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------------------------------------------------------------------------------
-- --
-- GNAT RUN-TIME LIBRARY (GNARL) COMPONENTS --
-- --
-- S Y S T E M . V E C T O R S . B O O L E A N _ O P E R A T I O N S --
-- --
-- B o d y --
-- --
-- Copyright (C) 2002-2022, Free Software Foundation, Inc. --
-- --
-- GNAT is free software; you can redistribute it and/or modify it under --
-- terms of the GNU General Public License as published by the Free Soft- --
-- ware Foundation; either version 3, or (at your option) any later ver- --
-- sion. GNAT is distributed in the hope that it will be useful, but WITH- --
-- OUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY --
-- or FITNESS FOR A PARTICULAR PURPOSE. --
-- --
-- As a special exception under Section 7 of GPL version 3, you are granted --
-- additional permissions described in the GCC Runtime Library Exception, --
-- version 3.1, as published by the Free Software Foundation. --
-- --
-- You should have received a copy of the GNU General Public License and --
-- a copy of the GCC Runtime Library Exception along with this program; --
-- see the files COPYING3 and COPYING.RUNTIME respectively. If not, see --
-- <http://www.gnu.org/licenses/>. --
-- --
-- GNAT was originally developed by the GNAT team at New York University. --
-- Extensive contributions were provided by Ada Core Technologies Inc. --
-- --
------------------------------------------------------------------------------
-- Ghost code, loop invariants and assertions in this unit are meant for
-- analysis only, not for run-time checking, as it would be too costly
-- otherwise. This is enforced by setting the assertion policy to Ignore.
pragma Assertion_Policy (Ghost => Ignore,
Loop_Invariant => Ignore,
Assert => Ignore);
package body System.Vectors.Boolean_Operations
with SPARK_Mode
is
SU : constant := Storage_Unit;
-- Convenient short hand, used throughout
-- The coding of this unit depends on the fact that the Component_Size
-- of a normally declared array of Boolean is equal to Storage_Unit. We
-- can't use the Component_Size directly since it is non-static. The
-- following declaration checks that this declaration is correct
type Boolean_Array is array (Integer range <>) of Boolean;
pragma Compile_Time_Error
(Boolean_Array'Component_Size /= SU, "run time compile failure");
-- NOTE: The boolean literals must be qualified here to avoid visibility
-- anomalies when this package is compiled through Rtsfind, in a context
-- that includes a user-defined type derived from boolean.
True_Val : constant Vector := Standard.True'Enum_Rep
+ Standard.True'Enum_Rep * 2**SU
+ Standard.True'Enum_Rep * 2**(SU * 2)
+ Standard.True'Enum_Rep * 2**(SU * 3)
+ Standard.True'Enum_Rep * 2**(SU * 4)
+ Standard.True'Enum_Rep * 2**(SU * 5)
+ Standard.True'Enum_Rep * 2**(SU * 6)
+ Standard.True'Enum_Rep * 2**(SU * 7);
-- This constant represents the bits to be flipped to perform a logical
-- "not" on a vector of booleans, independent of the actual
-- representation of True.
-- The representations of (False, True) are assumed to be zero/one and
-- the maximum number of unpacked booleans per Vector is assumed to be 8.
pragma Assert (Standard.False'Enum_Rep = 0);
pragma Assert (Standard.True'Enum_Rep = 1);
pragma Assert (Vector'Size / Storage_Unit <= 8);
-- The reason we need to do these gymnastics is that no call to
-- Unchecked_Conversion can be made at the library level since this
-- unit is pure. Also a conversion from the array type to the Vector type
-- inside the body of "not" is inefficient because of alignment issues.
-----------
-- "not" --
-----------
function "not" (Item : Vectors.Vector) return Vectors.Vector is
procedure Prove_Not (Result : Vectors.Vector)
with
Ghost,
Pre => Valid (Item)
and then Result = (Item xor True_Val),
Post => Valid (Result)
and then (for all J in 1 .. Vector_Boolean_Size =>
Model (Result) (J) = not Model (Item) (J));
procedure Prove_Not (Result : Vectors.Vector) is
begin
for J in 1 .. Vector_Boolean_Size loop
pragma Assert
(Element (Result, J) = 1 - Element (Item, J));
end loop;
end Prove_Not;
begin
Prove_Not (Item xor True_Val);
return Item xor True_Val;
end "not";
----------
-- Nand --
----------
function Nand (Left, Right : Boolean) return Boolean is
begin
return not (Left and Right);
end Nand;
function Nand (Left, Right : Vectors.Vector) return Vectors.Vector is
procedure Prove_And (Result : Vectors.Vector)
with
Ghost,
Pre => Valid (Left)
and then Valid (Right)
and then Result = (Left and Right),
Post => Valid (Result)
and then (for all J in 1 .. Vector_Boolean_Size =>
Model (Result) (J) =
(Model (Left) (J) and Model (Right) (J)));
procedure Prove_And (Result : Vectors.Vector) is
begin
for J in 1 .. Vector_Boolean_Size loop
pragma Assert
(Element (Result, J) =
(if Element (Left, J) = 1
and Element (Right, J) = 1
then 1
else 0));
end loop;
end Prove_And;
begin
Prove_And (Left and Right);
return not (Left and Right);
end Nand;
---------
-- Nor --
---------
function Nor (Left, Right : Boolean) return Boolean is
begin
return not (Left or Right);
end Nor;
function Nor (Left, Right : Vectors.Vector) return Vectors.Vector is
procedure Prove_Or (Result : Vectors.Vector)
with
Ghost,
Pre => Valid (Left)
and then Valid (Right)
and then Result = (Left or Right),
Post => Valid (Result)
and then (for all J in 1 .. Vector_Boolean_Size =>
Model (Result) (J) =
(Model (Left) (J) or Model (Right) (J)));
procedure Prove_Or (Result : Vectors.Vector) is
begin
for J in 1 .. Vector_Boolean_Size loop
pragma Assert
(Element (Result, J) =
(if Element (Left, J) = 1
or Element (Right, J) = 1
then 1
else 0));
end loop;
end Prove_Or;
begin
Prove_Or (Left or Right);
return not (Left or Right);
end Nor;
----------
-- Nxor --
----------
function Nxor (Left, Right : Boolean) return Boolean is
begin
return not (Left xor Right);
end Nxor;
function Nxor (Left, Right : Vectors.Vector) return Vectors.Vector is
procedure Prove_Xor (Result : Vectors.Vector)
with
Ghost,
Pre => Valid (Left)
and then Valid (Right)
and then Result = (Left xor Right),
Post => Valid (Result)
and then (for all J in 1 .. Vector_Boolean_Size =>
Model (Result) (J) =
(Model (Left) (J) xor Model (Right) (J)));
procedure Prove_Xor (Result : Vectors.Vector) is
begin
for J in 1 .. Vector_Boolean_Size loop
pragma Assert
(Element (Result, J) =
(if Element (Left, J) = 1
xor Element (Right, J) = 1
then 1
else 0));
end loop;
end Prove_Xor;
begin
Prove_Xor (Left xor Right);
return not (Left xor Right);
end Nxor;
end System.Vectors.Boolean_Operations;
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