A.5.6 Big Integers
Static Semantics
{
AI12-0208-1}
{
AI12-0366-1}
The library package Numerics.Big_Numbers.Big_Integers
has the following declaration:with Ada.Strings.Text_Buffers;
package Ada.Numerics.Big_Numbers.Big_Integers
with Preelaborate, Nonblocking, Global => in out synchronized is
function Is_Valid (Arg : Big_Integer) return Boolean
with Convention => Intrinsic;
Discussion: {
AI12-0005-1}
The result of Is_Valid on a default-initialized
object of type Big_Integer is unspecified, analogous to the value of
a Valid attribute_reference
applied to a default-initialized object of an integer type (see 13.9.2).
The language-provided functions in the Big_Integers package only return
values for which Is_Valid is certain to be True.
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;
function "<" (L, R : Valid_Big_Integer) return Boolean;
function "<=" (L, R : Valid_Big_Integer) return Boolean;
function ">" (L, R : Valid_Big_Integer) return Boolean;
function ">=" (L, R : Valid_Big_Integer) return Boolean;
function To_Big_Integer (Arg : Integer) return Valid_Big_Integer;
subtype Big_Positive is Big_Integer
with Dynamic_Predicate => (if Is_Valid (Big_Positive)
then Big_Positive > 0),
Predicate_Failure => (raise Constraint_Error);
subtype Big_Natural is Big_Integer
with Dynamic_Predicate => (if Is_Valid (Big_Natural)
then Big_Natural >= 0),
Predicate_Failure => (raise Constraint_Error);
function In_Range (Arg, Low, High : Valid_Big_Integer) return Boolean is
(Low <= Arg and Arg <= High);
function To_Integer (Arg : Valid_Big_Integer) return Integer
with Pre => In_Range (Arg,
Low => To_Big_Integer (Integer'First),
High => To_Big_Integer (Integer'Last))
or else raise Constraint_Error;
generic
type Int is range <>;
package Signed_Conversions is
function To_Big_Integer (Arg : Int) return Valid_Big_Integer;
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;
end Signed_Conversions;
generic
type Int is mod <>;
package Unsigned_Conversions is
function To_Big_Integer (Arg : Int) return Valid_Big_Integer;
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;
end Unsigned_Conversions;
function To_String (Arg : Valid_Big_Integer;
Width : Field := 0;
Base : Number_Base := 10) return String
with Post => To_String'Result'First = 1;
function From_String (Arg : String) return Valid_Big_Integer;
{
AI12-0407-1}
function From_Universal_Image (Arg : String) return Valid_Big_Integer
renames From_String; procedure Put_Image
(Buffer : in out Ada.Strings.Text_Buffers.Root_Buffer_Type'Class;
Arg : in Valid_Big_Integer);
function "+" (L : Valid_Big_Integer) return Valid_Big_Integer;
function "-" (L : Valid_Big_Integer) return Valid_Big_Integer;
function "abs" (L : Valid_Big_Integer) return Valid_Big_Integer;
function "+" (L, R : Valid_Big_Integer) return Valid_Big_Integer;
function "-" (L, R : Valid_Big_Integer) return Valid_Big_Integer;
function "*" (L, R : Valid_Big_Integer) return Valid_Big_Integer;
function "/" (L, R : Valid_Big_Integer) return Valid_Big_Integer;
function "mod" (L, R : Valid_Big_Integer) return Valid_Big_Integer;
function "rem" (L, R : Valid_Big_Integer) return Valid_Big_Integer;
function "**" (L : Valid_Big_Integer; R : Natural)
return Valid_Big_Integer;
function Min (L, R : Valid_Big_Integer) return Valid_Big_Integer;
function Max (L, R : Valid_Big_Integer) return Valid_Big_Integer;
function Greatest_Common_Divisor
(L, R : Valid_Big_Integer) return Big_Positive
with Pre => (L /= 0 and R /= 0) or else raise Constraint_Error;
private
... -- not specified by the language
end Ada.Numerics.Big_Numbers.Big_Integers;
{
AI12-0208-1}
{
AI12-0366-1}
To_String and From_String behave analogously to
the Put and Get procedures defined in Text_IO.Integer_IO (in particular,
with respect to the interpretation of the Width and Base parameters)
except that Constraint_Error, not Data_Error, is propagated in error
cases and the result of a call to To_String with a Width parameter of
0 and a nonnegative Arg parameter does not include a leading blank. Put_Image
calls To_String (passing in the default values for the Width and Base
parameters), prepends a leading blank if the argument is nonnegative,
and writes the resulting value to the buffer using Text_Buffers.Put.{
AI12-0208-1}
The other functions have their usual mathematical
meanings.Dynamic Semantics
{
AI12-0208-1}
{
AI12-0366-1}
For purposes of determining whether predicate checks
are performed as part of default initialization, the type Big_Integer
is considered to have a subcomponent that has a default_expression.Default_Initialized_Object : Valid_Big_Integer;
either produces a value
for which Is_Valid is True. or it propagates Program_Error.
Implementation Requirements
{
AI12-0208-1}
{
AI12-0366-1}
No storage associated with a Big_Integer object
shall be lost upon assignment or scope exit.Implementation Note:
{
AI12-0208-1}
The “No storage ... shall be lost”
requirement does not preclude implementation techniques such as caching
or unique number tables.
Extensions to Ada 2012
Ada 2005 and 2012 Editions sponsored in part by Ada-Europe
