Scalar Types
Author: JTC1/SC22/WG9/ARG, by Randall Brukardt, ARG Editor

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# 3.5 Scalar Types

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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

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range_constraint ::= range range
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range ::= range_attribute_reference
| simple_expression .. simple_expression
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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

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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

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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.
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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

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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.
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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.
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Attributes
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For every scalar subtype S, the following attributes are defined:
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S'First
  S'First denotes the lower bound of the range of S. The value of this attribute is of the type of S.

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

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

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

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

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`function S'Min(Left, Right : S'Base)
return S'Base`
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  The function returns the lesser of the values of the two parameters.

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

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`function S'Max(Left, Right : S'Base)
return S'Base`
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  The function returns the greater of the values of the two parameters.

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

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

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

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

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

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

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  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.

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  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 or implementation-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).

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  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.

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  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.

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

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

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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.

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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.

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

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`function S'Wide_Value(Arg : Wide_String)
return S'Base`
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  This function returns a value given an image of the value as a Wide_String, ignoring any leading or trailing spaces.

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  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.

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  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.

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  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:

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- numeric_literal

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- numeral.[exponent]

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- .numeral[exponent]

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- base#based_numeral.#[exponent]

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- base#.based_numeral#[exponent]

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  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.

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

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`function S'Value(Arg : String)
return S'Base`
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  This function returns a value given an image of the value as a String, ignoring any leading or trailing spaces.

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  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

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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
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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.
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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.
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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

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Examples of ranges:
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`-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)`
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Examples of range constraints:
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`range -999.0 .. +999.0
range S'First+1 .. S'Last-1`

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