A.5.6 Big Integers
Static Semantics
{
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{
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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 =>
null is
type Big_Integer
is private
with Integer_Literal => From_String,
Put_Image => Put_Image;
function Is_Valid (Arg : Big_Integer)
return Boolean
with Convention => Intrinsic;
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;
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;
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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_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.
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The other functions have their usual mathematical meanings.
Dynamic Semantics
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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.
Ramification:
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This means that the elaboration of
Default_Initialized_Object : Valid_Big_Integer;
is required to propagate Program_Error.
Implementation Requirements
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No storage associated with a Big_Integer object shall be lost upon assignment
or scope exit.
Implementation Note: {
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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