--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/gcc/ada/uintp.ads	Fri Oct 27 22:46:09 2017 +0900
@@ -0,0 +1,558 @@
+------------------------------------------------------------------------------
+--                                                                          --
+--                         GNAT COMPILER COMPONENTS                         --
+--                                                                          --
+--                                U I N T P                                 --
+--                                                                          --
+--                                 S p e c                                  --
+--                                                                          --
+--          Copyright (C) 1992-2016, Free Software Foundation, Inc.         --
+--                                                                          --
+-- GNAT is free software;  you can  redistribute it  and/or modify it under --
+-- terms of the  GNU General Public License as published  by the Free Soft- --
+-- ware  Foundation;  either version 3,  or (at your option) any later ver- --
+-- sion.  GNAT is distributed in the hope that it will be useful, but WITH- --
+-- OUT ANY WARRANTY;  without even the  implied warranty of MERCHANTABILITY --
+-- or FITNESS FOR A PARTICULAR PURPOSE.                                     --
+--                                                                          --
+-- As a special exception under Section 7 of GPL version 3, you are granted --
+-- additional permissions described in the GCC Runtime Library Exception,   --
+-- version 3.1, as published by the Free Software Foundation.               --
+--                                                                          --
+-- You should have received a copy of the GNU General Public License and    --
+-- a copy of the GCC Runtime Library Exception along with this program;     --
+-- see the files COPYING3 and COPYING.RUNTIME respectively.  If not, see    --
+-- <http://www.gnu.org/licenses/>.                                          --
+--                                                                          --
+-- GNAT was originally developed  by the GNAT team at  New York University. --
+-- Extensive contributions were provided by Ada Core Technologies Inc.      --
+--                                                                          --
+------------------------------------------------------------------------------
+
+--  Support for universal integer arithmetic
+
+--  WARNING: There is a C version of this package. Any changes to this
+--  source file must be properly reflected in the C header file uintp.h
+
+with Alloc;
+with Table;
+pragma Elaborate_All (Table);
+with Types; use Types;
+
+package Uintp is
+
+   -------------------------------------------------
+   -- Basic Types and Constants for Uintp Package --
+   -------------------------------------------------
+
+   type Uint is private;
+   --  The basic universal integer type
+
+   No_Uint : constant Uint;
+   --  A constant value indicating a missing or unset Uint value
+
+   Uint_0   : constant Uint;
+   Uint_1   : constant Uint;
+   Uint_2   : constant Uint;
+   Uint_3   : constant Uint;
+   Uint_4   : constant Uint;
+   Uint_5   : constant Uint;
+   Uint_6   : constant Uint;
+   Uint_7   : constant Uint;
+   Uint_8   : constant Uint;
+   Uint_9   : constant Uint;
+   Uint_10  : constant Uint;
+   Uint_11  : constant Uint;
+   Uint_12  : constant Uint;
+   Uint_13  : constant Uint;
+   Uint_14  : constant Uint;
+   Uint_15  : constant Uint;
+   Uint_16  : constant Uint;
+   Uint_24  : constant Uint;
+   Uint_32  : constant Uint;
+   Uint_63  : constant Uint;
+   Uint_64  : constant Uint;
+   Uint_80  : constant Uint;
+   Uint_128 : constant Uint;
+
+   Uint_Minus_1   : constant Uint;
+   Uint_Minus_2   : constant Uint;
+   Uint_Minus_3   : constant Uint;
+   Uint_Minus_4   : constant Uint;
+   Uint_Minus_5   : constant Uint;
+   Uint_Minus_6   : constant Uint;
+   Uint_Minus_7   : constant Uint;
+   Uint_Minus_8   : constant Uint;
+   Uint_Minus_9   : constant Uint;
+   Uint_Minus_12  : constant Uint;
+   Uint_Minus_36  : constant Uint;
+   Uint_Minus_63  : constant Uint;
+   Uint_Minus_80  : constant Uint;
+   Uint_Minus_128 : constant Uint;
+
+   type UI_Vector is array (Pos range <>) of Int;
+   --  Vector containing the integer values of a Uint value
+
+   --  Note: An earlier version of this package used pointers of arrays of Ints
+   --  (dynamically allocated) for the Uint type. The change leads to a few
+   --  less natural idioms used throughout this code, but eliminates all uses
+   --  of the heap except for the table package itself. For example, Uint
+   --  parameters are often converted to UI_Vectors for internal manipulation.
+   --  This is done by creating the local UI_Vector using the function N_Digits
+   --  on the Uint to find the size needed for the vector, and then calling
+   --  Init_Operand to copy the values out of the table into the vector.
+
+   -----------------
+   -- Subprograms --
+   -----------------
+
+   procedure Initialize;
+   --  Initialize Uint tables. Note that Initialize must not be called if
+   --  Tree_Read is used. Note also that there is no lock routine in this
+   --  unit, these are among the few tables that can be expanded during
+   --  gigi processing.
+
+   procedure Tree_Read;
+   --  Initializes internal tables from current tree file using the relevant
+   --  Table.Tree_Read routines. Note that Initialize should not be called if
+   --  Tree_Read is used. Tree_Read includes all necessary initialization.
+
+   procedure Tree_Write;
+   --  Writes out internal tables to current tree file using the relevant
+   --  Table.Tree_Write routines.
+
+   function UI_Abs (Right : Uint) return Uint;
+   pragma Inline (UI_Abs);
+   --  Returns abs function of universal integer
+
+   function UI_Add (Left : Uint; Right : Uint) return Uint;
+   function UI_Add (Left : Int;  Right : Uint) return Uint;
+   function UI_Add (Left : Uint; Right : Int)  return Uint;
+   --  Returns sum of two integer values
+
+   function UI_Decimal_Digits_Hi (U : Uint) return Nat;
+   --  Returns an estimate of the number of decimal digits required to
+   --  represent the absolute value of U. This estimate is correct or high,
+   --  i.e. it never returns a value that is too low. The accuracy of the
+   --  estimate affects only the effectiveness of comparison optimizations
+   --  in Urealp.
+
+   function UI_Decimal_Digits_Lo (U : Uint) return Nat;
+   --  Returns an estimate of the number of decimal digits required to
+   --  represent the absolute value of U. This estimate is correct or low,
+   --  i.e. it never returns a value that is too high. The accuracy of the
+   --  estimate affects only the effectiveness of comparison optimizations
+   --  in Urealp.
+
+   function UI_Div (Left : Uint; Right : Uint) return Uint;
+   function UI_Div (Left : Int;  Right : Uint) return Uint;
+   function UI_Div (Left : Uint; Right : Int)  return Uint;
+   --  Returns quotient of two integer values. Fatal error if Right = 0
+
+   function UI_Eq (Left : Uint; Right : Uint) return Boolean;
+   function UI_Eq (Left : Int;  Right : Uint) return Boolean;
+   function UI_Eq (Left : Uint; Right : Int)  return Boolean;
+   pragma Inline (UI_Eq);
+   --  Compares integer values for equality
+
+   function UI_Expon (Left : Uint; Right : Uint) return Uint;
+   function UI_Expon (Left : Int;  Right : Uint) return Uint;
+   function UI_Expon (Left : Uint; Right : Int)  return Uint;
+   function UI_Expon (Left : Int;  Right : Int)  return Uint;
+   --  Returns result of exponentiating two integer values.
+   --  Fatal error if Right is negative.
+
+   function UI_GCD (Uin, Vin : Uint) return Uint;
+   --  Computes GCD of input values. Assumes Uin >= Vin >= 0
+
+   function UI_Ge (Left : Uint; Right : Uint) return Boolean;
+   function UI_Ge (Left : Int;  Right : Uint) return Boolean;
+   function UI_Ge (Left : Uint; Right : Int)  return Boolean;
+   pragma Inline (UI_Ge);
+   --  Compares integer values for greater than or equal
+
+   function UI_Gt (Left : Uint; Right : Uint) return Boolean;
+   function UI_Gt (Left : Int;  Right : Uint) return Boolean;
+   function UI_Gt (Left : Uint; Right : Int)  return Boolean;
+   pragma Inline (UI_Gt);
+   --  Compares integer values for greater than
+
+   function UI_Is_In_Int_Range (Input : Uint) return Boolean;
+   pragma Inline (UI_Is_In_Int_Range);
+   --  Determines if universal integer is in Int range
+
+   function UI_Le (Left : Uint; Right : Uint) return Boolean;
+   function UI_Le (Left : Int;  Right : Uint) return Boolean;
+   function UI_Le (Left : Uint; Right : Int)  return Boolean;
+   pragma Inline (UI_Le);
+   --  Compares integer values for less than or equal
+
+   function UI_Lt (Left : Uint; Right : Uint) return Boolean;
+   function UI_Lt (Left : Int;  Right : Uint) return Boolean;
+   function UI_Lt (Left : Uint; Right : Int)  return Boolean;
+   --  Compares integer values for less than
+
+   function UI_Max (Left : Uint; Right : Uint) return Uint;
+   function UI_Max (Left : Int;  Right : Uint) return Uint;
+   function UI_Max (Left : Uint; Right : Int)  return Uint;
+   --  Returns maximum of two integer values
+
+   function UI_Min (Left : Uint; Right : Uint) return Uint;
+   function UI_Min (Left : Int;  Right : Uint) return Uint;
+   function UI_Min (Left : Uint; Right : Int)  return Uint;
+   --  Returns minimum of two integer values
+
+   function UI_Mod (Left : Uint; Right : Uint) return Uint;
+   function UI_Mod (Left : Int;  Right : Uint) return Uint;
+   function UI_Mod (Left : Uint; Right : Int)  return Uint;
+   pragma Inline (UI_Mod);
+   --  Returns mod function of two integer values
+
+   function UI_Mul (Left : Uint; Right : Uint) return Uint;
+   function UI_Mul (Left : Int;  Right : Uint) return Uint;
+   function UI_Mul (Left : Uint; Right : Int)  return Uint;
+   --  Returns product of two integer values
+
+   function UI_Ne (Left : Uint; Right : Uint) return Boolean;
+   function UI_Ne (Left : Int;  Right : Uint) return Boolean;
+   function UI_Ne (Left : Uint; Right : Int)  return Boolean;
+   pragma Inline (UI_Ne);
+   --  Compares integer values for inequality
+
+   function UI_Negate (Right : Uint) return Uint;
+   pragma Inline (UI_Negate);
+   --  Returns negative of universal integer
+
+   function UI_Rem (Left : Uint; Right : Uint) return Uint;
+   function UI_Rem (Left : Int;  Right : Uint) return Uint;
+   function UI_Rem (Left : Uint; Right : Int)  return Uint;
+   --  Returns rem of two integer values
+
+   function UI_Sub (Left : Uint; Right : Uint) return Uint;
+   function UI_Sub (Left : Int;  Right : Uint) return Uint;
+   function UI_Sub (Left : Uint; Right : Int)  return Uint;
+   pragma Inline (UI_Sub);
+   --  Returns difference of two integer values
+
+   function UI_Modular_Exponentiation
+     (B      : Uint;
+      E      : Uint;
+      Modulo : Uint) return Uint;
+   --  Efficiently compute (B**E) rem Modulo
+
+   function UI_Modular_Inverse (N : Uint; Modulo : Uint) return Uint;
+   --  Compute the multiplicative inverse of N in modular arithmetics with the
+   --  given Modulo (uses Euclid's algorithm). Note: the call is considered
+   --  to be erroneous (and the behavior is undefined) if n is not invertible.
+
+   function UI_From_Int (Input : Int) return Uint;
+   --  Converts Int value to universal integer form
+
+   function UI_From_CC (Input : Char_Code) return Uint;
+   --  Converts Char_Code value to universal integer form
+
+   function UI_To_Int (Input : Uint) return Int;
+   --  Converts universal integer value to Int. Constraint_Error if value is
+   --  not in appropriate range.
+
+   function UI_To_CC (Input : Uint) return Char_Code;
+   --  Converts universal integer value to Char_Code. Constraint_Error if value
+   --  is not in Char_Code range.
+
+   function Num_Bits (Input : Uint) return Nat;
+   --  Approximate number of binary bits in given universal integer. This
+   --  function is used for capacity checks, and it can be one bit off
+   --  without affecting its usage.
+
+   function Vector_To_Uint
+     (In_Vec   : UI_Vector;
+      Negative : Boolean) return Uint;
+   --  Functions that calculate values in UI_Vectors, call this function to
+   --  create and return the Uint value. In_Vec contains the multiple precision
+   --  (Base) representation of a non-negative value. Leading zeroes are
+   --  permitted. Negative is set if the desired result is the negative of the
+   --  given value. The result will be either the appropriate directly
+   --  represented value, or a table entry in the proper canonical format is
+   --  created and returned.
+   --
+   --  Note that Init_Operand puts a signed value in the result vector, but
+   --  Vector_To_Uint is always presented with a non-negative value. The
+   --  processing of signs is something that is done by the caller before
+   --  calling Vector_To_Uint.
+
+   ---------------------
+   -- Output Routines --
+   ---------------------
+
+   type UI_Format is (Hex, Decimal, Auto);
+   --  Used to determine whether UI_Image/UI_Write output is in hexadecimal
+   --  or decimal format. Auto, the default setting, lets the routine make a
+   --  decision based on the value.
+
+   UI_Image_Max    : constant := 48; -- Enough for a 128-bit number
+   UI_Image_Buffer : String (1 .. UI_Image_Max);
+   UI_Image_Length : Natural;
+   --  Buffer used for UI_Image as described below
+
+   procedure UI_Image (Input : Uint; Format : UI_Format := Auto);
+   --  Places a representation of Uint, consisting of a possible minus sign,
+   --  followed by the value in UI_Image_Buffer. The form of the value is an
+   --  integer literal in either decimal (no base) or hexadecimal (base 16)
+   --  format. If Hex is True on entry, then hex mode is forced, otherwise
+   --  UI_Image makes a guess at which output format is more convenient. The
+   --  value must fit in UI_Image_Buffer. The actual length of the result is
+   --  returned in UI_Image_Length. If necessary to meet this requirement, the
+   --  result is an approximation of the proper value, using an exponential
+   --  format. The image of No_Uint is output as a single question mark.
+
+   function UI_Image (Input : Uint; Format : UI_Format := Auto) return String;
+   --  Functional form, in which the result is returned as a string. This call
+   --  also leaves the result in UI_Image_Buffer/Length as described above.
+
+   procedure UI_Write (Input : Uint; Format : UI_Format := Auto);
+   --  Writes a representation of Uint, consisting of a possible minus sign,
+   --  followed by the value to the output file. The form of the value is an
+   --  integer literal in either decimal (no base) or hexadecimal (base 16)
+   --  format as appropriate. UI_Format shows which format to use. Auto, the
+   --  default, asks UI_Write to make a guess at which output format will be
+   --  more convenient to read.
+
+   procedure pid (Input : Uint);
+   pragma Export (Ada, pid);
+   --  Writes representation of Uint in decimal with a terminating line
+   --  return. This is intended for use from the debugger.
+
+   procedure pih (Input : Uint);
+   pragma Export (Ada, pih);
+   --  Writes representation of Uint in hex with a terminating line return.
+   --  This is intended for use from the debugger.
+
+   ------------------------
+   -- Operator Renamings --
+   ------------------------
+
+   function "+" (Left : Uint; Right : Uint) return Uint renames UI_Add;
+   function "+" (Left : Int;  Right : Uint) return Uint renames UI_Add;
+   function "+" (Left : Uint; Right : Int)  return Uint renames UI_Add;
+
+   function "/" (Left : Uint; Right : Uint) return Uint renames UI_Div;
+   function "/" (Left : Int;  Right : Uint) return Uint renames UI_Div;
+   function "/" (Left : Uint; Right : Int)  return Uint renames UI_Div;
+
+   function "*" (Left : Uint; Right : Uint) return Uint renames UI_Mul;
+   function "*" (Left : Int;  Right : Uint) return Uint renames UI_Mul;
+   function "*" (Left : Uint; Right : Int)  return Uint renames UI_Mul;
+
+   function "-" (Left : Uint; Right : Uint) return Uint renames UI_Sub;
+   function "-" (Left : Int;  Right : Uint) return Uint renames UI_Sub;
+   function "-" (Left : Uint; Right : Int)  return Uint renames UI_Sub;
+
+   function "**"  (Left : Uint; Right : Uint) return Uint renames UI_Expon;
+   function "**"  (Left : Uint; Right : Int)  return Uint renames UI_Expon;
+   function "**"  (Left : Int;  Right : Uint) return Uint renames UI_Expon;
+   function "**"  (Left : Int;  Right : Int)  return Uint renames UI_Expon;
+
+   function "abs" (Real : Uint) return Uint renames UI_Abs;
+
+   function "mod" (Left : Uint; Right : Uint) return Uint renames UI_Mod;
+   function "mod" (Left : Int;  Right : Uint) return Uint renames UI_Mod;
+   function "mod" (Left : Uint; Right : Int)  return Uint renames UI_Mod;
+
+   function "rem" (Left : Uint; Right : Uint) return Uint renames UI_Rem;
+   function "rem" (Left : Int;  Right : Uint) return Uint renames UI_Rem;
+   function "rem" (Left : Uint; Right : Int)  return Uint renames UI_Rem;
+
+   function "-"   (Real : Uint) return Uint renames UI_Negate;
+
+   function "="   (Left : Uint; Right : Uint) return Boolean renames UI_Eq;
+   function "="   (Left : Int;  Right : Uint) return Boolean renames UI_Eq;
+   function "="   (Left : Uint; Right : Int)  return Boolean renames UI_Eq;
+
+   function ">="  (Left : Uint; Right : Uint) return Boolean renames UI_Ge;
+   function ">="  (Left : Int;  Right : Uint) return Boolean renames UI_Ge;
+   function ">="  (Left : Uint; Right : Int)  return Boolean renames UI_Ge;
+
+   function ">"   (Left : Uint; Right : Uint) return Boolean renames UI_Gt;
+   function ">"   (Left : Int;  Right : Uint) return Boolean renames UI_Gt;
+   function ">"   (Left : Uint; Right : Int)  return Boolean renames UI_Gt;
+
+   function "<="  (Left : Uint; Right : Uint) return Boolean renames UI_Le;
+   function "<="  (Left : Int;  Right : Uint) return Boolean renames UI_Le;
+   function "<="  (Left : Uint; Right : Int)  return Boolean renames UI_Le;
+
+   function "<"   (Left : Uint; Right : Uint) return Boolean renames UI_Lt;
+   function "<"   (Left : Int;  Right : Uint) return Boolean renames UI_Lt;
+   function "<"   (Left : Uint; Right : Int)  return Boolean renames UI_Lt;
+
+   -----------------------------
+   -- Mark/Release Processing --
+   -----------------------------
+
+   --  The space used by Uint data is not automatically reclaimed. However, a
+   --  mark-release regime is implemented which allows storage to be released
+   --  back to a previously noted mark. This is used for example when doing
+   --  comparisons, where only intermediate results get stored that do not
+   --  need to be saved for future use.
+
+   type Save_Mark is private;
+
+   function Mark return Save_Mark;
+   --  Note mark point for future release
+
+   procedure Release (M : Save_Mark);
+   --  Release storage allocated since mark was noted
+
+   procedure Release_And_Save (M : Save_Mark; UI : in out Uint);
+   --  Like Release, except that the given Uint value (which is typically among
+   --  the data being released) is recopied after the release, so that it is
+   --  the most recent item, and UI is updated to point to its copied location.
+
+   procedure Release_And_Save (M : Save_Mark; UI1, UI2 : in out Uint);
+   --  Like Release, except that the given Uint values (which are typically
+   --  among the data being released) are recopied after the release, so that
+   --  they are the most recent items, and UI1 and UI2 are updated if necessary
+   --  to point to the copied locations. This routine is careful to do things
+   --  in the right order, so that the values do not clobber one another.
+
+   -----------------------------------
+   -- Representation of Uint Values --
+   -----------------------------------
+
+private
+
+   type Uint is new Int range Uint_Low_Bound .. Uint_High_Bound;
+   for Uint'Size use 32;
+
+   No_Uint : constant Uint := Uint (Uint_Low_Bound);
+
+   --  Uint values are represented as multiple precision integers stored in
+   --  a multi-digit format using Base as the base. This value is chosen so
+   --  that the product Base*Base is within the range of allowed Int values.
+
+   --  Base is defined to allow efficient execution of the primitive operations
+   --  (a0, b0, c0) defined in the section "The Classical Algorithms"
+   --  (sec. 4.3.1) of Donald Knuth's "The Art of Computer Programming",
+   --  Vol. 2. These algorithms are used in this package. In particular,
+   --  the product of two single digits in this base fits in a 32-bit integer.
+
+   Base_Bits : constant := 15;
+   --  Number of bits in base value
+
+   Base : constant Int := 2**Base_Bits;
+
+   --  Values in the range -(Base-1) .. Max_Direct are encoded directly as
+   --  Uint values by adding a bias value. The value of Max_Direct is chosen
+   --  so that a directly represented number always fits in two digits when
+   --  represented in base format.
+
+   Min_Direct : constant Int := -(Base - 1);
+   Max_Direct : constant Int := (Base - 1) * (Base - 1);
+
+   --  The following values define the bias used to store Uint values which
+   --  are in this range, as well as the biased values for the first and last
+   --  values in this range. We use a new derived type for these constants to
+   --  avoid accidental use of Uint arithmetic on these values, which is never
+   --  correct.
+
+   type Ctrl is new Int;
+
+   Uint_Direct_Bias  : constant Ctrl := Ctrl (Uint_Low_Bound) + Ctrl (Base);
+   Uint_Direct_First : constant Ctrl := Uint_Direct_Bias + Ctrl (Min_Direct);
+   Uint_Direct_Last  : constant Ctrl := Uint_Direct_Bias + Ctrl (Max_Direct);
+
+   Uint_0   : constant Uint := Uint (Uint_Direct_Bias + 0);
+   Uint_1   : constant Uint := Uint (Uint_Direct_Bias + 1);
+   Uint_2   : constant Uint := Uint (Uint_Direct_Bias + 2);
+   Uint_3   : constant Uint := Uint (Uint_Direct_Bias + 3);
+   Uint_4   : constant Uint := Uint (Uint_Direct_Bias + 4);
+   Uint_5   : constant Uint := Uint (Uint_Direct_Bias + 5);
+   Uint_6   : constant Uint := Uint (Uint_Direct_Bias + 6);
+   Uint_7   : constant Uint := Uint (Uint_Direct_Bias + 7);
+   Uint_8   : constant Uint := Uint (Uint_Direct_Bias + 8);
+   Uint_9   : constant Uint := Uint (Uint_Direct_Bias + 9);
+   Uint_10  : constant Uint := Uint (Uint_Direct_Bias + 10);
+   Uint_11  : constant Uint := Uint (Uint_Direct_Bias + 11);
+   Uint_12  : constant Uint := Uint (Uint_Direct_Bias + 12);
+   Uint_13  : constant Uint := Uint (Uint_Direct_Bias + 13);
+   Uint_14  : constant Uint := Uint (Uint_Direct_Bias + 14);
+   Uint_15  : constant Uint := Uint (Uint_Direct_Bias + 15);
+   Uint_16  : constant Uint := Uint (Uint_Direct_Bias + 16);
+   Uint_24  : constant Uint := Uint (Uint_Direct_Bias + 24);
+   Uint_32  : constant Uint := Uint (Uint_Direct_Bias + 32);
+   Uint_63  : constant Uint := Uint (Uint_Direct_Bias + 63);
+   Uint_64  : constant Uint := Uint (Uint_Direct_Bias + 64);
+   Uint_80  : constant Uint := Uint (Uint_Direct_Bias + 80);
+   Uint_128 : constant Uint := Uint (Uint_Direct_Bias + 128);
+
+   Uint_Minus_1   : constant Uint := Uint (Uint_Direct_Bias - 1);
+   Uint_Minus_2   : constant Uint := Uint (Uint_Direct_Bias - 2);
+   Uint_Minus_3   : constant Uint := Uint (Uint_Direct_Bias - 3);
+   Uint_Minus_4   : constant Uint := Uint (Uint_Direct_Bias - 4);
+   Uint_Minus_5   : constant Uint := Uint (Uint_Direct_Bias - 5);
+   Uint_Minus_6   : constant Uint := Uint (Uint_Direct_Bias - 6);
+   Uint_Minus_7   : constant Uint := Uint (Uint_Direct_Bias - 7);
+   Uint_Minus_8   : constant Uint := Uint (Uint_Direct_Bias - 8);
+   Uint_Minus_9   : constant Uint := Uint (Uint_Direct_Bias - 9);
+   Uint_Minus_12  : constant Uint := Uint (Uint_Direct_Bias - 12);
+   Uint_Minus_36  : constant Uint := Uint (Uint_Direct_Bias - 36);
+   Uint_Minus_63  : constant Uint := Uint (Uint_Direct_Bias - 63);
+   Uint_Minus_80  : constant Uint := Uint (Uint_Direct_Bias - 80);
+   Uint_Minus_128 : constant Uint := Uint (Uint_Direct_Bias - 128);
+
+   Uint_Max_Simple_Mul : constant := Uint_Direct_Bias + 2**15;
+   --  If two values are directly represented and less than or equal to this
+   --  value, then we know the product fits in a 32-bit integer. This allows
+   --  UI_Mul to efficiently compute the product in this case.
+
+   type Save_Mark is record
+      Save_Uint   : Uint;
+      Save_Udigit : Int;
+   end record;
+
+   --  Values outside the range that is represented directly are stored using
+   --  two tables. The secondary table Udigits contains sequences of Int values
+   --  consisting of the digits of the number in a radix Base system. The
+   --  digits are stored from most significant to least significant with the
+   --  first digit only carrying the sign.
+
+   --  There is one entry in the primary Uints table for each distinct Uint
+   --  value. This table entry contains the length (number of digits) and
+   --  a starting offset of the value in the Udigits table.
+
+   Uint_First_Entry : constant Uint := Uint (Uint_Table_Start);
+
+   --  Some subprograms defined in this package manipulate the Udigits table
+   --  directly, while for others it is more convenient to work with locally
+   --  defined arrays of the digits of the Universal Integers. The type
+   --  UI_Vector is defined for this purpose and some internal subprograms
+   --  used for converting from one to the other are defined.
+
+   type Uint_Entry is record
+      Length : Pos;
+      --  Length of entry in Udigits table in digits (i.e. in words)
+
+      Loc : Int;
+      --  Starting location in Udigits table of this Uint value
+   end record;
+
+   package Uints is new Table.Table (
+     Table_Component_Type => Uint_Entry,
+     Table_Index_Type     => Uint'Base,
+     Table_Low_Bound      => Uint_First_Entry,
+     Table_Initial        => Alloc.Uints_Initial,
+     Table_Increment      => Alloc.Uints_Increment,
+     Table_Name           => "Uints");
+
+   package Udigits is new Table.Table (
+     Table_Component_Type => Int,
+     Table_Index_Type     => Int,
+     Table_Low_Bound      => 0,
+     Table_Initial        => Alloc.Udigits_Initial,
+     Table_Increment      => Alloc.Udigits_Increment,
+     Table_Name           => "Udigits");
+
+   --  Note: the reason these tables are defined here in the private part of
+   --  the spec, rather than in the body, is that they are referenced directly
+   --  by gigi.
+
+end Uintp;