/usr/share/ada/adainclude/gmpada/gnu_multiple_precision-big_integers.ads is in libgmpada4-dev 0.0.20131223-1.
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-- Copyright (C) 2007-2010 Nicolas Boulenguez <nicolas.boulenguez@free.fr>
--
-- This program is free software: you can redistribute it and/or modify
-- it under the terms of the GNU General Public License as published by
-- the Free Software Foundation, either version 3 of the License, or
-- (at your option) any later version.
--
-- This program is distributed in the hope that it will be useful,
-- but WITHOUT ANY WARRANTY; without even the implied warranty of
-- MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-- GNU General Public License for more details.
--
-- You should have received a copy of the GNU General Public License
-- along with this program. If not, see <http://www.gnu.org/licenses/>.
package GNU_Multiple_Precision.Big_Integers is
pragma Preelaborate;
function "<" (Left, Right : Big_Integer) return Boolean;
function "<=" (Left, Right : Big_Integer) return Boolean;
function ">" (Left, Right : Big_Integer) return Boolean;
function ">=" (Left, Right : Big_Integer) return Boolean;
function "+" (Right : Big_Integer) return Big_Integer;
function "-" (Right : Big_Integer) return Big_Integer;
function "abs" (Right : Big_Integer) return Big_Integer;
function "+" (Left, Right : Big_Integer) return Big_Integer;
function "-" (Left, Right : Big_Integer) return Big_Integer;
function "*" (Left, Right : Big_Integer) return Big_Integer;
function "/" (Left, Right : Big_Integer) return Big_Integer;
function "rem" (Left, Right : Big_Integer) return Big_Integer;
function "mod" (Left, Right : Big_Integer) return Big_Integer;
function "**" (Left : Big_Integer; Right : Natural) return Big_Integer;
function "and"(Left, Right : Big_Integer) return Big_Integer;
function "or" (Left, Right : Big_Integer) return Big_Integer;
function "xor"(Left, Right : Big_Integer) return Big_Integer;
function Image (Item : Big_Integer) return String;
function Wide_Image (Item : Big_Integer) return Wide_String;
function Wide_Wide_Image (Item : Big_Integer) return Wide_Wide_String;
function Value (Item : String) return Big_Integer;
function Wide_Value (Item : Wide_String) return Big_Integer;
function Wide_Wide_Value (Item : Wide_Wide_String) return Big_Integer;
function Max (Left, Right : Big_Integer) return Big_Integer;
function Min (Left, Right : Big_Integer) return Big_Integer;
function Pred (Arg : Big_Integer) return Big_Integer;
function Succ (Arg : Big_Integer) return Big_Integer;
----------------------
-- Initialization --
----------------------
-- Initialization (to 0), Finalization and Assignment are handled
-- through a controlled type.
procedure Reallocate (Object : in out Big_Integer;
New_Space : in Bit_Count);
-- Change the space allocated for Object to New_Space bits. The
-- value in Object is preserved if it fits, or is set to 0 if not.
-- This function can be used to increase the space for a variable
-- in order to avoid repeated automatic reallocations, or to
-- decrease it to give memory back to the heap.
------------------
-- Assignment --
------------------
procedure Set (Rop : in out Big_Integer;
Op : in Big_Integer);
procedure Swap (Rop1, Rop2 : in out Big_Integer);
-------------------
-- Conversions --
-------------------
-- are provided below.
------------------
-- Arithmetic --
------------------
procedure Add
(Sum : in out Big_Integer;
Addend1, Addend2 : in Big_Integer);
procedure Subtract
(Difference : in out Big_Integer;
Minuend, Subtrahend : in Big_Integer);
procedure Multiply
(Product : in out Big_Integer;
Multiplier, Multiplicand : in Big_Integer);
procedure Add_A_Product
(Rop : in out Big_Integer;
Op1, Op2 : in Big_Integer);
procedure Subtract_A_Product
(Rop : in out Big_Integer;
Op1, Op2 : in Big_Integer);
procedure Multiply_2_Exp (Rop : in out Big_Integer;
Op1 : in Big_Integer;
Op2 : in Bit_Count);
procedure Negate
(Negated_Operand : in out Big_Integer;
Operand : in Big_Integer);
procedure Absolute_Value
(Rop : in out Big_Integer;
Op : in Big_Integer);
----------------
-- Division --
----------------
type Division_Style is (Ceil, Floor, Truncate);
procedure Divide (Q : in out Big_Integer;
N, D : in Big_Integer;
Style : in Division_Style := Truncate);
procedure Remainder (R : in out Big_Integer;
N, D : in Big_Integer;
Style : in Division_Style := Truncate);
procedure Divide (Q, R : in out Big_Integer;
N, D : in Big_Integer;
Style : in Division_Style := Truncate);
procedure Divide_2_Exp
(Q : in out Big_Integer;
N : in Big_Integer;
B : in Bit_Count;
Style : in Division_Style := Truncate);
procedure Remainder_2_Exp
(R : in out Big_Integer;
N : in Big_Integer;
B : in Bit_Count;
Style : in Division_Style := Truncate);
procedure Modulo (R : in out Big_Integer;
N, D : in Big_Integer);
procedure Divide_Exactly (Q : in out Big_Integer;
N, D : in Big_Integer);
-- Set q to n/d. This function produce correct results only when
-- it is known in advance that D divides N. This routine is much
-- faster than the other division functions, and are the best
-- choice when exact division is known to occur, for example
-- reducing a rational to lowest terms.
function Is_Divisible (N, D : Big_Integer) return Boolean;
function Is_Divisible_2_Exp (N : Big_Integer;
B : Bit_Count) return Boolean;
function Is_Congruent (N, C, Modulo : Big_Integer) return Boolean;
function Is_Congruent_2_Exp (N, C : Big_Integer;
B : Bit_Count) return Boolean;
----------------------
-- Exponentiation --
----------------------
procedure Exponentiate (Rop : in out Big_Integer;
Base, Exponent, Modulo : in Big_Integer);
procedure Exponentiate (Rop : in out Big_Integer;
Base : in Big_Integer;
Exponent : in Natural);
-----------------------
-- Root Extraction --
-----------------------
procedure Root
(Rop : in out Big_Integer;
Is_Exact_Power : out Boolean;
Op : in Big_Integer;
N : in Natural);
procedure Root_Remainder
(Root, Remainder : in out Big_Integer;
U : in Big_Integer;
N : in Natural);
procedure Square_Root
(Root : in out Big_Integer;
U : in Big_Integer);
procedure Square_Root_Remainder
(Root, Remainder : in out Big_Integer;
U : in Big_Integer);
function Is_Perfect_Power (Op : Big_Integer) return Boolean;
function Is_Perfect_Square (Op : Big_Integer) return Boolean;
---------------------
-- Number Theory --
---------------------
type Prime_Status is (Composite, Probably_Prime, Prime);
function Probably_Prime (N : Big_Integer;
Test_Count : Positive)
return Prime_Status;
procedure Next_Prime
(Rop : in out Big_Integer;
Op : in Big_Integer);
-- This function uses a probabilistic algorithm to identify
-- primes. For practical purposes it's adequate, The chance of a
-- composite passing will be extremely small.
procedure Greatest_Common_Divisor
(G : in out Big_Integer;
A, B : in Big_Integer);
procedure Greatest_Common_Divisor
(G, S : in out Big_Integer;
A, B : in Big_Integer);
procedure Greatest_Common_Divisor
(G, S, T : in out Big_Integer;
A, B : in Big_Integer);
-- 0<G=AS+BT
procedure Least_Common_Multiple
(Rop : in out Big_Integer;
Op1, Op2 : in Big_Integer);
procedure Invert
(Exists : out Boolean;
Rop : in out Big_Integer;
Op, Modulo : in Big_Integer);
function Jacobi (A, B : Big_Integer) return Integer;
function Legendre (A, P : Big_Integer) return Integer;
function Kronecker (A, B : Big_Integer) return Integer;
procedure Remove
(Rop : in out Big_Integer;
Op, Factor : in Big_Integer;
Count : out Natural);
procedure Factorial
(Rop : in out Big_Integer;
Op : in Natural);
procedure Binomial
(Rop : in out Big_Integer;
N : in Big_Integer;
K : in Natural);
procedure Fibonacci_Number
(Fn : in out Big_Integer;
N : in Natural);
procedure Fibonacci_2_Numbers
(Fn : in out Big_Integer;
Fn_Sub1 : in out Big_Integer;
N : in Natural);
procedure Lucas_Number
(Ln : in out Big_Integer;
N : in Natural);
procedure Lucas_2_Numbers
(Ln : in out Big_Integer;
Ln_Sub1 : in out Big_Integer;
N : in Natural);
------------------
-- Comparison --
------------------
function Sign (Item : in Big_Integer) return A_Sign;
------------------------------------
-- Logical and Bit Manipulation --
------------------------------------
procedure Logical_And
(Rop : in out Big_Integer;
Op1, Op2 : in Big_Integer);
procedure Logical_Or
(Rop : in out Big_Integer;
Op1, Op2 : in Big_Integer);
procedure Logical_Xor
(Rop : in out Big_Integer;
Op1, Op2 : in Big_Integer);
procedure One_S_Complement
(Rop : in out Big_Integer;
Op : in Big_Integer);
function Population_Count (Op : Big_Integer) return Bit_Count;
function Hamming_Distance (Op1, Op2 : Big_Integer) return Bit_Count;
function Scan0 (Op : Big_Integer; Starting_Bit : Bit_Count)
return Bit_Count;
function Scan1 (Op : Big_Integer; Starting_Bit : Bit_Count)
return Bit_Count;
procedure Set_Bit
(Rop : in out Big_Integer;
Bit_Index : in Bit_Count);
procedure Clear_Bit
(Rop : in out Big_Integer;
Bit_Index : in Bit_Count);
procedure Complement_Bit
(Rop : in out Big_Integer;
Bit_Index : in Bit_Count);
function Bit_Is_Set (Op : Big_Integer; Bit_Index : Bit_Count)
return Boolean;
-------------------------------------
-- Input and Output, Importation --
-------------------------------------
-- Text IO, string conversions are provided in the separate
-- packages Gnu_Multiple_Precision.[[Wide_]Wide_]Text_IO.
-- Use the Stream attributes Read, Write, Input, Output for raw IO
-- or memory storage. The format used is compatible with C mpz_t
-- raw IO functions.
---------------------
-- Random Number --
---------------------
-- are provided in the separate package Random.
---------------------
-- Miscellaneous --
---------------------
function Is_Odd (Op : Big_Integer) return Boolean;
function Is_Even (Op : Big_Integer) return Boolean;
function Size_In_Base (Op : Big_Integer;
Base : Positive) return Positive;
-- Return the size of Op measured in number of digits in the given
-- Base. Base can vary from 2 to 36. The sign of Op is ignored,
-- just the absolute value is used. The result will be either
-- exact or 1 too big. If Base is a power of 2, The result is
-- always exact. If Op is zero the return value is always 1.
generic
type Num is range <>;
package Integer_Conversions is
procedure Set (Rop : in out Big_Integer;
Op : in Num);
function To_Big_Integer (Item : Num) return Big_Integer;
function Fits_In_Num (Item : Big_Integer) return Boolean;
function To_Num (Item : Big_Integer) return Num;
-- Constraint_Error is raised if not Fits_In_Num (Item).
private
pragma Inline (Set);
pragma Inline (To_Big_Integer);
pragma Inline (Fits_In_Num);
pragma Inline (To_Num);
end Integer_Conversions;
generic
type Num is mod <>;
package Modular_Conversions is
procedure Set (Rop : in out Big_Integer;
Op : in Num);
function To_Big_Integer (Item : Num) return Big_Integer;
function Fits_In_Num (Item : Big_Integer) return Boolean;
function To_Num (Item : Big_Integer) return Num;
-- Constraint_Error is raised if not Fits_In_Num (Item).
private
pragma Inline (Set);
pragma Inline (To_Big_Integer);
pragma Inline (Fits_In_Num);
pragma Inline (To_Num);
end Modular_Conversions;
generic
type Num is digits <>;
package Float_Conversions is
procedure Set (Rop : in out Big_Integer;
Op : in Num);
function To_Big_Integer (Item : Num) return Big_Integer;
function Fits_In_Num (Item : Big_Integer) return Boolean;
function To_Num (Item : Big_Integer) return Num;
-- Constraint_Error is raised if not Fits_In_Num (Item).
procedure Split_Mantissa_Exponent
(Mantissa : out Num;
Exponent : out Integer;
Op : in Big_Integer);
-- The Mantissa is in The range 0.5<|D|< 1 and
-- Op = Mantissa * 2 ** Exponent = (Truncated towards 0) Op
-- Value. If Op is zero, both are zero.
private
pragma Inline (Set);
pragma Inline (To_Big_Integer);
pragma Inline (Fits_In_Num);
pragma Inline (To_Num);
pragma Inline (Split_Mantissa_Exponent);
end Float_Conversions;
private
pragma Convention (C, Prime_Status);
for Prime_Status use (Composite => 0,
Probably_Prime => 1,
Prime => 2);
for Prime_Status'Size use Interfaces.C.int'Size;
pragma Inline ("<=");
pragma Inline ("<");
pragma Inline (">=");
pragma Inline (">");
pragma Inline ("-");
pragma Inline ("/");
pragma Inline ("*");
pragma Inline ("**");
pragma Inline ("+");
pragma Inline ("abs");
pragma Inline (Absolute_Value);
pragma Inline (Add);
pragma Inline (Add_A_Product);
pragma Inline ("and");
pragma Inline (Binomial);
pragma Inline (Bit_Is_Set);
pragma Inline (Clear_Bit);
pragma Inline (Complement_Bit);
pragma Inline (Divide);
pragma Inline (Divide_2_Exp);
pragma Inline (Divide_Exactly);
pragma Inline (Exponentiate);
pragma Inline (Factorial);
pragma Inline (Fibonacci_2_Numbers);
pragma Inline (Fibonacci_Number);
pragma Inline (Greatest_Common_Divisor);
pragma Inline (Hamming_Distance);
pragma Inline (Invert);
pragma Inline (Is_Congruent);
pragma Inline (Is_Congruent_2_Exp);
pragma Inline (Is_Divisible);
pragma Inline (Is_Divisible_2_Exp);
pragma Inline (Is_Even);
pragma Inline (Is_Odd);
pragma Inline (Is_Perfect_Power);
pragma Inline (Is_Perfect_Square);
pragma Inline (Jacobi);
pragma Inline (Kronecker);
pragma Inline (Least_Common_Multiple);
pragma Inline (Legendre);
pragma Inline (Logical_And);
pragma Inline (Logical_Or);
pragma Inline (Logical_Xor);
pragma Inline (Lucas_2_Numbers);
pragma Inline (Lucas_Number);
pragma Inline (Max);
pragma Inline (Min);
pragma Inline ("mod");
pragma Inline (Modulo);
pragma Inline (Multiply);
pragma Inline (Multiply_2_Exp);
pragma Inline (Negate);
pragma Inline (Next_Prime);
pragma Inline (One_S_Complement);
pragma Inline ("or");
pragma Inline (Population_Count);
pragma Inline (Pred);
pragma Inline (Probably_Prime);
pragma Inline (Reallocate);
pragma Inline ("rem");
pragma Inline (Remainder);
pragma Inline (Remainder_2_Exp);
pragma Inline (Remove);
pragma Inline (Root);
pragma Inline (Root_Remainder);
pragma Inline (Scan0);
pragma Inline (Scan1);
pragma Inline (Set);
pragma Inline (Set_Bit);
pragma Inline (Sign);
pragma Inline (Size_In_Base);
pragma Inline (Square_Root);
pragma Inline (Square_Root_Remainder);
pragma Inline (Subtract);
pragma Inline (Subtract_A_Product);
pragma Inline (Succ);
pragma Inline (Swap);
pragma Inline (Wide_Image);
pragma Inline (Wide_Value);
pragma Inline (Wide_Wide_Image);
pragma Inline (Wide_Wide_Value);
pragma Inline ("xor");
end GNU_Multiple_Precision.Big_Integers;
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