1------------------------------------------------------------------------------
2--                                                                          --
3--                         GNAT COMPILER COMPONENTS                         --
4--                                                                          --
5--                       S Y S T E M . B I G N U M S                        --
6--                                                                          --
7--                                 S p e c                                  --
8--                                                                          --
9--            Copyright (C) 2012, 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--  This package provides arbitrary precision signed integer arithmetic for
33--  use in computing intermediate values in expressions for the case where
34--  pragma Overflow_Check (Eliminated) is in effect.
35
36with Interfaces;
37
38package System.Bignums is
39
40   pragma Assert (Long_Long_Integer'Size = 64);
41   --  This package assumes that Long_Long_Integer size is 64 bit (i.e. that it
42   --  has a range of -2**63 to 2**63-1). The front end ensures that the mode
43   --  ELIMINATED is not allowed for overflow checking if this is not the case.
44
45   subtype Length is Natural range 0 .. 2 ** 23 - 1;
46   --  Represent number of words in Digit_Vector
47
48   Base : constant := 2 ** 32;
49   --  Digit vectors use this base
50
51   subtype SD is Interfaces.Unsigned_32;
52   --  Single length digit
53
54   type Digit_Vector is array (Length range <>) of SD;
55   --  Represent digits of a number (most significant digit first)
56
57   type Bignum_Data (Len : Length) is record
58      Neg : Boolean;
59      --  Set if value is negative, never set for zero
60
61      D : Digit_Vector (1 .. Len);
62      --  Digits of number, most significant first, represented in base
63      --  2**Base. No leading zeroes are stored, and the value of zero is
64      --  represented using an empty vector for D.
65   end record;
66
67   for Bignum_Data use record
68      Len at 0 range 0 .. 23;
69      Neg at 3 range 0 .. 7;
70   end record;
71
72   type Bignum is access all Bignum_Data;
73   --  This is the type that is used externally. Possibly this could be a
74   --  private type, but we leave the structure exposed for now. For one
75   --  thing it helps with debugging. Note that this package never shares
76   --  an allocated Bignum value, so for example for X + 0, a copy of X is
77   --  returned, not X itself.
78
79   --  Note: none of the subprograms in this package modify the Bignum_Data
80   --  records referenced by Bignum arguments of mode IN.
81
82   function Big_Add (X, Y : Bignum) return Bignum;  --  "+"
83   function Big_Sub (X, Y : Bignum) return Bignum;  --  "-"
84   function Big_Mul (X, Y : Bignum) return Bignum;  --  "*"
85   function Big_Div (X, Y : Bignum) return Bignum;  --  "/"
86   function Big_Exp (X, Y : Bignum) return Bignum;  --  "**"
87   function Big_Mod (X, Y : Bignum) return Bignum;  --  "mod"
88   function Big_Rem (X, Y : Bignum) return Bignum;  --  "rem"
89   function Big_Neg (X    : Bignum) return Bignum;  --  "-"
90   function Big_Abs (X    : Bignum) return Bignum;  --  "abs"
91   --  Perform indicated arithmetic operation on bignum values. No exception
92   --  raised except for Div/Mod/Rem by 0 which raises Constraint_Error with
93   --  an appropriate message.
94
95   function Big_EQ  (X, Y : Bignum) return Boolean;  -- "="
96   function Big_NE  (X, Y : Bignum) return Boolean;  -- "/="
97   function Big_GE  (X, Y : Bignum) return Boolean;  -- ">="
98   function Big_LE  (X, Y : Bignum) return Boolean;  -- "<="
99   function Big_GT  (X, Y : Bignum) return Boolean;  --  ">"
100   function Big_LT  (X, Y : Bignum) return Boolean;  --  "<"
101   --  Perform indicated comparison on bignums, returning result as Boolean.
102   --  No exception raised for any input arguments.
103
104   function Bignum_In_LLI_Range (X : Bignum) return Boolean;
105   --  Returns True if the Bignum value is in the range of Long_Long_Integer,
106   --  so that a call to From_Bignum is guaranteed not to raise an exception.
107
108   function To_Bignum (X : Long_Long_Integer) return Bignum;
109   --  Convert Long_Long_Integer to Bignum. No exception can be raised for any
110   --  input argument.
111
112   function From_Bignum (X : Bignum) return Long_Long_Integer;
113   --  Convert Bignum to Long_Long_Integer. Constraint_Error raised with
114   --  appropriate message if value is out of range of Long_Long_Integer.
115
116end System.Bignums;
117