Impressum bipart.cpp Sprache: C

//
// Semigroups package for GAP
// Copyright (C) 2016 James D. Mitchell
//
// This program is free software: you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
//
// This program is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU General Public License
// along with this program.  If not, see <https://www.gnu.org/licenses/>.
//

// TODO(later) 1) if we use clear before resize maybe don't need fill
//             2) in-place product

#include "bipart.hpp"

#include <algorithm>    // for fill, min, max, all_of, max_element
#include <cstddef>      // for size_t, NULL
#include <cstdint>      // for uint32_t
#include <string>       // for string
#include <thread>       // for thread
#include <type_traits>  // for conditional<>::type
#include <utility>      // for pair, make_pair
#include <vector>       // for vector

// GAP headers
#include "gap_all.h"

// libsemigroups headers
#include "libsemigroups/bipart.hpp"  // for Blocks, Bipartition, validate
#include "libsemigroups/report.hpp"  // for Reporter, etc
#include "libsemigroups/timer.hpp"   // for Timer
#include "semigroups-config.hpp"     // for SEMIGROUPS_KERNEL_DEBUG

#include "gapbind14/gapbind14.hpp"  // for GAPBIND14_TRY

using libsemigroups::Bipartition;
using libsemigroups::Blocks;
using libsemigroups::REPORTER;
using libsemigroups::detail::Timer;

// Global variables

static std::vector<size_t> _BUFFER_size_t;
static std::vector<bool>   _BUFFER_bool;

// A T_BIPART Obj in GAP is of the form:
//
//   [pointer to C++ bipartition, left blocks Obj, right blocks Obj]

// Create a new GAP bipartition Obj from a C++ Bipartition pointer.

Obj bipart_new_obj(Bipartition* x) {
  size_t deg = x->degree() + 1;
  if (deg > static_cast<size_t>(LEN_PLIST(TYPES_BIPART))
      || ELM_PLIST(TYPES_BIPART, deg) == 0) {
    CALL_1ARGS(TYPE_BIPART, INTOBJ_INT(deg - 1));
  }

  Obj o          = NewBag(T_BIPART, 3 * sizeof(Obj));
  ADDR_OBJ(o)[0] = reinterpret_cast<Obj>(x);
  return o;
}

// A T_BLOCKS Obj in GAP is of the form:
//
//   [pointer to C++ blocks]

// Returns the pointer to the C++ blocks object from the GAP bipartition
// object.

// Create a new GAP blocks Obj from a C++ Blocks pointer.

inline Obj blocks_new_obj(Blocks* x) {
  Obj o          = NewBag(T_BLOCKS, 1 * sizeof(Obj));
  ADDR_OBJ(o)[0] = reinterpret_cast<Obj>(x);
  return o;
}

////////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////////
// Bipartitions
////////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////////

////////////////////////////////////////////////////////////////////////////////
// GAP level functions
////////////////////////////////////////////////////////////////////////////////

// Create a bipartition from the list gap_blocks. The argument gap_blocks must
// be a list which either represents:
//
//    * the internal rep of a bipartition (list of positive integers such that
//      gap_blocks[i] is the index of the class containing i); or
//
//    * the external rep of a bipartition (a list of lists of ints that
//    partition [-n ... -1] union [1 .. n].
//
// BIPART_NC does only minimal checks, and doesn't fully check if its argument
// is valid.

Obj BIPART_NC(Obj self, Obj gap_blocks) {
  SEMIGROUPS_ASSERT(IS_LIST(gap_blocks));
  std::vector<uint32_t> blocks;

  size_t degree         = 0;
  size_t nr_left_blocks = 0;
  size_t nr_blocks      = 0;

  if (LEN_LIST(gap_blocks) != 0) {
    if (IS_LIST(ELM_LIST(gap_blocks, 1))) {  // gap_blocks is a list of lists
      nr_blocks = LEN_LIST(gap_blocks);
      for (size_t i = 1; i <= nr_blocks; i++) {
        SEMIGROUPS_ASSERT(IS_LIST(ELM_LIST(gap_blocks, i)));
        degree += LEN_LIST(ELM_LIST(gap_blocks, i));
      }
      blocks.resize(degree);

      degree /= 2;

      for (size_t i = 1; i <= nr_blocks; i++) {
        Obj block = ELM_LIST(gap_blocks, i);
        for (size_t j = 1; j <= static_cast<size_t>(LEN_LIST(block)); j++) {
          SEMIGROUPS_ASSERT(IS_INTOBJ(ELM_LIST(block, j)));
          int jj = INT_INTOBJ(ELM_LIST(block, j));
          if (jj < 0) {
            blocks[-jj + degree - 1] = i - 1;
          } else {
            nr_left_blocks = i;
            blocks[jj - 1] = i - 1;
          }
        }
      }
    } else {  // gap_blocks is the internal rep of a bipartition
      blocks.reserve(LEN_LIST(gap_blocks));
      for (size_t i = 1; i <= static_cast<size_t>(LEN_LIST(gap_blocks)) / 2;
           i++) {
        SEMIGROUPS_ASSERT(IS_INTOBJ(ELM_LIST(gap_blocks, i))
                          && INT_INTOBJ(ELM_LIST(gap_blocks, i)) > 0);
        uint32_t index = INT_INTOBJ(ELM_LIST(gap_blocks, i)) - 1;
        blocks.push_back(index);
        nr_blocks = (index > nr_blocks ? index : nr_blocks);
      }
      nr_left_blocks = nr_blocks + 1;
      for (size_t i = (static_cast<size_t>(LEN_LIST(gap_blocks)) / 2) + 1;
           i <= static_cast<size_t>(LEN_LIST(gap_blocks));
           i++) {
        SEMIGROUPS_ASSERT(IS_INTOBJ(ELM_LIST(gap_blocks, i))
                          && INT_INTOBJ(ELM_LIST(gap_blocks, i)) > 0);
        uint32_t index = INT_INTOBJ(ELM_LIST(gap_blocks, i)) - 1;
        blocks.push_back(index);
        nr_blocks = (index > nr_blocks ? index : nr_blocks);
      }
      nr_blocks++;
    }
  }

  // construct C++ object
  Bipartition* x;
  // We could use Bipartition::make in the next line, but then we are repeating
  // the checks in the Semigroups package, which give more meaningful error
  // messages.
  GAPBIND14_TRY(x = new Bipartition(Bipartition(blocks));)
  x->set_number_of_left_blocks(nr_left_blocks);
  x->set_number_of_blocks(nr_blocks);

  return bipart_new_obj(x);
}

// Returns the external rep of a GAP bipartition, see description before
// BIPART_NC for more details.

Obj BIPART_EXT_REP(Obj self, Obj x) {
  SEMIGROUPS_ASSERT(TNUM_OBJ(x) == T_BIPART);

  Bipartition* xx = bipart_get_cpp(x);
  size_t       n  = xx->degree();

  Obj ext_rep
      = NEW_PLIST(n == 0 ? T_PLIST_EMPTY : T_PLIST_TAB, xx->number_of_blocks());
  SET_LEN_PLIST(ext_rep, (Int) xx->number_of_blocks());

  for (size_t i = 0; i < 2 * n; i++) {
    Obj entry = INTOBJ_INT((i < n ? i + 1 : -(i - n) - 1));
    if (ELM_PLIST(ext_rep, xx->at(i) + 1) == 0) {
      Obj block = NEW_PLIST(T_PLIST_CYC, 1);
      SET_LEN_PLIST(block, 1);
      SET_ELM_PLIST(block, 1, entry);
      SET_ELM_PLIST(ext_rep, xx->at(i) + 1, block);
      CHANGED_BAG(ext_rep);
    } else {
      Obj block = ELM_PLIST(ext_rep, xx->at(i) + 1);
      AssPlist(block, LEN_PLIST(block) + 1, entry);
    }
  }
  MakeImmutable(ext_rep);
  return ext_rep;
}

// Returns the internal rep of a GAP bipartition, see description before
// BIPART_NC for more details.

Obj BIPART_INT_REP(Obj self, Obj x) {
  SEMIGROUPS_ASSERT(TNUM_OBJ(x) == T_BIPART);

  Bipartition* xx = bipart_get_cpp(x);  // get C++ bipartition pointer
  size_t       n  = xx->degree();

  Obj int_rep = NEW_PLIST_IMM(n == 0 ? T_PLIST_EMPTY : T_PLIST_CYC, 2 * n);
  SET_LEN_PLIST(int_rep, (Int) 2 * n);

  for (size_t i = 0; i < 2 * n; i++) {
    SET_ELM_PLIST(int_rep, i + 1, INTOBJ_INT(xx->at(i) + 1));
  }
  return int_rep;
}

// Returns the hash value for a GAP bipartition from the C++ object.

Obj BIPART_HASH(Obj self, Obj x, Obj data) {
  SEMIGROUPS_ASSERT(TNUM_OBJ(x) == T_BIPART);
  SEMIGROUPS_ASSERT(IS_INTOBJ(data));

  return INTOBJ_INT((bipart_get_cpp(x)->hash_value() % INT_INTOBJ(data)) + 1);
}

// Returns the degree of a GAP bipartition from the C++ object. A bipartition
// is of degree n if it is defined on [-n .. -1] union [1 .. n].

Obj BIPART_DEGREE(Obj self, Obj x) {
  SEMIGROUPS_ASSERT(TNUM_OBJ(x) == T_BIPART);

  return INTOBJ_INT(bipart_get_cpp(x)->degree());
}

// Returns the number of blocks in the bipartition from the C++ object.

Obj BIPART_NR_BLOCKS(Obj self, Obj x) {
  SEMIGROUPS_ASSERT(TNUM_OBJ(x) == T_BIPART);

  return INTOBJ_INT(bipart_get_cpp(x)->number_of_blocks());
}

// Returns the number of blocks containing positive integers in the GAP
// bipartition from the C++ object.

Obj BIPART_NR_LEFT_BLOCKS(Obj self, Obj x) {
  SEMIGROUPS_ASSERT(TNUM_OBJ(x) == T_BIPART);

  return INTOBJ_INT(bipart_get_cpp(x)->number_of_left_blocks());
}

// Returns the number of blocks both positive and negative integers in the GAP
// bipartition from the C++ object.

Obj BIPART_RANK(Obj self, Obj x, Obj dummy) {
  SEMIGROUPS_ASSERT(TNUM_OBJ(x) == T_BIPART);

  return INTOBJ_INT(bipart_get_cpp(x)->rank());
}

// Returns the product of the GAP bipartitions x and y as a new GAP
// bipartition.

Obj BIPART_PROD(Obj x, Obj y) {
  SEMIGROUPS_ASSERT(TNUM_OBJ(x) == T_BIPART);
  SEMIGROUPS_ASSERT(TNUM_OBJ(y) == T_BIPART);

  Bipartition* xx = bipart_get_cpp(x);
  Bipartition* yy = bipart_get_cpp(y);

  Bipartition* z = new Bipartition(xx->degree());
  z->product_inplace(*xx, *yy);

  return bipart_new_obj(static_cast<Bipartition*>(z));
}

// Check if the GAP bipartitions x and y are equal.

Int BIPART_EQ(Obj x, Obj y) {
  return (*bipart_get_cpp(x) == *bipart_get_cpp(y) ? 1L : 0L);
}

// Check if x < y for the GAP bipartitions x and y.

Int BIPART_LT(Obj x, Obj y) {
  return (*bipart_get_cpp(x) < *bipart_get_cpp(y) ? 1L : 0L);
}

// Returns the permutation of the indices of the transverse blocks of (x ^ * y)
// induced by (x ^ * y). Assumes that the left and right blocks of x and y are
// equal.

Obj BIPART_PERM_LEFT_QUO(Obj self, Obj x, Obj y) {
  SEMIGROUPS_ASSERT(TNUM_OBJ(x) == T_BIPART);
  SEMIGROUPS_ASSERT(TNUM_OBJ(y) == T_BIPART);

// The following is done to avoid leaking memory
#ifdef SEMIGROUPS_KERNEL_DEBUG
  Blocks* xb = bipart_get_cpp(x)->left_blocks();
  Blocks* yb = bipart_get_cpp(y)->left_blocks();
  SEMIGROUPS_ASSERT(*xb == *yb);
  delete xb;
  delete yb;
  xb = bipart_get_cpp(x)->right_blocks();
  yb = bipart_get_cpp(y)->right_blocks();
  SEMIGROUPS_ASSERT(*xb == *yb);
  delete xb;
  delete yb;
#endif

  size_t deg  = bipart_get_cpp(x)->degree();
  Obj    p    = NEW_PERM4(deg);
  UInt4* ptrp = ADDR_PERM4(p);

  Bipartition* xx = bipart_get_cpp(x);
  Bipartition* yy = bipart_get_cpp(y);

  SEMIGROUPS_ASSERT(xx->degree() == yy->degree());

  // find indices of right blocks of <x>
  size_t index = 0;
  _BUFFER_size_t.clear();
  _BUFFER_size_t.resize(2 * deg, -1);

  for (size_t i = deg; i < 2 * deg; i++) {
    if (_BUFFER_size_t[xx->at(i)] == static_cast<size_t>(-1)) {
      _BUFFER_size_t[xx->at(i)] = index;
      index++;
    }
    ptrp[i - deg] = i - deg;
  }

  for (size_t i = deg; i < 2 * deg; i++) {
    if (yy->at(i) < xx->number_of_left_blocks()) {
      ptrp[_BUFFER_size_t[yy->at(i)]] = _BUFFER_size_t[xx->at(i)];
    }
  }
  return p;
}

// Returns the GAP bipartition xx ^ *.

Obj BIPART_LEFT_PROJ(Obj self, Obj x) {
  SEMIGROUPS_ASSERT(TNUM_OBJ(x) == T_BIPART);

  Bipartition* xx = bipart_get_cpp(x);

  size_t deg  = xx->degree();
  size_t next = xx->number_of_left_blocks();

  std::fill(_BUFFER_size_t.begin(),
            std::min(_BUFFER_size_t.end(), _BUFFER_size_t.begin() + 2 * deg),
            -1);
  _BUFFER_size_t.resize(2 * deg, -1);

  std::vector<uint32_t> blocks(2 * deg, -1);

  for (size_t i = 0; i < deg; i++) {
    blocks[i] = xx->at(i);
    if (xx->is_transverse_block(xx->at(i))) {
      blocks[i + deg] = xx->at(i);
    } else if (_BUFFER_size_t[xx->at(i)] != static_cast<size_t>(-1)) {
      blocks[i + deg] = _BUFFER_size_t[xx->at(i)];
    } else {
      _BUFFER_size_t[xx->at(i)] = next;
      blocks[i + deg]           = next;
      next++;
    }
  }

  Bipartition* out = new Bipartition(blocks);
  out->set_number_of_blocks(next);
  return bipart_new_obj(out);
}

// Returns the GAP bipartition x ^ *x.

Obj BIPART_RIGHT_PROJ(Obj self, Obj x) {
  SEMIGROUPS_ASSERT(TNUM_OBJ(x) == T_BIPART);

  Bipartition* xx = bipart_get_cpp(x);

  size_t deg     = xx->degree();
  size_t l_block = 0;
  size_t r_block = xx->number_of_right_blocks();

  _BUFFER_size_t.clear();
  _BUFFER_size_t.resize(4 * deg, -1);
  auto buf1 = _BUFFER_size_t.begin();
  auto buf2 = _BUFFER_size_t.begin() + 2 * deg;

  std::vector<uint32_t> blocks(2 * deg, -1);

  for (size_t i = deg; i < 2 * deg; i++) {
    if (buf2[xx->at(i)] == static_cast<size_t>(-1)) {
      if (xx->is_transverse_block(xx->at(i))) {
        buf2[xx->at(i)] = buf1[xx->at(i)] = l_block++;
      } else {
        buf2[xx->at(i)] = r_block++;
        buf1[xx->at(i)] = l_block++;
      }
    }
    blocks[i - deg] = buf1[xx->at(i)];
    blocks[i]       = buf2[xx->at(i)];
  }

  Bipartition* out = new Bipartition(blocks);
  out->set_number_of_blocks(r_block);
  return bipart_new_obj(out);
}

// Returns the GAP bipartition x ^ *.

Obj BIPART_STAR(Obj self, Obj x) {
  SEMIGROUPS_ASSERT(TNUM_OBJ(x) == T_BIPART);

  Bipartition* xx  = bipart_get_cpp(x);
  size_t       deg = xx->degree();

  std::fill(_BUFFER_size_t.begin(),
            std::min(_BUFFER_size_t.end(), _BUFFER_size_t.begin() + 2 * deg),
            -1);
  _BUFFER_size_t.resize(2 * deg, -1);

  std::vector<uint32_t> blocks(2 * deg, -1);

  size_t next = 0;

  for (size_t i = 0; i < deg; i++) {
    if (_BUFFER_size_t[xx->at(i + deg)] != static_cast<size_t>(-1)) {
      blocks[i] = _BUFFER_size_t[xx->at(i + deg)];
    } else {
      _BUFFER_size_t[xx->at(i + deg)] = next;
      blocks[i]                       = next;
      next++;
    }
  }

  size_t nr_left = next;

  for (size_t i = 0; i < deg; i++) {
    if (_BUFFER_size_t[xx->at(i)] != static_cast<size_t>(-1)) {
      blocks[i + deg] = _BUFFER_size_t[xx->at(i)];
    } else {
      _BUFFER_size_t[xx->at(i)] = next;
      blocks[i + deg]           = next;
      next++;
    }
  }

  Bipartition* out = new Bipartition(blocks);
  out->set_number_of_blocks(next);
  out->set_number_of_left_blocks(nr_left);

  return bipart_new_obj(out);
}

// Returns a permutation mapping the indices of the right transverse blocks of
// x and to the right transverse blocks of y. Assumes that x and y have equal
// left blocks.

Obj BIPART_LAMBDA_CONJ(Obj self, Obj x, Obj y) {
  SEMIGROUPS_ASSERT(TNUM_OBJ(x) == T_BIPART);
  SEMIGROUPS_ASSERT(TNUM_OBJ(y) == T_BIPART);

  Bipartition* xx = bipart_get_cpp(x);
  Bipartition* yy = bipart_get_cpp(y);

#ifdef SEMIGROUPS_KERNEL_DEBUG
  Blocks* xb = xx->left_blocks();
  Blocks* yb = yy->left_blocks();
  SEMIGROUPS_ASSERT(*xb == *yb);
  delete xb;
  delete yb;
#endif

  size_t deg            = xx->degree();
  size_t nr_left_blocks = xx->number_of_left_blocks();
  size_t nr_blocks = std::max(xx->number_of_blocks(), yy->number_of_blocks());

  _BUFFER_bool.clear();
  _BUFFER_bool.resize(3 * nr_blocks);
  auto seen = _BUFFER_bool.begin();
  auto src  = seen + nr_blocks;
  auto dst  = src + nr_blocks;

  _BUFFER_size_t.clear();
  _BUFFER_size_t.resize(nr_left_blocks);
  auto   lookup = _BUFFER_size_t.begin();
  size_t next   = 0;

  for (size_t i = deg; i < 2 * deg; i++) {
    if (!seen[yy->at(i)]) {
      seen[yy->at(i)] = true;
      if (yy->at(i) < nr_left_blocks) {  // connected block
        lookup[yy->at(i)] = next;
      }
      next++;
    }
  }

  std::fill(_BUFFER_bool.begin(), _BUFFER_bool.begin() + nr_blocks, false);

  Obj    p    = NEW_PERM4(nr_blocks);
  UInt4* ptrp = ADDR_PERM4(p);
  next        = 0;

  for (size_t i = deg; i < 2 * deg; i++) {
    if (!seen[xx->at(i)]) {
      seen[xx->at(i)] = true;
      if (xx->at(i) < nr_left_blocks) {  // connected block
        ptrp[next]             = lookup[xx->at(i)];
        src[next]              = true;
        dst[lookup[xx->at(i)]] = true;
      }
      next++;
    }
  }

  size_t j = 0;
  for (size_t i = 0; i < nr_blocks; i++) {
    if (!src[i]) {
      while (dst[j]) {
        j++;
      }
      ptrp[i] = j;
      j++;
    }
  }
  return p;
}

// Returns a GAP bipartition y such that the right blocks of y are the right
// blocks of x permuted by p.

Obj BIPART_STAB_ACTION(Obj self, Obj x, Obj p) {
  SEMIGROUPS_ASSERT(TNUM_OBJ(x) == T_BIPART);

  // find the largest moved point of the permutation p
  size_t pdeg;

  if (TNUM_OBJ(p) == T_PERM2) {
    UInt2* ptr = ADDR_PERM2(p);
    for (pdeg = DEG_PERM2(p); 1 <= pdeg; pdeg--) {
      if (ptr[pdeg - 1] != pdeg - 1) {
        break;
      }
    }
  } else if (TNUM_OBJ(p) == T_PERM4) {
    UInt4* ptr = ADDR_PERM4(p);
    for (pdeg = DEG_PERM4(p); 1 <= pdeg; pdeg--) {
      if (ptr[pdeg - 1] != pdeg - 1) {
        break;
      }
    }
  } else {
    ErrorQuit("usage:

must be a perm (not a %s)", (Int) TNAM_OBJ(p), 0L);
    return 0L;  // to keep the compiler happy
  }

  if (pdeg == 0) {
    return x;
  }
  Bipartition* xx = bipart_get_cpp(x);

  size_t deg       = xx->degree();
  size_t nr_blocks = xx->number_of_blocks();

  std::vector<uint32_t> blocks(2 * deg);

  _BUFFER_size_t.clear();
  _BUFFER_size_t.resize(2 * nr_blocks + std::max(deg, pdeg), -1);

  auto tab1 = _BUFFER_size_t.begin();
  auto tab2 = _BUFFER_size_t.begin() + nr_blocks;
  auto q    = tab2 + nr_blocks;  // the inverse of p

  if (TNUM_OBJ(p) == T_PERM2) {
    UInt2* ptr = ADDR_PERM2(p);
    UInt2  i;
    for (i = 0; i < pdeg; i++) {
      q[ptr[i]] = static_cast<size_t>(i);
    }
    for (; i < deg; i++) {
      q[i] = static_cast<size_t>(i);
    }
  } else if (TNUM_OBJ(p) == T_PERM4) {
    UInt4* ptr = ADDR_PERM4(p);
    UInt4  i;
    for (i = 0; i < pdeg; i++) {
      q[ptr[i]] = static_cast<size_t>(i);
    }
    for (; i < deg; i++) {
      q[i] = static_cast<size_t>(i);
    }
  }

  size_t next = 0;

  for (size_t i = deg; i < 2 * deg; i++) {
    if (tab1[xx->at(i)] == static_cast<size_t>(-1)) {
      tab1[xx->at(i)] = q[next];
      tab2[next]      = xx->at(i);
      next++;
    }
  }

  for (size_t i = 0; i < deg; i++) {
    blocks[i]       = xx->at(i);
    blocks[i + deg] = tab2[tab1[xx->at(i + deg)]];
  }

  return bipart_new_obj(new Bipartition(blocks));
}

// Returns the GAP Obj left block of the bipartition x. The left blocks are
// simply the subpartition of [1 .. n] induced by x.

Obj BIPART_LEFT_BLOCKS(Obj self, Obj x) {
  SEMIGROUPS_ASSERT(TNUM_OBJ(x) == T_BIPART);
  if (ADDR_OBJ(x)[1] == NULL) {
    Obj o          = blocks_new_obj(bipart_get_cpp(x)->left_blocks());
    ADDR_OBJ(x)[1] = o;
    CHANGED_BAG(x);
  }
  SEMIGROUPS_ASSERT(ADDR_OBJ(x)[1] != NULL);
  SEMIGROUPS_ASSERT(TNUM_OBJ(ADDR_OBJ(x)[1]) == T_BLOCKS);
  return ADDR_OBJ(x)[1];
}

// Returns the GAP Obj right block of the bipartition x. The right blocks are
// simply the subpartition of [-n .. -1] induced by x.

Obj BIPART_RIGHT_BLOCKS(Obj self, Obj x) {
  SEMIGROUPS_ASSERT(TNUM_OBJ(x) == T_BIPART);
  if (ADDR_OBJ(x)[2] == NULL) {
    Obj o          = blocks_new_obj(bipart_get_cpp(x)->right_blocks());
    ADDR_OBJ(x)[2] = o;
    CHANGED_BAG(x);
  }
  SEMIGROUPS_ASSERT(ADDR_OBJ(x)[2] != NULL);
  SEMIGROUPS_ASSERT(TNUM_OBJ(ADDR_OBJ(x)[2]) == T_BLOCKS);
  return ADDR_OBJ(x)[2];
}

////////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////////
// Blocks
////////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////////

// Forward declarations, see below for the definition of these functions.

static inline size_t fuse_it(size_t);

static void fuse(uint32_t,
                 typename std::vector<uint32_t>::const_iterator,
                 uint32_t,
                 typename std::vector<uint32_t>::const_iterator,
                 uint32_t,
                 bool);

////////////////////////////////////////////////////////////////////////////////
// GAP-level functions
////////////////////////////////////////////////////////////////////////////////

// Create a GAP blocks object from the list gap_blocks. The argument gap_blocks
// must be a list which is the external rep of a GAP blocks object (a list of
// lists of integers such that the absolute values of these lists partition
// [1 .. n], transverse blocks are indicated by positive integers and
// non-transverse by negative integers).
//
// BLOCKS_NC does only minimal checks, and doesn't fully check if its argument
// is valid.

Obj BLOCKS_NC(Obj self, Obj gap_blocks) {
  SEMIGROUPS_ASSERT(IS_LIST(gap_blocks));

  if (LEN_LIST(gap_blocks) == 0) {
    return blocks_new_obj(new Blocks());
  }

  SEMIGROUPS_ASSERT(IS_LIST(ELM_LIST(gap_blocks, 1)));

  size_t degree    = 0;
  size_t nr_blocks = LEN_LIST(gap_blocks);

  for (size_t i = 1; i <= nr_blocks; i++) {
    SEMIGROUPS_ASSERT(IS_LIST(ELM_LIST(gap_blocks, i)));
    degree += LEN_LIST(ELM_LIST(gap_blocks, i));
  }

  Blocks* blocks = new Blocks(degree);

  for (size_t i = 1; i <= nr_blocks; i++) {
    Obj block = ELM_LIST(gap_blocks, i);
    for (size_t j = 1; j <= static_cast<size_t>(LEN_LIST(block)); j++) {
      SEMIGROUPS_ASSERT(IS_INTOBJ(ELM_LIST(block, j)));
      int jj = INT_INTOBJ(ELM_LIST(block, j));
      if (jj < 0) {
        blocks->set_block(-jj - 1, i - 1);
        blocks->set_is_transverse_block(i - 1, false);
      } else {
        blocks->set_block(jj - 1, i - 1);
        blocks->set_is_transverse_block(i - 1, true);
      }
    }
  }
#ifdef SEMIGROUPS_KERNEL_DEBUG
  libsemigroups::validate(*blocks);
#endif
  return blocks_new_obj(blocks);
}

// Returns the external representation of a GAP blocks Obj, see the description
// before BLOCKS_NC for more details.

Obj BLOCKS_EXT_REP(Obj self, Obj x) {
  SEMIGROUPS_ASSERT(TNUM_OBJ(x) == T_BLOCKS);

  Blocks* xx = blocks_get_cpp(x);
  size_t  n  = xx->degree();

  Obj ext_rep
      = NEW_PLIST(n == 0 ? T_PLIST_EMPTY : T_PLIST_TAB, xx->number_of_blocks());
  SET_LEN_PLIST(ext_rep, (Int) xx->number_of_blocks());

  for (size_t i = 0; i < n; i++) {
    Obj block;
    Obj entry = (xx->is_transverse_block((*xx)[i]) ? INTOBJ_INT(i + 1)
                                                   : INTOBJ_INT(-i - 1));
    if (ELM_PLIST(ext_rep, (*xx)[i] + 1) == 0) {
      block = NEW_PLIST(T_PLIST_CYC, 1);
      SET_LEN_PLIST(block, 1);
      SET_ELM_PLIST(block, 1, entry);
      SET_ELM_PLIST(ext_rep, (*xx)[i] + 1, block);
      CHANGED_BAG(ext_rep);
    } else {
      block = ELM_PLIST(ext_rep, (*xx)[i] + 1);
      AssPlist(block, LEN_PLIST(block) + 1, entry);
    }
  }
  MakeImmutable(ext_rep);
  return ext_rep;
}

// Returns the hash value for a GAP bipartition from the C++ object.

Obj BLOCKS_HASH(Obj self, Obj x, Obj data) {
  SEMIGROUPS_ASSERT(TNUM_OBJ(x) == T_BLOCKS);

  return INTOBJ_INT((blocks_get_cpp(x)->hash_value() % INT_INTOBJ(data)) + 1);
}

// Returns the degree of a GAP blocks from the C++ object. A blocks object
// is of degree n if the union of the sets of absolute values of its blocks is
// [1 .. n].

Obj BLOCKS_DEGREE(Obj self, Obj x) {
  SEMIGROUPS_ASSERT(TNUM_OBJ(x) == T_BLOCKS);

  return INTOBJ_INT(blocks_get_cpp(x)->degree());
}

// Returns the rank of a GAP blocks from the C++ object. The rank of a blocks
// object is the number of transverse blocks (equivalently the number of blocks
// consisting of positive integers).

Obj BLOCKS_RANK(Obj self, Obj x) {
  SEMIGROUPS_ASSERT(TNUM_OBJ(x) == T_BLOCKS);

  return INTOBJ_INT(blocks_get_cpp(x)->rank());
}

// Returns the number of blocks in the partition represented by the GAP blocks
// object.

Obj BLOCKS_NR_BLOCKS(Obj self, Obj x) {
  SEMIGROUPS_ASSERT(TNUM_OBJ(x) == T_BLOCKS);

  return INTOBJ_INT(blocks_get_cpp(x)->number_of_blocks());
}

// Returns an idempotent GAP bipartition whose left and right blocks equal the
// GAP blocks object x.

Obj BLOCKS_PROJ(Obj self, Obj x) {
  SEMIGROUPS_ASSERT(TNUM_OBJ(x) == T_BLOCKS);

  Blocks& blocks = *blocks_get_cpp(x);

  _BUFFER_size_t.clear();
  _BUFFER_size_t.resize(blocks.number_of_blocks(), -1);

  std::vector<uint32_t> out(2 * blocks.degree());
  uint32_t              nr_blocks = blocks.number_of_blocks();

  for (uint32_t i = 0; i < blocks.degree(); i++) {
    uint32_t index = blocks[i];
    out[i]         = index;
    if (blocks.is_transverse_block(index)) {
      out[i + blocks.degree()] = index;
    } else {
      if (_BUFFER_size_t[index] == static_cast<size_t>(-1)) {
        _BUFFER_size_t[index] = nr_blocks;
        nr_blocks++;
      }
      out[i + blocks.degree()] = _BUFFER_size_t[index];
    }
  }
  return bipart_new_obj(new Bipartition(out));
}

// Check if two GAP blocks objects are equal.

Int BLOCKS_EQ(Obj x, Obj y) {
  SEMIGROUPS_ASSERT(TNUM_OBJ(x) == T_BLOCKS);
  SEMIGROUPS_ASSERT(TNUM_OBJ(y) == T_BLOCKS);

  return (*blocks_get_cpp(x) == *blocks_get_cpp(y) ? 1L : 0L);
}

// Check if x < y, when x and y are GAP blocks objects.

Int BLOCKS_LT(Obj x, Obj y) {
  SEMIGROUPS_ASSERT(TNUM_OBJ(x) == T_BLOCKS);
  SEMIGROUPS_ASSERT(TNUM_OBJ(y) == T_BLOCKS);

  return (*blocks_get_cpp(x) < *blocks_get_cpp(y) ? 1L : 0L);
}

// Returns True if there is an idempotent bipartition with left blocks equal to
// left_gap and right blocks equal to right_gap.

Obj BLOCKS_E_TESTER(Obj self, Obj left_gap, Obj right_gap) {
  SEMIGROUPS_ASSERT(TNUM_OBJ(left_gap) == T_BLOCKS);
  SEMIGROUPS_ASSERT(TNUM_OBJ(right_gap) == T_BLOCKS);

  Blocks* left  = blocks_get_cpp(left_gap);
  Blocks* right = blocks_get_cpp(right_gap);

  if (left->rank() != right->rank()) {
    return False;
  } else if (left->rank() == 0) {
    return True;
  }

  // prepare the _BUFFER_bool for detecting transverse fused blocks
  _BUFFER_bool.clear();
  _BUFFER_bool.resize(right->number_of_blocks() + 2 * left->number_of_blocks());
  std::copy(right->cbegin_lookup(),
            right->cend_lookup(),
            _BUFFER_bool.begin() + left->number_of_blocks());
  auto seen = _BUFFER_bool.begin() + right->number_of_blocks()
              + left->number_of_blocks();

  // after the following line:
  //
  // 1) [_BUFFER_size_t.begin() .. _BUFFER_size_t.begin() + left_nr_blocks +
  //    right_nr_blocks - 1] is the fuse table for left and right
  //
  // 2) _BUFFER_bool is a lookup for the transverse blocks of the fused left
  //     and right

  fuse(left->degree(),
       left->cbegin(),
       left->number_of_blocks(),
       right->cbegin(),
       right->number_of_blocks(),
       true);

  // check we are injective on transverse blocks of <left> and that the fused
  // blocks are also transverse.

  for (uint32_t i = 0; i < left->number_of_blocks(); i++) {
    if (left->is_transverse_block(i)) {
      size_t j = fuse_it(i);
      if (!_BUFFER_bool[j] || seen[j]) {
        return False;
      }
      seen[j] = true;
    }
  }
  return True;
}

// Returns the idempotent bipartition with left blocks equal to
// left_gap and right blocks equal to right_gap, assuming that this exists.

Obj BLOCKS_E_CREATOR(Obj self, Obj left_gap, Obj right_gap) {
  SEMIGROUPS_ASSERT(TNUM_OBJ(left_gap) == T_BLOCKS);
  SEMIGROUPS_ASSERT(TNUM_OBJ(right_gap) == T_BLOCKS);
  SEMIGROUPS_ASSERT(BLOCKS_E_TESTER(self, left_gap, right_gap) == True);

  Blocks* left  = blocks_get_cpp(left_gap);
  Blocks* right = blocks_get_cpp(right_gap);

  fuse(left->degree(),
       left->cbegin(),
       left->number_of_blocks(),
       right->cbegin(),
       right->number_of_blocks(),
       false);

  _BUFFER_size_t.resize(
      3 * (left->number_of_blocks() + right->number_of_blocks()), 0);
  std::fill(_BUFFER_size_t.begin()
                + 2 * (left->number_of_blocks() + right->number_of_blocks()),
            _BUFFER_size_t.begin()
                + 3 * (left->number_of_blocks() + right->number_of_blocks()),
            -1);

  auto tab1 = _BUFFER_size_t.begin() + left->number_of_blocks()
              + right->number_of_blocks();
  auto tab2 = _BUFFER_size_t.begin()
              + 2 * (left->number_of_blocks() + right->number_of_blocks());

  // find new names for the signed blocks of right
  for (size_t i = 0; i < right->number_of_blocks(); i++) {
    if (right->is_transverse_block(i)) {
      tab1[fuse_it(i + left->number_of_blocks())] = i;
    }
  }

  std::vector<uint32_t> blocks(2 * left->degree());

  size_t next = right->number_of_blocks();

  for (size_t i = 0; i < left->degree(); i++) {
    blocks[i] = (*right)[i];
    size_t j  = (*left)[i];
    if (left->is_transverse_block(j)) {
      blocks[i + left->degree()] = tab1[fuse_it(j)];
    } else {
      if (tab2[j] == static_cast<size_t>(-1)) {
        tab2[j] = next;
        next++;
      }
      blocks[i + left->degree()] = tab2[j];
    }
  }

  Bipartition* out = new Bipartition(blocks);
  out->set_number_of_blocks(next);
  out->set_number_of_left_blocks(right->number_of_blocks());

  return bipart_new_obj(out);
}

// Returns the left blocks of BLOCKS_PROJ(blocks_gap) * x_gap where the latter
// is a GAP bipartition.

Obj BLOCKS_LEFT_ACT(Obj self, Obj blocks_gap, Obj x_gap) {
  SEMIGROUPS_ASSERT(TNUM_OBJ(x_gap) == T_BIPART);
  SEMIGROUPS_ASSERT(TNUM_OBJ(blocks_gap) == T_BLOCKS);

  Bipartition* x      = bipart_get_cpp(x_gap);
  Blocks*      blocks = blocks_get_cpp(blocks_gap);

  if (blocks->degree() != x->degree()) {
    // hack to allow Lambda/RhoOrbSeed
    return blocks_new_obj(x->left_blocks());
  } else if (blocks->degree() == 0) {
    return blocks_gap;
  }

  // prepare the _BUFFER_bool for detecting transverse fused blocks
  _BUFFER_bool.clear();
  _BUFFER_bool.resize(x->number_of_blocks() + blocks->number_of_blocks());
  std::copy(blocks->cbegin_lookup(),
            blocks->cend_lookup(),
            _BUFFER_bool.begin() + x->number_of_blocks());

  fuse(x->degree(),
       x->cbegin() + x->degree(),
       x->number_of_blocks(),
       blocks->cbegin(),
       blocks->number_of_blocks(),
       true);

  _BUFFER_size_t.resize(
      2 * (x->number_of_blocks() + blocks->number_of_blocks()), -1);
  auto tab = _BUFFER_size_t.begin() + x->number_of_blocks()
             + blocks->number_of_blocks();

  Blocks* out_blocks = new Blocks(x->degree());

  uint32_t next = 0;
  for (uint32_t i = 0; i < x->degree(); i++) {
    uint32_t j = fuse_it(x->at(i));
    if (tab[j] == static_cast<size_t>(-1)) {
      tab[j] = next;
      next++;
    }
    out_blocks->set_block(i, tab[j]);
    out_blocks->set_is_transverse_block(tab[j], _BUFFER_bool[j]);
  }

#ifdef SEMIGROUPS_KERNEL_DEBUG
  libsemigroups::validate(*out_blocks);
#endif

  return blocks_new_obj(out_blocks);
}

// Returns the right blocks of x_gap * BLOCKS_PROJ(blocks_gap) where the former
// is a GAP bipartition.

Obj BLOCKS_RIGHT_ACT(Obj self, Obj blocks_gap, Obj x_gap) {
  SEMIGROUPS_ASSERT(TNUM_OBJ(x_gap) == T_BIPART);
  SEMIGROUPS_ASSERT(TNUM_OBJ(blocks_gap) == T_BLOCKS);

  Bipartition* x      = bipart_get_cpp(x_gap);
  Blocks*      blocks = blocks_get_cpp(blocks_gap);

  if (blocks->degree() != x->degree()) {
    // hack to allow Lambda/RhoOrbSeed
    return blocks_new_obj(x->right_blocks());
  } else if (blocks->degree() == 0) {
    return blocks_gap;
  }

  // prepare the _BUFFER_bool for detecting transverse fused blocks
  _BUFFER_bool.clear();
  _BUFFER_bool.resize(x->number_of_blocks() + blocks->number_of_blocks());
  std::copy(
      blocks->cbegin_lookup(), blocks->cend_lookup(), _BUFFER_bool.begin());

  fuse(x->degree(),
       blocks->cbegin(),
       blocks->number_of_blocks(),
       x->cbegin(),
       x->number_of_blocks(),
       true);

  _BUFFER_size_t.resize(
      2 * (x->number_of_blocks() + blocks->number_of_blocks()), -1);
  auto tab = _BUFFER_size_t.begin() + x->number_of_blocks()
             + blocks->number_of_blocks();

  Blocks*        out_blocks = new Blocks(x->degree());
  uint32_t       next       = 0;
  uint32_t const n          = x->degree();
  for (uint32_t i = n; i < 2 * n; i++) {
    uint32_t j = fuse_it(x->at(i) + blocks->number_of_blocks());
    if (tab[j] == static_cast<size_t>(-1)) {
      tab[j] = next;
      next++;
    }
    out_blocks->set_block(i - n, tab[j]);
    out_blocks->set_is_transverse_block(tab[j], _BUFFER_bool[j]);
  }
#ifdef SEMIGROUPS_KERNEL_DEBUG
  libsemigroups::validate(*out_blocks);
#endif
  return blocks_new_obj(out_blocks);
}

// Returns a GAP bipartition y such that if BLOCKS_LEFT_ACT(blocks_gap, x_gap)
// = Y, then BLOCKS_LEFT_ACT(Y, y) = blocks_gap, and y acts on Y as the inverse
// of x_gap on Y.

Obj BLOCKS_INV_LEFT(Obj self, Obj blocks_gap, Obj x_gap) {
  SEMIGROUPS_ASSERT(TNUM_OBJ(blocks_gap) == T_BLOCKS);
  SEMIGROUPS_ASSERT(TNUM_OBJ(x_gap) == T_BIPART);
  Blocks*      blocks = blocks_get_cpp(blocks_gap);
  Bipartition* x      = bipart_get_cpp(x_gap);
  SEMIGROUPS_ASSERT(x->degree() == blocks->degree());

  fuse(x->degree(),
       blocks->cbegin(),
       blocks->number_of_blocks(),
       x->cbegin() + x->degree(),
       x->number_of_blocks(),
       false);
  SEMIGROUPS_ASSERT(_BUFFER_size_t.size()
                    == blocks->number_of_blocks() + x->number_of_blocks());

  std::vector<uint32_t> out_blocks(2 * x->degree());

  _BUFFER_size_t.resize(2 * blocks->number_of_blocks() + x->number_of_blocks(),
                        -1);
  SEMIGROUPS_ASSERT(_BUFFER_size_t.size()
                    == 2 * blocks->number_of_blocks() + x->number_of_blocks());
  SEMIGROUPS_ASSERT(std::all_of(
      _BUFFER_size_t.cbegin() + blocks->number_of_blocks()
          + x->number_of_blocks(),
      _BUFFER_size_t.cend(),
      [](size_t i) -> bool { return i == static_cast<size_t>(-1); }));
  auto tab = _BUFFER_size_t.begin() + blocks->number_of_blocks()
             + x->number_of_blocks();
  SEMIGROUPS_ASSERT(_BUFFER_size_t.end() - tab == blocks->number_of_blocks());

  for (uint32_t i = 0; i < blocks->number_of_blocks(); i++) {
    if (blocks->is_transverse_block(i)) {
      SEMIGROUPS_ASSERT(fuse_it(i) < blocks->number_of_blocks());
      SEMIGROUPS_ASSERT(tab + fuse_it(i) < _BUFFER_size_t.end());
      tab[fuse_it(i)] = i;
    }
  }

  // find the left blocks of the output
  for (uint32_t i = 0; i < blocks->degree(); i++) {
    out_blocks[i] = (*blocks)[i];
    uint32_t j    = fuse_it(x->at(i) + blocks->number_of_blocks());
    if (j >= blocks->number_of_blocks() || tab[j] == static_cast<size_t>(-1)) {
      out_blocks[i + x->degree()] = blocks->number_of_blocks();  // junk
    } else {
      out_blocks[i + x->degree()] = tab[j];
    }
  }

  Bipartition* out = new Bipartition(out_blocks);
  out->set_number_of_left_blocks(blocks->number_of_blocks());

  return bipart_new_obj(out);
}

// Returns a GAP bipartition y such that if BLOCKS_RIGHT_ACT(blocks_gap, x_gap)
// = Y, then BLOCKS_RIGHT_ACT(Y, y) = blocks_gap, and y acts on Y as the inverse
// of x_gap on Y.
//
// We fuse <blocks_gap> with the left blocks of <x_gap> keeping track of
// the signs of the fused classes.
//
// The left blocks of the output are then:
//
// 1) disconnected right blocks of <x_gap> (before fusing)
//
// 2) disconnected right blocks of <x_gap> (after fusing)
//
// 3) connected right blocks of <x_gap> (after fusing)
//
// both types 1+2 of the disconnected blocks are unioned into one left block of
// the output with index <junk>. The connected blocks 3 of <x_gap> are given the
// next
// available index, if they have not been seen before. The table <tab1> keeps
// track of which connected right blocks of <x_gap> have been seen before and
// the
// corresponding index in the output, i.e. <tab1[x]> is the index in <out> of
// the
// fused block with index <x>.
//
// The right blocks of the output are:
//
// 1) disconnected blocks of <blocks_gap>; or
//
// 2) connected blocks of <blocks_gap>.
//
// The disconnected blocks 1 are given the next available index, if they have
// not
// been seen before. The table <tab2> keeps track of which disconnected blocks
// of
// <blocks_gap> have been seen before and the corresponding index in the output,
// i.e.
// <tab2[x]> is the index in <out> of the disconnected block of <blocks_gap>
// with
// index <x>. The connected blocks 2 of <blocks_gap> is given the index
// <tab1[x]>
// where <x> is the fused index of the block.

Obj BLOCKS_INV_RIGHT(Obj self, Obj blocks_gap, Obj x_gap) {
  Blocks*      blocks = blocks_get_cpp(blocks_gap);
  Bipartition* x      = bipart_get_cpp(x_gap);

  // prepare _BUFFER_bool for fusing

  _BUFFER_bool.clear();
  _BUFFER_bool.resize(blocks->number_of_blocks() + x->number_of_blocks());
  std::copy(
      blocks->cbegin_lookup(), blocks->cend_lookup(), _BUFFER_bool.begin());

  fuse(x->degree(),
       blocks->cbegin(),
       blocks->number_of_blocks(),
       x->cbegin(),
       x->number_of_blocks(),
       true);

  uint32_t junk = -1;
  uint32_t next = 0;

  std::vector<uint32_t> out_blocks(2 * x->degree());

  _BUFFER_size_t.resize(
      3 * blocks->number_of_blocks() + 2 * x->number_of_blocks(), -1);
  auto tab1 = _BUFFER_size_t.begin() + blocks->number_of_blocks()
              + x->number_of_blocks();
  auto tab2 = _BUFFER_size_t.begin()
              + 2 * (blocks->number_of_blocks() + x->number_of_blocks());

  // find the left blocks of the output
  for (uint32_t i = 0; i < blocks->degree(); i++) {
    if (x->at(i + x->degree()) < x->number_of_left_blocks()) {
      uint32_t j = fuse_it(x->at(i + x->degree()) + blocks->number_of_blocks());
      if (_BUFFER_bool[j]) {
        if (tab1[j] == static_cast<size_t>(-1)) {
          tab1[j] = next;
          next++;
        }
        out_blocks[i] = tab1[j];
        continue;
      }
    }
    if (junk == static_cast<uint32_t>(-1)) {
      junk = next;
      next++;
    }
    out_blocks[i] = junk;
  }

  uint32_t out_nr_left_blocks = next;

  // find the right blocks of the output

  for (uint32_t i = blocks->degree(); i < 2 * blocks->degree(); i++) {
    uint32_t j = (*blocks)[i - blocks->degree()];
    if (blocks->is_transverse_block(j)) {
      out_blocks[i] = tab1[fuse_it(j)];
    } else {
      if (tab2[j] == static_cast<size_t>(-1)) {
        tab2[j] = next;
        next++;
      }
      out_blocks[i] = tab2[j];
    }
  }

  Bipartition* out = new Bipartition(out_blocks);
  out->set_number_of_left_blocks(out_nr_left_blocks);
  out->set_number_of_blocks(next);
  return bipart_new_obj(out);
}

////////////////////////////////////////////////////////////////////////////////
// Non-GAP functions
////////////////////////////////////////////////////////////////////////////////

// The functions below do the Union-Find algorithm for finding the least
// equivalence relation containing two other equivalence relations. These are
// used by many of the functions above for blocks.

// Returns the class containing the number i (i.e. this is the Find part of
// Union-Find). This strongly relies on everything being set up correctly.

static inline size_t fuse_it(size_t i) {
  while (_BUFFER_size_t[i] < i) {
    i = _BUFFER_size_t[i];
  }
  return i;
}

// This function performs Union-Find to find the least equivalence relation
// containing the equivalence relations starting at left_begin, and
// right_begin (named left and right below).
//
// If it = left_begin or right_begin, then it must be an iterator such that:
//
//   * it.end() >= it.begin() + deg
//
//   * *(it.begin() + i) is the index of the block containing i in the
//   equivalence relation represented by it
//
//   * left_nr_blocks/right_nr_blocks is the number of blocks in the
//   equivalence relation represented by left_begin/right_begin.
//
//   * if we want to keep track of transverse blocks, then sign should be true,
//   otherwise it is false.
//
// After running fuse:
//
// 1) [_BUFFER_size_t.begin() .. _BUFFER_size_t.begin() + left_nr_blocks +
//    right_nr_blocks - 1] is the fuse table for left and right
//
// 2) If sign == true, then _BUFFER_bool is a lookup for the transverse blocks
//    of the fused left and right
//
// Note that _BUFFER_bool has to be pre-assigned with the correct values, i.e.
// it must be at least initialized (and have the appropriate length).

static void fuse(uint32_t                                       deg,
                 typename std::vector<uint32_t>::const_iterator left_begin,
                 uint32_t                                       left_nr_blocks,
                 typename std::vector<uint32_t>::const_iterator right_begin,
                 uint32_t                                       right_nr_blocks,
                 bool                                           sign) {
  _BUFFER_size_t.clear();
  _BUFFER_size_t.reserve(left_nr_blocks + right_nr_blocks);

  for (size_t i = 0; i < left_nr_blocks + right_nr_blocks; i++) {
    _BUFFER_size_t.push_back(i);
  }

  for (auto left_it = left_begin, right_it = right_begin;
       left_it < left_begin + deg;
       left_it++, right_it++) {
    size_t j = fuse_it(*left_it);
    size_t k = fuse_it(*right_it + left_nr_blocks);

    if (j != k) {
      if (j < k) {
        _BUFFER_size_t[k] = j;
        if (sign && _BUFFER_bool[k]) {
          _BUFFER_bool[j] = true;
        }
      } else {
        _BUFFER_size_t[j] = k;
        if (sign && _BUFFER_bool[j]) {
          _BUFFER_bool[k] = true;
        }
      }
    }
  }
}

////////////////////////////////////////////////////////////////////////////////
// Counting idempotents in regular *-semigroups of bipartitions
////////////////////////////////////////////////////////////////////////////////

// The class and functions below implement a parallel idempotent counting
// method for regular *-semigroups of bipartitions.

// IdempotentCounter is a class for containing the data required for the
// search for idempotents.

class IdempotentCounter {
  typedef std::vector<std::vector<size_t>> thrds_size_t;
  typedef std::vector<std::vector<bool>>   thrds_bool_t;
  typedef std::pair<size_t, size_t>        unpr_t;
  typedef std::vector<std::vector<unpr_t>> thrds_unpr_t;

public:
  IdempotentCounter(Obj orbit, Obj scc, Obj lookup, unsigned int nr_threads)
      : _nr_threads(std::min(nr_threads, std::thread::hardware_concurrency())),
        _fuse_tab(thrds_size_t(_nr_threads, std::vector<size_t>())),
        _lookup(thrds_bool_t(_nr_threads, std::vector<bool>())),
        _min_scc(),
        _orbit(),
        _scc(),
        _scc_pos(std::vector<size_t>(LEN_LIST(orbit), 0)),
        _seen(thrds_bool_t(_nr_threads, std::vector<bool>())),
        _threads(),
        _unprocessed(thrds_unpr_t(_nr_threads, std::vector<unpr_t>())),
        _vals(thrds_size_t(_nr_threads,
                           std::vector<size_t>(LEN_PLIST(scc) - 1, 0))) {
    // copy the GAP blocks from the orbit into _orbit
    _orbit.reserve(LEN_LIST(orbit));
    for (Int i = 2; i <= LEN_LIST(orbit); i++) {
      _orbit.push_back(blocks_get_cpp(ELM_LIST(orbit, i)));
    }

    size_t total_load = 0;
    size_t min_rank   = -1;
    // copy the scc from GAP to C++
    for (Int i = 2; i <= LEN_PLIST(scc); i++) {
      Obj comp = ELM_PLIST(scc, i);

      _scc.push_back(std::vector<size_t>());
      _scc.back().reserve(LEN_PLIST(comp));

      for (Int j = 1; j <= LEN_PLIST(comp); j++) {
        _scc.back().push_back(INT_INTOBJ(ELM_PLIST(comp, j)) - 2);
        _scc_pos[INT_INTOBJ(ELM_PLIST(comp, j)) - 2] = j - 1;
      }
      _ranks.push_back(_orbit[_scc.back()[0]]->rank());
      if (_ranks.back() < min_rank) {
        min_rank = _ranks.back();
        _min_scc = i - 2;
      }
      total_load += _scc.back().size() * (_scc.back().size() - 1) / 2;
    }

    total_load -= (_scc[_min_scc].size() * (_scc[_min_scc].size() - 1) / 2);

    // queue pairs for each thread
    size_t mean_load   = total_load / _nr_threads;
    size_t thread_id   = 0;
    size_t thread_load = 0;

    for (size_t i = 0; i < _orbit.size(); i++) {
      size_t comp = INT_INTOBJ(ELM_PLIST(lookup, i + 2)) - 2;
      if (comp != _min_scc) {
        _unprocessed[thread_id].push_back(std::make_pair(i, comp));
        thread_load += _scc[comp].size() - _scc_pos[i];
        if (thread_load >= mean_load && thread_id != _nr_threads - 1) {
          thread_id++;
          thread_load = 0;
        }
      }
    }
  }

  std::vector<size_t> count() {
    libsemigroups::THREAD_ID_MANAGER.reset();
    REPORT_DEFAULT("using %llu / %llu additional threads",
                   _nr_threads,
                   std::thread::hardware_concurrency());
    Timer timer;

    for (size_t i = 0; i < _nr_threads; i++) {
      _threads.push_back(
          std::thread(&IdempotentCounter::thread_counter, this, i));
    }

    for (size_t i = 0; i < _nr_threads; i++) {
      _threads[i].join();
    }

    REPORT_TIME(timer);

    size_t              max = *max_element(_ranks.begin(), _ranks.end()) + 1;
    std::vector<size_t> out = std::vector<size_t>(max, 0);

    for (size_t j = 0; j < _scc.size(); j++) {
      size_t rank = _ranks[j];
      if (j != _min_scc) {
        for (size_t i = 0; i < _nr_threads; i++) {
          out[rank] += _vals[i][j];
        }

      } else {
        out[rank] += _scc[_min_scc].size() * _scc[_min_scc].size();
      }
    }

    return out;
  }

private:
  void thread_counter(size_t thread_id) {
    Timer timer;

    for (unpr_t index : _unprocessed[thread_id]) {
      if (tester(thread_id, index.first, index.first)) {
        _vals[thread_id][index.second]++;
      }
      std::vector<size_t> comp  = _scc[index.second];
      auto                begin = comp.begin() + _scc_pos[index.first] + 1;
      for (auto it = begin; it < comp.end(); it++) {
        if (tester(thread_id, index.first, *it)) {
          _vals[thread_id][index.second] += 2;
        }
      }
    }
    REPORT_DEFAULT("finished in %llu", timer.string().c_str());
  }

  // This is basically the same as BLOCKS_E_TESTER, but is required because we
  // must have different temporary storage for every thread.
  bool tester(size_t thread_id, size_t i, size_t j) {
    Blocks* left  = _orbit[i];
    Blocks* right = _orbit[j];

    // prepare the _lookup for detecting transverse fused blocks
    _lookup[thread_id].clear();
    _lookup[thread_id].resize(right->number_of_blocks()
                              + left->number_of_blocks());
    std::copy(right->cbegin_lookup(),
              right->cend_lookup(),
              _lookup[thread_id].begin() + left->number_of_blocks());

    _seen[thread_id].clear();
    _seen[thread_id].resize(left->number_of_blocks());

    // prepare the _fuse_tab
    _fuse_tab[thread_id].clear();
    _fuse_tab[thread_id].reserve(left->number_of_blocks()
                                 + right->number_of_blocks());

    for (size_t k = 0; k < left->number_of_blocks() + right->number_of_blocks();
         k++) {
      _fuse_tab[thread_id].push_back(k);
    }

    for (auto left_it = left->cbegin(), right_it = right->cbegin();
         left_it < left->cbegin() + left->degree();
         left_it++, right_it++) {
      size_t k = fuse_it(thread_id, *left_it);
      size_t l = fuse_it(thread_id, *right_it + left->number_of_blocks());

      if (k != l) {
        if (k < l) {
          _fuse_tab[thread_id][l] = k;
          if (_lookup[thread_id][l]) {
            _lookup[thread_id][k] = true;
          }
        } else {
          _fuse_tab[thread_id][k] = l;
          if (_lookup[thread_id][k]) {
            _lookup[thread_id][l] = true;
          }
        }
      }
    }

    for (uint32_t k = 0; k < left->number_of_blocks(); k++) {
      if (left->is_transverse_block(k)) {
        size_t l = fuse_it(thread_id, k);
        if (!_lookup[thread_id][l] || _seen[thread_id][l]) {
          return false;
        }
        _seen[thread_id][l] = true;
      }
    }
    return true;
  }

  inline size_t fuse_it(size_t thread_id, size_t i) {
    while (_fuse_tab[thread_id][i] < i) {
      i = _fuse_tab[thread_id][i];
    }
    return i;
  }

  size_t               _nr_threads;
  thrds_size_t         _fuse_tab;
  thrds_bool_t         _lookup;
  size_t               _min_scc;
  std::vector<Blocks*> _orbit;
  std::vector<size_t>  _ranks;
  thrds_size_t         _scc;
  std::vector<size_t>  _scc_pos;
  // _scc_pos[i] is the position of _orbit[i] in its scc
  thrds_bool_t             _seen;
  std::vector<std::thread> _threads;
  thrds_unpr_t             _unprocessed;
  thrds_size_t             _vals;
  // map from the scc indices to the rank of elements in that scc
};

// GAP-level function

Obj BIPART_NR_IDEMPOTENTS(Obj self,
                          Obj o,
                          Obj scc,
                          Obj lookup,
                          Obj nr_threads) {
  IdempotentCounter   finder(o, scc, lookup, INT_INTOBJ(nr_threads));
  std::vector<size_t> vals = finder.count();

  Obj out = NEW_PLIST(T_PLIST_CYC, vals.size());
  SET_LEN_PLIST(out, vals.size());

  for (size_t i = 1; i <= vals.size(); i++) {
    SET_ELM_PLIST(out, i, INTOBJ_INT(vals[i - 1]));
  }

  return out;
}

quality91%

¤ Die Informationen auf dieser Webseite wurden nach bestem Wissen sorgfältig zusammengestellt. Es wird jedoch weder Vollständigkeit, noch Richtigkeit, noch Qualität der bereit gestellten Informationen zugesichert.0.7Bemerkung: (vorverarbeitet) ¤

Wurzel

Suchen

Beweissystem der NASA

Beweissystem Isabelle

NIST Cobol Testsuite

Cephes Mathematical Library

Wiener Entwicklungsmethode

Haftungshinweis

Die Informationen auf dieser Webseite wurden nach bestem Wissen sorgfältig zusammengestellt. Es wird jedoch weder Vollständigkeit, noch Richtigkeit, noch Qualität der bereit gestellten Informationen zugesichert.

Bemerkung:

Die farbliche Syntaxdarstellung ist noch experimentell.