M4RI  20200125
mzd.h
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1 
10 #ifndef M4RI_MZD
11 #define M4RI_MZD
12 
13 /*******************************************************************
14 *
15 * M4RI: Linear Algebra over GF(2)
16 *
17 * Copyright (C) 2007, 2008 Gregory Bard <bard@fordham.edu>
18 * Copyright (C) 2008-2013 Martin Albrecht <M.R.Albrecht@rhul.ac.uk>
19 * Copyright (C) 2011 Carlo Wood <carlo@alinoe.com>
20 *
21 * Distributed under the terms of the GNU General Public License (GPL)
22 * version 2 or higher.
23 *
24 * This code is distributed in the hope that it will be useful,
25 * but WITHOUT ANY WARRANTY; without even the implied warranty of
26 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
27 * General Public License for more details.
28 *
29 * The full text of the GPL is available at:
30 *
31 * http://www.gnu.org/licenses/
32 *
33 ********************************************************************/
34 
35 #ifdef HAVE_CONFIG_H
36 #include "config.h"
37 #endif
38 
39 #include <m4ri/m4ri_config.h>
40 
41 #include <assert.h>
42 #include <math.h>
43 #include <stdio.h>
44 
45 #if __M4RI_HAVE_SSE2
46 #include <emmintrin.h>
47 #endif
48 
49 #include <m4ri/misc.h>
50 #include <m4ri/debug_dump.h>
51 
58 #define __M4RI_MAX_MZD_BLOCKSIZE (((size_t)1) << 27)
59 
68 #define __M4RI_MUL_BLOCKSIZE MIN(((int)sqrt((double)(4 * __M4RI_CPU_L3_CACHE))) / 2, 2048)
69 
74 typedef struct {
75  size_t size;
77  word *end;
78 } mzd_block_t;
79 
86 typedef struct mzd_t {
87 
100 
109 
124  uint8_t flags;
125 
131  uint8_t blockrows_log;
132 
133  /* ensures sizeof(mzd_t) == 64 */
134  uint8_t padding[62 - 2 * sizeof(rci_t) - 4 * sizeof(wi_t) - sizeof(word) - 2 * sizeof(void *)];
135 
138  word **rows;
139 } mzd_t;
140 
144 static wi_t const mzd_paddingwidth = 1;
145 
150 static uint8_t const mzd_flag_nonzero_excess = 0x2;
151 
156 static uint8_t const mzd_flag_windowed_zerooffset = 0x4;
157 
162 static uint8_t const mzd_flag_windowed_zeroexcess = 0x8;
163 
168 static uint8_t const mzd_flag_windowed_ownsblocks = 0x10;
169 
174 static uint8_t const mzd_flag_multiple_blocks = 0x20;
175 
183 static inline int mzd_is_windowed(mzd_t const *M) { return M->flags & (mzd_flag_windowed_zerooffset); }
184 
192 static inline int mzd_owns_blocks(mzd_t const *M) {
193  return M->blocks && (!mzd_is_windowed(M) || ((M->flags & mzd_flag_windowed_ownsblocks)));
194 }
195 
204 static inline word *mzd_first_row(mzd_t const *M) {
205  word *result = M->blocks[0].begin + M->offset_vector;
206  assert(M->nrows == 0 || result == M->rows[0]);
207  return result;
208 }
209 
220 static inline word *mzd_first_row_next_block(mzd_t const *M, int n) {
221  assert(n > 0);
222  return M->blocks[n].begin + M->offset_vector - M->row_offset * M->rowstride;
223 }
224 
234 static inline int mzd_row_to_block(mzd_t const *M, rci_t row) { return (M->row_offset + row) >> M->blockrows_log; }
235 
249 static inline wi_t mzd_rows_in_block(mzd_t const *M, int n) {
251  if (__M4RI_UNLIKELY(n == 0)) {
252  return (1 << M->blockrows_log) - M->row_offset;
253  } else {
254  int const last_block = mzd_row_to_block(M, M->nrows - 1);
255  if (n < last_block) {
256  return (1 << M->blockrows_log);
257  }
258  return M->nrows + M->row_offset - (n << M->blockrows_log);
259  }
260  }
261  return n ? 0 : M->nrows;
262 }
263 
273 static inline wi_t mzd_remaining_rows_in_block(mzd_t const *M, rci_t r) {
274  const int n = mzd_row_to_block(M, r);
275  r = (r - (n << M->blockrows_log));
277  if (__M4RI_UNLIKELY(n == 0)) {
278  return (1 << M->blockrows_log) - M->row_offset - r;
279  } else {
280  int const last_block = mzd_row_to_block(M, M->nrows - 1);
281  if (n < last_block) {
282  return (1 << M->blockrows_log) - r;
283  }
284  return M->nrows + M->row_offset - (n << M->blockrows_log) - r;
285  }
286  }
287  return n ? 0 : M->nrows - r;
288 }
289 
299 static inline word *mzd_row(mzd_t const *M, rci_t row) {
300  wi_t big_vector = M->offset_vector + row * M->rowstride;
301  word *result = M->blocks[0].begin + big_vector;
303  int const n = (M->row_offset + row) >> M->blockrows_log;
304  result = M->blocks[n].begin + big_vector - n * (M->blocks[0].size / sizeof(word));
305  }
306  assert(result == M->rows[row]);
307  return result;
308 }
309 
320 mzd_t *mzd_init(rci_t const r, rci_t const c);
321 
328 void mzd_free(mzd_t *A);
329 
351 mzd_t *mzd_init_window(mzd_t *M, rci_t const lowr, rci_t const lowc, rci_t const highr, rci_t const highc);
352 
359 static inline mzd_t const *mzd_init_window_const(mzd_t const *M, rci_t const lowr, rci_t const lowc, rci_t const highr,
360  rci_t const highc) {
361  return mzd_init_window((mzd_t *)M, lowr, lowc, highr, highc);
362 }
363 
370 #define mzd_free_window mzd_free
371 
381 static inline void _mzd_row_swap(mzd_t *M, rci_t const rowa, rci_t const rowb, wi_t const startblock) {
382  if ((rowa == rowb) || (startblock >= M->width)) {
383  return;
384  }
385 
386  wi_t width = M->width - startblock - 1;
387  word *a = M->rows[rowa] + startblock;
388  word *b = M->rows[rowb] + startblock;
389  word tmp;
390  word const mask_end = M->high_bitmask;
391 
392  for (wi_t i = 0; i < width; ++i) {
393  tmp = a[i];
394  a[i] = b[i];
395  b[i] = tmp;
396  }
397  tmp = (a[width] ^ b[width]) & mask_end;
398  a[width] ^= tmp;
399  b[width] ^= tmp;
400 
401  __M4RI_DD_ROW(M, rowa);
402  __M4RI_DD_ROW(M, rowb);
403 }
404 
413 static inline void mzd_row_swap(mzd_t *M, rci_t const rowa, rci_t const rowb) { _mzd_row_swap(M, rowa, rowb, 0); }
414 
427 void mzd_copy_row(mzd_t *B, rci_t i, mzd_t const *A, rci_t j);
428 
437 void mzd_col_swap(mzd_t *M, rci_t const cola, rci_t const colb);
438 
449 static inline void mzd_col_swap_in_rows(mzd_t *M, rci_t const cola, rci_t const colb, rci_t const start_row,
450  rci_t const stop_row) {
451  if (cola == colb) {
452  return;
453  }
454 
455  rci_t const _cola = cola;
456  rci_t const _colb = colb;
457 
458  wi_t const a_word = _cola / m4ri_radix;
459  wi_t const b_word = _colb / m4ri_radix;
460 
461  int const a_bit = _cola % m4ri_radix;
462  int const b_bit = _colb % m4ri_radix;
463 
464  word *RESTRICT ptr = mzd_row(M, start_row);
465  int max_bit = MAX(a_bit, b_bit);
466  int count_remaining = stop_row - start_row;
467  int min_bit = a_bit + b_bit - max_bit;
468  int block = mzd_row_to_block(M, start_row);
469  int offset = max_bit - min_bit;
470  word mask = m4ri_one << min_bit;
471  int count = MIN(mzd_remaining_rows_in_block(M, start_row), count_remaining);
472 
473  // Apparently we're calling with start_row == stop_row sometimes (seems a bug to me).
474  if (count <= 0) {
475  return;
476  }
477 
478  if (a_word == b_word) {
479  while (1) {
480  count_remaining -= count;
481  ptr += a_word;
482  int fast_count = count / 4;
483  int rest_count = count - 4 * fast_count;
484  word xor_v[4];
485  wi_t const rowstride = M->rowstride;
486  while (fast_count--) {
487  xor_v[0] = ptr[0];
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;
495  xor_v[0] &= mask;
496  xor_v[1] &= mask;
497  xor_v[2] &= mask;
498  xor_v[3] &= mask;
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;
503  ptr[0] ^= xor_v[0];
504  ptr[rowstride] ^= xor_v[1];
505  ptr[2 * rowstride] ^= xor_v[2];
506  ptr[3 * rowstride] ^= xor_v[3];
507  ptr += 4 * rowstride;
508  }
509  while (rest_count--) {
510  word xor_v = *ptr;
511  xor_v ^= xor_v >> offset;
512  xor_v &= mask;
513  *ptr ^= xor_v | (xor_v << offset);
514  ptr += rowstride;
515  }
516  block++;
517  if ((count = MIN(mzd_rows_in_block(M, block), count_remaining)) <= 0) {
518  break;
519  }
520  ptr = mzd_first_row_next_block(M, block);
521  }
522  } else {
523  word *RESTRICT min_ptr;
524  wi_t max_offset;
525  if (min_bit == a_bit) {
526  min_ptr = ptr + a_word;
527  max_offset = b_word - a_word;
528  } else {
529  min_ptr = ptr + b_word;
530  max_offset = a_word - b_word;
531  }
532  while (1) {
533  count_remaining -= count;
534  wi_t const rowstride = M->rowstride;
535  while (count--) {
536  word xor_v = (min_ptr[0] ^ (min_ptr[max_offset] >> offset)) & mask;
537  min_ptr[0] ^= xor_v;
538  min_ptr[max_offset] ^= xor_v << offset;
539  min_ptr += rowstride;
540  }
541  block++;
542  if ((count = MIN(mzd_rows_in_block(M, +block), count_remaining)) <= 0) {
543  break;
544  }
545  ptr = mzd_first_row_next_block(M, block);
546  if (min_bit == a_bit) {
547  min_ptr = ptr + a_word;
548  } else {
549  min_ptr = ptr + b_word;
550  }
551  }
552  }
553 
554  __M4RI_DD_MZD(M);
555 }
556 
568 static inline BIT mzd_read_bit(mzd_t const *M, rci_t const row, rci_t const col) {
569  return __M4RI_GET_BIT(M->rows[row][col / m4ri_radix], col % m4ri_radix);
570 }
571 
584 static inline void mzd_write_bit(mzd_t *M, rci_t const row, rci_t const col, BIT const value) {
585  __M4RI_WRITE_BIT(M->rows[row][col / m4ri_radix], col % m4ri_radix, value);
586 }
587 
598 static inline void mzd_xor_bits(mzd_t const *M, rci_t const x, rci_t const y, int const n, word values) {
599  int const spot = y % m4ri_radix;
600  wi_t const block = y / m4ri_radix;
601  M->rows[x][block] ^= values << spot;
602  int const space = m4ri_radix - spot;
603  if (n > space) {
604  M->rows[x][block + 1] ^= values >> space;
605  }
606 }
607 
618 static inline void mzd_and_bits(mzd_t const *M, rci_t const x, rci_t const y, int const n, word values) {
619  /* This is the best way, since this will drop out once we inverse the bits in values: */
620  values >>= (m4ri_radix - n); /* Move the bits to the lowest columns */
621 
622  int const spot = y % m4ri_radix;
623  wi_t const block = y / m4ri_radix;
624  M->rows[x][block] &= values << spot;
625  int const space = m4ri_radix - spot;
626  if (n > space) {
627  M->rows[x][block + 1] &= values >> space;
628  }
629 }
630 
640 static inline void mzd_clear_bits(mzd_t const *M, rci_t const x, rci_t const y, int const n) {
641  assert(n > 0 && n <= m4ri_radix);
642  word values = m4ri_ffff >> (m4ri_radix - n);
643  int const spot = y % m4ri_radix;
644  wi_t const block = y / m4ri_radix;
645  M->rows[x][block] &= ~(values << spot);
646  int const space = m4ri_radix - spot;
647  if (n > space) {
648  M->rows[x][block + 1] &= ~(values >> space);
649  }
650 }
651 
664 static inline void mzd_row_add_offset(mzd_t *M, rci_t dstrow, rci_t srcrow, rci_t coloffset) {
665  assert(dstrow < M->nrows && srcrow < M->nrows && coloffset < M->ncols);
666  wi_t const startblock = coloffset / m4ri_radix;
667  wi_t wide = M->width - startblock;
668  word *src = M->rows[srcrow] + startblock;
669  word *dst = M->rows[dstrow] + startblock;
670  word const mask_begin = __M4RI_RIGHT_BITMASK(m4ri_radix - coloffset % m4ri_radix);
671  word const mask_end = M->high_bitmask;
672 
673  *dst++ ^= *src++ & mask_begin;
674  --wide;
675 
676 #if __M4RI_HAVE_SSE2
677  int not_aligned = __M4RI_ALIGNMENT(src, 16) != 0; /* 0: Aligned, 1: Not aligned */
678  if (wide > not_aligned + 1) /* Speed up for small matrices */
679  {
680  if (not_aligned) {
681  *dst++ ^= *src++;
682  --wide;
683  }
684  /* Now wide > 1 */
685  __m128i *__src = (__m128i *)src;
686  __m128i *__dst = (__m128i *)dst;
687  __m128i *const eof = (__m128i *)((unsigned long)(src + wide) & ~0xFUL);
688  do {
689  __m128i xmm1 = _mm_xor_si128(*__dst, *__src);
690  *__dst++ = xmm1;
691  } while (++__src < eof);
692  src = (word *)__src;
693  dst = (word *)__dst;
694  wide = ((sizeof(word) * wide) % 16) / sizeof(word);
695  }
696 #endif
697  wi_t i = -1;
698  while (++i < wide) {
699  dst[i] ^= src[i];
700  }
701  /*
702  * Revert possibly non-zero excess bits.
703  * Note that i == wide here, and wide can be 0.
704  * But really, src[wide - 1] is M->rows[srcrow][M->width - 1] ;)
705  * We use i - 1 here to let the compiler know these are the same addresses
706  * that we last accessed, in the previous loop.
707  */
708  dst[i - 1] ^= src[i - 1] & ~mask_end;
709 
710  __M4RI_DD_ROW(M, dstrow);
711 }
712 
724 void mzd_row_add(mzd_t *M, rci_t const sourcerow, rci_t const destrow);
725 
740 mzd_t *mzd_transpose(mzd_t *DST, mzd_t const *A);
741 
756 mzd_t *mzd_mul_naive(mzd_t *C, mzd_t const *A, mzd_t const *B);
757 
772 mzd_t *mzd_addmul_naive(mzd_t *C, mzd_t const *A, mzd_t const *B);
773 
785 mzd_t *_mzd_mul_naive(mzd_t *C, mzd_t const *A, mzd_t const *B, int const clear);
786 
796 mzd_t *_mzd_mul_va(mzd_t *C, mzd_t const *v, mzd_t const *A, int const clear);
797 
804 void mzd_randomize(mzd_t *M);
805 
814 typedef word (*m4ri_random_callback)(void* data);
815 
823 void mzd_randomize_custom(mzd_t *M, m4ri_random_callback rc, void* data);
824 
839 void mzd_set_ui(mzd_t *M, unsigned int const value);
840 
854 rci_t mzd_gauss_delayed(mzd_t *M, rci_t const startcol, int const full);
855 
869 rci_t mzd_echelonize_naive(mzd_t *M, int const full);
870 
878 int mzd_equal(mzd_t const *A, mzd_t const *B);
879 
891 int mzd_cmp(mzd_t const *A, mzd_t const *B);
892 
900 mzd_t *mzd_copy(mzd_t *DST, mzd_t const *A);
901 
920 mzd_t *mzd_concat(mzd_t *C, mzd_t const *A, mzd_t const *B);
921 
939 mzd_t *mzd_stack(mzd_t *C, mzd_t const *A, mzd_t const *B);
940 
953 mzd_t *mzd_submatrix(mzd_t *S, mzd_t const *M, rci_t const lowr, rci_t const lowc, rci_t const highr,
954  rci_t const highc);
955 
967 mzd_t *mzd_invert_naive(mzd_t *INV, mzd_t const *A, mzd_t const *I);
968 
980 mzd_t *mzd_add(mzd_t *C, mzd_t const *A, mzd_t const *B);
981 
990 mzd_t *_mzd_add(mzd_t *C, mzd_t const *A, mzd_t const *B);
991 
1000 #define mzd_sub mzd_add
1001 
1010 #define _mzd_sub _mzd_add
1011 
1021 static inline word mzd_read_bits(mzd_t const *M, rci_t const x, rci_t const y, int const n) {
1022  int const spot = y % m4ri_radix;
1023  wi_t const block = y / m4ri_radix;
1024  int const spill = spot + n - m4ri_radix;
1025  word temp = (spill <= 0) ? M->rows[x][block] << -spill
1026  : (M->rows[x][block + 1] << (m4ri_radix - spill)) | (M->rows[x][block] >> spill);
1027  return temp >> (m4ri_radix - n);
1028 }
1029 
1046 static inline void mzd_combine_even_in_place(mzd_t *A, rci_t const a_row, wi_t const a_startblock,
1047  mzd_t const *B, rci_t const b_row, wi_t const b_startblock) {
1048 
1049  wi_t wide = A->width - a_startblock - 1;
1050 
1051  word *a = A->rows[a_row] + a_startblock;
1052  word *b = B->rows[b_row] + b_startblock;
1053 
1054 #if __M4RI_HAVE_SSE2
1055  if (wide > 2) {
1057  if (__M4RI_ALIGNMENT(a, 16)) {
1058  *a++ ^= *b++;
1059  wide--;
1060  }
1061 
1062  if (__M4RI_ALIGNMENT(a, 16) == 0 && __M4RI_ALIGNMENT(b, 16) == 0) {
1063  __m128i *a128 = (__m128i *)a;
1064  __m128i *b128 = (__m128i *)b;
1065  const __m128i *eof = (__m128i *)((unsigned long)(a + wide) & ~0xFUL);
1066 
1067  do {
1068  *a128 = _mm_xor_si128(*a128, *b128);
1069  ++b128;
1070  ++a128;
1071  } while (a128 < eof);
1072 
1073  a = (word *)a128;
1074  b = (word *)b128;
1075  wide = ((sizeof(word) * wide) % 16) / sizeof(word);
1076  }
1077  }
1078 #endif // __M4RI_HAVE_SSE2
1079 
1080  if (wide > 0) {
1081  wi_t n = (wide + 7) / 8;
1082  switch (wide % 8) {
1083  case 0: do { *(a++) ^= *(b++);
1084  case 7: *(a++) ^= *(b++);
1085  case 6: *(a++) ^= *(b++);
1086  case 5: *(a++) ^= *(b++);
1087  case 4: *(a++) ^= *(b++);
1088  case 3: *(a++) ^= *(b++);
1089  case 2: *(a++) ^= *(b++);
1090  case 1: *(a++) ^= *(b++);
1091  } while (--n > 0);
1092  }
1093  }
1094 
1095  *a ^= *b & A->high_bitmask;
1096 
1097  __M4RI_DD_MZD(A);
1098 }
1099 
1119 static inline void mzd_combine_even(mzd_t *C, rci_t const c_row, wi_t const c_startblock,
1120  mzd_t const *A, rci_t const a_row, wi_t const a_startblock,
1121  mzd_t const *B, rci_t const b_row, wi_t const b_startblock) {
1122 
1123  wi_t wide = A->width - a_startblock - 1;
1124  word *a = A->rows[a_row] + a_startblock;
1125  word *b = B->rows[b_row] + b_startblock;
1126  word *c = C->rows[c_row] + c_startblock;
1127 
1128 #if __M4RI_HAVE_SSE2
1129  if (wide > 2) {
1131  if (__M4RI_ALIGNMENT(a, 16)) {
1132  *c++ = *b++ ^ *a++;
1133  wide--;
1134  }
1135 
1136  if ((__M4RI_ALIGNMENT(b, 16) | __M4RI_ALIGNMENT(c, 16)) == 0) {
1137  __m128i *a128 = (__m128i *)a;
1138  __m128i *b128 = (__m128i *)b;
1139  __m128i *c128 = (__m128i *)c;
1140  const __m128i *eof = (__m128i *)((unsigned long)(a + wide) & ~0xFUL);
1141 
1142  do {
1143  *c128 = _mm_xor_si128(*a128, *b128);
1144  ++c128;
1145  ++b128;
1146  ++a128;
1147  } while (a128 < eof);
1148 
1149  a = (word *)a128;
1150  b = (word *)b128;
1151  c = (word *)c128;
1152  wide = ((sizeof(word) * wide) % 16) / sizeof(word);
1153  }
1154  }
1155 #endif // __M4RI_HAVE_SSE2
1156 
1157  if (wide > 0) {
1158  wi_t n = (wide + 7) / 8;
1159  switch (wide % 8) {
1160  case 0: do { *(c++) = *(a++) ^ *(b++);
1161  case 7: *(c++) = *(a++) ^ *(b++);
1162  case 6: *(c++) = *(a++) ^ *(b++);
1163  case 5: *(c++) = *(a++) ^ *(b++);
1164  case 4: *(c++) = *(a++) ^ *(b++);
1165  case 3: *(c++) = *(a++) ^ *(b++);
1166  case 2: *(c++) = *(a++) ^ *(b++);
1167  case 1: *(c++) = *(a++) ^ *(b++);
1168  } while (--n > 0);
1169  }
1170  }
1171  *c ^= ((*a ^ *b ^ *c) & C->high_bitmask);
1172 
1173  __M4RI_DD_MZD(C);
1174 }
1175 
1194 static inline void mzd_combine(mzd_t *C, rci_t const c_row, wi_t const c_startblock,
1195  mzd_t const *A, rci_t const a_row, wi_t const a_startblock,
1196  mzd_t const *B, rci_t const b_row, wi_t const b_startblock) {
1197 
1198  if ((C == A) & (a_row == c_row) & (a_startblock == c_startblock)) {
1199  mzd_combine_even_in_place(C, c_row, c_startblock, B, b_row, b_startblock);
1200  } else {
1201  mzd_combine_even(C, c_row, c_startblock, A, a_row, a_startblock, B, b_row, b_startblock);
1202  }
1203  return;
1204 }
1205 
1214 static inline int mzd_read_bits_int(mzd_t const *M, rci_t const x, rci_t const y, int const n) {
1215  return __M4RI_CONVERT_TO_INT(mzd_read_bits(M, x, y, n));
1216 }
1217 
1224 int mzd_is_zero(mzd_t const *A);
1225 
1234 void mzd_row_clear_offset(mzd_t *M, rci_t const row, rci_t const coloffset);
1235 
1252 int mzd_find_pivot(mzd_t const *M, rci_t start_row, rci_t start_col, rci_t *r, rci_t *c);
1253 
1266 double mzd_density(mzd_t const *A, wi_t res);
1267 
1282 double _mzd_density(mzd_t const *A, wi_t res, rci_t r, rci_t c);
1283 
1292 rci_t mzd_first_zero_row(mzd_t const *A);
1293 
1300 static inline word mzd_hash(mzd_t const *A) {
1301  word hash = 0;
1302  for (rci_t r = 0; r < A->nrows; ++r) {
1303  hash ^= rotate_word(calculate_hash(A->rows[r], A->width), r % m4ri_radix);
1304  }
1305  return hash;
1306 }
1307 
1317 mzd_t *mzd_extract_u(mzd_t *U, mzd_t const *A);
1318 
1328 mzd_t *mzd_extract_l(mzd_t *L, mzd_t const *A);
1329 
1330 #endif // M4RI_MZD
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:640
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:2014
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:1709
#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:1300
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:1194
rci_t mzd_gauss_delayed(mzd_t *M, rci_t const startcol, int const full)
Gaussian elimination.
Definition: mzd.c:308
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:220
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:1740
Helper functions.
static word mzd_read_bits(mzd_t const *M, rci_t const x, rci_t const y, int const n)
Definition: mzd.h:1021
word high_bitmask
Definition: mzd.h:136
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:1438
mzd_block_t * blocks
Definition: mzd.h:137
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:1420
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:359
static uint8_t const mzd_flag_windowed_zeroexcess
flag for windowed matrix where ncols%64 == 0
Definition: mzd.h:162
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:1046
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:1867
int mzd_equal(mzd_t const *A, mzd_t const *B)
Return TRUE if A == B.
Definition: mzd.c:1605
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:1542
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:618
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:1680
void mzd_free(mzd_t *A)
Free a matrix created with mzd_init.
Definition: mzd.c:271
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:1389
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:584
mzd_t * mzd_add(mzd_t *C, mzd_t const *A, mzd_t const *B)
Set C = A+B.
Definition: mzd.c:1760
mzd_t * mzd_extract_l(mzd_t *L, mzd_t const *A)
Definition: mzd.c:2247
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:1453
rci_t mzd_echelonize_naive(mzd_t *M, int const full)
Gaussian elimination.
Definition: mzd.c:335
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:449
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:381
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:273
word ** rows
Definition: mzd.h:138
static uint8_t const mzd_flag_windowed_zerooffset
flag for windowed matrix
Definition: mzd.h:156
#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:229
void mzd_randomize(mzd_t *M)
Fill matrix M with uniformly distributed bits.
Definition: mzd.c:1558
#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:1655
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:284
static wi_t mzd_rows_in_block(mzd_t const *M, int n)
Total number of rows in this block.
Definition: mzd.h:249
static wi_t const mzd_paddingwidth
The minimum width where padding occurs.
Definition: mzd.h:144
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:1774
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:234
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:1214
mzd_t * mzd_extract_u(mzd_t *U, mzd_t const *A)
Definition: mzd.c:2231
static uint8_t const mzd_flag_multiple_blocks
flag for multiply blocks
Definition: mzd.h:174
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:413
static int mzd_is_windowed(mzd_t const *M)
Test if a matrix is windowed.
Definition: mzd.h:183
static int mzd_owns_blocks(mzd_t const *M)
Test if this mzd_t should free blocks.
Definition: mzd.h:192
mzd_t * mzd_init(rci_t const r, rci_t const c)
Create a new matrix of dimension r x c.
Definition: mzd.c:149
static word * mzd_first_row(mzd_t const *M)
Get a pointer the first word.
Definition: mzd.h:204
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:2170
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:1119
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:2001
double mzd_density(mzd_t const *A, wi_t res)
Return the number of nonzero entries divided by nrows * ncols.
Definition: mzd.c:2207
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:1907
word * end
Definition: mzd.h:77
void mzd_randomize_custom(mzd_t *M, m4ri_random_callback rc, void *data)
Fill matrix M with uniformly distributed bits.
Definition: mzd.c:1570
word(* m4ri_random_callback)(void *data)
Random callback that produces uniformly distributed random words on every call.
Definition: mzd.h:814
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:1582
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:2036
static uint8_t const mzd_flag_nonzero_excess
flag when ncols%64 == 0
Definition: mzd.h:150
static word * mzd_row(mzd_t const *M, rci_t row)
Get pointer to first word of row.
Definition: mzd.h:299
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:664
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:568
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:1627
#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:288
static uint8_t const mzd_flag_windowed_ownsblocks
flag for windowed matrix wich owns its memory
Definition: mzd.h:168
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:598
#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:2211