gcc/ada/uintp.adb

   1 ------------------------------------------------------------------------------
   2 --                                                                          --
   3 --                         GNAT COMPILER COMPONENTS                         --
   4 --                                                                          --
   5 --                                U I N T P                                 --
   6 --                                                                          --
   7 --                                 B o d y                                  --
   8 --                                                                          --
   9 --          Copyright (C) 1992-2009, 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 3,  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.                                     --
  17 --                                                                          --
  18 -- As a special exception under Section 7 of GPL version 3, you are granted --
  19 -- additional permissions described in the GCC Runtime Library Exception,   --
  20 -- version 3.1, as published by the Free Software Foundation.               --
  21 --                                                                          --
  22 -- You should have received a copy of the GNU General Public License and    --
  23 -- a copy of the GCC Runtime Library Exception along with this program;     --
  24 -- see the files COPYING3 and COPYING.RUNTIME respectively.  If not, see    --
  25 -- <http://www.gnu.org/licenses/>.                                          --
  26 --                                                                          --
  27 -- GNAT was originally developed  by the GNAT team at  New York University. --
  28 -- Extensive contributions were provided by Ada Core Technologies Inc.      --
  29 --                                                                          --
  30 ------------------------------------------------------------------------------
  31
  32 with Output;  use Output;
  33 with Tree_IO; use Tree_IO;
  34
  35 with GNAT.HTable; use GNAT.HTable;
  36
  37 package body Uintp is
  38
  39    ------------------------
  40    -- Local Declarations --
  41    ------------------------
  42
  43    Uint_Int_First : Uint := Uint_0;
  44    --  Uint value containing Int'First value, set by Initialize. The initial
  45    --  value of Uint_0 is used for an assertion check that ensures that this
  46    --  value is not used before it is initialized. This value is used in the
  47    --  UI_Is_In_Int_Range predicate, and it is right that this is a host value,
  48    --  since the issue is host representation of integer values.
  49
  50    Uint_Int_Last : Uint;
  51    --  Uint value containing Int'Last value set by Initialize
  52
  53    UI_Power_2 : array (Int range 0 .. 64) of Uint;
  54    --  This table is used to memoize exponentiations by powers of 2. The Nth
  55    --  entry, if set, contains the Uint value 2 ** N. Initially UI_Power_2_Set
  56    --  is zero and only the 0'th entry is set, the invariant being that all
  57    --  entries in the range 0 .. UI_Power_2_Set are initialized.
  58
  59    UI_Power_2_Set : Nat;
  60    --  Number of entries set in UI_Power_2;
  61
  62    UI_Power_10 : array (Int range 0 .. 64) of Uint;
  63    --  This table is used to memoize exponentiations by powers of 10 in the
  64    --  same manner as described above for UI_Power_2.
  65
  66    UI_Power_10_Set : Nat;
  67    --  Number of entries set in UI_Power_10;
  68
  69    Uints_Min   : Uint;
  70    Udigits_Min : Int;
  71    --  These values are used to make sure that the mark/release mechanism does
  72    --  not destroy values saved in the U_Power tables or in the hash table used
  73    --  by UI_From_Int. Whenever an entry is made in either of these tables,
  74    --  Uints_Min and Udigits_Min are updated to protect the entry, and Release
  75    --  never cuts back beyond these minimum values.
  76
  77    Int_0 : constant Int := 0;
  78    Int_1 : constant Int := 1;
  79    Int_2 : constant Int := 2;
  80    --  These values are used in some cases where the use of numeric literals
  81    --  would cause ambiguities (integer vs Uint).
  82
  83    ----------------------------
  84    -- UI_From_Int Hash Table --
  85    ----------------------------
  86
  87    --  UI_From_Int uses a hash table to avoid duplicating entries and wasting
  88    --  storage. This is particularly important for complex cases of back
  89    --  annotation.
  90
  91    subtype Hnum is Nat range 0 .. 1022;
  92
  93    function Hash_Num (F : Int) return Hnum;
  94    --  Hashing function
  95
  96    package UI_Ints is new Simple_HTable (
  97      Header_Num => Hnum,
  98      Element    => Uint,
  99      No_Element => No_Uint,
 100      Key        => Int,
 101      Hash       => Hash_Num,
 102      Equal      => "=");
 103
 104    -----------------------
 105    -- Local Subprograms --
 106    -----------------------
 107
 108    function Direct (U : Uint) return Boolean;
 109    pragma Inline (Direct);
 110    --  Returns True if U is represented directly
 111
 112    function Direct_Val (U : Uint) return Int;
 113    --  U is a Uint for is represented directly. The returned result is the
 114    --  value represented.
 115
 116    function GCD (Jin, Kin : Int) return Int;
 117    --  Compute GCD of two integers. Assumes that Jin >= Kin >= 0
 118
 119    procedure Image_Out
 120      (Input     : Uint;
 121       To_Buffer : Boolean;
 122       Format    : UI_Format);
 123    --  Common processing for UI_Image and UI_Write, To_Buffer is set True for
 124    --  UI_Image, and false for UI_Write, and Format is copied from the Format
 125    --  parameter to UI_Image or UI_Write.
 126
 127    procedure Init_Operand (UI : Uint; Vec : out UI_Vector);
 128    pragma Inline (Init_Operand);
 129    --  This procedure puts the value of UI into the vector in canonical
 130    --  multiple precision format. The parameter should be of the correct size
 131    --  as determined by a previous call to N_Digits (UI). The first digit of
 132    --  Vec contains the sign, all other digits are always non-negative. Note
 133    --  that the input may be directly represented, and in this case Vec will
 134    --  contain the corresponding one or two digit value. The low bound of Vec
 135    --  is always 1.
 136
 137    function Least_Sig_Digit (Arg : Uint) return Int;
 138    pragma Inline (Least_Sig_Digit);
 139    --  Returns the Least Significant Digit of Arg quickly. When the given Uint
 140    --  is less than 2**15, the value returned is the input value, in this case
 141    --  the result may be negative. It is expected that any use will mask off
 142    --  unnecessary bits. This is used for finding Arg mod B where B is a power
 143    --  of two. Hence the actual base is irrelevant as long as it is a power of
 144    --  two.
 145
 146    procedure Most_Sig_2_Digits
 147      (Left      : Uint;
 148       Right     : Uint;
 149       Left_Hat  : out Int;
 150       Right_Hat : out Int);
 151    --  Returns leading two significant digits from the given pair of Uint's.
 152    --  Mathematically: returns Left / (Base ** K) and Right / (Base ** K) where
 153    --  K is as small as possible S.T. Right_Hat < Base * Base. It is required
 154    --  that Left > Right for the algorithm to work.
 155
 156    function N_Digits (Input : Uint) return Int;
 157    pragma Inline (N_Digits);
 158    --  Returns number of "digits" in a Uint
 159
 160    function Sum_Digits (Left : Uint; Sign : Int) return Int;
 161    --  If Sign = 1 return the sum of the "digits" of Abs (Left). If the total
 162    --  has more then one digit then return Sum_Digits of total.
 163
 164    function Sum_Double_Digits (Left : Uint; Sign : Int) return Int;
 165    --  Same as above but work in New_Base = Base * Base
 166
 167    procedure UI_Div_Rem
 168      (Left, Right       : Uint;
 169       Quotient          : out Uint;
 170       Remainder         : out Uint;
 171       Discard_Quotient  : Boolean;
 172       Discard_Remainder : Boolean);
 173    --  Compute Euclidean division of Left by Right, and return Quotient and
 174    --  signed Remainder (Left rem Right).
 175    --
 176    --    If Discard_Quotient is True, Quotient is left unchanged.
 177    --    If Discard_Remainder is True, Remainder is left unchanged.
 178
 179    function Vector_To_Uint
 180      (In_Vec   : UI_Vector;
 181       Negative : Boolean) return Uint;
 182    --  Functions that calculate values in UI_Vectors, call this function to
 183    --  create and return the Uint value. In_Vec contains the multiple precision
 184    --  (Base) representation of a non-negative value. Leading zeroes are
 185    --  permitted. Negative is set if the desired result is the negative of the
 186    --  given value. The result will be either the appropriate directly
 187    --  represented value, or a table entry in the proper canonical format is
 188    --  created and returned.
 189    --
 190    --  Note that Init_Operand puts a signed value in the result vector, but
 191    --  Vector_To_Uint is always presented with a non-negative value. The
 192    --  processing of signs is something that is done by the caller before
 193    --  calling Vector_To_Uint.
 194
 195    ------------
 196    -- Direct --
 197    ------------
 198
 199    function Direct (U : Uint) return Boolean is
 200    begin
 201       return Int (U) <= Int (Uint_Direct_Last);
 202    end Direct;
 203
 204    ----------------
 205    -- Direct_Val --
 206    ----------------
 207
 208    function Direct_Val (U : Uint) return Int is
 209    begin
 210       pragma Assert (Direct (U));
 211       return Int (U) - Int (Uint_Direct_Bias);
 212    end Direct_Val;
 213
 214    ---------
 215    -- GCD --
 216    ---------
 217
 218    function GCD (Jin, Kin : Int) return Int is
 219       J, K, Tmp : Int;
 220
 221    begin
 222       pragma Assert (Jin >= Kin);
 223       pragma Assert (Kin >= Int_0);
 224
 225       J := Jin;
 226       K := Kin;
 227       while K /= Uint_0 loop
 228          Tmp := J mod K;
 229          J := K;
 230          K := Tmp;
 231       end loop;
 232
 233       return J;
 234    end GCD;
 235
 236    --------------
 237    -- Hash_Num --
 238    --------------
 239
 240    function Hash_Num (F : Int) return Hnum is
 241    begin
 242       return Standard."mod" (F, Hnum'Range_Length);
 243    end Hash_Num;
 244
 245    ---------------
 246    -- Image_Out --
 247    ---------------
 248
 249    procedure Image_Out
 250      (Input     : Uint;
 251       To_Buffer : Boolean;
 252       Format    : UI_Format)
 253    is
 254       Marks  : constant Uintp.Save_Mark := Uintp.Mark;
 255       Base   : Uint;
 256       Ainput : Uint;
 257
 258       Digs_Output : Natural := 0;
 259       --  Counts digits output. In hex mode, but not in decimal mode, we
 260       --  put an underline after every four hex digits that are output.
 261
 262       Exponent : Natural := 0;
 263       --  If the number is too long to fit in the buffer, we switch to an
 264       --  approximate output format with an exponent. This variable records
 265       --  the exponent value.
 266
 267       function Better_In_Hex return Boolean;
 268       --  Determines if it is better to generate digits in base 16 (result
 269       --  is true) or base 10 (result is false). The choice is purely a
 270       --  matter of convenience and aesthetics, so it does not matter which
 271       --  value is returned from a correctness point of view.
 272
 273       procedure Image_Char (C : Character);
 274       --  Internal procedure to output one character
 275
 276       procedure Image_Exponent (N : Natural);
 277       --  Output non-zero exponent. Note that we only use the exponent form in
 278       --  the buffer case, so we know that To_Buffer is true.
 279
 280       procedure Image_Uint (U : Uint);
 281       --  Internal procedure to output characters of non-negative Uint
 282
 283       -------------------
 284       -- Better_In_Hex --
 285       -------------------
 286
 287       function Better_In_Hex return Boolean is
 288          T16 : constant Uint := Uint_2 ** Int'(16);
 289          A   : Uint;
 290
 291       begin
 292          A := UI_Abs (Input);
 293
 294          --  Small values up to 2**16 can always be in decimal
 295
 296          if A < T16 then
 297             return False;
 298          end if;
 299
 300          --  Otherwise, see if we are a power of 2 or one less than a power
 301          --  of 2. For the moment these are the only cases printed in hex.
 302
 303          if A mod Uint_2 = Uint_1 then
 304             A := A + Uint_1;
 305          end if;
 306
 307          loop
 308             if A mod T16 /= Uint_0 then
 309                return False;
 310
 311             else
 312                A := A / T16;
 313             end if;
 314
 315             exit when A < T16;
 316          end loop;
 317
 318          while A > Uint_2 loop
 319             if A mod Uint_2 /= Uint_0 then
 320                return False;
 321
 322             else
 323                A := A / Uint_2;
 324             end if;
 325          end loop;
 326
 327          return True;
 328       end Better_In_Hex;
 329
 330       ----------------
 331       -- Image_Char --
 332       ----------------
 333
 334       procedure Image_Char (C : Character) is
 335       begin
 336          if To_Buffer then
 337             if UI_Image_Length + 6 > UI_Image_Max then
 338                Exponent := Exponent + 1;
 339             else
 340                UI_Image_Length := UI_Image_Length + 1;
 341                UI_Image_Buffer (UI_Image_Length) := C;
 342             end if;
 343          else
 344             Write_Char (C);
 345          end if;
 346       end Image_Char;
 347
 348       --------------------
 349       -- Image_Exponent --
 350       --------------------
 351
 352       procedure Image_Exponent (N : Natural) is
 353       begin
 354          if N >= 10 then
 355             Image_Exponent (N / 10);
 356          end if;
 357
 358          UI_Image_Length := UI_Image_Length + 1;
 359          UI_Image_Buffer (UI_Image_Length) :=
 360            Character'Val (Character'Pos ('0') + N mod 10);
 361       end Image_Exponent;
 362
 363       ----------------
 364       -- Image_Uint --
 365       ----------------
 366
 367       procedure Image_Uint (U : Uint) is
 368          H : constant array (Int range 0 .. 15) of Character :=
 369                "0123456789ABCDEF";
 370
 371       begin
 372          if U >= Base then
 373             Image_Uint (U / Base);
 374          end if;
 375
 376          if Digs_Output = 4 and then Base = Uint_16 then
 377             Image_Char ('_');
 378             Digs_Output := 0;
 379          end if;
 380
 381          Image_Char (H (UI_To_Int (U rem Base)));
 382
 383          Digs_Output := Digs_Output + 1;
 384       end Image_Uint;
 385
 386    --  Start of processing for Image_Out
 387
 388    begin
 389       if Input = No_Uint then
 390          Image_Char ('?');
 391          return;
 392       end if;
 393
 394       UI_Image_Length := 0;
 395
 396       if Input < Uint_0 then
 397          Image_Char ('-');
 398          Ainput := -Input;
 399       else
 400          Ainput := Input;
 401       end if;
 402
 403       if Format = Hex
 404         or else (Format = Auto and then Better_In_Hex)
 405       then
 406          Base := Uint_16;
 407          Image_Char ('1');
 408          Image_Char ('6');
 409          Image_Char ('#');
 410          Image_Uint (Ainput);
 411          Image_Char ('#');
 412
 413       else
 414          Base := Uint_10;
 415          Image_Uint (Ainput);
 416       end if;
 417
 418       if Exponent /= 0 then
 419          UI_Image_Length := UI_Image_Length + 1;
 420          UI_Image_Buffer (UI_Image_Length) := 'E';
 421          Image_Exponent (Exponent);
 422       end if;
 423
 424       Uintp.Release (Marks);
 425    end Image_Out;
 426
 427    -------------------
 428    -- Init_Operand --
 429    -------------------
 430
 431    procedure Init_Operand (UI : Uint; Vec : out UI_Vector) is
 432       Loc : Int;
 433
 434       pragma Assert (Vec'First = Int'(1));
 435
 436    begin
 437       if Direct (UI) then
 438          Vec (1) := Direct_Val (UI);
 439
 440          if Vec (1) >= Base then
 441             Vec (2) := Vec (1) rem Base;
 442             Vec (1) := Vec (1) / Base;
 443          end if;
 444
 445       else
 446          Loc := Uints.Table (UI).Loc;
 447
 448          for J in 1 .. Uints.Table (UI).Length loop
 449             Vec (J) := Udigits.Table (Loc + J - 1);
 450          end loop;
 451       end if;
 452    end Init_Operand;
 453
 454    ----------------
 455    -- Initialize --
 456    ----------------
 457
 458    procedure Initialize is
 459    begin
 460       Uints.Init;
 461       Udigits.Init;
 462
 463       Uint_Int_First := UI_From_Int (Int'First);
 464       Uint_Int_Last  := UI_From_Int (Int'Last);
 465
 466       UI_Power_2 (0) := Uint_1;
 467       UI_Power_2_Set := 0;
 468
 469       UI_Power_10 (0) := Uint_1;
 470       UI_Power_10_Set := 0;
 471
 472       Uints_Min := Uints.Last;
 473       Udigits_Min := Udigits.Last;
 474
 475       UI_Ints.Reset;
 476    end Initialize;
 477
 478    ---------------------
 479    -- Least_Sig_Digit --
 480    ---------------------
 481
 482    function Least_Sig_Digit (Arg : Uint) return Int is
 483       V : Int;
 484
 485    begin
 486       if Direct (Arg) then
 487          V := Direct_Val (Arg);
 488
 489          if V >= Base then
 490             V := V mod Base;
 491          end if;
 492
 493          --  Note that this result may be negative
 494
 495          return V;
 496
 497       else
 498          return
 499            Udigits.Table
 500             (Uints.Table (Arg).Loc + Uints.Table (Arg).Length - 1);
 501       end if;
 502    end Least_Sig_Digit;
 503
 504    ----------
 505    -- Mark --
 506    ----------
 507
 508    function Mark return Save_Mark is
 509    begin
 510       return (Save_Uint => Uints.Last, Save_Udigit => Udigits.Last);
 511    end Mark;
 512
 513    -----------------------
 514    -- Most_Sig_2_Digits --
 515    -----------------------
 516
 517    procedure Most_Sig_2_Digits
 518      (Left      : Uint;
 519       Right     : Uint;
 520       Left_Hat  : out Int;
 521       Right_Hat : out Int)
 522    is
 523    begin
 524       pragma Assert (Left >= Right);
 525
 526       if Direct (Left) then
 527          Left_Hat  := Direct_Val (Left);
 528          Right_Hat := Direct_Val (Right);
 529          return;
 530
 531       else
 532          declare
 533             L1 : constant Int :=
 534                    Udigits.Table (Uints.Table (Left).Loc);
 535             L2 : constant Int :=
 536                    Udigits.Table (Uints.Table (Left).Loc + 1);
 537
 538          begin
 539             --  It is not so clear what to return when Arg is negative???
 540
 541             Left_Hat := abs (L1) * Base + L2;
 542          end;
 543       end if;
 544
 545       declare
 546          Length_L : constant Int := Uints.Table (Left).Length;
 547          Length_R : Int;
 548          R1 : Int;
 549          R2 : Int;
 550          T  : Int;
 551
 552       begin
 553          if Direct (Right) then
 554             T := Direct_Val (Left);
 555             R1 := abs (T / Base);
 556             R2 := T rem Base;
 557             Length_R := 2;
 558
 559          else
 560             R1 := abs (Udigits.Table (Uints.Table (Right).Loc));
 561             R2 := Udigits.Table (Uints.Table (Right).Loc + 1);
 562             Length_R := Uints.Table (Right).Length;
 563          end if;
 564
 565          if Length_L = Length_R then
 566             Right_Hat := R1 * Base + R2;
 567          elsif Length_L = Length_R + Int_1 then
 568             Right_Hat := R1;
 569          else
 570             Right_Hat := 0;
 571          end if;
 572       end;
 573    end Most_Sig_2_Digits;
 574
 575    ---------------
 576    -- N_Digits --
 577    ---------------
 578
 579    --  Note: N_Digits returns 1 for No_Uint
 580
 581    function N_Digits (Input : Uint) return Int is
 582    begin
 583       if Direct (Input) then
 584          if Direct_Val (Input) >= Base then
 585             return 2;
 586          else
 587             return 1;
 588          end if;
 589
 590       else
 591          return Uints.Table (Input).Length;
 592       end if;
 593    end N_Digits;
 594
 595    --------------
 596    -- Num_Bits --
 597    --------------
 598
 599    function Num_Bits (Input : Uint) return Nat is
 600       Bits : Nat;
 601       Num  : Nat;
 602
 603    begin
 604       --  Largest negative number has to be handled specially, since it is in
 605       --  Int_Range, but we cannot take the absolute value.
 606
 607       if Input = Uint_Int_First then
 608          return Int'Size;
 609
 610       --  For any other number in Int_Range, get absolute value of number
 611
 612       elsif UI_Is_In_Int_Range (Input) then
 613          Num := abs (UI_To_Int (Input));
 614          Bits := 0;
 615
 616       --  If not in Int_Range then initialize bit count for all low order
 617       --  words, and set number to high order digit.
 618
 619       else
 620          Bits := Base_Bits * (Uints.Table (Input).Length - 1);
 621          Num  := abs (Udigits.Table (Uints.Table (Input).Loc));
 622       end if;
 623
 624       --  Increase bit count for remaining value in Num
 625
 626       while Types.">" (Num, 0) loop
 627          Num := Num / 2;
 628          Bits := Bits + 1;
 629       end loop;
 630
 631       return Bits;
 632    end Num_Bits;
 633
 634    ---------
 635    -- pid --
 636    ---------
 637
 638    procedure pid (Input : Uint) is
 639    begin
 640       UI_Write (Input, Decimal);
 641       Write_Eol;
 642    end pid;
 643
 644    ---------
 645    -- pih --
 646    ---------
 647
 648    procedure pih (Input : Uint) is
 649    begin
 650       UI_Write (Input, Hex);
 651       Write_Eol;
 652    end pih;
 653
 654    -------------
 655    -- Release --
 656    -------------
 657
 658    procedure Release (M : Save_Mark) is
 659    begin
 660       Uints.Set_Last   (Uint'Max (M.Save_Uint,   Uints_Min));
 661       Udigits.Set_Last (Int'Max  (M.Save_Udigit, Udigits_Min));
 662    end Release;
 663
 664    ----------------------
 665    -- Release_And_Save --
 666    ----------------------
 667
 668    procedure Release_And_Save (M : Save_Mark; UI : in out Uint) is
 669    begin
 670       if Direct (UI) then
 671          Release (M);
 672
 673       else
 674          declare
 675             UE_Len : constant Pos := Uints.Table (UI).Length;
 676             UE_Loc : constant Int := Uints.Table (UI).Loc;
 677
 678             UD : constant Udigits.Table_Type (1 .. UE_Len) :=
 679                    Udigits.Table (UE_Loc .. UE_Loc + UE_Len - 1);
 680
 681          begin
 682             Release (M);
 683
 684             Uints.Append ((Length => UE_Len, Loc => Udigits.Last + 1));
 685             UI := Uints.Last;
 686
 687             for J in 1 .. UE_Len loop
 688                Udigits.Append (UD (J));
 689             end loop;
 690          end;
 691       end if;
 692    end Release_And_Save;
 693
 694    procedure Release_And_Save (M : Save_Mark; UI1, UI2 : in out Uint) is
 695    begin
 696       if Direct (UI1) then
 697          Release_And_Save (M, UI2);
 698
 699       elsif Direct (UI2) then
 700          Release_And_Save (M, UI1);
 701
 702       else
 703          declare
 704             UE1_Len : constant Pos := Uints.Table (UI1).Length;
 705             UE1_Loc : constant Int := Uints.Table (UI1).Loc;
 706
 707             UD1 : constant Udigits.Table_Type (1 .. UE1_Len) :=
 708                     Udigits.Table (UE1_Loc .. UE1_Loc + UE1_Len - 1);
 709
 710             UE2_Len : constant Pos := Uints.Table (UI2).Length;
 711             UE2_Loc : constant Int := Uints.Table (UI2).Loc;
 712
 713             UD2 : constant Udigits.Table_Type (1 .. UE2_Len) :=
 714                     Udigits.Table (UE2_Loc .. UE2_Loc + UE2_Len - 1);
 715
 716          begin
 717             Release (M);
 718
 719             Uints.Append ((Length => UE1_Len, Loc => Udigits.Last + 1));
 720             UI1 := Uints.Last;
 721
 722             for J in 1 .. UE1_Len loop
 723                Udigits.Append (UD1 (J));
 724             end loop;
 725
 726             Uints.Append ((Length => UE2_Len, Loc => Udigits.Last + 1));
 727             UI2 := Uints.Last;
 728
 729             for J in 1 .. UE2_Len loop
 730                Udigits.Append (UD2 (J));
 731             end loop;
 732          end;
 733       end if;
 734    end Release_And_Save;
 735
 736    ----------------
 737    -- Sum_Digits --
 738    ----------------
 739
 740    --  This is done in one pass
 741
 742    --  Mathematically: assume base congruent to 1 and compute an equivalent
 743    --  integer to Left.
 744
 745    --  If Sign = -1 return the alternating sum of the "digits"
 746
 747    --     D1 - D2 + D3 - D4 + D5 ...
 748
 749    --  (where D1 is Least Significant Digit)
 750
 751    --  Mathematically: assume base congruent to -1 and compute an equivalent
 752    --  integer to Left.
 753
 754    --  This is used in Rem and Base is assumed to be 2 ** 15
 755
 756    --  Note: The next two functions are very similar, any style changes made
 757    --  to one should be reflected in both.  These would be simpler if we
 758    --  worked base 2 ** 32.
 759
 760    function Sum_Digits (Left : Uint; Sign : Int) return Int is
 761    begin
 762       pragma Assert (Sign = Int_1 or else Sign = Int (-1));
 763
 764       --  First try simple case;
 765
 766       if Direct (Left) then
 767          declare
 768             Tmp_Int : Int := Direct_Val (Left);
 769
 770          begin
 771             if Tmp_Int >= Base then
 772                Tmp_Int := (Tmp_Int / Base) +
 773                   Sign * (Tmp_Int rem Base);
 774
 775                   --  Now Tmp_Int is in [-(Base - 1) .. 2 * (Base - 1)]
 776
 777                if Tmp_Int >= Base then
 778
 779                   --  Sign must be 1
 780
 781                   Tmp_Int := (Tmp_Int / Base) + 1;
 782
 783                end if;
 784
 785                --  Now Tmp_Int is in [-(Base - 1) .. (Base - 1)]
 786
 787             end if;
 788
 789             return Tmp_Int;
 790          end;
 791
 792       --  Otherwise full circuit is needed
 793
 794       else
 795          declare
 796             L_Length : constant Int := N_Digits (Left);
 797             L_Vec    : UI_Vector (1 .. L_Length);
 798             Tmp_Int  : Int;
 799             Carry    : Int;
 800             Alt      : Int;
 801
 802          begin
 803             Init_Operand (Left, L_Vec);
 804             L_Vec (1) := abs L_Vec (1);
 805             Tmp_Int := 0;
 806             Carry := 0;
 807             Alt := 1;
 808
 809             for J in reverse 1 .. L_Length loop
 810                Tmp_Int := Tmp_Int + Alt * (L_Vec (J) + Carry);
 811
 812                --  Tmp_Int is now between [-2 * Base + 1 .. 2 * Base - 1],
 813                --  since old Tmp_Int is between [-(Base - 1) .. Base - 1]
 814                --  and L_Vec is in [0 .. Base - 1] and Carry in [-1 .. 1]
 815
 816                if Tmp_Int >= Base then
 817                   Tmp_Int := Tmp_Int - Base;
 818                   Carry := 1;
 819
 820                elsif Tmp_Int <= -Base then
 821                   Tmp_Int := Tmp_Int + Base;
 822                   Carry := -1;
 823
 824                else
 825                   Carry := 0;
 826                end if;
 827
 828                --  Tmp_Int is now between [-Base + 1 .. Base - 1]
 829
 830                Alt := Alt * Sign;
 831             end loop;
 832
 833             Tmp_Int := Tmp_Int + Alt * Carry;
 834
 835             --  Tmp_Int is now between [-Base .. Base]
 836
 837             if Tmp_Int >= Base then
 838                Tmp_Int := Tmp_Int - Base + Alt * Sign * 1;
 839
 840             elsif Tmp_Int <= -Base then
 841                Tmp_Int := Tmp_Int + Base + Alt * Sign * (-1);
 842             end if;
 843
 844             --  Now Tmp_Int is in [-(Base - 1) .. (Base - 1)]
 845
 846             return Tmp_Int;
 847          end;
 848       end if;
 849    end Sum_Digits;
 850
 851    -----------------------
 852    -- Sum_Double_Digits --
 853    -----------------------
 854
 855    --  Note: This is used in Rem, Base is assumed to be 2 ** 15
 856
 857    function Sum_Double_Digits (Left : Uint; Sign : Int) return Int is
 858    begin
 859       --  First try simple case;
 860
 861       pragma Assert (Sign = Int_1 or else Sign = Int (-1));
 862
 863       if Direct (Left) then
 864          return Direct_Val (Left);
 865
 866       --  Otherwise full circuit is needed
 867
 868       else
 869          declare
 870             L_Length      : constant Int := N_Digits (Left);
 871             L_Vec         : UI_Vector (1 .. L_Length);
 872             Most_Sig_Int  : Int;
 873             Least_Sig_Int : Int;
 874             Carry         : Int;
 875             J             : Int;
 876             Alt           : Int;
 877
 878          begin
 879             Init_Operand (Left, L_Vec);
 880             L_Vec (1) := abs L_Vec (1);
 881             Most_Sig_Int := 0;
 882             Least_Sig_Int := 0;
 883             Carry := 0;
 884             Alt := 1;
 885             J := L_Length;
 886
 887             while J > Int_1 loop
 888                Least_Sig_Int := Least_Sig_Int + Alt * (L_Vec (J) + Carry);
 889
 890                --  Least is in [-2 Base + 1 .. 2 * Base - 1]
 891                --  Since L_Vec in [0 .. Base - 1] and Carry in [-1 .. 1]
 892                --  and old Least in [-Base + 1 .. Base - 1]
 893
 894                if Least_Sig_Int >= Base then
 895                   Least_Sig_Int := Least_Sig_Int - Base;
 896                   Carry := 1;
 897
 898                elsif Least_Sig_Int <= -Base then
 899                   Least_Sig_Int := Least_Sig_Int + Base;
 900                   Carry := -1;
 901
 902                else
 903                   Carry := 0;
 904                end if;
 905
 906                --  Least is now in [-Base + 1 .. Base - 1]
 907
 908                Most_Sig_Int := Most_Sig_Int + Alt * (L_Vec (J - 1) + Carry);
 909
 910                --  Most is in [-2 Base + 1 .. 2 * Base - 1]
 911                --  Since L_Vec in [0 ..  Base - 1] and Carry in  [-1 .. 1]
 912                --  and old Most in [-Base + 1 .. Base - 1]
 913
 914                if Most_Sig_Int >= Base then
 915                   Most_Sig_Int := Most_Sig_Int - Base;
 916                   Carry := 1;
 917
 918                elsif Most_Sig_Int <= -Base then
 919                   Most_Sig_Int := Most_Sig_Int + Base;
 920                   Carry := -1;
 921                else
 922                   Carry := 0;
 923                end if;
 924
 925                --  Most is now in [-Base + 1 .. Base - 1]
 926
 927                J := J - 2;
 928                Alt := Alt * Sign;
 929             end loop;
 930
 931             if J = Int_1 then
 932                Least_Sig_Int := Least_Sig_Int + Alt * (L_Vec (J) + Carry);
 933             else
 934                Least_Sig_Int := Least_Sig_Int + Alt * Carry;
 935             end if;
 936
 937             if Least_Sig_Int >= Base then
 938                Least_Sig_Int := Least_Sig_Int - Base;
 939                Most_Sig_Int := Most_Sig_Int + Alt * 1;
 940
 941             elsif Least_Sig_Int <= -Base then
 942                Least_Sig_Int := Least_Sig_Int + Base;
 943                Most_Sig_Int := Most_Sig_Int + Alt * (-1);
 944             end if;
 945
 946             if Most_Sig_Int >= Base then
 947                Most_Sig_Int := Most_Sig_Int - Base;
 948                Alt := Alt * Sign;
 949                Least_Sig_Int :=
 950                  Least_Sig_Int + Alt * 1; -- cannot overflow again
 951
 952             elsif Most_Sig_Int <= -Base then
 953                Most_Sig_Int := Most_Sig_Int + Base;
 954                Alt := Alt * Sign;
 955                Least_Sig_Int :=
 956                  Least_Sig_Int + Alt * (-1); --  cannot overflow again.
 957             end if;
 958
 959             return Most_Sig_Int * Base + Least_Sig_Int;
 960          end;
 961       end if;
 962    end Sum_Double_Digits;
 963
 964    ---------------
 965    -- Tree_Read --
 966    ---------------
 967
 968    procedure Tree_Read is
 969    begin
 970       Uints.Tree_Read;
 971       Udigits.Tree_Read;
 972
 973       Tree_Read_Int (Int (Uint_Int_First));
 974       Tree_Read_Int (Int (Uint_Int_Last));
 975       Tree_Read_Int (UI_Power_2_Set);
 976       Tree_Read_Int (UI_Power_10_Set);
 977       Tree_Read_Int (Int (Uints_Min));
 978       Tree_Read_Int (Udigits_Min);
 979
 980       for J in 0 .. UI_Power_2_Set loop
 981          Tree_Read_Int (Int (UI_Power_2 (J)));
 982       end loop;
 983
 984       for J in 0 .. UI_Power_10_Set loop
 985          Tree_Read_Int (Int (UI_Power_10 (J)));
 986       end loop;
 987
 988    end Tree_Read;
 989
 990    ----------------
 991    -- Tree_Write --
 992    ----------------
 993
 994    procedure Tree_Write is
 995    begin
 996       Uints.Tree_Write;
 997       Udigits.Tree_Write;
 998
 999       Tree_Write_Int (Int (Uint_Int_First));
1000       Tree_Write_Int (Int (Uint_Int_Last));
1001       Tree_Write_Int (UI_Power_2_Set);
1002       Tree_Write_Int (UI_Power_10_Set);
1003       Tree_Write_Int (Int (Uints_Min));
1004       Tree_Write_Int (Udigits_Min);
1005
1006       for J in 0 .. UI_Power_2_Set loop
1007          Tree_Write_Int (Int (UI_Power_2 (J)));
1008       end loop;
1009
1010       for J in 0 .. UI_Power_10_Set loop
1011          Tree_Write_Int (Int (UI_Power_10 (J)));
1012       end loop;
1013
1014    end Tree_Write;
1015
1016    -------------
1017    -- UI_Abs --
1018    -------------
1019
1020    function UI_Abs (Right : Uint) return Uint is
1021    begin
1022       if Right < Uint_0 then
1023          return -Right;
1024       else
1025          return Right;
1026       end if;
1027    end UI_Abs;
1028
1029    -------------
1030    -- UI_Add --
1031    -------------
1032
1033    function UI_Add (Left : Int; Right : Uint) return Uint is
1034    begin
1035       return UI_Add (UI_From_Int (Left), Right);
1036    end UI_Add;
1037
1038    function UI_Add (Left : Uint; Right : Int) return Uint is
1039    begin
1040       return UI_Add (Left, UI_From_Int (Right));
1041    end UI_Add;
1042
1043    function UI_Add (Left : Uint; Right : Uint) return Uint is
1044    begin
1045       --  Simple cases of direct operands and addition of zero
1046
1047       if Direct (Left) then
1048          if Direct (Right) then
1049             return UI_From_Int (Direct_Val (Left) + Direct_Val (Right));
1050
1051          elsif Int (Left) = Int (Uint_0) then
1052             return Right;
1053          end if;
1054
1055       elsif Direct (Right) and then Int (Right) = Int (Uint_0) then
1056          return Left;
1057       end if;
1058
1059       --  Otherwise full circuit is needed
1060
1061       declare
1062          L_Length   : constant Int := N_Digits (Left);
1063          R_Length   : constant Int := N_Digits (Right);
1064          L_Vec      : UI_Vector (1 .. L_Length);
1065          R_Vec      : UI_Vector (1 .. R_Length);
1066          Sum_Length : Int;
1067          Tmp_Int    : Int;
1068          Carry      : Int;
1069          Borrow     : Int;
1070          X_Bigger   : Boolean := False;
1071          Y_Bigger   : Boolean := False;
1072          Result_Neg : Boolean := False;
1073
1074       begin
1075          Init_Operand (Left, L_Vec);
1076          Init_Operand (Right, R_Vec);
1077
1078          --  At least one of the two operands is in multi-digit form.
1079          --  Calculate the number of digits sufficient to hold result.
1080
1081          if L_Length > R_Length then
1082             Sum_Length := L_Length + 1;
1083             X_Bigger := True;
1084          else
1085             Sum_Length := R_Length + 1;
1086
1087             if R_Length > L_Length then
1088                Y_Bigger := True;
1089             end if;
1090          end if;
1091
1092          --  Make copies of the absolute values of L_Vec and R_Vec into X and Y
1093          --  both with lengths equal to the maximum possibly needed. This makes
1094          --  looping over the digits much simpler.
1095
1096          declare
1097             X      : UI_Vector (1 .. Sum_Length);
1098             Y      : UI_Vector (1 .. Sum_Length);
1099             Tmp_UI : UI_Vector (1 .. Sum_Length);
1100
1101          begin
1102             for J in 1 .. Sum_Length - L_Length loop
1103                X (J) := 0;
1104             end loop;
1105
1106             X (Sum_Length - L_Length + 1) := abs L_Vec (1);
1107
1108             for J in 2 .. L_Length loop
1109                X (J + (Sum_Length - L_Length)) := L_Vec (J);
1110             end loop;
1111
1112             for J in 1 .. Sum_Length - R_Length loop
1113                Y (J) := 0;
1114             end loop;
1115
1116             Y (Sum_Length - R_Length + 1) := abs R_Vec (1);
1117
1118             for J in 2 .. R_Length loop
1119                Y (J + (Sum_Length - R_Length)) := R_Vec (J);
1120             end loop;
1121
1122             if (L_Vec (1) < Int_0) = (R_Vec (1) < Int_0) then
1123
1124                --  Same sign so just add
1125
1126                Carry := 0;
1127                for J in reverse 1 .. Sum_Length loop
1128                   Tmp_Int := X (J) + Y (J) + Carry;
1129
1130                   if Tmp_Int >= Base then
1131                      Tmp_Int := Tmp_Int - Base;
1132                      Carry := 1;
1133                   else
1134                      Carry := 0;
1135                   end if;
1136
1137                   X (J) := Tmp_Int;
1138                end loop;
1139
1140                return Vector_To_Uint (X, L_Vec (1) < Int_0);
1141
1142             else
1143                --  Find which one has bigger magnitude
1144
1145                if not (X_Bigger or Y_Bigger) then
1146                   for J in L_Vec'Range loop
1147                      if abs L_Vec (J) > abs R_Vec (J) then
1148                         X_Bigger := True;
1149                         exit;
1150                      elsif abs R_Vec (J) > abs L_Vec (J) then
1151                         Y_Bigger := True;
1152                         exit;
1153                      end if;
1154                   end loop;
1155                end if;
1156
1157                --  If they have identical magnitude, just return 0, else swap
1158                --  if necessary so that X had the bigger magnitude. Determine
1159                --  if result is negative at this time.
1160
1161                Result_Neg := False;
1162
1163                if not (X_Bigger or Y_Bigger) then
1164                   return Uint_0;
1165
1166                elsif Y_Bigger then
1167                   if R_Vec (1) < Int_0 then
1168                      Result_Neg := True;
1169                   end if;
1170
1171                   Tmp_UI := X;
1172                   X := Y;
1173                   Y := Tmp_UI;
1174
1175                else
1176                   if L_Vec (1) < Int_0 then
1177                      Result_Neg := True;
1178                   end if;
1179                end if;
1180
1181                --  Subtract Y from the bigger X
1182
1183                Borrow := 0;
1184
1185                for J in reverse 1 .. Sum_Length loop
1186                   Tmp_Int := X (J) - Y (J) + Borrow;
1187
1188                   if Tmp_Int < Int_0 then
1189                      Tmp_Int := Tmp_Int + Base;
1190                      Borrow := -1;
1191                   else
1192                      Borrow := 0;
1193                   end if;
1194
1195                   X (J) := Tmp_Int;
1196                end loop;
1197
1198                return Vector_To_Uint (X, Result_Neg);
1199
1200             end if;
1201          end;
1202       end;
1203    end UI_Add;
1204
1205    --------------------------
1206    -- UI_Decimal_Digits_Hi --
1207    --------------------------
1208
1209    function UI_Decimal_Digits_Hi (U : Uint) return Nat is
1210    begin
1211       --  The maximum value of a "digit" is 32767, which is 5 decimal digits,
1212       --  so an N_Digit number could take up to 5 times this number of digits.
1213       --  This is certainly too high for large numbers but it is not worth
1214       --  worrying about.
1215
1216       return 5 * N_Digits (U);
1217    end UI_Decimal_Digits_Hi;
1218
1219    --------------------------
1220    -- UI_Decimal_Digits_Lo --
1221    --------------------------
1222
1223    function UI_Decimal_Digits_Lo (U : Uint) return Nat is
1224    begin
1225       --  The maximum value of a "digit" is 32767, which is more than four
1226       --  decimal digits, but not a full five digits. The easily computed
1227       --  minimum number of decimal digits is thus 1 + 4 * the number of
1228       --  digits. This is certainly too low for large numbers but it is not
1229       --  worth worrying about.
1230
1231       return 1 + 4 * (N_Digits (U) - 1);
1232    end UI_Decimal_Digits_Lo;
1233
1234    ------------
1235    -- UI_Div --
1236    ------------
1237
1238    function UI_Div (Left : Int; Right : Uint) return Uint is
1239    begin
1240       return UI_Div (UI_From_Int (Left), Right);
1241    end UI_Div;
1242
1243    function UI_Div (Left : Uint; Right : Int) return Uint is
1244    begin
1245       return UI_Div (Left, UI_From_Int (Right));
1246    end UI_Div;
1247
1248    function UI_Div (Left, Right : Uint) return Uint is
1249       Quotient  : Uint;
1250       Remainder : Uint;
1251       pragma Warnings (Off, Remainder);
1252    begin
1253       UI_Div_Rem
1254         (Left, Right,
1255          Quotient, Remainder,
1256          Discard_Quotient  => False,
1257          Discard_Remainder => True);
1258       return Quotient;
1259    end UI_Div;
1260
1261    ----------------
1262    -- UI_Div_Rem --
1263    ----------------
1264
1265    procedure UI_Div_Rem
1266      (Left, Right       : Uint;
1267       Quotient          : out Uint;
1268       Remainder         : out Uint;
1269       Discard_Quotient  : Boolean;
1270       Discard_Remainder : Boolean)
1271    is
1272       pragma Warnings (Off, Quotient);
1273       pragma Warnings (Off, Remainder);
1274    begin
1275       pragma Assert (Right /= Uint_0);
1276
1277       --  Cases where both operands are represented directly
1278
1279       if Direct (Left) and then Direct (Right) then
1280          declare
1281             DV_Left  : constant Int := Direct_Val (Left);
1282             DV_Right : constant Int := Direct_Val (Right);
1283
1284          begin
1285             if not Discard_Quotient then
1286                Quotient := UI_From_Int (DV_Left / DV_Right);
1287             end if;
1288
1289             if not Discard_Remainder then
1290                Remainder := UI_From_Int (DV_Left rem DV_Right);
1291             end if;
1292
1293             return;
1294          end;
1295       end if;
1296
1297       declare
1298          L_Length    : constant Int := N_Digits (Left);
1299          R_Length    : constant Int := N_Digits (Right);
1300          Q_Length    : constant Int := L_Length - R_Length + 1;
1301          L_Vec       : UI_Vector (1 .. L_Length);
1302          R_Vec       : UI_Vector (1 .. R_Length);
1303          D           : Int;
1304          Remainder_I : Int;
1305          Tmp_Divisor : Int;
1306          Carry       : Int;
1307          Tmp_Int     : Int;
1308          Tmp_Dig     : Int;
1309
1310          procedure UI_Div_Vector
1311            (L_Vec     : UI_Vector;
1312             R_Int     : Int;
1313             Quotient  : out UI_Vector;
1314             Remainder : out Int);
1315          pragma Inline (UI_Div_Vector);
1316          --  Specialised variant for case where the divisor is a single digit
1317
1318          procedure UI_Div_Vector
1319            (L_Vec     : UI_Vector;
1320             R_Int     : Int;
1321             Quotient  : out UI_Vector;
1322             Remainder : out Int)
1323          is
1324             Tmp_Int : Int;
1325
1326          begin
1327             Remainder := 0;
1328             for J in L_Vec'Range loop
1329                Tmp_Int := Remainder * Base + abs L_Vec (J);
1330                Quotient (Quotient'First + J - L_Vec'First) := Tmp_Int / R_Int;
1331                Remainder := Tmp_Int rem R_Int;
1332             end loop;
1333
1334             if L_Vec (L_Vec'First) < Int_0 then
1335                Remainder := -Remainder;
1336             end if;
1337          end UI_Div_Vector;
1338
1339       --  Start of processing for UI_Div_Rem
1340
1341       begin
1342          --  Result is zero if left operand is shorter than right
1343
1344          if L_Length < R_Length then
1345             if not Discard_Quotient then
1346                Quotient := Uint_0;
1347             end if;
1348             if not Discard_Remainder then
1349                Remainder := Left;
1350             end if;
1351             return;
1352          end if;
1353
1354          Init_Operand (Left, L_Vec);
1355          Init_Operand (Right, R_Vec);
1356
1357          --  Case of right operand is single digit. Here we can simply divide
1358          --  each digit of the left operand by the divisor, from most to least
1359          --  significant, carrying the remainder to the next digit (just like
1360          --  ordinary long division by hand).
1361
1362          if R_Length = Int_1 then
1363             Tmp_Divisor := abs R_Vec (1);
1364
1365             declare
1366                Quotient_V : UI_Vector (1 .. L_Length);
1367
1368             begin
1369                UI_Div_Vector (L_Vec, Tmp_Divisor, Quotient_V, Remainder_I);
1370
1371                if not Discard_Quotient then
1372                   Quotient :=
1373                     Vector_To_Uint
1374                       (Quotient_V, (L_Vec (1) < Int_0 xor R_Vec (1) < Int_0));
1375                end if;
1376
1377                if not Discard_Remainder then
1378                   Remainder := UI_From_Int (Remainder_I);
1379                end if;
1380                return;
1381             end;
1382          end if;
1383
1384          --  The possible simple cases have been exhausted. Now turn to the
1385          --  algorithm D from the section of Knuth mentioned at the top of
1386          --  this package.
1387
1388          Algorithm_D : declare
1389             Dividend     : UI_Vector (1 .. L_Length + 1);
1390             Divisor      : UI_Vector (1 .. R_Length);
1391             Quotient_V   : UI_Vector (1 .. Q_Length);
1392             Divisor_Dig1 : Int;
1393             Divisor_Dig2 : Int;
1394             Q_Guess      : Int;
1395
1396          begin
1397             --  [ NORMALIZE ] (step D1 in the algorithm). First calculate the
1398             --  scale d, and then multiply Left and Right (u and v in the book)
1399             --  by d to get the dividend and divisor to work with.
1400
1401             D := Base / (abs R_Vec (1) + 1);
1402
1403             Dividend (1) := 0;
1404             Dividend (2) := abs L_Vec (1);
1405
1406             for J in 3 .. L_Length + Int_1 loop
1407                Dividend (J) := L_Vec (J - 1);
1408             end loop;
1409
1410             Divisor (1) := abs R_Vec (1);
1411
1412             for J in Int_2 .. R_Length loop
1413                Divisor (J) := R_Vec (J);
1414             end loop;
1415
1416             if D > Int_1 then
1417
1418                --  Multiply Dividend by D
1419
1420                Carry := 0;
1421                for J in reverse Dividend'Range loop
1422                   Tmp_Int      := Dividend (J) * D + Carry;
1423                   Dividend (J) := Tmp_Int rem Base;
1424                   Carry        := Tmp_Int / Base;
1425                end loop;
1426
1427                --  Multiply Divisor by d
1428
1429                Carry := 0;
1430                for J in reverse Divisor'Range loop
1431                   Tmp_Int      := Divisor (J) * D + Carry;
1432                   Divisor (J)  := Tmp_Int rem Base;
1433                   Carry        := Tmp_Int / Base;
1434                end loop;
1435             end if;
1436
1437             --  Main loop of long division algorithm
1438
1439             Divisor_Dig1 := Divisor (1);
1440             Divisor_Dig2 := Divisor (2);
1441
1442             for J in Quotient_V'Range loop
1443
1444                --  [ CALCULATE Q (hat) ] (step D3 in the algorithm)
1445
1446                Tmp_Int := Dividend (J) * Base + Dividend (J + 1);
1447
1448                --  Initial guess
1449
1450                if Dividend (J) = Divisor_Dig1 then
1451                   Q_Guess := Base - 1;
1452                else
1453                   Q_Guess := Tmp_Int / Divisor_Dig1;
1454                end if;
1455
1456                --  Refine the guess
1457
1458                while Divisor_Dig2 * Q_Guess >
1459                      (Tmp_Int - Q_Guess * Divisor_Dig1) * Base +
1460                                                           Dividend (J + 2)
1461                loop
1462                   Q_Guess := Q_Guess - 1;
1463                end loop;
1464
1465                --  [ MULTIPLY & SUBTRACT ] (step D4). Q_Guess * Divisor is
1466                --  subtracted from the remaining dividend.
1467
1468                Carry := 0;
1469                for K in reverse Divisor'Range loop
1470                   Tmp_Int := Dividend (J + K) - Q_Guess * Divisor (K) + Carry;
1471                   Tmp_Dig := Tmp_Int rem Base;
1472                   Carry   := Tmp_Int / Base;
1473
1474                   if Tmp_Dig < Int_0 then
1475                      Tmp_Dig := Tmp_Dig + Base;
1476                      Carry   := Carry - 1;
1477                   end if;
1478
1479                   Dividend (J + K) := Tmp_Dig;
1480                end loop;
1481
1482                Dividend (J) := Dividend (J) + Carry;
1483
1484                --  [ TEST REMAINDER ] & [ ADD BACK ] (steps D5 and D6)
1485
1486                --  Here there is a slight difference from the book: the last
1487                --  carry is always added in above and below (cancelling each
1488                --  other). In fact the dividend going negative is used as
1489                --  the test.
1490
1491                --  If the Dividend went negative, then Q_Guess was off by
1492                --  one, so it is decremented, and the divisor is added back
1493                --  into the relevant portion of the dividend.
1494
1495                if Dividend (J) < Int_0 then
1496                   Q_Guess := Q_Guess - 1;
1497
1498                   Carry := 0;
1499                   for K in reverse Divisor'Range loop
1500                      Tmp_Int := Dividend (J + K) + Divisor (K) + Carry;
1501
1502                      if Tmp_Int >= Base then
1503                         Tmp_Int := Tmp_Int - Base;
1504                         Carry := 1;
1505                      else
1506                         Carry := 0;
1507                      end if;
1508
1509                      Dividend (J + K) := Tmp_Int;
1510                   end loop;
1511
1512                   Dividend (J) := Dividend (J) + Carry;
1513                end if;
1514
1515                --  Finally we can get the next quotient digit
1516
1517                Quotient_V (J) := Q_Guess;
1518             end loop;
1519
1520             --  [ UNNORMALIZE ] (step D8)
1521
1522             if not Discard_Quotient then
1523                Quotient := Vector_To_Uint
1524                  (Quotient_V, (L_Vec (1) < Int_0 xor R_Vec (1) < Int_0));
1525             end if;
1526
1527             if not Discard_Remainder then
1528                declare
1529                   Remainder_V : UI_Vector (1 .. R_Length);
1530                   Discard_Int : Int;
1531                   pragma Warnings (Off, Discard_Int);
1532                begin
1533                   UI_Div_Vector
1534                     (Dividend (Dividend'Last - R_Length + 1 .. Dividend'Last),
1535                      D,
1536                      Remainder_V, Discard_Int);
1537                   Remainder := Vector_To_Uint (Remainder_V, L_Vec (1) < Int_0);
1538                end;
1539             end if;
1540          end Algorithm_D;
1541       end;
1542    end UI_Div_Rem;
1543
1544    ------------
1545    -- UI_Eq --
1546    ------------
1547
1548    function UI_Eq (Left : Int; Right : Uint) return Boolean is
1549    begin
1550       return not UI_Ne (UI_From_Int (Left), Right);
1551    end UI_Eq;
1552
1553    function UI_Eq (Left : Uint; Right : Int) return Boolean is
1554    begin
1555       return not UI_Ne (Left, UI_From_Int (Right));
1556    end UI_Eq;
1557
1558    function UI_Eq (Left : Uint; Right : Uint) return Boolean is
1559    begin
1560       return not UI_Ne (Left, Right);
1561    end UI_Eq;
1562
1563    --------------
1564    -- UI_Expon --
1565    --------------
1566
1567    function UI_Expon (Left : Int; Right : Uint) return Uint is
1568    begin
1569       return UI_Expon (UI_From_Int (Left), Right);
1570    end UI_Expon;
1571
1572    function UI_Expon (Left : Uint; Right : Int) return Uint is
1573    begin
1574       return UI_Expon (Left, UI_From_Int (Right));
1575    end UI_Expon;
1576
1577    function UI_Expon (Left : Int; Right : Int) return Uint is
1578    begin
1579       return UI_Expon (UI_From_Int (Left), UI_From_Int (Right));
1580    end UI_Expon;
1581
1582    function UI_Expon (Left : Uint; Right : Uint) return Uint is
1583    begin
1584       pragma Assert (Right >= Uint_0);
1585
1586       --  Any value raised to power of 0 is 1
1587
1588       if Right = Uint_0 then
1589          return Uint_1;
1590
1591       --  0 to any positive power is 0
1592
1593       elsif Left = Uint_0 then
1594          return Uint_0;
1595
1596       --  1 to any power is 1
1597
1598       elsif Left = Uint_1 then
1599          return Uint_1;
1600
1601       --  Any value raised to power of 1 is that value
1602
1603       elsif Right = Uint_1 then
1604          return Left;
1605
1606       --  Cases which can be done by table lookup
1607
1608       elsif Right <= Uint_64 then
1609
1610          --  2 ** N for N in 2 .. 64
1611
1612          if Left = Uint_2 then
1613             declare
1614                Right_Int : constant Int := Direct_Val (Right);
1615
1616             begin
1617                if Right_Int > UI_Power_2_Set then
1618                   for J in UI_Power_2_Set + Int_1 .. Right_Int loop
1619                      UI_Power_2 (J) := UI_Power_2 (J - Int_1) * Int_2;
1620                      Uints_Min := Uints.Last;
1621                      Udigits_Min := Udigits.Last;
1622                   end loop;
1623
1624                   UI_Power_2_Set := Right_Int;
1625                end if;
1626
1627                return UI_Power_2 (Right_Int);
1628             end;
1629
1630          --  10 ** N for N in 2 .. 64
1631
1632          elsif Left = Uint_10 then
1633             declare
1634                Right_Int : constant Int := Direct_Val (Right);
1635
1636             begin
1637                if Right_Int > UI_Power_10_Set then
1638                   for J in UI_Power_10_Set + Int_1 .. Right_Int loop
1639                      UI_Power_10 (J) := UI_Power_10 (J - Int_1) * Int (10);
1640                      Uints_Min := Uints.Last;
1641                      Udigits_Min := Udigits.Last;
1642                   end loop;
1643
1644                   UI_Power_10_Set := Right_Int;
1645                end if;
1646
1647                return UI_Power_10 (Right_Int);
1648             end;
1649          end if;
1650       end if;
1651
1652       --  If we fall through, then we have the general case (see Knuth 4.6.3)
1653
1654       declare
1655          N       : Uint := Right;
1656          Squares : Uint := Left;
1657          Result  : Uint := Uint_1;
1658          M       : constant Uintp.Save_Mark := Uintp.Mark;
1659
1660       begin
1661          loop
1662             if (Least_Sig_Digit (N) mod Int_2) = Int_1 then
1663                Result := Result * Squares;
1664             end if;
1665
1666             N := N / Uint_2;
1667             exit when N = Uint_0;
1668             Squares := Squares *  Squares;
1669          end loop;
1670
1671          Uintp.Release_And_Save (M, Result);
1672          return Result;
1673       end;
1674    end UI_Expon;
1675
1676    ----------------
1677    -- UI_From_CC --
1678    ----------------
1679
1680    function UI_From_CC (Input : Char_Code) return Uint is
1681    begin
1682       return UI_From_Dint (Dint (Input));
1683    end UI_From_CC;
1684
1685    ------------------
1686    -- UI_From_Dint --
1687    ------------------
1688
1689    function UI_From_Dint (Input : Dint) return Uint is
1690    begin
1691
1692       if Dint (Min_Direct) <= Input and then Input <= Dint (Max_Direct) then
1693          return Uint (Dint (Uint_Direct_Bias) + Input);
1694
1695       --  For values of larger magnitude, compute digits into a vector and call
1696       --  Vector_To_Uint.
1697
1698       else
1699          declare
1700             Max_For_Dint : constant := 5;
1701             --  Base is defined so that 5 Uint digits is sufficient to hold the
1702             --  largest possible Dint value.
1703
1704             V : UI_Vector (1 .. Max_For_Dint);
1705
1706             Temp_Integer : Dint := Input;
1707
1708          begin
1709             for J in reverse V'Range loop
1710                V (J) := Int (abs (Temp_Integer rem Dint (Base)));
1711                Temp_Integer := Temp_Integer / Dint (Base);
1712             end loop;
1713
1714             return Vector_To_Uint (V, Input < Dint'(0));
1715          end;
1716       end if;
1717    end UI_From_Dint;
1718
1719    -----------------
1720    -- UI_From_Int --
1721    -----------------
1722
1723    function UI_From_Int (Input : Int) return Uint is
1724       U : Uint;
1725
1726    begin
1727       if Min_Direct <= Input and then Input <= Max_Direct then
1728          return Uint (Int (Uint_Direct_Bias) + Input);
1729       end if;
1730
1731       --  If already in the hash table, return entry
1732
1733       U := UI_Ints.Get (Input);
1734
1735       if U /= No_Uint then
1736          return U;
1737       end if;
1738
1739       --  For values of larger magnitude, compute digits into a vector and call
1740       --  Vector_To_Uint.
1741
1742       declare
1743          Max_For_Int : constant := 3;
1744          --  Base is defined so that 3 Uint digits is sufficient to hold the
1745          --  largest possible Int value.
1746
1747          V : UI_Vector (1 .. Max_For_Int);
1748
1749          Temp_Integer : Int := Input;
1750
1751       begin
1752          for J in reverse V'Range loop
1753             V (J) := abs (Temp_Integer rem Base);
1754             Temp_Integer := Temp_Integer / Base;
1755          end loop;
1756
1757          U := Vector_To_Uint (V, Input < Int_0);
1758          UI_Ints.Set (Input, U);
1759          Uints_Min := Uints.Last;
1760          Udigits_Min := Udigits.Last;
1761          return U;
1762       end;
1763    end UI_From_Int;
1764
1765    ------------
1766    -- UI_GCD --
1767    ------------
1768
1769    --  Lehmer's algorithm for GCD
1770
1771    --  The idea is to avoid using multiple precision arithmetic wherever
1772    --  possible, substituting Int arithmetic instead. See Knuth volume II,
1773    --  Algorithm L (page 329).
1774
1775    --  We use the same notation as Knuth (U_Hat standing for the obvious!)
1776
1777    function UI_GCD (Uin, Vin : Uint) return Uint is
1778       U, V : Uint;
1779       --  Copies of Uin and Vin
1780
1781       U_Hat, V_Hat : Int;
1782       --  The most Significant digits of U,V
1783
1784       A, B, C, D, T, Q, Den1, Den2 : Int;
1785
1786       Tmp_UI : Uint;
1787       Marks  : constant Uintp.Save_Mark := Uintp.Mark;
1788       Iterations : Integer := 0;
1789
1790    begin
1791       pragma Assert (Uin >= Vin);
1792       pragma Assert (Vin >= Uint_0);
1793
1794       U := Uin;
1795       V := Vin;
1796
1797       loop
1798          Iterations := Iterations + 1;
1799
1800          if Direct (V) then
1801             if V = Uint_0 then
1802                return U;
1803             else
1804                return
1805                  UI_From_Int (GCD (Direct_Val (V), UI_To_Int (U rem V)));
1806             end if;
1807          end if;
1808
1809          Most_Sig_2_Digits (U, V, U_Hat, V_Hat);
1810          A := 1;
1811          B := 0;
1812          C := 0;
1813          D := 1;
1814
1815          loop
1816             --  We might overflow and get division by zero here. This just
1817             --  means we cannot take the single precision step
1818
1819             Den1 := V_Hat + C;
1820             Den2 := V_Hat + D;
1821             exit when Den1 = Int_0 or else Den2 = Int_0;
1822
1823             --  Compute Q, the trial quotient
1824
1825             Q := (U_Hat + A) / Den1;
1826
1827             exit when Q /= ((U_Hat + B) / Den2);
1828
1829             --  A single precision step Euclid step will give same answer as a
1830             --  multiprecision one.
1831
1832             T := A - (Q * C);
1833             A := C;
1834             C := T;
1835
1836             T := B - (Q * D);
1837             B := D;
1838             D := T;
1839
1840             T := U_Hat - (Q * V_Hat);
1841             U_Hat := V_Hat;
1842             V_Hat := T;
1843
1844          end loop;
1845
1846          --  Take a multiprecision Euclid step
1847
1848          if B = Int_0 then
1849
1850             --  No single precision steps take a regular Euclid step
1851
1852             Tmp_UI := U rem V;
1853             U := V;
1854             V := Tmp_UI;
1855
1856          else
1857             --  Use prior single precision steps to compute this Euclid step
1858
1859             --  For constructs such as:
1860             --  sqrt_2: constant :=  1.41421_35623_73095_04880_16887_24209_698;
1861             --  sqrt_eps: constant long_float := long_float( 1.0 / sqrt_2)
1862             --    ** long_float'machine_mantissa;
1863             --
1864             --  we spend 80% of our time working on this step. Perhaps we need
1865             --  a special case Int / Uint dot product to speed things up. ???
1866
1867             --  Alternatively we could increase the single precision iterations
1868             --  to handle Uint's of some small size ( <5 digits?). Then we
1869             --  would have more iterations on small Uint. On the code above, we
1870             --  only get 5 (on average) single precision iterations per large
1871             --  iteration. ???
1872
1873             Tmp_UI := (UI_From_Int (A) * U) + (UI_From_Int (B) * V);
1874             V := (UI_From_Int (C) * U) + (UI_From_Int (D) * V);
1875             U := Tmp_UI;
1876          end if;
1877
1878          --  If the operands are very different in magnitude, the loop will
1879          --  generate large amounts of short-lived data, which it is worth
1880          --  removing periodically.
1881
1882          if Iterations > 100 then
1883             Release_And_Save (Marks, U, V);
1884             Iterations := 0;
1885          end if;
1886       end loop;
1887    end UI_GCD;
1888
1889    ------------
1890    -- UI_Ge --
1891    ------------
1892
1893    function UI_Ge (Left : Int; Right : Uint) return Boolean is
1894    begin
1895       return not UI_Lt (UI_From_Int (Left), Right);
1896    end UI_Ge;
1897
1898    function UI_Ge (Left : Uint; Right : Int) return Boolean is
1899    begin
1900       return not UI_Lt (Left, UI_From_Int (Right));
1901    end UI_Ge;
1902
1903    function UI_Ge (Left : Uint; Right : Uint) return Boolean is
1904    begin
1905       return not UI_Lt (Left, Right);
1906    end UI_Ge;
1907
1908    ------------
1909    -- UI_Gt --
1910    ------------
1911
1912    function UI_Gt (Left : Int; Right : Uint) return Boolean is
1913    begin
1914       return UI_Lt (Right, UI_From_Int (Left));
1915    end UI_Gt;
1916
1917    function UI_Gt (Left : Uint; Right : Int) return Boolean is
1918    begin
1919       return UI_Lt (UI_From_Int (Right), Left);
1920    end UI_Gt;
1921
1922    function UI_Gt (Left : Uint; Right : Uint) return Boolean is
1923    begin
1924       return UI_Lt (Left => Right, Right => Left);
1925    end UI_Gt;
1926
1927    ---------------
1928    -- UI_Image --
1929    ---------------
1930
1931    procedure UI_Image (Input : Uint; Format : UI_Format := Auto) is
1932    begin
1933       Image_Out (Input, True, Format);
1934    end UI_Image;
1935
1936    -------------------------
1937    -- UI_Is_In_Int_Range --
1938    -------------------------
1939
1940    function UI_Is_In_Int_Range (Input : Uint) return Boolean is
1941    begin
1942       --  Make sure we don't get called before Initialize
1943
1944       pragma Assert (Uint_Int_First /= Uint_0);
1945
1946       if Direct (Input) then
1947          return True;
1948       else
1949          return Input >= Uint_Int_First
1950            and then Input <= Uint_Int_Last;
1951       end if;
1952    end UI_Is_In_Int_Range;
1953
1954    ------------
1955    -- UI_Le --
1956    ------------
1957
1958    function UI_Le (Left : Int; Right : Uint) return Boolean is
1959    begin
1960       return not UI_Lt (Right, UI_From_Int (Left));
1961    end UI_Le;
1962
1963    function UI_Le (Left : Uint; Right : Int) return Boolean is
1964    begin
1965       return not UI_Lt (UI_From_Int (Right), Left);
1966    end UI_Le;
1967
1968    function UI_Le (Left : Uint; Right : Uint) return Boolean is
1969    begin
1970       return not UI_Lt (Left => Right, Right => Left);
1971    end UI_Le;
1972
1973    ------------
1974    -- UI_Lt --
1975    ------------
1976
1977    function UI_Lt (Left : Int; Right : Uint) return Boolean is
1978    begin
1979       return UI_Lt (UI_From_Int (Left), Right);
1980    end UI_Lt;
1981
1982    function UI_Lt (Left : Uint; Right : Int) return Boolean is
1983    begin
1984       return UI_Lt (Left, UI_From_Int (Right));
1985    end UI_Lt;
1986
1987    function UI_Lt (Left : Uint; Right : Uint) return Boolean is
1988    begin
1989       --  Quick processing for identical arguments
1990
1991       if Int (Left) = Int (Right) then
1992          return False;
1993
1994       --  Quick processing for both arguments directly represented
1995
1996       elsif Direct (Left) and then Direct (Right) then
1997          return Int (Left) < Int (Right);
1998
1999       --  At least one argument is more than one digit long
2000
2001       else
2002          declare
2003             L_Length : constant Int := N_Digits (Left);
2004             R_Length : constant Int := N_Digits (Right);
2005
2006             L_Vec : UI_Vector (1 .. L_Length);
2007             R_Vec : UI_Vector (1 .. R_Length);
2008
2009          begin
2010             Init_Operand (Left, L_Vec);
2011             Init_Operand (Right, R_Vec);
2012
2013             if L_Vec (1) < Int_0 then
2014
2015                --  First argument negative, second argument non-negative
2016
2017                if R_Vec (1) >= Int_0 then
2018                   return True;
2019
2020                --  Both arguments negative
2021
2022                else
2023                   if L_Length /= R_Length then
2024                      return L_Length > R_Length;
2025
2026                   elsif L_Vec (1) /= R_Vec (1) then
2027                      return L_Vec (1) < R_Vec (1);
2028
2029                   else
2030                      for J in 2 .. L_Vec'Last loop
2031                         if L_Vec (J) /= R_Vec (J) then
2032                            return L_Vec (J) > R_Vec (J);
2033                         end if;
2034                      end loop;
2035
2036                      return False;
2037                   end if;
2038                end if;
2039
2040             else
2041                --  First argument non-negative, second argument negative
2042
2043                if R_Vec (1) < Int_0 then
2044                   return False;
2045
2046                --  Both arguments non-negative
2047
2048                else
2049                   if L_Length /= R_Length then
2050                      return L_Length < R_Length;
2051                   else
2052                      for J in L_Vec'Range loop
2053                         if L_Vec (J) /= R_Vec (J) then
2054                            return L_Vec (J) < R_Vec (J);
2055                         end if;
2056                      end loop;
2057
2058                      return False;
2059                   end if;
2060                end if;
2061             end if;
2062          end;
2063       end if;
2064    end UI_Lt;
2065
2066    ------------
2067    -- UI_Max --
2068    ------------
2069
2070    function UI_Max (Left : Int; Right : Uint) return Uint is
2071    begin
2072       return UI_Max (UI_From_Int (Left), Right);
2073    end UI_Max;
2074
2075    function UI_Max (Left : Uint; Right : Int) return Uint is
2076    begin
2077       return UI_Max (Left, UI_From_Int (Right));
2078    end UI_Max;
2079
2080    function UI_Max (Left : Uint; Right : Uint) return Uint is
2081    begin
2082       if Left >= Right then
2083          return Left;
2084       else
2085          return Right;
2086       end if;
2087    end UI_Max;
2088
2089    ------------
2090    -- UI_Min --
2091    ------------
2092
2093    function UI_Min (Left : Int; Right : Uint) return Uint is
2094    begin
2095       return UI_Min (UI_From_Int (Left), Right);
2096    end UI_Min;
2097
2098    function UI_Min (Left : Uint; Right : Int) return Uint is
2099    begin
2100       return UI_Min (Left, UI_From_Int (Right));
2101    end UI_Min;
2102
2103    function UI_Min (Left : Uint; Right : Uint) return Uint is
2104    begin
2105       if Left <= Right then
2106          return Left;
2107       else
2108          return Right;
2109       end if;
2110    end UI_Min;
2111
2112    -------------
2113    -- UI_Mod --
2114    -------------
2115
2116    function UI_Mod (Left : Int; Right : Uint) return Uint is
2117    begin
2118       return UI_Mod (UI_From_Int (Left), Right);
2119    end UI_Mod;
2120
2121    function UI_Mod (Left : Uint; Right : Int) return Uint is
2122    begin
2123       return UI_Mod (Left, UI_From_Int (Right));
2124    end UI_Mod;
2125
2126    function UI_Mod (Left : Uint; Right : Uint) return Uint is
2127       Urem : constant Uint := Left rem Right;
2128
2129    begin
2130       if (Left < Uint_0) = (Right < Uint_0)
2131         or else Urem = Uint_0
2132       then
2133          return Urem;
2134       else
2135          return Right + Urem;
2136       end if;
2137    end UI_Mod;
2138
2139    -------------------------------
2140    -- UI_Modular_Exponentiation --
2141    -------------------------------
2142
2143    function UI_Modular_Exponentiation
2144      (B      : Uint;
2145       E      : Uint;
2146       Modulo : Uint) return Uint
2147    is
2148       M : constant Save_Mark := Mark;
2149
2150       Result   : Uint := Uint_1;
2151       Base     : Uint := B;
2152       Exponent : Uint := E;
2153
2154    begin
2155       while Exponent /= Uint_0 loop
2156          if Least_Sig_Digit (Exponent) rem Int'(2) = Int'(1) then
2157             Result := (Result * Base) rem Modulo;
2158          end if;
2159
2160          Exponent := Exponent / Uint_2;
2161          Base := (Base * Base) rem Modulo;
2162       end loop;
2163
2164       Release_And_Save (M, Result);
2165       return Result;
2166    end UI_Modular_Exponentiation;
2167
2168    ------------------------
2169    -- UI_Modular_Inverse --
2170    ------------------------
2171
2172    function UI_Modular_Inverse (N : Uint; Modulo : Uint) return Uint is
2173       M : constant Save_Mark := Mark;
2174       U : Uint;
2175       V : Uint;
2176       Q : Uint;
2177       R : Uint;
2178       X : Uint;
2179       Y : Uint;
2180       T : Uint;
2181       S : Int := 1;
2182
2183    begin
2184       U := Modulo;
2185       V := N;
2186
2187       X := Uint_1;
2188       Y := Uint_0;
2189
2190       loop
2191          UI_Div_Rem
2192            (U, V,
2193             Quotient => Q, Remainder => R,
2194             Discard_Quotient  => False,
2195             Discard_Remainder => False);
2196
2197          U := V;
2198          V := R;
2199
2200          T := X;
2201          X := Y + Q * X;
2202          Y := T;
2203          S := -S;
2204
2205          exit when R = Uint_1;
2206       end loop;
2207
2208       if S = Int'(-1) then
2209          X := Modulo - X;
2210       end if;
2211
2212       Release_And_Save (M, X);
2213       return X;
2214    end UI_Modular_Inverse;
2215
2216    ------------
2217    -- UI_Mul --
2218    ------------
2219
2220    function UI_Mul (Left : Int; Right : Uint) return Uint is
2221    begin
2222       return UI_Mul (UI_From_Int (Left), Right);
2223    end UI_Mul;
2224
2225    function UI_Mul (Left : Uint; Right : Int) return Uint is
2226    begin
2227       return UI_Mul (Left, UI_From_Int (Right));
2228    end UI_Mul;
2229
2230    function UI_Mul (Left : Uint; Right : Uint) return Uint is
2231    begin
2232       --  Simple case of single length operands
2233
2234       if Direct (Left) and then Direct (Right) then
2235          return
2236            UI_From_Dint
2237              (Dint (Direct_Val (Left)) * Dint (Direct_Val (Right)));
2238       end if;
2239
2240       --  Otherwise we have the general case (Algorithm M in Knuth)
2241
2242       declare
2243          L_Length : constant Int := N_Digits (Left);
2244          R_Length : constant Int := N_Digits (Right);
2245          L_Vec    : UI_Vector (1 .. L_Length);
2246          R_Vec    : UI_Vector (1 .. R_Length);
2247          Neg      : Boolean;
2248
2249       begin
2250          Init_Operand (Left, L_Vec);
2251          Init_Operand (Right, R_Vec);
2252          Neg := (L_Vec (1) < Int_0) xor (R_Vec (1) < Int_0);
2253          L_Vec (1) := abs (L_Vec (1));
2254          R_Vec (1) := abs (R_Vec (1));
2255
2256          Algorithm_M : declare
2257             Product : UI_Vector (1 .. L_Length + R_Length);
2258             Tmp_Sum : Int;
2259             Carry   : Int;
2260
2261          begin
2262             for J in Product'Range loop
2263                Product (J) := 0;
2264             end loop;
2265
2266             for J in reverse R_Vec'Range loop
2267                Carry := 0;
2268                for K in reverse L_Vec'Range loop
2269                   Tmp_Sum :=
2270                     L_Vec (K) * R_Vec (J) + Product (J + K) + Carry;
2271                   Product (J + K) := Tmp_Sum rem Base;
2272                   Carry := Tmp_Sum / Base;
2273                end loop;
2274
2275                Product (J) := Carry;
2276             end loop;
2277
2278             return Vector_To_Uint (Product, Neg);
2279          end Algorithm_M;
2280       end;
2281    end UI_Mul;
2282
2283    ------------
2284    -- UI_Ne --
2285    ------------
2286
2287    function UI_Ne (Left : Int; Right : Uint) return Boolean is
2288    begin
2289       return UI_Ne (UI_From_Int (Left), Right);
2290    end UI_Ne;
2291
2292    function UI_Ne (Left : Uint; Right : Int) return Boolean is
2293    begin
2294       return UI_Ne (Left, UI_From_Int (Right));
2295    end UI_Ne;
2296
2297    function UI_Ne (Left : Uint; Right : Uint) return Boolean is
2298    begin
2299       --  Quick processing for identical arguments. Note that this takes
2300       --  care of the case of two No_Uint arguments.
2301
2302       if Int (Left) = Int (Right) then
2303          return False;
2304       end if;
2305
2306       --  See if left operand directly represented
2307
2308       if Direct (Left) then
2309
2310          --  If right operand directly represented then compare
2311
2312          if Direct (Right) then
2313             return Int (Left) /= Int (Right);
2314
2315          --  Left operand directly represented, right not, must be unequal
2316
2317          else
2318             return True;
2319          end if;
2320
2321       --  Right operand directly represented, left not, must be unequal
2322
2323       elsif Direct (Right) then
2324          return True;
2325       end if;
2326
2327       --  Otherwise both multi-word, do comparison
2328
2329       declare
2330          Size      : constant Int := N_Digits (Left);
2331          Left_Loc  : Int;
2332          Right_Loc : Int;
2333
2334       begin
2335          if Size /= N_Digits (Right) then
2336             return True;
2337          end if;
2338
2339          Left_Loc  := Uints.Table (Left).Loc;
2340          Right_Loc := Uints.Table (Right).Loc;
2341
2342          for J in Int_0 .. Size - Int_1 loop
2343             if Udigits.Table (Left_Loc + J) /=
2344                Udigits.Table (Right_Loc + J)
2345             then
2346                return True;
2347             end if;
2348          end loop;
2349
2350          return False;
2351       end;
2352    end UI_Ne;
2353
2354    ----------------
2355    -- UI_Negate --
2356    ----------------
2357
2358    function UI_Negate (Right : Uint) return Uint is
2359    begin
2360       --  Case where input is directly represented. Note that since the range
2361       --  of Direct values is non-symmetrical, the result may not be directly
2362       --  represented, this is taken care of in UI_From_Int.
2363
2364       if Direct (Right) then
2365          return UI_From_Int (-Direct_Val (Right));
2366
2367       --  Full processing for multi-digit case. Note that we cannot just copy
2368       --  the value to the end of the table negating the first digit, since the
2369       --  range of Direct values is non-symmetrical, so we can have a negative
2370       --  value that is not Direct whose negation can be represented directly.
2371
2372       else
2373          declare
2374             R_Length : constant Int := N_Digits (Right);
2375             R_Vec    : UI_Vector (1 .. R_Length);
2376             Neg      : Boolean;
2377
2378          begin
2379             Init_Operand (Right, R_Vec);
2380             Neg := R_Vec (1) > Int_0;
2381             R_Vec (1) := abs R_Vec (1);
2382             return Vector_To_Uint (R_Vec, Neg);
2383          end;
2384       end if;
2385    end UI_Negate;
2386
2387    -------------
2388    -- UI_Rem --
2389    -------------
2390
2391    function UI_Rem (Left : Int; Right : Uint) return Uint is
2392    begin
2393       return UI_Rem (UI_From_Int (Left), Right);
2394    end UI_Rem;
2395
2396    function UI_Rem (Left : Uint; Right : Int) return Uint is
2397    begin
2398       return UI_Rem (Left, UI_From_Int (Right));
2399    end UI_Rem;
2400
2401    function UI_Rem (Left, Right : Uint) return Uint is
2402       Sign : Int;
2403       Tmp  : Int;
2404
2405       subtype Int1_12 is Integer range 1 .. 12;
2406
2407    begin
2408       pragma Assert (Right /= Uint_0);
2409
2410       if Direct (Right) then
2411          if Direct (Left) then
2412             return UI_From_Int (Direct_Val (Left) rem Direct_Val (Right));
2413
2414          else
2415
2416             --  Special cases when Right is less than 13 and Left is larger
2417             --  larger than one digit. All of these algorithms depend on the
2418             --  base being 2 ** 15 We work with Abs (Left) and Abs(Right)
2419             --  then multiply result by Sign (Left)
2420
2421             if (Right <= Uint_12) and then (Right >= Uint_Minus_12) then
2422
2423                if Left < Uint_0 then
2424                   Sign := -1;
2425                else
2426                   Sign := 1;
2427                end if;
2428
2429                --  All cases are listed, grouped by mathematical method It is
2430                --  not inefficient to do have this case list out of order since
2431                --  GCC sorts the cases we list.
2432
2433                case Int1_12 (abs (Direct_Val (Right))) is
2434
2435                   when 1 =>
2436                      return Uint_0;
2437
2438                   --  Powers of two are simple AND's with LS Left Digit GCC
2439                   --  will recognise these constants as powers of 2 and replace
2440                   --  the rem with simpler operations where possible.
2441
2442                   --  Least_Sig_Digit might return Negative numbers
2443
2444                   when 2 =>
2445                      return UI_From_Int (
2446                         Sign * (Least_Sig_Digit (Left) mod 2));
2447
2448                   when 4 =>
2449                      return UI_From_Int (
2450                         Sign * (Least_Sig_Digit (Left) mod 4));
2451
2452                   when 8 =>
2453                      return UI_From_Int (
2454                         Sign * (Least_Sig_Digit (Left) mod 8));
2455
2456                   --  Some number theoretical tricks:
2457
2458                   --    If B Rem Right = 1 then
2459                   --    Left Rem Right = Sum_Of_Digits_Base_B (Left) Rem Right
2460
2461                   --  Note: 2^32 mod 3 = 1
2462
2463                   when 3 =>
2464                      return UI_From_Int (
2465                         Sign * (Sum_Double_Digits (Left, 1) rem Int (3)));
2466
2467                   --  Note: 2^15 mod 7 = 1
2468
2469                   when 7 =>
2470                      return UI_From_Int (
2471                         Sign * (Sum_Digits (Left, 1) rem Int (7)));
2472
2473                   --  Note: 2^32 mod 5 = -1
2474
2475                   --  Alternating sums might be negative, but rem is always
2476                   --  positive hence we must use mod here.
2477
2478                   when 5 =>
2479                      Tmp := Sum_Double_Digits (Left, -1) mod Int (5);
2480                      return UI_From_Int (Sign * Tmp);
2481
2482                   --  Note: 2^15 mod 9 = -1
2483
2484                   --  Alternating sums might be negative, but rem is always
2485                   --  positive hence we must use mod here.
2486
2487                   when 9  =>
2488                      Tmp := Sum_Digits (Left, -1) mod Int (9);
2489                      return UI_From_Int (Sign * Tmp);
2490
2491                   --  Note: 2^15 mod 11 = -1
2492
2493                   --  Alternating sums might be negative, but rem is always
2494                   --  positive hence we must use mod here.
2495
2496                   when 11 =>
2497                      Tmp := Sum_Digits (Left, -1) mod Int (11);
2498                      return UI_From_Int (Sign * Tmp);
2499
2500                   --  Now resort to Chinese Remainder theorem to reduce 6, 10,
2501                   --  12 to previous special cases
2502
2503                   --  There is no reason we could not add more cases like these
2504                   --  if it proves useful.
2505
2506                   --  Perhaps we should go up to 16, however we have no "trick"
2507                   --  for 13.
2508
2509                   --  To find u mod m we:
2510
2511                   --  Pick m1, m2 S.T.
2512                   --     GCD(m1, m2) = 1 AND m = (m1 * m2).
2513
2514                   --  Next we pick (Basis) M1, M2 small S.T.
2515                   --     (M1 mod m1) = (M2 mod m2) = 1 AND
2516                   --     (M1 mod m2) = (M2 mod m1) = 0
2517
2518                   --  So u mod m = (u1 * M1 + u2 * M2) mod m Where u1 = (u mod
2519                   --  m1) AND u2 = (u mod m2); Under typical circumstances the
2520                   --  last mod m can be done with a (possible) single
2521                   --  subtraction.
2522
2523                   --  m1 = 2; m2 = 3; M1 = 3; M2 = 4;
2524
2525                   when 6  =>
2526                      Tmp := 3 * (Least_Sig_Digit (Left) rem 2) +
2527                               4 * (Sum_Double_Digits (Left, 1) rem 3);
2528                      return UI_From_Int (Sign * (Tmp rem 6));
2529
2530                   --  m1 = 2; m2 = 5; M1 = 5; M2 = 6;
2531
2532                   when 10 =>
2533                      Tmp := 5 * (Least_Sig_Digit (Left) rem 2) +
2534                               6 * (Sum_Double_Digits (Left, -1) mod 5);
2535                      return UI_From_Int (Sign * (Tmp rem 10));
2536
2537                   --  m1 = 3; m2 = 4; M1 = 4; M2 = 9;
2538
2539                   when 12 =>
2540                      Tmp := 4 * (Sum_Double_Digits (Left, 1) rem 3) +
2541                               9 * (Least_Sig_Digit (Left) rem 4);
2542                      return UI_From_Int (Sign * (Tmp rem 12));
2543                end case;
2544
2545             end if;
2546
2547             --  Else fall through to general case
2548
2549             --  The special case Length (Left) = Length (Right) = 1 in Div
2550             --  looks slow. It uses UI_To_Int when Int should suffice. ???
2551          end if;
2552       end if;
2553
2554       declare
2555          Remainder : Uint;
2556          Quotient  : Uint;
2557          pragma Warnings (Off, Quotient);
2558       begin
2559          UI_Div_Rem
2560            (Left, Right, Quotient, Remainder,
2561             Discard_Quotient  => True,
2562             Discard_Remainder => False);
2563          return Remainder;
2564       end;
2565    end UI_Rem;
2566
2567    ------------
2568    -- UI_Sub --
2569    ------------
2570
2571    function UI_Sub (Left : Int; Right : Uint) return Uint is
2572    begin
2573       return UI_Add (Left, -Right);
2574    end UI_Sub;
2575
2576    function UI_Sub (Left : Uint; Right : Int) return Uint is
2577    begin
2578       return UI_Add (Left, -Right);
2579    end UI_Sub;
2580
2581    function UI_Sub (Left : Uint; Right : Uint) return Uint is
2582    begin
2583       if Direct (Left) and then Direct (Right) then
2584          return UI_From_Int (Direct_Val (Left) - Direct_Val (Right));
2585       else
2586          return UI_Add (Left, -Right);
2587       end if;
2588    end UI_Sub;
2589
2590    --------------
2591    -- UI_To_CC --
2592    --------------
2593
2594    function UI_To_CC (Input : Uint) return Char_Code is
2595    begin
2596       if Direct (Input) then
2597          return Char_Code (Direct_Val (Input));
2598
2599       --  Case of input is more than one digit
2600
2601       else
2602          declare
2603             In_Length : constant Int := N_Digits (Input);
2604             In_Vec    : UI_Vector (1 .. In_Length);
2605             Ret_CC    : Char_Code;
2606
2607          begin
2608             Init_Operand (Input, In_Vec);
2609
2610             --  We assume value is positive
2611
2612             Ret_CC := 0;
2613             for Idx in In_Vec'Range loop
2614                Ret_CC := Ret_CC * Char_Code (Base) +
2615                                   Char_Code (abs In_Vec (Idx));
2616             end loop;
2617
2618             return Ret_CC;
2619          end;
2620       end if;
2621    end UI_To_CC;
2622
2623    ----------------
2624    -- UI_To_Int --
2625    ----------------
2626
2627    function UI_To_Int (Input : Uint) return Int is
2628    begin
2629       if Direct (Input) then
2630          return Direct_Val (Input);
2631
2632       --  Case of input is more than one digit
2633
2634       else
2635          declare
2636             In_Length : constant Int := N_Digits (Input);
2637             In_Vec    : UI_Vector (1 .. In_Length);
2638             Ret_Int   : Int;
2639
2640          begin
2641             --  Uints of more than one digit could be outside the range for
2642             --  Ints. Caller should have checked for this if not certain.
2643             --  Fatal error to attempt to convert from value outside Int'Range.
2644
2645             pragma Assert (UI_Is_In_Int_Range (Input));
2646
2647             --  Otherwise, proceed ahead, we are OK
2648
2649             Init_Operand (Input, In_Vec);
2650             Ret_Int := 0;
2651
2652             --  Calculate -|Input| and then negates if value is positive. This
2653             --  handles our current definition of Int (based on 2s complement).
2654             --  Is it secure enough???
2655
2656             for Idx in In_Vec'Range loop
2657                Ret_Int := Ret_Int * Base - abs In_Vec (Idx);
2658             end loop;
2659
2660             if In_Vec (1) < Int_0 then
2661                return Ret_Int;
2662             else
2663                return -Ret_Int;
2664             end if;
2665          end;
2666       end if;
2667    end UI_To_Int;
2668
2669    --------------
2670    -- UI_Write --
2671    --------------
2672
2673    procedure UI_Write (Input : Uint; Format : UI_Format := Auto) is
2674    begin
2675       Image_Out (Input, False, Format);
2676    end UI_Write;
2677
2678    ---------------------
2679    -- Vector_To_Uint --
2680    ---------------------
2681
2682    function Vector_To_Uint
2683      (In_Vec   : UI_Vector;
2684       Negative : Boolean)
2685       return     Uint
2686    is
2687       Size : Int;
2688       Val  : Int;
2689
2690    begin
2691       --  The vector can contain leading zeros. These are not stored in the
2692       --  table, so loop through the vector looking for first non-zero digit
2693
2694       for J in In_Vec'Range loop
2695          if In_Vec (J) /= Int_0 then
2696
2697             --  The length of the value is the length of the rest of the vector
2698
2699             Size := In_Vec'Last - J + 1;
2700
2701             --  One digit value can always be represented directly
2702
2703             if Size = Int_1 then
2704                if Negative then
2705                   return Uint (Int (Uint_Direct_Bias) - In_Vec (J));
2706                else
2707                   return Uint (Int (Uint_Direct_Bias) + In_Vec (J));
2708                end if;
2709
2710             --  Positive two digit values may be in direct representation range
2711
2712             elsif Size = Int_2 and then not Negative then
2713                Val := In_Vec (J) * Base + In_Vec (J + 1);
2714
2715                if Val <= Max_Direct then
2716                   return Uint (Int (Uint_Direct_Bias) + Val);
2717                end if;
2718             end if;
2719
2720             --  The value is outside the direct representation range and must
2721             --  therefore be stored in the table. Expand the table to contain
2722             --  the count and digits. The index of the new table entry will be
2723             --  returned as the result.
2724
2725             Uints.Append ((Length => Size, Loc => Udigits.Last + 1));
2726
2727             if Negative then
2728                Val := -In_Vec (J);
2729             else
2730                Val := +In_Vec (J);
2731             end if;
2732
2733             Udigits.Append (Val);
2734
2735             for K in 2 .. Size loop
2736                Udigits.Append (In_Vec (J + K - 1));
2737             end loop;
2738
2739             return Uints.Last;
2740          end if;
2741       end loop;
2742
2743       --  Dropped through loop only if vector contained all zeros
2744
2745       return Uint_0;
2746    end Vector_To_Uint;
2747
2748 end Uintp;