text: /* Copyright (c) 2000, 2010 Oracle and/or its affiliates. All rights reserved.
     Copyright (C) 2011 Monty Program Ab.
  
     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; version 2 of the License.
  
     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, write to the Free Software
     Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1335 USA */
  
  
  #include "mariadb.h"
  #include <my_sys.h>
  #include <m_string.h>
  
  #ifdef HAVE_SPATIAL
  
  #include "gcalc_slicescan.h"
  
  
  #define PH_DATA_OFFSET 8
  #define coord_to_float(d) ((double) d)
  #define coord_eq(a, b) (a == b)
  
  typedef int (*sc_compare_func)(const void*, const void*);
  
  #define LS_LIST_ITEM Gcalc_dyn_list::Item
  #define LS_COMPARE_FUNC_DECL sc_compare_func compare,
  #define LS_COMPARE_FUNC_CALL(list_el1, list_el2) (*compare)(list_el1, list_el2)
  #define LS_NEXT(A) (A)->next
  #define LS_SET_NEXT(A,val) (A)->next= val
  #define LS_P_NEXT(A) &(A)->next
  #define LS_NAME sort_list
  #define LS_SCOPE static
  #define LS_STRUCT_NAME sort_list_stack_struct
  #include "plistsort.c"
  
  
  #define GCALC_COORD_MINUS     0x80000000
  #define FIRST_DIGIT(d) ((d) & 0x7FFFFFFF)
  #define GCALC_SIGN(d)  ((d) & 0x80000000)
  
  static Gcalc_scan_iterator::point *eq_sp(const Gcalc_heap::Info *pi)
  {
    GCALC_DBUG_ASSERT(pi->type == Gcalc_heap::nt_eq_node);
    return (Gcalc_scan_iterator::point *) pi->node.eq.data;
  }
  
  
  static Gcalc_scan_iterator::intersection_info *i_data(const Gcalc_heap::Info *pi)
  {
    GCALC_DBUG_ASSERT(pi->type == Gcalc_heap::nt_intersection);
    return (Gcalc_scan_iterator::intersection_info *) pi->node.intersection.data;
  }
  
  
  #ifndef GCALC_DBUG_OFF
  
  int gcalc_step_counter= 0;
  
  void GCALC_DBUG_CHECK_COUNTER()
  {
    if (++gcalc_step_counter == 0)
      GCALC_DBUG_PRINT(("step_counter_0"));
    else
      GCALC_DBUG_PRINT(("%d step_counter", gcalc_step_counter));
  }
  
  
  const char *gcalc_ev_name(int ev)
  {
    switch (ev)
    {
      case scev_none:
        return "n";
      case scev_thread:
        return "t";
      case scev_two_threads:
        return "tt";
      case scev_end:
        return "e";
      case scev_two_ends:
        return "ee";
      case scev_intersection:
        return "i";
      case scev_point:
        return "p";
      case scev_single_point:
        return "sp";
      default:;
    };
    GCALC_DBUG_ASSERT(0);
    return "unk";
  }
  
  
  static int gcalc_pi_str(char *str, const Gcalc_heap::Info *pi, const char *postfix)
  {
    return sprintf(str, "%s %d %d | %s %d %d%s",
                       GCALC_SIGN(pi->node.shape.ix[0]) ? "-":"", FIRST_DIGIT(pi->node.shape.ix[0]),pi->node.shape.ix[1],
                       GCALC_SIGN(pi->node.shape.iy[0]) ? "-":"", FIRST_DIGIT(pi->node.shape.iy[0]),pi->node.shape.iy[1],
                       postfix);
  
  }
  
  
  static void GCALC_DBUG_PRINT_PI(const Gcalc_heap::Info *pi)
  {
    char buf[128];
    int n_buf;
    if (pi->type == Gcalc_heap::nt_intersection)
    {
      const Gcalc_scan_iterator::intersection_info *ic= i_data(pi);
  
      GCALC_DBUG_PRINT(("intersection point %d %d",
                        ic->edge_a->thread, ic->edge_b->thread));
      return;
    }
    if (pi->type == Gcalc_heap::nt_eq_node)
    {
      const Gcalc_scan_iterator::point *e= eq_sp(pi);
      GCALC_DBUG_PRINT(("eq point %d", e->thread));
      return;
    }
    n_buf= gcalc_pi_str(buf, pi, "");
    buf[n_buf]= 0;
    GCALC_DBUG_PRINT(("%s", buf));
  }
  
  
  static void GCALC_DBUG_PRINT_SLICE(const char *header,
                                     const Gcalc_scan_iterator::point *slice)
  {
    size_t nbuf;
    char buf[1024];
    nbuf= strlen(header);
    strcpy(buf, header);
    for (; slice; slice= slice->get_next())
    {
      size_t lnbuf= nbuf;
      lnbuf+= sprintf(buf + lnbuf, "%d\t", slice->thread);
      lnbuf+= sprintf(buf + lnbuf, "%s\t", gcalc_ev_name(slice->event));
  
      lnbuf+= gcalc_pi_str(buf + lnbuf, slice->pi, "\t");
      if (slice->is_bottom())
        lnbuf+= sprintf(buf+lnbuf, "bt\t");
      else
        lnbuf+= gcalc_pi_str(buf+lnbuf, slice->next_pi, "\t");
      buf[lnbuf]= 0;
      GCALC_DBUG_PRINT(("%s", buf));
    }
  }
  
  
  #else
  #define GCALC_DBUG_CHECK_COUNTER()              do { } while(0)
  #define GCALC_DBUG_PRINT_PI(pi)                 do { } while(0)
  #define GCALC_DBUG_PRINT_SLICE(a, b)            do { } while(0)
  #define GCALC_DBUG_PRINT_INTERSECTIONS(a)       do { } while(0)
  #define GCALC_DBUG_PRINT_STATE(a)               do { } while(0)
  #endif /*GCALC_DBUG_OFF*/
  
  
  Gcalc_dyn_list::Gcalc_dyn_list(size_t blk_size, size_t sizeof_item):
    m_blk_size(blk_size - ALLOC_ROOT_MIN_BLOCK_SIZE),
    m_sizeof_item(ALIGN_SIZE(sizeof_item)),
    m_points_per_blk((uint)((m_blk_size - PH_DATA_OFFSET) / m_sizeof_item)),
    m_blk_hook(&m_first_blk),
    m_free(NULL),
    m_keep(NULL)
  {}
  
  
  Gcalc_dyn_list::Gcalc_dyn_list(const Gcalc_dyn_list &dl)
  {
    m_blk_size= dl.m_blk_size;
    m_sizeof_item= dl.m_sizeof_item;
    m_points_per_blk= dl.m_points_per_blk;
    m_blk_hook= &m_first_blk;
    m_free= NULL;
    m_keep= NULL;
  }
  
  
  void Gcalc_dyn_list::format_blk(void* block)
  {
    Item *pi_end, *cur_pi, *first_pi;
    GCALC_DBUG_ASSERT(m_free == NULL);
    first_pi= cur_pi= (Item *)(((char *)block) + PH_DATA_OFFSET);
    pi_end= ptr_add(first_pi, m_points_per_blk - 1);
    do {
      cur_pi= cur_pi->next= ptr_add(cur_pi, 1);
    } while (cur_pi<pi_end);
    cur_pi->next= m_free;
    m_free= first_pi;
  }
  
  
  Gcalc_dyn_list::Item *Gcalc_dyn_list::alloc_new_blk()
  {
    void *new_block= my_malloc(PSI_INSTRUMENT_ME, m_blk_size, MYF(MY_WME));
    if (!new_block)
      return NULL;
    *m_blk_hook= new_block;
    m_blk_hook= (void**)new_block;
    format_blk(new_block);
    return new_item();
  }
  
  
  static void free_blk_list(void *list)
  {
    void *next_blk;
    while (list)
    {
      next_blk= *((void **)list);
      my_free(list);
      list= next_blk;
    }
  }
  
  
  void Gcalc_dyn_list::cleanup()
  {
    *m_blk_hook= NULL;
    free_blk_list(m_first_blk);
    m_first_blk= NULL;
    m_blk_hook= &m_first_blk;
    m_free= NULL;
  }
  
  
  Gcalc_dyn_list::~Gcalc_dyn_list()
  {
    cleanup();
  }
  
  
  void Gcalc_dyn_list::reset()
  {
    *m_blk_hook= NULL;
    if (m_first_blk)
    {
      free_blk_list(*((void **)m_first_blk));
      m_blk_hook= (void**)m_first_blk;
      m_free= NULL;
      format_blk(m_first_blk);
    }
  }
  
  
  /* Internal coordinate operations implementations */
  
  void gcalc_set_zero(Gcalc_internal_coord *d, int d_len)
  {
    do
    {
      d[--d_len]= 0;
    } while (d_len); 
  }
  
  
  int gcalc_is_zero(const Gcalc_internal_coord *d, int d_len)
  {
    do
    {
      if (d[--d_len] != 0)
        return 0;
    } while (d_len); 
    return 1;
  }
  
  
  #ifdef GCALC_CHECK_WITH_FLOAT
  static double *gcalc_coord_extent= NULL;
  
  long double gcalc_get_double(const Gcalc_internal_coord *d, int d_len)
  {
    int n= 1;
    long double res= (long double) FIRST_DIGIT(d[0]);
    do
    {
      res*= (long double) GCALC_DIG_BASE;
      res+= (long double) d[n];
    } while(++n < d_len);
  
    n= 0;
    do
    {
      if ((n & 1) && gcalc_coord_extent)
        res/= *gcalc_coord_extent;
    } while(++n < d_len);
  
    if (GCALC_SIGN(d[0]))
      res*= -1.0;
    return res;
  }
  #endif /*GCALC_CHECK_WITH_FLOAT*/
  
  
  static void do_add(Gcalc_internal_coord *result, int result_len,
                     const Gcalc_internal_coord *a,
                     const Gcalc_internal_coord *b)
  {
    int n_digit= result_len-1;
    gcalc_digit_t carry= 0;
  
    do
    {
      if ((result[n_digit]=
            a[n_digit] + b[n_digit] + carry) >= GCALC_DIG_BASE)
      {
        carry= 1;
        result[n_digit]-= GCALC_DIG_BASE;
      }
      else
        carry= 0;
    } while (--n_digit);
  
    result[0]= (a[0] + FIRST_DIGIT(b[0]) + carry);
  
    GCALC_DBUG_ASSERT(FIRST_DIGIT(result[0]) < GCALC_DIG_BASE);
  }
  
  
  static void do_sub(Gcalc_internal_coord *result, int result_len,
                     const Gcalc_internal_coord *a,
                     const Gcalc_internal_coord *b)
  {
    int n_digit= result_len-1;
    gcalc_digit_t carry= 0;
    gcalc_digit_t cur_b, cur_a;
  
    do
    {
      cur_b= b[n_digit] + carry;
      cur_a= a[n_digit];
      if (cur_a < cur_b)
      {
        carry= 1;
        result[n_digit]= (GCALC_DIG_BASE - cur_b) + cur_a;
      }
      else
      {
        carry= 0;
        result[n_digit]= cur_a - cur_b;
      }
    } while (--n_digit);
  
  
    result[0]= a[0] - FIRST_DIGIT(b[0]) - carry;
  
    GCALC_DBUG_ASSERT(FIRST_DIGIT(a[0]) >= FIRST_DIGIT(b[0]) + carry);
    GCALC_DBUG_ASSERT(!gcalc_is_zero(result, result_len));
  }
  /*
  static void do_sub(Gcalc_internal_coord *result, int result_len,
                     const Gcalc_internal_coord *a,
                     const Gcalc_internal_coord *b)
  {
    int n_digit= result_len-1;
    gcalc_digit_t carry= 0;
  
    do
    {
      if ((result[n_digit]= a[n_digit] - b[n_digit] - carry) < 0)
      {
        carry= 1;
        result[n_digit]+= GCALC_DIG_BASE;
      }
      else
        carry= 0;
    } while (--n_digit);
  
  
    result[0]= a[0] - FIRST_DIGIT(b[0]) - carry;
  
    GCALC_DBUG_ASSERT(FIRST_DIGIT(a[0]) - FIRST_DIGIT(b[0]) - carry >= 0);
    GCALC_DBUG_ASSERT(!gcalc_is_zero(result, result_len));
  }
  */
  
  static int do_cmp(const Gcalc_internal_coord *a,
                    const Gcalc_internal_coord *b, int len)
  {
    int n_digit= 1;
  
    if ((FIRST_DIGIT(a[0]) != FIRST_DIGIT(b[0])))
      return FIRST_DIGIT(a[0]) > FIRST_DIGIT(b[0]) ? 1 : -1;
  
    do
    {
      if ((a[n_digit] != b[n_digit]))
        return a[n_digit] > b[n_digit] ? 1 : -1;
    } while (++n_digit < len);
  
    return 0;
  }
  
  
  #ifdef GCALC_CHECK_WITH_FLOAT
  static int de_weak_check(long double a, long double b, long double ex)
  {
    long double d= a - b;
    if (d < ex && d > -ex)
      return 1;
  
    d/= fabsl(a) + fabsl(b);
    if (d < ex && d > -ex)
      return 1;
    return 0;
  }
  
  static int de_check(long double a, long double b)
  {
    return de_weak_check(a, b, (long double) 1e-9);
  }
  #endif /*GCALC_CHECK_WITH_FLOAT*/
  
  
  void gcalc_mul_coord(Gcalc_internal_coord *result, int result_len,
                       const Gcalc_internal_coord *a, int a_len,
                       const Gcalc_internal_coord *b, int b_len)
  {
    GCALC_DBUG_ASSERT(result_len == a_len + b_len);
    GCALC_DBUG_ASSERT(a_len >= b_len);
    int n_a, n_b, n_res;
    gcalc_digit_t carry= 0;
  
    gcalc_set_zero(result, result_len);
  
    n_a= a_len - 1;
    do
    {
      gcalc_coord2 cur_a= n_a ? a[n_a] : FIRST_DIGIT(a[0]);
      n_b= b_len - 1;
      do
      {
        gcalc_coord2 cur_b= n_b ? b[n_b] : FIRST_DIGIT(b[0]);
        gcalc_coord2 mul= cur_a * cur_b + carry + result[n_a + n_b + 1];
        result[n_a + n_b + 1]= mul % GCALC_DIG_BASE;
        carry= (gcalc_digit_t) (mul / (gcalc_coord2) GCALC_DIG_BASE);
      } while (n_b--);
      if (carry)
      {
        for (n_res= n_a; (result[n_res]+= carry) >= GCALC_DIG_BASE;
             n_res--)
        {
          result[n_res]-= GCALC_DIG_BASE;
          carry= 1;
        }
        carry= 0;
      }
    } while (n_a--);
    if (!gcalc_is_zero(result, result_len))
      result[0]|= GCALC_SIGN(a[0] ^ b[0]);
  #ifdef GCALC_CHECK_WITH_FLOAT
    GCALC_DBUG_ASSERT(de_check(gcalc_get_double(a, a_len) *
                                 gcalc_get_double(b, b_len),
                         gcalc_get_double(result, result_len)));
  #endif /*GCALC_CHECK_WITH_FLOAT*/
  }
  
  
  inline void gcalc_mul_coord1(Gcalc_coord1 result,
                               const Gcalc_coord1 a, const Gcalc_coord1 b)
  {
    return gcalc_mul_coord(result, GCALC_COORD_BASE2,
                           a, GCALC_COORD_BASE, b, GCALC_COORD_BASE);
  }
  
  
  void gcalc_add_coord(Gcalc_internal_coord *result, int result_len,
                       const Gcalc_internal_coord *a,
                       const Gcalc_internal_coord *b)
  {
    if (GCALC_SIGN(a[0]) == GCALC_SIGN(b[0]))
      do_add(result, result_len, a, b);
    else
    {
      int cmp_res= do_cmp(a, b, result_len);
      if (cmp_res == 0)
        gcalc_set_zero(result, result_len);
      else if (cmp_res > 0)
        do_sub(result, result_len, a, b);
      else
        do_sub(result, result_len, b, a);
    }
  #ifdef GCALC_CHECK_WITH_FLOAT
    GCALC_DBUG_ASSERT(de_check(gcalc_get_double(a, result_len) +
                                 gcalc_get_double(b, result_len),
                         gcalc_get_double(result, result_len)));
  #endif /*GCALC_CHECK_WITH_FLOAT*/
  }
  
  
  void gcalc_sub_coord(Gcalc_internal_coord *result, int result_len,
                       const Gcalc_internal_coord *a,
                       const Gcalc_internal_coord *b)
  {
    if (GCALC_SIGN(a[0] ^ b[0]))
      do_add(result, result_len, a, b);
    else
    {
      int cmp_res= do_cmp(a, b, result_len);
      if (cmp_res == 0)
        gcalc_set_zero(result, result_len);
      else if (cmp_res > 0)
        do_sub(result, result_len, a, b);
      else
      {
        do_sub(result, result_len, b, a);
        result[0]^= GCALC_COORD_MINUS;
      }
    }
  #ifdef GCALC_CHECK_WITH_FLOAT
    GCALC_DBUG_ASSERT(de_check(gcalc_get_double(a, result_len) -
                                 gcalc_get_double(b, result_len),
                         gcalc_get_double(result, result_len)));
  #endif /*GCALC_CHECK_WITH_FLOAT*/
  }
  
  
  inline void gcalc_sub_coord1(Gcalc_coord1 result,
                               const Gcalc_coord1 a, const Gcalc_coord1 b)
  {
    return gcalc_sub_coord(result, GCALC_COORD_BASE, a, b);
  }
  
  
  int gcalc_cmp_coord(const Gcalc_internal_coord *a,
                      const Gcalc_internal_coord *b, int len)
  {
    int n_digit= 0;
    int result= 0;
  
    do
    {
      if (a[n_digit] == b[n_digit])
      {
        n_digit++;
        continue;
      }
      if (a[n_digit] > b[n_digit])
        result= GCALC_SIGN(a[0]) ? -1 : 1;
      else
        result= GCALC_SIGN(b[0]) ? 1 : -1;
      break;
  
    } while (n_digit < len);
  
  #ifdef GCALC_CHECK_WITH_FLOAT
    if (result == 0)
      GCALC_DBUG_ASSERT(de_check(gcalc_get_double(a, len),
                                   gcalc_get_double(b, len)));
    else if (result == 1)
      GCALC_DBUG_ASSERT(de_check(gcalc_get_double(a, len),
                                   gcalc_get_double(b, len)) ||
                  gcalc_get_double(a, len) > gcalc_get_double(b, len));
    else
      GCALC_DBUG_ASSERT(de_check(gcalc_get_double(a, len),
                                   gcalc_get_double(b, len)) ||
                  gcalc_get_double(a, len) < gcalc_get_double(b, len));
  #endif /*GCALC_CHECK_WITH_FLOAT*/
    return result;
  }
  
  
  #define gcalc_cmp_coord1(a, b) gcalc_cmp_coord(a, b, GCALC_COORD_BASE)
  
  int gcalc_set_double(Gcalc_internal_coord *c, double d, double ext)
  {
    int sign;
    double ds= d * ext;
    if ((sign= ds < 0))
      ds= -ds;
    c[0]= (gcalc_digit_t) (ds / (double) GCALC_DIG_BASE);
    c[1]= (gcalc_digit_t) (ds - ((double) c[0]) * (double) GCALC_DIG_BASE);
    if (c[1] >= GCALC_DIG_BASE)
    {
      c[1]= 0;
      c[0]++;
    }
    if (sign && (c[0] | c[1]))
      c[0]|= GCALC_COORD_MINUS;
  #ifdef GCALC_CHECK_WITH_FLOAT
    GCALC_DBUG_ASSERT(de_check(d, gcalc_get_double(c, 2)));
  #endif /*GCALC_CHECK_WITH_FLOAT*/
    return 0;
  } 
  
  
  typedef gcalc_digit_t Gcalc_coord4[GCALC_COORD_BASE*4];
  typedef gcalc_digit_t Gcalc_coord5[GCALC_COORD_BASE*5];
  
  
  void Gcalc_scan_iterator::intersection_info::do_calc_t()
  {
    Gcalc_coord1 a2_a1x, a2_a1y;
    Gcalc_coord2 x1y2, x2y1;
  
    gcalc_sub_coord1(a2_a1x, edge_b->pi->node.shape.ix, edge_a->pi->node.shape.ix);
    gcalc_sub_coord1(a2_a1y, edge_b->pi->node.shape.iy, edge_a->pi->node.shape.iy);
  
    GCALC_DBUG_ASSERT(!gcalc_is_zero(edge_a->dy, GCALC_COORD_BASE) ||
                      !gcalc_is_zero(edge_b->dy, GCALC_COORD_BASE));
  
    gcalc_mul_coord1(x1y2, edge_a->dx, edge_b->dy);
    gcalc_mul_coord1(x2y1, edge_a->dy, edge_b->dx);
    gcalc_sub_coord(t_b, GCALC_COORD_BASE2, x1y2, x2y1);
  
  
    gcalc_mul_coord1(x1y2, a2_a1x, edge_b->dy);
    gcalc_mul_coord1(x2y1, a2_a1y, edge_b->dx);
    gcalc_sub_coord(t_a, GCALC_COORD_BASE2, x1y2, x2y1);
    t_calculated= 1;
  }
  
  
  void Gcalc_scan_iterator::intersection_info::do_calc_y()
  {
    GCALC_DBUG_ASSERT(t_calculated);
  
    Gcalc_coord3 a_tb, b_ta;
  
    gcalc_mul_coord(a_tb, GCALC_COORD_BASE3,
                    t_b, GCALC_COORD_BASE2, edge_a->pi->node.shape.iy, GCALC_COORD_BASE);
    gcalc_mul_coord(b_ta, GCALC_COORD_BASE3,
                    t_a, GCALC_COORD_BASE2, edge_a->dy, GCALC_COORD_BASE);
  
    gcalc_add_coord(y_exp, GCALC_COORD_BASE3, a_tb, b_ta);
    y_calculated= 1;
  }
  
  
  void Gcalc_scan_iterator::intersection_info::do_calc_x()
  {
    GCALC_DBUG_ASSERT(t_calculated);
  
    Gcalc_coord3 a_tb, b_ta;
  
    gcalc_mul_coord(a_tb, GCALC_COORD_BASE3,
                    t_b, GCALC_COORD_BASE2, edge_a->pi->node.shape.ix, GCALC_COORD_BASE);
    gcalc_mul_coord(b_ta, GCALC_COORD_BASE3,
                    t_a, GCALC_COORD_BASE2, edge_a->dx, GCALC_COORD_BASE);
  
    gcalc_add_coord(x_exp, GCALC_COORD_BASE3, a_tb, b_ta);
    x_calculated= 1;
  }
  
  
  static int cmp_node_isc(const Gcalc_heap::Info *node,
                          const Gcalc_heap::Info *isc)
  {
    GCALC_DBUG_ASSERT(node->type == Gcalc_heap::nt_shape_node);
    Gcalc_scan_iterator::intersection_info *inf= i_data(isc);
    Gcalc_coord3 exp;
    int result;
  
    inf->calc_t();
    inf->calc_y_exp();
  
    gcalc_mul_coord(exp, GCALC_COORD_BASE3,
                    inf->t_b, GCALC_COORD_BASE2, node->node.shape.iy, GCALC_COORD_BASE);
  
    result= gcalc_cmp_coord(exp, inf->y_exp, GCALC_COORD_BASE3);
  #ifdef GCALC_CHECK_WITH_FLOAT
    long double int_x, int_y;
    isc->calc_xy_ld(&int_x, &int_y);
    if (result < 0)
    {
      if (!de_check(int_y, node->node.shape.y) && node->node.shape.y > int_y)
        GCALC_DBUG_PRINT(("floatcheck cmp_nod_iscy %g < %LG", node->node.shape.y, int_y));
    }
    else if (result > 0)
    {
      if (!de_check(int_y, node->node.shape.y) && node->node.shape.y < int_y)
        GCALC_DBUG_PRINT(("floatcheck cmp_nod_iscy %g > %LG", node->node.shape.y, int_y));
    }
    else
    {
      if (!de_check(int_y, node->node.shape.y))
        GCALC_DBUG_PRINT(("floatcheck cmp_nod_iscy %g == %LG", node->node.shape.y, int_y));
    }
  #endif /*GCALC_CHECK_WITH_FLOAT*/
    if (result)
      goto exit;
  
  
    inf->calc_x_exp();
    gcalc_mul_coord(exp, GCALC_COORD_BASE3,
                    inf->t_b, GCALC_COORD_BASE2, node->node.shape.ix, GCALC_COORD_BASE);
  
    result= gcalc_cmp_coord(exp, inf->x_exp, GCALC_COORD_BASE3);
  #ifdef GCALC_CHECK_WITH_FLOAT
    if (result < 0)
    {
      if (!de_check(int_x, node->node.shape.x) && node->node.shape.x > int_x)
        GCALC_DBUG_PRINT(("floatcheck cmp_nod_iscx failed %g < %LG",
                           node->node.shape.x, int_x));
    }
    else if (result > 0)
    {
      if (!de_check(int_x, node->node.shape.x) && node->node.shape.x < int_x)
        GCALC_DBUG_PRINT(("floatcheck cmp_nod_iscx failed %g > %LG",
                          node->node.shape.x, int_x));
    }
    else
    {
      if (!de_check(int_x, node->node.shape.x))
        GCALC_DBUG_PRINT(("floatcheck cmp_nod_iscx failed %g == %LG",
                          node->node.shape.x, int_x));
    }
  #endif /*GCALC_CHECK_WITH_FLOAT*/
  exit:
    return result;
  }
  
  
  static int cmp_intersections(const Gcalc_heap::Info *i1,
                               const Gcalc_heap::Info *i2)
  {
    Gcalc_scan_iterator::intersection_info *inf1= i_data(i1);
    Gcalc_scan_iterator::intersection_info *inf2= i_data(i2);
    Gcalc_coord5 exp_a, exp_b;
    int result;
  
    inf1->calc_t();
    inf2->calc_t();
  
    inf1->calc_y_exp();
    inf2->calc_y_exp();
  
    gcalc_mul_coord(exp_a, GCALC_COORD_BASE5,
                    inf1->y_exp, GCALC_COORD_BASE3, inf2->t_b, GCALC_COORD_BASE2);
    gcalc_mul_coord(exp_b, GCALC_COORD_BASE5,
                    inf2->y_exp, GCALC_COORD_BASE3, inf1->t_b, GCALC_COORD_BASE2);
  
    result= gcalc_cmp_coord(exp_a, exp_b, GCALC_COORD_BASE5);
  #ifdef GCALC_CHECK_WITH_FLOAT
    long double x1, y1, x2, y2;
    i1->calc_xy_ld(&x1, &y1);
    i2->calc_xy_ld(&x2, &y2);
  
    if (result < 0)
    {
      if (!de_check(y1, y2) && y2 > y1)
        GCALC_DBUG_PRINT(("floatcheck cmp_intersections_y failed %LG < %LG",
                          y2, y1));
    }
    else if (result > 0)
    {
      if (!de_check(y1, y2) && y2 < y1)
        GCALC_DBUG_PRINT(("floatcheck cmp_intersections_y failed %LG > %LG",
                          y2, y1));
    }
    else
    {
      if (!de_check(y1, y2))
        GCALC_DBUG_PRINT(("floatcheck cmp_intersections_y failed %LG == %LG",
                          y2, y1));
    }
  #endif /*GCALC_CHECK_WITH_FLOAT*/
  
    if (result != 0)
      return result;
  
  
    inf1->calc_x_exp();
    inf2->calc_x_exp();
    gcalc_mul_coord(exp_a, GCALC_COORD_BASE5,
                    inf1->x_exp, GCALC_COORD_BASE3, inf2->t_b, GCALC_COORD_BASE2);
    gcalc_mul_coord(exp_b, GCALC_COORD_BASE5,
                    inf2->x_exp, GCALC_COORD_BASE3, inf1->t_b, GCALC_COORD_BASE2);
  
    result= gcalc_cmp_coord(exp_a, exp_b, GCALC_COORD_BASE5);
  #ifdef GCALC_CHECK_WITH_FLOAT
    if (result < 0)
    {
      if (!de_check(x1, x2) && x2 > x1)
        GCALC_DBUG_PRINT(("floatcheck cmp_intersectionsx failed %LG < %LG",
                          x2, x1));
    }
    else if (result > 0)
    {
      if (!de_check(x1, x2) && x2 < x1)
        GCALC_DBUG_PRINT(("floatcheck cmp_intersectionsx failed %LG > %LG",
                          x2, x1));
    }
    else
    {
      if (!de_check(x1, x2))
        GCALC_DBUG_PRINT(("floatcheck cmp_intersectionsx failed %LG == %LG",
                          x2, x1));
    }
  #endif /*GCALC_CHECK_WITH_FLOAT*/
    return result;
  }
  /* Internal coordinates implementation end */
  
  
  #define GCALC_SCALE_1 1e18
  
  static double find_scale(double extent)
  {
    double scale= 1e-2;
    while (scale < extent)
      scale*= (double ) 10;
    return GCALC_SCALE_1 / scale / 10;
  }
  
  
  void Gcalc_heap::set_extent(double xmin, double xmax, double ymin, double ymax)
  {
    xmin= fabs(xmin);
    xmax= fabs(xmax);
    ymin= fabs(ymin);
    ymax= fabs(ymax);
  
    if (xmax < xmin)
      xmax= xmin;
    if (ymax < ymin)
      ymax= ymin;
  
    coord_extent= xmax > ymax ? xmax : ymax;
    coord_extent= find_scale(coord_extent);
  #ifdef GCALC_CHECK_WITH_FLOAT
    gcalc_coord_extent= &coord_extent;
  #endif /*GCALC_CHECK_WITH_FLOAT*/
  }
  
  
  void Gcalc_heap::free_point_info(Gcalc_heap::Info *i,
                                   Gcalc_dyn_list::Item **i_hook)
  {
    if (m_hook == &i->next)
      m_hook= i_hook;
    *i_hook= i->next;
    free_item(i);
    m_n_points--;
  }
  
  
  Gcalc_heap::Info *Gcalc_heap::new_point_info(double x, double y,
                                               gcalc_shape_info shape)
  {
    Info *result= (Info *)new_item();
    if (!result)
      return NULL;
    *m_hook= result;
    m_hook= &result->next;
    result->node.shape.x= x;
    result->node.shape.y= y;
    result->node.shape.shape= shape;
    result->node.shape.top_node= 1;
    result->type= nt_shape_node;
    gcalc_set_double(result->node.shape.ix, x, coord_extent);
    gcalc_set_double(result->node.shape.iy, y, coord_extent);
  
    m_n_points++;
    return result;
  }
  
  
  static Gcalc_heap::Info *new_intersection(
      Gcalc_heap *heap, Gcalc_scan_iterator::intersection_info *ii)
  {
    Gcalc_heap::Info *isc= (Gcalc_heap::Info *)heap->new_item();
    if (!isc)
      return 0;
    isc->type= Gcalc_heap::nt_intersection;
    isc->node.intersection.p1= ii->edge_a->pi;
    isc->node.intersection.p2= ii->edge_a->next_pi;
    isc->node.intersection.p3= ii->edge_b->pi;
    isc->node.intersection.p4= ii->edge_b->next_pi;
    isc->node.intersection.data= ii;
    return isc;
  }
  
  
  static Gcalc_heap::Info *new_eq_point(
      Gcalc_heap *heap, const Gcalc_heap::Info *p,
      Gcalc_scan_iterator::point *edge)
  {
    Gcalc_heap::Info *eqp= (Gcalc_heap::Info *)heap->new_item();
    if (!eqp)
      return 0;
    eqp->type= Gcalc_heap::nt_eq_node;
    eqp->node.eq.node= p;
    eqp->node.eq.data= edge;
    return eqp;
  }
  
  
  void Gcalc_heap::Info::calc_xy(double *x, double *y) const
  {
    double b0_x= node.intersection.p2->node.shape.x - node.intersection.p1->node.shape.x;
    double b0_y= node.intersection.p2->node.shape.y - node.intersection.p1->node.shape.y;
    double b1_x= node.intersection.p4->node.shape.x - node.intersection.p3->node.shape.x;
    double b1_y= node.intersection.p4->node.shape.y - node.intersection.p3->node.shape.y;
    double b0xb1= b0_x * b1_y - b0_y * b1_x;
    double t= (node.intersection.p3->node.shape.x - node.intersection.p1->node.shape.x) * b1_y - (node.intersection.p3->node.shape.y - node.intersection.p1->node.shape.y) * b1_x;
  
    t/= b0xb1;
  
    *x= node.intersection.p1->node.shape.x + b0_x * t;
    *y= node.intersection.p1->node.shape.y + b0_y * t;
  }
  
  
  #ifdef GCALC_CHECK_WITH_FLOAT
  void Gcalc_heap::Info::calc_xy_ld(long double *x, long double *y) const
  {
    long double b0_x= ((long double) p2->node.shape.x) - p1->node.shape.x;
    long double b0_y= ((long double) p2->node.shape.y) - p1->node.shape.y;
    long double b1_x= ((long double) p4->node.shape.x) - p3->node.shape.x;
    long double b1_y= ((long double) p4->node.shape.y) - p3->node.shape.y;
    long double b0xb1= b0_x * b1_y - b0_y * b1_x;
    long double ax=   ((long double) p3->node.shape.x) - p1->node.shape.x;
    long double ay=   ((long double) p3->node.shape.y) - p1->node.shape.y;
    long double t_a= ax * b1_y - ay * b1_x;
    long double hx= (b0xb1 * (long double) p1->node.shape.x + b0_x * t_a);
    long double hy= (b0xb1 * (long double) p1->node.shape.y + b0_y * t_a);
  
    if (fabs(b0xb1) < 1e-15)
    {
      *x= p1->node.shape.x;
      *y= p1->node.shape.y;
      return;
    }
  
    *x= hx/b0xb1;
    *y= hy/b0xb1;
  }
  #endif /*GCALC_CHECK_WITH_FLOAT*/
  
  
  static int cmp_point_info(const Gcalc_heap::Info *i0,
                            const Gcalc_heap::Info *i1)
  {
    int cmp_y= gcalc_cmp_coord1(i0->node.shape.iy, i1->node.shape.iy);
    if (cmp_y)
      return cmp_y;
    return gcalc_cmp_coord1(i0->node.shape.ix, i1->node.shape.ix);
  }
  
  
  static inline void trim_node(Gcalc_heap::Info *node, Gcalc_heap::Info *prev_node)
  {
    if (!node)
      return;
    node->node.shape.top_node= 0;
    GCALC_DBUG_ASSERT((node->node.shape.left == prev_node) || (node->node.shape.right == prev_node));
    if (node->node.shape.left == prev_node)
      node->node.shape.left= node->node.shape.right;
    node->node.shape.right= NULL;
    GCALC_DBUG_ASSERT(cmp_point_info(node, prev_node));
  }
  
  
  static int compare_point_info(const void *e0, const void *e1)
  {
    const Gcalc_heap::Info *i0= (const Gcalc_heap::Info *)e0;
    const Gcalc_heap::Info *i1= (const Gcalc_heap::Info *)e1;
    return cmp_point_info(i0, i1) > 0;
  }
  
  
  void Gcalc_heap::prepare_operation()
  {
    Info *cur;
    GCALC_DBUG_ASSERT(m_hook);
    *m_hook= NULL;
    m_hook= NULL; /* just to check it's not called twice */
    m_first= sort_list(compare_point_info, m_first, m_n_points);
  
    /* TODO - move this to the 'normal_scan' loop */
    for (cur= get_first(); cur; cur= cur->get_next())
    {
      trim_node(cur->node.shape.left, cur);
      trim_node(cur->node.shape.right, cur);
    }
  }
  
  
  void Gcalc_heap::reset()
  {
    if (m_n_points)
    {
      if (m_hook)
        *m_hook= NULL;
      free_list(m_first);
      m_n_points= 0;
    }
    m_hook= &m_first;
  }
  
  
  int Gcalc_shape_transporter::int_single_point(gcalc_shape_info Info,
                                                double x, double y)
  {
    Gcalc_heap::Info *point= m_heap->new_point_info(x, y, Info);
    if (!point)
      return 1;
    point->node.shape.left= point->node.shape.right= 0;
    return 0;
  }
  
  
  int Gcalc_shape_transporter::int_add_point(gcalc_shape_info Info,
                                             double x, double y)
  {
    Gcalc_heap::Info *point;
    Gcalc_dyn_list::Item **hook;
  
    hook= m_heap->get_cur_hook();
  
    if (!(point= m_heap->new_point_info(x, y, Info)))
      return 1;
    if (m_first)
    {
      if (cmp_point_info(m_prev, point) == 0)
      {
        /* Coinciding points, do nothing */
        m_heap->free_point_info(point, hook);
        return 0;
      }
      GCALC_DBUG_ASSERT(!m_prev || m_prev->node.shape.x != x || m_prev->node.shape.y != y);
      m_prev->node.shape.left= point;
      point->node.shape.right= m_prev;
    }
    else
      m_first= point;
    m_prev= point;
    m_prev_hook= hook;
    return 0;
  }
  
  
  void Gcalc_shape_transporter::int_complete()
  {
    GCALC_DBUG_ASSERT(m_shape_started == 1 || m_shape_started == 3);
  
    if (!m_first)
      return;
  
    /* simple point */
    if (m_first == m_prev)
    {
      m_first->node.shape.right= m_first->node.shape.left= NULL;
      return;
    }
  
    /* line */
    if (m_shape_started == 1)
    {
      m_first->node.shape.right= NULL;
      m_prev->node.shape.left= m_prev->node.shape.right;
      m_prev->node.shape.right= NULL;
      return;
    }
  
    /* polygon */
    if (cmp_point_info(m_first, m_prev) == 0)
    {
      /* Coinciding points, remove the last one from the list */
      m_prev->node.shape.right->node.shape.left= m_first;
      m_first->node.shape.right= m_prev->node.shape.right;
      m_heap->free_point_info(m_prev, m_prev_hook);
    }
    else
    {
      GCALC_DBUG_ASSERT(m_prev->node.shape.x != m_first->node.shape.x || m_prev->node.shape.y != m_first->node.shape.y);
      m_first->node.shape.right= m_prev;
      m_prev->node.shape.left= m_first;
    }
  }
  
  
  inline void calc_dx_dy(Gcalc_scan_iterator::point *p)
  {
    gcalc_sub_coord1(p->dx, p->next_pi->node.shape.ix, p->pi->node.shape.ix);
    gcalc_sub_coord1(p->dy, p->next_pi->node.shape.iy, p->pi->node.shape.iy);
    if (GCALC_SIGN(p->dx[0]))
    {
      p->l_border= &p->next_pi->node.shape.ix;
      p->r_border= &p->pi->node.shape.ix;
    }
    else
    {
      p->r_border= &p->next_pi->node.shape.ix;
      p->l_border= &p->pi->node.shape.ix;
    }
  }
  
  
  Gcalc_scan_iterator::Gcalc_scan_iterator(size_t blk_size) :
    Gcalc_dyn_list(blk_size, sizeof(point) > sizeof(intersection_info) ?
                               sizeof(point) :
                               sizeof(intersection_info))
  {
    state.slice= NULL;
    m_bottom_points= NULL;
    m_bottom_hook= &m_bottom_points;
  }
  		  
  
  void Gcalc_scan_iterator::init(Gcalc_heap *points)
  {
    GCALC_DBUG_ASSERT(points->ready());
    GCALC_DBUG_ASSERT(!state.slice);
  
    if (!(m_cur_pi= points->get_first()))
      return;
    m_heap= points;
    state.event_position_hook= &state.slice;
    state.event_end= NULL;
  #ifndef GCALC_DBUG_OFF
    m_cur_thread= 0;
  #endif /*GCALC_DBUG_OFF*/
    GCALC_SET_TERMINATED(killed, 0);
  }
  
  void Gcalc_scan_iterator::reset()
  {
    state.slice= NULL;
    m_bottom_points= NULL;
    m_bottom_hook= &m_bottom_points;
    Gcalc_dyn_list::reset();
  }
  
  
  int Gcalc_scan_iterator::point::cmp_dx_dy(const Gcalc_coord1 dx_a,
                                            const Gcalc_coord1 dy_a,
                                            const Gcalc_coord1 dx_b,
                                            const Gcalc_coord1 dy_b)
  {
    Gcalc_coord2 dx_a_dy_b;
    Gcalc_coord2 dy_a_dx_b;
    gcalc_mul_coord1(dx_a_dy_b, dx_a, dy_b);
    gcalc_mul_coord1(dy_a_dx_b, dy_a, dx_b);
  
    return gcalc_cmp_coord(dx_a_dy_b, dy_a_dx_b, GCALC_COORD_BASE2);
  }
  
  
  int Gcalc_scan_iterator::point::cmp_dx_dy(const Gcalc_heap::Info *p1,
                                            const Gcalc_heap::Info *p2,
                                            const Gcalc_heap::Info *p3,
                                            const Gcalc_heap::Info *p4)
  {
    Gcalc_coord1 dx_a, dy_a, dx_b, dy_b;
    gcalc_sub_coord1(dx_a, p2->node.shape.ix, p1->node.shape.ix);
    gcalc_sub_coord1(dy_a, p2->node.shape.iy, p1->node.shape.iy);
    gcalc_sub_coord1(dx_b, p4->node.shape.ix, p3->node.shape.ix);
    gcalc_sub_coord1(dy_b, p4->node.shape.iy, p3->node.shape.iy);
    return cmp_dx_dy(dx_a, dy_a, dx_b, dy_b);
  }
  
  
  int Gcalc_scan_iterator::point::cmp_dx_dy(const point *p) const
  {
    GCALC_DBUG_ASSERT(!is_bottom());
    return cmp_dx_dy(dx, dy, p->dx, p->dy);
  }
  
  
  #ifdef GCALC_CHECK_WITH_FLOAT
  void Gcalc_scan_iterator::point::calc_x(long double *x, long double y,
                                          long double ix) const
  {
    long double ddy= gcalc_get_double(dy, GCALC_COORD_BASE);
    if (fabsl(ddy) < (long double) 1e-20)
    {
      *x= ix;
    }
    else
      *x= (ddy * (long double) pi->node.shape.x + gcalc_get_double(dx, GCALC_COORD_BASE) *
            (y - pi->node.shape.y)) / ddy;
  }
  #endif /*GCALC_CHECK_WITH_FLOAT*/
  
  
  static int compare_events(const void *e0, const void *e1)
  {
    const Gcalc_scan_iterator::point *p0= (const Gcalc_scan_iterator::point *)e0;
    const Gcalc_scan_iterator::point *p1= (const Gcalc_scan_iterator::point *)e1;
    return p0->cmp_dx_dy(p1) > 0;
  }
  
  
  int Gcalc_scan_iterator::arrange_event(int do_sorting, int n_intersections)
  {
    int ev_counter;
    point *sp;
    point **sp_hook;
  
    ev_counter= 0;
  
    *m_bottom_hook= NULL;
    for (sp= m_bottom_points; sp; sp= sp->get_next())
      sp->ev_next= sp->get_next();
  
    for (sp= state.slice, sp_hook= &state.slice;
         sp; sp_hook= sp->next_ptr(), sp= sp->get_next())
    {
      if (sp->event)
      {
        state.event_position_hook= sp_hook;
        break;
      }
    }
  
    for (sp= *(sp_hook= state.event_position_hook);
         sp && sp->event; sp_hook= sp->next_ptr(), sp= sp->get_next())
    {
      ev_counter++;
      if (sp->get_next() && sp->get_next()->event)
        sp->ev_next= sp->get_next();
      else
        sp->ev_next= m_bottom_points;
    }
  
  #ifndef GCALC_DBUG_OFF
    {
      point *cur_p= sp;
      for (; cur_p; cur_p= cur_p->get_next())
        GCALC_DBUG_ASSERT(!cur_p->event);
    }
  #endif /*GCALC_DBUG_OFF*/
  
    state.event_end= sp;
  
    if (ev_counter == 2 && n_intersections == 1)
    {
      /* If we had only intersection, just swap the two points. */
      sp= *state.event_position_hook;
      *state.event_position_hook= sp->get_next();
      sp->next= (*state.event_position_hook)->next;
      (*state.event_position_hook)->next= sp;
  
      /* The list of the events should be restored. */
      (*state.event_position_hook)->ev_next= sp;
      sp->ev_next= m_bottom_points;
    }
    else if (ev_counter == 2 && get_events()->event == scev_two_threads)
    {
      /* Do nothing. */
    }
    else if (ev_counter > 1 && do_sorting)
    {
      point *cur_p;
      *sp_hook= NULL;
      sp= (point *) sort_list(compare_events, *state.event_position_hook,
                              ev_counter);
      /* Find last item in the list, it's changed after the sorting. */
      for (cur_p= sp->get_next(); cur_p->get_next();
          cur_p= cur_p->get_next())
      {}
      cur_p->next= state.event_end;
      *state.event_position_hook= sp;
      /* The list of the events should be restored. */
      for (; sp && sp->event; sp= sp->get_next())
      {
        if (sp->get_next() && sp->get_next()->event)
          sp->ev_next= sp->get_next();
        else
          sp->ev_next= m_bottom_points;
      }
    }
  
  #ifndef GCALC_DBUG_OFF
    {
      const event_point *ev= get_events();
      for (; ev && ev->get_next(); ev= ev->get_next())
      {
        if (ev->is_bottom() || ev->get_next()->is_bottom())
          break;
        GCALC_DBUG_ASSERT(ev->cmp_dx_dy(ev->get_next()) <= 0);
      }
    }
  #endif /*GCALC_DBUG_OFF*/
    return 0;
  }
  
  
  int Gcalc_heap::Info::equal_pi(const Info *pi) const
  {
    if (type == nt_intersection)
      return node.intersection.equal;
    if (pi->type == nt_eq_node)
      return 1;
    if (type == nt_eq_node || pi->type == nt_intersection)
      return 0;
    return cmp_point_info(this, pi) == 0;
  }
  
  int Gcalc_scan_iterator::step()
  {
    int result= 0;
    int do_sorting= 0;
    int n_intersections= 0;
    point *sp;
    GCALC_DBUG_ENTER("Gcalc_scan_iterator::step");
    GCALC_DBUG_ASSERT(more_points());
  
    if (GCALC_TERMINATED(killed))
      GCALC_DBUG_RETURN(0xFFFF);
  
    /* Clear the old event marks. */
    if (m_bottom_points)
    {
      free_list((Gcalc_dyn_list::Item **) &m_bottom_points,
                (Gcalc_dyn_list::Item **) m_bottom_hook);
      m_bottom_points= NULL;
      m_bottom_hook= &m_bottom_points;
    }
    for (sp= *state.event_position_hook;
         sp != state.event_end; sp= sp->get_next())
      sp->event= scev_none;
  
  //#ifndef GCALC_DBUG_OFF
    state.event_position_hook= NULL;
    state.pi= NULL;
  //#endif /*GCALC_DBUG_OFF*/
  
    do
    {
  #ifndef GCALC_DBUG_OFF
      if (m_cur_pi->type == Gcalc_heap::nt_intersection &&
          m_cur_pi->get_next()->type == Gcalc_heap::nt_intersection &&
          m_cur_pi->node.intersection.equal)
        GCALC_DBUG_ASSERT(cmp_intersections(m_cur_pi, m_cur_pi->get_next()) == 0);
  #endif /*GCALC_DBUG_OFF*/
      GCALC_DBUG_CHECK_COUNTER();
      GCALC_DBUG_PRINT_SLICE("step:", state.slice);
      GCALC_DBUG_PRINT_PI(m_cur_pi);
      if (m_cur_pi->type == Gcalc_heap::nt_shape_node)
      {
        if (m_cur_pi->is_top())
        {
          result= insert_top_node();
          if (!m_cur_pi->is_bottom())
            do_sorting++;
        }
        else if (m_cur_pi->is_bottom())
          remove_bottom_node();
        else
        {
          do_sorting++;
          result= node_scan();
        }
        if (result)
          GCALC_DBUG_RETURN(result);
        state.pi= m_cur_pi;
      }
      else if (m_cur_pi->type == Gcalc_heap::nt_eq_node)
      {
        do_sorting++;
        eq_scan();
      }
      else
      {
        /* nt_intersection */
        do_sorting++;
        n_intersections++;
        intersection_scan();
        if (!state.pi || state.pi->type == Gcalc_heap::nt_intersection)
          state.pi= m_cur_pi;
      }
  
      m_cur_pi= m_cur_pi->get_next();
    } while (m_cur_pi && state.pi->equal_pi(m_cur_pi));
  
    GCALC_DBUG_RETURN(arrange_event(do_sorting, n_intersections));
  }
  
  
  static int node_on_right(const Gcalc_heap::Info *node, 
      const Gcalc_heap::Info *edge_a, const Gcalc_heap::Info *edge_b)
  {
    Gcalc_coord1 a_x, a_y;
    Gcalc_coord1 b_x, b_y;
    Gcalc_coord2 ax_by, ay_bx;
    int result;
  
    gcalc_sub_coord1(a_x, node->node.shape.ix, edge_a->node.shape.ix);
    gcalc_sub_coord1(a_y, node->node.shape.iy, edge_a->node.shape.iy);
    gcalc_sub_coord1(b_x, edge_b->node.shape.ix, edge_a->node.shape.ix);
    gcalc_sub_coord1(b_y, edge_b->node.shape.iy, edge_a->node.shape.iy);
    gcalc_mul_coord1(ax_by, a_x, b_y);
    gcalc_mul_coord1(ay_bx, a_y, b_x);
    result= gcalc_cmp_coord(ax_by, ay_bx, GCALC_COORD_BASE2);
  #ifdef GCALC_CHECK_WITH_FLOAT
    {
      long double dx= gcalc_get_double(edge_b->node.shape.ix, GCALC_COORD_BASE) -
                        gcalc_get_double(edge_a->node.shape.ix, GCALC_COORD_BASE);
      long double dy= gcalc_get_double(edge_b->node.shape.iy, GCALC_COORD_BASE) -
                        gcalc_get_double(edge_a->node.shape.iy, GCALC_COORD_BASE);
      long double ax= gcalc_get_double(node->node.shape.ix, GCALC_COORD_BASE) -
                        gcalc_get_double(edge_a->node.shape.ix, GCALC_COORD_BASE);
      long double ay= gcalc_get_double(node->node.shape.iy, GCALC_COORD_BASE) -
                        gcalc_get_double(edge_a->node.shape.iy, GCALC_COORD_BASE);
      long double d= ax * dy - ay * dx;
      if (result == 0)
        GCALC_DBUG_ASSERT(de_check(d, 0.0));
      else if (result < 0)
        GCALC_DBUG_ASSERT(de_check(d, 0.0) || d < 0);
      else
        GCALC_DBUG_ASSERT(de_check(d, 0.0) || d > 0);
    }
  #endif /*GCALC_CHECK_WITH_FLOAT*/
    return result;
  }
  
  
  static int cmp_tops(const Gcalc_heap::Info *top_node, 
      const Gcalc_heap::Info *edge_a, const Gcalc_heap::Info *edge_b)
  {
    int cmp_res_a, cmp_res_b;
  
    cmp_res_a= gcalc_cmp_coord1(edge_a->node.shape.ix, top_node->node.shape.ix);
    cmp_res_b= gcalc_cmp_coord1(edge_b->node.shape.ix, top_node->node.shape.ix);
  
    if (cmp_res_a <= 0 && cmp_res_b > 0)
      return -1;
    if (cmp_res_b <= 0 && cmp_res_a > 0)
      return 1;
    if (cmp_res_a == 0 && cmp_res_b == 0)
      return 0;
  
    return node_on_right(edge_a, top_node, edge_b);
  }
  
  
  int Gcalc_scan_iterator::insert_top_node()
  {
    point *sp= state.slice;
    point **prev_hook= &state.slice;
    point *sp1= NULL;
    point *sp0= new_slice_point();
    int cmp_res;
  
    GCALC_DBUG_ENTER("Gcalc_scan_iterator::insert_top_node");
    if (!sp0)
      GCALC_DBUG_RETURN(1);
    sp0->pi= m_cur_pi;
    sp0->next_pi= m_cur_pi->node.shape.left;
  #ifndef GCALC_DBUG_OFF
    sp0->thread= m_cur_thread++;
  #endif /*GCALC_DBUG_OFF*/
    if (m_cur_pi->node.shape.left)
    {
      calc_dx_dy(sp0);
      if (m_cur_pi->node.shape.right)
      {
        if (!(sp1= new_slice_point()))
          GCALC_DBUG_RETURN(1);
        sp1->event= sp0->event= scev_two_threads;
        sp1->pi= m_cur_pi;
        sp1->next_pi= m_cur_pi->node.shape.right;
  #ifndef GCALC_DBUG_OFF
        sp1->thread= m_cur_thread++;
  #endif /*GCALC_DBUG_OFF*/
        calc_dx_dy(sp1);
        /* We have two threads so should decide which one will be first */
        cmp_res= cmp_tops(m_cur_pi, m_cur_pi->node.shape.left, m_cur_pi->node.shape.right);
        if (cmp_res > 0)
        {
          point *tmp= sp0;
          sp0= sp1;
          sp1= tmp;
        }
        else if (cmp_res == 0)
        {
          /* Exactly same direction of the edges. */
          cmp_res= gcalc_cmp_coord1(m_cur_pi->node.shape.left->node.shape.iy, m_cur_pi->node.shape.right->node.shape.iy);
          if (cmp_res != 0)
          {
            if (cmp_res < 0)
            {
              if (add_eq_node(sp0->next_pi, sp1))
                GCALC_DBUG_RETURN(1);
            }
            else
            {
              if (add_eq_node(sp1->next_pi, sp0))
                GCALC_DBUG_RETURN(1);
            }
          }
          else
          {
            cmp_res= gcalc_cmp_coord1(m_cur_pi->node.shape.left->node.shape.ix, m_cur_pi->node.shape.right->node.shape.ix);
            if (cmp_res != 0)
            {
              if (cmp_res < 0)
              {
                if (add_eq_node(sp0->next_pi, sp1))
                  GCALC_DBUG_RETURN(1);
              }
              else
              {
                if (add_eq_node(sp1->next_pi, sp0))
                  GCALC_DBUG_RETURN(1);
              }
            }
          }
        }
      }
      else
        sp0->event= scev_thread;
    }
    else
      sp0->event= scev_single_point;
  
  
    /* Check if we already have an event - then we'll place the node there */
    for (; sp && !sp->event; prev_hook= sp->next_ptr(), sp=sp->get_next())
    {}
    if (!sp)
    {
      sp= state.slice;
      prev_hook= &state.slice;
      /* We need to find the place to insert. */
      for (; sp; prev_hook= sp->next_ptr(), sp=sp->get_next())
      {
        if (sp->event || gcalc_cmp_coord1(*sp->r_border, m_cur_pi->node.shape.ix) < 0)
          continue;
        cmp_res= node_on_right(m_cur_pi, sp->pi, sp->next_pi);
        if (cmp_res == 0)
        {
          /* The top node lies on the edge. */
          /* Nodes of that edge will be handled in other places. */
          sp->event= scev_intersection;
        }
        else if (cmp_res < 0)
          break;
      }
    }
  
    if (sp0->event == scev_single_point)
    {
      /* Add single point to the bottom list. */
      *m_bottom_hook= sp0;
      m_bottom_hook= sp0->next_ptr();
      state.event_position_hook= prev_hook;
    }
    else
    {
      *prev_hook= sp0;
      sp0->next= sp;
      if (add_events_for_node(sp0))
        GCALC_DBUG_RETURN(1);
  
      if (sp0->event == scev_two_threads)
      {
        *prev_hook= sp1;
        sp1->next= sp;
        if (add_events_for_node(sp1))
          GCALC_DBUG_RETURN(1);
  
        sp0->next= sp1;
        *prev_hook= sp0;
      }
    }
  
    GCALC_DBUG_RETURN(0);
  }
  
  
  void Gcalc_scan_iterator::remove_bottom_node()
  {
    point *sp= state.slice;
    point **sp_hook= &state.slice;
    point *first_bottom_point= NULL;
  
    GCALC_DBUG_ENTER("Gcalc_scan_iterator::remove_bottom_node");
    for (; sp; sp= sp->get_next())
    {
      if (sp->next_pi == m_cur_pi)
      {
        *sp_hook= sp->get_next();
        sp->pi= m_cur_pi;
        sp->next_pi= NULL;
        if (first_bottom_point)
        {
          first_bottom_point->event= sp->event= scev_two_ends;
          break;
        }
        first_bottom_point= sp;
        sp->event= scev_end;
        state.event_position_hook= sp_hook;
      }
      else
        sp_hook= sp->next_ptr();
    }
    GCALC_DBUG_ASSERT(first_bottom_point);
    *m_bottom_hook= first_bottom_point;
    m_bottom_hook= first_bottom_point->next_ptr();
    if (sp)
    {
      *m_bottom_hook= sp;
      m_bottom_hook= sp->next_ptr();
    }
  
    GCALC_DBUG_VOID_RETURN;
  }
  
  
  int Gcalc_scan_iterator::add_events_for_node(point *sp_node)
  {
    point *sp= state.slice;
    int cur_pi_r, sp_pi_r;
  
    GCALC_DBUG_ENTER("Gcalc_scan_iterator::add_events_for_node");
  
    /* Scan to the event point. */
    for (; sp != sp_node; sp= sp->get_next())
    {
      GCALC_DBUG_ASSERT(!sp->is_bottom());
      GCALC_DBUG_PRINT(("left cut_edge %d", sp->thread));
      if (sp->next_pi == sp_node->next_pi ||
          gcalc_cmp_coord1(*sp->r_border, *sp_node->l_border) < 0)
        continue;
      sp_pi_r= node_on_right(sp->next_pi, sp_node->pi, sp_node->next_pi);
      if (sp_pi_r < 0)
        continue;
      cur_pi_r= node_on_right(sp_node->next_pi, sp->pi, sp->next_pi);
      if (cur_pi_r > 0)
        continue;
      if (cur_pi_r == 0 && sp_pi_r == 0)
      {
        int cmp_res= cmp_point_info(sp->next_pi, sp_node->next_pi);
        if (cmp_res > 0)
        {
          if (add_eq_node(sp_node->next_pi, sp))
            GCALC_DBUG_RETURN(1);
        }
        else if (cmp_res < 0)
        {
          if (add_eq_node(sp->next_pi, sp_node))
            GCALC_DBUG_RETURN(1);
        }
        continue;
      }
  
      if (cur_pi_r == 0)
      {
        if (add_eq_node(sp_node->next_pi, sp))
          GCALC_DBUG_RETURN(1);
        continue;
      }
      else if (sp_pi_r == 0)
      {
        if (add_eq_node(sp->next_pi, sp_node))
          GCALC_DBUG_RETURN(1);
        continue;
      }
  
      if (sp->event)
      {
  #ifndef GCALC_DBUG_OFF
        cur_pi_r= node_on_right(sp_node->pi, sp->pi, sp->next_pi);
        GCALC_DBUG_ASSERT(cur_pi_r == 0);
  #endif /*GCALC_DBUG_OFF*/
        continue;
      }
      cur_pi_r= node_on_right(sp_node->pi, sp->pi, sp->next_pi);
      GCALC_DBUG_ASSERT(cur_pi_r >= 0);
      //GCALC_DBUG_ASSERT(cur_pi_r > 0); /* Is it ever violated? */
      if (cur_pi_r > 0 && add_intersection(sp, sp_node, m_cur_pi))
        GCALC_DBUG_RETURN(1);
    }
  
    /* Scan to the end of the slice */
    sp= sp->get_next();
  
    for (; sp; sp= sp->get_next())
    {
      GCALC_DBUG_ASSERT(!sp->is_bottom());
      GCALC_DBUG_PRINT(("right cut_edge %d", sp->thread));
      if (sp->next_pi == sp_node->next_pi ||
          gcalc_cmp_coord1(*sp_node->r_border, *sp->l_border) < 0)
        continue;
      sp_pi_r= node_on_right(sp->next_pi, sp_node->pi, sp_node->next_pi);
      if (sp_pi_r > 0)
        continue;
      cur_pi_r= node_on_right(sp_node->next_pi, sp->pi, sp->next_pi);
      if (cur_pi_r < 0)
        continue;
      if (cur_pi_r == 0 && sp_pi_r == 0)
      {
        int cmp_res= cmp_point_info(sp->next_pi, sp_node->next_pi);
        if (cmp_res > 0)
        {
          if (add_eq_node(sp_node->next_pi, sp))
            GCALC_DBUG_RETURN(1);
        }
        else if (cmp_res < 0)
        {
          if (add_eq_node(sp->next_pi, sp_node))
            GCALC_DBUG_RETURN(1);
        }
        continue;
      }
      if (cur_pi_r == 0)
      {
        if (add_eq_node(sp_node->next_pi, sp))
          GCALC_DBUG_RETURN(1);
        continue;
      }
      else if (sp_pi_r == 0)
      {
        if (add_eq_node(sp->next_pi, sp_node))
          GCALC_DBUG_RETURN(1);
        continue;
      }
  
      if (sp->event)
      {
  #ifndef GCALC_DBUG_OFF
        cur_pi_r= node_on_right(sp_node->pi, sp->pi, sp->next_pi);
        GCALC_DBUG_ASSERT(cur_pi_r == 0);
  #endif /*GCALC_DBUG_OFF*/
        continue;
      }
      cur_pi_r= node_on_right(sp_node->pi, sp->pi, sp->next_pi);
      GCALC_DBUG_ASSERT(cur_pi_r <= 0);
      //GCALC_DBUG_ASSERT(cur_pi_r < 0); /* Is it ever violated? */
      if (cur_pi_r < 0 && add_intersection(sp_node, sp, m_cur_pi))
        GCALC_DBUG_RETURN(1);
    }
  
    GCALC_DBUG_RETURN(0);
  }
  
  
  int Gcalc_scan_iterator::node_scan()
  {
    point *sp= state.slice;
    Gcalc_heap::Info *cur_pi= m_cur_pi;
  
    GCALC_DBUG_ENTER("Gcalc_scan_iterator::node_scan");
  
    /* Scan to the event point.                             */
    /* Can be avoided if we add link to the sp to the Info. */
    for (; sp->next_pi != cur_pi; sp= sp->get_next())
    {}
  
    GCALC_DBUG_PRINT(("node for %d", sp->thread));
    /* Handle the point itself. */
    sp->pi= cur_pi;
    sp->next_pi= cur_pi->node.shape.left;
    sp->event= scev_point;
    calc_dx_dy(sp);
  
    GCALC_DBUG_RETURN(add_events_for_node(sp));
  }
  
  
  void Gcalc_scan_iterator::eq_scan()
  {
    point *sp= eq_sp(m_cur_pi);
    GCALC_DBUG_ENTER("Gcalc_scan_iterator::eq_scan");
    
  #ifndef GCALC_DBUG_OFF
    {
      point *cur_p= state.slice;
      for (; cur_p && cur_p != sp; cur_p= cur_p->get_next())
      {}
      GCALC_DBUG_ASSERT(cur_p);
    }
  #endif /*GCALC_DBUG_OFF*/
    if (!sp->event)
    {
      sp->event= scev_intersection;
      sp->ev_pi= m_cur_pi;
    }
  
    GCALC_DBUG_VOID_RETURN;
  }
  
  
  void Gcalc_scan_iterator::intersection_scan()
  {
    intersection_info *ii= i_data(m_cur_pi);
    GCALC_DBUG_ENTER("Gcalc_scan_iterator::intersection_scan");
    
  #ifndef GCALC_DBUG_OFF
    {
      point *sp= state.slice;
      for (; sp && sp != ii->edge_a; sp= sp->get_next())
      {}
      GCALC_DBUG_ASSERT(sp);
      for (; sp && sp != ii->edge_b; sp= sp->get_next())
      {}
      GCALC_DBUG_ASSERT(sp);
    }
  #endif /*GCALC_DBUG_OFF*/
  
    ii->edge_a->event= ii->edge_b->event= scev_intersection;
    ii->edge_a->ev_pi= ii->edge_b->ev_pi= m_cur_pi;
    free_item(ii);
    m_cur_pi->node.intersection.data= NULL;
  
    GCALC_DBUG_VOID_RETURN;
  }
  
  
  int Gcalc_scan_iterator::add_intersection(point *sp_a, point *sp_b,
                                            Gcalc_heap::Info *pi_from)
  {
    Gcalc_heap::Info *ii;
    intersection_info *i_calc;
    int cmp_res;
    int skip_next= 0;
  
    GCALC_DBUG_ENTER("Gcalc_scan_iterator::add_intersection");
    if (!(i_calc= new_intersection_info(sp_a, sp_b)) ||
        !(ii= new_intersection(m_heap, i_calc)))
      GCALC_DBUG_RETURN(1);
  
    ii->node.intersection.equal= 0;
  
    for (;
         pi_from->get_next() != sp_a->next_pi &&
           pi_from->get_next() != sp_b->next_pi;
         pi_from= pi_from->get_next())
    {
      Gcalc_heap::Info *cur= pi_from->get_next();
      if (skip_next)
      {
        if (cur->type == Gcalc_heap::nt_intersection)
          skip_next= cur->node.intersection.equal;
        else
          skip_next= 0;
        continue;
      }
      if (cur->type == Gcalc_heap::nt_intersection)
      {
        cmp_res= cmp_intersections(cur, ii);
        skip_next= cur->node.intersection.equal;
      }
      else if (cur->type == Gcalc_heap::nt_eq_node)
        continue;
      else
        cmp_res= cmp_node_isc(cur, ii);
      if (cmp_res == 0)
      {
        ii->node.intersection.equal= 1;
        break;
      }
      else if (cmp_res > 0)
        break;
    }
  
    /* Intersection inserted before the equal point. */
    ii->next= pi_from->get_next();
    pi_from->next= ii;
  
    GCALC_DBUG_RETURN(0);
  }
  
  
  int Gcalc_scan_iterator::add_eq_node(Gcalc_heap::Info *node, point *sp)
  {
    Gcalc_heap::Info *en;
  
    GCALC_DBUG_ENTER("Gcalc_scan_iterator::add_intersection");
    en= new_eq_point(m_heap, node, sp);
    if (!en)
      GCALC_DBUG_RETURN(1);
  
    /* eq_node inserted after the equal point. */
    en->next= node->get_next();
    node->next= en;
  
    GCALC_DBUG_RETURN(0);
  }
  
  
  void calc_t(Gcalc_coord2 t_a, Gcalc_coord2 t_b,
              Gcalc_coord1 dxa, Gcalc_coord1 dxb,
              const Gcalc_heap::Info *p1, const Gcalc_heap::Info *p2,
              const Gcalc_heap::Info *p3, const Gcalc_heap::Info *p4)
  {
    Gcalc_coord1 a2_a1x, a2_a1y;
    Gcalc_coord2 x1y2, x2y1;
    Gcalc_coord1 dya, dyb;
  
    gcalc_sub_coord1(a2_a1x, p3->node.shape.ix, p1->node.shape.ix);
    gcalc_sub_coord1(a2_a1y, p3->node.shape.iy, p1->node.shape.iy);
  
    gcalc_sub_coord1(dxa, p2->node.shape.ix, p1->node.shape.ix);
    gcalc_sub_coord1(dya, p2->node.shape.iy, p1->node.shape.iy);
    gcalc_sub_coord1(dxb, p4->node.shape.ix, p3->node.shape.ix);
    gcalc_sub_coord1(dyb, p4->node.shape.iy, p3->node.shape.iy);
  
    gcalc_mul_coord1(x1y2, dxa, dyb);
    gcalc_mul_coord1(x2y1, dya, dxb);
    gcalc_sub_coord(t_b, GCALC_COORD_BASE2, x1y2, x2y1);
  
  
    gcalc_mul_coord1(x1y2, a2_a1x, dyb);
    gcalc_mul_coord1(x2y1, a2_a1y, dxb);
    gcalc_sub_coord(t_a, GCALC_COORD_BASE2, x1y2, x2y1);
  }
  
  
  double Gcalc_scan_iterator::get_y() const
  {
    if (state.pi->type == Gcalc_heap::nt_intersection)
    {
      Gcalc_coord1 dxa, dya;
      Gcalc_coord2 t_a, t_b;
      Gcalc_coord3 a_tb, b_ta, y_exp;
      calc_t(t_a, t_b, dxa, dya,
             state.pi->node.intersection.p1, state.pi->node.intersection.p2, state.pi->node.intersection.p3, state.pi->node.intersection.p4);
  
  
      gcalc_mul_coord(a_tb, GCALC_COORD_BASE3,
          t_b, GCALC_COORD_BASE2, state.pi->node.intersection.p1->node.shape.iy, GCALC_COORD_BASE);
      gcalc_mul_coord(b_ta, GCALC_COORD_BASE3,
          t_a, GCALC_COORD_BASE2, dya, GCALC_COORD_BASE);
  
      gcalc_add_coord(y_exp, GCALC_COORD_BASE3, a_tb, b_ta);
  
      return (get_pure_double(y_exp, GCALC_COORD_BASE3) /
               get_pure_double(t_b, GCALC_COORD_BASE2)) / m_heap->coord_extent;
    }
    else
      return state.pi->node.shape.y;
  }
  
  
  double Gcalc_scan_iterator::get_event_x() const
  {
    if (state.pi->type == Gcalc_heap::nt_intersection)
    {
      Gcalc_coord1 dxa, dya;
      Gcalc_coord2 t_a, t_b;
      Gcalc_coord3 a_tb, b_ta, x_exp;
      calc_t(t_a, t_b, dxa, dya,
             state.pi->node.intersection.p1, state.pi->node.intersection.p2, state.pi->node.intersection.p3, state.pi->node.intersection.p4);
  
  
      gcalc_mul_coord(a_tb, GCALC_COORD_BASE3,
          t_b, GCALC_COORD_BASE2, state.pi->node.intersection.p1->node.shape.ix, GCALC_COORD_BASE);
      gcalc_mul_coord(b_ta, GCALC_COORD_BASE3,
          t_a, GCALC_COORD_BASE2, dxa, GCALC_COORD_BASE);
  
      gcalc_add_coord(x_exp, GCALC_COORD_BASE3, a_tb, b_ta);
  
      return (get_pure_double(x_exp, GCALC_COORD_BASE3) /
               get_pure_double(t_b, GCALC_COORD_BASE2)) / m_heap->coord_extent;
    }
    else
      return state.pi->node.shape.x;
  }
  
  double Gcalc_scan_iterator::get_h() const
  {
    double cur_y= get_y();
    double next_y;
    if (state.pi->type == Gcalc_heap::nt_intersection)
    {
      double x;
      state.pi->calc_xy(&x, &next_y);
    }
    else
      next_y= state.pi->next ? state.pi->get_next()->node.shape.y : 0.0;
    return next_y - cur_y;
  }
  
  
  double Gcalc_scan_iterator::get_sp_x(const point *sp) const
  {
    double dy;
    if (sp->event & (scev_end | scev_two_ends | scev_point))
      return sp->pi->node.shape.x;
    dy= sp->next_pi->node.shape.y - sp->pi->node.shape.y;
    if (fabs(dy) < 1e-12)
      return sp->pi->node.shape.x;
    return sp->pi->node.shape.x + (sp->next_pi->node.shape.x - sp->pi->node.shape.x) * dy;
  }
  
  
  double Gcalc_scan_iterator::get_pure_double(const Gcalc_internal_coord *d,
                                              int d_len)
  {
    int n= 1;
    long double res= (long double) FIRST_DIGIT(d[0]);
    do
    {
      res*= (long double) GCALC_DIG_BASE;
      res+= (long double) d[n];
    } while(++n < d_len);
  
    if (GCALC_SIGN(d[0]))
      res*= -1.0;
    return res;
  }
  
  
  #endif /* HAVE_SPATIAL */
  