3.5.4 Integer Types
defines an integer type; it defines either a signed
or a modular
integer type. The base range of a signed integer
type includes at least the values of the specified range. A modular type
is an integer type with all arithmetic modulo a specified positive modulus
such a type corresponds to an unsigned type with wrap-around semantics.
Name Resolution Rules
of a modular_type_definition
shall be static, and its value (the modulus
) shall be positive,
and shall be no greater than System.Max_Binary_Modulus if a power of
2, or no greater than System.Max_Nonbinary_Modulus if not.
The set of values for a signed integer type is the
(infinite) set of mathematical integers, though only values of the base
range of the type are fully supported for run-time operations. The set
of values for a modular integer type are the values from 0 to one less
than the modulus, inclusive.
defines a modular type whose base range is from zero to one less than
the given modulus.
also defines a constrained first subtype of the type with a range that
is the same as the base range of the type.
There is a predefined signed
integer subtype named Integer, declared in the visible part of package
Standard. It is constrained to the base range of its type.
has two predefined subtypes, declared in the visible part of package
subtype Natural is Integer range 0 .. Integer'Last;
subtype Positive is Integer range 1 .. Integer'Last;
type defined by an integer_type_definition
is implicitly derived from root_integer
, an anonymous predefined
(specific) integer type, whose base range is System.Min_Int .. System.Max_Int.
However, the base range of the new type is not inherited from root_integer
but is instead determined by the range or modulus specified by the integer_type_definition
Integer literals are all of the
, the universal type (see 3.4.1
for the class rooted at root_integer
, allowing their use with
the operations of any integer type.
The position number
an integer value is equal to the value.
For every modular subtype
S, the following attributes are defined:
S'Mod denotes a function with
the following specification:
function S'Mod (Arg : universal_integer)
This function returns Arg mod
S'Modulus, as a value of the type of S.
S'Modulus yields the modulus
of the type of S, as a value of the type universal_integer
For a modular type, if the result of the execution
of a predefined operator (see 4.5
) is outside
the base range of the type, the result is reduced modulo the modulus
of the type to a value that is within the base range of the type.
a signed integer type, the exception Constraint_Error is raised by the
execution of an operation that cannot deliver the correct result because
it is outside the base range of the type.
any integer type, Constraint_Error is raised by the operators "/",
", and "mod
" if the right operand
In an implementation, the range
of Integer shall include the range –2**15+1 .. +2**15–1.
If Long_Integer is predefined
for an implementation, then its range shall include the range –2**31+1
System.Max_Binary_Modulus shall be at least 2**16.
For the execution of a predefined operation of a
signed integer type, the implementation need not raise Constraint_Error
if the result is outside the base range of the type, so long as the correct
result is produced.
may provide additional predefined signed integer types, declared in the
visible part of Standard, whose first subtypes have names of the form
Short_Integer, Long_Integer, Short_Short_Integer, Long_Long_Integer,
etc. Different predefined integer types are allowed to have the same
base range. However, the range of Integer should be no wider than that
of Long_Integer. Similarly, the range of Short_Integer (if provided)
should be no wider than Integer. Corresponding recommendations apply
to any other predefined integer types. There need not be a named integer
type corresponding to each distinct base range supported by an implementation.
The range of each first subtype should be the base range of its type.
An implementation may provide
nonstandard integer types
, descendants of root_integer
that are declared outside of the specification of package Standard, which
need not have all the standard characteristics of a type defined by an
For example, a nonstandard integer type might have an asymmetric base
range or it might not be allowed as an array or loop index (a very long
integer). Any type descended from a nonstandard integer type is also
nonstandard. An implementation may place arbitrary restrictions on the
use of such types; it is implementation defined whether operators that
are predefined for “any integer type” are defined for a particular
nonstandard integer type. In any case, such types are not permitted as
for formal scalar types — see 12.5.2
For a one's complement machine,
the high bound of the base range of a modular type whose modulus is one
less than a power of 2 may be equal to the modulus, rather than one less
than the modulus. It is implementation defined for which powers of 2,
if any, this permission is exercised.
For a one's complement machine, implementations
may support non-binary modulus values greater than System.Max_Nonbinary_Modulus.
It is implementation defined which specific values greater than System.Max_Nonbinary_Modulus,
if any, are supported.
An implementation should support
Long_Integer in addition to Integer if the target machine supports 32-bit
(or longer) arithmetic. No other named integer subtypes are recommended
for package Standard. Instead, appropriate named integer subtypes should
be provided in the library package Interfaces (see B.2
An implementation for a two's
complement machine should support modular types with a binary modulus
up to System.Max_Int*2+2. An implementation should support a nonbinary
modulus up to Integer'Last.
literals are of the anonymous predefined integer type universal_integer
Other integer types have no literals. However, the overload resolution
rules (see 8.6
Context of Overload Resolution
”) allow expressions of the type
whenever an integer type is expected.
28 The same arithmetic operators are predefined
for all signed integer types defined by a signed_integer_type_definition
and Expression Evaluation
”). For modular types, these same
operators are predefined, plus bit-wise logical operators (and
, and not
). In addition, for the unsigned
types declared in the language-defined package Interfaces (see B.2
functions are defined that provide bit-wise shifting and rotating.
Examples of integer
types and subtypes:
type Page_Num is range 1 .. 2_000;
type Line_Size is range 1 .. Max_Line_Size;
subtype Small_Int is Integer range -10 .. 10;
subtype Column_Ptr is Line_Size range 1 .. 10;
subtype Buffer_Size is Integer range 0 .. Max;
type Byte is mod 256; -- an unsigned byte
type Hash_Index is mod 97; -- modulus is prime