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|
------------------------------------------------------------------------------
-- --
-- GNAT RUN-TIME COMPONENTS --
-- --
-- ADA.NUMERICS.BIG_NUMBERS.BIG_INTEGERS_GHOST --
-- --
-- S p e c --
-- --
-- This specification is derived from the Ada Reference Manual for use with --
-- GNAT. In accordance with the copyright of that document, you can freely --
-- copy and modify this specification, provided that if you redistribute a --
-- modified version, any changes that you have made are clearly indicated. --
-- --
------------------------------------------------------------------------------
-- This unit is provided as a replacement for the standard unit
-- Ada.Numerics.Big_Numbers.Big_Integers when only proof with SPARK is
-- intended. It cannot be used for execution, as all subprograms are marked
-- imported with no definition.
-- Contrary to Ada.Numerics.Big_Numbers.Big_Integers, this unit does not
-- depend on System or Ada.Finalization, which makes it more convenient for
-- use in run-time units.
-- Ghost code in this unit is meant for analysis only, not for run-time
-- checking. This is enforced by setting the assertion policy to Ignore.
pragma Assertion_Policy (Ghost => Ignore);
package Ada.Numerics.Big_Numbers.Big_Integers_Ghost with
SPARK_Mode,
Ghost,
Pure,
Always_Terminates
is
type Big_Integer is private
with Integer_Literal => From_Universal_Image;
function Is_Valid (Arg : Big_Integer) return Boolean
with
Import,
Global => null;
subtype Valid_Big_Integer is Big_Integer
with Dynamic_Predicate => Is_Valid (Valid_Big_Integer),
Predicate_Failure => raise Program_Error;
function "=" (L, R : Valid_Big_Integer) return Boolean with
Import,
Global => null;
function "<" (L, R : Valid_Big_Integer) return Boolean with
Import,
Global => null;
function "<=" (L, R : Valid_Big_Integer) return Boolean with
Import,
Global => null;
function ">" (L, R : Valid_Big_Integer) return Boolean with
Import,
Global => null;
function ">=" (L, R : Valid_Big_Integer) return Boolean with
Import,
Global => null;
function To_Big_Integer (Arg : Integer) return Valid_Big_Integer
with
Import,
Global => null;
subtype Big_Positive is Big_Integer
with Dynamic_Predicate =>
(if Is_Valid (Big_Positive)
then Big_Positive > To_Big_Integer (0)),
Predicate_Failure => raise Constraint_Error;
subtype Big_Natural is Big_Integer
with Dynamic_Predicate =>
(if Is_Valid (Big_Natural)
then Big_Natural >= To_Big_Integer (0)),
Predicate_Failure => raise Constraint_Error;
function In_Range
(Arg : Valid_Big_Integer; Low, High : Big_Integer) return Boolean
is (Low <= Arg and Arg <= High)
with
Import,
Global => null;
function To_Integer (Arg : Valid_Big_Integer) return Integer
with
Import,
Pre => In_Range (Arg,
Low => To_Big_Integer (Integer'First),
High => To_Big_Integer (Integer'Last))
or else raise Constraint_Error,
Global => null;
generic
type Int is range <>;
package Signed_Conversions is
function To_Big_Integer (Arg : Int) return Valid_Big_Integer
with
Global => null;
function From_Big_Integer (Arg : Valid_Big_Integer) return Int
with
Pre => In_Range (Arg,
Low => To_Big_Integer (Int'First),
High => To_Big_Integer (Int'Last))
or else raise Constraint_Error,
Global => null;
end Signed_Conversions;
generic
type Int is mod <>;
package Unsigned_Conversions is
function To_Big_Integer (Arg : Int) return Valid_Big_Integer
with
Global => null;
function From_Big_Integer (Arg : Valid_Big_Integer) return Int
with
Pre => In_Range (Arg,
Low => To_Big_Integer (Int'First),
High => To_Big_Integer (Int'Last))
or else raise Constraint_Error,
Global => null;
end Unsigned_Conversions;
function From_String (Arg : String) return Valid_Big_Integer
with
Import,
Global => null;
function From_Universal_Image (Arg : String) return Valid_Big_Integer
renames From_String;
function "+" (L : Valid_Big_Integer) return Valid_Big_Integer
with
Import,
Global => null;
function "-" (L : Valid_Big_Integer) return Valid_Big_Integer
with
Import,
Global => null;
function "abs" (L : Valid_Big_Integer) return Valid_Big_Integer
with
Import,
Global => null;
function "+" (L, R : Valid_Big_Integer) return Valid_Big_Integer
with
Import,
Global => null;
function "-" (L, R : Valid_Big_Integer) return Valid_Big_Integer
with
Import,
Global => null;
function "*" (L, R : Valid_Big_Integer) return Valid_Big_Integer
with
Import,
Global => null;
function "/" (L, R : Valid_Big_Integer) return Valid_Big_Integer
with
Import,
Global => null;
function "mod" (L, R : Valid_Big_Integer) return Valid_Big_Integer
with
Import,
Global => null;
function "rem" (L, R : Valid_Big_Integer) return Valid_Big_Integer
with
Import,
Global => null;
function "**" (L : Valid_Big_Integer; R : Natural) return Valid_Big_Integer
with
Import,
Global => null;
function Min (L, R : Valid_Big_Integer) return Valid_Big_Integer
with
Import,
Global => null;
function Max (L, R : Valid_Big_Integer) return Valid_Big_Integer
with
Import,
Global => null;
function Greatest_Common_Divisor
(L, R : Valid_Big_Integer) return Big_Positive
with
Import,
Pre => (L /= To_Big_Integer (0) and R /= To_Big_Integer (0))
or else raise Constraint_Error,
Global => null;
private
pragma SPARK_Mode (Off);
type Big_Integer is null record;
end Ada.Numerics.Big_Numbers.Big_Integers_Ghost;
|
