1 ------------------------------------------------------------------------------
3 -- GNAT COMPILER COMPONENTS --
9 -- Copyright (C) 1992-2010, Free Software Foundation, Inc. --
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. --
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. --
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/>. --
27 -- GNAT was originally developed by the GNAT team at New York University. --
28 -- Extensive contributions were provided by Ada Core Technologies Inc. --
30 ------------------------------------------------------------------------------
32 with Output; use Output;
33 with Tree_IO; use Tree_IO;
35 with GNAT.HTable; use GNAT.HTable;
39 ------------------------
40 -- Local Declarations --
41 ------------------------
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.
51 -- Uint value containing Int'Last value set by Initialize
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.
60 -- Number of entries set in UI_Power_2;
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.
66 UI_Power_10_Set : Nat;
67 -- Number of entries set in UI_Power_10;
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.
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).
83 ----------------------------
84 -- UI_From_Int Hash Table --
85 ----------------------------
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
91 subtype Hnum is Nat range 0 .. 1022;
93 function Hash_Num (F : Int) return Hnum;
96 package UI_Ints is new Simple_HTable (
99 No_Element => No_Uint,
104 -----------------------
105 -- Local Subprograms --
106 -----------------------
108 function Direct (U : Uint) return Boolean;
109 pragma Inline (Direct);
110 -- Returns True if U is represented directly
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.
116 function GCD (Jin, Kin : Int) return Int;
117 -- Compute GCD of two integers. Assumes that Jin >= Kin >= 0
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.
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
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
146 procedure Most_Sig_2_Digits
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.
156 function N_Digits (Input : Uint) return Int;
157 pragma Inline (N_Digits);
158 -- Returns number of "digits" in a Uint
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.
164 function Sum_Double_Digits (Left : Uint; Sign : Int) return Int;
165 -- Same as above but work in New_Base = Base * Base
170 Remainder : out Uint;
171 Discard_Quotient : Boolean := False;
172 Discard_Remainder : Boolean := False);
173 -- Compute Euclidean division of Left by Right. If Discard_Quotient is
174 -- False then the quotient is returned in Quotient (otherwise Quotient is
175 -- set to No_Uint). If Discard_Remainder is False, then the remainder is
176 -- returned in Remainder (otherwise Remainder is set to No_Uint).
178 -- If Discard_Quotient is True, Quotient is set to No_Uint
179 -- If Discard_Remainder is True, Remainder is set to No_Uint
181 function Vector_To_Uint
183 Negative : Boolean) return Uint;
184 -- Functions that calculate values in UI_Vectors, call this function to
185 -- create and return the Uint value. In_Vec contains the multiple precision
186 -- (Base) representation of a non-negative value. Leading zeroes are
187 -- permitted. Negative is set if the desired result is the negative of the
188 -- given value. The result will be either the appropriate directly
189 -- represented value, or a table entry in the proper canonical format is
190 -- created and returned.
192 -- Note that Init_Operand puts a signed value in the result vector, but
193 -- Vector_To_Uint is always presented with a non-negative value. The
194 -- processing of signs is something that is done by the caller before
195 -- calling Vector_To_Uint.
201 function Direct (U : Uint) return Boolean is
203 return Int (U) <= Int (Uint_Direct_Last);
210 function Direct_Val (U : Uint) return Int is
212 pragma Assert (Direct (U));
213 return Int (U) - Int (Uint_Direct_Bias);
220 function GCD (Jin, Kin : Int) return Int is
224 pragma Assert (Jin >= Kin);
225 pragma Assert (Kin >= Int_0);
229 while K /= Uint_0 loop
242 function Hash_Num (F : Int) return Hnum is
244 return Types."mod" (F, Hnum'Range_Length);
256 Marks : constant Uintp.Save_Mark := Uintp.Mark;
260 Digs_Output : Natural := 0;
261 -- Counts digits output. In hex mode, but not in decimal mode, we
262 -- put an underline after every four hex digits that are output.
264 Exponent : Natural := 0;
265 -- If the number is too long to fit in the buffer, we switch to an
266 -- approximate output format with an exponent. This variable records
267 -- the exponent value.
269 function Better_In_Hex return Boolean;
270 -- Determines if it is better to generate digits in base 16 (result
271 -- is true) or base 10 (result is false). The choice is purely a
272 -- matter of convenience and aesthetics, so it does not matter which
273 -- value is returned from a correctness point of view.
275 procedure Image_Char (C : Character);
276 -- Internal procedure to output one character
278 procedure Image_Exponent (N : Natural);
279 -- Output non-zero exponent. Note that we only use the exponent form in
280 -- the buffer case, so we know that To_Buffer is true.
282 procedure Image_Uint (U : Uint);
283 -- Internal procedure to output characters of non-negative Uint
289 function Better_In_Hex return Boolean is
290 T16 : constant Uint := Uint_2 ** Int'(16);
296 -- Small values up to 2**16 can always be in decimal
302 -- Otherwise, see if we are a power of 2 or one less than a power
303 -- of 2. For the moment these are the only cases printed in hex.
305 if A mod Uint_2 = Uint_1 then
310 if A mod T16 /= Uint_0 then
320 while A > Uint_2 loop
321 if A mod Uint_2 /= Uint_0 then
336 procedure Image_Char (C : Character) is
339 if UI_Image_Length + 6 > UI_Image_Max then
340 Exponent := Exponent + 1;
342 UI_Image_Length := UI_Image_Length + 1;
343 UI_Image_Buffer (UI_Image_Length) := C;
354 procedure Image_Exponent (N : Natural) is
357 Image_Exponent (N / 10);
360 UI_Image_Length := UI_Image_Length + 1;
361 UI_Image_Buffer (UI_Image_Length) :=
362 Character'Val (Character'Pos ('0') + N mod 10);
369 procedure Image_Uint (U : Uint) is
370 H : constant array (Int range 0 .. 15) of Character :=
375 Image_Uint (U / Base);
378 if Digs_Output = 4 and then Base = Uint_16 then
383 Image_Char (H (UI_To_Int (U rem Base)));
385 Digs_Output := Digs_Output + 1;
388 -- Start of processing for Image_Out
391 if Input = No_Uint then
396 UI_Image_Length := 0;
398 if Input < Uint_0 then
406 or else (Format = Auto and then Better_In_Hex)
420 if Exponent /= 0 then
421 UI_Image_Length := UI_Image_Length + 1;
422 UI_Image_Buffer (UI_Image_Length) := 'E';
423 Image_Exponent (Exponent);
426 Uintp.Release (Marks);
433 procedure Init_Operand (UI : Uint; Vec : out UI_Vector) is
436 pragma Assert (Vec'First = Int'(1));
440 Vec (1) := Direct_Val (UI);
442 if Vec (1) >= Base then
443 Vec (2) := Vec (1) rem Base;
444 Vec (1) := Vec (1) / Base;
448 Loc := Uints.Table (UI).Loc;
450 for J in 1 .. Uints.Table (UI).Length loop
451 Vec (J) := Udigits.Table (Loc + J - 1);
460 procedure Initialize is
465 Uint_Int_First := UI_From_Int (Int'First);
466 Uint_Int_Last := UI_From_Int (Int'Last);
468 UI_Power_2 (0) := Uint_1;
471 UI_Power_10 (0) := Uint_1;
472 UI_Power_10_Set := 0;
474 Uints_Min := Uints.Last;
475 Udigits_Min := Udigits.Last;
480 ---------------------
481 -- Least_Sig_Digit --
482 ---------------------
484 function Least_Sig_Digit (Arg : Uint) return Int is
489 V := Direct_Val (Arg);
495 -- Note that this result may be negative
502 (Uints.Table (Arg).Loc + Uints.Table (Arg).Length - 1);
510 function Mark return Save_Mark is
512 return (Save_Uint => Uints.Last, Save_Udigit => Udigits.Last);
515 -----------------------
516 -- Most_Sig_2_Digits --
517 -----------------------
519 procedure Most_Sig_2_Digits
526 pragma Assert (Left >= Right);
528 if Direct (Left) then
529 Left_Hat := Direct_Val (Left);
530 Right_Hat := Direct_Val (Right);
536 Udigits.Table (Uints.Table (Left).Loc);
538 Udigits.Table (Uints.Table (Left).Loc + 1);
541 -- It is not so clear what to return when Arg is negative???
543 Left_Hat := abs (L1) * Base + L2;
548 Length_L : constant Int := Uints.Table (Left).Length;
555 if Direct (Right) then
556 T := Direct_Val (Left);
557 R1 := abs (T / Base);
562 R1 := abs (Udigits.Table (Uints.Table (Right).Loc));
563 R2 := Udigits.Table (Uints.Table (Right).Loc + 1);
564 Length_R := Uints.Table (Right).Length;
567 if Length_L = Length_R then
568 Right_Hat := R1 * Base + R2;
569 elsif Length_L = Length_R + Int_1 then
575 end Most_Sig_2_Digits;
581 -- Note: N_Digits returns 1 for No_Uint
583 function N_Digits (Input : Uint) return Int is
585 if Direct (Input) then
586 if Direct_Val (Input) >= Base then
593 return Uints.Table (Input).Length;
601 function Num_Bits (Input : Uint) return Nat is
606 -- Largest negative number has to be handled specially, since it is in
607 -- Int_Range, but we cannot take the absolute value.
609 if Input = Uint_Int_First then
612 -- For any other number in Int_Range, get absolute value of number
614 elsif UI_Is_In_Int_Range (Input) then
615 Num := abs (UI_To_Int (Input));
618 -- If not in Int_Range then initialize bit count for all low order
619 -- words, and set number to high order digit.
622 Bits := Base_Bits * (Uints.Table (Input).Length - 1);
623 Num := abs (Udigits.Table (Uints.Table (Input).Loc));
626 -- Increase bit count for remaining value in Num
628 while Types.">" (Num, 0) loop
640 procedure pid (Input : Uint) is
642 UI_Write (Input, Decimal);
650 procedure pih (Input : Uint) is
652 UI_Write (Input, Hex);
660 procedure Release (M : Save_Mark) is
662 Uints.Set_Last (Uint'Max (M.Save_Uint, Uints_Min));
663 Udigits.Set_Last (Int'Max (M.Save_Udigit, Udigits_Min));
666 ----------------------
667 -- Release_And_Save --
668 ----------------------
670 procedure Release_And_Save (M : Save_Mark; UI : in out Uint) is
677 UE_Len : constant Pos := Uints.Table (UI).Length;
678 UE_Loc : constant Int := Uints.Table (UI).Loc;
680 UD : constant Udigits.Table_Type (1 .. UE_Len) :=
681 Udigits.Table (UE_Loc .. UE_Loc + UE_Len - 1);
686 Uints.Append ((Length => UE_Len, Loc => Udigits.Last + 1));
689 for J in 1 .. UE_Len loop
690 Udigits.Append (UD (J));
694 end Release_And_Save;
696 procedure Release_And_Save (M : Save_Mark; UI1, UI2 : in out Uint) is
699 Release_And_Save (M, UI2);
701 elsif Direct (UI2) then
702 Release_And_Save (M, UI1);
706 UE1_Len : constant Pos := Uints.Table (UI1).Length;
707 UE1_Loc : constant Int := Uints.Table (UI1).Loc;
709 UD1 : constant Udigits.Table_Type (1 .. UE1_Len) :=
710 Udigits.Table (UE1_Loc .. UE1_Loc + UE1_Len - 1);
712 UE2_Len : constant Pos := Uints.Table (UI2).Length;
713 UE2_Loc : constant Int := Uints.Table (UI2).Loc;
715 UD2 : constant Udigits.Table_Type (1 .. UE2_Len) :=
716 Udigits.Table (UE2_Loc .. UE2_Loc + UE2_Len - 1);
721 Uints.Append ((Length => UE1_Len, Loc => Udigits.Last + 1));
724 for J in 1 .. UE1_Len loop
725 Udigits.Append (UD1 (J));
728 Uints.Append ((Length => UE2_Len, Loc => Udigits.Last + 1));
731 for J in 1 .. UE2_Len loop
732 Udigits.Append (UD2 (J));
736 end Release_And_Save;
742 -- This is done in one pass
744 -- Mathematically: assume base congruent to 1 and compute an equivalent
747 -- If Sign = -1 return the alternating sum of the "digits"
749 -- D1 - D2 + D3 - D4 + D5 ...
751 -- (where D1 is Least Significant Digit)
753 -- Mathematically: assume base congruent to -1 and compute an equivalent
756 -- This is used in Rem and Base is assumed to be 2 ** 15
758 -- Note: The next two functions are very similar, any style changes made
759 -- to one should be reflected in both. These would be simpler if we
760 -- worked base 2 ** 32.
762 function Sum_Digits (Left : Uint; Sign : Int) return Int is
764 pragma Assert (Sign = Int_1 or else Sign = Int (-1));
766 -- First try simple case;
768 if Direct (Left) then
770 Tmp_Int : Int := Direct_Val (Left);
773 if Tmp_Int >= Base then
774 Tmp_Int := (Tmp_Int / Base) +
775 Sign * (Tmp_Int rem Base);
777 -- Now Tmp_Int is in [-(Base - 1) .. 2 * (Base - 1)]
779 if Tmp_Int >= Base then
783 Tmp_Int := (Tmp_Int / Base) + 1;
787 -- Now Tmp_Int is in [-(Base - 1) .. (Base - 1)]
794 -- Otherwise full circuit is needed
798 L_Length : constant Int := N_Digits (Left);
799 L_Vec : UI_Vector (1 .. L_Length);
805 Init_Operand (Left, L_Vec);
806 L_Vec (1) := abs L_Vec (1);
811 for J in reverse 1 .. L_Length loop
812 Tmp_Int := Tmp_Int + Alt * (L_Vec (J) + Carry);
814 -- Tmp_Int is now between [-2 * Base + 1 .. 2 * Base - 1],
815 -- since old Tmp_Int is between [-(Base - 1) .. Base - 1]
816 -- and L_Vec is in [0 .. Base - 1] and Carry in [-1 .. 1]
818 if Tmp_Int >= Base then
819 Tmp_Int := Tmp_Int - Base;
822 elsif Tmp_Int <= -Base then
823 Tmp_Int := Tmp_Int + Base;
830 -- Tmp_Int is now between [-Base + 1 .. Base - 1]
835 Tmp_Int := Tmp_Int + Alt * Carry;
837 -- Tmp_Int is now between [-Base .. Base]
839 if Tmp_Int >= Base then
840 Tmp_Int := Tmp_Int - Base + Alt * Sign * 1;
842 elsif Tmp_Int <= -Base then
843 Tmp_Int := Tmp_Int + Base + Alt * Sign * (-1);
846 -- Now Tmp_Int is in [-(Base - 1) .. (Base - 1)]
853 -----------------------
854 -- Sum_Double_Digits --
855 -----------------------
857 -- Note: This is used in Rem, Base is assumed to be 2 ** 15
859 function Sum_Double_Digits (Left : Uint; Sign : Int) return Int is
861 -- First try simple case;
863 pragma Assert (Sign = Int_1 or else Sign = Int (-1));
865 if Direct (Left) then
866 return Direct_Val (Left);
868 -- Otherwise full circuit is needed
872 L_Length : constant Int := N_Digits (Left);
873 L_Vec : UI_Vector (1 .. L_Length);
881 Init_Operand (Left, L_Vec);
882 L_Vec (1) := abs L_Vec (1);
890 Least_Sig_Int := Least_Sig_Int + Alt * (L_Vec (J) + Carry);
892 -- Least is in [-2 Base + 1 .. 2 * Base - 1]
893 -- Since L_Vec in [0 .. Base - 1] and Carry in [-1 .. 1]
894 -- and old Least in [-Base + 1 .. Base - 1]
896 if Least_Sig_Int >= Base then
897 Least_Sig_Int := Least_Sig_Int - Base;
900 elsif Least_Sig_Int <= -Base then
901 Least_Sig_Int := Least_Sig_Int + Base;
908 -- Least is now in [-Base + 1 .. Base - 1]
910 Most_Sig_Int := Most_Sig_Int + Alt * (L_Vec (J - 1) + Carry);
912 -- Most is in [-2 Base + 1 .. 2 * Base - 1]
913 -- Since L_Vec in [0 .. Base - 1] and Carry in [-1 .. 1]
914 -- and old Most in [-Base + 1 .. Base - 1]
916 if Most_Sig_Int >= Base then
917 Most_Sig_Int := Most_Sig_Int - Base;
920 elsif Most_Sig_Int <= -Base then
921 Most_Sig_Int := Most_Sig_Int + Base;
927 -- Most is now in [-Base + 1 .. Base - 1]
934 Least_Sig_Int := Least_Sig_Int + Alt * (L_Vec (J) + Carry);
936 Least_Sig_Int := Least_Sig_Int + Alt * Carry;
939 if Least_Sig_Int >= Base then
940 Least_Sig_Int := Least_Sig_Int - Base;
941 Most_Sig_Int := Most_Sig_Int + Alt * 1;
943 elsif Least_Sig_Int <= -Base then
944 Least_Sig_Int := Least_Sig_Int + Base;
945 Most_Sig_Int := Most_Sig_Int + Alt * (-1);
948 if Most_Sig_Int >= Base then
949 Most_Sig_Int := Most_Sig_Int - Base;
952 Least_Sig_Int + Alt * 1; -- cannot overflow again
954 elsif Most_Sig_Int <= -Base then
955 Most_Sig_Int := Most_Sig_Int + Base;
958 Least_Sig_Int + Alt * (-1); -- cannot overflow again.
961 return Most_Sig_Int * Base + Least_Sig_Int;
964 end Sum_Double_Digits;
970 procedure Tree_Read is
975 Tree_Read_Int (Int (Uint_Int_First));
976 Tree_Read_Int (Int (Uint_Int_Last));
977 Tree_Read_Int (UI_Power_2_Set);
978 Tree_Read_Int (UI_Power_10_Set);
979 Tree_Read_Int (Int (Uints_Min));
980 Tree_Read_Int (Udigits_Min);
982 for J in 0 .. UI_Power_2_Set loop
983 Tree_Read_Int (Int (UI_Power_2 (J)));
986 for J in 0 .. UI_Power_10_Set loop
987 Tree_Read_Int (Int (UI_Power_10 (J)));
996 procedure Tree_Write is
1001 Tree_Write_Int (Int (Uint_Int_First));
1002 Tree_Write_Int (Int (Uint_Int_Last));
1003 Tree_Write_Int (UI_Power_2_Set);
1004 Tree_Write_Int (UI_Power_10_Set);
1005 Tree_Write_Int (Int (Uints_Min));
1006 Tree_Write_Int (Udigits_Min);
1008 for J in 0 .. UI_Power_2_Set loop
1009 Tree_Write_Int (Int (UI_Power_2 (J)));
1012 for J in 0 .. UI_Power_10_Set loop
1013 Tree_Write_Int (Int (UI_Power_10 (J)));
1022 function UI_Abs (Right : Uint) return Uint is
1024 if Right < Uint_0 then
1035 function UI_Add (Left : Int; Right : Uint) return Uint is
1037 return UI_Add (UI_From_Int (Left), Right);
1040 function UI_Add (Left : Uint; Right : Int) return Uint is
1042 return UI_Add (Left, UI_From_Int (Right));
1045 function UI_Add (Left : Uint; Right : Uint) return Uint is
1047 -- Simple cases of direct operands and addition of zero
1049 if Direct (Left) then
1050 if Direct (Right) then
1051 return UI_From_Int (Direct_Val (Left) + Direct_Val (Right));
1053 elsif Int (Left) = Int (Uint_0) then
1057 elsif Direct (Right) and then Int (Right) = Int (Uint_0) then
1061 -- Otherwise full circuit is needed
1064 L_Length : constant Int := N_Digits (Left);
1065 R_Length : constant Int := N_Digits (Right);
1066 L_Vec : UI_Vector (1 .. L_Length);
1067 R_Vec : UI_Vector (1 .. R_Length);
1072 X_Bigger : Boolean := False;
1073 Y_Bigger : Boolean := False;
1074 Result_Neg : Boolean := False;
1077 Init_Operand (Left, L_Vec);
1078 Init_Operand (Right, R_Vec);
1080 -- At least one of the two operands is in multi-digit form.
1081 -- Calculate the number of digits sufficient to hold result.
1083 if L_Length > R_Length then
1084 Sum_Length := L_Length + 1;
1087 Sum_Length := R_Length + 1;
1089 if R_Length > L_Length then
1094 -- Make copies of the absolute values of L_Vec and R_Vec into X and Y
1095 -- both with lengths equal to the maximum possibly needed. This makes
1096 -- looping over the digits much simpler.
1099 X : UI_Vector (1 .. Sum_Length);
1100 Y : UI_Vector (1 .. Sum_Length);
1101 Tmp_UI : UI_Vector (1 .. Sum_Length);
1104 for J in 1 .. Sum_Length - L_Length loop
1108 X (Sum_Length - L_Length + 1) := abs L_Vec (1);
1110 for J in 2 .. L_Length loop
1111 X (J + (Sum_Length - L_Length)) := L_Vec (J);
1114 for J in 1 .. Sum_Length - R_Length loop
1118 Y (Sum_Length - R_Length + 1) := abs R_Vec (1);
1120 for J in 2 .. R_Length loop
1121 Y (J + (Sum_Length - R_Length)) := R_Vec (J);
1124 if (L_Vec (1) < Int_0) = (R_Vec (1) < Int_0) then
1126 -- Same sign so just add
1129 for J in reverse 1 .. Sum_Length loop
1130 Tmp_Int := X (J) + Y (J) + Carry;
1132 if Tmp_Int >= Base then
1133 Tmp_Int := Tmp_Int - Base;
1142 return Vector_To_Uint (X, L_Vec (1) < Int_0);
1145 -- Find which one has bigger magnitude
1147 if not (X_Bigger or Y_Bigger) then
1148 for J in L_Vec'Range loop
1149 if abs L_Vec (J) > abs R_Vec (J) then
1152 elsif abs R_Vec (J) > abs L_Vec (J) then
1159 -- If they have identical magnitude, just return 0, else swap
1160 -- if necessary so that X had the bigger magnitude. Determine
1161 -- if result is negative at this time.
1163 Result_Neg := False;
1165 if not (X_Bigger or Y_Bigger) then
1169 if R_Vec (1) < Int_0 then
1178 if L_Vec (1) < Int_0 then
1183 -- Subtract Y from the bigger X
1187 for J in reverse 1 .. Sum_Length loop
1188 Tmp_Int := X (J) - Y (J) + Borrow;
1190 if Tmp_Int < Int_0 then
1191 Tmp_Int := Tmp_Int + Base;
1200 return Vector_To_Uint (X, Result_Neg);
1207 --------------------------
1208 -- UI_Decimal_Digits_Hi --
1209 --------------------------
1211 function UI_Decimal_Digits_Hi (U : Uint) return Nat is
1213 -- The maximum value of a "digit" is 32767, which is 5 decimal digits,
1214 -- so an N_Digit number could take up to 5 times this number of digits.
1215 -- This is certainly too high for large numbers but it is not worth
1218 return 5 * N_Digits (U);
1219 end UI_Decimal_Digits_Hi;
1221 --------------------------
1222 -- UI_Decimal_Digits_Lo --
1223 --------------------------
1225 function UI_Decimal_Digits_Lo (U : Uint) return Nat is
1227 -- The maximum value of a "digit" is 32767, which is more than four
1228 -- decimal digits, but not a full five digits. The easily computed
1229 -- minimum number of decimal digits is thus 1 + 4 * the number of
1230 -- digits. This is certainly too low for large numbers but it is not
1231 -- worth worrying about.
1233 return 1 + 4 * (N_Digits (U) - 1);
1234 end UI_Decimal_Digits_Lo;
1240 function UI_Div (Left : Int; Right : Uint) return Uint is
1242 return UI_Div (UI_From_Int (Left), Right);
1245 function UI_Div (Left : Uint; Right : Int) return Uint is
1247 return UI_Div (Left, UI_From_Int (Right));
1250 function UI_Div (Left, Right : Uint) return Uint is
1253 pragma Warnings (Off, Remainder);
1257 Quotient, Remainder,
1258 Discard_Remainder => True);
1266 procedure UI_Div_Rem
1267 (Left, Right : Uint;
1268 Quotient : out Uint;
1269 Remainder : out Uint;
1270 Discard_Quotient : Boolean := False;
1271 Discard_Remainder : Boolean := False)
1273 pragma Warnings (Off, Quotient);
1274 pragma Warnings (Off, Remainder);
1276 pragma Assert (Right /= Uint_0);
1278 Quotient := No_Uint;
1279 Remainder := No_Uint;
1281 -- Cases where both operands are represented directly
1283 if Direct (Left) and then Direct (Right) then
1285 DV_Left : constant Int := Direct_Val (Left);
1286 DV_Right : constant Int := Direct_Val (Right);
1289 if not Discard_Quotient then
1290 Quotient := UI_From_Int (DV_Left / DV_Right);
1293 if not Discard_Remainder then
1294 Remainder := UI_From_Int (DV_Left rem DV_Right);
1302 L_Length : constant Int := N_Digits (Left);
1303 R_Length : constant Int := N_Digits (Right);
1304 Q_Length : constant Int := L_Length - R_Length + 1;
1305 L_Vec : UI_Vector (1 .. L_Length);
1306 R_Vec : UI_Vector (1 .. R_Length);
1314 procedure UI_Div_Vector
1317 Quotient : out UI_Vector;
1318 Remainder : out Int);
1319 pragma Inline (UI_Div_Vector);
1320 -- Specialised variant for case where the divisor is a single digit
1322 procedure UI_Div_Vector
1325 Quotient : out UI_Vector;
1326 Remainder : out Int)
1332 for J in L_Vec'Range loop
1333 Tmp_Int := Remainder * Base + abs L_Vec (J);
1334 Quotient (Quotient'First + J - L_Vec'First) := Tmp_Int / R_Int;
1335 Remainder := Tmp_Int rem R_Int;
1338 if L_Vec (L_Vec'First) < Int_0 then
1339 Remainder := -Remainder;
1343 -- Start of processing for UI_Div_Rem
1346 -- Result is zero if left operand is shorter than right
1348 if L_Length < R_Length then
1349 if not Discard_Quotient then
1353 if not Discard_Remainder then
1360 Init_Operand (Left, L_Vec);
1361 Init_Operand (Right, R_Vec);
1363 -- Case of right operand is single digit. Here we can simply divide
1364 -- each digit of the left operand by the divisor, from most to least
1365 -- significant, carrying the remainder to the next digit (just like
1366 -- ordinary long division by hand).
1368 if R_Length = Int_1 then
1369 Tmp_Divisor := abs R_Vec (1);
1372 Quotient_V : UI_Vector (1 .. L_Length);
1375 UI_Div_Vector (L_Vec, Tmp_Divisor, Quotient_V, Remainder_I);
1377 if not Discard_Quotient then
1380 (Quotient_V, (L_Vec (1) < Int_0 xor R_Vec (1) < Int_0));
1383 if not Discard_Remainder then
1384 Remainder := UI_From_Int (Remainder_I);
1391 -- The possible simple cases have been exhausted. Now turn to the
1392 -- algorithm D from the section of Knuth mentioned at the top of
1395 Algorithm_D : declare
1396 Dividend : UI_Vector (1 .. L_Length + 1);
1397 Divisor : UI_Vector (1 .. R_Length);
1398 Quotient_V : UI_Vector (1 .. Q_Length);
1404 -- [ NORMALIZE ] (step D1 in the algorithm). First calculate the
1405 -- scale d, and then multiply Left and Right (u and v in the book)
1406 -- by d to get the dividend and divisor to work with.
1408 D := Base / (abs R_Vec (1) + 1);
1411 Dividend (2) := abs L_Vec (1);
1413 for J in 3 .. L_Length + Int_1 loop
1414 Dividend (J) := L_Vec (J - 1);
1417 Divisor (1) := abs R_Vec (1);
1419 for J in Int_2 .. R_Length loop
1420 Divisor (J) := R_Vec (J);
1425 -- Multiply Dividend by D
1428 for J in reverse Dividend'Range loop
1429 Tmp_Int := Dividend (J) * D + Carry;
1430 Dividend (J) := Tmp_Int rem Base;
1431 Carry := Tmp_Int / Base;
1434 -- Multiply Divisor by d
1437 for J in reverse Divisor'Range loop
1438 Tmp_Int := Divisor (J) * D + Carry;
1439 Divisor (J) := Tmp_Int rem Base;
1440 Carry := Tmp_Int / Base;
1444 -- Main loop of long division algorithm
1446 Divisor_Dig1 := Divisor (1);
1447 Divisor_Dig2 := Divisor (2);
1449 for J in Quotient_V'Range loop
1451 -- [ CALCULATE Q (hat) ] (step D3 in the algorithm)
1453 Tmp_Int := Dividend (J) * Base + Dividend (J + 1);
1457 if Dividend (J) = Divisor_Dig1 then
1458 Q_Guess := Base - 1;
1460 Q_Guess := Tmp_Int / Divisor_Dig1;
1465 while Divisor_Dig2 * Q_Guess >
1466 (Tmp_Int - Q_Guess * Divisor_Dig1) * Base +
1469 Q_Guess := Q_Guess - 1;
1472 -- [ MULTIPLY & SUBTRACT ] (step D4). Q_Guess * Divisor is
1473 -- subtracted from the remaining dividend.
1476 for K in reverse Divisor'Range loop
1477 Tmp_Int := Dividend (J + K) - Q_Guess * Divisor (K) + Carry;
1478 Tmp_Dig := Tmp_Int rem Base;
1479 Carry := Tmp_Int / Base;
1481 if Tmp_Dig < Int_0 then
1482 Tmp_Dig := Tmp_Dig + Base;
1486 Dividend (J + K) := Tmp_Dig;
1489 Dividend (J) := Dividend (J) + Carry;
1491 -- [ TEST REMAINDER ] & [ ADD BACK ] (steps D5 and D6)
1493 -- Here there is a slight difference from the book: the last
1494 -- carry is always added in above and below (cancelling each
1495 -- other). In fact the dividend going negative is used as
1498 -- If the Dividend went negative, then Q_Guess was off by
1499 -- one, so it is decremented, and the divisor is added back
1500 -- into the relevant portion of the dividend.
1502 if Dividend (J) < Int_0 then
1503 Q_Guess := Q_Guess - 1;
1506 for K in reverse Divisor'Range loop
1507 Tmp_Int := Dividend (J + K) + Divisor (K) + Carry;
1509 if Tmp_Int >= Base then
1510 Tmp_Int := Tmp_Int - Base;
1516 Dividend (J + K) := Tmp_Int;
1519 Dividend (J) := Dividend (J) + Carry;
1522 -- Finally we can get the next quotient digit
1524 Quotient_V (J) := Q_Guess;
1527 -- [ UNNORMALIZE ] (step D8)
1529 if not Discard_Quotient then
1530 Quotient := Vector_To_Uint
1531 (Quotient_V, (L_Vec (1) < Int_0 xor R_Vec (1) < Int_0));
1534 if not Discard_Remainder then
1536 Remainder_V : UI_Vector (1 .. R_Length);
1538 pragma Warnings (Off, Discard_Int);
1541 (Dividend (Dividend'Last - R_Length + 1 .. Dividend'Last),
1543 Remainder_V, Discard_Int);
1544 Remainder := Vector_To_Uint (Remainder_V, L_Vec (1) < Int_0);
1555 function UI_Eq (Left : Int; Right : Uint) return Boolean is
1557 return not UI_Ne (UI_From_Int (Left), Right);
1560 function UI_Eq (Left : Uint; Right : Int) return Boolean is
1562 return not UI_Ne (Left, UI_From_Int (Right));
1565 function UI_Eq (Left : Uint; Right : Uint) return Boolean is
1567 return not UI_Ne (Left, Right);
1574 function UI_Expon (Left : Int; Right : Uint) return Uint is
1576 return UI_Expon (UI_From_Int (Left), Right);
1579 function UI_Expon (Left : Uint; Right : Int) return Uint is
1581 return UI_Expon (Left, UI_From_Int (Right));
1584 function UI_Expon (Left : Int; Right : Int) return Uint is
1586 return UI_Expon (UI_From_Int (Left), UI_From_Int (Right));
1589 function UI_Expon (Left : Uint; Right : Uint) return Uint is
1591 pragma Assert (Right >= Uint_0);
1593 -- Any value raised to power of 0 is 1
1595 if Right = Uint_0 then
1598 -- 0 to any positive power is 0
1600 elsif Left = Uint_0 then
1603 -- 1 to any power is 1
1605 elsif Left = Uint_1 then
1608 -- Any value raised to power of 1 is that value
1610 elsif Right = Uint_1 then
1613 -- Cases which can be done by table lookup
1615 elsif Right <= Uint_64 then
1617 -- 2 ** N for N in 2 .. 64
1619 if Left = Uint_2 then
1621 Right_Int : constant Int := Direct_Val (Right);
1624 if Right_Int > UI_Power_2_Set then
1625 for J in UI_Power_2_Set + Int_1 .. Right_Int loop
1626 UI_Power_2 (J) := UI_Power_2 (J - Int_1) * Int_2;
1627 Uints_Min := Uints.Last;
1628 Udigits_Min := Udigits.Last;
1631 UI_Power_2_Set := Right_Int;
1634 return UI_Power_2 (Right_Int);
1637 -- 10 ** N for N in 2 .. 64
1639 elsif Left = Uint_10 then
1641 Right_Int : constant Int := Direct_Val (Right);
1644 if Right_Int > UI_Power_10_Set then
1645 for J in UI_Power_10_Set + Int_1 .. Right_Int loop
1646 UI_Power_10 (J) := UI_Power_10 (J - Int_1) * Int (10);
1647 Uints_Min := Uints.Last;
1648 Udigits_Min := Udigits.Last;
1651 UI_Power_10_Set := Right_Int;
1654 return UI_Power_10 (Right_Int);
1659 -- If we fall through, then we have the general case (see Knuth 4.6.3)
1663 Squares : Uint := Left;
1664 Result : Uint := Uint_1;
1665 M : constant Uintp.Save_Mark := Uintp.Mark;
1669 if (Least_Sig_Digit (N) mod Int_2) = Int_1 then
1670 Result := Result * Squares;
1674 exit when N = Uint_0;
1675 Squares := Squares * Squares;
1678 Uintp.Release_And_Save (M, Result);
1687 function UI_From_CC (Input : Char_Code) return Uint is
1689 return UI_From_Int (Int (Input));
1696 function UI_From_Int (Input : Int) return Uint is
1700 if Min_Direct <= Input and then Input <= Max_Direct then
1701 return Uint (Int (Uint_Direct_Bias) + Input);
1704 -- If already in the hash table, return entry
1706 U := UI_Ints.Get (Input);
1708 if U /= No_Uint then
1712 -- For values of larger magnitude, compute digits into a vector and call
1716 Max_For_Int : constant := 3;
1717 -- Base is defined so that 3 Uint digits is sufficient to hold the
1718 -- largest possible Int value.
1720 V : UI_Vector (1 .. Max_For_Int);
1722 Temp_Integer : Int := Input;
1725 for J in reverse V'Range loop
1726 V (J) := abs (Temp_Integer rem Base);
1727 Temp_Integer := Temp_Integer / Base;
1730 U := Vector_To_Uint (V, Input < Int_0);
1731 UI_Ints.Set (Input, U);
1732 Uints_Min := Uints.Last;
1733 Udigits_Min := Udigits.Last;
1742 -- Lehmer's algorithm for GCD
1744 -- The idea is to avoid using multiple precision arithmetic wherever
1745 -- possible, substituting Int arithmetic instead. See Knuth volume II,
1746 -- Algorithm L (page 329).
1748 -- We use the same notation as Knuth (U_Hat standing for the obvious!)
1750 function UI_GCD (Uin, Vin : Uint) return Uint is
1752 -- Copies of Uin and Vin
1755 -- The most Significant digits of U,V
1757 A, B, C, D, T, Q, Den1, Den2 : Int;
1760 Marks : constant Uintp.Save_Mark := Uintp.Mark;
1761 Iterations : Integer := 0;
1764 pragma Assert (Uin >= Vin);
1765 pragma Assert (Vin >= Uint_0);
1771 Iterations := Iterations + 1;
1778 UI_From_Int (GCD (Direct_Val (V), UI_To_Int (U rem V)));
1782 Most_Sig_2_Digits (U, V, U_Hat, V_Hat);
1789 -- We might overflow and get division by zero here. This just
1790 -- means we cannot take the single precision step
1794 exit when Den1 = Int_0 or else Den2 = Int_0;
1796 -- Compute Q, the trial quotient
1798 Q := (U_Hat + A) / Den1;
1800 exit when Q /= ((U_Hat + B) / Den2);
1802 -- A single precision step Euclid step will give same answer as a
1803 -- multiprecision one.
1813 T := U_Hat - (Q * V_Hat);
1819 -- Take a multiprecision Euclid step
1823 -- No single precision steps take a regular Euclid step
1830 -- Use prior single precision steps to compute this Euclid step
1832 -- For constructs such as:
1833 -- sqrt_2: constant := 1.41421_35623_73095_04880_16887_24209_698;
1834 -- sqrt_eps: constant long_float := long_float( 1.0 / sqrt_2)
1835 -- ** long_float'machine_mantissa;
1837 -- we spend 80% of our time working on this step. Perhaps we need
1838 -- a special case Int / Uint dot product to speed things up. ???
1840 -- Alternatively we could increase the single precision iterations
1841 -- to handle Uint's of some small size ( <5 digits?). Then we
1842 -- would have more iterations on small Uint. On the code above, we
1843 -- only get 5 (on average) single precision iterations per large
1846 Tmp_UI := (UI_From_Int (A) * U) + (UI_From_Int (B) * V);
1847 V := (UI_From_Int (C) * U) + (UI_From_Int (D) * V);
1851 -- If the operands are very different in magnitude, the loop will
1852 -- generate large amounts of short-lived data, which it is worth
1853 -- removing periodically.
1855 if Iterations > 100 then
1856 Release_And_Save (Marks, U, V);
1866 function UI_Ge (Left : Int; Right : Uint) return Boolean is
1868 return not UI_Lt (UI_From_Int (Left), Right);
1871 function UI_Ge (Left : Uint; Right : Int) return Boolean is
1873 return not UI_Lt (Left, UI_From_Int (Right));
1876 function UI_Ge (Left : Uint; Right : Uint) return Boolean is
1878 return not UI_Lt (Left, Right);
1885 function UI_Gt (Left : Int; Right : Uint) return Boolean is
1887 return UI_Lt (Right, UI_From_Int (Left));
1890 function UI_Gt (Left : Uint; Right : Int) return Boolean is
1892 return UI_Lt (UI_From_Int (Right), Left);
1895 function UI_Gt (Left : Uint; Right : Uint) return Boolean is
1897 return UI_Lt (Left => Right, Right => Left);
1904 procedure UI_Image (Input : Uint; Format : UI_Format := Auto) is
1906 Image_Out (Input, True, Format);
1909 -------------------------
1910 -- UI_Is_In_Int_Range --
1911 -------------------------
1913 function UI_Is_In_Int_Range (Input : Uint) return Boolean is
1915 -- Make sure we don't get called before Initialize
1917 pragma Assert (Uint_Int_First /= Uint_0);
1919 if Direct (Input) then
1922 return Input >= Uint_Int_First
1923 and then Input <= Uint_Int_Last;
1925 end UI_Is_In_Int_Range;
1931 function UI_Le (Left : Int; Right : Uint) return Boolean is
1933 return not UI_Lt (Right, UI_From_Int (Left));
1936 function UI_Le (Left : Uint; Right : Int) return Boolean is
1938 return not UI_Lt (UI_From_Int (Right), Left);
1941 function UI_Le (Left : Uint; Right : Uint) return Boolean is
1943 return not UI_Lt (Left => Right, Right => Left);
1950 function UI_Lt (Left : Int; Right : Uint) return Boolean is
1952 return UI_Lt (UI_From_Int (Left), Right);
1955 function UI_Lt (Left : Uint; Right : Int) return Boolean is
1957 return UI_Lt (Left, UI_From_Int (Right));
1960 function UI_Lt (Left : Uint; Right : Uint) return Boolean is
1962 -- Quick processing for identical arguments
1964 if Int (Left) = Int (Right) then
1967 -- Quick processing for both arguments directly represented
1969 elsif Direct (Left) and then Direct (Right) then
1970 return Int (Left) < Int (Right);
1972 -- At least one argument is more than one digit long
1976 L_Length : constant Int := N_Digits (Left);
1977 R_Length : constant Int := N_Digits (Right);
1979 L_Vec : UI_Vector (1 .. L_Length);
1980 R_Vec : UI_Vector (1 .. R_Length);
1983 Init_Operand (Left, L_Vec);
1984 Init_Operand (Right, R_Vec);
1986 if L_Vec (1) < Int_0 then
1988 -- First argument negative, second argument non-negative
1990 if R_Vec (1) >= Int_0 then
1993 -- Both arguments negative
1996 if L_Length /= R_Length then
1997 return L_Length > R_Length;
1999 elsif L_Vec (1) /= R_Vec (1) then
2000 return L_Vec (1) < R_Vec (1);
2003 for J in 2 .. L_Vec'Last loop
2004 if L_Vec (J) /= R_Vec (J) then
2005 return L_Vec (J) > R_Vec (J);
2014 -- First argument non-negative, second argument negative
2016 if R_Vec (1) < Int_0 then
2019 -- Both arguments non-negative
2022 if L_Length /= R_Length then
2023 return L_Length < R_Length;
2025 for J in L_Vec'Range loop
2026 if L_Vec (J) /= R_Vec (J) then
2027 return L_Vec (J) < R_Vec (J);
2043 function UI_Max (Left : Int; Right : Uint) return Uint is
2045 return UI_Max (UI_From_Int (Left), Right);
2048 function UI_Max (Left : Uint; Right : Int) return Uint is
2050 return UI_Max (Left, UI_From_Int (Right));
2053 function UI_Max (Left : Uint; Right : Uint) return Uint is
2055 if Left >= Right then
2066 function UI_Min (Left : Int; Right : Uint) return Uint is
2068 return UI_Min (UI_From_Int (Left), Right);
2071 function UI_Min (Left : Uint; Right : Int) return Uint is
2073 return UI_Min (Left, UI_From_Int (Right));
2076 function UI_Min (Left : Uint; Right : Uint) return Uint is
2078 if Left <= Right then
2089 function UI_Mod (Left : Int; Right : Uint) return Uint is
2091 return UI_Mod (UI_From_Int (Left), Right);
2094 function UI_Mod (Left : Uint; Right : Int) return Uint is
2096 return UI_Mod (Left, UI_From_Int (Right));
2099 function UI_Mod (Left : Uint; Right : Uint) return Uint is
2100 Urem : constant Uint := Left rem Right;
2103 if (Left < Uint_0) = (Right < Uint_0)
2104 or else Urem = Uint_0
2108 return Right + Urem;
2112 -------------------------------
2113 -- UI_Modular_Exponentiation --
2114 -------------------------------
2116 function UI_Modular_Exponentiation
2119 Modulo : Uint) return Uint
2121 M : constant Save_Mark := Mark;
2123 Result : Uint := Uint_1;
2125 Exponent : Uint := E;
2128 while Exponent /= Uint_0 loop
2129 if Least_Sig_Digit (Exponent) rem Int'(2) = Int'(1) then
2130 Result := (Result * Base) rem Modulo;
2133 Exponent := Exponent / Uint_2;
2134 Base := (Base * Base) rem Modulo;
2137 Release_And_Save (M, Result);
2139 end UI_Modular_Exponentiation;
2141 ------------------------
2142 -- UI_Modular_Inverse --
2143 ------------------------
2145 function UI_Modular_Inverse (N : Uint; Modulo : Uint) return Uint is
2146 M : constant Save_Mark := Mark;
2164 UI_Div_Rem (U, V, Quotient => Q, Remainder => R);
2174 exit when R = Uint_1;
2177 if S = Int'(-1) then
2181 Release_And_Save (M, X);
2183 end UI_Modular_Inverse;
2189 function UI_Mul (Left : Int; Right : Uint) return Uint is
2191 return UI_Mul (UI_From_Int (Left), Right);
2194 function UI_Mul (Left : Uint; Right : Int) return Uint is
2196 return UI_Mul (Left, UI_From_Int (Right));
2199 function UI_Mul (Left : Uint; Right : Uint) return Uint is
2201 -- Case where product fits in the range of a 32-bit integer
2203 if Int (Left) <= Int (Uint_Max_Simple_Mul)
2205 Int (Right) <= Int (Uint_Max_Simple_Mul)
2207 return UI_From_Int (Direct_Val (Left) * Direct_Val (Right));
2210 -- Otherwise we have the general case (Algorithm M in Knuth)
2213 L_Length : constant Int := N_Digits (Left);
2214 R_Length : constant Int := N_Digits (Right);
2215 L_Vec : UI_Vector (1 .. L_Length);
2216 R_Vec : UI_Vector (1 .. R_Length);
2220 Init_Operand (Left, L_Vec);
2221 Init_Operand (Right, R_Vec);
2222 Neg := (L_Vec (1) < Int_0) xor (R_Vec (1) < Int_0);
2223 L_Vec (1) := abs (L_Vec (1));
2224 R_Vec (1) := abs (R_Vec (1));
2226 Algorithm_M : declare
2227 Product : UI_Vector (1 .. L_Length + R_Length);
2232 for J in Product'Range loop
2236 for J in reverse R_Vec'Range loop
2238 for K in reverse L_Vec'Range loop
2240 L_Vec (K) * R_Vec (J) + Product (J + K) + Carry;
2241 Product (J + K) := Tmp_Sum rem Base;
2242 Carry := Tmp_Sum / Base;
2245 Product (J) := Carry;
2248 return Vector_To_Uint (Product, Neg);
2257 function UI_Ne (Left : Int; Right : Uint) return Boolean is
2259 return UI_Ne (UI_From_Int (Left), Right);
2262 function UI_Ne (Left : Uint; Right : Int) return Boolean is
2264 return UI_Ne (Left, UI_From_Int (Right));
2267 function UI_Ne (Left : Uint; Right : Uint) return Boolean is
2269 -- Quick processing for identical arguments. Note that this takes
2270 -- care of the case of two No_Uint arguments.
2272 if Int (Left) = Int (Right) then
2276 -- See if left operand directly represented
2278 if Direct (Left) then
2280 -- If right operand directly represented then compare
2282 if Direct (Right) then
2283 return Int (Left) /= Int (Right);
2285 -- Left operand directly represented, right not, must be unequal
2291 -- Right operand directly represented, left not, must be unequal
2293 elsif Direct (Right) then
2297 -- Otherwise both multi-word, do comparison
2300 Size : constant Int := N_Digits (Left);
2305 if Size /= N_Digits (Right) then
2309 Left_Loc := Uints.Table (Left).Loc;
2310 Right_Loc := Uints.Table (Right).Loc;
2312 for J in Int_0 .. Size - Int_1 loop
2313 if Udigits.Table (Left_Loc + J) /=
2314 Udigits.Table (Right_Loc + J)
2328 function UI_Negate (Right : Uint) return Uint is
2330 -- Case where input is directly represented. Note that since the range
2331 -- of Direct values is non-symmetrical, the result may not be directly
2332 -- represented, this is taken care of in UI_From_Int.
2334 if Direct (Right) then
2335 return UI_From_Int (-Direct_Val (Right));
2337 -- Full processing for multi-digit case. Note that we cannot just copy
2338 -- the value to the end of the table negating the first digit, since the
2339 -- range of Direct values is non-symmetrical, so we can have a negative
2340 -- value that is not Direct whose negation can be represented directly.
2344 R_Length : constant Int := N_Digits (Right);
2345 R_Vec : UI_Vector (1 .. R_Length);
2349 Init_Operand (Right, R_Vec);
2350 Neg := R_Vec (1) > Int_0;
2351 R_Vec (1) := abs R_Vec (1);
2352 return Vector_To_Uint (R_Vec, Neg);
2361 function UI_Rem (Left : Int; Right : Uint) return Uint is
2363 return UI_Rem (UI_From_Int (Left), Right);
2366 function UI_Rem (Left : Uint; Right : Int) return Uint is
2368 return UI_Rem (Left, UI_From_Int (Right));
2371 function UI_Rem (Left, Right : Uint) return Uint is
2375 subtype Int1_12 is Integer range 1 .. 12;
2378 pragma Assert (Right /= Uint_0);
2380 if Direct (Right) then
2381 if Direct (Left) then
2382 return UI_From_Int (Direct_Val (Left) rem Direct_Val (Right));
2386 -- Special cases when Right is less than 13 and Left is larger
2387 -- larger than one digit. All of these algorithms depend on the
2388 -- base being 2 ** 15 We work with Abs (Left) and Abs(Right)
2389 -- then multiply result by Sign (Left)
2391 if (Right <= Uint_12) and then (Right >= Uint_Minus_12) then
2393 if Left < Uint_0 then
2399 -- All cases are listed, grouped by mathematical method It is
2400 -- not inefficient to do have this case list out of order since
2401 -- GCC sorts the cases we list.
2403 case Int1_12 (abs (Direct_Val (Right))) is
2408 -- Powers of two are simple AND's with LS Left Digit GCC
2409 -- will recognise these constants as powers of 2 and replace
2410 -- the rem with simpler operations where possible.
2412 -- Least_Sig_Digit might return Negative numbers
2415 return UI_From_Int (
2416 Sign * (Least_Sig_Digit (Left) mod 2));
2419 return UI_From_Int (
2420 Sign * (Least_Sig_Digit (Left) mod 4));
2423 return UI_From_Int (
2424 Sign * (Least_Sig_Digit (Left) mod 8));
2426 -- Some number theoretical tricks:
2428 -- If B Rem Right = 1 then
2429 -- Left Rem Right = Sum_Of_Digits_Base_B (Left) Rem Right
2431 -- Note: 2^32 mod 3 = 1
2434 return UI_From_Int (
2435 Sign * (Sum_Double_Digits (Left, 1) rem Int (3)));
2437 -- Note: 2^15 mod 7 = 1
2440 return UI_From_Int (
2441 Sign * (Sum_Digits (Left, 1) rem Int (7)));
2443 -- Note: 2^32 mod 5 = -1
2445 -- Alternating sums might be negative, but rem is always
2446 -- positive hence we must use mod here.
2449 Tmp := Sum_Double_Digits (Left, -1) mod Int (5);
2450 return UI_From_Int (Sign * Tmp);
2452 -- Note: 2^15 mod 9 = -1
2454 -- Alternating sums might be negative, but rem is always
2455 -- positive hence we must use mod here.
2458 Tmp := Sum_Digits (Left, -1) mod Int (9);
2459 return UI_From_Int (Sign * Tmp);
2461 -- Note: 2^15 mod 11 = -1
2463 -- Alternating sums might be negative, but rem is always
2464 -- positive hence we must use mod here.
2467 Tmp := Sum_Digits (Left, -1) mod Int (11);
2468 return UI_From_Int (Sign * Tmp);
2470 -- Now resort to Chinese Remainder theorem to reduce 6, 10,
2471 -- 12 to previous special cases
2473 -- There is no reason we could not add more cases like these
2474 -- if it proves useful.
2476 -- Perhaps we should go up to 16, however we have no "trick"
2479 -- To find u mod m we:
2482 -- GCD(m1, m2) = 1 AND m = (m1 * m2).
2484 -- Next we pick (Basis) M1, M2 small S.T.
2485 -- (M1 mod m1) = (M2 mod m2) = 1 AND
2486 -- (M1 mod m2) = (M2 mod m1) = 0
2488 -- So u mod m = (u1 * M1 + u2 * M2) mod m Where u1 = (u mod
2489 -- m1) AND u2 = (u mod m2); Under typical circumstances the
2490 -- last mod m can be done with a (possible) single
2493 -- m1 = 2; m2 = 3; M1 = 3; M2 = 4;
2496 Tmp := 3 * (Least_Sig_Digit (Left) rem 2) +
2497 4 * (Sum_Double_Digits (Left, 1) rem 3);
2498 return UI_From_Int (Sign * (Tmp rem 6));
2500 -- m1 = 2; m2 = 5; M1 = 5; M2 = 6;
2503 Tmp := 5 * (Least_Sig_Digit (Left) rem 2) +
2504 6 * (Sum_Double_Digits (Left, -1) mod 5);
2505 return UI_From_Int (Sign * (Tmp rem 10));
2507 -- m1 = 3; m2 = 4; M1 = 4; M2 = 9;
2510 Tmp := 4 * (Sum_Double_Digits (Left, 1) rem 3) +
2511 9 * (Least_Sig_Digit (Left) rem 4);
2512 return UI_From_Int (Sign * (Tmp rem 12));
2517 -- Else fall through to general case
2519 -- The special case Length (Left) = Length (Right) = 1 in Div
2520 -- looks slow. It uses UI_To_Int when Int should suffice. ???
2527 pragma Warnings (Off, Quotient);
2530 (Left, Right, Quotient, Remainder, Discard_Quotient => True);
2539 function UI_Sub (Left : Int; Right : Uint) return Uint is
2541 return UI_Add (Left, -Right);
2544 function UI_Sub (Left : Uint; Right : Int) return Uint is
2546 return UI_Add (Left, -Right);
2549 function UI_Sub (Left : Uint; Right : Uint) return Uint is
2551 if Direct (Left) and then Direct (Right) then
2552 return UI_From_Int (Direct_Val (Left) - Direct_Val (Right));
2554 return UI_Add (Left, -Right);
2562 function UI_To_CC (Input : Uint) return Char_Code is
2564 if Direct (Input) then
2565 return Char_Code (Direct_Val (Input));
2567 -- Case of input is more than one digit
2571 In_Length : constant Int := N_Digits (Input);
2572 In_Vec : UI_Vector (1 .. In_Length);
2576 Init_Operand (Input, In_Vec);
2578 -- We assume value is positive
2581 for Idx in In_Vec'Range loop
2582 Ret_CC := Ret_CC * Char_Code (Base) +
2583 Char_Code (abs In_Vec (Idx));
2595 function UI_To_Int (Input : Uint) return Int is
2597 if Direct (Input) then
2598 return Direct_Val (Input);
2600 -- Case of input is more than one digit
2604 In_Length : constant Int := N_Digits (Input);
2605 In_Vec : UI_Vector (1 .. In_Length);
2609 -- Uints of more than one digit could be outside the range for
2610 -- Ints. Caller should have checked for this if not certain.
2611 -- Fatal error to attempt to convert from value outside Int'Range.
2613 pragma Assert (UI_Is_In_Int_Range (Input));
2615 -- Otherwise, proceed ahead, we are OK
2617 Init_Operand (Input, In_Vec);
2620 -- Calculate -|Input| and then negates if value is positive. This
2621 -- handles our current definition of Int (based on 2s complement).
2622 -- Is it secure enough???
2624 for Idx in In_Vec'Range loop
2625 Ret_Int := Ret_Int * Base - abs In_Vec (Idx);
2628 if In_Vec (1) < Int_0 then
2641 procedure UI_Write (Input : Uint; Format : UI_Format := Auto) is
2643 Image_Out (Input, False, Format);
2646 ---------------------
2647 -- Vector_To_Uint --
2648 ---------------------
2650 function Vector_To_Uint
2651 (In_Vec : UI_Vector;
2659 -- The vector can contain leading zeros. These are not stored in the
2660 -- table, so loop through the vector looking for first non-zero digit
2662 for J in In_Vec'Range loop
2663 if In_Vec (J) /= Int_0 then
2665 -- The length of the value is the length of the rest of the vector
2667 Size := In_Vec'Last - J + 1;
2669 -- One digit value can always be represented directly
2671 if Size = Int_1 then
2673 return Uint (Int (Uint_Direct_Bias) - In_Vec (J));
2675 return Uint (Int (Uint_Direct_Bias) + In_Vec (J));
2678 -- Positive two digit values may be in direct representation range
2680 elsif Size = Int_2 and then not Negative then
2681 Val := In_Vec (J) * Base + In_Vec (J + 1);
2683 if Val <= Max_Direct then
2684 return Uint (Int (Uint_Direct_Bias) + Val);
2688 -- The value is outside the direct representation range and must
2689 -- therefore be stored in the table. Expand the table to contain
2690 -- the count and digits. The index of the new table entry will be
2691 -- returned as the result.
2693 Uints.Append ((Length => Size, Loc => Udigits.Last + 1));
2701 Udigits.Append (Val);
2703 for K in 2 .. Size loop
2704 Udigits.Append (In_Vec (J + K - 1));
2711 -- Dropped through loop only if vector contained all zeros