#include <NTL/LLL.h>
#include <NTL/fileio.h>

#include <NTL/new.h>

NTL_START_IMPL

static void RowTransform(vec_ZZ& A, vec_ZZ& B, const ZZ& MU1)
// x = x - y*MU
{
   NTL_ZZRegister(T);
   NTL_ZZRegister(MU);
   long k;

   long n = A.length();
   long i;

   MU = MU1;

   if (MU == 1) {
      for (i = 1; i <= n; i++)
         sub(A(i), A(i), B(i));

      return;
   }

   if (MU == -1) {
      for (i = 1; i <= n; i++)
         add(A(i), A(i), B(i));

      return;
   }

   if (MU == 0) return;

   if (NumTwos(MU) >= NTL_ZZ_NBITS)
      k = MakeOdd(MU);
   else
      k = 0;

   if (MU.WideSinglePrecision()) {
      long mu1;
      conv(mu1, MU);

      for (i = 1; i <= n; i++) {
         mul(T, B(i), mu1);
         if (k > 0) LeftShift(T, T, k);
         sub(A(i), A(i), T);
      }
   }
   else {
      for (i = 1; i <= n; i++) {
         mul(T, B(i), MU);
         if (k > 0) LeftShift(T, T, k);
         sub(A(i), A(i), T);
      }
   }
}

static void RowTransform2(vec_ZZ& A, vec_ZZ& B, const ZZ& MU1)
// x = x + y*MU
{
   NTL_ZZRegister(T);
   NTL_ZZRegister(MU);
   long k;

   long n = A.length();
   long i;

   MU = MU1;

   if (MU == 1) {
      for (i = 1; i <= n; i++)
         add(A(i), A(i), B(i));

      return;
   }

   if (MU == -1) {
      for (i = 1; i <= n; i++)
         sub(A(i), A(i), B(i));

      return;
   }

   if (MU == 0) return;

   if (NumTwos(MU) >= NTL_ZZ_NBITS)
      k = MakeOdd(MU);
   else
      k = 0;

   if (MU.WideSinglePrecision()) {
      long mu1;
      conv(mu1, MU);

      for (i = 1; i <= n; i++) {
         mul(T, B(i), mu1);
         if (k > 0) LeftShift(T, T, k);
         add(A(i), A(i), T);
      }
   }
   else {
      for (i = 1; i <= n; i++) {
         mul(T, B(i), MU);
         if (k > 0) LeftShift(T, T, k);
         add(A(i), A(i), T);
      }
   }
}

void ComputeGS(const mat_ZZ& B, mat_RR& B1,
               mat_RR& mu, vec_RR& b,
               vec_RR& c, long k, const RR& bound, long st,
               vec_RR& buf, const RR& bound2)
{
   long i, j;
   RR s, t, t1;
   ZZ T1;

   if (st < k) {
      for (i = 1; i < st; i++)
         mul(buf(i), mu(k,i), c(i));
   }

   for (j = st; j <= k-1; j++) {
      InnerProduct(s, B1(k), B1(j));

      sqr(t1, s);
      mul(t1, t1, bound);
      mul(t, b(k), b(j));

      if (t >= bound2 && t >= t1) {
         InnerProduct(T1, B(k), B(j));
         conv(s, T1);
      }

      clear(t1);
      for (i = 1; i <= j-1; i++) {
         mul(t, mu(j, i), buf(i));
         add(t1, t1, t);
      }

      sub(t, s, t1);
      buf(j) = t;
      div(mu(k, j), t, c(j));
   }

   clear(s);
   for (j = 1; j <= k-1; j++) {
      mul(t, mu(k, j), buf(j));
      add(s, s, t);
   }

   sub(c(k), b(k), s);
}

NTL_THREAD_LOCAL static RR red_fudge;
NTL_THREAD_LOCAL static long log_red = 0;

static void init_red_fudge()
{
   log_red = long(0.50*RR::precision());

   power2(red_fudge, -log_red);
}

static void inc_red_fudge()
{

   mul(red_fudge, red_fudge, 2);
   log_red--;

   cerr << "LLL_RR: warning--relaxing reduction (" << log_red << ")\n";

   if (log_red < 4)
      ResourceError("LLL_RR: can not continue...sorry");
}

NTL_THREAD_LOCAL static long verbose = 0;
NTL_THREAD_LOCAL static unsigned long NumSwaps = 0;
NTL_THREAD_LOCAL static double StartTime = 0;
NTL_THREAD_LOCAL static double LastTime = 0;

static void LLLStatus(long max_k, double t, long m, const mat_ZZ& B)
{
   cerr << "---- LLL_RR status ----\n";
   cerr << "elapsed time: ";
   PrintTime(cerr, t-StartTime);
   cerr << ", stage: " << max_k;
   cerr << ", rank: " << m;
   cerr << ", swaps: " << NumSwaps << "\n";

   ZZ t1;
   long i;
   double prodlen = 0;

   for (i = 1; i <= m; i++) {
      InnerProduct(t1, B(i), B(i));
      if (!IsZero(t1))
         prodlen += log(t1);
   }

   cerr << "log of prod of lengths: " << prodlen/(2.0*log(2.0)) << "\n";

   if (LLLDumpFile) {
      cerr << "dumping to " << LLLDumpFile << "...";

      ofstream f;
      OpenWrite(f, LLLDumpFile);

      f << "[";
      for (i = 1; i <= m; i++) {
         f << B(i) << "\n";
      }
      f << "]\n";

      f.close();

      cerr << "\n";
   }

   LastTime = t;

}

static
long ll_LLL_RR(mat_ZZ& B, mat_ZZ* U, const RR& delta, long deep,
           LLLCheckFct check, mat_RR& B1, mat_RR& mu,
           vec_RR& b, vec_RR& c, long m, long init_k, long &quit)
{
   long n = B.NumCols();

   long i, j, k, Fc1;
   ZZ MU;
   RR mu1, t1, t2, cc;
   ZZ T1;

   RR bound;

      // we tolerate a 15% loss of precision in computing
      // inner products in ComputeGS.

   power2(bound, 2*long(0.15*RR::precision()));

   RR bound2;

   power2(bound2, 2*RR::precision());

   quit = 0;
   k = init_k;

   vec_long st_mem;
   st_mem.SetLength(m+2);
   long *st = st_mem.elts();

   for (i = 1; i < k; i++)
      st[i] = i;

   for (i = k; i <= m+1; i++)
      st[i] = 1;

   vec_RR buf;
   buf.SetLength(m);

   long rst;
   long counter;

   long trigger_index;
   long small_trigger;
   long cnt;

   RR half;
   conv(half,  0.5);
   RR half_plus_fudge;
   add(half_plus_fudge, half, red_fudge);

   long max_k = 0;
   double tt;

   while (k <= m) {

      if (k > max_k) {
         max_k = k;
      }

      if (verbose) {
         tt = GetTime();

         if (tt > LastTime + LLLStatusInterval)
            LLLStatus(max_k, tt, m, B);
      }

      if (st[k] == k)
         rst = 1;
      else
         rst = k;

      if (st[k] < st[k+1]) st[k+1] = st[k];
      ComputeGS(B, B1, mu, b, c, k, bound, st[k], buf, bound2);
      st[k] = k;

      counter = 0;
      trigger_index = k;
      small_trigger = 0;
      cnt = 0;

      do {
         // size reduction

         counter++;
         if (counter > 10000) {
            cerr << "LLL_XD: warning--possible infinite loop\n";
            counter = 0;
         }

         Fc1 = 0;

         for (j = rst-1; j >= 1; j--) {
            abs(t1, mu(k,j));
            if (t1 > half_plus_fudge) {

               if (!Fc1) {
                  if (j > trigger_index ||
                      (j == trigger_index && small_trigger)) {

                     cnt++;

                     if (cnt > 10) {
                        inc_red_fudge();
                        add(half_plus_fudge, half, red_fudge);
                        cnt = 0;
                     }
                  }

                  trigger_index = j;
                  small_trigger = (t1 < 4);
               }

               Fc1 = 1;

               mu1 = mu(k,j);
               if (sign(mu1) >= 0) {
                  sub(mu1, mu1, half);
                  ceil(mu1, mu1);
               }
               else {
                  add(mu1, mu1, half);
                  floor(mu1, mu1);
               }

               if (mu1 == 1) {
                  for (i = 1; i <= j-1; i++)
                     sub(mu(k,i), mu(k,i), mu(j,i));
               }
               else if (mu1 == -1) {
                  for (i = 1; i <= j-1; i++)
                     add(mu(k,i), mu(k,i), mu(j,i));
               }
               else {
                  for (i = 1; i <= j-1; i++) {
                     mul(t2, mu1, mu(j,i));
                     sub(mu(k,i), mu(k,i), t2);
                  }
               }

               conv(MU, mu1);

               sub(mu(k,j), mu(k,j), mu1);

               RowTransform(B(k), B(j), MU);
               if (U) RowTransform((*U)(k), (*U)(j), MU);
            }
         }

         if (Fc1) {
            for (i = 1; i <= n; i++)
               conv(B1(k, i), B(k, i));

            InnerProduct(b(k), B1(k), B1(k));
            ComputeGS(B, B1, mu, b, c, k, bound, 1, buf, bound2);
         }
      } while (Fc1);

      if (check && (*check)(B(k)))
         quit = 1;

      if (IsZero(b(k))) {
         for (i = k; i < m; i++) {
            // swap i, i+1
            swap(B(i), B(i+1));
            swap(B1(i), B1(i+1));
            swap(b(i), b(i+1));
            if (U) swap((*U)(i), (*U)(i+1));
         }

         for (i = k; i <= m+1; i++) st[i] = 1;

         m--;
         if (quit) break;
         continue;
      }

      if (quit) break;

      if (deep > 0) {
         // deep insertions

         cc = b(k);
         long l = 1;
         while (l <= k-1) {
            mul(t1, delta, c(l));
            if (t1 > cc) break;
            sqr(t1, mu(k,l));
            mul(t1, t1, c(l));
            sub(cc, cc, t1);
            l++;
         }

         if (l <= k-1 && (l <= deep || k-l <= deep)) {
            // deep insertion at position l

            for (i = k; i > l; i--) {
               // swap rows i, i-1
               swap(B(i), B(i-1));
               swap(B1(i), B1(i-1));
               swap(mu(i), mu(i-1));
               swap(b(i), b(i-1));
               if (U) swap((*U)(i), (*U)(i-1));
            }

            k = l;
            continue;
         }
      } // end deep insertions

      // test LLL reduction condition

      if (k <= 1) {
         k++;
      }
      else {
         sqr(t1, mu(k,k-1));
         mul(t1, t1, c(k-1));
         add(t1, t1, c(k));
         mul(t2, delta, c(k-1));
         if (t2 > t1) {
            // swap rows k, k-1
            swap(B(k), B(k-1));
            swap(B1(k), B1(k-1));
            swap(mu(k), mu(k-1));
            swap(b(k), b(k-1));
            if (U) swap((*U)(k), (*U)(k-1));

            k--;
            NumSwaps++;
         }
         else {
            k++;
         }
      }
   }

   if (verbose) {
      LLLStatus(m+1, GetTime(), m, B);
   }

   return m;
}

static
long LLL_RR(mat_ZZ& B, mat_ZZ* U, const RR& delta, long deep,
           LLLCheckFct check)
{
   long m = B.NumRows();
   long n = B.NumCols();

   long i, j;
   long new_m, dep, quit;
   RR s;
   ZZ MU;
   RR mu1;

   RR t1;
   ZZ T1;

   init_red_fudge();

   if (U) ident(*U, m);

   mat_RR B1;  // approximates B
   B1.SetDims(m, n);

   mat_RR mu;
   mu.SetDims(m, m);

   vec_RR c;  // squared lengths of Gramm-Schmidt basis vectors
   c.SetLength(m);

   vec_RR b; // squared lengths of basis vectors
   b.SetLength(m);

   for (i = 1; i <=m; i++)
      for (j = 1; j <= n; j++)
         conv(B1(i, j), B(i, j));

   for (i = 1; i <= m; i++) {
      InnerProduct(b(i), B1(i), B1(i));
   }

   new_m = ll_LLL_RR(B, U, delta, deep, check, B1, mu, b, c, m, 1, quit);
   dep = m - new_m;
   m = new_m;

   if (dep > 0) {
      // for consistency, we move all of the zero rows to the front

      for (i = 0; i < m; i++) {
         swap(B(m+dep-i), B(m-i));
         if (U) swap((*U)(m+dep-i), (*U)(m-i));
      }
   }

   return m;
}

long LLL_RR(mat_ZZ& B, double delta, long deep,
            LLLCheckFct check, long verb)
{
   verbose = verb;
   NumSwaps = 0;
   if (verbose) {
      StartTime = GetTime();
      LastTime = StartTime;
   }

   if (delta < 0.50 || delta >= 1) LogicError("LLL_RR: bad delta");
   if (deep < 0) LogicError("LLL_RR: bad deep");
   RR Delta;
   conv(Delta, delta);
   return LLL_RR(B, 0, Delta, deep, check);
}

long LLL_RR(mat_ZZ& B, mat_ZZ& U, double delta, long deep,
           LLLCheckFct check, long verb)
{
   verbose = verb;
   NumSwaps = 0;
   if (verbose) {
      StartTime = GetTime();
      LastTime = StartTime;
   }

   if (delta < 0.50 || delta >= 1) LogicError("LLL_RR: bad delta");
   if (deep < 0) LogicError("LLL_RR: bad deep");
   RR Delta;
   conv(Delta, delta);
   return LLL_RR(B, &U, Delta, deep, check);
}

NTL_THREAD_LOCAL static vec_RR BKZConstant;

static
void ComputeBKZConstant(long beta, long p)
{
   RR c_PI;
   ComputePi(c_PI);

   RR LogPI = log(c_PI);

   BKZConstant.SetLength(beta-1);

   vec_RR Log;
   Log.SetLength(beta);

   long i, j, k;
   RR x, y;

   for (j = 1; j <= beta; j++)
      Log(j) = log(to_RR(j));

   for (i = 1; i <= beta-1; i++) {
      // First, we compute x = gamma(i/2)^{2/i}

      k = i/2;

      if ((i & 1) == 0) { // i even
         x = 0;
         for (j = 1; j <= k; j++)
            x += Log(j);

         x = exp(x/k);

      }
      else { // i odd
         x = 0;
         for (j = k + 2; j <= 2*k + 2; j++)
            x += Log(j);

         x += 0.5*LogPI - 2*(k+1)*Log(2);

         x = exp(2*x/i);
      }

      // Second, we compute y = 2^{2*p/i}

      y = exp(-(2*p/to_RR(i))*Log(2));

      BKZConstant(i) = x*y/c_PI;
   }

}

NTL_THREAD_LOCAL static vec_RR BKZThresh;

static
void ComputeBKZThresh(RR *c, long beta)
{
   BKZThresh.SetLength(beta-1);

   long i;
   RR x;
   RR t1;

   x = 0;

   for (i = 1; i <= beta-1; i++) {
      log(t1, c[i-1]);
      add(x, x, t1);
      div(t1, x, i);
      exp(t1, t1);
      mul(BKZThresh(i), t1, BKZConstant(i));
   }
}

static
void BKZStatus(double tt, double enum_time, unsigned long NumIterations,
               unsigned long NumTrivial, unsigned long NumNonTrivial,
               unsigned long NumNoOps, long m,
               const mat_ZZ& B)
{
   cerr << "---- BKZ_RR status ----\n";
   cerr << "elapsed time: ";
   PrintTime(cerr, tt-StartTime);
   cerr << ", enum time: ";
   PrintTime(cerr, enum_time);
   cerr << ", iter: " << NumIterations << "\n";
   cerr << "triv: " << NumTrivial;
   cerr << ", nontriv: " << NumNonTrivial;
   cerr << ", no ops: " << NumNoOps;
   cerr << ", rank: " << m;
   cerr << ", swaps: " << NumSwaps << "\n";

   ZZ t1;
   long i;
   double prodlen = 0;

   for (i = 1; i <= m; i++) {
      InnerProduct(t1, B(i), B(i));
      if (!IsZero(t1))
         prodlen += log(t1);
   }

   cerr << "log of prod of lengths: " << prodlen/(2.0*log(2.0)) << "\n";

   if (LLLDumpFile) {
      cerr << "dumping to " << LLLDumpFile << "...";

      ofstream f;
      OpenWrite(f, LLLDumpFile);

      f << "[";
      for (i = 1; i <= m; i++) {
         f << B(i) << "\n";
      }
      f << "]\n";

      f.close();

      cerr << "\n";
   }

   LastTime = tt;

}

static
long BKZ_RR(mat_ZZ& BB, mat_ZZ* UU, const RR& delta,
         long beta, long prune, LLLCheckFct check)
{
   long m = BB.NumRows();
   long n = BB.NumCols();
   long m_orig = m;

   long i, j;
   ZZ MU;

   RR t1, t2;
   ZZ T1;

   init_red_fudge();

   mat_ZZ B;
   B = BB;

   B.SetDims(m+1, n);

   mat_RR B1;
   B1.SetDims(m+1, n);

   mat_RR mu;
   mu.SetDims(m+1, m);

   vec_RR c;
   c.SetLength(m+1);

   vec_RR b;
   b.SetLength(m+1);

   RR cbar;

   vec_RR ctilda;
   ctilda.SetLength(m+1);

   vec_RR vvec;
   vvec.SetLength(m+1);

   vec_RR yvec;
   yvec.SetLength(m+1);

   vec_RR uvec;
   uvec.SetLength(m+1);

   vec_RR utildavec;
   utildavec.SetLength(m+1);

   vec_long Deltavec;
   Deltavec.SetLength(m+1);

   vec_long deltavec;
   deltavec.SetLength(m+1);

   mat_ZZ Ulocal;
   mat_ZZ *U;

   if (UU) {
      Ulocal.SetDims(m+1, m);
      for (i = 1; i <= m; i++)
         conv(Ulocal(i, i), 1);
      U = &Ulocal;
   }
   else
      U = 0;

   long quit;
   long new_m;
   long z, jj, kk;
   long s, t;
   long h;

   for (i = 1; i <=m; i++)
      for (j = 1; j <= n; j++)
         conv(B1(i, j), B(i, j));

   for (i = 1; i <= m; i++) {
      InnerProduct(b(i), B1(i), B1(i));
   }

   // cerr << "\n";
   // cerr << "first LLL\n";

   m = ll_LLL_RR(B, U, delta, 0, check, B1, mu, b, c, m, 1, quit);

   double tt;

   double enum_time = 0;
   unsigned long NumIterations = 0;
   unsigned long NumTrivial = 0;
   unsigned long NumNonTrivial = 0;
   unsigned long NumNoOps = 0;

   long verb = verbose;

   verbose = 0;

   if (m < m_orig) {
      for (i = m_orig+1; i >= m+2; i--) {
         // swap i, i-1

         swap(B(i), B(i-1));
         if (U) swap((*U)(i), (*U)(i-1));
      }
   }

   long clean = 1;

   if (!quit && m > 1) {
      // cerr << "continuing\n";

      if (beta > m) beta = m;

      if (prune > 0)
         ComputeBKZConstant(beta, prune);

      z = 0;
      jj = 0;

      while (z < m-1) {
         jj++;
         kk = min(jj+beta-1, m);

         if (jj == m) {
            jj = 1;
            kk = beta;
            clean = 1;
         }

         if (verb) {
            tt = GetTime();
            if (tt > LastTime + LLLStatusInterval)
               BKZStatus(tt, enum_time, NumIterations, NumTrivial,
                         NumNonTrivial, NumNoOps, m, B);
         }

         // ENUM

         double tt1;

         if (verb) {
            tt1 = GetTime();
         }

         if (prune > 0)
            ComputeBKZThresh(&c(jj), kk-jj+1);

         cbar = c(jj);
         conv(utildavec(jj), 1);
         conv(uvec(jj), 1);

         conv(yvec(jj), 0);
         conv(vvec(jj), 0);
         Deltavec(jj) = 0;

         s = t = jj;
         deltavec(jj) = 1;

         for (i = jj+1; i <= kk+1; i++) {
            conv(ctilda(i), 0);
            conv(uvec(i), 0);
            conv(utildavec(i), 0);
            conv(yvec(i), 0);
            Deltavec(i) = 0;
            conv(vvec(i), 0);
            deltavec(i) = 1;
         }

         long enum_cnt = 0;

         while (t <= kk) {
            if (verb) {
               enum_cnt++;
               if (enum_cnt > 100000) {
                  enum_cnt = 0;
                  tt = GetTime();
                  if (tt > LastTime + LLLStatusInterval) {
                     enum_time += tt - tt1;
                     tt1 = tt;
                     BKZStatus(tt, enum_time, NumIterations, NumTrivial,
                               NumNonTrivial, NumNoOps, m, B);
                  }
               }
            }

            add(t1, yvec(t), utildavec(t));
            sqr(t1, t1);
            mul(t1, t1, c(t));
            add(ctilda(t), ctilda(t+1), t1);

            if (prune > 0 && t > jj)
               sub(t1, cbar, BKZThresh(t-jj));
            else
               t1 = cbar;

            if (ctilda(t) <t1) {
               if (t > jj) {
                  t--;
                  clear(t1);
                  for (i = t+1; i <= s; i++) {
                     mul(t2, utildavec(i), mu(i,t));
                     add(t1, t1, t2);
                  }

                  yvec(t) = t1;
                  negate(t1, t1);
                  if (sign(t1) >= 0) {
                     sub(t1, t1, 0.5);
                     ceil(t1, t1);
                  }
                  else {
                     add(t1, t1, 0.5);
                     floor(t1, t1);
                  }

                  utildavec(t) = t1;
                  vvec(t) = t1;
                  Deltavec(t) = 0;

                  negate(t1, t1);

                  if (t1 < yvec(t))
                     deltavec(t) = -1;
                  else
                     deltavec(t) = 1;
               }
               else {
                  cbar = ctilda(jj);
                  for (i = jj; i <= kk; i++) {
                     uvec(i) = utildavec(i);
                  }
               }
            }
            else {
               t++;
               s = max(s, t);
               if (t < s) Deltavec(t) = -Deltavec(t);
               if (Deltavec(t)*deltavec(t) >= 0) Deltavec(t) += deltavec(t);
               add(utildavec(t), vvec(t), Deltavec(t));
            }
         }

         if (verb) {
            tt1 = GetTime() - tt1;
            enum_time += tt1;
         }

         NumIterations++;

         h = min(kk+1, m);

         mul(t1, red_fudge, -8);
         add(t1, t1, delta);
         mul(t1, t1, c(jj));

         if (t1 > cbar) {

            clean = 0;

            // we treat the case that the new vector is b_s (jj < s <= kk)
            // as a special case that appears to occur most of the time.

            s = 0;
            for (i = jj+1; i <= kk; i++) {
               if (uvec(i) != 0) {
                  if (s == 0)
                     s = i;
                  else
                     s = -1;
               }
            }

            if (s == 0) LogicError("BKZ_RR: internal error");

            if (s > 0) {
               // special case
               // cerr << "special case\n";

               NumTrivial++;

               for (i = s; i > jj; i--) {
                  // swap i, i-1
                  swap(B(i-1), B(i));
                  swap(B1(i-1), B1(i));
                  swap(b(i-1), b(i));
                  if (U) swap((*U)(i-1), (*U)(i));
               }

               new_m = ll_LLL_RR(B, U, delta, 0, check,
                                B1, mu, b, c, h, jj, quit);
               if (new_m != h) LogicError("BKZ_RR: internal error");
               if (quit) break;
            }
            else {
               // the general case

               NumNonTrivial++;

               for (i = 1; i <= n; i++) conv(B(m+1, i), 0);

               if (U) {
                  for (i = 1; i <= m_orig; i++)
                     conv((*U)(m+1, i), 0);
               }

               for (i = jj; i <= kk; i++) {
                  if (uvec(i) == 0) continue;
                  conv(MU, uvec(i));
                  RowTransform2(B(m+1), B(i), MU);
                  if (U) RowTransform2((*U)(m+1), (*U)(i), MU);
               }

               for (i = m+1; i >= jj+1; i--) {
                  // swap i, i-1
                  swap(B(i-1), B(i));
                  swap(B1(i-1), B1(i));
                  swap(b(i-1), b(i));
                  if (U) swap((*U)(i-1), (*U)(i));
               }

               for (i = 1; i <= n; i++)
                  conv(B1(jj, i), B(jj, i));

               InnerProduct(b(jj), B1(jj), B1(jj));

               if (b(jj) == 0) LogicError("BKZ_RR: internal error");

               // remove linear dependencies

               // cerr << "general case\n";
               new_m = ll_LLL_RR(B, U, delta, 0, 0, B1, mu, b, c, kk+1, jj, quit);

               if (new_m != kk) LogicError("BKZ_RR: internal error");

               // remove zero vector

               for (i = kk+2; i <= m+1; i++) {
                  // swap i, i-1
                  swap(B(i-1), B(i));
                  swap(B1(i-1), B1(i));
                  swap(b(i-1), b(i));
                  if (U) swap((*U)(i-1), (*U)(i));
               }

               quit = 0;
               if (check) {
                  for (i = 1; i <= kk; i++)
                     if ((*check)(B(i))) {
                        quit = 1;
                        break;
                     }
               }

               if (quit) break;

               if (h > kk) {
                  // extend reduced basis

                  new_m = ll_LLL_RR(B, U, delta, 0, check,
                                   B1, mu, b, c, h, h, quit);

                  if (new_m != h) LogicError("BKZ_RR: internal error");
                  if (quit) break;
               }
            }

            z = 0;
         }
         else {
            // LLL_RR
            // cerr << "progress\n";

            NumNoOps++;

            if (!clean) {
               new_m =
                  ll_LLL_RR(B, U, delta, 0, check, B1, mu, b, c, h, h, quit);
               if (new_m != h) LogicError("BKZ_RR: internal error");
               if (quit) break;
            }

            z++;
         }
      }
   }

   if (verb) {
      BKZStatus(GetTime(), enum_time, NumIterations, NumTrivial, NumNonTrivial,
                NumNoOps, m, B);
   }

   // clean up

   if (m_orig > m) {
      // for consistency, we move zero vectors to the front

      for (i = m+1; i <= m_orig; i++) {
         swap(B(i), B(i+1));
         if (U) swap((*U)(i), (*U)(i+1));
      }

      for (i = 0; i < m; i++) {
         swap(B(m_orig-i), B(m-i));
         if (U) swap((*U)(m_orig-i), (*U)(m-i));
      }
   }

   B.SetDims(m_orig, n);
   BB = B;

   if (U) {
      U->SetDims(m_orig, m_orig);
      *UU = *U;
   }

   return m;
}

long BKZ_RR(mat_ZZ& BB, mat_ZZ& UU, double delta,
         long beta, long prune, LLLCheckFct check, long verb)
{
   verbose = verb;
   NumSwaps = 0;
   if (verbose) {
      StartTime = GetTime();
      LastTime = StartTime;
   }

   if (delta < 0.50 || delta >= 1) LogicError("BKZ_RR: bad delta");
   if (beta < 2) LogicError("BKZ_RR: bad block size");

   RR Delta;
   conv(Delta, delta);

   return BKZ_RR(BB, &UU, Delta, beta, prune, check);
}

long BKZ_RR(mat_ZZ& BB, double delta,
         long beta, long prune, LLLCheckFct check, long verb)
{
   verbose = verb;
   NumSwaps = 0;
   if (verbose) {
      StartTime = GetTime();
      LastTime = StartTime;
   }

   if (delta < 0.50 || delta >= 1) LogicError("BKZ_RR: bad delta");
   if (beta < 2) LogicError("BKZ_RR: bad block size");

   RR Delta;
   conv(Delta, delta);

   return BKZ_RR(BB, 0, Delta, beta, prune, check);
}

void NearVector(vec_ZZ& ww, const mat_ZZ& BB, const vec_ZZ& a)
{
   long n = BB.NumCols();

   if (n != BB.NumRows())
      LogicError("NearVector: matrix must be square");

   if (n != a.length())
      LogicError("NearVector: dimension mismatch");

   long i, j;
   mat_ZZ B;

   B.SetDims(n+1, n);
   for (i = 1; i <= n; i++)
      B(i) = BB(i);

   B(n+1) = a;

   mat_RR B1, mu;
   vec_RR b, c;

   B1.SetDims(n+1, n);
   mu.SetDims(n+1, n+1);
   b.SetLength(n+1);
   c.SetLength(n+1);

   vec_RR buf;
   buf.SetLength(n+1);

   for (i = 1; i <= n+1; i++)
      for (j = 1; j <= n; j++)
         conv(B1(i, j), B(i, j));

   for (i = 1; i <= n+1; i++)
      InnerProduct(b(i), B1(i), B1(i));

   RR bound;
   power2(bound, 2*long(0.15*RR::precision()));

   RR bound2;
   power2(bound2, 2*RR::precision());

   for (i = 1; i <= n+1; i++)
      ComputeGS(B, B1, mu, b, c, i, bound, 1, buf, bound2);

   init_red_fudge();

   RR half;
   conv(half,  0.5);
   RR half_plus_fudge;
   add(half_plus_fudge, half, red_fudge);

   RR t1, t2, mu1;
   ZZ MU;

   long trigger_index = n+1;
   long small_trigger = 0;
   long cnt = 0;

   long Fc1;

   vec_ZZ w;
   w.SetLength(n);
   clear(w);

   do {
      Fc1 = 0;

      for (j = n; j >= 1; j--) {
         abs(t1, mu(n+1,j));
         if (t1 > half_plus_fudge) {

            if (!Fc1) {
               if (j > trigger_index ||
                   (j == trigger_index && small_trigger)) {

                  cnt++;

                  if (cnt > 10) {
                     inc_red_fudge();
                     add(half_plus_fudge, half, red_fudge);
                     cnt = 0;
                  }
               }

               trigger_index = j;
               small_trigger = (t1 < 4);
            }

            Fc1 = 1;

            mu1 = mu(n+1,j);
            if (sign(mu1) >= 0) {
               sub(mu1, mu1, half);
               ceil(mu1, mu1);
            }
            else {
               add(mu1, mu1, half);
               floor(mu1, mu1);
            }

            if (mu1 == 1) {
               for (i = 1; i <= j-1; i++)
                  sub(mu(n+1,i), mu(n+1,i), mu(j,i));
            }
            else if (mu1 == -1) {
               for (i = 1; i <= j-1; i++)
                  add(mu(n+1,i), mu(n+1,i), mu(j,i));
            }
            else {
               for (i = 1; i <= j-1; i++) {
                  mul(t2, mu1, mu(j,i));
                  sub(mu(n+1,i), mu(n+1,i), t2);
               }
            }

            conv(MU, mu1);

            sub(mu(n+1,j), mu(n+1,j), mu1);

            RowTransform(B(n+1), B(j), MU);
            RowTransform2(w, B(j), MU);
         }
      }

      if (Fc1) {
         for (i = 1; i <= n; i++)
            conv(B1(n+1, i), B(n+1, i));

         InnerProduct(b(n+1), B1(n+1), B1(n+1));
         ComputeGS(B, B1, mu, b, c, n+1, bound, 1, buf, bound2);
      }
   } while (Fc1);

   ww = w;
}

NTL_END_IMPL


#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
#include <CGAL/Surface_mesh.h>

#include <CGAL/Polygon_mesh_processing/triangulate_faces.h>

#include <boost/foreach.hpp>

#include <fstream>

typedef CGAL::Exact_predicates_inexact_constructions_kernel Kernel;
typedef Kernel::Point_3                    Point;
typedef CGAL::Surface_mesh<Point>          Surface_mesh;

int main(int argc, char* argv[])
{
  const char* filename = (argc > 1) ? argv[1] : "data/P.off";
  const char* outfilename = (argc > 2) ? argv[2] : "P_tri.off";
  std::ifstream input(filename);

  Surface_mesh mesh;
  if (!input || !(input >> mesh) || mesh.is_empty())
  {
    std::cerr << "Not a valid off file." << std::endl;
    return 1;
  }

  CGAL::Polygon_mesh_processing::triangulate_faces(mesh);

  // Confirm that all faces are triangles.
  BOOST_FOREACH(boost::graph_traits<Surface_mesh>::face_descriptor fit, faces(mesh))
    if (next(next(halfedge(fit, mesh), mesh), mesh)
        !=   prev(halfedge(fit, mesh), mesh))
      std::cerr << "Error: non-triangular face left in mesh." << std::endl;

  std::ofstream cube_off(outfilename);
  cube_off << mesh;

  return 0;
}


// ============================================================================
//
// Copyright (c) 2001-2006 Max-Planck-Institut Saarbruecken (Germany).
// All rights reserved.
//
// This file is part of EXACUS (http://www.mpi-inf.mpg.de/projects/EXACUS/).
// 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.
//
// Licensees holding a valid commercial license may use this file in
// accordance with the commercial license agreement provided with the software.
//
// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
//
// ----------------------------------------------------------------------------
//
// Library       : NiX
// File          : NiX/poly2ntl.C
// NiX_release   : $Name:  $
// Revision      : $Revision: 1.1 $
// Revision_date : $Date: 2009-06-30 13:14:58 $
//
// Author(s)     : ... ?
//
// ============================================================================

/*! \file NiX/poly2ntl.C
 *
 *  Conversion of polynomials to NTL format & back
 */

#include <CGAL/config.h>

#define NDEBUG 1
// #define CGAL_POLYNOMIAL_USE_NTL_MUL

// #define CGAL_ACK_BENCHMARK_RES

#ifdef CGAL_POLYNOMIAL_USE_NTL_MUL

//#include <CGAL/leda_integer.h>
#include <CGAL/CORE/BigInt.h>
#include <NTL/ZZX.h>

#include <CGAL/Arithmetic_kernel.h>
#include <CGAL/Polynomial.h>
#include <CGAL/Timer.h>

#define POLY_NTL_MIN_DEGREE 10 // minimal degree of polynomials to multiply
                                // using NTL

#endif // CGAL_POLYNOMIAL_USE_NTL_MUL

namespace CGAL {

#ifdef CGAL_POLYNOMIAL_USE_NTL_MUL

// namespace internal {
// int *primes = CGAL::CGALi::primes;
// }

struct NTL_bigint_rep {
    long alloc;
    long size;
    mp_limb_t data;
};

#endif

#ifdef CGAL_POLYNOMIAL_USE_NTL_MUL

namespace {

// typedef leda_integer CCC_int;
typedef CORE::BigInt Integer;

typedef Polynomial< Integer > Poly_1;

void poly2ntl(const Poly_1& p, NTL::ZZX& q) {

//     if(p.is_zero()) { // TODO should be handled earlier
//         //special handling
//         //a is zero if a.rep.length() == 0;
//         q = NTL::ZZX();
//     }
    q.rep.SetLength(p.degree() + 1);

    int i;
    Poly_1::const_iterator pit;
    for(i = 0, pit = p.begin(); pit != p.end(); pit++, i++) {

        NTL::ZZ& zz = q.rep[i];
        mpz_srcptr tmp = pit->get_mp();
        int sz = tmp->_mp_size;
        if(sz == 0)
            continue;
        if(sz < 0)
            sz = -sz;

        zz.SetSize(sz);
        NTL_bigint_rep *rep = (NTL_bigint_rep *)zz.rep;
        rep->size = tmp->_mp_size;
        // copy limbs directly
        memcpy(&rep->data, tmp->_mp_d, sz*sizeof(mp_limb_t));
         //std::cerr << "pit = " << *pit << "; and " <<
            //zz << "\n\n";
    }
}

} // anonymous namespace

#endif

#ifdef CGAL_ACK_BENCHMARK_RES
#warning timing resultants
extern Timer res_tm;
#endif

#ifdef CGAL_POLYNOMIAL_USE_NTL_MUL

#warning using NTL

template <>
Poly_1& Poly_1::operator *= (const Poly_1& p2) {

    Poly_1 p1 = *this;

    if(p1.is_zero() || p2.is_zero()) {
//         std::cout << "mul NTL: zero poly\n";
        return (*this) = Poly_1(Integer(0));
    }
//  TODO: use this if poly size is small..
    if(p1.degree() <= POLY_NTL_MIN_DEGREE &&
        p2.degree() <= POLY_NTL_MIN_DEGREE) {

        internal::Creation_tag TAG;
        Poly_1 p(TAG, p1.degree() + p2.degree() + 1);
        for (int i=0; i <= p1.degree(); ++i)
          for (int j=0; j <= p2.degree(); ++j)
            p.coeff(i+j) += (p1[i]*p2[j]);
        p.reduce();
//         std::cout << "mul usual: " << p << "\n\n";;
        return (*this) = p ;
    }
    NTL::ZZX q, q2;
    poly2ntl(p1, q);
    poly2ntl(p2, q2);

    q *= q2;

    int d = NTL::deg(q);
//     if(d == -1) {
//         std::cout << "Fatal: zero poly\n";
//         throw -1;
//     }

    this->copy_on_write(); // ??
    this->coeffs().resize(d + 1);

    // TODO: use reduce ??
    mpz_t tmp;
     mpz_init(tmp);
    for(int i = 0; i <= d; i++) {

        const NTL::ZZ& zz = q.rep[i];
        if(NTL::IsZero(zz)) {
            coeff(i) = Integer(0);
            continue;
        }

        NTL_bigint_rep *rep = (NTL_bigint_rep *)zz.rep;
        int sz = rep->size;
        if(sz < 0)
            sz = -sz;

        mpz_realloc2(tmp, sz * GMP_NUMB_BITS);
        tmp->_mp_size = rep->size;
        memcpy(tmp->_mp_d, &rep->data, sz*sizeof(mp_limb_t));

//         coeff(i).makeCopy();
//         mpz_ptr mpd = coeff(i).get_mp();
//         mpd->_mp_size = rep->size;
//         mpz_realloc2(mpd, sz * GMP_NUMB_BITS);
//         memcpy(mpd->_mp_d, &rep->data, sz*sizeof(mp_limb_t));
        coeff(i) = Integer(tmp);

//          mpz_init_set(coeff(i).get_mp(), tmp);
    }
    mpz_clear(tmp);

//         CGALi::Creation_tag TAG;
//         Poly_1 p(TAG, p1.degree() + p2.degree() + 1);
//         for (int i=0; i <= p1.degree(); ++i)
//           for (int j=0; j <= p2.degree(); ++j)
//             p.coeff(i+j) += (p1[i]*p2[j]);
//         //p.reduce();
// //         std::cout << "mul usual: " << p << "\n\n";;
//
//     if(*this != p) {
//
//         std::cout << "------------ p1: " << p1 << "---------- p2: " <<
//                 p2 << "\n";
//         std::cout << "FATAL: " << *this << "----------- and " << p << "\n";
//
//     }

//     Poly_1 pp(vec.begin(), vec.end());
    //p.reduce();
//       std::cout << "mul NTL: " << *this << "\n";
    return (*this);// = pp;
}

template <>
Integer prs_resultant_ufd< Integer >(Poly_1 A, Poly_1 B) {

#ifdef CGAL_ACK_BENCHMARK_RES
// std::cout << "start res " << "\n";
res_tm.start();
#endif

    // implemented using the subresultant algorithm for resultant computation
    // see [Cohen, 1993], algorithm 3.3.7

    typedef Integer NT;

    if (A.is_zero() || B.is_zero()) return NT(0);

    NTL::ZZX q1, q2;
    poly2ntl(A, q1);
    poly2ntl(B, q2);

    NTL::ZZ zz;
    NTL::resultant(zz, q1, q2);

    if(NTL::IsZero(zz))
        return Integer(0);

    Integer res;
    NTL_bigint_rep *rep = (NTL_bigint_rep *)zz.rep;
    int sz = rep->size;
    if(sz < 0)
        sz = -sz;

    mpz_ptr tmp = res.get_mp();
    mpz_realloc2(tmp, sz * GMP_NUMB_BITS);
    tmp->_mp_size = rep->size;
    memcpy(tmp->_mp_d, &rep->data, sz*sizeof(mp_limb_t));

//     std::cout << "stop res " << "\n";
#ifdef CGAL_ACK_BENCHMARK_RES
// std::cout << "stop res " << "\n";
res_tm.stop();
#endif

    return res;
}
#else // CGAL_POLYNOMIAL_USE_NTL_MUL

#if 0
template <>
Integer prs_resultant_ufd< Integer >(Poly_1 A, Poly_1 B) {

#ifdef CGAL_ACK_BENCHMARK_RES
res_tm.start();
#endif

    // implemented using the subresultant algorithm for resultant computation
    // see [Cohen, 1993], algorithm 3.3.7

    typedef Integer NT;

    if (A.is_zero() || B.is_zero()) return NT(0);

    int signflip;
    if (A.degree() <123 B.degree()) {
        Polynomial<NT> T = A; A = B; B = T;
        signflip = (A.degree() & B.degree() & 1);
    } else {
        signflip = 0;
    }

    NT a = A.content(), b = B.content();
    NT g(1), h(1), t = CGAL::ipower(a, B.degree()) * CGAL::ipower(b, A.degree());
    Polynomial<NT> Q, R; NT d;
    int delta;

    A /= a; B /= b;
    do {
        signflip ^= (A.degree() & B.degree() & 1);
        Polynomial<NT>::pseudo_division(A, B, Q, R, d);
        delta = A.degree() - B.degree();
        typedef CGAL::Algebraic_structure_traits<NT>::Is_exact
          Is_exact;

        A = B;
        B = R / (g * CGAL::ipower(h, delta));
        g = A.lcoeff();
        // h = h^(1-delta) * g^delta
        CGALi::hgdelta_update(h, g, delta);
    } while (B.degree() > 0);
    // h = h^(1-deg(A)) * lcoeff(B)^deg(A)
    delta = A.degree();
    g = B.lcoeff();
    CGALi::hgdelta_update(h, g, delta);
    h = signflip ? -(t*h) : t*h;
    Algebraic_structure_traits<NT>::Simplify simplify;
    simplify(h);

   return h;
}
#endif

#endif // CGAL_POLYNOMIAL_USE_NTL_MUL

} // namespace CGAL


//==================================================================================================
/*!
  @file

  @copyright 2016 NumScale SAS

  Distributed under the Boost Software License, Version 1.0.
  (See accompanying file LICENSE.md or copy at http://boost.org/LICENSE_1_0.txt)
*/
//==================================================================================================
#ifndef BOOST_SIMD_FUNCTION_IFLOOR_HPP_INCLUDED
#define BOOST_SIMD_FUNCTION_IFLOOR_HPP_INCLUDED

#if defined(DOXYGEN_ONLY)
namespace boost { namespace simd
{

 /*!

    @ingroup group-arithmetic
    Function object implementing ifloor capabilities

    Computes the integer conversion of the floor of its parameter.

    @par semantic:
    For any given value @c x of type @c T:

    @code
    as_integer_t<T> r = ifloor(x);
    @endcode

    is equivalent to:

    @code
    as_integer_t<T> r = saturated_(toint)(floor(x));
    @endcode

    @par Note:
    This operation is properly saturated

  **/
  as_integer_T<Value> ifloor(Value const & v0);
} }
#endif

#include <boost/simd/function/scalar/ifloor.hpp>
#include <boost/simd/function/simd/ifloor.hpp>

#endif


// Software License for MTL
//
// Copyright (c) 2007 The Trustees of Indiana University.
//               2008 Dresden University of Technology and the Trustees of Indiana University.
//               2010 SimuNova UG (haftungsbeschränkt), www.simunova.com.
// All rights reserved.
// Authors: Peter Gottschling and Andrew Lumsdaine
//
// This file is part of the Matrix Template Library
//
// See also license.mtl.txt in the distribution.

#ifndef MTL_TWO_NORM_INCLUDE
#define MTL_TWO_NORM_INCLUDE

#include <iostream>
#include <cmath>

#include <boost/numeric/mtl/concept/collection.hpp>
#include <boost/numeric/mtl/concept/magnitude.hpp>
#include <boost/numeric/mtl/utility/tag.hpp>
#include <boost/numeric/mtl/utility/category.hpp>
#include <boost/numeric/mtl/vector/lazy_reduction.hpp>
#include <boost/numeric/mtl/vector/reduction.hpp>
#include <boost/numeric/mtl/vector/reduction_functors.hpp>
#include <boost/numeric/mtl/interface/vpt.hpp>

namespace mtl {

    namespace vec {

	template <unsigned long Unroll, typename Value>
	typename RealMagnitude<typename Collection<Value>::value_type>::type
	inline two_norm(const Value& value)
	{
	    using std::sqrt;
	    vampir_trace<2039> tracer;
	    typedef typename RealMagnitude<typename Collection<Value>::value_type>::type result_type;
	    return sqrt(reduction<Unroll, two_norm_functor, result_type>::apply(value));
	}

	/*! Two-norm for vectors: two_norm(x) \f$\rightarrow |x|_2\f$.
	    \retval The magnitude type of the respective value type, see Magnitude.
	    The norms are defined as \f$|v|_2=\sqrt{\sum_i |v_i|^2}\f$.

	    Vector norms are unrolled 8-fold by default.
	    An n-fold unrolling can be generated with two_norm<n>(x).
	    The maximum for n is 8 (it might be increased later).
	**/
	template <typename Value>
	typename RealMagnitude<typename Collection<Value>::value_type>::type
	inline two_norm(const Value& value)
	{
	    return two_norm<4>(value);
	}

	template <typename Vector>
	lazy_reduction<Vector, two_norm_functor> inline lazy_two_norm(const Vector& v)
	{  return lazy_reduction<Vector, two_norm_functor>(v); 	}

    } // namespace vector

    // two_norm for matrices not implemented (would need enable_if like one_norm)

    using vec::two_norm;
    using vec::lazy_two_norm;

} // namespace mtl

#endif // MTL_TWO_NORM_INCLUDE


//          Copyright Rein Halbersma 2010-2021.
// Distributed under the Boost Software License, Version 1.0.
//    (See accompanying file LICENSE_1_0.txt or copy at
//          http://www.boost.org/LICENSE_1_0.txt)

#include <core/board/group.hpp>         // is_idempotent, is_identity, is_involution
#include <dctl/core/board/angle.hpp>    // _deg, inverse, rotate, mirror
#include <boost/range/irange.hpp>       // irange
#include <boost/test/unit_test.hpp>     // BOOST_AUTO_TEST_SUITE, BOOST_AUTO_TEST_SUITE_END, BOOST_AUTO_TEST_CASE, BOOST_CHECK
#include <algorithm>                    // all_of

using namespace dctl::core;
using namespace literals;

BOOST_AUTO_TEST_SUITE(AngleTransform)

auto const angles = boost::irange(-2 * 360, 2 * 360 + 1);

BOOST_AUTO_TEST_CASE(AngleConstructorIsIdempotentOnIntegers)
{
        BOOST_CHECK(
                std::all_of(angles.begin(), angles.end(), [](auto i) {
                        return group::is_idempotent{}([](auto j) { return j; }, angle{i});
                })
        );
}

BOOST_AUTO_TEST_CASE(RotateZeroDegIsIdentityOnAllAngles)
{
        BOOST_CHECK(
                std::all_of(angles.begin(), angles.end(), [](auto i) {
                        return group::is_identity{}([](auto j) { return rotate(j, 0_deg); }, angle{i});
                })
        );
}

BOOST_AUTO_TEST_CASE(ReverseIsInvolutionOnAllAngles)
{
        BOOST_CHECK(
                std::all_of(angles.begin(), angles.end(), [](auto i) {
                        return group::is_involution{}([](auto j) { return reverse(j); }, angle{i});
                })
        );
}

BOOST_AUTO_TEST_CASE(InverseIsInvolutionOnAllAngles)
{
        BOOST_CHECK(
                std::all_of(angles.begin(), angles.end(), [](auto i) {
                        return group::is_involution{}([](auto j) { return inverse(j); }, angle{i});
                })
        );
}

BOOST_AUTO_TEST_CASE(MirrorIsInvolutionOnAllanglePairs)
{
        BOOST_CHECK(
                std::all_of(angles.begin(), angles.end(), [](auto i) {
                        return std::all_of(angles.begin(), angles.end(), [=](auto j) {
                                return group::is_involution{}([=](auto k) { return mirror(k, angle{j}); }, angle{i});
                        });
                })
        );
}

BOOST_AUTO_TEST_SUITE_END()


/**
 * @file boost_backport.hpp
 * @author Yannis Mentekidis
 *
 * Centralized control of what boost files to include. We have backported the
 * following boost functionality here:
 *
 *  * trigamma and polygamma function evaluation (added in boost 1.58.0)
 *
 * For versions 1.56, 1.57 we include the backported polygamma and trigamma
 * functions.  Anything newer, we include from Boost.
 */
#ifndef MLPACK_CORE_BOOST_BACKPORT_MATH_HPP
#define MLPACK_CORE_BOOST_BACKPORT_MATH_HPP

#include <boost/version.hpp>

#if BOOST_VERSION < 105800
  // Backported trigamma and polygamma.
  #include "mlpack/core/boost_backport/trigamma.hpp"
  #include "mlpack/core/boost_backport/polygamma.hpp"
#else
  // Boost's version.
  #include <boost/math/special_functions/trigamma.hpp>
  #include <boost/math/special_functions/polygamma.hpp>
#endif

#endif // MLPACK_CORE_BOOST_BACKPORT_HPP


// Software License for MTL
//
// Copyright (c) 2007 The Trustees of Indiana University.
//               2008 Dresden University of Technology and the Trustees of Indiana University.
//               2010 SimuNova UG (haftungsbeschränkt), www.simunova.com.
// All rights reserved.
// Authors: Peter Gottschling and Andrew Lumsdaine
//
// This file is part of the Matrix Template Library
//
// See also license.mtl.txt in the distribution.

#ifndef MTL_ADJOINT_INCLUDE
#define MTL_ADJOINT_INCLUDE

#include <boost/numeric/mtl/operation/hermitian.hpp>

namespace mtl { namespace mat {

namespace traits {

    template <typename LinOp>
    struct adjoint
    {
	typedef typename mtl::mat::detail::hermitian<LinOp>::result_type  type;
	type operator()(const LinOp& A)
	{
	    return hermitian(A);
	}
    };
}

/// Adjoint linear operator, typically Hermitian transposed
template <typename LinOp>
typename traits::adjoint<LinOp>::type
inline adjoint(const LinOp& A)
{
    return traits::adjoint<LinOp>()(A);
}

}} // namespace mtl::matrix

#endif // MTL_ADJOINT_INCLUDE


/*
@copyright Louis Dionne 2014
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE.md or copy at http://boost.org/LICENSE_1_0.txt)
 */

#include <boost/hana/range.hpp>

#include <boost/hana/detail/assert.hpp>
#include <boost/hana/integral.hpp>
using namespace boost::hana;

void test_drop() {
    BOOST_HANA_CONSTANT_ASSERT(drop(int_<0>, range(int_<0>, int_<0>)) == range(int_<0>, int_<0>));
    BOOST_HANA_CONSTANT_ASSERT(drop(int_<1>, range(int_<0>, int_<0>)) == range(int_<0>, int_<0>));
    BOOST_HANA_CONSTANT_ASSERT(drop(int_<2>, range(int_<0>, int_<0>)) == range(int_<0>, int_<0>));

    BOOST_HANA_CONSTANT_ASSERT(drop(int_<0>, range(int_<0>, int_<1>)) == range(int_<0>, int_<1>));
    BOOST_HANA_CONSTANT_ASSERT(drop(int_<1>, range(int_<0>, int_<1>)) == range(int_<1>, int_<1>));
    BOOST_HANA_CONSTANT_ASSERT(drop(int_<2>, range(int_<0>, int_<1>)) == range(int_<1>, int_<1>));

    BOOST_HANA_CONSTANT_ASSERT(drop(int_<0>, range(int_<0>, int_<2>)) == range(int_<0>, int_<2>));
    BOOST_HANA_CONSTANT_ASSERT(drop(int_<1>, range(int_<0>, int_<2>)) == range(int_<1>, int_<2>));
    BOOST_HANA_CONSTANT_ASSERT(drop(int_<2>, range(int_<0>, int_<2>)) == range(int_<2>, int_<2>));

    BOOST_HANA_CONSTANT_ASSERT(drop(int_<0>, range(int_<0>, int_<3>)) == range(int_<0>, int_<3>));
    BOOST_HANA_CONSTANT_ASSERT(drop(int_<1>, range(int_<0>, int_<3>)) == range(int_<1>, int_<3>));
    BOOST_HANA_CONSTANT_ASSERT(drop(int_<2>, range(int_<0>, int_<3>)) == range(int_<2>, int_<3>));
    BOOST_HANA_CONSTANT_ASSERT(drop(int_<3>, range(int_<0>, int_<3>)) == range(int_<3>, int_<3>));

    BOOST_HANA_CONSTANT_ASSERT(drop(int_<10>, range(int_<20>, int_<50>)) == range(int_<30>, int_<50>));
}

int main() {
    BOOST_HANA_CONSTANT_ASSERT(is_empty(range(int_<0>, int_<0>)));
    BOOST_HANA_CONSTANT_ASSERT(!is_empty(range(int_<0>, int_<1>)));
    BOOST_HANA_CONSTANT_ASSERT(!is_empty(range(int_<0>, int_<2>)));

    BOOST_HANA_CONSTANT_ASSERT(head(range(int_<0>, int_<1>)) == int_<0>);
    BOOST_HANA_CONSTANT_ASSERT(head(range(int_<0>, int_<2>)) == int_<0>);
    BOOST_HANA_CONSTANT_ASSERT(head(range(int_<2>, int_<5>)) == int_<2>);
    BOOST_HANA_CONSTANT_ASSERT(head(range(int_<5>, int_<6>)) == int_<5>);

    BOOST_HANA_CONSTANT_ASSERT(tail(range(int_<0>, int_<1>)) == range(int_<1>, int_<1>));
    BOOST_HANA_CONSTANT_ASSERT(tail(range(int_<0>, int_<2>)) == range(int_<1>, int_<2>));
    BOOST_HANA_CONSTANT_ASSERT(tail(range(int_<0>, int_<3>)) == range(int_<1>, int_<3>));
    BOOST_HANA_CONSTANT_ASSERT(tail(range(int_<4>, int_<7>)) == range(int_<5>, int_<7>));

    BOOST_HANA_CONSTANT_ASSERT(at(int_<0>, range(int_<0>, int_<1>)) == int_<0>);
    BOOST_HANA_CONSTANT_ASSERT(at(int_<0>, range(int_<0>, int_<2>)) == int_<0>);
    BOOST_HANA_CONSTANT_ASSERT(at(int_<1>, range(int_<0>, int_<2>)) == int_<1>);
    BOOST_HANA_CONSTANT_ASSERT(at(int_<46>, range(int_<4>, int_<90>)) == int_<50>);

    BOOST_HANA_CONSTANT_ASSERT(last(range(int_<0>, int_<1>)) == int_<0>);
    BOOST_HANA_CONSTANT_ASSERT(last(range(int_<0>, int_<2>)) == int_<1>);
    BOOST_HANA_CONSTANT_ASSERT(last(range(int_<0>, int_<3>)) == int_<2>);
    BOOST_HANA_CONSTANT_ASSERT(last(range(int_<3>, int_<6>)) == int_<5>);

    test_drop();
}