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3.5.4 Integer Types

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   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 semantics.

Syntax

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integer_type_definition ::= signed_integer_type_definition | modular_type_definition
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signed_integer_type_definition ::= range static_simple_expression .. static_simple_expression
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modular_type_definition ::= mod static_expression

Name Resolution Rules

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   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.

Legality Rules

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   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.
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   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.

Static Semantics

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   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.
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   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.
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    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.
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    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.
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    Integer has two predefined subtypes, declared in the visible part of package Standard:
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subtype Natural  is Integer range 0 .. Integer'Last;
subtype Positive is Integer range 1 .. Integer'Last;
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    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 integer type.
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    The position number of an integer value is equal to the value.
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    For every modular subtype S, the following attribute is defined:
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    S'Modulus
S'Modulus yields the modulus of the type of S, as a value of the type universal_integer.

Dynamic Semantics

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    The elaboration of an integer_type_definition creates the integer type and its first subtype.
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    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.
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    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 is zero.

Implementation Requirements

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    In an implementation, the range of Integer shall include the range -2**15+1 .. +2**15-1.
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    If Long_Integer is predefined for an implementation, then its range shall include the range -2**31+1 .. +2**31-1.
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    System.Max_Binary_Modulus shall be at least 2**16.

Implementation Permissions

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    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.
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    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.
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    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 -- see 12.5.2.
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    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.
27.1/1
        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.

Implementation Advice

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    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).
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    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.
NOTES
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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.
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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.
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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

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    Examples of integer types and subtypes:
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type Page_Num  is range 1 .. 2_000;
type Line_Size is range 1 .. Max_Line_Size;
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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;
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type Byte        is mod 256; -- an unsigned byte
type Hash_Index  is mod 97;  -- modulus is prime

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