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3.5 Scalar Types
1
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
2
range_constraint
::= range range
3
range
::= range_attribute_reference

simple_expression ..
simple_expression
4
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
5
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
6
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.
7
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
8
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.
9
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.
10
Attributes
11
For every scalar
subtype S, the following attributes are defined:
12
 S'First

S'First denotes the lower bound
of the range of S. The value of this attribute is of the type of S.
13
 S'Last

S'Last denotes the upper bound
of the range of S. The value of this attribute is of the type of S.
14
 S'Range

S'Range is equivalent to the
range S'First .. S'Last.
15
 S'Base

S'Base denotes an unconstrained
subtype of the type of S. This unconstrained subtype is called the base
subtype of the type.
16
 S'Min

S'Min denotes a function with
the following specification:
17
function S'Min(Left, Right : S'Base)
return S'Base
18
 The function returns the lesser
of the values of the two parameters.
19
 S'Max

S'Max denotes a function with
the following specification:
20
function S'Max(Left, Right : S'Base)
return S'Base
21
 The function returns the greater
of the values of the two parameters.
22
 S'Succ

S'Succ denotes a function with
the following specification:
23
function S'Succ(Arg : S'Base)
return S'Base
24
 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 3.5.7)
immediately above the value of Arg; Constraint_Error
is raised if there is no such machine number.
25
 S'Pred

S'Pred denotes a function with
the following specification:
26
function S'Pred(Arg : S'Base)
return S'Base
27
 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 3.5.7)
immediately below the value of Arg; Constraint_Error
is raised if there is no such machine number.
28
 S'Wide_Image

S'Wide_Image denotes a function
with the following specification:
29
function S'Wide_Image(Arg : S'Base)
return Wide_String
30
 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.
31
 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.
32
 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).
33
 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 3.5.8)
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.
34
 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
3.5.10) digits after the decimal point.
35
 S'Image

S'Image denotes a function with
the following specification:
36
function S'Image(Arg : S'Base)
return String
37
 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).
38
 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.
39
 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.
40
 S'Wide_Value

S'Wide_Value denotes a function
with the following specification:
41
function S'Wide_Value(Arg : Wide_String)
return S'Base
42
 This function returns a value
given an image of the value as a Wide_String, ignoring any leading or
trailing spaces.
43
 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.
44
 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.
45
 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:
46
47
48
49
 base#based_numeral.#[exponent]
50
 base#.based_numeral#[exponent]
51
 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.
52
 S'Value

S'Value denotes a function with
the following specification:
53
function S'Value(Arg : String)
return S'Base
54
 This function returns a value
given an image of the value as a String, ignoring any leading or trailing
spaces.
55
 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
56
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.
57
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.
58
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.
59
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
60
Examples of
ranges:
61
10 .. 10
X .. X + 1
0.0 .. 2.0*Pi
Red .. Green  see 3.5.1
1 .. 0  a null range
Table'Range  a range attribute reference (see 3.6)
62
Examples of
range constraints:
63
range 999.0 .. +999.0
range S'First+1 .. S'Last1
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