3.5 Scalar Types
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
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
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.
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
3.5.7)
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
3.5.7)
immediately below the value of
Arg;
Constraint_Error
is raised if there is no such machine number.
S'Wide_Wide_Image
S'Wide_Wide_Image denotes a function
with the following specification:
function S'Wide_Wide_Image(Arg : S'Base)
return Wide_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 language-defined 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'Digits–1 (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.
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.
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 as a Wide_String. The lower bound
of the result is one. The image has the same sequence of graphic characters
as defined for S'Wide_Wide_Image if all the graphic characters are defined
in Wide_Character; otherwise, the sequence of characters is implementation
defined (but no shorter than that of S'Wide_Wide_Image for the same value
of Arg).
Paragraphs
31 through 34 were moved to Wide_Wide_Image.
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_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_Wide_Image for the same value of Arg).
S'Wide_Wide_Width
S'Wide_Wide_Width denotes the
maximum length of a Wide_Wide_String returned by S'Wide_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'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_Wide_Value
S'Wide_Wide_Value denotes a function
with the following specification:
function S'Wide_Wide_Value(Arg : Wide_Wide_String)
return S'Base
This function returns a value given an
image of the value as a Wide_Wide_String, ignoring any leading or trailing
spaces.
For
the evaluation of a call on S'Wide_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_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_Wide_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_Wide_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:
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'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 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'Wide_Value
with
Arg of type Wide_String is equivalent to a call on S'Wide_Wide_Value
for a corresponding
Arg of type Wide_Wide_String.
Paragraphs
44 through 51 were moved to Wide_Wide_Value.
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_Wide_Value
for a corresponding
Arg of type Wide_Wide_String.
For a
prefix
X that denotes an object of a scalar type (after any implicit dereference),
the following attributes are defined:
X'Wide_Wide_Image
X'Wide_Wide_Image denotes the
result of calling function S'Wide_Wide_Image with
Arg being X,
where S is the nominal subtype of X.
X'Wide_Image
X'Wide_Image denotes the result
of calling function S'Wide_Image with
Arg being X, where S is
the nominal subtype of X.
X'Image
X'Image denotes the result of
calling function S'Image with
Arg being X, where S is the nominal
subtype of X.
Implementation Permissions
An implementation may extend the Wide_Wide_Value,
Wide_Value, Value, Wide_Wide_Image, Wide_Image, and Image attributes
of a floating point type to support special values such as infinities
and NaNs.
An implementation may extend the Wide_Wide_Value,
Wide_Value, and Value attributes of a character type to accept strings
of the form “Hex_
hhhhhhhh” (ignoring case) for any
character (not just the ones for which Wide_Wide_Image would produce
that form — see
3.5.2), as well as
three-character strings of the form “'
X'”, where
X
is any character, including nongraphic characters.
Static Semantics
For a scalar type,
the following language-defined representation aspect may be specified
with an
aspect_specification
(see
13.1.1):
Default_Value
This aspect shall be specified by a static expression, and that expression
shall be explicit, even if the aspect has a boolean type. Default_Value
shall be specified only on a
full_type_declaration.
If a derived type with no primitive subprograms
inherits a boolean Default_Value aspect, the aspect may be specified
to have any value for the derived type.
Name Resolution Rules
27 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.
28 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.
29 For any value V (including any nongraphic
character) of an enumeration subtype S, S'Value(S'Image(V)) equals V,
as do S'Wide_Value(S'Wide_Image(V)) and S'Wide_Wide_Value(S'Wide_Wide_Image(V)).
None of these expressions ever raise Constraint_Error.
Examples
Examples of ranges:
-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)Examples of range
constraints:
range -999.0 .. +999.0
range S'First+1 .. S'Last-1
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