39 #include <m4ri/m4ri_config.h>
46 #include <emmintrin.h>
50 #include <m4ri/debug_dump.h>
58 #define __M4RI_MAX_MZD_BLOCKSIZE (((size_t)1) << 27)
68 #define __M4RI_MUL_BLOCKSIZE MIN(((int)sqrt((double)(4 * __M4RI_CPU_L3_CACHE))) / 2, 2048)
207 assert(M->
nrows == 0 || result == M->
rows[0]);
263 return n ? 0 : M->
nrows;
288 return n ? 0 : M->
nrows - r;
307 assert(result == M->
rows[row]);
372 #define mzd_free_window mzd_free
384 if ((rowa == rowb) || (startblock >= M->
width))
388 word *a = M->
rows[rowa] + startblock;
389 word *b = M->
rows[rowb] + startblock;
393 for(
wi_t i = 0; i < width; ++i) {
398 tmp = (a[width] ^ b[width]) & mask_end;
402 __M4RI_DD_ROW(M, rowa);
403 __M4RI_DD_ROW(M, rowb);
456 rci_t const _cola = cola;
457 rci_t const _colb = colb;
466 int max_bit =
MAX(a_bit, b_bit);
467 int count_remaining = stop_row - start_row;
468 int min_bit = a_bit + b_bit - max_bit;
470 int offset = max_bit - min_bit;
478 if (a_word == b_word) {
480 count_remaining -= count;
482 int fast_count = count / 4;
483 int rest_count = count - 4 * fast_count;
486 while (fast_count--) {
488 xor_v[1] = ptr[rowstride];
489 xor_v[2] = ptr[2 * rowstride];
490 xor_v[3] = ptr[3 * rowstride];
491 xor_v[0] ^= xor_v[0] >> offset;
492 xor_v[1] ^= xor_v[1] >> offset;
493 xor_v[2] ^= xor_v[2] >> offset;
494 xor_v[3] ^= xor_v[3] >> offset;
499 xor_v[0] |= xor_v[0] << offset;
500 xor_v[1] |= xor_v[1] << offset;
501 xor_v[2] |= xor_v[2] << offset;
502 xor_v[3] |= xor_v[3] << offset;
504 ptr[rowstride] ^= xor_v[1];
505 ptr[2 * rowstride] ^= xor_v[2];
506 ptr[3 * rowstride] ^= xor_v[3];
507 ptr += 4 * rowstride;
509 while (rest_count--) {
511 xor_v ^= xor_v >> offset;
513 *ptr ^= xor_v | (xor_v << offset);
522 word* RESTRICT min_ptr;
524 if (min_bit == a_bit) {
525 min_ptr = ptr + a_word;
526 max_offset = b_word - a_word;
528 min_ptr = ptr + b_word;
529 max_offset = a_word - b_word;
532 count_remaining -= count;
535 word xor_v = (min_ptr[0] ^ (min_ptr[max_offset] >> offset)) & mask;
537 min_ptr[max_offset] ^= xor_v << offset;
538 min_ptr += rowstride;
544 if (min_bit == a_bit)
545 min_ptr = ptr + a_word;
547 min_ptr = ptr + b_word;
599 M->
rows[x][block] ^= values << spot;
602 M->
rows[x][block + 1] ^= values >> space;
621 M->
rows[x][block] &= values << spot;
624 M->
rows[x][block + 1] &= values >> space;
641 M->
rows[x][block] &= ~(values << spot);
644 M->
rows[x][block + 1] &= ~(values >> space);
660 assert(dstrow < M->nrows && srcrow < M->nrows && coloffset < M->ncols);
663 word *src = M->
rows[srcrow] + startblock;
664 word *dst = M->
rows[dstrow] + startblock;
668 *dst++ ^= *src++ & mask_begin;
673 if (wide > not_aligned + 1)
680 __m128i* __src = (__m128i*)src;
681 __m128i* __dst = (__m128i*)dst;
682 __m128i*
const eof = (__m128i*)((
unsigned long)(src + wide) & ~0xFUL);
685 __m128i xmm1 = _mm_xor_si128(*__dst, *__src);
688 while(++__src < eof);
691 wide = ((
sizeof(
word)*wide)%16)/
sizeof(
word);
704 dst[i - 1] ^= src[i - 1] & ~mask_end;
706 __M4RI_DD_ROW(M, dstrow);
978 #define mzd_sub mzd_add
988 #define _mzd_sub _mzd_add
1005 word temp = (spill <= 0) ? M->
rows[x][block] << -spill : (M->
rows[x][block + 1] << (m4ri_radix - spill)) | (M->
rows[x][block] >> spill);
1006 return temp >> (m4ri_radix - n);
1029 wi_t wide = A->
width - a_startblock - 1;
1031 word *a = A->
rows[a_row] + a_startblock;
1032 word *b = B->
rows[b_row] + b_startblock;
1034 #if __M4RI_HAVE_SSE2
1043 __m128i *a128 = (__m128i*)a;
1044 __m128i *b128 = (__m128i*)b;
1045 const __m128i *eof = (__m128i*)((
unsigned long)(a + wide) & ~0xFUL);
1048 *a128 = _mm_xor_si128(*a128, *b128);
1051 }
while(a128 < eof);
1055 wide = ((
sizeof(
word) * wide) % 16) /
sizeof(
word);
1058 #endif // __M4RI_HAVE_SSE2
1061 wi_t n = (wide + 7) / 8;
1063 case 0:
do { *(a++) ^= *(b++);
1064 case 7: *(a++) ^= *(b++);
1065 case 6: *(a++) ^= *(b++);
1066 case 5: *(a++) ^= *(b++);
1067 case 4: *(a++) ^= *(b++);
1068 case 3: *(a++) ^= *(b++);
1069 case 2: *(a++) ^= *(b++);
1070 case 1: *(a++) ^= *(b++);
1104 wi_t wide = A->
width - a_startblock - 1;
1105 word *a = A->
rows[a_row] + a_startblock;
1106 word *b = B->
rows[b_row] + b_startblock;
1107 word *c = C->
rows[c_row] + c_startblock;
1109 #if __M4RI_HAVE_SSE2
1118 __m128i *a128 = (__m128i*)a;
1119 __m128i *b128 = (__m128i*)b;
1120 __m128i *c128 = (__m128i*)c;
1121 const __m128i *eof = (__m128i*)((
unsigned long)(a + wide) & ~0xFUL);
1124 *c128 = _mm_xor_si128(*a128, *b128);
1128 }
while(a128 < eof);
1133 wide = ((
sizeof(
word) * wide) % 16) /
sizeof(
word);
1136 #endif // __M4RI_HAVE_SSE2
1139 wi_t n = (wide + 7) / 8;
1141 case 0:
do { *(c++) = *(a++) ^ *(b++);
1142 case 7: *(c++) = *(a++) ^ *(b++);
1143 case 6: *(c++) = *(a++) ^ *(b++);
1144 case 5: *(c++) = *(a++) ^ *(b++);
1145 case 4: *(c++) = *(a++) ^ *(b++);
1146 case 3: *(c++) = *(a++) ^ *(b++);
1147 case 2: *(c++) = *(a++) ^ *(b++);
1148 case 1: *(c++) = *(a++) ^ *(b++);
1180 if( (C == A) & (a_row == c_row) & (a_startblock == c_startblock) )
1183 mzd_combine_even(C, c_row, c_startblock, A, a_row, a_startblock, B, b_row, b_startblock);
static void mzd_clear_bits(mzd_t const *M, rci_t const x, rci_t const y, int const n)
Clear n bits in M starting a position (x,y).
Definition: mzd.h:636
void mzd_copy_row(mzd_t *B, rci_t i, mzd_t const *A, rci_t j)
copy row j from A to row i from B.
Definition: mzd.c:1999
mzd_t * mzd_stack(mzd_t *C, mzd_t const *A, mzd_t const *B)
Stack A on top of B and write the result to C.
Definition: mzd.c:1694
#define __M4RI_WRITE_BIT(w, spot, value)
Write the value to the bit spot in the word w.
Definition: misc.h:236
static word mzd_hash(mzd_t const *A)
Return hash value for matrix.
Definition: mzd.h:1284
static void mzd_combine(mzd_t *C, rci_t const c_row, wi_t const c_startblock, mzd_t const *A, rci_t const a_row, wi_t const a_startblock, mzd_t const *B, rci_t const b_row, wi_t const b_startblock)
row3[col3:] = row1[col1:] + row2[col2:]
Definition: mzd.h:1176
rci_t mzd_gauss_delayed(mzd_t *M, rci_t const startcol, int const full)
Gaussian elimination.
Definition: mzd.c:309
static word * mzd_first_row_next_block(mzd_t const *M, int n)
Get a pointer to the first word in block n.
Definition: mzd.h:221
mzd_t * mzd_invert_naive(mzd_t *INV, mzd_t const *A, mzd_t const *I)
Invert the matrix target using Gaussian elimination.
Definition: mzd.c:1725
static word mzd_read_bits(mzd_t const *M, rci_t const x, rci_t const y, int const n)
Definition: mzd.h:1001
word high_bitmask
Definition: mzd.h:133
struct mzd_t mzd_t
Dense matrices over GF(2).
mzd_t * mzd_addmul_naive(mzd_t *C, mzd_t const *A, mzd_t const *B)
Naive cubic matrix multiplication and addition.
Definition: mzd.c:1435
mzd_block_t * blocks
Definition: mzd.h:134
int BIT
Pretty for a boolean int.
Definition: misc.h:64
#define __M4RI_RIGHT_BITMASK(n)
create a bit mask to zero out all but the n rightmost bits.
Definition: misc.h:296
static int const m4ri_radix
The number of bits in a word.
Definition: misc.h:141
mzd_t * mzd_mul_naive(mzd_t *C, mzd_t const *A, mzd_t const *B)
Naive cubic matrix multiplication.
Definition: mzd.c:1417
uint8_t flags
Definition: mzd.h:124
static mzd_t const * mzd_init_window_const(mzd_t const *M, rci_t const lowr, rci_t const lowc, rci_t const highr, rci_t const highc)
Create a const window/view into a const matrix M.
Definition: mzd.h:361
static uint8_t const mzd_flag_windowed_zeroexcess
flag for windowed matrix where ncols%64 == 0
Definition: mzd.h:161
uint64_t dummy
Definition: mzd.h:136
Dense matrices over GF(2).
Definition: mzd.h:86
static void mzd_combine_even_in_place(mzd_t *A, rci_t const a_row, wi_t const a_startblock, mzd_t const *B, rci_t const b_row, wi_t const b_startblock)
a_row[a_startblock:] += b_row[b_startblock:] for offset 0
Definition: mzd.h:1026
int rci_t
Type of row and column indexes.
Definition: misc.h:72
#define MIN(x, y)
Return the minimal element of x and y.
Definition: misc.h:174
mzd_t * mzd_submatrix(mzd_t *S, mzd_t const *M, rci_t const lowr, rci_t const lowc, rci_t const highr, rci_t const highc)
Copy a submatrix.
Definition: mzd.c:1852
int mzd_equal(mzd_t const *A, mzd_t const *B)
Return TRUE if A == B.
Definition: mzd.c:1590
mzd_t * _mzd_mul_va(mzd_t *C, mzd_t const *v, mzd_t const *A, int const clear)
Matrix multiplication optimized for v*A where v is a vector.
Definition: mzd.c:1539
static void mzd_and_bits(mzd_t const *M, rci_t const x, rci_t const y, int const n, word values)
AND n bits from values to M starting a position (x,y).
Definition: mzd.h:615
mzd_t * mzd_concat(mzd_t *C, mzd_t const *A, mzd_t const *B)
Concatenate B to A and write the result to C.
Definition: mzd.c:1665
void mzd_free(mzd_t *A)
Free a matrix created with mzd_init.
Definition: mzd.c:272
static word const m4ri_ffff
A word with all bits set.
Definition: misc.h:153
mzd_t * mzd_transpose(mzd_t *DST, mzd_t const *A)
Transpose a matrix.
Definition: mzd.c:1386
static void mzd_write_bit(mzd_t *M, rci_t const row, rci_t const col, BIT const value)
Write the bit value to position M[row,col].
Definition: mzd.h:581
mzd_t * mzd_add(mzd_t *C, mzd_t const *A, mzd_t const *B)
Set C = A+B.
Definition: mzd.c:1745
mzd_t * mzd_extract_l(mzd_t *L, mzd_t const *A)
Definition: mzd.c:2232
mzd_t * _mzd_mul_naive(mzd_t *C, mzd_t const *A, mzd_t const *B, int const clear)
Naive cubic matrix multiplication with the pre-transposed B.
Definition: mzd.c:1450
rci_t mzd_echelonize_naive(mzd_t *M, int const full)
Gaussian elimination.
Definition: mzd.c:336
rci_t nrows
Definition: mzd.h:88
static void mzd_col_swap_in_rows(mzd_t *M, rci_t const cola, rci_t const colb, rci_t const start_row, rci_t const stop_row)
Swap the two columns cola and colb but only between start_row and stop_row.
Definition: mzd.h:452
static void _mzd_row_swap(mzd_t *M, rci_t const rowa, rci_t const rowb, wi_t const startblock)
Swap the two rows rowa and rowb starting at startblock.
Definition: mzd.h:383
size_t size
Definition: mzd.h:75
static wi_t mzd_remaining_rows_in_block(mzd_t const *M, rci_t r)
Number of rows in this block including r.
Definition: mzd.h:275
word ** rows
Definition: mzd.h:135
static uint8_t const mzd_flag_windowed_zerooffset
flag for windowed matrix
Definition: mzd.h:155
#define MAX(x, y)
Return the maximal element of x and y.
Definition: misc.h:163
mzd_t * mzd_init_window(mzd_t *M, rci_t const lowr, rci_t const lowc, rci_t const highr, rci_t const highc)
Create a window/view into the matrix M.
Definition: mzd.c:230
void mzd_randomize(mzd_t *M)
Fill matrix M with uniformly distributed bits.
Definition: mzd.c:1555
#define __M4RI_ALIGNMENT(addr, n)
Return alignment of addr w.r.t. n. For example the address 17 would be 1 aligned w.r.t. 16.
Definition: misc.h:421
mzd_t * mzd_copy(mzd_t *DST, mzd_t const *A)
Copy matrix A to DST.
Definition: mzd.c:1640
Data containers containing the values packed into words.
Definition: mzd.h:74
void mzd_row_add(mzd_t *M, rci_t const sourcerow, rci_t const destrow)
Add the rows sourcerow and destrow and stores the total in the row destrow.
Definition: mzd.c:285
static wi_t mzd_rows_in_block(mzd_t const *M, int n)
Total number of rows in this block.
Definition: mzd.h:252
static wi_t const mzd_paddingwidth
The minimum width where padding occurs.
Definition: mzd.h:143
wi_t offset_vector
Definition: mzd.h:108
mzd_t * _mzd_add(mzd_t *C, mzd_t const *A, mzd_t const *B)
Same as mzd_add but without any checks on the input.
Definition: mzd.c:1759
wi_t row_offset
Definition: mzd.h:110
static int mzd_row_to_block(mzd_t const *M, rci_t row)
Convert row to blocks index.
Definition: mzd.h:235
static int mzd_read_bits_int(mzd_t const *M, rci_t const x, rci_t const y, int const n)
Get n bits starting a position (x,y) from the matrix M.
Definition: mzd.h:1195
mzd_t * mzd_extract_u(mzd_t *U, mzd_t const *A)
Definition: mzd.c:2216
static uint8_t const mzd_flag_multiple_blocks
flag for multiply blocks
Definition: mzd.h:173
static void mzd_row_swap(mzd_t *M, rci_t const rowa, rci_t const rowb)
Swap the two rows rowa and rowb.
Definition: mzd.h:414
static int mzd_is_windowed(mzd_t const *M)
Test if a matrix is windowed.
Definition: mzd.h:182
static int mzd_owns_blocks(mzd_t const *M)
Test if this mzd_t should free blocks.
Definition: mzd.h:193
mzd_t * mzd_init(rci_t const r, rci_t const c)
Create a new matrix of dimension r x c.
Definition: mzd.c:150
static word * mzd_first_row(mzd_t const *M)
Get a pointer the first word.
Definition: mzd.h:205
double _mzd_density(mzd_t const *A, wi_t res, rci_t r, rci_t c)
Return the number of nonzero entries divided by nrows * ncols considering only the submatrix starting...
Definition: mzd.c:2155
uint8_t blockrows_log
Definition: mzd.h:131
static void mzd_combine_even(mzd_t *C, rci_t const c_row, wi_t const c_startblock, mzd_t const *A, rci_t const a_row, wi_t const a_startblock, mzd_t const *B, rci_t const b_row, wi_t const b_startblock)
c_row[c_startblock:] = a_row[a_startblock:] + b_row[b_startblock:] for offset 0
Definition: mzd.h:1100
static word const m4ri_one
The number one as a word.
Definition: misc.h:147
int mzd_is_zero(mzd_t const *A)
Zero test for matrix.
Definition: mzd.c:1986
double mzd_density(mzd_t const *A, wi_t res)
Return the number of nonzero entries divided by nrows * ncols.
Definition: mzd.c:2192
void mzd_col_swap(mzd_t *M, rci_t const cola, rci_t const colb)
Swap the two columns cola and colb.
Definition: mzd.c:1892
word * end
Definition: mzd.h:77
void mzd_set_ui(mzd_t *M, unsigned int const value)
Set the matrix M to the value equivalent to the integer value provided.
Definition: mzd.c:1567
wi_t rowstride
Definition: mzd.h:99
int mzd_find_pivot(mzd_t const *M, rci_t start_row, rci_t start_col, rci_t *r, rci_t *c)
Find the next nonzero entry in M starting at start_row and start_col.
Definition: mzd.c:2021
static uint8_t const mzd_flag_nonzero_excess
flag when ncols%64 == 0
Definition: mzd.h:149
static word * mzd_row(mzd_t const *M, rci_t row)
Get pointer to first word of row.
Definition: mzd.h:300
static void mzd_row_add_offset(mzd_t *M, rci_t dstrow, rci_t srcrow, rci_t coloffset)
Add the rows sourcerow and destrow and stores the total in the row destrow, but only begins at the co...
Definition: mzd.h:659
rci_t ncols
Definition: mzd.h:89
static BIT mzd_read_bit(mzd_t const *M, rci_t const row, rci_t const col)
Read the bit at position M[row,col].
Definition: mzd.h:565
int mzd_cmp(mzd_t const *A, mzd_t const *B)
Return -1,0,1 if if A < B, A == B or A > B respectively.
Definition: mzd.c:1612
#define __M4RI_UNLIKELY(cond)
Macro to help with branch prediction.
Definition: misc.h:449
wi_t width
Definition: mzd.h:90
uint64_t word
A word is the typical packed data structure to represent packed bits.
Definition: misc.h:87
int wi_t
Type of word indexes.
Definition: misc.h:80
#define __M4RI_GET_BIT(w, spot)
Get the bit spot (counting from the left) in the word w.
Definition: misc.h:226
void mzd_row_clear_offset(mzd_t *M, rci_t const row, rci_t const coloffset)
Clear the given row, but only begins at the column coloffset.
Definition: mzd.c:289
static uint8_t const mzd_flag_windowed_ownsblocks
flag for windowed matrix wich owns its memory
Definition: mzd.h:167
static void mzd_xor_bits(mzd_t const *M, rci_t const x, rci_t const y, int const n, word values)
XOR n bits from values to M starting a position (x,y).
Definition: mzd.h:596
#define __M4RI_CONVERT_TO_INT(w)
Explicit conversion macro.
Definition: misc.h:99
word * begin
Definition: mzd.h:76
rci_t mzd_first_zero_row(mzd_t const *A)
Return the first row with all zero entries.
Definition: mzd.c:2196