## 3.5 Scalar Types

18
Jun

### Scalar Types

1 Scalar types comprise enumeration types, integer types, and real types. Enumeration types and integer types are called discrete types; {position number} each value of a discrete type has a position number which is an integer value. {numeric type} 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

3.a Discussion: These need to be simple_expressions rather than more general expressions because ranges appear in membership tests and other contexts where expression .. expression would be ambiguous.

4 {range} {lower bound (of a range)} {upper bound (of a range)} {type of a 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”. {null range} 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. {belong (to a range)} 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. {satisfies (a range constraint) [partial]} A value satisfies a range constraint if it belongs to the associated range. {included (one range in another)} One range is included in another if all values that belong to the first range also belong to the second.

#### Name Resolution Rules

5 {expected type (range_constraint range) [partial]} 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. {expected type (range simple_expressions) [partial]} 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.

5.a Discussion: In Ada 95, constraints only appear within subtype_indications; things that look like constraints that appear in type declarations are called something else like range_specifications.

5.b We say "the expected type is ..." or "the type is expected to be ..." depending on which reads better. They are fundamentally equivalent, and both feed into the type resolution rules of clause §8.6.

5.c In some cases, it doesn't work to use expected types. For example, in the above rule, we say that the “type of the range shall resolve to ...” rather than “the expected type for the range is ...”. We then use “expected type” for the bounds. If we used “expected” at both points, there would be an ambiguity, since one could apply the rules of §8.6 either on determining the type of the range, or on determining the types of the individual bounds. It is clearly important to allow one bound to be of a universal type, and the other of a specific type, so we need to use “expected type” for the bounds. Hence, we used “shall resolve to” for the type of the range as a whole. There are other situations where “expected type” is not quite right, and we use “shall resolve to” instead.

#### Static Semantics

6 {base range (of a scalar type) [distributed]} 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.

6.a Implementation Note: Note that in some machine architectures intermediates in an expression (particularly if static), and register-resident variables might accommodate a wider range. The base range does not include the values of this wider range that are not assignable without overflow to memory-resident objects.

6.b Ramification: {base range (of an enumeration type) [partial]} The base range of an enumeration type is the range of values of the enumeration type.

6.c Reason: If the representation supports infinities, the base range is nevertheless restricted to include only the representable finite values, so that 'Base'First and 'Base'Last are always guaranteed to be finite.

6.d To be honest: By a "value that can be assigned without overflow" we don't mean to restrict ourselves to values that can be represented exactly. Values between machine representable values can be assigned, but on subsequent reading, a slightly different value might be retrieved, as (partially) determined by the number of digits of precision of the type.

7 {constrained (subtype)} {unconstrained (subtype)} [A constrained scalar subtype is one to which a range constraint applies.] {range (of a scalar subtype)} 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 {compatibility (range with a scalar subtype) [partial]} 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. {compatibility (range_constraint with a scalar subtype) [partial]} A range_constraint is compatible with a scalar subtype if and only if its range is compatible with the subtype.

8.a Ramification: Only range_constraints (explicit or implicit) impose conditions on the values of a scalar subtype. The other scalar_constraints, digit_constraints and delta_constraints impose conditions on the subtype denoted by the subtype_mark in a subtype_indication, but don't impose a condition on the values of the subtype being defined. Therefore, a scalar subtype is not called constrained if all that applies to it is a digits_constraint. Decimal subtypes are subtle, because a digits_constraint without a range_constraint nevertheless includes an implicit range_constraint

9 {elaboration (range_constraint) [partial]} The elaboration of a range_constraint consists of the evaluation of the range. {evaluation (range) [partial]} 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. {implicit subtype conversion (bounds of a range) [partial]}  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.

12.a Ramification: Evaluating S'First never raises Constraint_Error.

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.

13.a Ramification: Evaluating S'Last never raises Constraint_Error.

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. {base subtype (of a 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.

18.a Discussion: {italics (formal parameters of attribute functions)} The formal parameter names are italicized because they cannot be used in calls — see §6.4. Such a specification cannot be written by the user because an attribute_reference is not permitted as the designator of a user-defined function, nor can its formal parameters be anonymous.

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

23

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

24 {Constraint_Error (raised by failure of run-time check)} For an enumeration type, the function returns the value whose position number is one more than that of the value of Arg; {Range_Check [partial]} {check, language-defined (Range_Check)} 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; {Range_Check [partial]} {check, language-defined (Range_Check)} Constraint_Error is raised if there is no such machine number.

24.a Ramification: S'Succ for a modular integer subtype wraps around if the value of Arg is S'Base'Last. S'Succ for a signed integer subtype might raise Constraint_Error if the value of Arg is S'Base'Last, or it might return the out-of-base-range value S'Base'Last+1, as is permitted for all predefined numeric operations.

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

26

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

27 {Constraint_Error (raised by failure of run-time check)} For an enumeration type, the function returns the value whose position number is one less than that of the value of Arg; {Range_Check [partial]} {check, language-defined (Range_Check)} 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; {Range_Check [partial]} {check, language-defined (Range_Check)} Constraint_Error is raised if there is no such machine number.

27.a Ramification: S'Pred for a modular integer subtype wraps around if the value of Arg is S'Base'First. S'Pred for a signed integer subtype might raise Constraint_Error if the value of Arg is S'Base'First, or it might return the out-of-base-range value S'Base'First–1, as is permitted for all predefined numeric operations.

27.1/2 S'Wide_Wide_ImageS'Wide_Wide_Image denotes a function with the following specification:

27.2/2

`function S'Wide_Wide_Image(Arg : S'Base)   return Wide_Wide_String`

27.3/2 {image (of a value)} 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.

27.4/2 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.

27.b/2 Implementation Note: If the machine supports negative zeros for signed integer types, it is not specified whether " 0" or "–0" should be returned for negative zero. We don't have enough experience with such machines to know what is appropriate, and what other languages do. In any case, the implementation should be consistent.

27.5/2 {nongraphic character} 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).

27.c/2 Implementation Note: For an enumeration type T that has “holes” (caused by an enumeration_representation_clause), {Program_Error (raised by failure of run-time check)} T'Wide_Image should raise Program_Error if the value is one of the holes (which is a bounded error anyway, since holes can be generated only via uninitialized variables and similar things.

27.6/2 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.

27.d/2 To be honest: Leading zeros are present in the exponent only if necessary to make the exponent at least two digits.

27.e/2 Reason: This image is intended to conform to that produced by Text_IO.Float_IO.Put in its default format.

27.f/2 Implementation Note: The rounding direction is specified here to ensure portability of output results.

27.7/2 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.

27.g/2 Reason: This image is intended to conform to that produced by Text_IO.Fixed_IO.Put.

27.h/2 Implementation Note: The rounding direction is specified here to ensure portability of output results.

27.i/2 Implementation Note: For a machine that supports negative zeros, it is not specified whether " 0.000" or "–0.000" is returned. See corresponding comment above about integer types with signed zeros.

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```

30/2 {image (of a value)} 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 character 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).

30.a/2 Implementation defined: The sequence of characters of the value returned by S'Wide_Image when some of the graphic characters of S'Wide_Wide_Image are not defined in Wide_Character.

Paragraphs 31 through 34 were moved to Wide_Wide_Image.

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

36

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

37/2 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).

37.a/2 Implementation defined: The sequence of characters of the value returned by S'Image when some of the graphic characters of S'Wide_Wide_Image are not defined in Character.

37.1/2 S'Wide_Wide_WidthS'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.

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.

39.1/2 S'Wide_Wide_ValueS'Wide_Wide_Value denotes a function with the following specification:

39.2/2

`function S'Wide_Wide_Value(Arg : Wide_Wide_String)   return S'Base`

39.3/2 This function returns a value given an image of the value as a Wide_Wide_String, ignoring any leading or trailing spaces.

39.4/2 {evaluation (Wide_Wide_Value) [partial]} {Constraint_Error (raised by failure of run-time check)} 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; {Range_Check [partial]} {check, language-defined (Range_Check)} otherwise Constraint_Error is raised.

39.a.1/2 Discussion: It's not crystal clear that Range_Check is appropriate here, but it doesn't seem worthwhile to invent a whole new check name just for this weird case, so we decided to lump it in with Range_Check.

39.a.2/2 To be honest: A sequence of characters corresponds to the result of S'Wide_Wide_Image if it is the same ignoring case. Thus, the case of an image of a nongraphic character does not matter. For example, Character'Wide_Wide_Value("nul") does not raise Constraint_Error, even though Character'Wide_Wide_Image returns "NUL" for the nul character.

39.5/2 {Constraint_Error (raised by failure of run-time check)} 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; {Range_Check [partial]} {check, language-defined (Range_Check)} otherwise Constraint_Error is raised.

39.a.3/2 Discussion: We considered allowing 'Value to return a representable but out-of-range value without a Constraint_Error. However, we currently require (see §4.9) in an assignment_statement like "X := <numeric_literal>;" that the value of the numeric-literal be in X's base range (at compile time), so it seems unfriendly and confusing to have a different range allowed for 'Value. Furthermore, for modular types, without the requirement for being in the base range, 'Value would have to handle arbitrarily long literals (since overflow never occurs for modular types).

39.6/2 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:

39.12/2 {Constraint_Error (raised by failure of run-time check)} 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; {Range_Check [partial]} {check, language-defined (Range_Check)} 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.

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.

43/2 {evaluation (Wide_Value) [partial]} {Constraint_Error (raised by failure of run-time check)} 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; {Range_Check [partial]} {check, language-defined (Range_Check)} 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.

43.b/2 Reason: S'Wide_Value is subtly different from S'Wide_Wide_Value for enumeration subtypes since S'Wide_Image might produce a different sequence of characters than S'Wide_Wide_Image if the enumeration literal uses characters outside of the predefined type Wide_Character. That is why we don't just define S'Wide_Value in terms of S'Wide_Wide_Value for enumeration subtypes. S'Wide_Value and S'Wide_Wide_Value for numeric subtypes yield the same result given the same sequence of characters.

Paragraphs 44 through 51 were moved to Wide_Wide_Value.

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.

55/2 {evaluation (Value) [partial]} {Constraint_Error (raised by failure of run-time check)} 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; {Range_Check [partial]} {check, language-defined (Range_Check)} 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.

55.a/2 Reason:  S'Value is subtly different from S'Wide_Wide_Value for enumeration subtypes; see the discussion under S'Wide_Value.

#### Implementation Permissions

56/2 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.

56.a/2 Proof:  The permission is really only necessary for Wide_Wide_Value, because Value and Wide_Value are defined in terms of Wide_Wide_Value, and because the behavior of Wide_Wide_Image, Wide_Image, and Image is already unspecified for things like infinities and NaNs.

56.b Reason: This is to allow implementations to define full support for IEEE arithmetic. See also the similar permission for Get in §A.10.9.

NOTES

57 (21)  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.

57.a Discussion: This paragraph addresses an issue that came up with Ada 83, where for fixed point types, the end points of the range specified in the type definition were not necessarily within the base range of the type. However, it was later clarified (and we reconfirm it in §3.5.9, “Fixed Point Types”) that the First and Last attributes reflect the true bounds chosen for the type, not the bounds specified in the type definition (which might be outside the ultimately chosen base range).

58 (22)  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 (23)  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

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'Last-1```

63.a/1 {incompatibilities with Ada 83} S'Base is no longer defined for nonscalar types. One conceivable existing use of S'Base for nonscalar types is S'Base'Size where S is a generic formal private type. However, that is not generally useful because the actual subtype corresponding to S might be a constrained array or discriminated type, which would mean that S'Base'Size might very well overflow (for example, S'Base'Size where S is a constrained subtype of String will generally be 8 * (Integer'Last + 1)). For derived discriminated types that are packed, S'Base'Size might not even be well defined if the first subtype is constrained, thereby allowing some amount of normally required “dope” to have been squeezed out in the packing. Hence our conclusion is that S'Base'Size is not generally useful in a generic, and does not justify keeping the attribute Base for nonscalar types just so it can be used as a prefix.

63.b {extensions to Ada 83} The attribute S'Base for a scalar subtype is now permitted anywhere a subtype_mark is permitted. S'Base'First .. S'Base'Last is the base range of the type. Using an attribute_definition_clause, one cannot specify any subtype-specific attributes for the subtype denoted by S'Base (the base subtype).

63.c The attribute S'Range is now allowed for scalar subtypes.

63.d The attributes S'Min and S'Max are now defined, and made available for all scalar types.

63.e The attributes S'Succ, S'Pred, S'Image, S'Value, and S'Width are now defined for real types as well as discrete types.

63.f Wide_String versions of S'Image and S'Value are defined. These are called S'Wide_Image and S'Wide_Value to avoid introducing ambiguities involving uses of these attributes with string literals.

#### Wording Changes from Ada 83

63.g We now use the syntactic category range_attribute_reference since it is now syntactically distinguished from other attribute references.

63.h The definition of S'Base has been moved here from 3.3.3 since it now applies only to scalar types.

63.i More explicit rules are provided for nongraphic characters.