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Up to [local] / OpenXM_contrib / PHC / Ada / Math_Lib / Numbers

Import the second public release of PHCpack.

OKed by Jan Verschelde.

with unchecked_deallocation;

package body Multprec_Integer_Numbers is

-- NOTES ON THE CHOICE OF REPRESENTATION AND IMPLEMENTATION :
--   0) See also the notes in the body of Multprec_Natural_Numbers.
--      This package inherits the operations on natural numbers, with
--      additionally the tests on signs.
--      Integer numbers are in fact signed natural numbers.
--   1) The construction of tagged records was judged not appropriate to
--      extend the natural numbers, as this construction only applies to
--      records, it would have changed the privacy of the implementation.

-- DATA STRUCTURE :

  type Integer_Number_Rep is record
    plus : boolean;
    numb : Natural_Number;
  end record;

  procedure free is
      new unchecked_deallocation(Integer_Number_Rep,Integer_Number);

-- CREATORS :

  function Natural_Create ( n : natural ) return Integer_Number is

    res : Integer_Number;
    res_rep : Integer_Number_Rep;

  begin
    res_rep.plus := true;
    res_rep.numb := Create(n);
    res := new Integer_Number_Rep'(res_rep);
    return res;
  end Natural_Create;

  function Create ( n : Array_of_Naturals ) return Integer_Number is

    res : Integer_Number;
    res_rep : Integer_Number_Rep;

  begin
    res_rep.plus := true;
    res_rep.numb := Create(n);
    res := new Integer_Number_Rep'(res_rep);
    return res;
  end Create;

  function Create ( n : Natural_Number ) return Integer_Number is

    res : Integer_Number;
    res_rep : Integer_Number_Rep;

  begin
    res_rep.plus := true;
    res_rep.numb := +n;       --Copy(n,res_rep.numb);
    res := new Integer_Number_Rep'(res_rep);
    return res;
  end Create;

  function Create ( i : integer ) return Integer_Number is

    res : Integer_Number;
    n : natural;

  begin
    if i >= 0
     then n := i;
          res := Natural_Create(n);
          res.plus := true;
     else n := -i;
          res := Natural_Create(n);
          res.plus := false;
    end if;
    return res;
  end Create;

  function Convert ( n : Natural_Number ) return Integer_Number is

    res : Integer_Number;
    res_rep : Integer_Number_Rep;

  begin
    res_rep.numb := n;
    res_rep.plus := true;
    res := new Integer_Number_Rep'(res_rep);
    return res;
  end Convert;

  function Create ( i : Integer_Number ) return integer is

    res : integer;
    nres : natural;

  begin
    if (Empty(i) or else Empty(i.numb))
     then res := 0;
     else nres := Create(i.numb);
          if i.plus
           then res := nres;
           else res := -nres;
          end if;
    end if;
    return res;
  end Create;

-- SELECTORS :

  function Empty ( i : Integer_Number ) return boolean is
  begin
    return (i=null);
  end Empty;

  function Size ( i : Integer_Number ) return natural is
  begin
    if Empty(i)
     then return 0;
     else return Size(i.numb);
    end if;
  end Size;

  function Coefficient ( i : Integer_Number; k : natural ) return natural is
  begin
    if (Empty(i) or else (k > Size(i)))
     then return 0;
     else return Coefficient(i.numb,k);
    end if;
  end Coefficient;

  function Coefficients ( i : Integer_Number ) return Array_of_Naturals is

    nullres : Array_of_Naturals(0..0) := (0..0 => 0);

  begin
    if not Empty(i)
     then return Coefficients(i.numb);
     else return nullres;
    end if;
  end Coefficients;

  function Decimal_Places ( i : Integer_Number ) return natural is
  begin
    if Empty(i)
     then return 0;
     else return Decimal_Places(i.numb);
    end if;
  end Decimal_Places;

  function Positive ( i : Integer_Number ) return boolean is
  begin
    if Empty(i)
     then return false;
     elsif Empty(i.numb)
         then return false;
--         elsif Equal(i.numb,0)   -- whatever sign you wish to give to 0
--             then return false;  -- convenient to work with for input
             else return i.plus;
    end if;
  end Positive;

  function Negative ( i : Integer_Number ) return boolean is
  begin
    if Empty(i)
     then return false;
     elsif Empty(i.numb)
         then return false;
--         elsif Equal(i.numb,0)    -- for input of floating-point numbers
--             then return false;   -- convenient for reading -0.01
             else return not i.plus;
    end if;
  end Negative;

  function Sign ( i : Integer_Number ) return integer is
  begin
    if Empty(i) or Equal(i,0)
     then return 0;
     elsif Positive(i)
         then return +1;
         else return -1;
    end if;
  end Sign;

  function Unsigned ( i : Integer_Number ) return Natural_Number is

    res : Natural_Number;

  begin
    if not Empty(i)
     then res := i.numb;
    end if;
    return res;
  end Unsigned;

-- COMPARISON AND COPYING :

  function Equal ( i1 : Integer_Number; i2 : integer ) return boolean is
  begin
    if Empty(i1)
     then return (i2 = 0);
     elsif ((i1.plus and i2 < 0) or else (not i1.plus and i2 > 0))
         then return false;
         elsif Empty(i1.numb)
             then if i2 = 0
                   then return true;
                   else return false;
                  end if; 
             elsif i2 >= 0
                 then return Equal(i1.numb,i2);
                 else return Equal(i1.numb,-i2);
    end if;
  end Equal;

  function Equal ( i1,i2 : Integer_Number ) return boolean is
  begin
    if Empty(i1)
     then return Equal(i2,0);
     elsif Empty(i2)
         then return Equal(i1,0);
         else if (Positive(i1) and Negative(i2))
                or else (Negative(i1) and Positive(i2))
               then return false;
               else return Equal(i1.numb,i2.numb);
              end if;
    end if;
  end Equal;

  function "<" ( i1 : Integer_Number; i2 : integer ) return boolean is
  begin
    if Empty(i1)
     then return (i2 > 0);
     else if Positive(i1) 
           then if i2 <= 0
                 then return false;
                 else return (i1.numb < i2);
                end if;
           elsif Negative(i1) 
               then if i2 >= 0
                     then return true;
                     else return (i1.numb > -i2);
                    end if;
               else return (i2 > 0);
          end if;
    end if;
  end "<";

  function "<" ( i1 : integer; i2 : Integer_Number ) return boolean is
  begin
    if Empty(i2)
     then return (i1 < 0);
     else if Positive(i2)
           then if i1 <= 0
                 then return true;
                 else return (i1 < i2.numb);
                end if;
           elsif Negative(i2)
               then if i1 >= 0
                     then return false;
                     else return (-i1 > i2.numb);
                    end if;
               else return (i1 < 0);
          end if;
    end if;
  end "<";

  function "<" ( i1,i2 : Integer_Number ) return boolean is
  begin
    if Empty(i1)
     then return Positive(i2);
     elsif Empty(i2)
         then return Negative(i1);
         elsif Positive(i1)
             then if Negative(i2)
                   then return false;
                   else return (i1.numb < i2.numb);
                  end if;
             elsif Negative(i1)
                 then if Positive(i2)
                       then return true;
                       else return (i1.numb > i2.numb);
                      end if;
                 else return Positive(i2);
    end if;
  end "<";

  function ">" ( i1 : Integer_Number; i2 : integer ) return boolean is
  begin
    if Empty(i1)
     then return (i2 < 0);
     else if Negative(i1)
           then if i2 >= 0
                 then return false;
                 else return (i1.numb < -i2);
                end if;
           elsif Positive(i1)
               then if i2 <= 0
                     then return true;
                     else return (i1.numb > i2);
                    end if;
               else return (i2 < 0);
          end if;
    end if;
  end ">";

  function ">" ( i1 : integer; i2 : Integer_Number ) return boolean is
  begin
    if Empty(i2)
     then return (i1 > 0);
     else if Positive(i2)
           then if i1 <= 0
                 then return false;
                 else return (i1 > i2.numb);
                end if;
           elsif Negative(i2)
               then if i1 >= 0
                     then return true;
                     else return (-i1 < i2.numb);
                    end if;
               else return (i1 > 0);
          end if;
    end if;
  end ">";

  function ">" ( i1,i2 : Integer_Number ) return boolean is
  begin
    if Empty(i1)
     then return Negative(i2);
     elsif Empty(i2)
         then return Positive(i1);
         elsif Positive(i1)
             then if Negative(i2)
                   then return true;
                   else return (i1.numb > i2.numb);
                  end if;
             elsif Negative(i1)
                 then if Positive(i2)
                       then return false;
                       else return (i1.numb < i2.numb);
                      end if;
                 else return Negative(i2);
    end if;
  end ">";

  procedure Copy ( i1 : in integer; i2 : in out Integer_Number ) is
  begin
    Clear(i2);
    i2 := Create(i1);
  end Copy;

  procedure Copy ( i1 : in Integer_Number; i2 : in out Integer_Number ) is
  begin
    Clear(i2);
    if not Empty(i1)
     then declare
            i2rep : Integer_Number_Rep;
          begin
            i2rep.plus := i1.plus;
            i2rep.numb := +i1.numb;
            i2 := new Integer_Number_Rep'(i2rep);
          end;
    end if;
  end Copy;

-- ARITHMETIC OPERATIONS as functions :

  function "+" ( i1 : Integer_Number; i2 : integer ) return Integer_Number is

    res : Integer_Number;
    res_rep : Integer_Number_Rep;
    n : natural;

  begin
    if (Empty(i1) or else Empty(i1.numb))
     then res := Create(i2);
     else if i1.plus
           then if i2 >= 0
                 then n := i2;
                      res_rep.plus := true;
                      res_rep.numb := i1.numb + n;
                      res := new Integer_Number_Rep'(res_rep);
                 else n := -i2;
                      if not Equal(i1.numb,n)
                       then if i1.numb > n 
                             then res_rep.plus := true;
                                  res_rep.numb := i1.numb - n;
                             else res_rep.plus := false;
                                  res_rep.numb := n - i1.numb;
                            end if;
                            res := new Integer_Number_Rep'(res_rep);
                      end if;
                end if;
           else if i2 <= 0
                 then n := -i2;
                      res_rep.plus := false;
                      res_rep.numb := i1.numb + n;
                      res := new Integer_Number_Rep'(res_rep);
                 else n := i2;
                      if not Equal(i1.numb,n)
                       then if i1.numb < n
                             then res_rep.plus := true;
                                  res_rep.numb := n - i1.numb;
                             else res_rep.plus := false;
                                  res_rep.numb := i1.numb - n;
                            end if;
                            res := new Integer_Number_Rep'(res_rep);
                      end if;
                end if;
          end if;
    end if;
    return res;
  end "+";

  function "+" ( i1 : integer; i2 : Integer_Number ) return Integer_Number is
  begin
    return (i2+i1);
  end "+";

  function "+" ( i1,i2 : Integer_Number ) return Integer_Number is

    res : Integer_Number;
    res_rep : Integer_Number_Rep;

  begin
    if (Empty(i1) or else Empty(i1.numb))
     then Copy(i2,res);
     else if (Empty(i2) or else Empty(i2.numb))
           then Copy(i1,res);
           else if i1.plus
                 then if i2.plus
                       then res_rep.plus := true;
                            res_rep.numb := i1.numb + i2.numb;
                            res := new Integer_Number_Rep'(res_rep);
                       else if not Equal(i1.numb,i2.numb)
                             then if i1.numb > i2.numb
                                   then res_rep.plus := true;
                                        res_rep.numb := i1.numb - i2.numb;
                                   else res_rep.plus := false;
                                        res_rep.numb := i2.numb - i1.numb;
                                  end if;
                                  res := new Integer_Number_Rep'(res_rep);
                            end if;
                      end if;
                 else if not i2.plus
                       then res_rep.plus := false;
                            res_rep.numb := i1.numb + i2.numb;
                            res := new Integer_Number_Rep'(res_rep);
                       else if not Equal(i1.numb,i2.numb)
                             then if i1.numb < i2.numb
                                   then res_rep.plus := true;
                                        res_rep.numb := i2.numb - i1.numb;
                                   else res_rep.plus := false;
                                        res_rep.numb := i1.numb - i2.numb;
                                  end if;
                                  res := new Integer_Number_Rep'(res_rep);
                            end if;
                      end if;
               end if;
          end if;
    end if;
    return res;
  end "+";

  function "+" ( i : Integer_Number ) return Integer_Number is

    res : Integer_Number;

  begin
    Copy(i,res);
    return res;
  end "+";

  function "-" ( i : Integer_Number ) return Integer_Number is

    res : Integer_Number;
    res_rep : Integer_Number_Rep;

  begin
    if not Empty(i)
     then res_rep.plus := not i.plus;
          res_rep.numb := +i.numb;    -- Copy(i.numb,res_rep.numb);
          res := new Integer_Number_Rep'(res_rep);
    end if;
    return res;
  end "-";

  function "-" ( i1 : Integer_Number; i2 : integer ) return Integer_Number is

    mini2 : constant integer := -i2;

  begin
    return (i1+mini2);
  end "-";

  function "-" ( i1 : integer; i2 : Integer_Number ) return Integer_Number is

    res : Integer_Number := i2 - i1;

  begin
    Min(res);
    return res;
  end "-";

  function "-" ( i1,i2 : Integer_Number ) return Integer_Number is

    res,mini2 : Integer_Number;
    mini2rep : Integer_Number_Rep;

  begin
    if (Empty(i2) or else Empty(i2.numb))
     then Copy(i1,res);
     else mini2rep.numb := i2.numb;
          mini2rep.plus := not i2.plus;
          mini2 := new Integer_Number_Rep'(mini2rep);
          res := i1 + mini2;
          free(mini2);
    end if;
    return res;
  end "-";

  function "*" ( i1 : Integer_Number; i2 : integer ) return Integer_Number is

    res : Integer_Number;
    res_rep : Integer_Number_Rep;
    n : natural;

  begin
    if not ((i2 = 0) or else Empty(i1) or else Empty(i1.numb))
     then if i2 > 0
           then n := i2;
                res_rep.plus := i1.plus;
           else n := -i2;
                res_rep.plus := not i1.plus;
          end if;
          res_rep.numb := i1.numb*n;
          res := new Integer_Number_Rep'(res_rep);
    end if;
    return res;
  end "*";

  function "*" ( i1 : integer; i2 : Integer_Number ) return Integer_Number is
  begin
    return (i2*i1);
  end "*";

  function "*" ( i1,i2 : Integer_Number ) return Integer_Number is

    res : Integer_Number;
    res_rep : Integer_Number_Rep;

  begin
    if (not (Empty(i1) or else Empty(i1.numb)))
       and then (not (Empty(i2) or else Empty(i2.numb)))
     then res_rep.numb := i1.numb*i2.numb;
          res_rep.plus := i1.plus;
          if not i2.plus
           then res_rep.plus := not res_rep.plus;
          end if;
          res := new Integer_Number_Rep'(res_rep);
    end if;
    return res;
  end "*";

  function "**" ( i : Integer_Number; n : natural ) return Integer_Number is

    res : Integer_Number;
    res_rep : Integer_Number_Rep;

  begin
    if n = 0
     then res := Create(1);
     else if not (Empty(i) or else Empty(i.numb))
           then res_rep.numb := i.numb**n;
                res_rep.plus := i.plus;
                if ((not i.plus) and then (n mod 2 = 1))
                 then res_rep.plus := not res_rep.plus;
                end if;
                res := new Integer_Number_Rep'(res_rep);
          end if;
    end if;
    return res;
  end "**";

  function "**" ( i : integer; n : Natural_Number ) return Integer_Number is

    res : Integer_Number;
    res_rep : Integer_Number_Rep;
    ni : natural;

  begin
    if (Empty(n) or else Equal(n,0))
     then res := Create(1);
     else if i /= 0
           then if i > 0
                 then ni := i;
                      res_rep.plus := true;
                 else ni := -i;
                      res_rep.plus := false;
                end if;
                res_rep.numb := ni**n;
                if (i < 0 and then (Rmd(n,2) = 0))
                 then res_rep.plus := not res_rep.plus;
                end if;
                res := new Integer_Number_Rep'(res_rep);
          end if;
    end if; 
    return res;
  end "**";

  function "**" ( i : Integer_Number; n : Natural_Number )
                return Integer_Number is

    res : Integer_Number;
    res_rep : Integer_Number_Rep;

  begin
    if (Empty(n) or else Equal(n,0))
     then res := Create(1);
     else if not (Empty(i) or else Empty(i.numb))
           then res_rep.numb := i.numb**n;
                res_rep.plus := i.plus;
                if ((not i.plus) and then (Rmd(n,2) = 0))
                 then res_rep.plus := not res_rep.plus;
                end if;
                res := new Integer_Number_Rep'(res_rep);
          end if;
    end if;
    return res;
  end "**";

  function "/" ( i1 : Integer_Number; i2 : integer ) return Integer_Number is

    res : Integer_Number;
    i2n : natural;
    res_rep : Integer_Number_Rep;

  begin
    if i2 /= 0
     then if not (Empty(i1) or else Empty(i1.numb))
           then if i2 > 0
                 then i2n := i2;
                 else i2n := -i2;
                end if;
                res_rep.numb := i1.numb/i2n;
                if (i1.plus and (i2 > 0)) or ((not i1.plus) and (i2 < 0))
                 then res_rep.plus := true;
                 else res_rep.plus := false;
                end if;
                res := new Integer_Number_Rep'(res_rep);
          end if;
     else raise NUMERIC_ERROR;
    end if;
    return res;
  end "/";

  function "/" ( i1 : integer; i2 : Integer_Number ) return integer is

    res : integer;
    i1n,nres : natural;

  begin
    if (Empty(i2) or else Empty(i2.numb))
     then raise NUMERIC_ERROR;
     else if i1 > 0
           then i1n := i1;
           else i1n := -i1;
          end if;
          nres := i1n/i2.numb;
          if ((i1 > 0) and i2.plus) or ((i1 < 0) and (not i2.plus))
           then res := nres;
           else res := -nres;
          end if;
    end if;
    return res;
  end "/";

  function "/" ( i1,i2 : Integer_Number ) return Integer_Number is

    res : Integer_Number;
    res_rep : Integer_Number_Rep;

  begin
    if not (Empty(i1) or else Empty(i1.numb))
     then if (Empty(i2) or else Empty(i2.numb))
           then raise NUMERIC_ERROR;
           else res_rep.numb := i1.numb/i2.numb;
                if (i1.plus and i2.plus) or ((not i1.plus) and (not i2.plus))
                 then res_rep.plus := true;
                 else res_rep.plus := false;
                end if;
                res := new Integer_Number_Rep'(res_rep);
          end if;
    end if;
    return res;
  end "/";

  function Rmd ( i1 : Integer_Number; i2 : integer ) return integer is

    res : integer;
    i2n,nres : natural;

  begin
    if i2 /= 0
     then if (Empty(i1) or else Empty(i1.numb))
           then res := 0;
           else if i2 > 0
                 then i2n := i2;
                 else i2n := -i2;
                end if;
                nres := Rmd(i1.numb,i2n);
                if i1.plus
                 then res := nres;
                 else res := -nres;
                end if;
          end if;
     else raise NUMERIC_ERROR;
    end if;
    return res;
  end Rmd;

  function Rmd ( i1 : integer; i2 : Integer_Number ) return integer is

    res : integer;
    i1n,nres : natural;

  begin
    if i1 = 0
     then res := 0;
     else if (Empty(i2) or else Empty(i2.numb))
           then raise NUMERIC_ERROR;
           else if i1 > 0
                 then i1n := i1;
                 else i1n := -i1;
                end if; 
                nres := Rmd(i1n,i2.numb);
                if i1 > 0
                 then res := nres;
                 else res := -nres;
                end if;
          end if;
    end if;
    return res;
  end Rmd;

  function Rmd ( i1,i2 : Integer_Number ) return Integer_Number is

    res : Integer_Number;
    res_rep : Integer_Number_Rep;

  begin
    if not (Empty(i1) or else Empty(i1.numb))
     then if (Empty(i2) or else Empty(i2.numb))
           then raise NUMERIC_ERROR;
           else res_rep.numb := Rmd(i1.numb,i2.numb);
                res_rep.plus := i1.plus;
                res := new Integer_Number_Rep'(res_rep);
          end if;
    end if;
    return res;
  end Rmd;

-- ARITHMETIC OPERATIONS as procedures for memory management :

  procedure Add ( i1 : in out Integer_Number; i2 : in integer ) is

    n : natural;
    nn : Natural_Number;

  begin
    if (Empty(i1) or else Empty(i1.numb))
     then i1 := Create(i2);
     else if i1.plus
           then if i2 >= 0
                 then n := i2;
                      Add(i1.numb,n);
                 else n := -i2;
                      if not Equal(i1.numb,n)
                       then if i1.numb > n
                             then Sub(i1.numb,n);
                             else i1.plus := false;
                                  nn := Create(n);
                                  Sub(nn,i1.numb);
                                  Clear(i1.numb); i1.numb := nn;
                            end if;
                       else Clear(i1);
                      end if;
                end if;
           else if i2 <= 0
                 then n := -i2;
                      Add(i1.numb,n);
                 else n := i2;
                      if not Equal(i1.numb,n)
                       then if i1.numb < n
                             then i1.plus := true;
                                  nn := Create(n);
                                  Sub(nn,i1.numb);
                                  Clear(i1.numb); i1.numb := nn;
                             else Sub(i1.numb,n);
                            end if;
                       else Clear(i1);
                      end if;
                end if;
          end if;
    end if;
  end Add;

  procedure Add ( i1 : in out Integer_Number; i2 : in Integer_Number ) is

    nn : Natural_Number;

  begin
    if (Empty(i1) or else Empty(i1.numb))
     then Copy(i2,i1);
     else if not (Empty(i2) or else Empty(i2.numb))
           then if i1.plus
                 then if i2.plus
                       then Add(i1.numb,i2.numb);
                       else if not Equal(i1.numb,i2.numb)
                             then if i1.numb > i2.numb
                                   then Sub(i1.numb,i2.numb);
                                   else Copy(i2.numb,nn);
                                        Sub(nn,i1.numb);
                                        Clear(i1.numb);
                                        i1.plus := false;
                                        i1.numb := nn;
                                  end if;
                             else Clear(i1);
                            end if;
                      end if;
                 else if not i2.plus
                       then Add(i1.numb,i2.numb);
                       else if not Equal(i1.numb,i2.numb)
                             then if i1.numb < i2.numb
                                   then Copy(i2.numb,nn);
                                        Sub(nn,i1.numb);
                                        Clear(i1.numb);
                                        i1.plus := true;
                                        i1.numb := nn;
                                   else Sub(i1.numb,i2.numb);
                                  end if;
                             else Clear(i1);
                            end if;
                      end if;
               end if;
          end if;
    end if;
  end Add;

  procedure Min ( i : in out Integer_Number ) is
  begin
    if not Empty(i)
     then i.plus := not i.plus;
    end if;
  end Min;

  procedure Sub ( i1 : in out Integer_Number; i2 : in integer ) is
  begin
    Add(i1,-i2);
  end Sub;

  procedure Sub ( i1 : in out Integer_Number; i2 : in Integer_Number ) is

    mini2 : Integer_Number;
    mini2rep : Integer_Number_Rep;

  begin
    if not (Empty(i2) or else Empty(i2.numb))
     then mini2rep.numb := i2.numb;
          mini2rep.plus := not i2.plus;
          mini2 := new Integer_Number_Rep'(mini2rep);
          Add(i1,mini2);
          free(mini2);
    end if;
  end Sub;

  procedure Mul ( i1 : in out Integer_Number; i2 : in integer ) is

    n : natural;

  begin
    if not (Empty(i1) or else Empty(i1.numb))
     then if i2 = 0
           then Clear(i1);
           else if i2 > 0
                 then n := i2;
                 else n := -i2;
                      i1.plus := not i1.plus;
                end if;
                Mul(i1.numb,n);
          end if;
    end if;
  end Mul;

  procedure Mul ( i1 : in out Integer_Number; i2 : in Integer_Number ) is
  begin
    if (not (Empty(i1) or else Empty(i1.numb)))
     then if (Empty(i2) or else Empty(i2.numb))
           then Clear(i1);
           else Mul(i1.numb,i2.numb);
                if not i2.plus
                 then i1.plus := not i1.plus;
                end if;
          end if;
    end if;
  end Mul;

  procedure Rmd ( i1 : in out Integer_Number; i2 : in integer ) is

    res : Integer_Number := Create(Rmd(i1,i2));

  begin
    Clear(i1); i1 := res;
  end Rmd;

  procedure Rmd ( i1 : in out Integer_Number; i2 : in Integer_Number ) is

    res : Integer_Number := Rmd(i1,i2);

  begin
    Clear(i1); i1 := res;
  end Rmd;

  procedure Div ( i1 : in out Integer_Number; i2 : in integer ) is

    r : integer;

  begin
    Div(i1,i2,r);
  end Div;

  procedure Div ( i1 : in out Integer_Number; i2 : in Integer_Number ) is

    r : Integer_Number;

  begin
    Div(i1,i2,r);
    Clear(r);
  end Div;

  procedure Div ( i1 : in Integer_Number; i2 : in integer;
                  q : out Integer_Number; r : out integer ) is

    qrep : Integer_Number_Rep;
    i2n,rn : natural;

  begin
    if i2 /= 0
     then if not (Empty(i1) or else Empty(i1.numb))
           then if i2 > 0
                 then i2n := i2;
                 else i2n := -i2;
                end if; 
                Div(i1.numb,i2n,qrep.numb,rn);
                if (i1.plus and (i2 > 0)) or ((not i1.plus) and (i2 < 0))
                 then qrep.plus := true;
                 else qrep.plus := false;
                end if;
                q := new Integer_Number_Rep'(qrep);
                if i1.plus
                 then r := rn;
                 else r := -rn;
                end if;
          end if;
     else raise NUMERIC_ERROR;
    end if;
  end Div;

  procedure Div ( i1 : in out Integer_Number; i2 : in integer;
                  r : out integer ) is

    i2n,rn : natural;
 
  begin
    if i2 /= 0
     then if not (Empty(i1) or else Empty(i1.numb))
           then if i2 > 0
                 then i2n := i2;
                 else i2n := -i2;
                end if;
                Div(i1.numb,i2n,rn);
                if i1.plus
                 then r := rn;
                 else r := -rn;
                end if;
                if (i1.plus and (i2 > 0)) or ((not i1.plus) and (i2 < 0))
                 then i1.plus := true;
                 else i1.plus := false;
                end if;
          end if;
     else raise NUMERIC_ERROR;
    end if;
  end Div;

  procedure Div ( i1,i2 : in Integer_Number; q,r : out Integer_Number ) is

    qrep,rrep : Integer_Number_Rep;

  begin
    if not (Empty(i2) or else Empty(i2.numb))
     then if not (Empty(i1) or else Empty(i1.numb))
           then Div(i1.numb,i2.numb,qrep.numb,rrep.numb);
                if (i1.plus and (i2 > 0)) or ((not i1.plus) and (i2 < 0))
                 then qrep.plus := true;
                 else qrep.plus := false;
                end if;
                q := new Integer_Number_Rep'(qrep);
                rrep.plus := i1.plus;
                r := new Integer_Number_Rep'(rrep);
          end if;
     else raise NUMERIC_ERROR;
    end if;
  end Div;

  procedure Div ( i1 : in out Integer_Number; i2 : in Integer_Number;
                  r : out Integer_Number ) is

    rrep : Integer_Number_Rep;

  begin
    if not (Empty(i2) or else Empty(i2.numb))
     then if not (Empty(i1) or else Empty(i1.numb))
           then Div(i1.numb,i2.numb,rrep.numb);
                rrep.plus := i1.plus;
                r := new Integer_Number_Rep'(rrep);
                if (i1.plus and (i2 > 0)) or ((not i1.plus) and (i2 < 0))
                 then i1.plus := true;
                 else i1.plus := false;
                end if;
          end if;
     else raise NUMERIC_ERROR;
    end if;
  end Div;

-- DESTRUCTOR :

  procedure Clear ( i : in out Integer_Number ) is
  begin
    if not Empty(i)
     then Clear(i.numb);
          free(i);
          i := null;
    end if;
  end Clear;

end Multprec_Integer_Numbers;