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For floating point types, the
error bound is specified as a relative precision by giving the required
minimum number of significant decimal digits.

The *requested decimal precision*,
which is the minimum number of significant decimal digits required for
the floating point type, is specified by the value of the expression
given after the reserved word **digits**. This
expression
is expected to be of any integer type.

Each simple_expression
of a real_range_specification
is expected to be of any real type[; the types need not be the same].

The requested decimal precision
shall be specified by a static expression
whose value is positive and no greater than System.Max_Base_Digits. Each
simple_expression
of a real_range_specification
shall also be static. If the real_range_specification
is omitted, the requested decimal precision shall be no greater than
System.Max_Digits.

A floating_point_definition
is illegal if the implementation does not support a floating point type
that satisfies the requested decimal precision and range.

The set of values for a floating point type is the
(infinite) set of rational numbers. The *machine
numbers* of a floating point type are the values of the type that
can be represented exactly in every unconstrained variable of the type.
The base range (see 3.5)
of a floating point type is symmetric around zero, except that it can
include some extra negative values in some implementations.

The *base decimal precision*
of a floating point type is the number of decimal digits of precision
representable in objects of the type. The *safe
range* of a floating point type is that part of its base range for
which the accuracy corresponding to the base decimal precision is preserved
by all predefined operations.

A floating_point_definition
defines a floating point type whose base decimal precision is no less
than the requested decimal precision. If
a real_range_specification
is given, the safe range of the floating point type (and hence, also
its base range) includes at least the values of the simple expressions
given in the real_range_specification.
If a real_range_specification
is not given, the safe (and base) range of the type includes at least
the values of the range –10.0**(4*D) .. +10.0**(4*D) where D is
the requested decimal precision. [The safe range might include other
values as well. The attributes Safe_First and Safe_Last give the actual
bounds of the safe range.]

A floating_point_definition
also defines a first subtype of the type. If
a real_range_specification
is given, then the subtype is constrained to a range whose bounds are
given by a conversion of the values of the simple_expressions
of the real_range_specification
to the type being defined. Otherwise, the subtype is unconstrained.

There is a predefined, unconstrained,
floating point subtype named Float[, declared in the visible part of
package Standard].

[The elaboration of a floating_point_definition
creates the floating point type and its first subtype.]

In an implementation that supports
floating point types with 6 or more digits of precision, the requested
decimal precision for Float shall be at least 6.

If Long_Float is predefined for
an implementation, then its requested decimal precision shall be at least
11.

An implementation
is allowed to provide additional predefined floating point types[, declared
in the visible part of Standard], whose (unconstrained) first subtypes
have names of the form Short_Float, Long_Float, Short_Short_Float, Long_Long_Float,
etc. Different predefined floating point types are allowed to have the
same base decimal precision. However, the precision of Float should be
no greater than that of Long_Float. Similarly, the precision of Short_Float
(if provided) should be no greater than Float. Corresponding recommendations
apply to any other predefined floating point types. There need not be
a named floating point type corresponding to each distinct base decimal
precision supported by an implementation.

An implementation should support
Long_Float in addition to Float if the target machine supports 11 or
more digits of precision. No other named floating point subtypes are
recommended for package Standard. Instead, appropriate named floating
point subtypes should be provided in the library package Interfaces (see
B.2).

NOTES

41 If a floating point subtype is unconstrained,
then assignments to variables of the subtype involve only Overflow_Checks,
never Range_Checks.

No Range_Checks, only Overflow_Checks,
are performed on variables (or parameters) of an unconstrained floating
point subtype. This is upward compatible for programs that do not raise
Constraint_Error. For those that do raise Constraint_Error, it is possible
that the exception will be raised at a later point, or not at all, if
extended range floating point registers are used to hold the value of
the variable (or parameter).

The syntax rules for floating_point_constraint
and floating_accuracy_definition are removed.
The syntax rules for floating_point_definition
and real_range_specification
are new.

A syntax rule for digits_constraint
is given in 3.5.9, “Fixed
Point Types”. In J.3 we indicate
that a digits_constraint
may be applied to a floating point subtype_mark
as well (to be compatible with Ada 83's floating_point_constraint).

Discussion of model numbers is postponed to
3.5.8 and G.2.
The concept of safe numbers has been replaced by the concept of the safe
range of values. The bounds of the safe range are given by T'Safe_First
.. T'Safe_Last, rather than -T'Safe_Large .. T'Safe_Large, since on some
machines the safe range is not perfectly symmetric. The concept of machine
numbers is new, and is relevant to the definition of Succ and Pred for
floating point numbers.

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