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A fixed point type is either an ordinary fixed point type, or a decimal
fixed point type. The error bound of a fixed point type is specified as
an absolute value, called the delta of the fixed point type.
Syntax

fixed_point_definition ::=
ordinary_fixed_point_definition  decimal_fixed_point_definition

ordinary_fixed_point_definition ::=
delta static_expression real_range_specification

decimal_fixed_point_definition ::=
delta static_expression digits static_expression
[real_range_specification]

digits_constraint ::=
digits static_expression [range_constraint]
Name Resolution Rules

For a type defined by a fixed_point_definition, the delta of the type is
specified by the value of the expression given after the reserved word
delta; this expression is expected to be of any real type. For a type
defined by a decimal_fixed_point_definition (a decimal fixed point
type), the number of significant decimal digits for its first subtype
(the digits of the first subtype) is specified by the expression given
after the reserved word digits; this expression is expected to be of any
integer type.
Legality Rules

In a fixed_point_definition or digits_constraint, the expressions given
after the reserved words delta and digits shall be static; their values
shall be positive.

The set of values of a fixed point type comprise the integral multiples
of a number called the small of the type. For a type defined by an
ordinary_fixed_point_definition (an ordinary fixed point type), the
small may be specified by an attribute_definition_clause, See section 13.3 Representation Attributes,
if so specified, it shall be no greater than the delta of the type. If
not specified, the small of an ordinary fixed point type is an
implementationdefined power of two less than or equal to the delta.

For a decimal fixed point type, the small equals the delta; the delta
shall be a power of 10. If a real_range_specification is given, both
bounds of the range shall be in the range (10**digits1)*delta ..
+(10**digits1)*delta.

A fixed_point_definition is illegal if the implementation does not
support a fixed point type with the given small and specified range or
digits.

For a subtype_indication with a digits_constraint, the subtype_mark
shall denote a decimal fixed point subtype.
Static Semantics

The base range, See section 3.5 Scalar Types of a fixed point type is symmetric around
zero, except possibly for an extra negative value in some
implementations.

An ordinary_fixed_point_definition defines an ordinary fixed point type
whose base range includes at least all multiples of small that are
between the bounds specified in the real_range_specification. The base
range of the type does not necessarily include the specified bounds
themselves. An ordinary_fixed_point_definition also defines a
constrained first subtype of the type, with each bound of its range
given by the closer to zero of:

the value of the conversion to the fixed point type of the corresponding
expression of the real_range_specification;

the corresponding bound of the base range.

A decimal_fixed_point_definition defines a decimal fixed point type
whose base range includes at least the range (10**digits1)*delta ..
+(10**digits1)*delta. A decimal_fixed_point_definition also defines a
constrained first subtype of the type. If a real_range_specification is
given, the bounds of the first subtype are given by a conversion of the
values of the expressions of the real_range_specification. Otherwise,
the range of the first subtype is (10**digits1)*delta ..
+(10**digits1)*delta.
Dynamic Semantics

The elaboration of a fixed_point_definition creates the fixed point type
and its first subtype.

For a digits_constraint on a decimal fixed point subtype with a given
delta, if it does not have a range_constraint, then it specifies an
implicit range (10**D1)*delta .. +(10**D1)*delta, where D is the
value of the expression. A digits_constraint is compatible with a
decimal fixed point subtype if the value of the expression is no greater
than the digits of the subtype, and if it specifies (explicitly or
implicitly) a range that is compatible with the subtype.

The elaboration of a digits_constraint consists of the elaboration of
the range_constraint, if any. If a range_constraint is given, a check is
made that the bounds of the range are both in the range (10**D1)*delta
.. +(10**D1)*delta, where D is the value of the (static) expression
given after the reserved word digits. If this check fails,
Constraint_Error is raised.
Implementation Requirements

The implementation shall support at least 24 bits of precision
(including the sign bit) for fixed point types.
Implementation Permissions

Implementations are permitted to support only smalls that are a power of
two. In particular, all decimal fixed point type declarations can be
disallowed. Note however that conformance with the Information Systems
Annex requires support for decimal smalls, and decimal fixed point type
declarations with digits up to at least 18.
NOTES

(36) The base range of an ordinary fixed point type need not include
the specified bounds themselves so that the range specification can be
given in a natural way, such as:

type Fraction is delta 2.0**(15) range 1.0 .. 1.0;

With 2's complement hardware, such a type could have a signed 16bit
representation, using 1 bit for the sign and 15 bits for fraction,
resulting in a base range of 1.0 .. 1.02.0**(15).
Examples

Examples of fixed point types and subtypes:

type Volt is delta 0.125 range 0.0 .. 255.0;

 A pure fraction which requires all the available
 space in a word can be declared as the type Fraction:
type Fraction is delta System.Fine_Delta range 1.0 .. 1.0;
 Fraction'Last = 1.0  System.Fine_Delta

type Money is delta 0.01 digits 15;  decimal fixed point
subtype Salary is Money digits 10;
 Money'Last = 10.0**13  0.01, Salary'Last = 10.0**8  0.01
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