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Scalar types comprise enumeration types, integer types, and real types.
Enumeration types and integer types are called discrete types; each
value of a discrete type has a position number which is an integer
value. Integer types and real types are called numeric types. All scalar
types are ordered, that is, all relational operators are predefined for
their values.
Syntax

range_constraint ::= range range

range ::=
range_attribute_reference
 simple_expression .. simple_expression

A range has a lower bound and an upper bound and specifies a subset of
the values of some scalar type (the type of the range). A range with
lower bound L and upper bound R is described by "L .. R". If R is less
than L, then the range is a null range, and specifies an empty set of
values. Otherwise, the range specifies the values of the type from the
lower bound to the upper bound, inclusive. A value belongs to a range if
it is of the type of the range, and is in the subset of values specified
by the range. A value satisfies a range constraint if it belongs to the
associated range. One range is included in another if all values that
belong to the first range also belong to the second.
Name Resolution Rules

For a subtype_indication containing a range_constraint, either directly
or as part of some other scalar_constraint, the type of the range shall
resolve to that of the type determined by the subtype_mark of the
subtype_indication. For a range of a given type, the simple_expressions
of the range (likewise, the simple_expressions of the equivalent range
for a range_attribute_reference) are expected to be of the type of the
range.
Static Semantics

The base range of a scalar type is the range of finite values of the
type that can be represented in every unconstrained object of the type;
it is also the range supported at a minimum for intermediate values
during the evaluation of expressions involving predefined operators of
the type.

A constrained scalar subtype is one to which a range constraint applies.
The range of a constrained scalar subtype is the range associated with
the range constraint of the subtype. The range of an unconstrained
scalar subtype is the base range of its type.
Dynamic Semantics

A range is compatible with a scalar subtype if and only if it is either
a null range or each bound of the range belongs to the range of the
subtype. A range_constraint is compatible with a scalar subtype if and
only if its range is compatible with the subtype.

The elaboration of a range_constraint consists of the evaluation of the
range. The evaluation of a range determines a lower bound and an upper
bound. If simple_expressions are given to specify bounds, the evaluation
of the range evaluates these simple_expressions in an arbitrary order,
and converts them to the type of the range. If a
range_attribute_reference is given, the evaluation of the range consists
of the evaluation of the range_attribute_reference.

Attributes

For every scalar subtype S, the following attributes are defined:

S'First
S'First denotes the lower bound of the range of S. The value
of this attribute is of the type of S.

S'Last
S'Last denotes the upper bound of the range of S. The value
of this attribute is of the type of S.

S'Range
S'Range is equivalent to the range S'First .. S'Last.

S'Base
S'Base denotes an unconstrained subtype of the type of
S. This unconstrained subtype is called the base subtype of
the type.

S'Min
S'Min denotes a function with the following specification:

function S'Min(Left, Right : S'Base)
return S'Base

The function returns the lesser of the values of the two parameters.

S'Max
S'Max denotes a function with the following specification:

function S'Max(Left, Right : S'Base)
return S'Base

The function returns the greater of the values of the two parameters.

S'Succ
S'Succ denotes a function with the following specification:

function S'Succ(Arg : S'Base)
return S'Base

For an enumeration type, the function returns the value whose position
number is one more than that of the value of Arg; Constraint_Error is
raised if there is no such value of the type. For an integer type, the
function returns the result of adding one to the value of Arg. For a
fixed point type, the function returns the result of adding small to the
value of Arg. For a floating point type, the function returns the
machine number (as defined in See section 3.5.7 Floating Point Types.) immediately above the value
of Arg; Constraint_Error is raised if there is no such machine number.

S'Pred
S'Pred denotes a function with the following specification:

function S'Pred(Arg : S'Base)
return S'Base

For an enumeration type, the function returns the value whose position
number is one less than that of the value of Arg; Constraint_Error is
raised if there is no such value of the type. For an integer type, the
function returns the result of subtracting one from the value of Arg.
For a fixed point type, the function returns the result of subtracting
small from the value of Arg. For a floating point type, the function
returns the machine number (as defined in See section 3.5.7 Floating Point Types.) immediately
below the value of Arg; Constraint_Error is raised if there is no such
machine number.

S'Wide_Image
S'Wide_Image denotes a function with the following
specification:

function S'Wide_Image(Arg : S'Base)
return Wide_String

The function returns an image of the value of Arg, that is, a sequence
of characters representing the value in display form. The lower bound of
the result is one.

The image of an integer value is the corresponding decimal literal,
without underlines, leading zeros, exponent, or trailing spaces, but
with a single leading character that is either a minus sign or a space.

The image of an enumeration value is either the corresponding identifier
in upper case or the corresponding character literal (including the two
apostrophes); neither leading nor trailing spaces are included. For a
nongraphic character (a value of a character type that has no
enumeration literal associated with it), the result is a corresponding
languagedefined or implementationdefined name in upper case (for
example, the image of the nongraphic character identified as nul is
"NUL"  the quotes are not part of the image).

The image of a floating point value is a decimal real literal best
approximating the value (rounded away from zero if halfway between) with
a single leading character that is either a minus sign or a space, a
single digit (that is nonzero unless the value is zero), a decimal
point, S'Digits1, See section 3.5.8 Operations of Floating Point Types, digits after the decimal point (but one
if S'Digits is one), an upper case E, the sign of the exponent (either +
or ), and two or more digits (with leading zeros if necessary)
representing the exponent. If S'Signed_Zeros is True, then the leading
character is a minus sign for a negatively signed zero.

The image of a fixed point value is a decimal real literal best
approximating the value (rounded away from zero if halfway between) with
a single leading character that is either a minus sign or a space, one
or more digits before the decimal point (with no redundant leading
zeros), a decimal point, and S'Aft, See section 3.5.10 Operations of Fixed Point Types, digits after the
decimal point.

S'Image
S'Image denotes a function with the following specification:

function S'Image(Arg : S'Base)
return String

The function returns an image of the value of Arg as a String. The lower
bound of the result is one. The image has the same sequence of graphic
characters as that defined for S'Wide_Image if all the graphic
characters are defined in Character; otherwise the sequence of
characters is implementation defined (but no shorter than that of
S'Wide_Image for the same value of Arg).

S'Wide_Width
S'Wide_Width denotes the maximum length of a Wide_String
returned by S'Wide_Image over all values of the subtype S. It
denotes zero for a subtype that has a null range. Its type
is universal_integer.

S'Width
S'Width denotes the maximum length of a String returned by
S'Image over all values of the subtype S. It denotes
zero for a subtype that has a null range. Its type is
universal_integer.

S'Wide_Value
S'Wide_Value denotes a function with the following
specification:

function S'Wide_Value(Arg : Wide_String)
return S'Base

This function returns a value given an image of the value as a
Wide_String, ignoring any leading or trailing spaces.

For the evaluation of a call on S'Wide_Value for an enumeration subtype
S, if the sequence of characters of the parameter (ignoring leading and
trailing spaces) has the syntax of an enumeration literal and if it
corresponds to a literal of the type of S (or corresponds to the result
of S'Wide_Image for a nongraphic character of the type), the result is
the corresponding enumeration value; otherwise Constraint_Error is
raised.

For the evaluation of a call on S'Wide_Value (or S'Value) for an integer
subtype S, if the sequence of characters of the parameter (ignoring
leading and trailing spaces) has the syntax of an integer literal, with
an optional leading sign character (plus or minus for a signed type;
only plus for a modular type), and the corresponding numeric value
belongs to the base range of the type of S, then that value is the
result; otherwise Constraint_Error is raised.

For the evaluation of a call on S'Wide_Value (or S'Value) for a real
subtype S, if the sequence of characters of the parameter (ignoring
leading and trailing spaces) has the syntax of one of the following:

numeric_literal

numeral.[exponent]

.numeral[exponent]

base#based_numeral.#[exponent]

base#.based_numeral#[exponent]

with an optional leading sign character (plus or minus), and if the
corresponding numeric value belongs to the base range of the type of S,
then that value is the result; otherwise Constraint_Error is raised. The
sign of a zero value is preserved (positive if none has been specified)
if S'Signed_Zeros is True.

S'Value
S'Value denotes a function with the following specification:

function S'Value(Arg : String)
return S'Base

This function returns a value given an image of the value as a String,
ignoring any leading or trailing spaces.

For the evaluation of a call on S'Value for an enumeration subtype S, if
the sequence of characters of the parameter (ignoring leading and
trailing spaces) has the syntax of an enumeration literal and if it
corresponds to a literal of the type of S (or corresponds to the result
of S'Image for a value of the type), the result is the corresponding
enumeration value; otherwise Constraint_Error is raised. For a numeric
subtype S, the evaluation of a call on S'Value with Arg of type String
is equivalent to a call on S'Wide_Value for a corresponding Arg of type
Wide_String.
Implementation Permissions

An implementation may extend the Wide_Value, Value, Wide_Image, and
Image attributes of a floating point type to support special values such
as infinities and NaNs.
NOTES

(19) The evaluation of S'First or S'Last never raises an exception. If a
scalar subtype S has a nonnull range, S'First and S'Last belong to this
range. These values can, for example, always be assigned to a variable
of subtype S.

(20) For a subtype of a scalar type, the result delivered by the
attributes Succ, Pred, and Value might not belong to the subtype;
similarly, the actual parameters of the attributes Succ, Pred, and Image
need not belong to the subtype.

(21) For any value V (including any nongraphic character) of an
enumeration subtype S, S'Value(S'Image(V)) equals V, as does
S'Wide_Value(S'Wide_Image(V)). Neither expression ever raises
Constraint_Error.
Examples

Examples of ranges:

10 .. 10
X .. X + 1
0.0 .. 2.0*Pi
Red .. Green  See section 3.5.1 Enumeration Types
1 .. 0  a null range
Table'Range  a range attribute reference, See section 3.6 Array Types

Examples of range constraints:

range 999.0 .. +999.0
range S'First+1 .. S'Last1
 3.5.1: Enumeration Types
 3.5.2: Character Types
 3.5.3: Boolean Types
 3.5.4: Integer Types
 3.5.5: Operations of Discrete Types
 3.5.6: Real Types
 3.5.7: Floating Point Types
 3.5.8: Operations of Floating Point Types
 3.5.9: Fixed Point Types
 3.5.10: Operations of Fixed Point Types
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