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3.5.9 Fixed Point Types
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
fixed point type.
delta static_expression real_range_specification
delta static_expression digits static_expression
Name Resolution Rules
For a type defined by a fixed_point_definition
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.
a type defined by a decimal_fixed_point_definition
fixed point type), the number of significant decimal
digits for its first subtype (the digits
of the first subtype)
is specified by the expression
after the reserved word digits
; this expression
is expected to be of any integer type.
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
fixed point type), the small
may be specified
by an attribute_definition_clause
); 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 implementation-defined 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**digits-1)*delta
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.
The base range (see 3.5
of a fixed point type is symmetric around zero, except possibly for an
extra negative value in some implementations.
defines an ordinary fixed point type whose base range includes at least
all multiples of small
that are between the bounds specified in
base range of the type does not necessarily include the specified bounds
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
defines a decimal fixed point type whose base range includes at least
the range -(10**digits
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 expression
the range of the first subtype is -(10**digits
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
it specifies an implicit range -(10**D
is the value of the expression
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 a range_constraint
is given, a check is made that the bounds of the range are both in the
is the value of the (static) expression
given after the reserved word digits
check fails, Constraint_Error is raised.
The implementation shall support at least 24
bits of precision (including the sign bit) for fixed point types.
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
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 16-bit representation, using 1 bit for the
sign and 15 bits for fraction, resulting in a base range of -1.0 .. 1.0-2.0**(-15).
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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