H->start_rows[c]];
if(e < 0)
FAIL("entries[%d][%d] (%d) < 0", c, r - H->start_rows[c], e);
if(e > 0) {
if(r > H->end_row)
FAIL("%d,%d (%d) > end_row (%d)\n", c, r, e, H->end_row);
nnz++;
total+= e;
row_total[r]+= e;
}
}
}
if(H->nnz != nnz) FAIL("nnz (%ld) != calculated nnz (%ld)\n",
H->nnz, nnz);
if(H->total != total) FAIL("total (%d) != calculated total (%d)\n",
H->total, total);
for(r= 0; r < H->end_row; r++) {
if(H->row_total[r] != row_total[r])
FAIL("row_total[%d] (%d) != calculated row_total[%d] (%d)\n",
r, H->row_total[r], r, row_total[r]);
}
SUCCEED();
}
/* Sanity check the matrix structure. */
int
csc_check(csc_mat_t *M, int verbose) {
int64_t i;
if(!M) FAIL("M is null\n");
if(M->ver > CSC_VERSION) FAIL("Unknown version %d\n", M->ver);
if(M->flags & ~CSC_M_ALLFLAGS) FAIL("Unknown flags\n");
if(M->nrow < 0) FAIL("nrow is negative\n");
if(M->ncol < 0) FAIL("ncol is negative\n");
if(M->nnz < 0) FAIL("nnz is negative\n");
if(STRIDE_OF(M) > 1) {
int32_t last= 0;
if(M->ci) FAIL("Stride is %d but ci is not NULL.\n", STRIDE_OF(M));
if(!M->si) FAIL("Stride is %d but si is NULL.\n", STRIDE_OF(M));
if(M->flags & CSC_F_CFREE) {
if(!M->row_offsets)
FAIL("CFREE is true but row_offsets is NULL\n");
if(M->sc) FAIL("CFREE is true d but sc is not NULL.\n");
for(i= 0; i < M->nnz; i++) {
if(M->row_offsets[i] >= SPAN_OF(M))
FAIL("Row offset %d too large at element %lld\n",
M->row_offsets[i], (long long int)i);
}
}
else {
if(M->row_offsets)
FAIL("CFREE is false but row_offsets is not NULL\n");
if(!M->sc) FAIL("Stride is %d but sc is NULL.\n", STRIDE_OF(M));
for(i= 0; i < M->nnz; i++) {
if(M->sc[i] > STRIDE_OF(M))
FAIL("Stride column %d is greater than stride width"
" %d at element %lld\n", M->sc[i], STRIDE_OF(M),
(long long int)i);
}
}
for(i= 0; i < M->ncol / STRIDE_OF(M) + 1; i++) {
int j;
int32_t last_row= 0;
if(M->si[i] < 0 || M->si[i] > M->nnz)
FAIL("Stride index %d out of range at element %lld\n",
M->si[i], (long long int)i);
if(M->si[i] < last)
FAIL("Stride index %d out of order at element %lld\n",
M->si[i], (long long int)i);
last= M->si[i];
if(M->flags & CSC_F_CFREE) {
if(M->si[i] % STRIDE_OF(M))
FAIL("Index for stride %lld (%d) not a multiple of"
" stride\n", (long long int)i, M->si[i]);
for(j= M->si[i]; j < M->si[i+1]; j+= STRIDE_OF(M)) {
if(M->rows[j/STRIDE_OF(M)] < last_row)
FAIL("Row %d out of order at element %lld\n",
M->rows[j/STRIDE_OF(M)], (long long int)j);
last_row= M->rows[j/STRIDE_OF(M)];
}
}
else {
for(j= M->si[i]; j < M->si[i+1]; j++) {
if(M->rows[j] < last_row)
FAIL("Row %d out of order at element %lld\n",
M->rows[j], (long long int)j);
last_row= M->rows[j];
}
}
}
}
else {
int32_t last = 0;
if(M->flags & CSC_F_CFREE)
FAIL("Stride is %d but flag CFREE set\n", STRIDE_OF(M));
if(!M->ci) FAIL("Stride is %d but ci is NULL.\n", STRIDE_OF(M));
for(i= 0; i < M->ncol+1; i++) {
if(M->ci[i] < 0 || M->ci[i] > M->nnz)
FAIL("Column index %d out of range at element %lld\n",
M->ci[i], (long long int)i);
if(M->ci[i] < last)
FAIL("Column index %d out of order at element %lld\n",
M->ci[i], (long long int)i);
last= M->ci[i];
}
if(M->si) FAIL("Stride is %d but si is not NULL.\n", STRIDE_OF(M));
if(M->sc) FAIL("Stride is %d but sc is not NULL.\n", STRIDE_OF(M));
}
if(!M->rows) FAIL("rows is NULL\n");
if(M->flags & CSC_F_CFREE) {
for(i= 0; i < M->nnz/STRIDE_OF(M); i++) {
if(M->rows[i] < 0 || M->rows[i] >= M->nrow)
FAIL("Invalid row number %d in entry %lld\n",
M->rows[i], (long long int)i);
}
}
else {
for(i= 0; i < M->nnz; i++) {
if(M->rows[i] < 0 || M->rows[i] >= M->nrow)
FAIL("Invalid row number %d in entry %lld\n",
M->rows[i], (long long int)i);
}
}
if(!M->entries) FAIL("entries is NULL\n");
SUCCEED();
}
/* Size (in bytes) of the allocated matrix. */
uint64_t
csc_size(csc_mat_t *M) {
/* Strided matrix. */
if(STRIDE_OF(M) > 1) {
/* root struct */
return sizeof(csc_mat_t) +
/* si */
(M->ncol/STRIDE_OF(M)+1) * sizeof(int32_t) +
/* sc */
(M->nnz) * sizeof(uint8_t) +
/* rows */
(M->nnz) * sizeof(int32_t) +
/* entries */
(M->nnz) * sizeof(float);
}
/* Unstrided matrix. */
else {
/* root struct */
return sizeof(csc_mat_t) +
/* ci */
(M->ncol+1) * sizeof(int32_t) +
/* rows */
(M->nnz) * sizeof(int32_t) +
/* entries */
(M->nnz) * sizeof(float);
}
}
/* Deallocate matrix. */
void
csc_mat_destroy(csc_mat_t *M) {
assert(M);
if(STRIDE_OF(M) > 1) {
assert(M->si);
free(M->si);
if(M->flags & CSC_F_CFREE) {
assert(M->row_offsets);
free(M->row_offsets);
}
else {
assert(M->sc);
free(M->sc);
}
}
else {
assert(M->ci);
free(M->ci);
}
assert(M->rows);
free(M->rows);
assert(M->entries);
free(M->entries);
free(M);
}
static const char *csc_errstr[] = {
"Success",
"File truncated",
"Bad magic bytes",
"System error - check errno",
};
/* Readable errors. */
void
csc_perror(csc_errno_t e, const char *s) {
if(e < 0 || e >= E_CSC_COUNT) return;
if(e == E_CSC_ERRNO) perror(s);
else fprintf(stderr, "%s: %s\n", s, csc_errstr[e]);
}
/* Serialise into FD f */
csc_errno_t
csc_store_binary(csc_mat_t *M, FILE *f) {
if(fputs(CSC_MAGIC, f) == EOF) return E_CSC_ERRNO;
if(fwrite(&M->ver, sizeof(int32_t), 1, f) != 1)
return E_CSC_ERRNO;
if(fwrite(&M->flags, sizeof(int32_t), 1, f) != 1)
return E_CSC_ERRNO;
if(fwrite(&M->nrow, sizeof(int32_t), 1, f) != 1)
return E_CSC_ERRNO;
if(fwrite(&M->ncol, sizeof(int32_t), 1, f) != 1)
return E_CSC_ERRNO;
if(fwrite(&M->nnz, sizeof(int64_t), 1, f) != 1)
return E_CSC_ERRNO;
if(STRIDE_OF(M) > 1) {
if(fwrite(M->si, sizeof(int32_t),
M->ncol/STRIDE_OF(M)+1, f) != M->ncol/STRIDE_OF(M)+1)
return E_CSC_ERRNO;
if(M->flags & CSC_F_CFREE) {
if(fwrite(M->row_offsets, sizeof(uint8_t), M->nnz, f) != M->nnz)
return E_CSC_ERRNO;
}
else {
if(fwrite(M->sc, sizeof(uint8_t), M->nnz, f) != M->nnz)
return E_CSC_ERRNO;
}
}
else {
if(fwrite(M->ci, sizeof(int32_t), M->ncol+1, f) != M->ncol+1)
return E_CSC_ERRNO;
}
if(fwrite(M->rows, sizeof(int32_t), M->nnz, f) != M->nnz)
return E_CSC_ERRNO;
if(fwrite(M->entries, sizeof(float), M->nnz, f) != M->nnz)
return E_CSC_ERRNO;
return E_CSC_SUCCESS;
}
/* Deserialise from FD f */
csc_mat_t *
csc_load_binary(FILE *f, csc_errno_t *e) {
csc_mat_t *M;
size_t n;
char magic[12];
/* Check for magic */
n= fread(magic, 1, 12, f);
if(ferror(f)) { *e= E_CSC_ERRNO; return NULL; }
if(n < 12) { *e= E_CSC_TRUNC; return NULL; }
if(strncmp(magic, CSC_MAGIC, 12)) { *e= E_CSC_BADMAGIC; return NULL; }
/* Allocate root struct */
M= (csc_mat_t *)calloc(1,sizeof(csc_mat_t));
if(!M) { *e= E_CSC_ERRNO; return NULL; }
/* Read header */
n= 0;
n+= fread(&M->ver, sizeof(int32_t), 1, f);
if(ferror(f)) { *e= E_CSC_ERRNO; return NULL; }
n+= fread(&M->flags, sizeof(int32_t), 1, f);
if(ferror(f)) { *e= E_CSC_ERRNO; return NULL; }
n+= fread(&M->nrow, sizeof(int32_t), 1, f);
if(ferror(f)) { *e= E_CSC_ERRNO; return NULL; }
n+= fread(&M->ncol, sizeof(int32_t), 1, f);
if(ferror(f)) { *e= E_CSC_ERRNO; return NULL; }
n+= fread(&M->nnz, sizeof(int64_t), 1, f);
if(ferror(f)) { *e= E_CSC_ERRNO; return NULL; }
if(n != 5) { free(M); *e= E_CSC_TRUNC; return NULL; }
/* Allocate tables */
M->rows= memalign(64, M->nnz * sizeof(int32_t));
if(!M->rows) { free(M); *e= E_CSC_ERRNO; return NULL; }
M->entries= memalign(64, M->nnz * sizeof(int32_t));
if(!M->entries) { free(M->rows); free(M); *e= E_CSC_ERRNO; return NULL; }
if(STRIDE_OF(M) > 1) {
M->si= memalign(64, (M->ncol/STRIDE_OF(M) + 1) * sizeof(int32_t));
if(!M->si) { free(M->entries); free(M->rows); free(M);
*e= E_CSC_ERRNO; return NULL; }
if(M->flags & CSC_F_CFREE) {
M->row_offsets= memalign(64, M->nnz * sizeof(uint8_t));
if(!M->row_offsets) { free(M->si); free(M->entries);
*e= E_CSC_ERRNO; free(M->rows); free(M);
return NULL; }
}
else {
M->sc= memalign(64, M->nnz * sizeof(uint8_t));
if(!M->sc) { free(M->si); free(M->entries); *e= E_CSC_ERRNO;
free(M->rows); free(M); return NULL; }
}
}
else {
M->ci= memalign(64, (M->ncol + 1) * sizeof(int32_t));
if(!M->ci) { free(M->entries); free(M->rows); free(M);
*e= E_CSC_ERRNO; return NULL; }
}
/* Read tables */
if(STRIDE_OF(M) > 1) {
n= 0;
n+= fread(M->si, sizeof(int32_t), M->ncol/STRIDE_OF(M) + 1, f);
if(ferror(f)) { *e= E_CSC_ERRNO; return NULL; }
if(M->flags & CSC_F_CFREE) {
n+= fread(M->row_offsets, sizeof(uint8_t), M->nnz, f);
}
else {
n+= fread(M->sc, sizeof(uint8_t), M->nnz, f);
}
if(ferror(f)) { *e= E_CSC_ERRNO; return NULL; }
n+= fread(M->rows, sizeof(int32_t), M->nnz, f);
if(ferror(f)) { *e= E_CSC_ERRNO; return NULL; }
n+= fread(M->entries, sizeof(float), M->nnz, f);
if(ferror(f)) { *e= E_CSC_ERRNO; return NULL; }
if(n != M->ncol/STRIDE_OF(M) + 1 + 3 * M->nnz) {
free(M->si); free(M->sc); free(M->entries);
free(M->rows); free(M);
*e= E_CSC_TRUNC; return NULL;
}
}
else {
n= 0;
n+= fread(M->ci, sizeof(int32_t), M->ncol + 1, f);
if(ferror(f)) { *e= E_CSC_ERRNO; return NULL; }
n+= fread(M->rows, sizeof(int32_t), M->nnz, f);
if(ferror(f)) { *e= E_CSC_ERRNO; return NULL; }
n+= fread(M->entries, sizeof(float), M->nnz, f);
if(ferror(f)) { *e= E_CSC_ERRNO; return NULL; }
if(n != M->ncol+1 + 2 * M->nnz) {
free(M->ci); free(M->entries);
free(M->rows); free(M); *e= E_CSC_TRUNC; return NULL;
}
}
return M;
}
/* Prune (remove) empty columns. */
void
csc_prune_cols(csc_mat_t *M) {
int c_old, c_new;
assert(STRIDE_OF(M) == 1);
c_new= 0;
for(c_old= 0; c_old < M->ncol; c_old++) {
/* Only preserve nonempty columns. */
if(M->ci[c_old] != M->ci[c_old+1]) {
assert(c_new <= c_old);
/* Re-index the column. We never move anything to the right. */
M->ci[c_new]= M->ci[c_old];
c_new++;
}
}
/* Move the sentinel. */
M->ci[c_new]= M->ci[c_old];
/* Shrink the array. */
M->ncol= c_new;
M->ci= realloc(M->ci, (M->ncol+1) * sizeof(int32_t));
if(!M->ci) { perror("realloc"); abort(); }
}
void
mult_csc_dv_range(dv_t *y, dv_t *x, csc_mat_t *A, int start, int end) {
int c, i;
assert(x); assert(A); assert(y);
assert(STRIDE_OF(A) == 1);
assert(A->nrow == x->length);
assert(A->ncol == y->length);
assert(0 <= start && start <= end && end <= A->ncol);
#ifdef __AVX__
#if 0
mult_csc_dv_avx(y, x, A, 0, A->ncol);
return;
#endif
#endif
/* Step through the columns */
for(c= start; c < end; c++) {
float tmp= 0.0;
/* Step through the non-zero entries of this column. */
for(i= A->ci[c]; i < A->ci[c+1]; i++) {
/* Multiply by the appropriate entry of y. */
tmp+= A->entries[i] * x->entries[A->rows[i]];
}
y->entries[c]= tmp;
}
}
/* Compute y= x*A, where A is a Compressed-Sparse-Column sparse matrix,
and y and x are dense vectors. */
void
mult_csc_dv(dv_t *y, dv_t *x, csc_mat_t *A) {
mult_csc_dv_range(y, x, A, 0, A->ncol);
}
/* Threaded multiplication. */
struct mult_args {
dv_t *y, *x;
csc_mat_t *A;
int start, end;
};
void *
mult_thread(void *_args) {
struct mult_args *args= (struct mult_args *)_args;
mult_csc_dv_range(args->y, args->x, args->A, args->start, args->end);
return NULL;
}
void
mult_csc_dv_p(dv_t *y, dv_t *x, csc_mat_t *A, int n) {
pthread_t threads[n];
pthread_attr_t attr;
struct mult_args args[n];
int i;
int block= A->ncol / n;
assert(0 < n);
if(pthread_attr_init(&attr))
{ perror("pthread_attr_init"); abort(); }
for(i= 0; i < n - 1; i++) {
args[i].y= y;
args[i].x= x;
args[i].A= A;
args[i].start= i * block;
args[i].end= (i+1) * block;
if(pthread_create(&threads[i], &attr, mult_thread, &args[i]))
{ perror("pthread_create"); abort(); }
}
args[n-1].y= y;
args[n-1].x= x;
args[n-1].A= A;
args[n-1].start= (n-1) * block;
args[n-1].end= A->ncol;
if(pthread_create(&threads[n-1], &attr, mult_thread, &args[n-1]))
{ perror("pthread_create"); abort(); }
for(i= 0; i < n; i++) {
if(pthread_join(threads[i], NULL))
{ perror("pthread_join"); abort(); }
}
if(pthread_attr_destroy(&attr))
{ perror("pthread_attr_destroy"); abort(); }
}
/* Fallback non-vectorised multiply for strided matrix. */
void
csc_str_mult_nv(dv_t *y, dv_t *x, csc_mat_t *A) {
int s;
int stride;
assert(x); assert(A); assert(y);
assert(A->nrow == x->length);
assert(A->ncol == y->length);
assert(A->ncol % STRIDE_OF(A) == 0);
#ifdef __AVX__
if(STRIDE_OF(A) == 4) {
csc_str_mult_nv_4(y, x, A);
return;
}
else if(STRIDE_OF(A) == 8) {
csc_str_mult_nv_8(y, x, A);
return;
}
#endif
stride= STRIDE_OF(A);
for(s= 0; s < A->ncol/stride; s++) {
int i;
float tmp[stride];
memset(tmp, 0, stride * sizeof(float));
for(i= A->si[s]; i < A->si[s+1]; i++) {
assert(A->sc[i] < stride);
tmp[A->sc[i]]+= A->entries[i] * x->entries[A->rows[i]];
}
for(i= 0; i < stride; i++) {
y->entries[s * stride + i]= tmp[i];
}
}
}
/* Collision-free multiplication. */
void
csc_mult_cf(dv_t *y, dv_t *x, csc_mat_t *A) {
int s;
int stride;
assert(x); assert(A); assert(y);
assert(A->nrow == x->length);
assert(A->ncol == y->length);
assert(A->ncol % STRIDE_OF(A) == 0);
assert(A->nnz % STRIDE_OF(A) == 0);
assert(A->flags & CSC_F_CFREE);
#ifdef __AVX__
if(STRIDE_OF(A) == 4 && SPAN_OF(A) == 4) {
csc_mult_cf_4_4(y, x, A);
return ;
}
#endif
stride= STRIDE_OF(A);
dv_zero(y);
for(s= 0; s < A->ncol/stride; s++) {
int i;
float tmp[stride];
memset(tmp, 0, stride * sizeof(float));
assert(A->si[s] % stride == 0);
assert(A->si[s+1] % stride == 0);
for(i= A->si[s]; i < A->si[s+1]; i++) {
int row= A->rows[i/stride] + A->row_offsets[i];
tmp[i%stride]+= A->entries[i] * x->entries[row];
}
for(i= 0; i < stride; i++) {
y->entries[s * stride + i]= tmp[i];
}
}
}
int
find_row(int32_t *rows, int s, int e, int32_t r) {
assert(s <= e);
assert(s < INT_MAX/2);
assert(e < INT_MAX/2);
/* Binary search. */
while(s < e) {
int i= (s + e) / 2;
if(rows[i] <= r) s= i+1;
else e= i;
}
assert(s == e);
return e;
}
void
sort_stride(csc_mat_t *M, int s) {
int stride_start= M->si[s];
int stride_end= M->si[s+1];
int i;
printf("Stride %d, length %d\n", s, stride_end - stride_start);
/* An insertion sort for the moment. */
for(i= stride_start + 1; i < stride_end; i++) {
/* INV: M->rows[stride_start,i) is sorted. */
/* Find a spot for element i in [stride_start,i]. */
int j= find_row(M->rows, stride_start, i, M->rows[i]);
/* This guard is technically unnecessary. */
if(j != i) {
/* Save the values to move. */
uint8_t sc_i= M->sc[i];
int32_t rows_i= M->rows[i];
float entries_i= M->entries[i];
/* Shift the array tails along. */
memmove(&M->sc[j+1], &M->sc[j], (i-j) * sizeof(uint8_t));
memmove(&M->rows[j+1], &M->rows[j], (i-j) * sizeof(int32_t));
memmove(&M->entries[j+1], &M->entries[j], (i-j) * sizeof(float));
/* Put the saved values at j. */
M->sc[j]= sc_i;
M->rows[j]= rows_i;
M->entries[j]= entries_i;
}
}
}
void
merge_stride(csc_mat_t *M, int s, int width) {
int stride_start= M->si[s];
int stride_end= M->si[s+1];
int len= stride_end - stride_start;
uint8_t *sc_tmp= malloc(len * sizeof(uint8_t));
int32_t *rows_tmp= malloc(len * sizeof(int32_t));;
float *entries_tmp= malloc(len * sizeof(float));;
int *sc_i= malloc(width * sizeof(int));
int i;
if(width == 0) return;
if(!sc_tmp || !rows_tmp || !entries_tmp)
{ perror("malloc"); exit(EXIT_FAILURE); }
/* printf("Merging stride %d, length %d, width %d\n", s, len, width); */
/* Initialise the column indices. */
for(i= 0; i < width; i++) sc_i[i]= M->ci[s * STRIDE_OF(M) + i];
/* Merge columns element-by-element into temporary space. */
for(i= 0; i < len; i++) {
int j;
int min_j= -1, min_row= INT_MAX;
/* Find the smallest remaining head. */
for(j= 0; j < width; j++) {
/* Skip exhausted columns. */
if(sc_i[j] == M->ci[s * STRIDE_OF(M) + j + 1]) continue;
if(M->rows[sc_i[j]] < min_row) {
min_j= j;
min_row= M->rows[sc_i[j]];
}
}
assert(min_j != -1); /* We must have found something. */
/* Copy the elements. */
sc_tmp[i]= M->sc[sc_i[min_j]];
rows_tmp[i]= M->rows[sc_i[min_j]];
entries_tmp[i]= M->entries[sc_i[min_j]];
/* Cut the head off the column we just used. */
sc_i[min_j]++;
}
/* We should have exhausted all columns. */
for(i= 0; i < width; i++)
assert(sc_i[i] == M->ci[s * STRIDE_OF(M) + i + 1]);
free(sc_i);
/* Write back the temporary workspace. */
memcpy(&M->sc[stride_start], sc_tmp, len * sizeof(uint8_t));
memcpy(&M->rows[stride_start], rows_tmp, len * sizeof(int32_t));
memcpy(&M->entries[stride_start], entries_tmp, len * sizeof(float));
free(entries_tmp); free(rows_tmp); free(sc_tmp);
}
/* Convert a matrix to strided format, in-place. */
void
csc_stride(csc_mat_t *M, int r_stride) {
int s, c;
int ncol_new;
int stride= 1<<r_stride;
assert(M);
assert(0 <= r_stride && r_stride <= CSC_MAX_STRIDE);
assert(STRIDE_OF(M) == 1);
/* Set the stride. */
M->flags &= ~CSC_M_STRIDERADIX;
M->flags |= r_stride & CSC_M_STRIDERADIX;
/* Round up the number of columns. */
ncol_new= ROUND_UP(M->ncol, stride);
/* Allocate the stride structures. */
M->si= malloc(sizeof(int32_t) * (ncol_new / stride + 1));
M->sc= malloc(sizeof(uint8_t) * M->nnz);
if(!M->si || !M->sc) { perror("malloc"); exit(EXIT_FAILURE); }
/* Strides start at the beginning of the first column contained. */
for(s= 0; s < ncol_new / stride; s++) {
M->si[s]= M->ci[s * stride];
}
/* The sentinel must be moved explicitly. */
M->si[ncol_new / stride]= M->ci[M->ncol];
/* The entries all start out grouped by column. */
for(c= 0; c < M->ncol; c++) {
int i;
for(i= M->ci[c]; i < M->ci[c+1]; i++) M->sc[i]= c % stride;
}
/* Now sort the buggers */
for(s= 0; s < M->ncol / STRIDE_OF(M); s++)
merge_stride(M, s, STRIDE_OF(M));
/* The last stride may be incomplete in the original index. */
merge_stride(M, s, M->ncol % STRIDE_OF(M));
/* We're now done with the column indices (they're now
invalid anyway), so free them. */
free(M->ci); M->ci= NULL;
M->ncol= ncol_new;
}
/* Estimate the number of blocks required to make the matrix
collision-free. */