gcc/ada/uintp.ads

   1 ------------------------------------------------------------------------------
   2 --                                                                          --
   3 --                         GNAT COMPILER COMPONENTS                         --
   4 --                                                                          --
   5 --                                U I N T P                                 --
   6 --                                                                          --
   7 --                                 S p e c                                  --
   8 --                                                                          --
   9 --          Copyright (C) 1992-2008, Free Software Foundation, Inc.         --
  10 --                                                                          --
  11 -- GNAT is free software;  you can  redistribute it  and/or modify it under --
  12 -- terms of the  GNU General Public License as published  by the Free Soft- --
  13 -- ware  Foundation;  either version 2,  or (at your option) any later ver- --
  14 -- sion.  GNAT is distributed in the hope that it will be useful, but WITH- --
  15 -- OUT ANY WARRANTY;  without even the  implied warranty of MERCHANTABILITY --
  16 -- or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License --
  17 -- for  more details.  You should have  received  a copy of the GNU General --
  18 -- Public License  distributed with GNAT;  see file COPYING.  If not, write --
  19 -- to  the  Free Software Foundation,  51  Franklin  Street,  Fifth  Floor, --
  20 -- Boston, MA 02110-1301, USA.                                              --
  21 --                                                                          --
  22 -- As a special exception,  if other files  instantiate  generics from this --
  23 -- unit, or you link  this unit with other files  to produce an executable, --
  24 -- this  unit  does not  by itself cause  the resulting  executable  to  be --
  25 -- covered  by the  GNU  General  Public  License.  This exception does not --
  26 -- however invalidate  any other reasons why  the executable file  might be --
  27 -- covered by the  GNU Public License.                                      --
  28 --                                                                          --
  29 -- GNAT was originally developed  by the GNAT team at  New York University. --
  30 -- Extensive contributions were provided by Ada Core Technologies Inc.      --
  31 --                                                                          --
  32 ------------------------------------------------------------------------------
  33
  34 --  Support for universal integer arithmetic
  35
  36 --  WARNING: There is a C version of this package. Any changes to this
  37 --  source file must be properly reflected in the C header file sinfo.h
  38
  39 with Alloc;
  40 with Table;
  41 pragma Elaborate_All (Table);
  42 with Types; use Types;
  43
  44 package Uintp is
  45
  46    -------------------------------------------------
  47    -- Basic Types and Constants for Uintp Package --
  48    -------------------------------------------------
  49
  50    type Uint is private;
  51    --  The basic universal integer type
  52
  53    No_Uint : constant Uint;
  54    --  A constant value indicating a missing or unset Uint value
  55
  56    Uint_0   : constant Uint;
  57    Uint_1   : constant Uint;
  58    Uint_2   : constant Uint;
  59    Uint_3   : constant Uint;
  60    Uint_4   : constant Uint;
  61    Uint_5   : constant Uint;
  62    Uint_6   : constant Uint;
  63    Uint_7   : constant Uint;
  64    Uint_8   : constant Uint;
  65    Uint_9   : constant Uint;
  66    Uint_10  : constant Uint;
  67    Uint_11  : constant Uint;
  68    Uint_12  : constant Uint;
  69    Uint_13  : constant Uint;
  70    Uint_14  : constant Uint;
  71    Uint_15  : constant Uint;
  72    Uint_16  : constant Uint;
  73    Uint_24  : constant Uint;
  74    Uint_32  : constant Uint;
  75    Uint_63  : constant Uint;
  76    Uint_64  : constant Uint;
  77    Uint_80  : constant Uint;
  78    Uint_128 : constant Uint;
  79
  80    Uint_Minus_1   : constant Uint;
  81    Uint_Minus_2   : constant Uint;
  82    Uint_Minus_3   : constant Uint;
  83    Uint_Minus_4   : constant Uint;
  84    Uint_Minus_5   : constant Uint;
  85    Uint_Minus_6   : constant Uint;
  86    Uint_Minus_7   : constant Uint;
  87    Uint_Minus_8   : constant Uint;
  88    Uint_Minus_9   : constant Uint;
  89    Uint_Minus_12  : constant Uint;
  90    Uint_Minus_36  : constant Uint;
  91    Uint_Minus_63  : constant Uint;
  92    Uint_Minus_80  : constant Uint;
  93    Uint_Minus_128 : constant Uint;
  94
  95    -----------------
  96    -- Subprograms --
  97    -----------------
  98
  99    procedure Initialize;
 100    --  Initialize Uint tables. Note that Initialize must not be called if
 101    --  Tree_Read is used. Note also that there is no lock routine in this
 102    --  unit, these are among the few tables that can be expanded during
 103    --  gigi processing.
 104
 105    procedure Tree_Read;
 106    --  Initializes internal tables from current tree file using the relevant
 107    --  Table.Tree_Read routines. Note that Initialize should not be called if
 108    --  Tree_Read is used. Tree_Read includes all necessary initialization.
 109
 110    procedure Tree_Write;
 111    --  Writes out internal tables to current tree file using the relevant
 112    --  Table.Tree_Write routines.
 113
 114    function UI_Abs (Right : Uint) return Uint;
 115    pragma Inline (UI_Abs);
 116    --  Returns abs function of universal integer
 117
 118    function UI_Add (Left : Uint; Right : Uint) return Uint;
 119    function UI_Add (Left : Int;  Right : Uint) return Uint;
 120    function UI_Add (Left : Uint; Right : Int)  return Uint;
 121    --  Returns sum of two integer values
 122
 123    function UI_Decimal_Digits_Hi (U : Uint) return Nat;
 124    --  Returns an estimate of the number of decimal digits required to
 125    --  represent the absolute value of U. This estimate is correct or high,
 126    --  i.e. it never returns a value that is too low. The accuracy of the
 127    --  estimate affects only the effectiveness of comparison optimizations
 128    --  in Urealp.
 129
 130    function UI_Decimal_Digits_Lo (U : Uint) return Nat;
 131    --  Returns an estimate of the number of decimal digits required to
 132    --  represent the absolute value of U. This estimate is correct or low,
 133    --  i.e. it never returns a value that is too high. The accuracy of the
 134    --  estimate affects only the effectiveness of comparison optimizations
 135    --  in Urealp.
 136
 137    function UI_Div (Left : Uint; Right : Uint) return Uint;
 138    function UI_Div (Left : Int;  Right : Uint) return Uint;
 139    function UI_Div (Left : Uint; Right : Int)  return Uint;
 140    --  Returns quotient of two integer values. Fatal error if Right = 0
 141
 142    function UI_Eq (Left : Uint; Right : Uint) return Boolean;
 143    function UI_Eq (Left : Int;  Right : Uint) return Boolean;
 144    function UI_Eq (Left : Uint; Right : Int)  return Boolean;
 145    pragma Inline (UI_Eq);
 146    --  Compares integer values for equality
 147
 148    function UI_Expon (Left : Uint; Right : Uint) return Uint;
 149    function UI_Expon (Left : Int;  Right : Uint) return Uint;
 150    function UI_Expon (Left : Uint; Right : Int)  return Uint;
 151    function UI_Expon (Left : Int;  Right : Int)  return Uint;
 152    --  Returns result of exponentiating two integer values.
 153    --  Fatal error if Right is negative.
 154
 155    function UI_GCD (Uin, Vin : Uint) return Uint;
 156    --  Computes GCD of input values. Assumes Uin >= Vin >= 0
 157
 158    function UI_Ge (Left : Uint; Right : Uint) return Boolean;
 159    function UI_Ge (Left : Int;  Right : Uint) return Boolean;
 160    function UI_Ge (Left : Uint; Right : Int)  return Boolean;
 161    pragma Inline (UI_Ge);
 162    --  Compares integer values for greater than or equal
 163
 164    function UI_Gt (Left : Uint; Right : Uint) return Boolean;
 165    function UI_Gt (Left : Int;  Right : Uint) return Boolean;
 166    function UI_Gt (Left : Uint; Right : Int)  return Boolean;
 167    pragma Inline (UI_Gt);
 168    --  Compares integer values for greater than
 169
 170    function UI_Is_In_Int_Range (Input : Uint) return Boolean;
 171    pragma Inline (UI_Is_In_Int_Range);
 172    --  Determines if universal integer is in Int range
 173
 174    function UI_Le (Left : Uint; Right : Uint) return Boolean;
 175    function UI_Le (Left : Int;  Right : Uint) return Boolean;
 176    function UI_Le (Left : Uint; Right : Int)  return Boolean;
 177    pragma Inline (UI_Le);
 178    --  Compares integer values for less than or equal
 179
 180    function UI_Lt (Left : Uint; Right : Uint) return Boolean;
 181    function UI_Lt (Left : Int;  Right : Uint) return Boolean;
 182    function UI_Lt (Left : Uint; Right : Int)  return Boolean;
 183    --  Compares integer values for less than
 184
 185    function UI_Max (Left : Uint; Right : Uint) return Uint;
 186    function UI_Max (Left : Int;  Right : Uint) return Uint;
 187    function UI_Max (Left : Uint; Right : Int)  return Uint;
 188    --  Returns maximum of two integer values
 189
 190    function UI_Min (Left : Uint; Right : Uint) return Uint;
 191    function UI_Min (Left : Int;  Right : Uint) return Uint;
 192    function UI_Min (Left : Uint; Right : Int)  return Uint;
 193    --  Returns minimum of two integer values
 194
 195    function UI_Mod (Left : Uint; Right : Uint) return Uint;
 196    function UI_Mod (Left : Int;  Right : Uint) return Uint;
 197    function UI_Mod (Left : Uint; Right : Int)  return Uint;
 198    pragma Inline (UI_Mod);
 199    --  Returns mod function of two integer values
 200
 201    function UI_Mul (Left : Uint; Right : Uint) return Uint;
 202    function UI_Mul (Left : Int;  Right : Uint) return Uint;
 203    function UI_Mul (Left : Uint; Right : Int)  return Uint;
 204    --  Returns product of two integer values
 205
 206    function UI_Ne (Left : Uint; Right : Uint) return Boolean;
 207    function UI_Ne (Left : Int;  Right : Uint) return Boolean;
 208    function UI_Ne (Left : Uint; Right : Int)  return Boolean;
 209    pragma Inline (UI_Ne);
 210    --  Compares integer values for inequality
 211
 212    function UI_Negate (Right : Uint) return Uint;
 213    pragma Inline (UI_Negate);
 214    --  Returns negative of universal integer
 215
 216    function UI_Rem (Left : Uint; Right : Uint) return Uint;
 217    function UI_Rem (Left : Int;  Right : Uint) return Uint;
 218    function UI_Rem (Left : Uint; Right : Int)  return Uint;
 219    --  Returns rem of two integer values
 220
 221    function UI_Sub (Left : Uint; Right : Uint) return Uint;
 222    function UI_Sub (Left : Int;  Right : Uint) return Uint;
 223    function UI_Sub (Left : Uint; Right : Int)  return Uint;
 224    pragma Inline (UI_Sub);
 225    --  Returns difference of two integer values
 226
 227    function UI_Modular_Exponentiation
 228      (B      : Uint;
 229       E      : Uint;
 230       Modulo : Uint) return Uint;
 231    --  Efficiently compute (B ** E) rem Modulo
 232
 233    function UI_Modular_Inverse (N : Uint; Modulo : Uint) return Uint;
 234    --  Compute the multiplicative inverse of N in modular arithmetics with the
 235    --  given Modulo (uses Euclid's algorithm). Note: the call is considered
 236    --  to be erroneous (and the behavior is undefined) if n is not invertible.
 237
 238    function UI_From_Dint (Input : Dint) return Uint;
 239    --  Converts Dint value to universal integer form
 240
 241    function UI_From_Int (Input : Int) return Uint;
 242    --  Converts Int value to universal integer form
 243
 244    function UI_From_CC (Input : Char_Code) return Uint;
 245    --  Converts Char_Code value to universal integer form
 246
 247    function UI_To_Int (Input : Uint) return Int;
 248    --  Converts universal integer value to Int. Fatal error if value is not in
 249    --  appropriate range.
 250
 251    function UI_To_CC (Input : Uint) return Char_Code;
 252    --  Converts universal integer value to Char_Code. Fatal error if value is
 253    --  not in Char_Code range.
 254
 255    function Num_Bits (Input : Uint) return Nat;
 256    --  Approximate number of binary bits in given universal integer.
 257    --  This function is used for capacity checks, and it can be one
 258    --  bit off without affecting its usage.
 259
 260    ---------------------
 261    -- Output Routines --
 262    ---------------------
 263
 264    type UI_Format is (Hex, Decimal, Auto);
 265    --  Used to determine whether UI_Image/UI_Write output is in hexadecimal
 266    --  or decimal format. Auto, the default setting, lets the routine make
 267    --  a decision based on the value.
 268
 269    UI_Image_Max    : constant := 32;
 270    UI_Image_Buffer : String (1 .. UI_Image_Max);
 271    UI_Image_Length : Natural;
 272    --  Buffer used for UI_Image as described below
 273
 274    procedure UI_Image (Input : Uint; Format : UI_Format := Auto);
 275    --  Places a representation of Uint, consisting of a possible minus sign,
 276    --  followed by the value in UI_Image_Buffer. The form of the value is an
 277    --  integer literal in either decimal (no base) or hexadecimal (base 16)
 278    --  format. If Hex is True on entry, then hex mode is forced, otherwise
 279    --  UI_Image makes a guess at which output format is more convenient. The
 280    --  value must fit in UI_Image_Buffer. If necessary, the result is an
 281    --  approximation of the proper value, using an exponential format. The
 282    --  image of No_Uint is output as a single question mark.
 283
 284    procedure UI_Write (Input : Uint; Format : UI_Format := Auto);
 285    --  Writes a representation of Uint, consisting of a possible minus sign,
 286    --  followed by the value to the output file. The form of the value is an
 287    --  integer literal in either decimal (no base) or hexadecimal (base 16)
 288    --  format as appropriate. UI_Format shows which format to use. Auto,
 289    --  the default, asks UI_Write to make a guess at which output format
 290    --  will be more convenient to read.
 291
 292    procedure pid (Input : Uint);
 293    pragma Export (Ada, pid);
 294    --  Writes representation of Uint in decimal with a terminating line
 295    --  return. This is intended for use from the debugger.
 296
 297    procedure pih (Input : Uint);
 298    pragma Export (Ada, pih);
 299    --  Writes representation of Uint in hex with a terminating line return.
 300    --  This is intended for use from the debugger.
 301
 302    ------------------------
 303    -- Operator Renamings --
 304    ------------------------
 305
 306    function "+" (Left : Uint; Right : Uint) return Uint renames UI_Add;
 307    function "+" (Left : Int;  Right : Uint) return Uint renames UI_Add;
 308    function "+" (Left : Uint; Right : Int)  return Uint renames UI_Add;
 309
 310    function "/" (Left : Uint; Right : Uint) return Uint renames UI_Div;
 311    function "/" (Left : Int;  Right : Uint) return Uint renames UI_Div;
 312    function "/" (Left : Uint; Right : Int)  return Uint renames UI_Div;
 313
 314    function "*" (Left : Uint; Right : Uint) return Uint renames UI_Mul;
 315    function "*" (Left : Int;  Right : Uint) return Uint renames UI_Mul;
 316    function "*" (Left : Uint; Right : Int)  return Uint renames UI_Mul;
 317
 318    function "-" (Left : Uint; Right : Uint) return Uint renames UI_Sub;
 319    function "-" (Left : Int;  Right : Uint) return Uint renames UI_Sub;
 320    function "-" (Left : Uint; Right : Int)  return Uint renames UI_Sub;
 321
 322    function "**"  (Left : Uint; Right : Uint) return Uint renames UI_Expon;
 323    function "**"  (Left : Uint; Right : Int)  return Uint renames UI_Expon;
 324    function "**"  (Left : Int;  Right : Uint) return Uint renames UI_Expon;
 325    function "**"  (Left : Int;  Right : Int)  return Uint renames UI_Expon;
 326
 327    function "abs" (Real : Uint) return Uint renames UI_Abs;
 328
 329    function "mod" (Left : Uint; Right : Uint) return Uint renames UI_Mod;
 330    function "mod" (Left : Int;  Right : Uint) return Uint renames UI_Mod;
 331    function "mod" (Left : Uint; Right : Int)  return Uint renames UI_Mod;
 332
 333    function "rem" (Left : Uint; Right : Uint) return Uint renames UI_Rem;
 334    function "rem" (Left : Int;  Right : Uint) return Uint renames UI_Rem;
 335    function "rem" (Left : Uint; Right : Int)  return Uint renames UI_Rem;
 336
 337    function "-"   (Real : Uint) return Uint renames UI_Negate;
 338
 339    function "="   (Left : Uint; Right : Uint) return Boolean renames UI_Eq;
 340    function "="   (Left : Int;  Right : Uint) return Boolean renames UI_Eq;
 341    function "="   (Left : Uint; Right : Int)  return Boolean renames UI_Eq;
 342
 343    function ">="  (Left : Uint; Right : Uint) return Boolean renames UI_Ge;
 344    function ">="  (Left : Int;  Right : Uint) return Boolean renames UI_Ge;
 345    function ">="  (Left : Uint; Right : Int)  return Boolean renames UI_Ge;
 346
 347    function ">"   (Left : Uint; Right : Uint) return Boolean renames UI_Gt;
 348    function ">"   (Left : Int;  Right : Uint) return Boolean renames UI_Gt;
 349    function ">"   (Left : Uint; Right : Int)  return Boolean renames UI_Gt;
 350
 351    function "<="  (Left : Uint; Right : Uint) return Boolean renames UI_Le;
 352    function "<="  (Left : Int;  Right : Uint) return Boolean renames UI_Le;
 353    function "<="  (Left : Uint; Right : Int)  return Boolean renames UI_Le;
 354
 355    function "<"   (Left : Uint; Right : Uint) return Boolean renames UI_Lt;
 356    function "<"   (Left : Int;  Right : Uint) return Boolean renames UI_Lt;
 357    function "<"   (Left : Uint; Right : Int)  return Boolean renames UI_Lt;
 358
 359    -----------------------------
 360    -- Mark/Release Processing --
 361    -----------------------------
 362
 363    --  The space used by Uint data is not automatically reclaimed. However,
 364    --  a mark-release regime is implemented which allows storage to be
 365    --  released back to a previously noted mark. This is used for example
 366    --  when doing comparisons, where only intermediate results get stored
 367    --  that do not need to be saved for future use.
 368
 369    type Save_Mark is private;
 370
 371    function Mark return Save_Mark;
 372    --  Note mark point for future release
 373
 374    procedure Release (M : Save_Mark);
 375    --  Release storage allocated since mark was noted
 376
 377    procedure Release_And_Save (M : Save_Mark; UI : in out Uint);
 378    --  Like Release, except that the given Uint value (which is typically
 379    --  among the data being released) is recopied after the release, so
 380    --  that it is the most recent item, and UI is updated to point to
 381    --  its copied location.
 382
 383    procedure Release_And_Save (M : Save_Mark; UI1, UI2 : in out Uint);
 384    --  Like Release, except that the given Uint values (which are typically
 385    --  among the data being released) are recopied after the release, so
 386    --  that they are the most recent items, and UI1 and UI2 are updated if
 387    --  necessary to point to the copied locations. This routine is careful
 388    --  to do things in the right order, so that the values do not clobber
 389    --  one another.
 390
 391    -----------------------------------
 392    -- Representation of Uint Values --
 393    -----------------------------------
 394
 395 private
 396
 397    type Uint is new Int range Uint_Low_Bound .. Uint_High_Bound;
 398    for Uint'Size use 32;
 399
 400    No_Uint : constant Uint := Uint (Uint_Low_Bound);
 401
 402    --  Uint values are represented as multiple precision integers stored in
 403    --  a multi-digit format using Base as the base. This value is chosen so
 404    --  that the product Base*Base is within the range of allowed Int values.
 405
 406    --  Base is defined to allow efficient execution of the primitive operations
 407    --  (a0, b0, c0) defined in the section "The Classical Algorithms"
 408    --  (sec. 4.3.1) of Donald Knuth's "The Art of Computer  Programming",
 409    --  Vol. 2. These algorithms are used in this package.
 410
 411    Base_Bits : constant := 15;
 412    --  Number of bits in base value
 413
 414    Base : constant Int := 2 ** Base_Bits;
 415
 416    --  Values in the range -(Base+1) .. Max_Direct are encoded directly as
 417    --  Uint values by adding a bias value. The value of Max_Direct is chosen
 418    --  so that a directly represented number always fits in two digits when
 419    --  represented in base format.
 420
 421    Min_Direct : constant Int := -(Base - 1);
 422    Max_Direct : constant Int := (Base - 1) * (Base - 1);
 423
 424    --  The following values define the bias used to store Uint values which
 425    --  are in this range, as well as the biased values for the first and last
 426    --  values in this range. We use a new derived type for these constants to
 427    --  avoid accidental use of Uint arithmetic on these values, which is never
 428    --  correct.
 429
 430    type Ctrl is range Int'First .. Int'Last;
 431
 432    Uint_Direct_Bias  : constant Ctrl := Ctrl (Uint_Low_Bound) + Ctrl (Base);
 433    Uint_Direct_First : constant Ctrl := Uint_Direct_Bias + Ctrl (Min_Direct);
 434    Uint_Direct_Last  : constant Ctrl := Uint_Direct_Bias + Ctrl (Max_Direct);
 435
 436    Uint_0   : constant Uint := Uint (Uint_Direct_Bias);
 437    Uint_1   : constant Uint := Uint (Uint_Direct_Bias + 1);
 438    Uint_2   : constant Uint := Uint (Uint_Direct_Bias + 2);
 439    Uint_3   : constant Uint := Uint (Uint_Direct_Bias + 3);
 440    Uint_4   : constant Uint := Uint (Uint_Direct_Bias + 4);
 441    Uint_5   : constant Uint := Uint (Uint_Direct_Bias + 5);
 442    Uint_6   : constant Uint := Uint (Uint_Direct_Bias + 6);
 443    Uint_7   : constant Uint := Uint (Uint_Direct_Bias + 7);
 444    Uint_8   : constant Uint := Uint (Uint_Direct_Bias + 8);
 445    Uint_9   : constant Uint := Uint (Uint_Direct_Bias + 9);
 446    Uint_10  : constant Uint := Uint (Uint_Direct_Bias + 10);
 447    Uint_11  : constant Uint := Uint (Uint_Direct_Bias + 11);
 448    Uint_12  : constant Uint := Uint (Uint_Direct_Bias + 12);
 449    Uint_13  : constant Uint := Uint (Uint_Direct_Bias + 13);
 450    Uint_14  : constant Uint := Uint (Uint_Direct_Bias + 14);
 451    Uint_15  : constant Uint := Uint (Uint_Direct_Bias + 15);
 452    Uint_16  : constant Uint := Uint (Uint_Direct_Bias + 16);
 453    Uint_24  : constant Uint := Uint (Uint_Direct_Bias + 24);
 454    Uint_32  : constant Uint := Uint (Uint_Direct_Bias + 32);
 455    Uint_63  : constant Uint := Uint (Uint_Direct_Bias + 63);
 456    Uint_64  : constant Uint := Uint (Uint_Direct_Bias + 64);
 457    Uint_80  : constant Uint := Uint (Uint_Direct_Bias + 80);
 458    Uint_128 : constant Uint := Uint (Uint_Direct_Bias + 128);
 459
 460    Uint_Minus_1   : constant Uint := Uint (Uint_Direct_Bias - 1);
 461    Uint_Minus_2   : constant Uint := Uint (Uint_Direct_Bias - 2);
 462    Uint_Minus_3   : constant Uint := Uint (Uint_Direct_Bias - 3);
 463    Uint_Minus_4   : constant Uint := Uint (Uint_Direct_Bias - 4);
 464    Uint_Minus_5   : constant Uint := Uint (Uint_Direct_Bias - 5);
 465    Uint_Minus_6   : constant Uint := Uint (Uint_Direct_Bias - 6);
 466    Uint_Minus_7   : constant Uint := Uint (Uint_Direct_Bias - 7);
 467    Uint_Minus_8   : constant Uint := Uint (Uint_Direct_Bias - 8);
 468    Uint_Minus_9   : constant Uint := Uint (Uint_Direct_Bias - 9);
 469    Uint_Minus_12  : constant Uint := Uint (Uint_Direct_Bias - 12);
 470    Uint_Minus_36  : constant Uint := Uint (Uint_Direct_Bias - 36);
 471    Uint_Minus_63  : constant Uint := Uint (Uint_Direct_Bias - 63);
 472    Uint_Minus_80  : constant Uint := Uint (Uint_Direct_Bias - 80);
 473    Uint_Minus_128 : constant Uint := Uint (Uint_Direct_Bias - 128);
 474
 475    type Save_Mark is record
 476       Save_Uint   : Uint;
 477       Save_Udigit : Int;
 478    end record;
 479
 480    --  Values outside the range that is represented directly are stored using
 481    --  two tables. The secondary table Udigits contains sequences of Int values
 482    --  consisting of the digits of the number in a radix Base system. The
 483    --  digits are stored from most significant to least significant with the
 484    --  first digit only carrying the sign.
 485
 486    --  There is one entry in the primary Uints table for each distinct Uint
 487    --  value. This table entry contains the length (number of digits) and
 488    --  a starting offset of the value in the Udigits table.
 489
 490    Uint_First_Entry : constant Uint := Uint (Uint_Table_Start);
 491
 492    --  Some subprograms defined in this package manipulate the Udigits table
 493    --  directly, while for others it is more convenient to work with locally
 494    --  defined arrays of the digits of the Universal Integers. The type
 495    --  UI_Vector is defined for this purpose and some internal subprograms
 496    --  used for converting from one to the other are defined.
 497
 498    type UI_Vector is array (Pos range <>) of Int;
 499    --  Vector containing the integer values of a Uint value
 500
 501    --  Note: An earlier version of this package used pointers of arrays
 502    --  of Ints (dynamically allocated) for the Uint type. The change
 503    --  leads to a few less natural idioms used throughout this code, but
 504    --  eliminates all uses of the heap except for the table package itself.
 505    --  For example, Uint parameters are often converted to UI_Vectors for
 506    --  internal manipulation. This is done by creating the local UI_Vector
 507    --  using the function N_Digits on the Uint to find the size needed for
 508    --  the vector, and then calling Init_Operand to copy the values out
 509    --  of the table into the vector.
 510
 511    type Uint_Entry is record
 512       Length : Pos;
 513       --  Length of entry in Udigits table in digits (i.e. in words)
 514
 515       Loc : Int;
 516       --  Starting location in Udigits table of this Uint value
 517    end record;
 518
 519    package Uints is new Table.Table (
 520      Table_Component_Type => Uint_Entry,
 521      Table_Index_Type     => Uint'Base,
 522      Table_Low_Bound      => Uint_First_Entry,
 523      Table_Initial        => Alloc.Uints_Initial,
 524      Table_Increment      => Alloc.Uints_Increment,
 525      Table_Name           => "Uints");
 526
 527    package Udigits is new Table.Table (
 528      Table_Component_Type => Int,
 529      Table_Index_Type     => Int,
 530      Table_Low_Bound      => 0,
 531      Table_Initial        => Alloc.Udigits_Initial,
 532      Table_Increment      => Alloc.Udigits_Increment,
 533      Table_Name           => "Udigits");
 534
 535    --  Note: the reason these tables are defined here in the private part of
 536    --  the spec, rather than in the body, is that they are referenced directly
 537    --  by gigi.
 538
 539 end Uintp;