- An integer_type_definition defines an integer type; it defines either a
signed integer type, 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
integer_type_definition ::= signed_integer_type_definition | modular_type_definition
signed_integer_type_definition ::= range static_simple_expression .. static_simple_expression
modular_type_definition ::= mod static_expression
Name Resolution Rules
- Each simple_expression in a signed_integer_type_definition is expected to
be of any integer type; they need not be of the same type. The expression in
a modular_type_definition is likewise expected to be of any integer type.
- The simple_expressions of a signed_integer_type_definition shall be
static, and their values shall be in the range System.Min_Int .. System.Max_Int.
- The expression 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.
- A signed_integer_type_definition defines an integer type whose base range
includes at least the values of the simple_expressions and is symmetric about
zero, excepting possibly an extra negative value. A signed_integer_type_definition also defines a constrained first subtype of the type, with a range
whose bounds are given by the values of the simple_expressions, converted to
the type being defined.
- A modular_type_definition defines a modular type whose base range is
from zero to one less than the given modulus. A modular_type_definition 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
- Integer has two predefined subtypes, declared in the visible part of
subtype Natural is Integer range 0 .. Integer'Last;
subtype Positive is Integer range 1 .. Integer'Last;
- A 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 type universal_integer, the universal type (see 3.4.1) for the
class rooted at root_integer, allowing their use with the operations of any
- The position number of an integer value is equal to the value.
- For every modular subtype S, the following attribute is defined:
S'Modulus yields the modulus of the type of S, as a value of
the type universal_integer.
- The elaboration of an integer_type_definition creates the integer type
and its first subtype.
- 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.
- For 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. For any integer type, Constraint_Error is raised by the operators "/", "rem", 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 .. +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.
- An implementation 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 integer_type_definition. 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 explicit_generic_actual_parameters for formal scalar types --
- 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.
- 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
- 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.
(25) Integer literals are of the anonymous predefined integer type
universal_integer. Other integer types have no literals. However, the
overload resolution rules (see 8.6, ``The Context of Overload
Resolution'') allow expressions of the type universal_integer whenever
an integer type is expected.
(26) The same arithmetic operators are predefined for all signed integer
types defined by a signed_integer_type_definition (see 4.5, ``Operators
and Expression Evaluation''). For modular types, these same operators
are predefined, plus bit-wise logical operators (and, or, xor, 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.
(27) Modular types match a generic_formal_parameter_declaration of the
form "type T is mod <>;"; signed integer types match "type T is range
<>;" (see 12.5.2).
- 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
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